ollama-model-training-5060ti/training_data/text/9efde802c22b9167d882e1c5ef844de3f4acf48955a91059268f6ddf8d07f8b1.txt

The  
InTellI genT  
OpTIOn  
Inves TOr
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The 
InTellI genT 
OpTIOn 
Inves TOr
Applying Value Investing to the 
World of Options
erik Kobayashi-solomon
new Y ork Chicago s an Francisco Athens l ondon Madrid Mexico City 
Milan n ew Delhi s ingapore s ydney Toronto
Copyright © 2015 by Erik Kobayashi-Solomon. All rights reserved. Except as permitted under the 
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To Fred Solomon
(1930–2013)
To my family and my “tribe”
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vii
Contents
Acknowledgments xi
Introduction xiii
Part I: options for the Intelligent Investor 1
Chapter 1: Option Fundamentals 3
Characteristics and history 4
Directionality 9
Flexibility 20
Chapter 2: The Black-scholes-Merton Model 29
The BsM’s Main Job is to predict stock prices 30
The BsM is lousy at Its Main Job 39
Chapter 3: The Intelligent Investor’s guide to Option pricing 49
how Option prices are Determined 50
Time value versus Intrinsic value 56
how Changing Market Conditions Affect Option prices 59
Part II: A sound Intellectual Framework for Assessing Value 75
Chapter 4: The golden rule of valuation 77
The value of an Asset  78
Cash Flows generated on Behalf of Owners 80
The Company’s economic life 82
Time value of Money: summing Up Cash Flows Over Time 87
Chapter 5: The Four Drivers of value 91
Bird’s eye view of the valuation process 91
A Detailed look at the Drivers of value 97
viii  •   Contents
Chapter 6: Understanding and Overcoming Investing pitfalls 113
Behavioral Biases 114
structural Impediments 131
Part III: Intelligent option Investing 141
Chapter 7: Finding Mispriced Options 143
Making sense of Option Quotes 144
Delta: The Most Useful of the greeks 151
Comparing an Intelligent valuation range with a BsM range 155
Chapter 8: Understanding and Managing leverage 163
Investment leverage 164
simple Ways of Measuring Option Investment leverage 169
Understanding leverage’s effects on a portfolio 174
Managing leverage 183
Chapter 9: gaining exposure 187
long Call 189
long put 201
strangle 205
straddle 208
Chapter 10: Accepting exposure 211
short put 212
short Call (Call spread) 220
short straddle/short strangle 230
Chapter 11: Mixing exposure 233
long Diagonal 235
short Diagonal 238
Covered Call 240
protective puts 248
Collar 258
Chapter 12: risk and the Intelligent Option Investor 263
Market risk 263
valuation risk 265
Intelligent Option Investing 267
Appendix A: Choose Y our Battles Wisely 269
Where the BsM Works Best 269
Where the BsM Works Worst 273
Appendix B: The Many Faces of leverage 282
Operational leverage 282
Financial leverage 285
Appendix C: p ut-Call parity 287
Dividend Arbitrage and put-Call parity 288
Notes 295
Index 305
Contents    • ix
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xi
ACknowledgments
Many thanks to all the people who have been part of the process during 
the writing of this book. I am indebted to three people in particular, 
Mr. Brent Farler, Mr. Ben louviere, and Mr. neil Kozarsky, who have gra-
ciously offered their time, help, and business expertise in bringing this pro-
ject to fruition. Certainly this book would be much different and of not 
nearly the quality without Brent’s guidance, thorough reading, and insight-
ful, helpful suggestions, starting with the very first draft in late 2012. 
In the literary world, I cannot say enough good things about Mr. sam 
Fleishman, of l iterary Arts r epresentatives, and Mr. Knox h uston and 
Ms. Daina penikas, my editors at Mcgraw-hill, all of whom have allowed 
this work to move from conception to completion and whose advice and 
support have made all the hard work worthwhile.
In the investment-management world, I am indebted to Mr. steve 
silverman, owner and portfolio manager of Ironbound Capital Manage-
ment, who taught me important lessons about the business of investing and 
about how to critically assess the value of a company, and to Mr. Deepinder 
Bhatia, Founding partner of Bayard Asset Management llC, a true expert 
in the art and science of equity research and analysis.
In addition, I thank Mr. rafael garcia, of the International Financial 
Corporation; Mr. Joe Miramonti, of Fedora Investment p artners;  
Mr. Franco Dal pont, of Batalha Capital Management; and Mr. paul neff, 
of the Federal reserve Bank of Chicago, for the excellent discussions about 
valuation, option theory, and bringing the touchstone of valuation into the 
realm of option investments.
When I began work on this book, I did not realize just what an 
enormous process it would be. Truly, without the help and support of 
all the people mentioned here and all my friends and family around 
the world, I would have had a much more difficult time completing 
this work.
xii  •   Acknowledgments
xiii
IntroduCtIon
You have a tremendous advantage over algorithmic trading models, 
investment bank trading desks, hedge funds, and anyone who appears on or 
pays attention to cable business news shows. This book is written to show 
where that advantage lies and how to exploit it to make confident and suc-
cessful investment choices. In doing so, it explains how options work and 
what they can tell you about the market’s estimation of the value of stocks. 
even if, after reading it, you decide to stick with straight stock in-
vesting and never make an option transaction, understanding how options 
work will give you a tremendous advantage as an investor. The reason for 
this is simple: by understanding options, you can understand what the rest 
of the market is expecting the future price of a stock to be. Understanding 
what future stock prices are implied by the market is like playing cards with 
an opponent who always leaves his or her hand face up on the table. Y ou 
can look at the cards you are dealt, compare them with your opponent’s, 
and play the round only when you are sure that you have the winning hand.
By incorporating options into your portfolio, you will enjoy an even 
greater advantage because of a peculiarity about how option prices are 
determined. Option prices are set by market participants making trans-
actions, but those market participants all base their sale and purchase 
decisions on the same statistical models. These models are like sausage 
grinders. They contain no intelligence or insight but rather take in a few 
simple inputs, grind them up in a mechanical way, and spit out an option 
price of a specific form. 
An option model does not, for instance, care about the operational 
details of a company. This oversight can lead to situations that seem to be 
too good to be true. For instance, I have seen a case in which an investor 
could commit to buy a strong, profitable company for less than the amount 
of cash it held—in effect, allowing the investor to pay $0.90 to receive a 
dollar plus a share of the company’s future profits! Although it is true that 
these kinds of opportunities do not come along every day, they do indeed 
come along for patient, insightful investors.
This example lies at the heart of intelligent option investing, the es-
sence of which can be expressed as a three-step process:
1. Understanding the value of a stock
2. Comparing that intelligently estimated value with the mechani-
cally derived one implied by the option market
3. Tilting the risk-reward balance in one’s favor by investing in the 
best opportunities using a combination of stocks and options
The goal of this book is to provide you with the knowledge you need to be 
an intelligent option investor from the standpoint of these three steps. 
There is a lot of information contained within this book but also a lot 
of information left out. This is not meant to be an encyclopedia of option 
equations, a handbook of colorfully named option strategies, or a treatise on 
financial statement analysis. Unlike academic books covering options, such 
as hull’s excellent book,
1 not a single integration symbol or mathematical 
proof is found between this book’s covers. Understanding how options are 
priced is an important step in being an intelligent option investor; doing dif-
ferential partial equations or working out mathematical proofs is not. 
Unlike option books written for professional practitioners, such as 
natenberg’s book,2 you will not find explanations about complex strategies 
or graphs about how “the greeks”3 vary under different conditions. Floor 
traders need to know these things, but intelligent option investors—those 
making considered long-term investments in the financial outcomes of 
companies—have very different motivations, resources, and time horizons 
from floor traders. Intelligent option investors, it turns out, do better not 
even worrying about the great majority of things that floor traders must 
consider every day.
Unlike how-to books about day trading options, this book does not 
have one word to say about chart patterns, market timing, get-rich-quick 
schemes, or any of the many other delusions popular among people who 
xiv  •   Introduction
Introduction    • xv
will soon be paupers. Making good decisions is a vital part of being an 
intelligent option investor; frenetic, haphazard, and unconsidered trading 
is most certainly not.
Unlike books about securities analysis, you will not find detailed dis-
cussions about every line item on a financial statement. Understanding 
how a company creates value for its owners and how to measure that value 
is an important step in being an intelligent option investor; being able to 
rattle off information about arcane accounting conventions is not.
To paraphrase Warren Buffett,
4 this book aims to provide you with 
a sound intellectual framework for assessing the value of a company and 
making rational, fact-based decisions about how to invest in them with the 
help of the options market.
The book is split into three parts:
• part I provides an explanation of what options are, how they are 
priced, and what they can tell you about what the market thinks the 
future price of a stock will be. This part corresponds to the second 
step of intelligent option investing listed earlier.
• part II sets forth a model for determining the value of a company 
based on only a handful of drivers. It also discusses some of the 
behavioral and structural pitfalls that can and do affect investors’ 
emotions and how to avoid them to become a better, more rational 
investor. This part corresponds to the first step of intelligent option 
investing listed earlier. 
• part III turns theory into practice—showing how to read the nec-
essary information on an option pricing screen; teaching how 
to measure and manage leverage in a portfolio containing cash, 
stocks, and options; and going into detail about the handful of op-
tion strategies that an intelligent option investor needs to know to 
generate income, boost growth, and protect gains in an equity port-
folio. This part corresponds to the final step of intelligent option 
investing listed earlier.
no part of this book assumes any prior knowledge about options or 
stock valuation. That said, it is not some sort of “Options for Beginners” or 
“My First Book of valuation” treatment either. 
Investing beginners will learn all the skills—soup to nuts—they need 
to successfully and confidently invest in the stock and options market. peo-
ple who have some experience in options and who may have used covered 
calls, protective puts, and the like will find out how to greatly improve their 
results from these investments and how to use options in other ways as 
well. professional money managers and analysts will develop a thorough 
understanding of how to effectively incorporate option investments into 
their portfolio strategies and may in fact be encouraged to consider ques-
tions about valuation and behavioral biases in a new light as well.
The approach used here to teach about valuation and options is 
unique, simple without being simpleminded, and extremely effective in 
communicating these complex topics in a memorable, vivid way. r ead-
ers used to seeing option books littered with hockey-stick diagrams and 
partial differential equations may have some unlearning to do, but no mat-
ter your starting point—whether you are a novice investor or a seasoned 
hedge fund manager—by the end of this book, I believe that you will look 
at equity investing in a new light.
xvi  •   Introduction
1
Part I
OptiOns FOr the 
intelligent invest Or
Don’t believe anything you have heard or read about options.
If you listen to media stories, you will learn that options are modern 
financial innovations so complex that only someone with an advanced 
degree in mathematics can properly understand them. 
Every contention in the preceding sentence is wrong.
If you listen to the pundits and traders blabbing on the cable business 
channels, you will think that you will never be successful using options 
unless you understand what “put backspreads, ” “iron condors, ” and count- 
less other colorfully named option strategies are. Y ou will also learn that 
options are short-term trading tools and that you’ll have to be a razor-sharp 
“technical analyst” who can “read charts” and jump in and out of positions 
a few times a week (if not a few times a day) to do well.
Every contention in the preceding paragraph is so wrong that believing 
them is liable to send you to the poor house.
The truth is that options are simple, directional instruments that 
we understand perfectly well from countless encounters with them in 
our daily lives. They are the second-oldest financial instrument known to 
humanity—in a quite literal sense, modern economic life would not be 
possible without them. Options are instruments that not only can be used 
but should be used in long-term strategies; they most definitely should be 
traded in and out of as infrequently as possible.
2  •   The Intelligent Option Investor
The first part of this book will give you a good understanding of 
what options are, how their prices are determined, and how those prices 
fluctuate based on changes in market conditions.
There is a good reason to develop a solid understanding of this 
theoretical background: the framework the option market uses to determine 
the price of options is based on provably faulty premises that, while 
“approximately right” in certain circumstances, are laughably wrong in 
other circumstances. The faults can be exploited by intelligent, patient inves-
tors who understand which circumstances to avoid and which to seek out.
Without understanding the framework the market uses to value 
options and where that framework breaks down, there is no way to exploit 
the faults. Part I of this book, in a nutshell, is designed to give you an 
understanding of the framework the market uses to value options.
This book makes extensive use of diagrams to explain option theory, 
pricing, and investment strategies. Those readers of the printed copy of this 
book are encouraged to visit the Intelligent Option Investor website (www 
.IntelligentOptionInvestor.com) to see the full-color versions of the type of 
illustrations listed here. Doing so will allow you to visualize options even 
more effectively in the distinctive intelligent option investing way.
3
Chapter 1
OptiOn Fundamentals
This chapter introduces what an option is and how to visualize options in 
an intelligent way while hinting at the great flexibility and power a sensible 
use of options gives an investor. It is split into three sections:
1. Option Overview: Characteristics, everyday options, and a brief 
option history.
2. Option Directionality: An investigation of similarities and differ -
ences between stocks and options. This section also contains an 
introduction to the unique way that this book visualizes options 
and to the inescapable jargon used in the options world and a bit 
of intelligent option investor–specific jargon as well.
3. Option Flexibility: An explanation of why options are much more 
investor-friendly than stocks, as well as examples of the handful of 
strategies an intelligent option investor uses most often.
Even those of you who know something about options should at the 
very least read the last section. Y ou will find that the intelligent option 
investor makes very close to zero use of the typical hockey-stick diagrams 
shown in other books. Instead, this book uses the concept of a range of 
exposure. The rest of the book—discussing option pricing, corporate 
valuation, and option strategies—builds on this range-of-exposure concept, 
so skipping it is likely to lead to confusion later.
This chapter is an important first step in being an intelligent option 
investor. Someone who knows how options work does not qualify as be-
ing an intelligent option investor, but certainly, one cannot become an 
4  •   The Intelligent Option Investor
intelligent option investor without understanding these basic facts. The 
concepts discussed here will be covered in greater detail and depth later in 
this book. For now, it is enough to get a sense for what options are, how to 
think about them, and why they might be useful investment tools.
Characteristics and History
By the end of this section, you should know the four key characteristics 
of options, be able to name a few options that are common in our daily 
lives, and understand a bit about the long history of options as a financial 
product and how modern option markets operate.
Jargon introduced in this section is as follows:
Black-Scholes-Merton model (BSM)
Listed look-alike
Central counterparty
Characteristics of Options
Rather than giving a definition for options, I’ll list the four most important 
characteristics that all options share and provide a few common examples. 
Once you understand the basic characteristics of options, have seen a few 
examples, and have spent some time thinking about them, you will start to 
see elements of optionality in nearly every situation in life.
An option
1. Is a contractual right
2. Is in force for a specified time 
3. Allows an investor to profit from the change in value of another 
asset
4. Has value as long as it is still in force
This definition is broad enough that it applies to all sorts of options—
those traded on a public exchange such as the Chicago Board Options 
Exchange and those familiar to us in our daily lives. 
Option Fundamentals   • 5
Options in Daily Life
The type of option with which people living in developed economies are 
most familiar is an insurance contract. Let’s say that you want to fully insure 
your $30,000 car. Y ou sign a contract (option characteristic number 1)  
with your insurance company that covers you for a specified amount of time 
(option characteristic number 2)—let’s say one year. If during the coverage 
period your car is totaled, your insurance company buys your wreck of a 
car (worth $0 or close to it) for $30,000—allowing you to buy an identical 
car. When this happens, you as the car owner (or investor in a real asset)  
realize a profit of $30,000 over the market value of your destroyed car  
(option characteristic number 3). Obviously, the insurance company is 
bound to uphold its promise to indemnify you from loss for the entire term 
of the contract; the fact that you have a right to sell a worthless car to your 
insurance company for the price you paid for it implies that the insurance 
has value during its entire term (option characteristic number 4). 
Another type of option, while perhaps not as widely used by everyday 
folks, is easily recognizable. Imagine that you are a struggling author who 
has just penned your first novel. The novel was not a great seller, but one day 
you get a call from a movie producer offering you $50,000 for the right to 
draft a screenplay based on your work. This payment will grant the producer 
exclusive right (option characteristic number 1) to turn the novel into a 
movie, as well as the right to all proceeds from a potential future movie 
for a specific period of time (option characteristic number 2)—let’s say  
10 years. After that period is up, you as the author are free to renegotiate an-
other contract. As a struggling artist working in an unfulfilling day job, you 
happily agree to the deal. Three weeks later, a popular daytime talk show 
host features your novel on her show, and suddenly, you have a New York 
Times bestseller on your hands. The value of your literary work has gone 
from slight to great in a single week. Now the movie producer hires the 
Cohen brothers to adapt your film to the screen and hires George Clooney, 
Matt Damon, and Julia Roberts to star in the movie. When it is released, 
the film breaks records at the box office. How much does the producer pay 
to you? Nothing. The producer had a contractual right to profit from the 
screenplay based on your work. When the producer bought this right, your 
literary work was not worth much; suddenly, it is worth a great deal, and 
6  •   The Intelligent Option Investor
the producer owns the upside potential from the increase in value of your 
story (option characteristic number 3). Again, it is obvious that the right 
to the literary work has value for the entire term of the contract (option 
characteristic number 4).
Keep these characteristics in mind, and we will go on to look at how 
these defining elements are expressed in financial markets later in this 
chapter. Now that you have an idea of what an option looks like, let’s turn 
briefly to a short history of these financial instruments.
A Brief History of Options
Many people believe that options are a new financial invention, but in 
fact, they have been in use for more than two millennia—one of the first 
historically attested uses of options was by a pre-Socratic philosopher 
named Miletus, who lived in ancient Greece. Miletus the philosopher was 
accused of being useless by his fellow citizens because he spent his time 
considering philosophical matters (which at the time included a study of 
natural phenomena as well) rather than putting his nose to the grindstone 
and weaving fishing nets or some such thing.
Miletus told them that his knowledge was in fact not useless and that 
he could apply it to something people cared about, but he simply chose not 
to. As proof of his contention, when his studies related to weather revealed 
to him that the area would enjoy a bumper crop of olives in the upcoming 
season, he went around to the owners of all the olive presses and paid them 
a fee to reserve the presses (i.e., he entered into a contractual agreement—
option characteristic number 1) through harvest time (i.e., the contract 
had a prespecified life—option characteristic number 2). 
Indeed, Miletus’s prediction was correct, and the following season 
yielded a bumper crop of olives. The price of olives must have fallen because 
of the huge surge of supply, and demand for olive presses skyrocketed  
(because turning the olive fruit into oil allowed the produce to be stored 
longer). Because Miletus had cornered the olive press market, he was able 
to generate huge profits, turning the low-value olives into high-value oil  
(i.e., he profited from the change in value of an underlying asset—option 
characteristic number 3). His rights to the olive presses ended after the har-
vest but not before he had become very wealthy thanks to his philosophical 
Option Fundamentals   • 7
studies (i.e., his contractual rights had value through expiration—option 
characteristic number 4).
This is only one example of an ancient option transaction (a few thou-
sand years before the first primitive common stock came into existence),  
but as long as there has been insurance, option contracts have been a well-
understood and widely used financial instrument. Can you imagine how 
little cross-border trade would occur if sellers and buyers could not shift the 
risk of transporting goods to a third party such as an insurance company? 
How many ships would have set out for the Spice Islands during the Age of 
Exploration, for instance? Indeed, it is hard to imagine what trade would 
look like today if buyers and sellers did not have some way to mitigate the 
risks associated with uncertain investments.
For hundreds of years, options existed as private contracts specifying 
rights to an economic exposure of a certain quantity of a certain good over 
a given time period. Frequently, these contracts were sealed between the 
producers and sellers of a commodity product and wholesale buyers of 
that commodity. Both sides had an existing exposure to the commodity  
(the producer wanted to sell the commodity, and the wholesaler wanted to 
buy it), and both sides wanted to insure themselves against interim price 
movements in the underlying commodity.
But there was a problem with this system. Let’s say that you were a 
Renaissance merchant who wanted to insure your shipment of spice from 
India to Europe, and so you entered into an agreement with an insurer. The 
insurer asked you to pay a certain amount of premium up front in return 
for guaranteeing the value of your cargo. Y our shipment leaves Goa but is 
lost off Madagascar, and all your investment capital goes down with the 
ship to the bottom of the Indian Ocean. However, when you try to find 
your option counterparty—your insurer—it seems that he has absconded 
with your premium money and is living a life of pleasure and song in 
another country. In the parlance of modern financial markets, your option 
investment failed because of counterparty risk. 
Private contracts still exist today in commodity markets as well as 
the stock market (the listed look-alike option market—private contracts 
specifying the right to upside and downside exposure to single stocks, 
exchange-traded funds, and baskets is one example that institutional 
investors use heavily). However, private contracts still bring with them a 
8  •   The Intelligent Option Investor
risk of default by one’s counterparty, so they are usually only entered into 
after both parties have fully assessed the creditworthiness of the other. 
Obviously, individual investors—who might simply want to speculate on 
the value of an underlying stock or exchange-traded fund (ETF)—cannot 
spend the time doing a credit check on every counterparty with whom 
they might do business.
1 Without a way to make sure that both parties are 
financially able to keep up their half of the option bargain, public option 
markets simply could not exist.
The modern solution to this quandary is that of the central counter -
party. This is an organization that standardizes the terms of the option con-
tracts transacted and ensures the financial fulfillment of the participating 
counterparties. Central counterparties are associated with securities 
exchanges and regulate the parties with which they deal. They set rules 
regarding collateral that must be placed in escrow before a transaction 
can be made and request additional funds if market price changes cause 
a counterparty’s account to become undercollateralized. In the United 
States, the central counterparty for options transactions is the Options 
Clearing Corporation (OCC). The OCC is an offshoot of the oldest option 
exchange, the Chicago Board Option Exchange (CBOE).
In the early 1970s, the CBOE itself began as an offshoot of a large 
futures exchange—the Chicago Mercantile Exchange—and subsequently 
started the process of standardizing option contracts (i.e., specifying the 
exact per-contract quantity and quality of the underlying good and the 
expiration date of the contract) and building the other infrastructure and 
regulatory framework necessary to create and manage a public market. 
Although market infrastructure and mechanics are very important for 
the brokers and other professional participants in the options market, 
most aspects are not terribly important from an investor’s point of view  
(the things that are—such as margin—will be discussed in detail later in 
this book). The one thing an investor must know is simply that the option 
market is transparent, well regulated, and secure. Those of you who have a 
bit of extra time and want to learn more about market mechanics should 
take a look through the information on the CBOE’s and OCC’s websites.
Listing of option contracts on the CBOE meant that investors needed 
to have a sense for what a fair price for an option was. Three academics, 
Fischer Black, Myron Scholes, and Robert Merton, were responsible for 
Option Fundamentals   • 9
developing and refining an option pricing model known as the Black-
Scholes or Black-Scholes-Merton model, which I will hereafter abbreviate 
as the BSM.
The BSM is a testament to human ingenuity and theoretical elegance, 
and even though new methods and refinements have been developed 
since its introduction, the underlying assumptions for new option pricing 
methods are the same as the BSM. In fact, throughout this book, when you 
see “BSM, ” think “any statistically based algorithm for determining option 
p r i c e s .”
The point of all this background information is that options are not 
only not new-fangled financial instruments but in fact have a long and 
proud history that is deeply intertwined with the development of modern 
economies themselves. Those of you interested in a much more thorough 
coverage of the history of options would do well to read the book, Against 
the Gods: The Remarkable History of Risk, by Peter Bernstein (New Y ork: 
Wiley, 1998).
Now that you have a good sense of what options are and how they are 
used in everyday life, let’s now turn to the single most important thing for a 
fundamental investor to appreciate about these financial instruments: their 
inherent ability to exploit directionality.
Directionality
The key takeaway from this section is evident from the title. In addition to 
demonstrating the directional power inherent in options, this section also 
introduces the graphic tools that I will use throughout the rest of this book 
to show the risk and reward inherent in any investment—whether it is an 
investment in a stock or an option.
For those of you who are not well versed in options yet, this is the 
section in which I explain most of the jargon that you simply cannot escape 
when transacting in options. However, even readers who are familiar with 
options should at least skim through this explanation. Doing so will likely 
increase your appreciation for the characteristics of options that make 
them such powerful investment tools and also will introduce you to this 
novel way of visualizing them.
10  •   The Intelligent Option Investor
Jargon introduced in this section is as follows:
Call option Moneyness
Put option In the money (ITM)
Range of exposure At the money (ATM)
Strike price Out of the money (OTM)
Gain exposure Premium
Accept exposure American style
Canceling exposure European style
Exercise (an option)
Visual Representation of a Stock
Visually, a good stock investment looks like this: 
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Future Stock Price
Last Stock Price
Y ou can make a lot of mistakes when investing, but as long as you are right 
about the ultimate direction a stock will take and act accordingly, all those 
mistakes will be dwarfed by the success of your position.
Good investing, then, is essentially a process of recognizing and 
exploiting the directionality of mispriced stocks. Usually, investors get 
exposure to a stock’s directionality by buying, or going long, that stock. This 
is what the investor’s risk and reward profile looks like when he or she buys 
the stock:
Option Fundamentals   • 11
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GREEN
RED
As soon as the “Buy” button is pushed, the investor gains expo-
sure to the upside potential of the stock—this is the shaded region la-
beled “green” in the figure. However, at the same time, the investor 
also must accept exposure to downside risk—this is the shaded region 
labeled “red. ”
Anyone who has invested in stocks has a visceral understanding of 
stock directionality. We all know the joy of being right as our investment 
soars into the green and we’ve all felt the sting as an investment we own 
falls into the red. We also know that to the extent that we want to gain 
exposure to the upside potential of a stock, we must necessarily simultane-
ously accept its downside risk.
Options, like stocks, are directional instruments that come in two 
types. These two types can be defined in directional terms:
Call option  A security that allows an investor exposure to a stock’s 
upside potential (remember, “Call up”)
Put option  A security that allows an investor exposure to a stock’s 
downside potential (remember, “Put down”)
The fact that options split the directionality of stocks in half—up and 
down—is a great advantage to an investor that we will investigate more in 
a moment. 
Right now, let’s take a look at each of these directional instruments—
call options and put options—one by one.
12  •   The Intelligent Option Investor
Visual Representation of Call Options
In a similar way that we created a diagram of the risk-reward profile of owner-
ship in a common stock, a nice way of understanding how options work is to 
look at a visual representation. The following diagram represents a call option.
There are a few things to note about this representation:
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1. The shaded area (green) represents the price and time range over 
which the investor has economic exposure—I term this the range 
of exposure. Because we are talking about call options, and because 
call options deal with the upside potential of a stock, you see that 
the range of exposure lies higher than the present stock price 
(remember, “Call up”). 
2. True to one of the defining characteristics of an option mentioned 
earlier, our range of exposure is limited by time; the option pictured 
in the preceding figure expires 500 days in the future, after which 
we have no economic exposure to the stock’s upside potential. 
3. The present stock price is $50 per share, but our upside exposure only 
begins at $60 per share. The price at which economic exposure begins 
is called the strike price of an option. In this case, the strike price is 
$60 per share, but we could have picked a strike price at the market price 
of the stock, further above the market price of the stock (e.g., a strike 
price of $75), or even below the market price of the stock. We will inves-
tigate optimal strike prices for certain option strategies later in this book.
Option Fundamentals   • 13
4. The arrow at the top of the shaded region in the figure indicates 
that our exposure extends infinitely upward. If, for some reason, 
this stock suddenly jumped not from $50 to $60 per share but 
from $50 to $1,234 per share, we would have profitable exposure 
to all that upside.
5. Clearly, the diagram showing a purchased call option looks a great deal 
like the top of the diagram for a purchased stock. Look back at the top 
of the stock purchase figure and compare it with the preceding figure: 
the inherent directionality of options should be completely obvious.
Any time you see a green region on diagrams like this, you should 
take it to mean that an investor has the potential to realize a gain on the 
investment and that the investor has gained exposure. Any time an option 
investor gains exposure, he or she must pay up front for that potential gain. 
The money one pays up front for an option is called premium (just like the 
fee you pay for insurance coverage).
In the preceding diagram, then, we have gained exposure to a range 
of the stock’s upside potential by buying a call option (also known as a long 
call). If the stock moves into this range before or at option expiration, we 
have the right to buy the stock at our $60 strike price (this is termed exer -
cising an option) or simply sell the option in the option market. It is almost 
always the wrong thing to exercise an option for reasons we discuss shortly.
2
If, instead, the stock is trading below our strike price at expiration, the 
option is obviously worthless—we owned the right to an upside scenario 
that did not materialize, so our ownership right is worth nothing.
It turns out that there is special jargon that is used to describe the 
relationship between the stock price and the range of option exposure:
Jargon Situation
In the money (ITM) Stock price is within the option’s range of exposure
Out of the money (OTM) Stock price is outside the option’s range of exposure
At the money (ATM) Stock price is just at the border of the option’s range of 
exposure
Each of these situations is said to describe the moneyness of the option. 
Graphically, moneyness can be represented by the following diagram:
14  •   The Intelligent Option Investor
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ITM
ATM
OTM
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749 999
GREEN
As we will discuss in greater detail later, not only can an investor use 
options to gain exposure to a stock, but the investor also can choose to accept 
exposure to it. Accepting exposure means running the risk of a financial loss if 
the stock moves into an option’s range of exposure. If we were to accept expo-
sure to the stock’s upside potential, we would graphically represent it like this:
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RED
Any time you see a shaded region labeled “red” on diagrams like this, you 
should take it to mean that the investor has accepted the risk of realizing a loss 
on the investment and should say that the investor has accepted exposure. Any 
time an option investor accepts exposure, he or she gets to receive premium 
up front in return for accepting the risk. In the preceding example, the investor 
has accepted upside exposure by selling a call option (a.k.a. a short call).
Option Fundamentals   • 15
In this sold call example, we again see the shaded area representing 
the exposure range. We also see that the exposure is limited to 500 days 
and that it starts at the $60 strike price. The big difference we see between 
this diagram and the one before it is that when we gained upside exposure 
by buying a call, we had potentially profitable exposure infinitely upward; 
in the case of a short call, we are accepting the possibility of an infinite 
loss. Needless to say, the decision to accept such risk should not be taken 
lightly. We will discuss in what circumstances an investor might want to 
accept this type of risk and what techniques might be used to manage that 
risk later in this book. For right now, think of this diagram as part of an 
explanation of how options work, not why someone might want to use this 
particular strategy.
Let’s go back to the example of a long call because it’s easier for 
most people to think of call options this way. Recall that you must pay a  
premium if you want to gain exposure to a stock’s directional potential. In 
the diagrams, you will mark the amount of premium you have to pay as a 
straight line, as can be seen here:
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Breakeven Line: $62.50
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GREEN
I have labeled the straight line the “Breakeven line” for now and have as-
sumed that the option’s premium totals $2.50. 
Y ou can think of the breakeven line as a hurdle the stock must cross 
by expiration time. If, at expiration, the stock is trading for $61, you have 
the right to purchase the shares for $60. Y ou make a $1 profit on this trans-
action, which partially offsets the original $2.50 cost of the option.
16  •   The Intelligent Option Investor
It is important to note that a stock does not have to cross this line for 
your option investment to be profitable. We will discuss this dynamic in 
Chapter 2 when we learn more about the time value of options.
Visual Representation of Put Options
Now that you understand the conventions we use for our diagrams, let’s 
think about how we might represent the other type of option, dealing with 
downside exposure—the put. First, let’s assume that we want to gain expo-
sure to the downside potential of a stock. Graphically, we would represent 
this in the following way:
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First, notice that, in contrast to the diagram of the call option, the 
directional exposure of a put option is bounded on the downside by $0, 
so we do not draw an arrow indicating infinite exposure. This is the same 
downside exposure of a stock because a stock cannot fall below zero dollars 
per share.
In this diagram, the time range for the put option is the same 500 days 
as for our call option, but the price range at which we have exposure starts 
at a strike price of $50—the current market price of the stock—making this 
an at-the-money (ATM) put. If you think about moneyness in terms of a 
range of exposure, the difference between out of the money (OTM) and in 
the money (ITM) becomes easy and sensible. Here are examples of differ-
ent moneyness cases for put options:
Option Fundamentals   • 17
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OTM
ATM
ITMGREEN
We are assuming that this put option costs $5, leading to a breakeven 
line of $45. This breakeven line is like an upside-down hurdle in that we 
would like the stock to finish below $45; if it expires below $50 but above 
$45, again, we will be able to profit from the exercise, but this profit will not 
be great enough to cover the cost of the option. 
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Breakeven Line: $45.00
GREEN
Obviously, if we can gain downside exposure to a stock, we must be 
able to accept it as well. We can accept downside exposure by selling a put; 
this book represents a sold put graphically like this:
18  •   The Intelligent Option Investor
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Breakeven Line: $45.00
RED
In this diagram, we are receiving a $5 premium payment in return for 
accepting exposure to the stock’s downside. As such, as long as the stock 
expires above $45, we will realize a profit on this investment.
Visual Representation of Options Canceling Exposure
Let’s take a look again at our visual representation of the risk and reward 
of a stock:
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GREEN
RED
We bought this stock at $50 per share and will experience an unreal-
ized gain if the stock goes up and an unrealized loss if it goes down. What 
might happen if we were to simultaneously buy a put, expiring in 365 days 
and struck at $50, on the same stock?
Because we are purchasing a put, we know that we are gaining expo-
sure to the downside. Any time we gain exposure, we shade the exposure 
Option Fundamentals   • 19
in green. Let’s overlay this gain of downside exposure on the preceding 
risk-return diagram and see what we get.
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GREEN
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The region representing the downside exposure we gained by buy-
ing the put perfectly overlaps part of the region representing the downside 
exposure we accepted when we bought the stock. When there is a region 
such as this, where we are simultaneously gaining and accepting exposure, 
the two exposures cancel out, creating no economic exposure whatsoever.
From here on out, to show a canceling of economic exposure, we will 
shade the region in gray, like the following:
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GREEN
REDGRAY
20  •   The Intelligent Option Investor
Any time a gain of exposure overlaps another gain of exposure, 
the potential gain from an investment if the stock price moves into that 
region rises. We will not represent this in the diagrams of this book, 
but you can think of overlapping gains as deeper and deeper shades of 
green (when gaining exposure) and deeper and deeper shades of red  
(when accepting it).
Now that you understand how to graphically represent gaining and 
accepting exposure to both upside and downside directionality and how to 
represent situations when opposing exposures overlap, we can move onto 
the next section, which introduces the great flexibility options grant to an 
investor and discusses how that flexibility can be used as a force of either 
good or evil.
Flexibility
Again, the main takeaway of this section should be obvious from the title. 
Here we will see the only two choices stock investors have with regard to 
risk and return, and we will contrast that with the great flexibility an option 
investor has. We will also discuss the concept of an effective buy price and 
an effective sell price—two bits of intelligent option investor jargon. Last, 
we will look at a typical option strategy that might be recommended by 
an option “guru” and note that these types of strategies actually are at 
cross-purposes with the directional nature of options that makes them so 
powerful in the first place.
Jargon introduced in this chapter is as follows:
Effective buy price (EBP) Covered call
Effective sell price (ESP) Long strangle
Leg
Stocks Give Investors Few Choices
A stock investor only has two choices when it comes to investing: going 
long or going short. Using our visualization technique, those two choices 
look like this:
Option Fundamentals   • 21
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RED
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Going long a stock (i.e., buying 
a stock).
    Going short a stock (i.e., short 
selling a stock).
If you want to gain exposure to a stock’s upside potential by going 
long (left-hand diagram), you also must simultaneously accept exposure to 
the stock’s downside risk. Similarly, if you want to gain exposure to a stock’s 
downside potential by going short (right-hand diagram), you also must ac-
cept exposure to the stock’s upside risk. 
In contrast, option investors are completely unrestrained in their 
ability to choose what directionality to accept or gain. An option investor 
could, for example, very easily decide to establish exposure to the direc-
tionality of a stock in the following way:
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GREEN
GREEN
GRAY
GRAY
GREEN
RED
RED
RED
Why an investor would want to do something like this is completely beyond 
me, but the point is that options are flexible enough to allow this type of a 
crazy structure to be built.
22  •   The Intelligent Option Investor
The beautiful thing about this flexibility is that an intelligent option in-
vestor can pick and choose what exposure he or she wants to gain or accept in 
order to tailor his or her risk-return profile to an underlying stock. By tailoring 
your risk-return profile, you can increase growth, boost income, and insure 
your portfolio from downside shocks. Let’s take a look at a few examples.
Options Give Investors Many Choices
Buying a Call for Growth
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BE = $55
GREEN
Above an investor is bullish on the prospects of the stock and is using a call op-
tion to gain exposure to a stock’s upside potential above $50 per share. Rather 
than accepting exposure to the stock’s entire downside potential (maximum 
of a $50 loss) as he or she would have by buying the stock outright, the call-
option investor would pay an upfront premium of, in this case, $5.
Selling a Put for Income
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BE = $45
RED
Option Fundamentals   • 23
Here an investor is bullish on the prospects of the stock, so he or she doesn’t 
mind accepting exposure to the stock’s downside risk below $50. In return for 
accepting this risk, the option investor receives a premium—let’s say $5. This 
$5 is income to the investor—kind of like a do-it-yourself dividend payment.
By the way, as you will discover later in this book, this is also the risk-
return profile of a covered call.
Buying a Put for Protection
50
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REDGRAY
Above an investor wants to enjoy exposure to the stock’s upside potential 
while limiting his or her losses in case of a market fall. By buying a put 
option struck a few dollars under the market price of the stock, the investor 
cancels out the downside exposure he or she accepted when buying the 
stock. With this protective put overlay in place, any loss on the stock will be 
compensated for through a gain on the put contract. The investor can use 
these gains to buy more of the stock at a lower price or to buy another put 
contract as protection when the first contract expires.
Tailoring Exposure with Puts and Calls
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BE = $60.50
GREEN
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24  •   The Intelligent Option Investor
Here an investor is bullish on the prospects of the stock and is tailor -
ing where to gain and accept exposure by selling a short-term put and 
simultaneously buying a longer-term call. By doing this, the investor 
basically subsidizes the purchase of the call option with the sale of the 
put option, thereby reducing the level the stock needs to exceed on the 
upside before one breaks even. In this case, we’re assuming that the call 
option costs $1.50 and the put option trades for $1.00. The cash inflow 
from the put option partially offsets the cash outflow from the call op-
tion, so the total breakeven amount is just the call’s $60 strike price plus 
the net of $0.50.
Effective Buy Price/Effective Sell Price
One thing that I hope you realized while looking at each of the preceding 
diagrams is how similar each of them looks to a particular part of our long 
and short stock diagrams:
Buying a stock.
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GREEN
RED
Short selling a stock.
For example, doesn’t the diagram labeled “Buying a call for growth” 
in the preceding section look just like the top part of the buying stock 
diagram? 
Option Fundamentals   • 25
In fact, many of the option strategies I will introduce in this book 
simply represent a carving up of the risk-reward profile of a long or short 
stock position and isolating one piece of it. To make it more clear and easy 
to remember the rules for breaking even on different strategies, I will actu-
ally use a different nomenclature from breakeven.
If a diagram has one or both of the elements of the risk-return profile 
of buying a stock, I will call the breakeven line the effective buy price  and 
abbreviate it EBP. For example, if we sell a put option, we accept downside 
risk in the same way that we do when we buy a stock: 
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EBP = $45
RED
Basically, what we are saying when we accept downside risk is that 
we are willing to buy the stock if it goes below the strike price. In return 
for accepting this risk, we are paid $5 in premium, and this cash inflow 
effectively lowers the buying price at which we own the stock. If, when the 
option expires, the stock is trading at $47, we can think of the situation 
not as “being $3 less than the strike price” but rather as “being $2 over the 
b u y  p r i c e .”
Conversely, if a diagram has one or both of the elements of the risk-
return profile of short selling a stock, I will call the breakeven line the 
effective sell price and abbreviate it ESP. For example, if we buy a put option 
anticipating a fall in the stock, we would represent it graphically like this:
26  •   The Intelligent Option Investor
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ESP = $45
GREEN
When a short seller sells a stock, he or she gets immediate profit exposure 
to the stock’s downside potential. The seller is selling at $50 and hopes to make 
a profit by buying the shares back later at a lower price—let’s say $35. When we 
get profit exposure to a stock’s downside potential using options, we are getting 
the same exposure as if we sold the stock at $50, except that we do not have to 
worry about losing our shirts if the stock moves up instead of down. In order to 
get this peace of mind, though, we must spend $5 in premium. This means that 
if we hold the position to expiration, we will only realize a net profit if the stock 
is trading at the $50 mark less the money we have already paid to buy that ex-
posure—$5 in this case. As such, we are effectively selling the stock short at $45.
There are some option strategies that end up not looking like one of 
the two stock positions—the flexibility of options allows an investor to do 
things a stock investor cannot. For example, here is the graphic representa-
tion of a strategy commonly called a long strangle:
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BE 1 = $80.75
BE 2 = $19.25
GREEN
GREEN
Option Fundamentals   • 27
Here we have a stock trading at $50 per share, and we have bought 
one put option and one call option. The put option is struck at $20 and 
is trading for $0.35. The call option is struck at $80 and is trading for 
$0.40. Note that the top part of the diagram looks like the top part of the 
long-stock diagram and that the bottom part looks like the bottom part 
of the short-stock diagram. Because a stock investor cannot be simulta-
neously long and short the same stock, we cannot use such terminology 
as effective buy  or effective sell  price. In this case, we use breakeven  and 
abbreviate it BE.
This option strategy illustrates one way in which options are much 
more flexible than stocks because it allows us to profit if the stock moves 
up (into the call’s range of exposure) or down (into the put’s range of 
exposure). If the stock moves up quickly, the call option will be in the 
money, but the put option will be far, far, far out of the money . Thus, if 
we are ITM on the call, the premium paid on the puts probably will end 
up a total loss, and vice versa. For this reason, we calculate both break-
even prices as the sum of both legs  of our option structure (where a leg 
is defined as a single option in a multioption strategy). As long as the leg 
that winds up ITM is ITM enough to cover the cost of the other leg, we 
will make a profit on this investment. The only way we can fail to make a 
profit is if the stock does not move one way or another enough before the 
options expire.
Flexibility without Directionality Is a Sucker’s Game
Despite this great flexibility in determining what directional invest-
ments one wishes to make, as I mentioned earlier, option market mak-
ers and floor traders generally attempt to mostly (in the case of floor 
traders) or wholly (in the case of market makers) insulate themselves 
against large moves in the underlying stock or figure out how to lim-
it the cost of the exposure they are gaining and do so to such an ex-
tent that they severely curtail their ability to profit from large moves. 
I do not want to belabor the point, but I do want to leave you with one 
graphic illustration of a “typical” complex option strategy sometimes 
called a condor :
28  •   The Intelligent Option Investor
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BE 1
BE 2
RED
RED
There are a few important things to notice. First, notice how much shorter 
the time frame is—we have moved from a 500-day time exposure to a two-week 
exposure. In general, a floor trader has no idea of what the long-term value of a 
stock should be, so he or she tries to protect himself or herself from large moves 
by limiting his or her time exposure as much as possible. Second, look at how 
little price exposure the trader is accepting! He or she is attempting to control his 
or her price risk by making several simultaneous option trades (which, by the 
way, puts the trader in a worse position in terms of breakeven points) that end up 
canceling out most of his or her risk exposure to underlying moves of the stock.
With this position, the trader is speculating that over the next short 
time period, this stock’s market price will remain close to $50 per share; 
what basis the trader has for this belief is beyond me. In my mind, winning 
this sort of bet is no better than going to Atlantic City and betting that the 
marble on the roulette wheel will land on red—completely random and 
with only about a 50 percent chance of success.
3
It is amazing to me that, after reading books, subscribing to newslet-
ters, and listening to TV pundits advocating positions such as this, inves-
tors continue to have any interest in option investing whatsoever!
With the preceding explanation, you have a good foundation in the 
concept of options, their inherent directionality, and their peerless flex-
ibility. We will revisit these themes again in Part III of this book when we 
investigate the specifics of how to set up specific option investments.
However, before we do that, any option investor must have a good 
sense of how options are priced in the open market. We cover the topic of 
option pricing in Chapter 2.
29
Chapter 2
The black-scholes-
merTon model
As you can tell from Chapter 1, options are in fact simple financial instru-
ments that allow investors to split the financial exposure to a stock into upside 
and downside ranges and then allow investors to gain or accept that expo-
sure with great flexibility. Although the concept of an option is simple, trying 
to figure out what a fair price is for an option’s range of exposure is trickier. The 
first part of this chapter details how options are priced according to the Black-
Scholes-Merton model (BSM)—the mathematical option pricing model  
mentioned in Chapter 1—and how these prices predict future stock prices.
Many facets of the BSM have been identified by the market at large 
as incorrect, and you will see in Part III of this book that when the rubber 
of theory meets the road of practice, it is the rubber of theory that gets 
deformed. The second half of this chapter gives a step-by-step refutation 
to the principles underlying the BSM. Intelligent investors should be very, 
very happy that the BSM is such a poor tool for pricing options and pre-
dicting future stock prices. It is the BSM’s shortcomings and the general 
market’s unwillingness or inability to spot its structural deficiencies that 
allow us the opportunity to increase our wealth.
Most books that discuss option pricing models require the reader to have 
a high level of mathematical sophistication. I have interviewed candidates with 
master’s degrees in financial engineering who indeed had a very high level 
of mathematical competence and sophistication yet could not translate that 
sophistication into the simple images that you will see over the next few pages.
30  •   The Intelligent Option Investor
This chapter is vital to someone aspiring to be an intelligent options 
investor. Contrary to what you might imagine, option pricing is in itself 
something that intelligent option investors seldom worry about. Much 
more important to an intelligent option investor is what option prices im-
ply about the future price of a stock and in what circumstances option 
prices are likely to imply the wrong stock prices. In terms of our intelligent 
option investing process, we need two pieces of information:
1. A range of future prices determined mechanically by the option 
market according to the BSM
2. A rationally determined valuation range generated through an 
insightful valuation analysis
This chapter gives the theoretical background necessary to derive the 
former.
The BSM’s Main Job is to Predict Stock Prices
By the end of this section, you should have a big-picture sense of how the 
BSM prices options that is put in terms of an everyday example. Y ou will also 
understand the assumptions underlying the BSM and how, when combined, 
these assumptions provide a prediction of the likely future value of a stock.
Jargon introduced in this section includes the following:
Stock price efficiency Forward price (stock)
Lognormal distribution Efficient market hypothesis (EMH)
Normal distribution  BSM cone
Drift
The Big Picture
Before we delve into the theory of option pricing, let me give you a general 
idea of the theory of option prices. Imagine that you and your spouse or 
significant other have reservations at a nice restaurant. The reservation time 
is coming up quickly, and you are still at home. The restaurant is extremely 
hard to get reservations for, and if you are not there at your reservation time, 
The Black-Scholes-Merton Model   • 31
your seats are given to someone else. Now let’s assume that in the midst 
of the relationship stress you are likely feeling at the moment, you decide 
to lighten the mood by betting with your spouse or significant other as to 
whether you will be able to make it to the restaurant in time for your seating.
If you were a statistician attempting to lighten the mood of the 
evening, before you placed your bet, you would have attempted to factor in 
answers to the following questions to figure out how likely or unlikely you 
would be to make it on time:
1. How long do you have until your reservation time?
2. How far away is the restaurant?
3. How many stop signs/stoplights are there, and how heavy is traffic?
4. What is the speed limit on the streets?
5. Does your car have enough gasoline to get to the restaurant?
Let’s say that your reservation time is 6 p.m. and it is now 5:35 p.m . 
Y ou realize that you will not be able to calculate an exact arrival time be -
cause there are some unknown factors—especially how heavy traffic is and 
how often you’ll have to stop at stoplights. Instead of trying to pick a point 
estimate of your arrival time, you decide to calculate the upper and lower 
bounds of a range of time over which you may arrive.
After assessing the input factors, let’s say that your estimated arrival 
time range looks something like this:
Moderate traffic
No traffic
Heavy traffic
12
6 5
4
39
10
11
8
7
2
1
In other words, you think that your best chance of arrival is the 15-minute 
range between 5:50 and 6:05 p.m. If traffic is light, you’ll make it toward the 
beginning of that interval; if traffic is heavy, you’ll make it toward the end 
of that interval or may not make it at all. How willing would you be to bet 
on making it on time? How much would be a fair amount to bet?
32  •   The Intelligent Option Investor
This example illustrates precisely the process on which the BSM and 
all other statistically based option pricing formulas work. The BSM has a 
fixed number of inputs regarding the underlying asset and the contract itself. 
Inputting these variables into the BSM generates a range of likely future values 
for the price of the underlying security and for the statistical probability of the 
security reaching each price. The statistical probability of the security reach-
ing a certain price (that certain price being a strike price at which we are inter-
ested in buying or selling an option) is directly tied to the value of the option.
Now that you have a feel for the BSM on a conceptual dining-
reservation level, let’s dig into a specific stock-related example.
Step-by-Step Method for Predicting Future Stock 
Price Ranges—BSM-Style
In order to understand the process by which the BSM generates stock price 
predictions, we should first look at the assumptions underlying the model. 
We will investigate the assumptions, their tested veracity, and their impli-
cations in Chapter 3, but first let us just accept at face value what Messrs. 
Black, Scholes, and Merton take as axiomatic.
According to the BSM,
• Securities markets are “efficient” in that market prices perfectly 
reflect all publicly available information about the securities. This 
implies that the current market price of a stock represents its fair 
value. New information regarding the securities is equally likely to 
be positive as negative; as such, asset prices are as likely to move up 
as they are to move down.
• Stock prices drift upward over time. This drift cannot exceed the 
risk-free rate of return or arbitrage opportunities will be available.
• Asset price movements are random and their percentage returns 
follow a normal (Gaussian) distribution.
• There are no restrictions on short selling, and all hedgers can bor -
row at the risk-free rate. There are no transaction costs or taxes. 
Trading never closes (24/7), and stock prices are mathematically 
continuous (i.e., they never gap up or down), arbitrage opportuni-
ties cannot persist, and you can trade infinitely small increments of 
shares at infinitely small increments of prices.
The Black-Scholes-Merton Model  • 33
Okay, even if the last assumption is a little hard to swallow, the first 
three sound plausible, especially if you have read something about the 
efficient market hypothesis (EMH). Suffice it to say that these assumptions 
express the “orthodox” opinion held by financial economists. Most finan-
cial economists would say that these assumptions describe correctly, in 
broad-brush terms, how markets work. They acknowledge that there may 
be some exceptions and market frictions that skew things a bit in the real 
world but that on the whole the assumptions are true.
Let us now use these assumptions to build a picture of the future 
stock price range predicted by the BSM.
Start with an Underlying Asset
First, imagine that we have a stock that is trading at exactly $50 right now 
after having fluctuated a bit in the past.
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70
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50
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Date/Day Count
Stock Price
I am just showing one year of historical trading data and three years 
of calendar days into the future. Let’s assume that we want to use the BSM 
to predict the likely price of this asset, Advanced Building Corp. (ABC), 
three years in the future.
The BSM’s first assumption—that markets are efficient and stock 
prices are perfect reflections of the worth of the corporation—means that if 
34  •   The Intelligent Option Investor
there is no additional information about this company, the best prediction 
of its future price is simply its present price. In graphic terms, we would 
represent this first step in the following way:
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80
70
60
50
40
30
20
Date/Day Count
Stock Price
Here the dotted straight line represents a prediction of the future 
price of the stock at any point in time. However, to the extent that the world 
simply cannot stop spinning, news never stops flowing. Some of this news 
likely will have an impact on the economic value of the firm, but as stated 
earlier, according to the EMH, the incoming information is random and is 
just as likely to be positive for valuation as it is to be negative. 
The first step of the BSM prediction is pretty raw. Stated simply, at 
this point in the process, the BSM predicts that the future price of the stock 
most likely will be the present price of the stock, with a possible range of 
values around that expected price randomly fluctuating from $0 to infinity. 
To refine this decidedly unhelpful range, the BSM must incorporate 
its second axiom into its prediction methodology. 
Calculate the Forward Price of the Stock
Looking at a long-range chart of stock markets, one fact sticks out: mar -
kets tend to rise over the long term. Although this is obvious to even a 
The Black-Scholes-Merton Model  • 35
casual observer, the fact that markets tend to rise is contradictory to our 
first principal—that stocks are as likely to go up as they are to go down.
Indeed, if stocks in general did not go up, people would not think to 
invest in them as long as there were other investment choices such as risk-
free bonds available. Thus the theorists modified their first assumption 
slightly, saying that stock prices are just as likely to go up as they are to 
go down over a very short period of time; over longer time periods, they 
would have to drift upward. The amount of this drift is set to the risk-free 
rate via a wonderfully elegant argument involving the no-arbitrage condi-
tion in the fourth assumption listed earlier.
Increasing the present price of the stock into the future at the risk-
free rate generates what is known as the forward price of the stock. Here is 
what the forward price of our asset looks.
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80
70
60
50
40
30
20
Date/Day Count
Stock Price
Here we see the stock being subject to risk-free drift—moving up 
steadily to $52 at the end of three years—this is the forward price. In terms 
of the BSM’s prediction of the future stock price, this forward price line 
represents its most likely value.
The only slight modification to this calculation of forward price 
involves dividend-paying stocks. For dividend-paying stocks, the expected 
36  •   The Intelligent Option Investor
dividend serves as a downward drift that cancels out some of the upward 
drift of the risk-free rate. Simplistically, if the risk-free rate is 3 percent 
per year and the company has a dividend yield of 1 percent per year, the 
upward-drift term will be 2 percent (= 3 percent − 1 percent).
Add a Range around the Forward Price
Now even an academic would look at the preceding diagram and have his 
or her doubts that the model regarding whether the future price of this 
asset will ever be proven correct. This is when the academic will start to 
backpedal and remind us of the first axiom by saying, “Markets are effi-
cient, but stock prices fluctuate based on new data coming into the market. 
Because good news is as likely to come into the market as bad news, stock 
prices should fluctuate up and down in equal probability. ” Because they 
are fluctuating randomly, our prediction should be a statistical one based 
on a range.
To make the predictive range more usable than our earlier condition 
(i.e., a predicted stock price between $0 and infinity), we must take a look 
at the next axiom—the percentage return of stocks follows a normal  (also 
called Gaussian) distribution. A normal distribution is simply a bell curve, 
with which most people are very familiar in the context of IQ scores and 
other natural phenomena. A bell curve is perfectly symmetrical—the most 
commonly found value (e.g., an IQ of 100) is the value at the tallest point 
of the curve, and there are approximately as many instances of profound 
genius as there are of profound mental disability.
Note that the BSM assumes that percentage returns are normally dis-
tributed. In our graphs, we are showing price rather than percentage return 
on the vertical axis, so we will have to translate a percentage return into a 
price. Translating a percentage return into a price gives us a distribution 
that is skewed to the right called a lognormal distribution.
Thinking about stock prices for a moment, it becomes obvious that it 
is likely that stock prices will follow a skewed distribution simply because 
the price cannot fall any further than $0 per share but has no upward 
bound. For further evidence that this skewed distribution is correct, 
take a look at what happens to the prices of two stocks, both of which 
start initially at $50, but one of which decreases by 10 percent for three 
The Black-Scholes-Merton Model  • 37
consecutive days and the other which increases by 10 percent for three 
consecutive days.
Losing Stock Winning Stock
Original price $50.00 Original price $50.00
Price after falling 10% $45.00 Price after rising 10% $55.00
Price after falling 
another 10%
$40.50 Price after rising 
another 10%
$60.50
Price after falling 
another 10%
$36.45 Price after rising 
another 10%
$66.55
Final difference  
from $50
$13.55 Final difference  
from $50
$16.55
Notice that even though both have changed by the same percentage 
each day, the stock that has increased has done so more than the losing stock 
has decreased. This experiment shows that if we assume a normal distribu-
tion of returns, we should wind up with a distribution that is skewed toward 
higher prices. Mathematically, this distribution is called the lognormal curve.
If we use the forward price as a base and then draw a cone 
representing the lognormal distribution around it, we end up with the 
following diagram:
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Date/Day Count
Stock Price
38  •   The Intelligent Option Investor
This diagram shows that the most likely future price projected by the 
BSM still lies along the straight dotted line, and the most likely range lies 
between the solid lines of the curve. In this diagram, note that even though 
the skew is subtle, the lower bound is closer to the forward price of the 
stock than is the upper bound. This confirms that the BSM’s predictive 
model is consistent with its third assumption. It also gives us a much more 
sensible prediction of the future price of this stock than when we started 
out. We will term this graph the BSM cone.
According to the BSM, if you want to know the price at which a stock 
will trade at any point in the future, you can look within the bounds of 
the BSM cone. The prices within this cone are more likely to be near the 
forward price line and less likely to be near the lines of the cone itself. In 
a phrase, the BSM tells an investor, “If you want to know what the future 
price of a stock will be, look within the cone. ”
With the refinements we have made, we can say that our best guess 
for the value of this stock in three years will be $52, and the range of 
values between which the stock will most plausibly fall will be anywhere 
from around $37 to just over $70. One thing to note is that the cone as 
I have drawn it here does not, in fact, show the outline of the entire log-
normal price distribution for the stock but rather just the most plausible  
range. 
Also, as mentioned earlier, the likelihood of the stock price reaching 
each of the prices along the vertical axis is not equal. The most likely future 
value according to the BSM is the forward price. Most likely means, in the 
statistical sense, that there is a 50-50 chance that the stock will be above or 
below that line. 
As one moves up the vertical (price) axis from the forward price 
line, the likelihood that the stock price will be above that point is pro-
gressively lower. By the time you reach the upper line of the cone, the 
chance that the stock price will be higher than that is only around 16 
percent. Conversely, as you move down the vertical axis from the for -
ward price line, the likelihood that the stock price will be below that 
point is progressively lower. By the time you reach the lower line of the 
cone, the chance that the stock price will fall lower than that is again 
around 16 percent.
The Black-Scholes-Merton Model  • 39
Stock has ~16% chance
of rising above this line
50% chance of stock being
above or below this price
Stock has ~16% chance of
falling below this line
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Advanced Building Corp. (ABC)
Date/Day Count
Stock Price
Because the BSM assumes that stock returns are lognormally distrib-
uted, and because the properties of the lognormal curve are very well un-
derstood by mathematicians, every single point on the vertical price axis 
is associated with a distinct probability. In other words, with just the few 
simple inputs we have discussed, the BSM mechanically churns out pre-
dictions of future stock prices by associating a future stock price with a 
theoretically derived probability.
Now that we know what the theory says and have created a predic-
tion of the future price of a stock based on the theory, let’s look at key areas 
where the BSM breaks down. 
The BSM is Lousy at Its Main Job
By the end of this section, you will have a good understanding why the 
BSM—although a testament to human ingenuity and logical reasoning—is 
deeply flawed as a model to predict asset prices in general and stock prices 
specifically. 
40  •   The Intelligent Option Investor
Jargon that will be introduced in this section is as follows:
Leptokurtic
Fat-tailed
Critiques of the Base Assumptions of the BSM
Before we head into the critique section, let us remind ourselves of the 
base assumptions of the BSM. When I introduced these assumptions ear -
lier, I suggested that you should just accept them at face value, but this time 
around, let’s look at the assumptions with a more critical eye.
• Securities markets are efficient in that market prices perfectly reflect all 
publicly available information about the securities. This implies that the 
current market price of a stock represents its fair value. New information 
regarding the securities is equally likely to be positive as negative; as 
such, asset prices are as likely to move up as they are to move down.
• Stock prices drift upward over time. This drift cannot exceed the 
risk-free rate of return, or arbitrage opportunities will be available.
• Asset price percentage returns follow a normal (Gaussian) distribution.
• There are no restrictions on short selling, and all hedgers can bor -
row at the risk-free rate. There are no transaction costs or taxes. 
Trading never closes (24/7), and stock prices are mathematically 
continuous (i.e., they never gap up or down), arbitrage opportuni-
ties cannot persist, and you can trade infinitely small increments of 
shares at infinitely small increments of prices.
Although the language is formal and filled with jargon, you need not be in-
timidated by the special terminology but should simply look at the assumptions 
from a commonsense perspective. Doing so, you will see how ridiculous each 
of these assumptions appears. Indeed, each one of them has either been proven 
wrong through experimental evidence (i.e., the first three assumptions) or is 
plainly false (the fourth assumption). Let’s look at each assumption one by one.
Markets Are Efficient
The first two assumptions spring from a theory in financial economics 
called the efficient market hypothesis (EMH), which is strongly associated 
The Black-Scholes-Merton Model  • 41
with the University of Chicago and which, more or less, still holds truck 
with many theorists to this day. Stock prices, under this theory, move in ac-
cordance with the random-walk principal—having a 50-50 chance of going 
up or down in a short time period because they are bought and sold on the 
basis of new information coming into the market, and this new informa-
tion can be either good or bad.
The EMH proposes that there are different levels of efficiency in fi-
nancial markets. The weakest form of efficiency holds that one cannot gen-
erate returns that are disproportionate to risk in a market simply by having 
access to information related to historical prices of the market (i.e., refut-
ing so-called technical analysis). The strongest form of efficiency holds that 
even an investor with inside information about a company cannot generate 
returns that are disproportionate to the risk they assume by investing (this 
form is usually rejected even by supporters of the EMH).
In short, the EMH says that investors, in aggregate, dispassionately 
assess all available facts regarding the economic environment and 
rationally and methodically incorporate their well-informed expectations 
about likely future outcomes into their decisions to buy or sell a given 
stock. They always act in such a way as to maximize their utility in a ra-
tional, considered way.
Now, before running to your favorite search engine to look for aca-
demic papers refuting or defending the EMH, just step back and ask one sim-
ple question: Does this model of human behavior seem right to you? How 
many people on the road with you during rush hour or attending a sporting 
event or going holiday shopping seem to make calculated, rational, and well-
considered decisions? When it comes to something dealing with money and 
investing, how many people do you know who act in the way just described? 
No matter what mathematical proof may or may not support the EMH, as a 
model of human behavior, the EMH simply does not ring true—to us at least.
Aside from the fundamental criticism that the EMH does not pre-
sent a model of human behavior that seems, well, human, there have been 
empirical refutations of the EMH from almost its conception. Studies 
showing that stocks with low price-to-book ratios, price-to-sales ratios, 
and price-to-earnings ratios outperform those with high ratios have been 
well documented, and the effects mentioned seem to persist. One of my 
professors in business school, Graeme Rankine, helped to discover the 
42  •   The Intelligent Option Investor
so-called stock-split effect—the fact that stocks that split (i.e., the owners 
were simply told that for every share they previously owned, they now owned 
multiple shares, a change that should not have any effect whatsoever on the 
value of the firm) performed better after the split than those that did not 
split. More recently, Andrew Lo and Craig MacKinlay have demonstrated 
that financial markets are not efficient on even a weak basis but that they 
have some sort of a long-term price “memory” and seem to act more like 
an organic system than a mechanical one.
Later in this book we will discuss behavioral factors that affect invest-
ing, and in fact, several prominent behavioral economics theorists (Daniel 
Kahneman and Robert Shiller) have won Nobel prizes in economics as a 
result of their groundbreaking work in this field. In essence, what behav-
ioral economics points out is that when given questions that test decision-
making ability and process, most people—even highly trained people—do 
not make decisions in a way described by the tenants of the EMH. In fact, 
economists have found that experimentally, human decision makers are 
swayed by all sorts of issues that someone subscribing to the EMH would 
find irrational. Human decision makers do not, it turns out, act as perfectly 
rational economic animals as the EMH posits but rather are swayed by 
emotion, illusion, and ingrained prejudice that cause their decisions to 
be made in consistently flawed ways. Obviously, the experimental evi-
dence that behavioral economics researchers have highlighted regarding 
how economic actors make decisions casts doubt on the basic premises of 
the EMH.
Indeed, proponents of EMH would argue (do argue in the case of 
Eugene Fama, a Nobel prize–winning economist at the University of 
Chicago and one of the intellectual godfathers of the EMH) that asset price 
bubbles cannot occur. If markets are efficient, they incorporate all avail-
able information regarding the likely future outcome of stocks and other 
financial assets in their present prices—meaning that even when prices are 
very high, as they were during the Internet boom and the mortgage finance 
boom, market participants’ expectations are “rational. ” Fama has famously 
said, “I don’t even know what a ‘bubble’ is. ”
This type of pedagogical rigidity in the face of clear evidence of 
the existence of bubbles and crashes, and in fact the enormous human 
costs that the bursting of bubbles bring about (e.g., in the wake of the 
The Black-Scholes-Merton Model  • 43
bursting of the mortgage finance bubble), has soured many laypeople on 
the philosophical underpinnings of the EMH, even if they have never 
heard the term specifically mentioned. Academic responses to the ten-
ants of the EMH from economists such as Nobel prize–winner Rob-
ert Shiller and Australian Steven Keen have been gaining strength and 
acceptance in recent years, whereas only a few years ago they would have 
been considered apostate and would have been ridiculed by “respectable” 
orthodox economists.
Whatever the arguments both for and against the EMH, if you are 
reading this book, you implicitly must hold the belief that stock markets 
are inefficient because by reading this book, you must be trying to “beat” 
the markets—an act that the EMH maintains is impossible. Although it is a 
pretty blunt tool for someone trying to accurately describe the complexity 
of markets, the one thing the EMH does have to recommend it is that if you 
hold to its assumptions, the mathematics describing asset prices is made 
much easier, and this ease leads to the ability to develop a pricing model 
such as the BSM. 
In fact, although one of my favorite indoor sports is making fun of 
EMH assumptions, I do not disagree that, especially over short time frames 
and especially for certain types of assets, the EMH assumptions hold up 
pretty well and that the BSM is useful in describing likely price ranges. 
I discuss when the BSM is more useful and correct in Appendix A because 
in those instances an intelligent investor has a small chance of success. 
It goes without saying that intelligent investors choose not to invest in 
situations in which there is a small chance of success!
A good theory must be simple, but it also must be provably correct 
under all conditions. While the EMH is certainly simple, I maintain that it 
cannot be considered a good theory because it does not explain phenom-
ena in financial markets correctly in all (most?) circumstances. This means 
that the first pillar on which the BSM is built is, for the purposes of intel-
ligent investors, wrong.
Stock Returns Are Normally Distributed
A picture is worth a thousand words. Here is a picture of a normal 
distribution probability curve:
44  •   The Intelligent Option Investor
-3σ 0
x
.1359
.0214
Gaussian or
“normal”
distribution
fg(x)
.00135 .3413 .3413 .1359
.0214
.00135
-2σ 2σ 3σ-σ σ
The numbers near the horizontal axis show the percent of cases in 
each region (e.g., between the 0 and σ, you see the number 0.3413—this 
means that for a normally distributed quantity such as IQ, you would ex-
pect 34.13 percent of cases to lie in that region), and the regions are marked 
off into numbers of standard deviations [denoted by the lowercase Greek 
letter sigma (σ)].
Now that you’ve seen a normal curve, let’s take a look at daily returns 
for the Standard & Poor’s 500 Index (S&P 500) over the past 50 years:
-21% -19% -17% -15% -13% -11% -9%- 7% -5%- 3% -1%3 %1% 5% 7% 9% 11%
0
100
200
300
400
500
900
800
700
600
S&P Returns
Frequency
S&P 500 Daily Returns
The Black-Scholes-Merton Model  • 45
There is a very easily recognizable difference between this curve and 
the preceding one—namely that this one looks much pointier than the 
other. However, a more profound difference can be seen by looking at the 
cases out near the –21 percent mark and the +11 percent mark. If the S&P 
500’s actual returns were normally distributed, these points simply would 
not exist—not for another billion years or so. The huge fall (a 20-standard-
deviation event) might be expected to happen in financial markets every 
few billion years if in fact daily returns were normally distributed. Instead, 
they seem to happen about once every 70 years or so. 
These observations should provide good anecdotal evidence that the 
assumption of normally distributed returns is unfounded. Indeed, empir-
ical evidence has shown that stock market returns are what are termed 
strongly leptokurtic (a.k.a. fat-tailed) to the extent that it is not helpful to 
think of them as normal at all. The two characteristics of leptokurtic distri-
butions are that (1) they are pointy and (2) they contain a relatively large 
proportion of extreme tail values. Some theorists think that the best way to 
understand stock returns is actually to conceive of them as multiple over -
lapping (and non-Gaussian) distributions. Whatever statistical distribu-
tion stock returns follow, it is certainly not Gaussian.
Option traders, in fact, took markets to be normally distributed 
until the great crash of 1987. After that time, the practitioner response 
to the obvious leptokurtic nature of stock price returns—charging a 
much higher than theoretically justified price for far out-of-the money 
(OTM) puts and far in-the-money (ITM) calls—came into being, and the 
volatility smile, a feature we will discuss in detail in Part III of the book, 
came into existence. This means that the second pillar on which the BSM 
is built is wrong.
Stock Prices Drift Upward at the Risk-Free Rate
On average, the compound annual growth of the stock market since 
1926 has been on the order of 10 percent. The average annual compound 
growth of U.S. government Treasury bonds (our risk-free benchmark) 
has been on the order of 5 percent. Therefore, just comparing these 
averages, it would seem that stocks drift upward at roughly twice the 
risk-free rate.
46  •   The Intelligent Option Investor
Averages can be misleading, however, so in the following graph I have 
plotted the five-year rolling compound annual growth rate for both the 
S&P 500 and T-bonds:
35%
30%
25%
20%
15%
10%
5%
0%
-5%
-10%
-15%1932 1937 1942 1947 1952 1957 1962 1967 1972 1977 1982 1987 1992 1997 2002 2007
Stocks 5-year CAGR T-Bonds 5-year CAGR
Y ou can see that there are some significant outliers in the Great 
Depression area of the graph, but in general, stock returns are much higher 
than those of risk-free instruments on this rolling basis as well. In fact, 
if you asked me to guess what any randomly selected rolling five-year 
compound annual growth rate (CAGR) for stocks was going to be, I would 
probably pick a number like 13 percent and figure that I would at least be in 
the ballpark 80 percent of the time. Certainly, by looking at the preceding 
graph, you can tell that there is no reasonable basis to believe that stocks 
should increase anywhere around the rate of risk-free securities! As such, 
we can discard the third pillar of the BSM.
No Taxes, No Trading Restrictions, and All Market Participants 
Can Borrow at the Risk-Free Rate, Etc.
No comment, other than to say, “Ha!” With no pillars left, the edifice of the 
BSM crumbles in on itself after even just a cursory look.
The Black-Scholes-Merton Model  • 47
The fact that the theoretical basis of option pricing is provably wrong 
is very good news for intelligent investors. The essence of intelligent option 
investing involves comparing the mechanically determined and unreason-
able range of stock price predictions made by the BSM with an intelligent 
and rational valuation range made by a human investor. Because the BSM 
is using such ridiculous assumptions, it implies that intelligent, rational 
investors will have a big investing advantage. Indeed, I believe that they do.
Now that we have seen how the BSM forecasts future price ranges for 
stocks and why the predictions made by the BSM are usually wrong, let us 
now turn to an explanation of how the stock price predictions made by the 
BSM tie into the option prices we see on an option exchange such as the 
Chicago Board Option Exchange (CBOE).
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49
Chapter 3
The InTellIgenT 
InvesTor’s guIde To 
opTIon prIcIng
By the end of this chapter, you should understand how changes in the follow-
ing Black-Scholes-Merton model (BSM) drivers affect the price of an option:
1. Moneyness
2. Forward volatility
3. Time to expiration
4. Interest rates and dividend yields
Y ou will also learn about the three measures of volatility—forward, im-
plied, and statistical. Y ou will also understand what drivers affect option 
prices the most and how simultaneous changes to more than one variable 
may work for or against an option investment position.
In this chapter and throughout this book in general, we will not try to 
figure out a precise value for any options but just learn to realize when an op-
tion is clearly too expensive or too cheap vis-à-vis our rational expectations 
for a fair value of the underlying stock. As such, we will discuss pricing in 
general terms; for example, “This option will be much more expensive than 
that one. ” This generality frees us from the computational difficulties that 
come about when one tries to calculate too precise a price for a given op-
tion. The BSM is designed to give a precise answer, but for investing, simply 
knowing that the price of some security is significantly different from what 
it should be is enough to give one an investing edge.
50  •   The Intelligent Option Investor
In terms of how this chapter fits in with the goal of being an 
intelligent option investor, it is in this chapter that we start overlaying 
the range of exposure introduced in Chapter 1 with the implied stock 
price range given by the BSM cone that was introduced in Chapter 2. 
This perspective will allow us to get a sense of how expensive it will 
be to gain exposure to a given range or, conversely, to see how much 
we are likely to be able to generate in revenue by accepting exposure 
to that range. Understanding the value of a given range of exposure as 
perceived by the marketplace will allow us to determine what option 
strategy will be best to use after we determine our own intelligent 
valuation range for a stock.
Jargon introduced in this chapter is as follows:
Strike–stock price ratio Volatility (Vol) 
Time value  Forward volatility
Intrinsic value  Implied volatility
Tenor   Statistical volatility
Time decay  Historical volatility
How Option Prices are Determined
In Chapter 1, we saw what options looked like from the perspective of 
ranges of exposure. One of the takeaways of that chapter was how flexible 
options are in comparison with stocks. Thinking about it a moment, it is 
clear that the flexibility of options must be a valuable thing. What would 
it be worth to you to only gain upside to a stock without having to worry 
about losing capital as a result of a stock price decline? 
The BSM, the principles of which we discussed in detail in Chapter 2, 
was intended to answer this question precisely—“What is the fair value of 
an option?” Let us think about option prices in the same sort of probabilis-
tic sense that we now know the BSM is using.
First, let’s assume that we want to gain exposure to the upside poten-
tial of a $50 stock by buying a call option with a strike price of $70 and a 
time to expiration of 365 days. Here is the risk-return profile of this option 
position merged with the image of the BSM cone:
The Intelligent Investor’s Guide to Option Pricing  •  51
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20
30
40
50
60
70
80
90
100
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Advanced Building Corp. (ABC)
Date/Day Count
Stock Price
GREEN
Notice that because this call option is struck at $70, the upside po-
tential we have gained lies completely outside the cone of values the BSM 
sees as reasonably likely. This option, according to the BSM, is something 
like the bet that a seven-year-old might make with another seven-year-
old: “If you can [insert practically impossible action here], I’ll pay you a 
zillion dollars. ” The action is so risky or impossible that in order to entice 
his or her classmate to take the bet, the darer must offer a phenomenal 
return.
Off the playground and into the world of high finance, the way to 
offer someone a phenomenal return is to set the price of a risky asset very 
low. Following this logic, we can guess that the price for this option should 
be very low. In fact, we can quantify this “very low” a bit more by thinking 
about the probabilities surrounding this call option investment.
Remembering back to the contention in Chapter 2 that the lines of 
the BSM cone represent around a 16 percent probability of occurrence, 
we can see that the range of exposure lies outside this, so the chance of 
the stock making it into this range is lower than 16 percent. Let’s say that 
the range of exposure sits at just the 5 percent probability level. What this 
means is that if you can find 20 identical investments like this and invest in 
all of them, only one will pay off (1/20 = 5 percent). 
52  •   The Intelligent Option Investor
Thus, if you thought that you would win $1 for each successful invest-
ment you made, you might only be willing to pay $0.04 to play the game. In 
this case, you would be wagering $0.04 twenty times in the hope of making 
$1 once—paying $0.80 total to net $0.20 for a (probabilistic) 25 percent 
return.
Now how much would you be willing to bet if the perceived chance 
of success was not 1 in 20 but rather 1 in 5? With options, we can increase 
the chance of success simply by altering the range of exposure. Let’s try this 
now by moving the strike price down to $60:
5/18/2012 5/20/2013 249 499 749
20
30
40
50
60
70
80
90
100
999
Advanced Building Corp. (ABC)
Date/Day Count
Stock Price
GREEN
After moving the strike price down, one corner of the range of 
exposure we have gained falls within the BSM probability cone. This option 
will be significantly more expensive than the $70 strike option because the 
perceived probability of the stock moving into this range is material.
If we say that the chance of this call option paying its owner $1 is 
1 in 5 rather than 1 in 20 (the range of exposure is within the 16 percent 
line, so we’re estimating it as a 20 percent chance—1 in 5, in other words), 
we should be willing to pay more to make this investment. If we expected 
to win $1 for every five tries, we should be willing to spend $0.16 per bet. 
Here we would again expect to pay $0.80 in total to net $0.20, and again 
our expected percentage return would be 25 percent. 
The Intelligent Investor’s Guide to Option Pricing  •  53
Notice that by moving the strike down from an expected 5 percent chance 
of success to an expected 20 percent chance of success, we have agreed that we 
would pay four times the amount to play. What would happen if we lowered the 
strike to $50 so that the exposure range started at the present price of the stock? 
Obviously, this at-the-money (ATM) option would be more expensive still:
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20
40
50
60
70
80
90
100
5/20/2013 249 499 749 999
Advanced Building Corp. (ABC)
Date/Day Count
Stock Price
GREEN
The range of upside exposure we have gained with this option is not only 
well within the BSM probability cone, but in fact it lies across the dotted line in-
dicating the “most likely” future stock value as predicted by the BSM. In other 
words, this option has a bit better than a 50 percent chance of paying off, so it 
should be proportionally more expensive than either of our previous options.
The payouts and probabilities I provided earlier are completely made 
up in order to show the principles underlying the probabilistic pricing of 
option contracts. However, by looking at an option pricing screen, it is very 
easy to extrapolate annualized prices associated with each of the probabil-
ity levels I mentioned—5, 20, and 50 percent.
The following table lists the relative market prices of call options cor-
responding to each of the preceding diagrams.
1 The table also shows the 
calculation of the call price as a percentage of the present price of the stock 
($50) as well as the strike–stock price ratio , which shows how far above or 
below the present stock price a given strike price is.
54  •   The Intelligent Option Investor
Strike Price Strike–Stock Price Ratio Call Price
Call Price as a Percent 
of Stock Price
70 140% $0.25 0.5
60 120% $1.15 2.3
50 100% $4.15 8.3
Notice that each time we lowered the strike price in successive 
examples, we lowered the ratio of the strike price to the stock price. This 
relationship (sometimes abbreviated as K/S, where K stands for strike price 
and S stands for stock price) and the change in option prices associated 
with it are easy for stock investors to understand because of the obvious tie 
to directionality. This is precisely the reason why we have used changes in 
the strike–stock price ratio as a vehicle to explain option pricing. There are 
other variables that can cause option prices to change, and we will discuss 
these in a later section.
I will not make such a long-winded explanation, but, of course, 
put options are priced in just the same way. In other words, this put 
option,
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GREEN
The Intelligent Investor’s Guide to Option Pricing  •  55
would be more expensive than the following put option, which looks like 
this:
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-
10
20
30
40
50
60
70
80
90
100
Advanced Building Corp. (ABC)
Date/Day Count
Stock Price
GREEN
The former would be more expensive than the latter simply because the 
range of exposure for the first lies further within the BSM cone of prob-
ability than the latter.
We can extrapolate these lessons regarding calls and puts to come 
up with a generalized rule about comparing the prices of two or more op-
tions. Options will be more expensive in proportion to the total range of 
exposure that lies within the BSM cone. Graphically, we can represent this 
rule as follows:
This call option will be much less 
expensive…
GREEN
GREEN
than this call option.
56  •   The Intelligent Option Investor
This is so because the area of the range of exposure for the option on 
the left that is bounded by the BSM probability cone is much smaller than 
the range of exposure for the option on the right that is bounded by the 
same BSM probability cone.
Time Value versus Intrinsic Value
One thing that I hope you will have noticed is that so far we have talked 
about options that are either out of the money (OTM) or at the money 
(ATM). In-the-money (ITM) options—options whose range of exposure 
already contains the present stock price—may be bought and sold in just 
the same way as ATM and OTM options, and the pricing principle is ex-
actly the same. That is, an ITM option is priced in proportion to how much 
of its range of exposure is contained within the BSM probability cone.
However, if we think about the case of an OTM call option, we realize 
that the price we are paying to gain access to the stock’s upside potential 
is based completely on potentiality. Contrast this case with the case of an 
ITM call option, where an investor is paying not only for potential upside 
exposure but also for actual upside as well. 
It makes sense that when we think about pricing for an ITM call option, 
we divide the total option price into one portion that represents the poten-
tial for future upside and another portion that represents the actual upside. 
These two portions are known by the terms time value and intrinsic value, 
respectively. It is easier to understand this concept if we look at a specific 
example, so let’s consider the case of purchasing a call option struck at $40 
and having it expire in one year for a stock presently trading at $50 per share. 
We know that a call option deals with the upside potential of a stock 
and that buying a call option allows an investor to gain exposure to that up-
side potential. As such, if we buy a call option struck at $40, we have access 
to all the upside potential over that $40 mark. Because the stock is trading 
at $50 right now, we are buying two bits of upside: the actual bit and the 
potential bit. The actual upside we are buying is $10 worth (= $50 − $40) 
and is termed the intrinsic value of the option. 
A simple way to think of intrinsic value that is valid for both call options 
and put options is the amount by which an option is ITM. However, the option’s 
cost will be greater than only the intrinsic value as long as there is still time 
The Intelligent Investor’s Guide to Option Pricing  •  57
before the option expires. The reason for this is that although the intrinsic value 
represents the actual upside of the stock’s price over the option strike price, 
there is still the possibility that the stock price will move further upward in the 
future. This possibility for the stock to move further upward is the potential bit 
mentioned earlier. Formally, this is called the time value of an option.
Let us say that our one-year call option struck at $40 on a $50 stock 
costs $11.20. Here is the breakdown of this example’s option price into in-
trinsic and time value:
 $10.00 Intrinsic value: the amount by which the option is ITM
+ $1.20 Time value: represents the future upside potential of the stock
= $11.20 Overall option price
Recall that earlier in this book I mentioned that it is almost always a mis-
take to exercise a call option when it is ITM. The reason that it is almost always 
a mistake is the existence of time value. If we exercised the preceding option, 
we would generate a gain of exactly the amount of intrinsic value—$10. How-
ever, if instead we sold the preceding option, we would generate a gain totaling 
both the intrinsic value and the time value—$11.20 in this example—and then 
we could use that gain to purchase the stock in the open market if we wanted.
Our way of representing the purchase of an ITM call option from a 
risk-reward perspective is as follows:
Advanced Building Corp. (ABC)
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EBP = $51.25
999
100
90
80
70
60
50
40
30
20
Date/Day Count
Stock Price
GREEN
ORANGE
58  •   The Intelligent Option Investor
Usually, our convention is to shade a gain of exposure in green, but 
in the  case of an ITM option, we will represent the range of exposure with 
intrinsic value in orange. This will remind us that if the stock falls from its 
present price of $50, we stand to lose the intrinsic value for which we have 
already paid. 
Notice also that our (two-tone) range of exposure completely over -
laps with the BSM probability cone. Recalling that each upper and lower 
line of the cone represents about a 16 percent chance of going higher or 
lower, respectively, we can tell that according to the option market, this 
stock has a little better than an 84 percent chance of trading for $40 or 
above in one year’s time.
2 
Again, the pricing used in this example is made up, but if we take a 
look at option prices in the market today and redo our earlier table to in-
clude this ITM option, we will get the following:
Strike Price ($)
Strike–Stock 
Price Ratio (%) Call Price ($)
Call Price as a Percent 
of Stock Price
70 140 $0.25  0.5
60 120 $1.15  2.3
50 100 $4.15  8.3
40 80 10.85  21.7
Again, it might seem confounding that anyone would want to use the 
ITM strategy as part of their investment plan. After all, you end up paying 
much more and being exposed to losses if the stock price drops. I ask you 
to suspend your disbelief until we go into more detail regarding option 
investment strategies in Part III of this book. For now, the important points 
are (1) to understand the difference between time and intrinsic value, 
(2) to see how ITM options are priced, and (3) to understand our convention 
for diagramming ITM options.
From these diagrams and examples it is clear that moving the range 
of exposure further and further into the BSM probability cone will increase 
the price of the option. However, this is not the only case in which options 
will change price. Every moment that time passes, changes can occur to 
The Intelligent Investor’s Guide to Option Pricing  •  59
the size of the BSM’s probability cone itself. When the cone changes size, 
the range-of-exposure area within the cone also changes. Let’s explore this 
concept more.
How Changing Market Conditions 
Affect Option Prices
At the beginning of Chapter 2, I started with an intuitive example related 
to a friendly bet on whether a couple would make it to a restaurant in time 
for a dinner reservation. Let’s go back to that example now and see how the 
inputs translate into the case of stock options.
Dinner Reservation Example Stock Option Equivalent
How long before seating time Tenor 3 of the option
Distance between home and restaurant Difference between strike price and 
present market price (i.e., strike–stock 
price ratio)
Amount of traffic/likelihood of getting caught 
at a stoplight
How much the stock returns are 
thought likely to vary up and down 
Average traveling speed Stock market drift
Gas expenditure Dividend payout
Looking at these inputs, it is clear that the only input that is not known 
with certainty when we start for the restaurant is the amount of traffic/
number of stoplights measure.
Similarly, when the BSM is figuring a range of future stock prices, 
the one input factor that is unknowable and that must be estimated is 
how much the stock will vary over the time of the option contract. It is 
no surprise, then, that expectations regarding this variable become the 
single most important factor for determining the price of an option and 
the factor that people talk most about when they talk about options—
volatility (vol). 
This factor is properly known as forward volatility  and is formally 
defined as the expected one-standard-deviation fluctuation up and 
down around the forward stock price. If this definition sounds familiar,  
60  •   The Intelligent Option Investor
it is because it is also the definition of the BSM cone. To the extent that 
expectations are not directly observable, forward volatility can only be 
guessed at.
The option market’s best guess for the forward volatility, as expressed 
through the option prices themselves, is known as implied volatility. We 
will discuss implied volatility in more detail in the next section and will 
see how to build a BSM cone using option market prices and the forward 
volatility they imply in Part III.
The one other measure of volatility that is sometimes mentioned is sta-
tistical volatility (a.k.a. historical volatility). This is a purely descriptive statis-
tic that measures the amount the stock price actually fluctuated in the past. 
Because it is simply a backward-looking statistic, it does not directly affect 
option pricing. Although the effect of statistical volatility on option prices 
is not direct, it can have an indirect effect, thanks to a behavioral bias called 
anchoring. Volatility is a hard concept to understand, let alone a quantity to 
attempt to predict. Rather than attempt to predict what forward volatility 
should be, most market participants simply look at the recent past statistical 
volatility and tack on some cushion to come to what they think is a reason-
able value for implied volatility. In other words, they mentally anchor on the 
statistical volatility and use that anchor as an aid to decide what forward vola-
tility should be. The amount of cushion people use to pad statistical volatility 
differs for different types of stocks, but usually we can figure that the market’s 
implied volatility will be about 10 percentage points higher than statistical 
volatility. It is important to realize that this is a completely boneheaded way 
of figuring what forward volatility will be (so don’t emulate it yourself), but 
people do boneheaded things in the financial markets all the time.
However people come to an idea of what forward volatility is rea-
sonable for a given option, it is certain that changing perceptions about 
volatility are one of the main drivers of option prices in the market. To 
understand how this works, let’s take a look at what happens to the BSM 
cone as our view of forward volatility changes. 
Changing Volatility Assumptions
Let’s say that we are analyzing an option that expires in two years, with a 
strike price of $70. Further assume that the market is expecting a forward 
The Intelligent Investor’s Guide to Option Pricing  •  61
volatility of 20 percent per year for this stock. Visually, our assumptions 
yield the following:
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Date/Day Count
Stock Price
GREEN
A forward volatility of 20 percent per year suggests that after 
three years, the most likely range for the stock’s price according to the 
BSM will be around $41 on the low side to around $82 on the high 
side. Furthermore, we can tell from our investigations in Chapter 2 that 
this option will be worth something, but probably not much—about the 
same as or maybe a little more than the one-year, $60 strike call option 
we saw in Chapter 2.
4
Now let’s increase our assumption for volatility over the life of the 
contract to 40 percent per year. Increasing the volatility means that the 
BSM probability cone becomes wider at each point. In simple terms, what 
we are saying is that it is likely for there to be many more large swings in 
price over the term of the option, so the range of the possible outcomes 
is wider.
Here is what the graph looks like if we double our assumptions 
regarding implied volatility from 20 to 40 percent:
62  •   The Intelligent Option Investor
Advanced Building Corp. (ABC)
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100
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130
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10
-
Date/Day Count
Stock Price
GREEN
Compared with the preceding diagram, look how far into the exposure 
range the new BSM probability cone extends! Under an assumption of 
40 percent per year forward volatility, the most likely price range for the 
stock as calculated by the BSM is around $30 to nearly $120.
Looking at the range of exposure contained within the new BSM 
probability cone, we can tell that the likelihood of the stock being at $70 or 
greater in two years is much higher than it was when we assumed a forward 
volatility of 20 percent. Because the area of the range of exposure contained 
within the new BSM cone is much greater, we can be sure that the option 
will be much more expensive now.
Let’s now take a look at the opposite case—volatility is assumed to be 
half that of our original 20 percent per year assumption:
Advanced Building Corp. (ABC)
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80
70
60
50
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The Intelligent Investor’s Guide to Option Pricing  •  63
With this change in assumptions, we can see that the most likely 
range for the stock’s price three years in the future is between about $50 and 
about $70. As such, the chance of the stock price hitting $70 in two years 
moves from somewhat likely (20 percent volatility in the first example) to 
very likely (40 percent volatility in the second example) to very unlikely 
(10 percent volatility in the third example) in the eyes of the BSM. This 
characterization of “very unlikely” is seen clearly by the fact that the BSM 
probability cone contains not one whit of the call option’s exposure range.
In each of these cases, we have drawn the graphs by first picking an 
assumed volatility rate and then checking the worth of an option at a cer -
tain strike price. In actuality, option market participants operate in reverse 
order to this. In other words, they observe the price of an option being 
transacted in the marketplace and then use that price and the BSM model 
to mathematically back out the percentage volatility implied by the option 
price. This is what is meant by the term implied volatility and is the process 
by which option prices themselves display the best guesses of the option 
market’s participants regarding forward volatility. 
Indeed, many short-term option speculators are not interested in the 
range of stock prices implied by the BSM at all but rather the dramatic change in 
price of the option that comes about with a change in the width of the volatility 
cone. For example, a trader who saw the diagram representing 10 percent annu-
alized forward volatility earlier might assume that the company should be trad-
ing at 20 percent volatility and would buy options hoping that the price of the 
options will increase as the implied volatility on the contracts return to normal.
This type of market participant talks about buying and selling volatility as if 
implied volatility were a commodity in its own right. In this style of option trad-
ing, investors assume that option contracts for a specific stock or index should 
always trade at roughly the same levels of implied volatility.
5 When implied vola-
tilities change from the normal range—either by increasing or decreasing—an 
option investor in this vein sells or buys options, respectively. Notice that this 
style of option transaction completely ignores not only the ultimate value of the 
underlying company but also the very price of the underlying stock. 
It is precisely this type of strategy that gives rise to the complex short-
term option trading strategies we mentioned in Chapter 1—the ones that are 
set up in such a way as to shield the investor transacting options from any of 
the directionality inherent in options. Our take on this kind of trading is that 
64  •   The Intelligent Option Investor
although it is indeed possible to make money using these types of strategies, 
because multiple options must be transacted at one time (in order to control 
directional risk), and because in the course of one year many similar trades 
will need to be made, after you pay the transaction costs and assuming that 
you will not be able to consistently win these bets, the returns you stand to 
make using these strategies are low when one accounts for the risk undertaken.
Of course, because this style of option trading benefits brokers by 
allowing them to profit from the bid-ask spread and from a fee on each 
transaction, they tend to encourage clients to trade in this way. What is 
good for the goose is most definitely not good for the gander in the case of 
brokers and investors, so, in general, strategies that will benefit the investor 
relatively more than they benefit the investor’s broker—like the intelligent 
option investing we will discuss in Part III—are greatly preferable.
The two drivers that have the most profound day-to-day impact 
on option prices are the ones we have already discussed: a change in the 
strike–stock price ratio and a change in forward volatility expectations. 
However, over the life of a contract, the most consistent driver of option 
value change is time to expiration. We discuss this factor next.
Changing Time-to-Expiration Assumptions
To see why time to expiration is important to option pricing, let us leave 
our volatility assumptions fixed at 20 percent per year and assume that we 
are buying a call option struck at $60 and expiring in two years. First, let’s 
look at our base diagram—two years to expiration:
Advanced Building Corp. (ABC)
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The Intelligent Investor’s Guide to Option Pricing  •  65
It is clear from the large area of the exposure range bordered by the 
BSM probability cone that this option will be fairly expensive.
Let’s now look at an option struck at the same price on the same un-
derlying equity but with only one year until expiration:
Advanced Building Corp. (ABC)
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100
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70
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Date/Day Count
Stock Price
GREEN
Consistent with our expectations, shortening the time to expiration 
to 365 days from 730 days does indeed change the likelihood as calculated 
by the BSM of a call option going above $60 from quite likely to just barely 
likely. Again, this can be confirmed visually by noting the much smaller 
area of the exposure range bounded by the BSM probability cone in the 
case of the one-year option versus the two-year one.
Indeed, even without drawing two diagrams, we can see that the 
chance of this stock rising above $60 decreases the fewer days until expira-
tion simply because the outline of the BSM probability cone cuts diagonal-
ly through the exposure range. As the cone’s outline gets closer to the edge 
of the exposure range and finally falls below it, the perceived chance falls 
to 16 percent and then lower. We would expect, just by virtue of the cone’s 
shape, that options would lose value with the passage of time.
This effect has a special name in the options world—time decay. Time 
decay means that even if neither a stock’s price nor its volatility change very 
much over the duration of an option contract, the value of that option will 
66  •   The Intelligent Option Investor
still fall slowly. Time decay is governed by the shape of the BSM cone and 
the degree to which an option’s range of exposure is contained within the 
BSM cone. The two basic rules to remember are:
1. Time decay is slowest when more than three months are left  
before expiration and becomes faster the closer one moves toward 
expiration.
2. Time decay is slowest for ITM options and becomes faster the 
closer to OTM the option is.
Visually, we can understand the first rule—that time decay increases 
as the option nears expiration—by observing the following:
Slope is shallow here...
But steep here...
The steepness of the slope of the curve at the two different points 
shows the relative speed of time decay. Because the slope is steeper the less 
time there is on the contract, time decay is faster at this point as well.
Visually, we can understand the second rule—that OTM options lose 
value faster than ITM ones—by observing the following:
Time BT ime A Time BT ime A
GREEN
GREEN
ORANGE
OTM option ITM option
The Intelligent Investor’s Guide to Option Pricing  •  67
At time A for the OTM option, we see that there is a bit of the range of 
exposure contained within the cone; however, after some time has passed 
and we are at time B, none of the range of exposure is contained within 
the BSM cone. In contrast, at times A and B for the ITM option, the entire 
range of exposure is contained within the BSM cone. Granted, the area of 
the range of exposure is not as great at time B as it was at time A, but still, 
what there is of the area is completely contained within the cone.
Theoretically, time decay is a constant thing, but sometimes actual 
market pricing does not conform well to theory, especially for thinly traded 
options. For example, you might not see any change in the price of an option 
for a few days and then see the quoted price suddenly fall by a nickel even 
though the stock price has not changed much. This is a function of the way 
prices are quoted—often moving in 5-cent increments rather than in 1-cent 
increments—and lack of “interest” in the option as measured by liquidity.
Changing Other Assumptions
The other input assumptions for the BSM (stock market drift and dividend 
yield) have very small effects on the range of predicted future outcomes in 
what I would call “normal” economic circumstances. The reason for this is 
that these assumptions do not change the width of the BSM cone but rather 
change the tilt of the forward stock price line.
Remember that the effect of raising interest rates by a few points is 
simply to tilt the forward stock price line up by a few degrees; increasing 
your dividend assumptions has the opposite effect. As long as interest rates 
and dividend yields stay within typical limits, you hardly see a difference in 
predicted ranges (or option prices) on the basis of a change in these variables. 
Simultaneous Changes in Variables
In all the preceding examples, we have held all variables but one constant 
and seen how the option price changes with a change in the one “free” 
variable. The thing that takes some time to get used to when one is first 
dealing with options is that, in fact, the variables don’t all hold still when 
another variable changes. The two biggest determinants of option price 
are, as we’ve seen, the strike–stock price ratio and the forward volatility 
68  •   The Intelligent Option Investor
assumption. Because these are the two biggest determinants, let’s take a 
look at some common examples in which a change in one offsets or exac-
erbates a change in the other. 
Following are a few examples of how interactions between the variables 
sometimes appear. For each of these examples, I am assuming a shorter 
investment time horizon than I usually do because most people who get hurt 
by some adverse combination of variables exacerbate their pain by trading 
short-term contracts, where the effect of time value is particularly severe.
Falling Volatility Offsets Accurate Directional Prediction
Let’s say that we are expecting Advanced Building Corp. to announce that it 
will release a new product and that we believe that this product announcement 
will generate a significant short-term boost in the stock price. We think that 
the $50 stock price could pop up to $55, so we buy some short-dated calls 
struck at $55, figuring that if the price does pop, we can sell the calls struck at 
$55 for a handsome profit. Here’s a diagram of what we are doing:
20
25
30
35
40Stock Price
45
50
55
60
Advanced Building Corp. (ABC)
65
GREEN
As you should be able to tell by this diagram, this call option should 
be pretty cheap—there is a little corner of the call option’s range of expo-
sure within the BSM cone, but not much.
The Intelligent Investor’s Guide to Option Pricing  •  69
Now let’s say that our analysis is absolutely right. Just after we buy the 
call options, the company makes its announcement, and the shares pop up 
by 5 percent. This changes the strike–stock price ratio from 1.05 to 1.00. 
All things being held equal, this should increase the price of the option 
because there would be a larger portion of the range of exposure contained 
within the BSM cone.
However, as the stock price moves up, let’s assume that not everything 
remains constant but that, instead, implied volatility falls. This does hap-
pen all the time in actuality; the option market is full of bright, insightful 
people, and as they recognize that the uncertainty surrounding a product 
announcement or whatever is growing, they bid up the price of the options 
to try to profit in case of a swift stock price move.
In the preceding diagram, we’ve assumed an implied volatility of 35 
percent per year. Let’s say that the volatility falls dramatically to 15 percent 
per year and see what happens to our diagram:
20
25
30
35
40Stock Price
45
50
55
60
Advanced Building Corp. (ABC)
65
Stock price jumps
Implied volatility drops
GREEN
The stock price moves up rapidly, but as you can see, the BSM cone shrinks 
as the market reassesses the uncertainty of the stock’s price range in the 
short term. The tightening of the BSM cone is so drastic that it more than 
offsets the rapid price change of the underlying stock, so now the option is 
actually worth less! 
70  •   The Intelligent Option Investor
We, of course, know that it is worth less because after the announce-
ment, there is only the smallest sliver of the call’s range of exposure con-
tained within the BSM cone. 
Volatility Rise Fails to Offset Inaccurate Directional Prediction
Let’s say that we are bullish on the Antelope Bicycle Co. (ABC) and, noting 
that the volatility looks “cheap, ” buy call options on the shares. In this case, 
an investor would be expecting to make money on both the stock price and 
the implied volatility increasing—a situation that would indeed create an 
amplification of investor profits.
We buy a 10 percent OTM call on ABC that expires in 60 days when 
the stock is trading for $50.
20
25
30
35
40Stock Price 45
50
55
Antelope Bicycle Corp. (ABC)
60
GREEN
The next morning, while checking our e-mail and stock alerts, we find 
that ABC has been using a metal alloy in its crankshafts that spontaneously 
combusts after a certain number of cranks. This process has led to severe 
burn injuries to some of ABC’s riders, and the possibility of a class-action 
lawsuit is high. The market opens, and ABC’s shares crash by 10 percent. At 
the same time, the volatility on the options skyrocket from 15 to 35 percent 
The Intelligent Investor’s Guide to Option Pricing  •  71
because of the added uncertainty surrounding product liability claims. 
Here is what the situation looks like now:
20
25
30
35
40Stock Price 45
50
55
Antelope Bicycle Corp. (ABC)
60
GREEN
This time we were right that ABC’s implied volatility looked too cheap, but 
because we were directionally wrong, our correct volatility prediction does us 
no good financially. The stock has fallen heavily, and even with a large increase 
in the implied volatility, our option is likely worth less than it was when we 
bought it. Also, because the option is now further OTM than it originally was, 
time decay is more pronounced. Thus, to the extent that the stock price stays at 
the new $45 level, our option’s value will slip away quickly with each passing day.
Rise in Volatility Amplifies Accurate Directional Prediction
These examples have shown cases in which changes in option pricing 
variables work to the investor’s disadvantage, but it turns out that changes 
can indeed work to an investor’s advantage as well. For instance, let’s say 
that we find a company—Agricultural Boron Co. (ABC)—that we think, 
because of its patented method of producing agricultural boron com-
pounds, is relatively undervalued. We decide to buy 10 percent OTM calls 
on it. Implied volatility is sitting at around 25 percent, but our option is far 
enough OTM that it is not very expensive.
72  •   The Intelligent Option Investor
20
30
40Stock Price
50
60
70
Agricultural Boron Co.
80
GREEN
The morning after we buy these call options, chemical giant 
DuPont (DD) announces that it is initiating a hostile takeover and of-
fering shareholders of ABC a 20 percent premium to the present mar -
ket price—$60 per share. DuPont’s statement mentions that it wants to 
gain exclusive access to ABC’s boron processing technology. The market 
immediately thinks of German chemical giant BASF and believes BASF 
will make a higher counteroffer so as to keep ABC’s revolutionary boron 
processing technology out of DuPont’s hands. Because there is uncer -
tainty surrounding the possibility of a counterbid and perhaps even the 
uncertainty that DuPont’s offer will not be accepted, forward volatility on 
the contracts increases. The net result is this
6:
20
30
40Stock Price
50
60
70
Agricultural Boron Co. (ABC)
80
GREEN
The Intelligent Investor’s Guide to Option Pricing  •  73
With this happy news story, our call options went from nearly 
worthless to worth quite a bit—the increase in volatility amplified the 
rising stock price and allowed us to profit from changes to two drivers of 
option pricing.
There is an important follow-up to this happy story that is well worth 
keeping in the back of your mind when you are thinking about investing 
in possible takeover targets using options. That is, our BSM cone widened 
a great deal when the announcement was made because the market be-
lieved that there might be a higher counteroffer or that the deal would fall 
through. If instead the announcement from DuPont was that it had made 
a friendly approach to the ABC board of directors and that its offer had 
already been accepted, uncertainty surrounding the future of ABC would 
fall to zero (i.e., the market would know that barring any antitrust con-
cerns, DuPont would close on this deal when it said it would). In this case, 
implied volatility would simply fall away, and the call option’s value would 
become the intrinsic value (in other words, there is no potential or time 
value left in the option). The situation would look like this:
20
30
40 Stock Price
50
60
70
Agricultural Boron Co. (ABC)
80
GREEN
We would still make $5 worth of intrinsic value on an invested base 
that must have been very small (let’s say $0.50 or so), but were the situation 
to remain uncertain, we would make much more.
74  •   The Intelligent Option Investor
Y ou now have a good understanding of how options work and how 
they are priced from a theoretical perspective. Although it is clear from 
Chapter 2 that the BSM has its faults, it is undeniable that in certain times 
and under certain conditions, it works well. Please see Appendix A for a 
brief discussion of the situations in which the BSM is fairly good at pricing 
options—intelligent option investors will want to avoid these—and when 
it is poor—cases that present the most attractive chances for intelligent in-
vestors.
Now that you have a good idea of how options work and are priced, 
let’s turn to how we can do a better job of predicting valuation ranges than 
the BSM does. This is the subject of Part II.
75
Part II
A sound intellectuAl 
frAmework for 
Assessing vAlue
After reading Part I, you should have a very good theoretical grasp on 
how options work and how option prices predict the future prices of stocks. 
This takes us partway to the goal of becoming intelligent option investors. 
The next step is to understand how to make intelligent, rational es-
timates of the value of a company. It makes no sense at all for a person to 
invest his or her own capital buying or selling an option if he or she does not 
have a good understanding of the value of the underlying stock.
The problem for most investors—both professional and individual—
is that they are confused about how to estimate the value of a stock. As such, 
even those who understand how the Black-Scholes-Merton model (BSM) 
predicts future stock prices are not confident that they can do any better. 
There is a good reason for the confusion among both professional and 
private investors: they are not taught to pay attention to the right things. 
Individual investors, by and large, do not receive training in the basic tools 
of valuation analysis—discounted cash flows and how economic transac-
tions are represented in a set of financial statements. Professional investors 
are exquisitely trained in these tools but too often spend time spinning 
their wheels considering immaterial details simply because that is what 
they have been trained to do and because their compensation usually relies 
on short- rather than long-term performance. They have all the tools in the 
world but are taught to apply them to answering the wrong questions.
76  •   The Intelligent Option Investor
Part II of this book sets forth a commonsense approach to determining 
the value of a company. It aims to provide individual investors with the 
tools they need and to offer both individual and professional investors a 
framework that allows them to focus their attention on the most important 
things and ignore the rest.
Chapter 4 discusses what I call the golden rule of valuation. Chapter 5 
looks at the only four things that can affect the long-term value of a stock 
and offers a way to estimate the value a company will create over its entire 
economic life. Chapter 6 investigates the behavioral biases and structural 
impediments working against us in our investment decisions and offers 
tools to avoid them.
In general, I have written these chapters to present the valuation 
framework from a conceptual perspective and have thus left out many de-
tails regarding financial statement line items and the like. These details are 
important, however, and it is unrealistic to think that you could translate 
theory into practice without knowing them. For this reason, I have provid-
ed a detailed valuation example on the Intelligent Option Investor website, 
complete with descriptions of all the financial statements I analyzed and 
explanations of the thought processes I used when doing the analysis.
77
Chapter 4
the golden rule of 
v AluAtion
Commit the following definition to memory:
The value of an asset is the sum of the cash flows it creates on 
behalf of its owners over its economic life.
Contrary to popular opinion, valuation is easy. One does not need a master’s 
degree in accounting or to be an expert in financial statement analysis to com-
petently value a company and estimate a fair value range for a stock. The only 
thing a person needs is to internalize the preceding sentence and understand 
the handful of factors that affect the cash flows of a firm over time. 
This chapter focuses on developing a theoretical framework using the 
golden rule of valuation—which you have already memorized—and looks 
at each part of that simple definition phrase by phrase, with each phrase a 
different section of the chapter. The sections are as follows:
1. The Value of an Asset: Here we offer a specific definition for an as-
set and discuss the distinction between value and price.
2. Cash Flows Generated on Behalf of the Owners: Specifies which 
cash flows we will measure when valuing an asset.
3. The Company’s Economic Life: Breaks the life of the firm into 
three stages to help make the valuation process easier and more 
transparent. 
For those new to the subject of valuation, I present an additional 
section that provides overviews of specific topics such as time value of 
78  •   The Intelligent Option Investor
money and discount rates, but even being unacquainted with these terms 
right now will not be a handicap. 
Business is essentially a collection of very simple transactions—pro-
ducing, selling, and investing excess profits. In my experience, one of the 
biggest investing mistakes occurs when people forget to think about busi-
ness in terms of these simple transactions. 
Having a firm grasp of valuation is an essential part of being an in-
telligent option investor. The biggest drawback of the BSM is its initial as-
sumption that all stock prices represent the true values of the stocks in 
question. It follows that the best opportunity for investors comes when a 
stock’s present price is far from its true intrinsic value. In order to assess 
how attractive an investment opportunity is, we must have a good under-
standing of the source of value for a firm and the factors that contribute to 
it. These are the topics of this chapter and the next. 
In terms of our intelligent option investing process, we need two 
pieces of information:
1. A range of future prices determined mechanically by the option 
market according to the BSM
2. A rationally determined valuation range generated through an in-
sightful valuation analysis
This chapter and the next give the theoretical background necessary to de-
rive the latter. 
Jargon to be introduced in this chapter is as follows:
Asset Structural constraints
Demand-side constraints Supply-side constraints
Owners’ cash profit (OCP) Expansionary cash flow
Free cash flow to owner(s) (FCFO) Working capital
The Value of an Asset 
The meaning of asset , in financial terms, is different from the vernacular 
meaning of “something I’ d be upset about if it broke or was stolen. ” In 
financial terms, an asset is anything that can be owned that (1) was created 
The Golden Rule of Valuation    • 79
through an expenditure and (2) has the capacity to generate revenues 
and/or to increase profits. Thinking about assets from the perspective of 
revenue creation and profit growth, it is clear that things such as family cars 
are usually not assets but are rather convenience items.
A collection of assets is also an asset—if you own a taxi cab, you own 
an asset; if you own a taxi-cab company, you also own an asset. Modern 
corporations are extremely complex, frequently with multiple business 
lines and operations in multiple states and countries and with assets com-
prised of machinery, land, and intellectual property. However, even though 
corporations are complex, they are still assets in the sense that they are a 
collection of discrete assets themselves.
An asset is created through an expenditure, so it follows that all assets 
have a price; this price may be greater or less than the asset’s value. The distinc-
tion between the price of an asset and its value lies at the heart of what is known 
as value investing, so it is an important one to grasp. As an example, let’s say that 
you would like to start a suburban taxi service, and frame the difference be-
tween price and value of the main asset you need to start this business: a car. In 
order for your business to be successful, the car you buy should be roomy, reli-
able, and attractive to customers. Y ou do some research and decide to buy one 
of the two following cars—both of which fit your above-stated requirements:
1. 2013 Bentley Mulsanne: Manufacturer’s suggested retail price 
(MSRP) of $300,000
2. 2013 Toyota Camry: MSRP of $28,000
The choice between the two cars for a typical taxi business is simple. 
The price of the Mulsanne is clearly too high. It is hard to imagine that 
the cash flows that would accrue to the owner of a Mulsanne taxi service 
would ever be enough to cover the cost of the car itself. In this case, the 
asset’s value as a cab is much less than its price. In the parlance of modern 
financial theorists, a company paying the price of a Mulsanne for a car to 
start a suburban taxi service is “destroying shareholder value. ”
Obviously, it is not necessary to do complex calculations to see that 
value would be destroyed in this case with the purchase of the Bentley. We 
cannot be sure of what the value of a suburban taxi service is without some 
more information, but we can pretty easily guess that the cash generated 
from such a service would not be enough to pay off the price of the Mulsanne.
80  •   The Intelligent Option Investor
Whether the purchase of the Camry is a good idea or not is a bit more 
complicated. However, our conception of value for the service should not 
change, so our decision to invest will be driven completely by the relation-
ship of the price of the Camry to our best idea for the value it can create. If 
the likely value of the car is higher than its price, it’s an investment worth 
considering; if the likely value of the car is less than its price (as was the 
case in the Mulsanne), it is folly to do anything but walk away. If the likely 
value is much, much higher than the price, to the extent that it would pro-
vide you much more wealth than you might generate with another simi-
larly sized, similarly risky investment, it would be irrational not  to make 
the investment.
All of this—determination of the value and considerations 
surrounding investment—should seem very sensible to you. Indeed, it is 
only common sense. The problem is that when it comes to the investment 
process, many investors—professional and amateur alike—throw this 
common sense to the wind and start getting confused by what other people 
are saying about chart patterns and multiples and potential demand for a 
company’s nascent product line. 
I will talk about where this confusion might come from in Chapter 6. 
Now that we have an understanding of what an asset is—something 
that can be owned, that is created through expenditures, and has the capac-
ity to generate revenue or increase profits—let’s investigate the next phrase 
in our golden rule: “cash flows generated on behalf of owners. ”
Cash Flows Generated on Behalf of Owners
Our taxi-cab entrepreneur buys the Camry—an act that, in the parlance of 
financiers, is called a capital expense—and opens the taxi service. In order 
to receive revenues, she will have to do a few things:
• Advertise
• Pay herself a salary
• Spend money to maintain the taxi in good working condition (gas, 
oil changes, etc.)
• Spend money on such things as insurance, licensing, mobile phone 
service, and banking and professional fees
The Golden Rule of Valuation    • 81
Let’s assume that the owner runs the business for an entire year, and 
she leaves what is left over after paying the preceding expenses in her bank 
account. At the end of the year, the owner is sitting on excess profits of 
$5,000. Y ou might be tempted to say that this amount is the cash flow gen-
erated on behalf of the owner, but let’s think about it more carefully for a 
moment. 
The owner is a good businessperson, so she realizes that the Camry is 
not going to last forever. At some point, the owner will need to buy another 
one, so she wants to set some money aside for a down payment—let’s say 
she sets aside $1,000.
Now the owner has $4,000 that is not spoken for—perhaps this is the 
amount of the total cash flow generated on behalf of the owner. It could be. 
The owner might simply be interested in running the business at the pre-
sent level and may be content with the $4,000 in cash or so that she figures 
she can generate in excess of expenses every year. If so, the owner might 
pay herself a special “bonus” and use the $4,000 to go on a cruise.
However, let’s say that the owner has an idea that she can schedule 
more efficiently if she uses an online ordering system that is tied into her 
accounting system. She thinks this online ordering system will allow her to 
schedule a few more fares a week just from improved order efficiency and 
will also save her a few hours a month 10-keying data into her accounting 
system. In other words, she believes that if she invests in the system, she will 
be able to increase the rate of growth of both revenues (through more fares 
per week) and profits (from the reduced time expended on bookkeeping). 
The online ordering system and related equipment cost $2,000.
If the owner does not spend the $2,000, she can be pretty confident 
that her business will keep buzzing along and will generate about $4,000 
in cash flow for her the next year. If she spends the $2,000, she figures that 
she will be able to generate $4,500 next year—the extra $500 representing 
a nice return on her investment of 25 percent (=  $500/$2,000). This extra 
return is at risk—it could be that the investment in the computerized 
system will not pay off, in which case the $2,000 she spent will simply 
be a waste—but if successful, the expenditure will pay for itself in just a 
few years.
If the taxi owner decides to spend the money on the new system, she 
ends up with $2,000 free and clear in her bank account. This money—the 
82  •   The Intelligent Option Investor
money that is left over after paying all her daily expenses, setting aside 
money for the maintenance of her business, and purchasing an asset de-
signed to help her business expand—is the amount that we will term cash 
flows generated on behalf of the owner.
We have developed some terms to use in this book to describe each 
step of the process of generating cash flows on behalf of an owner. These are:
1. Owners’ Cash Profit (OCP): Cash available to owners after all nec-
essary direct costs of the business have been paid and after money 
is spent or set aside to maintain the business as a going concern 
(e.g., gas, insurance, maintenance, and setting aside funds for the 
next taxi).
2. Expansionary Cash Flows: Any money invested to try to generate 
more revenues or increase profit in the future. Expansionary cash 
flows are an investment, so are not guaranteed of being successful 
(e.g., online ordering system).
3. Free Cash Flow to Owners (FCFO): Any OCP left over after 
expansionary cash flows are made. 
Free cash flow to owners is the quantity that we will measure and 
project to get an estimate of the value of a company. 
From these descriptions, you can certainly identify the OCP , ex-
pansionary cash flows, and FCFO for our taxi entrepreneur. To analyze a 
public company, we need to associate these concepts with particular line 
items on a financial statement. On my website, I have a detailed valuation 
example (of enterprise software giant, Oracle) that shows what specific line 
items to estimate each of the quantities mentioned here. 
Now that we have a good understanding of what cash flows we are 
looking at in order to value a company, let’s investigate the phrase over the 
company’s economic life.
The Company’s Economic Life
The economic life of a company involves the firm struggling to generate 
cash flow subject to various constraints that change as the company 
grows older. When a company is young, like our taxi company, the main 
The Golden Rule of Valuation    • 83
constraint it is likely to face is a supply-side one. Our taxi company has only 
one car and one driver. Assuming that the average ride for a customer lasts 
15 minutes, the taxi company would be hard pressed to service more than 
about 40 customers a day or 240 customers a week (assuming a 10-hour 
work day and a 6-day work week). Because the taxi’s capital resource base 
is small—one car—no matter how many potential customers may exist, 
the volume of service that may be provided is also small. This is a classic 
example of supply-side constraints.
Money and credit are like oxygen to a fire for supply-constrained 
companies. Given extra money—whether generated through operations, 
borrowed from a bank, or raised by selling shares to other part owners—
our taxi company will be able to buy more cars and hire more drivers. If we 
think about these expenditures as investments, this is clearly an investor’s 
dream because virtually any investment made is guaranteed to have good 
results. 
“There is enough customer demand for 10 taxis in this town. We have 
three taxis and some money to invest. Let’s buy another taxi. ” This is not a 
difficult or intellectually draining analytical process!
As long as the company has access to capital
1 and is producing some-
thing consumers want, the percentage growth rates of its revenues year 
over year during this stage of the business’s economic life can be phenom-
enal; after all, if you own one cab and simply buy two others to serve a cab-
starved region, your revenues are likely to show a year-over-year growth 
rate of somewhere around 200 percent.
FCFO during this time may, in fact, be negative—a company can 
fund itself through debt and actually pay more on expansionary projects 
than it receives in profits—but this does not mean that the business is bad, 
merely that it is facing supply-side constraints and trying to expand its 
capital base to meet the size of the market’s demand.
We see this type of rapid growth in public companies all the time. 
Railroads in the 1800s, automobile companies in the 1900s, and Internet 
firms in the late 1990s all showed incredible revenue growth as customer 
demand swelled for products and services based on the latest technological 
advances.
If the taxi owner can navigate the process of raising money, eventu-
ally, she will have built up her capital base to match the size of the market 
84  •   The Intelligent Option Investor
opportunity. It is at this point that a company begins operating subject to 
demand-side constraints—constraints arising from the vagaries of competi-
tion and consumer choice.
When faced with demand-side constraints, the taxi cab owner is no 
longer concerned with finding new investment money to expand her capi-
tal base but rather with finding ways to keep her cash flows growing even 
though her capital base is sufficient to meet current customer demand. Dur-
ing this part of the company’s economic life, investment decisions become 
more difficult. One possible investment choice is to spend money on systems 
or processes to make the operation more efficient. This will not affect top-line 
(i.e., revenue) growth but likely will increase the flow of cash to the owner 
by allowing for a higher proportion of revenues to be converted into profits.
Other investment possibilities for our demand-constrained taxi 
entrepreneur include opening an operation in another geographic area—
maybe in the form of a joint venture (JV) with another entrepreneur in the 
new region who understands the local economy well—buying a rival taxi 
company, or indeed branching out to start some other business under the 
taxi company’s umbrella.
In terms of our original example to illustrate FCFO, in this period, for 
a single car in her fleet, our taxi owner may be receiving the same $5,000 in 
profits, setting aside the same $1,000 for a replacement vehicle, paying the 
driver a $500 profit-sharing bonus, spending $700 for an improved lighting 
and security system for the lot in which she parks her fleet of cars, and 
squirreling away the rest in case the opportunity to buy the taxi company 
across town presents itself. The company may look as though it is generat-
ing $2,800 in FCFO (= $5,000 − $1,000 − $500 − $700), but in fact, in the 
owner’s mind, that $2,800 may just be temporarily available. If a good, large 
investment opportunity presents itself, what had looked like free cash flow 
from years past might get used all at once in a major investment program.
To find examples of companies in this stage of development, one only 
needs to open the business section of the local newspaper. General Motors’ 
JVs with Chinese carmakers to get a toehold in the burgeoning China 
market, Procter & Gamble buying Gillette Razors to boost its personal-
care product lines, and Google stepping out of its turf of Internet search-
based advertising to buy Motorola Mobility Systems and manufacturing 
mobile phones are all cases in point.
The Golden Rule of Valuation    • 85
The growth of the taxi company’s cash flows will depend on how good 
the potential investment opportunities are and how skillful the company’s 
management is at exploiting those opportunities. If the opportunities are 
good and management is skillful, growth rates will continue to be high. 
They will certainly not be as high as during the “shooting fish in a barrel” 
investment environment when the company was supply constrained, but 
they will be higher than the growth rates of most of the companies in the 
larger economy.
At some point, however, good investment opportunities will become 
fewer and farther between. The taxi-cab company has bought up most of 
its regional competitors and is now constrained by the local regulator’s 
rules against monopoly power and anticompetitive practices. The JV in a 
neighboring region did well, so our taxi owner bought out her partner and 
has expanded that business as far as it will go as well. She dallied with set-
ting up a craft beer brewery (figuring that tipsy customers would be more 
likely to hire taxis) but abandoned that when it seemed like it was more 
trouble than it was worth. 
In fact, the taxi owner noticed that in general, as her business grew 
larger, her investment opportunities seemed to generate less and less mar-
ginal improvement in cash flow to her. As with the case of the brewery, 
sometimes the extra money flowing in was simply not worth the time and 
hassle of running the new business.
So it goes in listed companies as well. Eventually, all the low-hanging 
investment fruit is picked and in placed in the company’s basket, and get-
ting that next apple requires more energy than it is worth. Looking at long 
data series of companies’ profit growth, you can clearly see the downward 
trend over time as the investment opportunities become less and less com-
pelling. Part of the problem for listed firms is not only the availability of 
good investment opportunities but also the fact that they have grown so 
large that it takes not only a compelling investment but also a compelling 
investment that is enormous in size to really move the needle. This is col-
loquially known as the law of large numbers .
2 Stated simply, this rule says 
that if you are really big, it is hard to grow really fast.
Now what?
The taxi cab company has been operating under an environment 
of demand constraints for some time, and the company—through 
86  •   The Intelligent Option Investor
acquisitions, expansion, and the like—has expanded as far as it can into 
its local economy. From here on, as long as no one invents a teleportation 
device (which would fairly quickly make taxis obsolete), its growth will 
depend on structural constraints —factors such as population growth, 
general economic conditions, and inflation.
If our taxi cab owner is smart, when faced with structural constraints, 
she will stop looking to invest the excess profits her company is generating 
every year and instead start paying herself a bonus (which she should in-
vest wisely by buying a copy of this book, of course). In the world of listed 
companies, this bonus is termed a dividend.
There is, in fact, a structural speed limit for public companies as 
well—the rate of growth of the economy at large. And when a company is 
consistently growing at or near this structural rate, it is time for sharehold-
ers to demand to be paid dividends.
In the old days, before globalization, the rate of growth of the econ-
omy at large meant the growth rate of one’s domestic economy. However, 
more and more, reduced trade barriers and cheap transportation cost have 
meant that the limiting growth rate is closer to that of the global economy. 
There are investing cases in which a company can potentially grow very 
quickly overseas, but for large, well-established firms  (i.e, “Blue Chip” 
companies), usually their overseas exposure is much smaller or much less 
profitable than their domestic exposure, so the maximum growth rate ends 
up being pretty close to the domestic rate.
Thinking about this progression from start to finish, you can see that 
growth rates vary broadly in three stages—a startup stage (during which 
the firm faces supply constraints), an investment phase (during which the 
firm faces demand constraints), and a terminal phase (during which the 
firm faces structural constraints). It is important to realize that companies 
can sometimes jump between these growth stages, even though it is fairly 
rare.
3 
Throughout the life of a company, the firm is a machine generating 
profits and cash flows on behalf of its owners. I have said that the value of a 
company is the sum of the cash flows created by that company on behalf of 
its owners over its economic life. We only have one more tiny bit to inves-
tigate to have a complete understanding of this definition: how to sum up 
cash flows that are generated over time.
The Golden Rule of Valuation    • 87
Time Value of Money: Summing Up Cash Flows Over Time
It turns out that summing up cash flows is not as easy as simply adding 
one year’s cash flows to the next because the value of cash flows depends 
on when they are received. Have a hard time believing this? Look at this 
example: assume that you get stranded in the middle of the Mojave Desert 
and have to walk through the intense summer sun to find help at the next 
town. Y ou stumble into a convenience store, suffering from acute dehy-
dration—shaking, nauseous, and with an intense headache—but soon you 
realize that you have lost your wallet on the trek into town. The shopkeeper 
offers to loan you $5 now to buy drinks, but you will have to pay him $20 
when you return with your wallet.
Of course, under the circumstances, your need is so great for the $5 
worth of liquid now that you are glad to part with $20 a few hours later. 
In a sense, the difference between the two amounts is sort of an exchange 
rate between two different time periods. If you go to England, it takes 
one U.S. dollar to equal 0.66 of a British pound (let’s assume). In the case of 
the Mojave convenience store, it takes 20 future dollars to equal 5 dollars 
right now.
This is the basic idea behind the time value of money. I will not go into 
detail behind this concept here (because it is discussed in detail in various 
online and print sources), but the main point is the one I made earlier: cash 
flows from different periods cannot be directly summed. 
The main assumption behind modern finance is that cash flows that 
occur later are always worth proportionally less than cash flows that occur 
sooner. The formula to translate a future cash flow (CF) into its present 
value (PV) is
PV = CF × e
−rt
where r is what is called the discount rate, e is the exponential function, and 
t is the time before the future cash flow is set to occur.
When one raises an exponent to a negative power, the result is a num-
ber smaller than one. This is just the mathematical translation of the phrase 
“a dollar today is worth more than a dollar tomorrow. ”
4
Assuming we can forecast a future cash flow, the next most impor -
tant question we should ask is what we should use for the discount rate. 
88  •   The Intelligent Option Investor
According to the orthodox view of finance [embodied in something called 
the capital asset pricing model (CAPM), which is an idea closely related to 
the efficient market hypothesis (EMH)], there is a statistical formula that 
should generate the proper discount rate for any publicly traded asset by 
plugging in a few numbers. I will not go into detail as to why, but suffice it 
to say that I believe that the CAPM model’s discount rate should be ignored 
by anyone who believes that stocks can be mispriced in the marketplace.
Abandoning orthodoxy, I advocate use of a 10 percent discount rate 
for most U.S. large- or medium-cap investments and about 12 percent for 
U.S. small- and microcap investments. The reason for this is that the market 
as a whole has generated compounded returns for the last century or so of 
around 10 percent per year. If you restrict yourself to the small-cap stock 
universe, that number increases to around 12 percent. By using 10 and  
12 percent as fixed discount rates, the question I am answering is this: “If I 
expect this company to perform about as well as its peers, what is my best 
guess for what its peers will return?”
5 Using these set numbers allows you to 
measure different stocks according to a common yardstick, thereby taking 
out one source of error that one can make a mistake on in a valuation.
For now, let’s just see what happens to a nominal payment of  
$100 per year when discounted at 10 and 12 percent. In the following 
graph, I have assumed that a payment of $100 is made at the end of the next 
100 years. I discounted each of these payments at the discount rate listed and 
then kept the running sum of those discounted payments. Here is the graph:
1,200
1,000
800
600
400
200
0
048 12 16 20 24 28 32 36 40 44 48 52 56 60
Years
64 68 72 76 80 84 88 92 96 100
10% Discount Rate 12% Discount Rate
The Golden Rule of Valuation    • 89
The interesting thing to note is how much the value is in the first 
30 years or less of cash flows. At the 12 percent discount rate, the sum of 
the present value of all future cash flows trends toward around $506; at the 
10 percent discount rate, the value levels off at $1,051. The points at which 
each of the curves level off represent the total value of the respective stream 
of cash flows. Using a 12 percent discount rate, the sum of the first 13 years 
of cash flows already exceeds 95 percent of the total $506 value—in other 
words, by year 14, it is almost the same as if you stop counting. At a 10 
percent discount rate, it takes until year 29 to reach this point.
Thinking about this graph from a practical standpoint, it makes per-
fect sense. What if you loaned $100 to someone and he or she promised to 
repay you in 75 years. What value would you put on that promise of repay-
ment? Nothing or next to nothing, I wager. 
At a 10 percent discount rate, a promise to pay $100 in 75 years, using 
the preceding formula, is worth about $0.06; at a 12 percent discount rate, 
that promise is worth about $0.00001. These figures can surely be consid-
ered “next to nothing” and “nothing, ” respectively.
Look at the golden rule of valuation again:
The value of an asset is the sum of the cash flows it creates on 
behalf of its owners over its economic life.
After the preceding discussion, its meaning now should be perfectly clear.
And now that you have a good grasp of the golden rule, let’s take a 
look at the only four factors that can affect the value of a firm—I call them 
the drivers of value—and how we can analyze them to get a picture of what 
the company is worth.
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91
Chapter 5
the four Drivers of value
In my experience, most people who analyze investments spend far too 
much time getting distracted by trivialities. These trivialities end up pull-
ing them off course, confusing them, and creating valuation rationales that 
are so complex as to become gothic. Getting carried away with unimpor -
tant minutiae also contributes to the difficulties people have in making 
investing decisions—whether to invest in the first place and whether to 
decrease, increase, or close an investment.
This chapter introduces a process to estimate the value of a compa-
ny—based on the golden rule of valuation —by singling out and analyzing 
only a handful of drivers. It seems counterintuitive, but you will see later in 
this book that less information actually counts for more in many circum-
stances, especially when valuing a company’s stock. This chapter works 
hand in hand with Chapter 4 in teaching the skills of an intelligent option 
investor. Chapter 4 outlined how value accrues to the owner of a company. 
This chapter looks at the specific factors that allow that value to accrue.
Jargon introduced in this chapter is as follows:
Explicit forecast stage Structural growth stage
Investment stage
Bird’s Eye View of the Valuation Process
Before looking at each of the drivers in turn, let’s first get an idea of the goal 
we are trying to reach from a high level. Our golden rule of valuation ties 
the value of a company to the cash flows it creates over time. Cash flows are 
92  •   The Intelligent Option Investor
created through the process we saw in the example of the taxi company in 
Chapter 4: revenues come in, present costs are paid, likely future costs are 
saved up for, and some investments may be undertaken to expand the busi-
ness. Any cash that is left over after this process can be paid to the owners.
This is a pretty simple model, so it should not be hard to create a fairly 
accurate picture of how an individual company operates and how it is likely 
to operate in the future. All we need to understand is:
1. How revenues are likely to change 
2. How efficiently a company is translating those revenues into profits 
3. What proportion of the profits the company is investing in the 
growth of the business and how effective those investments are
Indeed, this picture also describes all the typical drivers of value for a 
company. There is one more driver, that I call “Balance Sheet Effects” and  
will describe in detail later in this chapter, but it is only applicable in a very 
few companies, so most of the time all you have to consider are the preced-
ing three. In tabular format, the drivers are as follows:
Driver Description
Revenue growth How fast sales will likely increase
Profitability How efficient the firm is in converting 
revenues to profits
Investment level and efficacy Proportion of profits that must be invested 
to allow profits to grow in the future
Balance-sheet effects The effect of hidden assets or liabilities 
on future cash flows
This seems like an easy enough task—just figure out three or maybe four 
things, and you are set—until you remember that you must make this analysis 
for the entire economic life of the firm. “How can I know what the revenues of 
this company are going to be 50 years in the future? What will its profitability 
be then? How should I know what kinds of investments it will be making?”
Indeed, having to forecast revenue growth and profitability 50, 75, or 
100 years into the future for a company is an impossible task, and an inves-
tor would be foolish to even try (although in my consulting work I have 
seen financial models extending 50 years into the future).
The Four Drivers of Value  •  93
Happily, the task of an intelligent investor can be made easier by 
doing three things:
1. Breaking up the economic life of a company into discrete stages 
and using shortcuts to make assumptions about what will happen 
in each stage
2. Recalling that based on the time value of money, future cash flows 
have increasingly shrinking present values
3. Focusing not on forecasting a single, exact number for each of the 
drivers but rather on developing a sensible best- and worst-case 
scenario for each one
Let’s first look at shortcut number one: breaking up the economic 
life of a company into stages. It is not rocket science—the stages are short, 
medium, and long term. In the short term (0–3 or 5 years, let’s say), we 
have a pretty easy time of thinking about how revenues, profitability, and 
investment levels are likely to change, so we can model the cash flows in 
this stage explicitly. For this reason, I call this the explicit forecast stage.
In the medium term (from the end of the short-term period to a point 
in time 5 or 10 years in the future for most companies), we would have a 
much more difficult time of forecasting explicit cash flows, so we dodge 
the difficulty by using a shortcut. We can see what investments are avail-
able to the company at present—whether the firm is supply- or demand-
constrained—and what the company’s track record has been regarding the 
outcomes of its past investments. Based on this analysis, we can say, “Con-
sidering the investment environment and management’s skill in investing 
in the past, this firm’s cash flows should be able to grow at an average rate 
of x percent during this period. ” Because this medium-term stage relies on 
the success of present investments, I call this the investment stage . Note, 
though, that mature companies—those that are already constrained by 
structural factors—will not, by definition, be able to grow any faster than 
the economy, no matter what investments they make. As such, for a mature 
firm in a mature industry, the investment stage usually does not have to be 
considered. The one case where it does is when a mature firm continues to 
invest in value-destructive projects. In this case, rather than factoring in 
above-normal growth, we should factor in below-normal growth because 
the owner’s cash profit is eaten up by poor investments.
1
94  •   The Intelligent Option Investor
In the long term (anything after the investment valuation stage), 
we know that a company will become constrained by structural factors 
and will, on average, only be able to grow as fast as the economy at large. 
Because of the structural constraints on growth, I call this the structural 
growth stage.
Pulling all these stages together in graphic format is instructive, and 
on careful inspection, we can also see something important about the 
second shortcut regarding the time value of money:
1,600
1,400
1,200
1,000
800
600
400
200
05 10 15 20 25 30
Years in the Future
Cash Flows
35 40 45 50
-
Nominal Cash Flow Cumulative DCF
This diagram shows the nominal amount of cash flow generated by the 
company over a period of 50 years—represented by the solid line—overlain 
by its discounted value—represented by the dashed line. The explicit fore-
cast stage is from zero to five years, the investment stage picks up after that 
and lasts five years, and the structural growth stage begins after that. Y ou 
will notice that the dashed line starts to level off at a figure of around $1,200. 
The point at which that line levels off represents the total discounted value 
of those cash flows and, by extension, the value of this firm.
The explicit forecast stage assumes that cash-flow growth will vary up 
and down because of various competitive pressures that we have forecast 
based on our understanding of the business environment. In this diagram, 
The Four Drivers of Value  •  95
the value of the discounted cash flows generated during the explicit fore-
cast stage makes up 39 percent of the total value of the firm.
During the investment stage, we have assumed that the company’s 
investments will be very successful and allow the firm to generate a growth 
in cash flows of 15 percent per year (suggesting that this is a company with a 
large number of high-quality investment possibilities). An assumption of a 
constant-percentage rate of growth implies that the resulting line will be an 
exponential curve, and indeed, we can see that exponential curve between 
the 5- and 10-year marks. In this example—assuming this quick 15 percent 
per year rate of growth—the sum of discounted cash flows generated during 
the investment stage makes up 23 percent of the total value of the firm.
The structural growth stage—covering years 11 onto forever—assumes 
that investment opportunities will dry up for the firm as it hits structurally 
based demand constraints and that cash flows from that point forward will 
grow at 5 percent per year. We are again assuming a constant-percentage 
growth per year that again will generate an exponential curve—this is the 
solid line starting after year 5 and continuing upward through year 50. Note, 
though, that the slope of the solid line during the structural growth stage is 
subtly shallower than the slope of the solid line during the investment stage. 
This subtle change of slope represents a pretty big slowdown from an average 
growth rate of 15 percent per year to only 5 percent per year. All in all, the 
discounted cash flows generated during the structural growth stage make up 
the remaining 38 percent of total value of this example firm.
Note how small a percentage of overall value cash flows generated 
during the explicit forecast stage represents—only 39 percent of the total. 
This obviously implies that more than three-fifths of the value of this stock is 
based on the cash flows generated in the investment and structural growth 
stages. The sadly amusing fact about almost all the target prices published 
by sell-side research companies (such as the big brokerage houses), the 
fair-value estimates published by third-party research companies, and the 
investment valuations used by buy-side companies (such as hedge and 
mutual funds) is that they are generated by analysts who spend the vast 
majority of their analytical energy on estimating only the explicit stage of 
the forecast—which proportionally makes up the least amount of value of a 
going concern—and only a tiny sliver of their time and energy on the most 
important, weightiest component of the forecast—future growth rates.
96  •   The Intelligent Option Investor
The best thing that we as intelligent investors can do is to understand 
the effect of medium- and long-term growth rates on the value of compa-
nies (this makes us less susceptible to being swayed by short-term, nonma-
terial developments such as the delayed launch of a product line or the like) 
and to attempt to rationally analyze the amount of cash flows likely to be 
generated along all three of the stages.
The final shortcut we use to improve the quality of our valuations is 
to not make the mistake of false precision and try to forecast one “right” 
number for each of the valuation drivers but rather to develop an idea of 
what the best- and worst-case scenarios are for each of the drivers. There 
are some very compelling benefits to taking this tact that I will discuss in 
greater detail in Chapter 6 on behavioral biases and later when we talk 
about finding option investments in Chapter 7. In the end, what we should 
be looking to develop is a series of ranges for our drivers in the first two 
stages
2 that looks something like this:
Explicit Forecast Stage
Best Case Worst Case
Revenues 8% 5%
Profits 18% 12 % 
Investment Level 30% of OCP 45% of OCP
Investment Stage
Best Case Worst Case Duration
Growth of cash flows 15% 8% 10 years
One last thing to note is that although the number of drivers we need 
to consider and forecast is few, we really need to understand what makes 
each of these drivers vary. In Chapter 6, I will address the idea of anchoring 
more, but in short, it is the assumption that the next number in a series will 
be close to the last number in that series. This assumption is not necessarily 
true and can, in fact, be dangerously false. For instance, just because a firm 
has expanded revenues at an average annual percentage rate of 37 percent 
over the past few years does not mean that the next yearly increase needs 
to be 35, 30, or 25 percent or even positive.
3
The Four Drivers of Value  •  97
So making projections for each of the drivers should never be just a pro-
cess of simply extrapolating past results. Making projections for each driver 
means really understanding what factors are influencing that driver and how 
those factors are likely to change in the future. Although this process of under-
standing the underlying factors and projecting driver values into the future is 
not as difficult or complex as neurosurgery or designing a manned spacecraft 
to Mars, it does require some creativity, insight, thought, and patience.
For an actual, specific example of a valuation done using this 
methodology, please see the detailed valuation example of Oracle posted 
on the Intelligent Option Investor (IOI) website www.IntelligentOptionInvestor 
.com. A general explanation of the valuation drivers, along with a few high-
level examples, follows.
A Detailed Look at the Drivers of Value
Now that we have an idea of where we are going in our valuation process, 
let us take a look at each of the valuation drivers one by one.
Revenue Growth
Revenue growth is the first determinant of value for a company—if rev-
enues are not coming in, it is obvious that cash will not flow to the com-
pany’s owners. Organic revenue growth (i.e., that which does not come 
from acquiring another company) can come from
1. Increased volume of sales (selling more stuff)
2. Increased value of sales (selling stuff for more)
At the heart of understanding a company’s revenues and forecasting 
the future growth rate of its revenues is understanding what the company 
is selling and to whom it is selling its product(s). The business model for 
a company such as Bentley that is selling $300,000 Mulsannes that we re-
jected for our taxi-cab company in Chapter 4 is going to be very different 
from that of the $30,000 Camry-selling Toyota. 
Toyota has very little ability to raise prices—that is, to sell its stuff for 
more money—so it must sell more stuff. Bentley, on the other hand, has 
enormous pricing power—its customers are more sensitive to the image 
98  •   The Intelligent Option Investor
that the possession of a Bentley conveys to them than they are to the mon-
etary cost of possession—and one of the ways Bentley maintains that pric-
ing power is by restricting its production—selling less stuff, in other words. 
Understanding the interplay between selling more stuff and selling stuff for 
more is essential to understanding the first driver of value to a firm.
Some people—experienced analysts included—tend to look at rev-
enues as year-over-year percent changes and simply extrapolate the recent 
percentage growth into the future. This is a big mistake and can be a very 
expensive one. Companies that are at the transition between the supply-
constrained early growth period and the demand-constrained investment-
based growth period can sometimes see some very rapid slowdowns in 
revenue growth from one year to the next. If you are trying to value a com-
pany as though its revenue stream will continue forever (or for a long time) 
or as though it were a supply-constrained startup—which is basically what 
people do when they extrapolate recent growth rate numbers too far into 
the future—you will estimate the value of the company as being too great. 
Likewise, when a company whose business tends to move with the business 
cycle—like a steel producer—is in a cyclic trough, and you assume that its 
business is going to keep growing at low rates or even shrinking far into 
the future, you will generate too low an estimate for the value of the firm.
Rather than extrapolating, really understanding the dynamics of the 
business is crucial. Most Wall Street analysts spend proportionally less of their 
time trying to figure out revenues than they do profit. In contrast, I usually 
suggest that people try to spend more time getting a very firm grasp of how 
a firm generates revenues. Who is buying the company’s products or services 
and why are they buying those products or services rather than another’s? 
Are customers using credit to buy the company’s products or services? And if 
so, how tenuous is that line of credit? How many of the company’s products 
might people need or want and how often would they be willing to buy them? 
These are all essential questions to answer, and once you have a good idea 
about them, you will have gone a long way to understanding the value of the 
company in which you are considering taking an ownership stake.
Profit generation, while undeniably an important factor, is for most 
companies, an almost mechanical process that is largely dependent upon 
the amount of revenues flowing into the firm. I will discuss why most of 
the market focuses so much on profitability in the next section, but readers 
The Four Drivers of Value  •  99
who are interested in seeing what parts of a financial statement I believe are 
the most important to dig into when analyzing revenues, please consult the 
valuation example on the IOI website. 
Profitability
Think back to our taxi-cab example in Chapter 4. After the first year of op-
eration, our transportation entrepreneur had $5,000 in her bank account. 
She was planning to set $1,000 aside for a down payment on a new taxi in 
a few years’ time, after her present car had used up its economic life; this 
would give her a total of $4,000 that she could decide how to spend—either 
on a Caribbean cruise or on a new computerized ordering system.
In this example, profitability means this $4,000 amount that we are 
calling owner’s cash profit.
As I mentioned earlier, most sell-side analysts and market specula-
tors spend their time trying to forecast profitability. Usually, the profitabil-
ity they are trying to predict is an accounting line item such as earnings per 
share (EPS), earnings before interest and taxes (EBIT), or earnings before 
interest, taxes, depreciation, and amortization (EBITDA). The reason for 
this is simple: most sell-side analysts’ target prices (and more than a few 
buy-side investment strategies) are generated by multiplying one of these 
quantities by some market multiple. For example, an analyst might say that 
the target price of ABC = 7.8 × EBITDA = $27.50 per share.
There are three main reasons why using multiples analysis to value a 
company should be used with circumspection. 
First and foremost, there is no law of nature saying that a stock price has 
to be a certain multiple of some financial statement line item. Just because 
other companies in a given industry are trading between 7.5 and 8.5 times 
EBITDA doesn’t mean that they can’t trade for higher or lower, nor does it 
mean that another company has to trade within that range either. 
Second, the financial statement quantities mentioned (EPS, EBIT, 
and EBITDA) can all vary fairly substantially because of various account-
ing technicalities and other measures that do not have a material impact on 
the firm’s long-term value. 
Last but not least, multiples imply future profitability growth rates, 
but simultaneously make these implied growth rates much less meaningful. 
100  •   The Intelligent Option Investor
To illustrate this point, consider the following question: Which of the fol-
lowing predictions seems more transparent and testable? 
1. I forecast this company’s medium-term cash flows will grow at an 
average of 10 percent per year for five years followed by GDP-like 
growth afterward.
2. I forecast this company is worth 23.5 times next year’s EPS estimates. 
Clearly, the former is preferable, since by specifying the growth rates, 
you are forced to think of how that growth might be achieved. The latter 
gives no hint of growth rates, so in effect detaches the value of the company 
from the operational details of the firm.
There are a few reasons why Wall Street analysts love to publish 
multiples-based target prices that I will discuss in Chapter 6 when I introduce 
structural impediments. For the time being, just realize that what is good for 
an investment banker or equity sales trader is rarely good for an investor.
Discounting the efficacy and transparency of market multiples-based 
valuation is not the same as saying that profitability is not important—of 
course it is. However, profitability is, to a surprisingly large extent, gov-
erned by structural factors and profit margins tend to be quite similar be-
tween companies in the same industry. For many companies, this makes 
estimating best- and worst-case profit margins fairly easy. 
For example, the grocery business is one in which a supermarket buys 
an item at a low price and sells it at a higher price. Because the items it sells 
are basically identical to the items sold at competitors’ stores, and because 
there are numerous competitors serving essentially the same customer base 
in the same area, it is impossible for the supermarket to raise its prices very 
much or for very long before customers start switching to another store. 
Because of these industry dynamics, the range over which grocery chain 
profitability varies is quite narrow. We can see an illustration of this in the 
following table of three large-capitalization pure-play grocery stores:
Company (Ticker) Market Cap Avg. 3-year OCP Margin
Kroger (KR) $23.9 B 1.5%
Whole Foods Mkt (WFM) $14.1 B 4.9%
Safeway (SWY) $7.9 B 1.4%
Data courtesy of YCharts.com
The Four Drivers of Value  •  101
Here we see that even the fancy Whole Foods Market, which, in terms 
of grocery stores operates on a sell-stuff-for-more model, is still generat-
ing OCP margins (i.e., OCP divided by revenues) of less than 5 percent. 
Kroger and Safeway—two supermarkets operating on a sell-more-stuff  
model—have virtually identical profit margins.
Of course, not all businesses are as stable and predictable as grocery 
stores. There are four effects that can alter the profitability of a company: 
operational leverage, demand changes, environmental factors, and 
efficiency increases.
The single most important factor affecting the ability to predict 
profitability at a firm is something called operating leverage. I describe this 
factor in Appendix B and go into detail about how to estimate the effects of 
operating leverage in the example valuation posted on the Intelligent Option 
Investor website. The takeaway from this material is that for companies with a 
high degree of operating leverage, the amount of revenues coming in will huge-
ly influence profitability. This dependence of profits on revenues provides a 
prospective investor in a company with high operational leverage more reason 
to understand the demand environment and how a firm generates revenues.
Of course, if there are changes in the demand environment that cause 
consumers’ preferences to change away from the product a company is 
providing and toward another that it is not (e.g., consumers preferring 
electronic tablets made by Apple over PCs made by Dell), or changes in 
the supply environment that causes a company’s capital base to be too large 
(e.g., American car companies’ factories having too much capacity after the 
U.S. car market saturated in the early 1980s), profit margins are not likely to 
settle into an historical range but may materially increase (e.g., Apple, after 
the release of iPads, iPhones, and so on) or decrease (e.g., Dell, after Apple’s 
release of iPads, iPhones, and so on). Being able to correctly forecast this 
type of secular shift is difficult, but can be extremely profitable.
In addition to these factors, there can be rapid drops and rises in 
profitability caused by changes in the economic environment. These might 
be company-specific events, such as a natural disaster destroying a supply 
of inventory, or economy-wide conditions, such as loose monetary policy 
encouraging consumers to use debt to make more purchases. While these 
kind of factors can have a large short-term effect on profitability, averaged 
over a longer time frame of a few years, most businesses’ profit margins end 
up returning to a fairly dependable range.
102  •   The Intelligent Option Investor
Another case in which the normal profit range of a company may 
change is through improvements in productivity. And although improve-
ments to productivity can take a long time to play out, they can be ex-
tremely important. The reason for this is that even if a company is in a 
stage in which revenues do not grow very quickly, if profit margins are in-
creasing, profit that can flow to the owner(s) will grow at a faster rate than 
revenues. Y ou can see this very clearly in the following table:
Year 0 1 2 3 4 5 6 7 8 9 10
Revenues 
($)
1,234 1,271 1,309 1,348 1,389 1,431 1,473 1,518 1,563 1,610 1,658
Revenue 
growth (%)
— 3 3 3 3 3 3 3 3 3 3
OCP ($) 
4 432 445 497 485 514 544 560 637 625 708 746
OCP 
margin (%)
35 35 38 36 37 38 38 42 40 44 45
OCP 
growth 
rate (%)
— 3 12 –2 6 6 3 14 –2 13 5
Even though revenues grew by a constant 3 percent per year over this 
time, OCP margin (owner’s cash profit/revenues) increased from 35 to 
45 percent, and the compound annual growth in OCP was nearly twice 
that of revenue growth—at 6 percent.
Thinking back to the earlier discussion of the life cycle of a company, 
recall that the rate at which a company’s cash flows grew was a very important 
determinant of the value of the firm. The dynamic of a company with a rela-
tively slow-growing revenue line and an increasing profit margin is common. 
A typical scenario is that a company whose revenues have been increasing 
quickly may be more focused on meeting demand by any means possible rath-
er than in the most efficient way. As revenue growth slows, attention starts to 
turn to increasing the efficiency of the production processes. As that efficiency 
increases, so does the profit margin. As the profit margin increases, as long as 
the revenue line has some positive growth, profit growth will be even faster. 
This dynamic is worth keeping in mind when analyzing companies 
and in the next section, where I discuss the next driver of company value—
investment level and efficacy.
The Four Drivers of Value  •  103
Investing Level and Efficacy
After our taxi company owner generated profits, she had to figure out if she 
was going to invest those profits or spend them, and if she invested them, 
she had to figure out what investment project was best. Listed companies 
also face the same process and choices. Managers are responsible for in-
vesting owners’ cash profits with the aim of generating greater profits in 
the future or for returning owners’ cash profits to the owners via dividends. 
Because modern companies are so large and have so many shareholders, 
most owners not only do not take an active role in shaping the investments of 
their company, but they also don’t even realize that the investment process is 
taking place.
5 In this environment, there are unfortunately many instances in 
which the owners’ cash profits are invested badly or otherwise squandered on 
wasteful projects. Ford paying top dollar to buy a decrepit Jaguar springs to 
mind, as does Time Warner’s miserable purchase of AOL at the very peak of the 
tech bubble. But these egregious examples are certainly just the tip of the ice-
berg. Companies routinely make implicit capital spending decisions by refus-
ing to close down an underperforming or obsolete business, thereby robbing 
owners of cash flows that should have been theirs and instead filling the wallets 
of consultants and employees.
6 Or the managers, realizing that their mature 
core business throws off an enormous amount of cash, decide to spend some 
of that cash on acquisitions of dubious economic benefit to the owners.
7 Luck-
ily, managers can always find an investment banker or two who are ready to 
talk about the numerous “synergies” that will no doubt someday come to pass, 
and too often boards and shareholders blithely accept the decisions and, once 
made, do not demand an accounting of owner benefits as a result of the union. 
Using an intelligent option investing framework, however, these here-
tofore hidden investment programs and their success or failure can be seen 
much more clearly. First, we must see how much of the owners’ cash profits 
for the company were spent on investing projects and forecast the amount that 
will likely be invested in the future. The online valuation example provides an 
actual look at precisely what financial line items go into this calculation. Right 
now, it is enough to frame the term investments as any cash outflows on capital 
projects that the company is making over and above the cash outflows neces-
sary to maintain the business as a going concern. Recall that in Chapter 4, I 
called this spending expansionary cash flows because they are designed to 
generate faster profit growth in the future. 
104  •   The Intelligent Option Investor
The phrase faster profit growth should prompt the question, “Faster 
than what?” It is at this point that we think back to the discussion of the 
life cycle of a company. After a company has cleared its supply-side con-
straints, and after it has done all it can to increase profits in an environment 
of demand-side constraints, it bumps up against structural constraints . 
Structural constraints represent the long-run “speed limit” for the growth 
of a firm. Because there is a speed limit for a firm in the long run, it is 
logical that during the investment stage of a company’s life we compare the 
investment-boosted growth with that structural speed limit.
The ultimate structural speed limit, as discussed earlier, is the nomi-
nal growth in U.S. gross domestic product (GDP). In this case, nominal  
means the GDP growth that includes the effect of inflation as well as the 
increase in economic activity. A graph of this nominal increase in GDP 
from the postwar period follows:
3/1/1947
100
1,000
10,000
Nominal U.S. GDP (Billions of USD)
March 1997–September 2013
U.S. GDP (Logarithmic Scale)
3/1/1957 3/1/1967 3/1/1977 3/1/1987 3/1/1997 3/1/2007
Note that I have displayed this on a logarithmic axis to show how 
consistent growth has been. The line representing U.S. nominal GDP 
swings above or below the straight trend line but seems to swing back 
toward the line eventually. 
The Four Drivers of Value  •  105
Over this very long period, the nominal GDP growth in the United 
States averaged just over 6 percent per year. If the investment projects 
of a company are generally successful, the company will be able to 
dependably grow its profits at a rate faster than this 6 percent (or so) 
benchmark. The length of time it will be able to grow faster than this 
benchmark will depend on various factors related to the competitive-
ness of the industry, the demand environment, and the investing skill 
of its managers.
Seeing whether or not investments have been successful over time is 
a simple matter of comparing OCP growth with nominal GDP . Let’s look at 
a few actual examples. Here is a graph of my calculation of Walmart’s OCP 
and OCP margin over the last 13 years:
2000 2005 2010
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
3.00%
3.50%
4.00%
4.50%
5.00%20,000
18,000
16,000
14,000
12,000
10,000
8,000
6,000
4,000
2,000
-
Estimated Owners’ Cash Profit and OCP Margin for Walmart
Total Estimated OCP (LH) OCP Margin (RH)
As one might expect with such a large, mature firm, OCP margin 
(shown on the right-hand axis) is very steady—barely breaking from the 
3.5 to 4.5 percent range over the last 10 years. At the same time, its to-
tal OCP (shown on the left-hand axis) grew nicely as a result of increases 
in revenues. Over the last seven years, Walmart has spent an average of 
around 2 percent of its revenues on expansionary projects, implying that 
106  •   The Intelligent Option Investor
cash flow left for shareholders amounted to about $0.02 (≈ $0.045 – $0.02) 
on every dollar, on average. How efficacious were these investments?
In the graph below, any point above the “0 ppt” horizontal axis 
indicates that Walmart’s year-over-year OCP growth has exceeded the 
U.S. GDP by that amount, and vice versa. The year-over-year OCP growth 
statistics are fairly noisy, bouncing back and forth above and below growth 
in GDP; however, looking at a five-year compound annual growth rate 
(CAGR) tells the same story as the linear trend line on the chart: Walmart’s 
growth has slowed significantly and now looks to be close to that of the 
economy at large on average. The rise in Walmart’s fiscal 2010 result (which 
corresponds with calendar year 2009) is more a function of the company’s 
revenues remaining resilient despite a U.S. recession than its growth out-
pacing a growing U.S. economy.
40 ppt
30 ppt
20 ppt
10 ppt
0 ppt
-10 ppt
-20 ppt
-30 ppt
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
Growth in Walmart’s OCP Over (Below) Nominal GDP
Real Growth in OCP Linear (Real Growth in OCP)
To the credit of Walmart’s management, the company has spent in-
creasingly smaller proportions of revenues on expansionary projects over 
the last few years, perhaps in recognition that its expansionary projects 
were bringing in less bang for the buck over time.
In contrast, let’s take a look at a firm whose investments seem to 
be adding considerable value—Oracle. First, let’s take a look at its OCP 
margin:
The Four Drivers of Value  •  107
35%
40%
30%
25%
20%
15%
10%
5%
0%
Estimated OCP Margin for Oracle
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
Other than the disastrous year of the tech bust in 2001, the company’s 
OCP margin has held fairly steadily in the 30 percent range, but recently 
it has started to move toward the 35 percent level. Over the last five years, 
the company’s expansionary spending has averaged around 15 percent of 
revenues per year, mainly through acquisitions. Because the expansionary 
spending is governed by its acquisitions, its investments are not uniform, 
and looking at the 2005–2008 period, the company was spending roughly 
half its revenues on expansion. Over this time period, how has Oracle’s 
OCP growth been vis-à-vis GDP? Let’s take a look: 
50 ppt
60 ppt
40 ppt
30 ppt
20 ppt
10 ppt
0 ppt
-10 ppt
-20 ppt
Growth in Oracle’s OCP Above (Below) Nominal GDP
2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
Real Growth in OCP Linear (Real Growth in OCP)
108  •   The Intelligent Option Investor
In contrast with Walmart, through this lens, we see that Oracle’s 
investments have generally allowed its OCP to grow at a much faster 
rate than the economy at large (2010 was the year Oracle acquired Sun 
Microsystems, and the OCP that year is an artifact of that acquisition—  
I believe that its OCP that year was actually higher than stated here).
The beauty of this way of looking at companies is that the hidden or 
implicit investments a company is making will show up in this as well. I 
believe that, like many large companies, Walmart is finding that it must 
spend money on expansion because it is investing ineffectually through its 
internal business processes. One percent of revenues worth of expansionary 
cash flows per year—roughly 25 percent of owners’ cash profits—is be-
ing spent so that the company can basically keep up with growth of the 
economy at large.
This discussion deals with investment efficacy. Investments—
especially in the corporate environment, where one company completely 
takes control of another and must integrate the acquiree into its own 
business systems and culture—take time for results to be visible. As such, 
it is easy to see why the table at the start of this section showed investment 
efficacy affecting the medium-term results of the company—its growth 
rates in particular.
Understanding the interaction among these three drivers—revenue 
growth, profitability, and investing efficacy—allows an investor to take the 
biggest step toward valuing a stock. Occasionally, though, one must take 
what I call balance-sheet effects into consideration.
Balance-Sheet Effects
Let’s think back to our taxi-cab service. Let’s say that our owner decided 
that after the first year, the investment prospects for her firm were so good 
that she would buy two new cars. She thought that she could save money 
by buying two low-mileage, off-lease cars rather than new ones.
Before putting the cars into service, she cleans each of the cars 
thoroughly. While cleaning out the trunk of the first car, she finds a 
tightly wrapped brown paper package. Curious, she opens the package 
to find a pound of illegal drugs. She calls the police, who come to 
The Four Drivers of Value  •  109
investigate. After looking over the situation, the police impound the 
car, telling our taxi entrepreneur that they had no estimate for when it 
would be returned.
The value of our taxi-cab company suddenly drops. Without the 
use of the car, there is no way for it to generate revenues. However, while 
revenues are not coming in, the company is still incurring costs (financing 
and insurance costs, in particular), so the new car is actually lowering the 
cash flow available to the owner. In the parlance of accounting experts, the 
company has experienced a nonoperational contingency that has resulted 
in a devaluation of one of its assets. This is a value-destroying balance-
sheet effect.
The taxi company owner, upset with the turn of events and her bad luck 
in picking automobiles, grumbles as she gets back to work cleaning out the 
second car. Cleaning between the back seats, she finds a valid lottery ticket 
that was forgotten by the previous owner. Expecting a couple bucks worth 
of winnings, she checks the number and is more than overjoyed to find that 
she is holding the winning ticket for a $500,000 prize! The disappointment 
from the police impounding her other car melts away as she realizes this 
little slip of paper represents 125 years’ worth (+$500,000/$4,000) of her 
company’s first-year OCP . This is one heck of a positive balance-sheet 
effect.
The base assumption we make when we analyze a company is that all 
the assets on the balance sheet are operating assets—that they are being 
fully exploited to generate cash flows on behalf of owner(s). However, this 
is sometimes not a valid assumption to make. Sometimes the true value of 
assets can be hidden and remain hidden for some time. 
On the hidden-asset side, one of the biggest jobs of the class of 
institutional investors known as activist investors is to dig into the operating 
details of a company to find assets that the company is not fully using or 
is using so badly that the company is not able to create maximum cash 
flows. Usually, the activist investor is looking to throw out the current 
management team and replace it with people he or she thinks can better 
use the assets. This is termed a hostile takeover , but it is important to 
remember that the term hostile  is only valid from the perspective of the 
target’s management team. An insightful activist investor with patience, 
110  •   The Intelligent Option Investor
foresight, and enough board seats to push through a change can be an 
enormous boon to investors in the company.
In the same way that there are hidden assets, there also can be 
hidden liabilities. Enron’s complex transactions with its “special-
purpose vehicles” are a vivid example of how dangerous hidden liabilities 
can be. Enron managers found ways to effectively channel financial 
transactions and obligations that they did not want on Enron’s own 
books (namely, losses and liabilities) onto the books of off-shore entities. 
Even though the off-shore entities were established and controlled by 
Enron’s management, they were not consolidated into Enron’s own 
financial statements, so the transactions and obligations effectively 
disappeared from most investors’ view. Several investor groups started 
putting two and two together and realized that the answer was less than 
four. Eventually, when the special-purpose vehicles became known by 
the investment community, it was obvious that there was much less 
equity for investors to own than they had thought previously, and the 
stock price plummeted. 
Whereas hidden assets can be thought of as a winning lottery ticket 
stuck in between the seats of a used car, an old colleague of mine in the 
hedge fund world used to call hidden liabilities “snakes sleeping in a 
basket. ” Usually, it takes some time and familiarity with a company or 
industry to understand where these lottery tickets or snakes may reside, 
but most companies have them to a greater or lesser extent. Mostly, these 
hidden items are not material to valuation and thus can be ignored, but 
when they are not material, they can be truly powerful influences on 
valuation.
It is impossible to explain precisely where to look for these hidden 
items, but there are a few places one can typically start looking:
Lottery Tickets
1. Real estate carried at historical cost
2. Intellectual property (e.g., patents, copyrighted material, etc.)
3. Government connections (not as important in developed markets 
but could be vitally important in certain emerging markets)
4. Overfunded pensions
The Four Drivers of Value  •  111
Snakes
1. Latent product/accident liability claims (e.g., asbestos, pollution 
remediation, etc.)
2. Manager malfeasance (e.g., price fixing, Foreign Corrupt Practices 
Act noncompliance, etc.)
3. Underfunded pensions
4. Off-balance-sheet corruption
5. Fraud
It’s usually hard to find these, but if you do, you should try to make an 
assumption about the best- and worst-case financial impacts of these items 
and simply tack that onto whatever cash-flow projections you have made.
Tying It All Together
Throughout our analysis of a company’s valuation drivers, our focus as 
investors should always be to estimate the free cash flow to owners that a 
firm will likely generate. 
In the short-term, FCFO is driven by how fast revenues are growing, 
how efficiently the company is converting those revenues to profits, and 
how much of the profits the firm is spending on expansionary projects. 
In the medium-term, FCFO is driven by how effective the investments 
the firm made in the preceding period are likely to be. 
In the long-term FCFO is driven by structural constraints because a 
firm cannot grow faster than the economy at large. 
Each driver has both best- and worst-case projections, so pooling all 
the best-case projections into a best-case FCFO scenario and all the worst-
case projections into a worst-case FCFO scenario gives us an idea of the 
most and least cash flow that the firm will generate for us in the future 
(you can see an example of this on the Intelligent Option Investor website). 
Discounting those FCFO scenarios generates a present value range for the 
company. If we can find any balance-sheet effects, we add or deduct those 
effects from the value found from discounting the FCFO scenarios. This is 
the final valuation range of the company that we can compare to the market 
price of the stock. When the valuation range of a company and the price of 
a stock differ by a great amount, we have an opportunity to invest profitably.
112  •   The Intelligent Option Investor
Advanced Building Corp. (ABC)
5/18/2012 5/20/2013 249 499 749 999
Worst Case, 45
Best Case, 70
80
60
40
20
-
Date/Day Count
Stock Price
These are the general principles of intelligent investing, but again, the 
reader is invited to work through the detailed valuation example on the IOI 
website to help bring these general principles to life.
The preceding chapter on understanding the golden rule of valuation 
and this chapter on recognizing the valuation drivers are a great step to-
ward building what Warren Buffett called a “sound framework for making 
[investment] decisions. ” 
The one thing that I hope you have realized while reading this and the 
preceding chapter is what a simple and commonsense process valuation is. 
It is worth asking why—if rational valuation is such a simple process—do 
people generally have such a very difficult time investing and run into so 
many pitfalls.
To understand this, I now turn to an explanation of the behavioral 
biases and structural impediments that trip investors up and make sugges-
tions on how to avoid them.
113
Chapter 6
understanding 
and overcoming 
investing pitfalls
You have seen that valuation is not a difficult thing. It requires 
understanding of a few key relationships, but it is basically a straightforward 
process most of the time.
Why then, do so many investors have such a hard time doing it well?
The main reason, I am sorry to say, is our nature as human beings and 
the weaknesses of our nature. This chapter discusses two facets of that—be-
havioral biases and structural impediments. The first facet—behavioral bi-
ases—involves how we as human beings try to figure out complex things and 
get caught in the process of doing so. The second facet—structural impedi-
ments—speaks about how we investors tend to buy—lock, stock, and bar-
rel—into a game designed only for us to lose, whereas the winners’ kids go to 
$50,000-a-year prep schools followed by a four-year tour of the Ivy Leagues.
There is hope. Don’t despair. The first step to not falling for these 
pitfalls is simply to understand that they exist. 
Obviously, being an intelligent option investor means investing 
intelligently, minimizing—as much as possible—the effects of irrational and 
emotional decision making. This chapter is designed to help you do just that. 
Jargon introduced in this chapter is as follows:
X-system Risk neutral
Risk seeking Risk averse
C-seeking Prospect theory
114  •   The Intelligent Option Investor
Behavioral Biases
Human intelligence evolved in an environment that is very different from 
the one in which we live today. Gone is the necessity to hunt and gather, 
protect ourselves from predators, and fashion our own shelter. In con-
trast, in our modern lives, we are safe from most environmental factors 
but are instead confronted with massive amounts of data. Groundbreak-
ing photographer Rick Smolan, in his book, The Human Face of Big Data 
(Sausalito, CA: Against All Odds Productions, 2012), contends that a mod-
ern person processes more information in a single day than the typical 
sixteenth-century person processed in an entire lifetime. I am not sure if 
there is a scientific way of proving such a contention, but it does seem at 
least plausible.
In terms of investing, the mismatch between how our mental processes 
have evolved and the tasks that we expect them to carry out becomes an 
issue because, by and large, we are still using mental strategies that served 
our Stone Age ancestors well but that serve us investing denizens of the 
“Information Age” much less well.
The study of human bias in economic decision making is a big topic—
called behavioral economics or behavioral finance—and it is not possible to 
cover it fully here. I will give a few examples here and suggest how you might 
work to counteract theses biases in your intelligent investing, but you are 
encouraged to study up on these issues themselves. It is a fascinating topic, 
and the more you learn, the more you will realize how much behavioral 
biases affect everyone’s decision-making processes.
Here I will discuss three issues:
1. Love of symmetry
2. Confidence and overconfidence
3. Humans’ kinky perception of risk
Love of Symmetry
Here is the chart of an asset that has had a smart 8.3 percent return in just 
50 trading days. Is this thing likely to keep going up from here or fall back 
down after its relatively rapid rise?
Understanding and Overcoming Investing Pitfalls   •  115
38.50
38.00
37.50
37.00
36.50
36.00
35.50
35.00
34.50
34.00
33.50
16 11 16 21 26 31 36 41 46 51
Trading Days
Price per Share
Y ou would be correct if you answered, “Neither of the above. ” This is a 
chart I created using the random-number-generator function in Excel. Be-
cause Excel recalculates the values on the sheet any time a change is made, 
I could not get the next value in this series—the series changed as soon as 
I asked Excel to calculate the next day’s return.
I have presented similar series to various groups, including groups 
of traders. It is fascinating to hear the predictions regarding this series and 
the reasoning behind the predictions. Usually, the crowd settles on an an-
swer that is acceptable to most people (e.g., “It will probably go higher, but 
I’ d set a stop loss at $37.25 and aggressively buy if it goes down to $35.50”).
1
Why do so many people see patterns where no patterns exist? Why 
do so many people put their faith in so-called technical analysis (which 
is neither technical nor analysis) even though they are just as likely to be 
successful consulting a Magic 8 Ball for investment advice?
To understand this, we need to realize that there are two separate 
human mental processes for analyzing and solving problems: X-system and 
C-system. 
The X-system is in control of refleXive thought processes, and these 
processes take place in some very primitive areas of the brain. This system 
116  •   The Intelligent Option Investor
is extremely good at perceiving patterns and symmetry and can operate 
very quickly to solve common problems. It is also capable of multitask-
ing. The C-system is in control of refleCtive thought processes, and these 
processes take place in parts of the brain associated with higher reasoning. 
This system works slowly to solve complex problems about which we have 
limited experience. Its ability to multitask is limited.
For an illustration of these two systems, consider this problem: you 
are walking in a house and are confronted with the following object:
Y our X-system recognizes this object as a door, quickly retrieves information 
about how to use objects of this type from your memory, and directs you 
Understanding and Overcoming Investing Pitfalls   •  117
to rotate the metal handle downward to open the door and move into the 
next room. Y ou can solve this problem extremely quickly, with no conscious 
thought, even while you are doing something else, like speaking with a friend.
Now let’s say that when you grab the handle and rotate it, rather than 
the door opening, the handle comes off in your hand. What do you do? Y our 
mind automatically switches from X-system mode to C-system mode, and 
you begin to solve the problem of the closed door in a logical, systematic way. 
Y ou would stop talking to your friend, push the door to see if it will open with-
out the latch, bend down to take a look at the handle mechanism, and so on.
Throughout the process of attempting to solve this problem, you 
may switch back and forth between X-system and C-system processing, 
using your C-system as the controller and the X-system to check on prior 
solutions to similar problems you may have faced.
With this example, you likely have a good intuitive feel for the char-
acteristics of the X- and C-systems, but for completeness’s sake, here is a 
grid describing them:
X-System C-System
Reflexive Reflective
Good for recognizing symmetry and 
patterns and for solving commonly 
experienced problems
Good for analyzing complex, multistep 
problems outside previous experience
Operates quickly Operates slowly
Separate processes do not interfere with 
one another, allowing for multitasking 
Separate processes do interfere with one 
another, making multitasking difficult 
or impossible
Uses amygdala, basal ganglia, and 
temporal cortex—the areas of the brain 
associated with “fight or flight,” reward 
training, identification of objects, and 
behavior
Uses anterior cingulate cortex, prefrontal 
cortex, medial temporal lobe, including 
the hippocampus—the areas of the 
brain associated with higher-order 
functions such as planning and control
Didactic style: analogy Didactic style: mathematical proof
Psychologically comfortable and easy Psychologically uncomfortable and difficult
The X-system is more psychologically comfortable to us (or to most of us) 
because it is the part of the brain we as a species have been using during most of 
our evolutionary history. The pattern-recognition portion of our brain is highly 
118  •   The Intelligent Option Investor
developed—so much so that even though computers such as Deep Blue can go 
toe to toe with chess grand masters, no computer has yet been designed that 
would be able to recognize a fork that is rotated 30 percent off center or a series 
of random items placed in front of it. Even the greatest computer “mind” can-
not carry out a pattern-recognition task that is simple even for human infants.
In investing, humans tend to lean on this X-system pattern recognition 
and try to use shortcuts to analysis based on it. We have mental models for cer-
tain kinds of companies, certain kinds of information, and certain situations, 
and we attempt to escape uncomfortable, analytical C-system processing by 
allowing our X-system to match current conditions with those mental models. 
When presented with a stimulus (e.g., bad quarterly earnings numbers), 
our tendency is to reflexively react rather than to analyze the information. 
This tendency is made more visceral because the X-system that is processing 
this stimulus is tied into the “fight or flight” response. We would rather act 
first, even if acting proves to be a detriment rather than a benefit.
This is a phenomenally difficult—I think impossible—bias to complete-
ly overcome. Although this bias can be extremely detrimental to us and our 
investing process, our highly developed X-system is also incredibly useful to 
us in our daily lives—allowing us to navigate the difficult problems present-
ed by doors, car operation, and so on. I discuss how to recognize and work 
around X-system biases, how to use the X-system when it is useful to do so, 
and how to frame investment decisions using C-system processes in the valu-
ation example of Oracle that can be found on the Intelligent Option Investor 
website. For now, let’s look at another behavioral bias—overconfidence.
Confidence and Overconfidence
Scientific research has shown that humans do not feel comfortable with  
C-system-style analysis and tend to doubt the results of these processes. As men-
tioned earlier, C-system processes do not seem intuitive and certainly do not jibe 
with the satisfying off-the-hip decision making that seems to be prized culturally.
In what may seem like a counterintuitive reaction to this feeling of 
discomfort with C-system processes, you often find analysts and investors 
attempting to collect every scrap and shred of detail regarding a company’s 
operations before making an investment decision. This phenomenon may 
have something to do not only with a certain discomfort with C-system 
Understanding and Overcoming Investing Pitfalls   •  119
processes but also with a natural human discomfort with the unknown. All 
investments are made in an environment of uncertainty, and uncertainty 
is an unsettling psychological state for humans to find themselves in. 
To ameliorate the discomfort from uncertainty, people have a tendency 
to attempt to gain control of the uncontrollable by not leaving any stone 
unturned in their analyses.
This may seem sensible, but in fact, studies have shown that more 
information does not help you to make better decisions—just the opposite, 
in fact. The first study showing this bias was done by a psychologist at the 
University of Oregon named Paul Slovic, who studied the accuracy and con-
fidence of professional horserace handicappers.
2 Similar studies have been 
performed on other groups—medical doctors and stock brokers among 
them—and the results from subsequent studies have been very similar.
Professor Slovic gave professional handicappers varying amounts of in-
formation about horses running in a series of races and then asked them to 
make a prediction about the first-place finisher in each race. The handicappers 
were then asked to assess the confidence they had in their predictions. Slovic 
had the actual race results and compared the professionals’ confidence with 
their actual accuracy. The results can be represented graphically as follows:
30%
20%
10%
0%
51 02 04 0
Number of Items of Information
Accuracy vs. Confidence of Professional Handicappers
Confidence and Accuracy
(Accuracy measured by correct first-place selections)
AccuracyC onfidence
120  •   The Intelligent Option Investor
This is an incredible graph. The horizontal line represents the accuracy 
of the expert predictions. The dotted line represents the confidence of the 
experts depending on the amount of information they had.
The fact that the predictive efficacy line remains horizontal and the 
confidence line increases so sharply indicates an interesting and, think-
ing about it, frightening facet of human behavior. Namely, even though 
the predictions made by the experts who had the most data were no 
more accurate in reality than those of their colleagues who had limit-
ed data, the ones with access to more and more data became more and 
more confident, to the extent that they were massively overconfident. 
Accuracy remains just under 20 percent, but confidence goes up to  
30 percent—a 10 percentage point difference in perception (confidence) 
versus reality (accuracy)!
This behavioral bias has two large negative effects on investors. First 
is a tendency to spend too much time looking at too many nonmaterial 
minutiae until finally one cannot come to a decision regarding whether or 
not to invest—or, as it is colloquially known, analysis paralysis. 
I think of the attempt to gather a huge amount of increasingly detailed 
information about an investment prospect as a sort of cosmic bargaining. 
The analyst or investor who spends hundreds of hours looking at very de-
tailed information not material to the valuation is doing something akin to 
making a burnt offering of old. The analyst or investor is, in some sense, 
making a prayer to the market gods: “I will sacrifice a lot of time and 
mental effort learning about this company. Please reward me with positive 
returns this year. ” 
In the attempt to bargain with the great unseen hand of the mar -
ket, an analyst spends more and more time collecting increasingly less and 
less important information about the potential investment until the cost 
of collecting the extra information greatly outweighs the benefit of having 
gathered it. The big problem with very detailed analyses is that the closer 
one looks at a given problem, the more involved that problem becomes. 
Every fact has some supporting details, and each supporting detail has a 
few scenarios that may be associated with it. To do a really thorough job, 
you must look at each scenario in turn. Ah! But these scenarios turn out to 
be interrelated, so you must think about not only first-order changes in the 
scenarios but also secondary and tertiary ones as well. Soon the analyst or 
Understanding and Overcoming Investing Pitfalls   •  121
investor’s spreadsheet model winds up being 45 tabs deep, and it still seems 
like there is more work that needs to be done before a decision can be 
made (“Where were those numbers regarding the depreciation of fixed as-
sets at the Malaysian subbranch?! How can I invest if I don’t know that?!”). 
At this point, the analysis has become thoroughly paralyzed, and frequently 
the investor will decide (after putting in all that hard work) just to drop 
the whole thing because he or she “can’t get his or her head around” the 
valuation.
Another cost to gathering a great amount of detailed information is 
more subtle but no less dangerous. Let’s say that the analyst has worked 
through all those secondary and tertiary scenarios and decides that the 
firm in question is undervalued. The company is trading for $X and is 
worth “$Y at a minimum. ” What is the analyst’s confidence level in that 
$Y valuation? If the scientific studies I mentioned earlier hold true, the 
analyst is 50 percent more confident than the position warrants. This is an 
unhealthy dose of overconfidence.
The investor hits the “Buy” button and hopes for the best. However, 
after a few quarters, some of the operational metrics at the firm begin to 
falter. The Capex project that was forecast to take 5 percent of sales in year 
one ends up taking closer to 9 percent. Sales are a bit lower than expected, 
and costs are a bit higher. But the investor has thought about all these pos-
sibilities and is still very confident in the valuation; these discrepancies 
are thus looked at like anomalies that will soon be corrected with another 
quarter or two of results. The situation can drag on for an extended time 
until suddenly the investor is confronted with the possibility that the firm 
is running out of cash, its new product line has failed, or whatever. The in-
vestor, once so confident, now has to face the unpleasant task of realizing a 
loss (why he or she may not want to realize a loss is discussed in the section 
“Humans’ Kinky Perception of Risk” later).
“Love is blind. ” Unfortunately, overconfidence in an investment opin-
ion can make one just as blind as love.
I believe that two facets of intelligent option investing can help to 
ameliorate these biases. First, recall that there are at most four—and most 
often only three—drivers determining company valuation. While you are 
reading about a company and analyzing its value, it is wise to constantly 
ask yourself two questions:
122  •   The Intelligent Option Investor
1. Is what I’m analyzing related to one of the drivers of company value?
2. Is what I’m analyzing material to the valuation?
Sure, there is some sort of satisfaction in knowing everything there 
is to know about coal-processing technology or oil reservoir structure and 
engineering, but recognize that this satisfaction is purely personal and is 
not going to make a bit of difference to the valuation. Understanding these 
kinds of technical details might help a tiny bit in understanding competi-
tive dynamics in an industry, but the cost of learning them almost always 
exceeds the benefit from the knowledge. For any technical points you are 
trying to learn about as a layperson, there are likely two armies of engi-
neers, specifically trained in that field, arguing with one another about 
whatever point you are learning about. No matter how large your band-
width is, it is not likely that you will be able to make a more informed deci-
sion than those people. And if the final result is, “Company A will likely 
be able to produce coal at a slightly cheaper cost than Company B because 
of the geology where Company A has its mines, ” this is a fact that can be 
reasonably ensured by a few minutes on Wikipedia rather than by checking 
out books from the local university’s engineering library.
Second, the online valuation example shows how you can create 
rational valuation ranges for a company, and I believe that those ranges 
can be very helpful. Estimating valuation ranges rather than tying them-
selves to point estimates of a specific stock value can help investors to re-
main more objective about information coming in and more observant of 
changing conditions. For example, if an investor sees one group of valua-
tion ranges clustered near $30 and one group clustered near $50, the inves-
tor can objectively assess operational data coming in over time and decide 
which set of projected economic results the actual results will match. The 
investor may have thought the economic results underlying the $50 cluster 
were more likely, but as time goes on, he or she may see that the results 
leading to the $30 cluster are closer to the truth. In this case, the investor 
can be confident and happy about making accurate projections (because 
the investor projected both the $30 level and the $50 level), even if he or 
she is not particularly pleased with the investment outcome. This may be 
the psychological slack required to combat the last behavioral bias we will 
discuss—humans’ kinky perception of risk.
Understanding and Overcoming Investing Pitfalls   •  123
Humans’ Kinky Perception of Risk
Take a look at the following questions: First question: you have a choice 
between playing two games with the following monetary payoffs. Which 
game would you play?
• Game 1: 75 percent chance of winning $6,000 and a 25 percent 
chance of winning $0
• Game 2: 100 percent certainty of winning $4,000
Make a note of your choice. Second question: you have a choice between 
playing two games with the following monetary payoffs. Which game 
would you play?
• Game 3: 75 percent chance of losing $6,000 and a 25 percent chance 
of losing $0.
• Game 4: 100 percent certainty of losing $4,000
What was your answer to this question?
Mathematically, you should choose to play games 1 and 4—these 
are the rational choices. Most people irrationally would choose to play 
games 2 and 3. The expected payout of game 1 =  75 percent ×  $6,000 + 
0 = $4,500. As such, game 1’s outcome generates a higher expected payoff  
than game 2. If you chose game 2 in this instance, it would indicate that 
you are risk averse.
Reversing the conditions of the games to generate losses instead of 
profits, you can see that game 3 yields an expected loss ($4,500) that is 
greater than the expected loss of game 4 ($4,000). If you chose to play 
game 3 over game 4, this would indicate that you are risk seeking  rather 
than risk averse.
Psychologists Amos Tversky and Daniel Kahnemann—two research-
ers who began the systematic study of behavioral biases—found that peo-
ple tend to be risk averse with respect to gains and risk seeking with respect 
to losses and have coined the term prospect theory  to describe this ten-
dency.
3 To understand risk aversion and risk seeking, let’s look at a simple 
betting example.
Y ou offer a test subject a choice of either receiving a certain payment 
of a certain amount or receiving an amount based on the result of a fair 
124  •   The Intelligent Option Investor
bet such as a coin toss. If the coin comes up heads, the subject wins $100; 
if it comes up tails, the subject walks away with no payment. The expected 
payoff from the fair bet from a mathematical perspective is
$100 × 50% + $0 × 50% = $50
Economists describe risk preferences for individuals on the basis of 
the fixed payment the individual would accept in order not to subject the 
payout to a risky outcome. The three risk preferences are
• Risk neutral
• Risk averse
• Risk seeking
The risk-neutral investor is completely rational. The mathematical expected 
payoff is $50, so the risk-neutral approach is not to accept any guaranteed 
payment other than $50 in lieu of making the bet. If you were to diagram 
the value the rational risk-neutral investor would assign to the expected 
value of a risky outcome (using what economists call a utility curve ), you 
would get the following:
0
0
Expected Value of a Risky Outcome
Risk-Neutral Utility Function
Value Placed on a Safe Outcome
Because $50 is not a great deal of money to some people, they can and 
do remain risk neutral at this monetary level. Increase the potential payout 
Understanding and Overcoming Investing Pitfalls   •  125
to $1 million, and I guarantee that people will most happily demonstrate 
risk aversion.
Risk aversion is demonstrated by someone who would be willing to 
accept a guaranteed amount of less than the mathematically calculated ex-
pected payout in order to avoid putting the total payout at risk. For exam-
ple, if you would prefer to accept a sure $45 instead of a 50 percent chance 
of winning $100, you are risk averse. The utility curve for a risk-averse 
investor would be represented like this:
0
0
Expected Value of a Risky Outcome
Risk-Averse Utility Function
Value Placed on a Safe Outcome
Most mentally healthy people with relatively low blood-alcohol levels 
are risk averse to a greater or lesser extent. As the amount in question 
becomes material (however the person in question defines materiality), the 
tendency toward risk aversion becomes much stronger. 
Risk-seeking behavior is seen in gambling addicts and people with 
high enough blood-alcohol levels that they should not be operating 
heavy machinery. It is, of course, the converse of risk aversion: a risk 
seeker requires a higher guaranteed payment than the mathematically 
expected payout in order to forgo the bet. For instance, a risk seeker 
would not want to stop betting unless he or she was offered $60 or more 
for an expected-value bet of $50. The utility curve for a risk-seeking 
investor looks like this:
126  •   The Intelligent Option Investor
0
0
Expected Value of a Risky Outcome
Risk-Seeking Utility Function
Value Placed on a Safe Outcome
Risk seeking may seem implausible for anyone whose problems are not the 
feature of a daytime psychology talk show, but as you will see, each and 
every person reading this now likely displays risk seeking many times in 
an investing career.
If you read an Economics 101 textbook, you will learn that peo-
ple are either risk neutral (professional economists always try hard to 
show that they are risk neutral because they generally pride themselves 
on being rational), risk averse, or risk seeking. In fact, we all display 
each of these profiles at different times depending on the situation. 
The unfortunate fact, discovered by Tversky and Kahnemann, is that 
humans tend to display the least  helpful of each profile in different 
situations.
When we are winning, we tend to be risk averse. We have made 
20 percent on an investment in a short time, and our tendency is to “take 
our money off the table” and realize our gains. The thing we fail to realize 
when we feel the pride and satisfaction of hitting the “Sell” button is that at 
the moment we close the position, our money is again sitting idle, and we 
are faced with the prospect of having to find another risky investment to 
replace the one we just closed.
Conversely, when we are losing, we tend to be risk seeking. For 
example, let’s say that we have lost 60 percent on an investment. Is our 
natural tendency to sell that position? No. Because the value of our stake 
Understanding and Overcoming Investing Pitfalls   •  127
has fallen so much, we sense that any small movement up will be a big 
improvement to the present situation. We “let it ride” and hope for a lucky 
break. This is the action of someone who realizes that he or she has little 
to lose (because so much is lost already) and everything to gain—which, 
of course, is the very definition of desperation (and the day-to-day modus 
operandi of many hedge fund employees).
This variable risk profile is depicted by the following graph. The top-
right quadrant shows a risk-averse profile—one would rather cap one’s 
gains than let them ride. The bottom-left quadrant shows a risk-seeking 
profile—one would rather bet than realize one’s losses.
Prospect theory utility curve
x
U(x)
Note how the curve in the upper right-hand quadrant looks like 
the risk-averse utility curve and that everything in the lower left-hand 
quadrant looks like the risk-seeking utility curve. This is an astounding 
graph, but perhaps an actual, visceral example would carry an even larger 
impact.
Think of the fellow who got in on the Google initial public offering, 
buying at $85 per share. A few months later, after more than doubling his 
money, he happily sells at just above $200 and again puts his capital at risk 
in another investment—starting over from square one in terms of making 
an investment decision.
128  •   The Intelligent Option Investor
250
Google (GOOG) Closing Price
A
200
150
100
50
0
8/19/2004 9/19/2004 11/19/2004 12/19/2004 1/19/200510/19/2004
This investor’s thought at point A: “I am an investing genius! I just 
made a 100 percent return in a couple months—time to take my money off 
the table. ” However, after selling the shares and feeling the sense of relief 
that he had reduced his risk exposure to Google, he eventually grows dis-
mayed about being hasty in realizing his gain:
800
Google (GOOG) Closing Price
B
C
D
E
F
A
700
600
500
400
300
200
100
0
8/19/2004 2/19/2005 2/19/20068 /19/20068 /19/20078/19/2005 2/19/2007
Understanding and Overcoming Investing Pitfalls   •  129
The investor’s reasoning may have gone like this:
A Original sale realizing profits
B “I did the right thing.”
C “I left a little on the table, but it’ll come back soon, and I’ll buy some more then.”
D “Should I short Google?!”
E “Aaaaaaaaaaaargh!”
F Second purchase
Finally, after his mail carrier comments that she is retiring early after 
selling her Google position for $675 per share and a person at the country 
club buys a new Lexus using his Google sale proceeds, our kinked utility 
curve investor does the thing that social creatures tend to do when faced 
with uncertainty and remorse—follow the herd. He is happy that his limit 
order to buy at $695 is filled at midday and happier still that he made a gain 
of 3 percent after buying the shares. 
Our hapless investor’s bad sense of timing is good for us because his 
purchase of Google shares at the local 2007 market peak and ownership 
through the fall allow us to simultaneously follow the psychological pain 
he suffered on the stock chart and the utility function curve:
800
Google (GOOG) Closing Price
B
C
A
700
600
500
400
300
200
100
0
11/1/2007 2/1/2008 5/1/2008 8/1/2008 11/1/2008
130  •   The Intelligent Option Investor
Thus an investor in Google at $695 feels pain extremely quickly when 
the value of the position drops slightly to the $620 per share level, let’s say; 
this is indicated at position A in the diagram. However, as the price continues 
to decline (let’s say to the $450 per share level indicated by position B ), 
human decision makers have a tendency to say something like, “If only I 
could get $475 for my shares, I’ d sell right now. ” If and when the shares do in-
deed reach $475, the curvature of the line in this quadrant implies that now 
the investor will require yet a higher guaranteed price (e.g., $525 per share) 
before he closes the bet. At some point, which may be one representing a 
significant loss of principal, the investor is largely inured to the prospect 
of further losses, and if the stock price goes far enough down, the investor 
is no longer tempted to bet on a small rise in price. This is the point that 
people usually sell—just as the $50 stock they bought is trading for $1.50 
on the Pink Sheets!
This psychological effect is dreadfully difficult to overcome—
perhaps impossible. However, again, I believe that the most important 
first step is having a rational, educated estimate of the fair value range of 
a company and understanding the drivers that go into the values making 
up that range.
Let’s say that you bought a stock for $30 after having determined a 
low-end valuation of $39 and the high-end valuation around $50. Now a 
quarterly earnings announcement reports good numbers—data suggesting 
that the valuation cluster around $50 is closer to correct—and the stock 
advances by 10 percent—to $33.
Under these conditions, you are less likely to excitedly take your 
profits after the 10 percent up day because you know that the stock still 
has about 50 percent to go before it gets to your best-case valuation range. 
Again, understanding the drivers of valuation and having an appreciation 
for (and humility in the face of) the uncertainty involved in any projection 
of future conditions (as reflected by a valuation range) constitute the best 
way I have found to combat the deep-seated bias related to the kinks in our 
perception of risk.
Now we’ll look briefly at structural impediments to rational investing 
before pulling together all the lessons learned so far to see how to invest 
intelligently using options.
Understanding and Overcoming Investing Pitfalls   •  131
Structural Impediments 
We know that we have an enemy living inside of us in the form of the behav-
ioral biases discussed earlier. If this weren’t bad enough, we are attempting to 
invest intelligently in an environment not conducive to intelligence. In other 
words, not only must we battle an enemy within, but enemies without as well. 
The enemies without are comprised of the forces arrayed against us—
the owners of capital attempting to invest intelligently. These forces are part 
of the very structure that has developed to trade, manage, custody, ana-
lyze, and report on securities that is such an integral part of the investing 
process. They consist of the many explicit messages we as investors receive 
every week telling us that we should “trade like a pro” and the implicit mes-
sages that we don’t know what we are doing so we should put our faith in 
this expert or the next if we hope to be successful. 
At the heart of these structural issues is the distinction between prin-
cipals and agents.
Principals versus Agents
Y ou cannot talk about structural impediments without making the distinc-
tion between principals and agents. Principals are the owners of capital 
who invest in risky projects or assets with the expectation of generating a 
positive return. Principals can be like you and me—individuals with finite 
lives—or can be legal entities such as endowments or companies—which 
are theoretically perpetual actors. Agents, on the other hand, are the inter-
mediaries who act on behalf of principals in return for salaries and who are 
paid for out of the capital of principals.
Any time a person is compensated for doing something, his or her 
own interests are on the line. When our own interests are on the line, we 
look for opportunities to protect and advance them. Unless a great deal of 
thought is put into how investment performance is measured and assessed 
and how compensation is awarded to agents as a result of that performance, 
in the process of advancing their own agendas, agents actually may end 
up working at cross-purposes to their principals. This tension between 
agents—who must work within the constraints of their industry to keep 
132  •   The Intelligent Option Investor
their jobs and advance their careers—and principals—who by and large 
are simply looking to save enough money to live comfortably in retirement 
and pass something on to their descendants—lies at the root of what I term 
structural impediments.
To investigate these structural impediments, we first need to figure 
out who is playing this investment game and what the rules are. To do this, 
I’ll introduce the teams: the buy side and the sell side—both of which are 
agents—and the principals. With this knowledge, we can better avoid the 
structural pitfalls established by the agents largely for their own benefit.
The Buy Side
The buy side consists of agents hired by principals to invest and manage 
the principals’ capital on their behalf. The most well-known buy-side play-
ers are mutual funds and hedge funds, but insurance companies, pension 
funds, and endowments also fit into this category. I tend to think of hedge 
funds and mutual funds as being different in approach from the others, so 
we’ll look at these two groups separately.
Perhaps the attitude of mutual and large hedge fund players can best 
be summed up by the words of a professional money manager, who once 
told me, “Erik, no one ever got fired for not making money; they got fired 
for losing money. ” Most people unfamiliar with the money-management 
industry think that performance is paramount for the managers. In fact, 
investment performance is only a slightly inconvenient means to an end 
for money managers. For the owner of a hedge or mutual fund, the real 
name of the game is assets under management  (AUM). AUM is the total 
amount of money a fund manages on behalf of its clients, and it is the main 
source of wealth for the owners of a fund. Mutual funds charge a load that 
represents a percentage of money clients leave with them to manage but are 
not usually directly rewarded for the performance of the fund. In the case of 
mutual funds, AUM is all important, and investment performance is merely 
a marketing tool. If fund A can generate good enough performance to stand 
prominently in the pack of other funds (i.e., “x  percent of our funds beat 
their Lipper averages”), and rating companies such as Morningstar give the 
fund a positive rating, present customers of fund A are less likely to take 
their money to another fund, and customers of lower-performing funds 
Understanding and Overcoming Investing Pitfalls   •  133
will move their money to be managed by fund A. Of course, at the annual 
bonus time, fund employees are compensated in rough proportion to the 
performance of their investment recommendations, so there is an incentive 
for analysts and portfolio managers to perform well. However, if an analyst 
is interested in keeping his or her revenue stream coming in in the form of 
salary, the analyst quickly learns that the best route is usually the safest one.
This leads to a phenomenon known as closet indexing , where an in-
vestment fund’s portfolio is so diversified that it effectively takes on a risk-
return profile equivalent to the index (or whatever benchmark the fund is 
using to measure relative performance). A 2011 study by Martijn Cremers 
and colleagues concluded the following (italics added by author):
In this paper we examine the prevalence of explicit and implicit 
(closet) indexing in equity mutual fund management across 30 
countries. We find that although little explicit indexing exists 
as a proportion of assets under management [N.B.: There are 
few low-load index funds in proportion to “actively managed” 
funds] in almost all countries, a large amount of closet indexing 
exists. That is, equity fund managers in many countries choose 
portfolios that track their stated benchmark closely.
Or, to put it simply, whether an investor puts money into an active 
fund or an index fund, the investor mainly just gets the performance of 
the index. In addition, bonuses and salary increases are apportioned out 
on an annual basis, meaning that the natural investing time horizon for 
an analyst or money manager is only one year. Almost everyone in the 
industry feels a sense of excitement and relief at the beginning of a new 
year because they know they are starting out with a fresh slate. Clearly, the 
agents—the employees and owners of the funds—are not acting in the best 
interests of the principals (because they are charging fees but not provid-
ing much or any benefit), and the agents’ investing time horizons are not, 
by and large, aligned with the investing time horizons of the principals 
(agents start again with a fresh slate every year whereas principals worry 
only about the value of their investment assets at some point in time, like 
college admission or retirement).
The same sort of dynamic occurs in the hedge fund industry, al-
though with a bit of a twist. Large hedge funds usually are set up in a 
134  •   The Intelligent Option Investor
“2-and-20” arrangement, where 2 percent of a client’s money every year 
goes immediately to the manager (this is the load in a mutual fund), and 
20 percent of profits (or profits over some benchmark) are apportioned out 
on a periodic basis. The owners of these prominent funds usually set up 
their businesses in such a way as to receive all the moneys based on AUM 
and leave the lion’s share of the risky, performance-based payout to the 
portfolio managers and analysts hired to manage the money. The owners 
of large hedge funds, in other words, have compensation structures that are 
very similar to those of the owners of large mutual funds and so are con-
cerned mainly with clients not moving their money to other hedge funds. 
For the owners of these funds, performance is, in a sense, just a necessary 
evil to their goal of generating wealth by safekeeping the wealth of others. 
The owners of small hedge funds and the managers/analysts of all 
hedge funds lead a much more tenuous existence. This business is extremely 
competitive, and the continuation of these agents’ salary- and bonus-gen-
erated revenue streams is extremely sensitive to recent performance. Small 
hedge fund owners are beholden to hedge funds of funds (HFoF)—another 
intermediary that funnels principals’ capital to different hedge funds in re-
turn for a fee—and their money is extremely “fast. ” If a small fund manager 
does not outperform the appropriate benchmark in a given quarter or can-
not convince the HFoF that performance lagged in the last quarter for some 
reason that will reverse itself in spades in the next quarter, it is very likely 
that the HFoF will pull its money from the fund. Similarly, a portfolio man-
ager working for a large fund must, at least on an annual basis, prove to the 
hedge fund owner that his or her performance has been good enough or will 
soon be good enough to deserve a continued allotment of the clients’ capital.
Strangely enough, as more and more hedge funds flood the market, 
soaking up opportunities to generate alpha (excess returns), hedge funds 
have come to display returns that are highly correlated with the underly-
ing index. A recent research report published by Morgan Stanley told this 
tale in figures—the correlation between the Standard and Poor’s 500 Index 
(S&P 500) and an index of hedge funds reached around 90 percent in mid-
2013.
4 This does not mean that an individual hedge fund will engage in 
closet indexing as a mutual fund might, but it does mean that if you invest 
your money in multiple hedge funds to try to generate better performance, 
your returns will start looking a lot like the returns of the index at large.
Understanding and Overcoming Investing Pitfalls   •  135
Turning now to the next buy-side group—insurance companies, 
pension funds, and endowments—we see a different business model and 
different motivations for employees. In general, these buy-side businesses 
have much less pressure to generate superlative returns and exist as a sort 
of appendage of another primary business. Life insurance companies 
invest their clients’ money but generally promise very limited returns—
structuring agreements with clients in such a way as to ensure that if their 
investment decisions are at least minimally competent, they will be able to 
fulfill their promises to clients. As such, investments tend to be a default se-
lection of blue chip equities and high-quality bonds. In this environment, 
the portfolio manager is not measured so much on his or her investment 
prowess but rather on his or her ability to allocate to bonds and stocks in 
a sensible enough proportion to be able to satisfy the insurance company’s 
obligations to its clients when they come due. The real risk to the insurance 
company is not collecting enough fees or promising its clients too much. 
The investment horizon for these funds is something like 10 to 20 years. 
Pension funds are much the same in terms of investment philosophy—
if a portfolio manager allocates assets sensibly between high-grade corporate 
bonds and blue chip stocks, his or her career is basically safe. It is rare to find 
private sector entities now that even offer pensions to their employees and 
tougher still to think of examples of pensions that are adequately or overfunded 
(meaning that they have enough funds to meet their future obligations). Again, 
the investment horizon for these entities is a long 10 to 20 years.
Until rather recently, university endowments were very similar to in-
surance or pension funds, but they naturally have much longer investment 
time horizons because the money is usually not promised to any specific 
purpose in some limited time frame. Endowments usually allocate to a 
wider range of asset classes—including hedge funds, private equity funds, 
real estate, and so on—and several gifted portfolio managers at Harvard 
and Y ale have done this to enormous effect on behalf of their schools in 
recent years. However, in general, asset selection or allocation risks are low 
for managers in this environment. Rather, the risks are much more related 
to the ability of managers to satisfy their schools’ boards of governors that 
they are managing the school assets with propriety and foresight.
One undeniable fact to all buy-side firms is that as the entity grows 
larger, it becomes harder and harder to invest in anything but very large 
136  •   The Intelligent Option Investor
and liquid stocks. Even if you have a small cap position that increases by 
100 percent in a single year, if your investment base is so large that the win-
ning position’s size is only 0.005 percent of the total AUM at the beginning 
of the year, it only represents 0.01 percent of the portfolio at the end of the 
year—hardly moving the needle in terms of excess performance.
To summarize the players in tabular format:
Player Clients Are . . . Time Horizon Risk
Investment 
Paradigm
Hedge funds Demanding, 
fast money
3 months to 
1 year
Owner: Losing 
clients
Managers: Not 
making risky 
enough bets
Anything that pro-
vides alpha
Mutual funds Docile and 
uninformed
1 year Breaking from the 
herd and see-
ing AUM drop
Closet indexing
Insurance 
companies 
and pension 
funds
Largely 
unaware 
of their 
investments
10 to 20 years Not charging 
clients enough 
(insurance); not 
retiring before 
the pension is 
discontinued/
defaulted on 
(pensions)
AAA bonds and blue 
chip stocks—risk 
aversion
Endowments Not born yet 10 years to 
100 years
Losing 
confidence 
of board of 
governors
Wide asset-class 
level allocation 
with long-term 
perspective
Look back at this table. As a principal owner of capital, is there any-
thing listed in the risk column that speaks to the risk of investing that you 
yourself have experienced or feel is most pressing to you?
The Sell Side
The sell side consists of companies whose job it is to connect principals 
(through their agents) who have capital with the financial markets. 
Understanding and Overcoming Investing Pitfalls   •  137
Broker-dealers are the sell-side counterparties for institutional investors, 
whereas stock brokers and online brokers are the counterparties for indi-
vidual ones.
The operative principle for this business is best summed up in the old 
adage, “Bears make money, and Bulls make money. Pigs get slaughtered. ” 
In other words, sell-siders do not care if the market goes up or down be-
cause their revenues depend only on investors accessing the market. The 
only way to lose this game is to get too greedy and take a risk position in a 
security that subsequently loses value.
5 
Sell-side players basically make money in proportion to how often 
their clients come to the market. As such, the sell side has a vested interest 
in getting its clients to trade as often as possible. Sell-side research groups 
hire very smart graduates from top universities and industry insiders 
who basically act as marketing arms for the firms’ sales and trading desks. 
The more short-term “catalysts” the research group can find that might 
prompt a client to make a stock purchase or sale, the better for them. 
Research groups’ bonuses are determined in large part by feedback from 
the sales and trading desk. Because the sales and trading team only makes 
money if a client trades, research that advocates long holding periods and 
infrequent trading is certainly not welcome, no matter how efficacious it 
might be.
The main duty of the people on the sales desks is to prompt clients 
to make a trading decision and to trade with them (rather than another 
bank), so salespeople spend a good bit of time making cold calls to hedge 
fund traders to give them some market “color” and point out opportunities 
to make short-term trades.
The End Result
The buy and sell sides interact with one another in such a way as to create 
an investing environment that values short-termism and dependence on 
large-capitalization stocks. The problem is that individual investors get 
wrapped up in these machinations and end up trying to act like agents 
when they are in fact principals. Agents, as we have seen, get paid a salary 
and bonus on the basis of various short-term factors that are, at best, neutral 
and, at worst, damaging to the interests of principals. Buy-side agents, as 
138  •   The Intelligent Option Investor
we have seen, are either relatively disinterested in investment performance 
(e.g., insurance companies and pension funds) or are interested only in 
relative outperformance over a very short time frame (e.g., hedge funds 
and mutual funds). Sell-side agents make money in proportion to trading 
volume and frequency, so they are happy to facilitate the enormous trade 
in a blue chip securities on behalf of a pension fund or the hundreds or 
thousands of individual trades in a day on behalf of an aggressive active 
hedge fund.
None of these agents are considering the economic value that may be 
created by the company in which they are investing, and in the attempt to 
maximize their own compensation, they are happy to ignore the long-term 
view in favor of a trade that will work within 90 days. Individual investors 
read sell-side research, and because the research analysts are so intelligent 
and well informed about various minutiae of a given company or industry, 
they think that the analysts’ recommendations will help them in the long 
term. Business news channels offer a constant stream of pundits from both 
buy and sell sides pontificating about things that matter to them—short-
term opportunities to generate a small advantage for the quarter—and that 
individual investors wrongly assume should be important to them as well.
An experienced technical analyst can find an investment opportu-
nity in any chart pattern. A sell-side investment banker can always talk 
about why one company looks cheap in comparison with another in the 
same industry based on some ratio analysis that has a shelf life of about 
two weeks. Discount brokerages are happy to supply individual investors 
with sophisticated software and data packages that are “free” as long as the 
investors make a certain number of trades per month, and they encourage 
their clients to “trade like a pro. ”
The end result of these structural factors is that individual investors 
get caught in a mental trap that if they are doing anything different from 
what they see their highly paid agents doing, they must be doing some-
thing wrong. This is reinforced by one behavioral bias I mentioned in pass-
ing earlier—herding—the human tendency to try to find safety in following 
the lead of others rather than risk independent action. 
In general, any information or strategy that does not hone in on the 
long-term economic value of a company should be considered by intel-
ligent investors to be a red herring and ignored. No individual investor is 
Understanding and Overcoming Investing Pitfalls   •  139
being compensated with respect to short-term or relative performance, so 
information that is purported to give them advantages in this realm should 
be taken with a grain of salt.
Now that you have a good idea of the theory behind options from 
Part I and the theory of how to assess rational valuation ranges for a stock 
without falling into behavioral or structural traps from Part II, let’s apply 
this knowledge to the practical task of investing. Part III discusses how to 
apply the principles of intelligent stock valuation to option investing and 
shows how to tilt the balance of risk and reward in our favor.
This page intentionally left blank 
141
Part III 
IntellIgent OptIOn 
InvestIng
Now that you understand how options work and how to value companies, 
it is time to move from the theoretical to the practical to see how to apply 
this knowledge to investing in the market. With Part III of this book, we 
make the transition from theoretical to practical, and by the time you finish 
this part, you will be an intelligent option investor.
To invest in options, you must know how to transact them; this is the 
subject of Chapter 7. In it, you will see how to interpret an option pricing 
screen and to break down the information there so that you can under -
stand what the option market is predicting for the future price of a stock. I 
also talk about the only one of the Greeks that an intelligent option investor 
needs to understand well—delta.
Chapter 8 deals with a subject that is essential for option investors—
leverage. Not all option strategies are levered ones, but many are. As such, 
without understanding what leverage is, how it can be measured and used, 
and how it can be safely and sanely incorporated into a portfolio, you can-
not be said to truly understand options.
Chapters 9–11 deal with specific strategies to gain, accept, and mix 
exposure. In these chapters I offer specific advice about what strike prices 
are most effective to select and what tenors, what to do when the expected 
outcomes of an investment materially change, and how to incorporate 
each strategy into your portfolio. Chapter 11 also gives guidance on so-
called option overlay strategies, where a position in a stock is overlain by 
an option to modify the stock’s risk-reward profile (e.g., protective puts for 
hedging and covered calls for generating income).
142  •   The Intelligent Option Investor
Unlike some books, this book includes only a handful of strategies, 
and most of those are very simple ones. I shun complex positions for two 
reasons. First, as you will see, transacting in options can be very expensive. 
The more complex an option strategy is, the less attractive the potential 
returns become. Second, the more complex a strategy is, the less the inher-
ent directionality of options can be used to an investor’s advantage. 
Simple strategies are best. If you understand these simple strategies 
well, you can start modifying them yourself to meet specific investing sce-
narios when and if the need arises. Perhaps by using these simple strategies 
you will not be able to chat with the local investment club option guru 
about the “gamma on an iron condor, ” but that will be his or her loss and 
not yours.
Chapter 12 looks at what it means to invest intelligently while under-
standing the two forms of risk you assume by selecting stocks in which to 
invest: market risk and valuation risk.
143
Chapter 7
FIndIng MIsprIced 
OptIOns
All our option-related discussions so far have been theoretical. Now it 
is time to delve into the practical to see how options work in the market. 
After finishing this chapter, you should understand
1. How to read an option chain pricing screen
2. Option-specific pricing features such as a wide bid-ask spread,  
volatility smile, bid and ask volatility, and limited liquidity/ 
availability
3. What delta is and why it is important to intelligent option investors
4. How to compare what the option market implies about future 
stock prices to an intelligently determined range
In terms of where this chapter fits into our goal of becoming intelligent 
option investors, obviously, even if you have a perfect understanding of 
option and valuation theory, if you do not understand the practical steps 
you must take to find actual investment opportunities in the real world, all 
the theory will do you no good.
New jargon introduced in this chapter includes the following:
Closing price Bid implied volatility
Settlement price Ask implied volatility
Contract size Volatility smile
Round-tripping Greeks
Bid-ask spread Delta
144  •   The Intelligent Option Investor
Making Sense of Option Quotes
Let’s start our practical discussion by taking a look at an actual option 
pricing screen. These screens can seem intimidating at first, but by the end 
of this chapter, they will be quite sensible.
Last
0.86 -0.23
-0.14
-0.04
-0.17
-0.14
-0.06
-0.13
-0.12
-0.07
-0.09
-0.14
-0.06
-0.20
-0.26
-0.10
+0.01
0.91 0.94 21.672% 24.733% 0.8387
0.4313
0.0631
0.0000
0.0000
0.0000
0.9580
0.9598
0.9620
0.7053
0.4743
0.2461
0.0357
0.0392
0.0482
21.722%
22.988%
62.849%
72.188%
81.286%
201.771%
192.670%
175.779%
20.098%
18.997%
18.491%
25.587%
29.201%
35.855%
55.427%
123.903%
64.054%
23.311%
22.407%
21.813%
21.147%
22.144%
23.409%
54.689%
66.920%
35.642%
23.656%
23.072%
22.553%
21.460%
21.374%
21.581%
32.597%
24.854%
23.426%
20.380%
19.627%
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
0.26
0.04
0.02
0.02
0.02
13.30
12.40
11.35
1.19
0.58
0.22
0.01
0.01
0.02
11.90
12.35
10.10
1.68
1.10
0.67
0.05
0.03
0.02
0.24
0.02
10.35
9.30
8.40
1.17 19.408%
18.405%
17.721%
0.56
0.20
11.75
10.70
9.50
1.65
1.08
0.65
0.04
0.01
0.01
11.55 12.30
12.00
10.00
2.48
1.93
1.48
0.41
0.29
0.21
12.20
3.60
1.75
10.05
9.85
2.44
1.91
1.45
0.39
0.27
0.18
12.10
3.50
1.70
0.00
0.23
0.02
C0.00
C0.00
C0.00
0.09
0.45
1.15
C4.99
C5.99
C6.99
C4.99
C5.99
C6.99
C12.01
C11.01
C10.01
1.16
0.54
0.22
C0.00
C0.00
C0.00
C0.00
C0.00
C0.00
0.33
0.76
1.40
C5.03
C6.00
C6.99
C0.00
C0.01
C0.03
0.84
1.23
1.88
C12.02
C11.03
C10.04
1.65
1.06
0.66
C0.06
0.03
0.02
C12.05
C11.07
C10.10
C2.58
1.93
12.10
3.40
1.69
0.68
4.25
C7.27
1.42
0.38
C0.30
C0.22
C0.11
C0.15
C0.19
1.80
2.27
2.73
C5.57
C6.43
C7.35
Chng Bid AskA skImpl.I mpl.Bid Vol. Vol. Delta JUL 26 ´13
31
32
33
37
38
39
20
21
22
31
32
33
37
38
39
Description
Call
Last Chng Bid AskA skImpl.I mpl.Bid Vol. Vol. Delta
Put
0.9897
0.9869
0.9834
0.6325
0.4997
0.3606
0.0463
0.0266
0.0155
0.9712
0.9628
0.9535
0.5890
0.5118
0.4324
0.1664
0.1258
0.0923
0.9064
0.5354
0.3336
+0.01
+0.10
+0.11
0.07 0.09 22.812%2 4.853% -0.1613
-0.5689
-0.9373
-1.0000
-1.0000
-1.0000
22.469%
24.612%
85.803%
203.970%
267.488%
20.456%
19.851%
N/A
N/A
N/A
0.42
1.20
5.25
7.25
8.90
0.39
1.17
4.90
4.85
5.40
+0.02
+0.09
+0.14
-0.0420
-0.0402
-0.0380
-0.2948
-0.5261
-0.7545
-0.9652
-0.9616
-0.9524
77.739%
70.681%
63.514%
20.303%
19.170%
19.011%
41.423%
61.602%
52.378%
N/A
N/A
N/A
N/A
N/A
N/A
0.02
0.02
0.02
0.34
0.73
1.38
5.30
6.55
7.30
0.33
0.71
1.35
4.95
19.958%
18.577%
17.954%
4.65
6.70
22.720%
22.019%
21.378%
20.455%
19.050%
21.354%
0.000%
23.193%
22.845%
22.218%
21.148%
20.913%
20.899%
+0.07
+0.05
+0.16
+0.09
+0.12
+0.04
50.831%
48.233%
46.993%
23.384%
22.672%
22.106%
36.111%
30.947%
44.342%
N/A
N/A
N/A
N/A
0.02
0.03
0.05
0.82
1.25
1.82
5.55
6.30
7.55
0.01
0.80
1.23
1.79
4.95
6.15
6.85
-0.0103
-0.0131
-0.0166
-0.3679
-0.5008
-0.6402
-0.9558
-0.9757
-0.9871
22.989%
22.284%
21.453%
17.134%
37.572%
38.919%
37.587%
35.246%
23.914%
23.485%
22.925%
22.967%
26.265%
28.715%
0.11 0.13
0.17
0.19
1.78
2.25
2.80
5.80
6.85
7.85
0.13
0.17
1.75
2.22
2.76
5.70
6.50
7.40
-0.0318
-0.0406
-0.0503
-0.4120
-0.4879
-0.5665
-0.8294
-0.8690
-0.9025
34.172%
23.567%
23.145%
22.479%
21.404%
19.420%
18.411%
37.790%
35.385%
30.523%
24.198%
23.081%
0.00
+0.09
33.497%
26.033%
24.745%
0.68
4.25
7.40
0.66
4.15
7.30
-0.0906
-0.4520
-0.6521
33.203%
25.378%
24.054%
AUG 16 ´13
20
21
22
31
32
33
37
38
39
SEP 20 ´13
20
21
22
31
32
33
37
38
39
20
32
37
JAN 17 ´14
JAN 16 ´15
I pulled this screen—showing the prices for options on Oracle (ORCL)—
on the weekend of July 20–21, 2013, when the market was closed. The last 
trade of Oracle’s stock on Friday, July 19, was at $31.86, down $0.15 from the 
Thursday’s close. Y our brokerage screen may look different from this one, but 
you should be able to pull back all the data columns shown here. I have limited 
the data I’m pulling back on this screen in order to increase its readability. 
More strikes were available, as well as more expiration dates. The expirations  
shown here are 1 week and 26, 60, 180, and 544 days in the future—the  
544-day expiry being the longest tenor available on the listed market.
Let’s first take a look at how the screen itself is set up without paying 
attention to the numbers listed.
Finding Mispriced Options    • 145
Calls are on the left, puts on the right.
Strike prices
and expirations
are listed here.
You can tell the stock was down on this day because most of the call
options are showing losses and all the put options are showing gains.
All the strikes for
each selected expiry
are listed grouped
together.
This query was set up
to pull back three
strikes at the three
moneyness regions
(20–22, 29–31, 37–39).
The 1-week options
and the LEAPS did
not have strikes at
each of the prices I
requested.
Now that you can see what the general setup is, let’s drill down and 
look at only the calls for one expiration to see what each column means.
Last
C12.02 11.75
10.70
9.50
1.65
1.08
0.65
0.04
0.01
0.01 0.02
0.03
0.05
0.67
1.10
1.68
10.10
12.35
11.90 N/A
N/A
N/A
22.720%
55.427% 20
SEP 20 ´13
21
22
31
32
33
37
38
39
0.9869
0.9834
0.6325
0.4997
0.3606
0.0463
0.0266
0.0155
123.903%
64.054%
23.311%
22.407%
21.813%
21.147%
22.144%
23.409%
22.019%
21.378%
20.455%
19.050%
21.354%
C11.03
C10.04
1.65
1.06
-0.13
-0.12
-0.07
0.00
+0.01
0.66
C0.06
0.03
0.02
Chnq Bid AskA skImpl.I mpl.Bid Vol. Vol. Delta Description
Call
0.9897
Red
(loss) Green
(gain)
146  •   The Intelligent Option Investor
Last
This is the last price at which the associated contract traded. Notice that 
the last price associated with the far in-the-money (ITM) strikes ($20, $21, 
$22) and one of the far out-of-the-money (OTM) strikes ($37) have the 
letter “C” in front of them. This is just my broker’s way of showing that the 
contract did not trade during that day’s trading session and that the last 
price listed was the closing price of the previous day. Closing prices are not 
necessarily market prices. At the end of the day, if a contract has not traded, 
the exchange will give an indicative closing price (or settlement price ) for 
that day. The Oracle options expiring on August 16, 2013, and struck at 
$20 may not have traded for six months or more, with the exchange simply 
“marking” a closing price every day.
One important fact to understand about option prices is that they 
are quoted in per-share terms but must be transacted in contracts that rep-
resent control of multiple shares. The number of shares controlled by one 
contract is called the contract size . In the U.S. market, one standard con-
tract represents control over 100 shares. Sometimes the number of shares 
controlled by a single contract differs (in the case of a company that was 
acquired through the exchange of shares), but these are not usually avail-
able to be traded. In general, one is safe remembering that the contract size 
is 100 shares.
Y ou cannot break a contract into smaller pieces or buy just part of a 
contract—transacting in options means you must do so with indivisible 
contracts, with each contract controlling 100 shares. Period. As such, every 
price you see on the preceding screenshot, if you were to transact in one of 
those options, would cost you 100 times the amount shown. For example, 
the last price for the $31-strike option was $1.65. The investor who bought 
that contract paid $165 for it (plus fees, taxes, and commissions, which are 
not included in the posted price). In the rest of this book, when I make 
calculations regarding money spent on a certain transaction, you will al-
ways see me multiply by 100.
Change
This is the change from the previous day’s closing price. My broker shows 
change only for contracts that were actively traded that day. It looks like 
Finding Mispriced Options    • 147
the near at-the-money (ATM) strikes were the most active because of the 
two far OTM options that traded; one’s price didn’t change at all, and the 
other went up by 1 cent. On a day in which the underlying stock fell, these 
calls theoretically should have fallen in price as well (because the K/S ratio, 
the ratio of strike price to stock price, was getting slightly larger). This just 
shows that sometimes there is a disconnect between theory and practice 
when it comes to options. 
To understand what is probably happening, we should understand 
something about market makers. Market makers  are employees at bro-
ker-dealers who are responsible for ensuring a liquid, orderly securi-
ties market. In return for agreeing to provide a minimum liquidity of 
10 contracts per strike price, market makers get the opportunity to earn 
the bid-ask spread every time a trade is made (I will talk about bid-ask 
spreads later). However, once a market maker posts a given price, he or 
she is guaranteeing a trade at that price. If, in this case (because we’re 
dealing with OTM call options), some unexpected positive news comes 
out that will create a huge rise in the stock price once it filters into the 
market and an observant, quick investor sees it before the market maker 
realizes it, the investor can get a really good price on those far OTM call 
options (i.e., the investor could buy a far OTM call option for 1 cent and 
sell it for 50 cents when the market maker realizes what has happened. 
To provide a little slack that prevents the market maker from losing too 
much money if this happens, market makers usually post prices for far 
OTM options or options on relatively illiquid stocks that are a bit unrea-
sonable—at a level where a smart investor would not trade with him or 
her at that price. If someone trades at that price, fine—the market maker 
has committed to provide liquidity, but the agreement does not stipulate 
that the liquidity must be provided at a reasonable price. For this reason, 
frequently you will see prices on far OTM options that do not follow the 
theoretical “rules” of options.
Bid-Ask
For a stock investor, the difference between a bid price and an ask price 
is inconsequential. For option investors, though, it is a factor that must 
be taken into consideration for reasons that I will detail in subsequent 
148  •   The Intelligent Option Investor
paragraphs. The easiest way to think of the bid-ask spread is to think in 
terms of buying a new car. If you buy a new car, you pay, let’s say, $20,000. 
This is the ask price. Y ou grab the keys, drive around the block, and 
return to the showroom offering to sell the car back to the dealership. The 
dealership buys it for $18,000. This is the bid price. The bid-ask spread is 
$2,000 in this example.
Bid-ask spreads are proportionally much larger for options than 
they are for stocks. For example, the options I’ve highlighted here are on 
a very large, important, and very liquid stock. The bid-ask spread on the 
$32-strike call option (which you will learn in the next section is exactly 
ATM) is $0.02 on a midprice of $1.09. This works out to a percentage bid-
ask spread of 1.8 percent. Compare this with the bid-ask spread on Ora-
cle’s stock itself, which was $0.01 on a midprice of $31.855—a percentage 
spread of 0.03 percent.
For smaller, less-liquid stocks, the percentage bid-ask spread is even 
larger. For instance, here is the option chain for Mueller Water (MW A):
2.5
5
7.5
10
Last
C5.30
C2.80
0.55
C0.00
Change Bid AskI mpl. Bid  Vol. Impl. Ask  Vol. Impl. Bid  Vol. Impl. Ask  Vol.Delta
2.5
5
7.5
10
2.5
5
7.5
10
12.5
DescriptionCall
Last Change BidA sk Delta
Put
C0.00
C0.00
C0.25
C2.25
C0.00
C0.00
C0.55
C2.35
C0.00
C0.10
C0.85
C2.55
C4.80
5.20 5.50 N/A 340.099% 0.9978
0.9978
0.7330
0.1316
0.9347
0.8524
0.6103
0.1516
0.9933
0.9190
0.6070
0.2566
0.1024
142.171%
46.039%
76.652%
N/A
N/A
2.95
0.55
0.10
0.20
0.10 N/A
N/A
N/A
0.10
0.30
2.35
40.733%
N/A
N/A
N/A
N/A
36.550%
38.181%
35.520%
35.509%
35.664%
2.10
0.50
0.05
0.10
0.60
2.402.30
0.05
0.15
0.15
0.85
2.60
4.90
0.70
2.45
4.60
2.70
0.500.00
5.20 5.50
3.00
0.90
0.20
2.80
0.80
0.10
5.505.10
3.102.85
1.151.05
0.400.30
0.200.05
39.708%
N/A
N/A
36.722%
N/A
38.754%
38.318%
39.127%
36.347%
36.336%
292.169% 0.0000
-0.0000
-0.2778
-0.8663
-0.0616
-0.1447
-0.3886
-0.8447
-0.0018
-0.0787
-0.3890
-0.7375
-0.8913
128.711%
53.108%
88.008%
117.369%
60.675%
42.433%
44.802%
110.810%
50.757%
42.074%
43.947%
49.401%
163.282%
75.219%
42.610%
45.215%
122.894%
64.543%
42.697%
44.728%
50.218%
C5.30
C2.80
C0.85
C0.10
C5.30
C1.10
C0.35
C0.10
3.00 +0.15
AUG 16 ´13
NOV 15 ´13
FEB 21 ´14
Looking at the closest to ATM call options for the November expiration—
the ones struck at $7.50 and circled in the screenshot—you can see that 
the bid-ask spread is $0.10 on a midprice of $0.85. This works out to 11.8 
percent.
Because the bid-ask spread is so very large on option contracts, 
round-tripping
1 an option contract creates a large hurdle that the returns 
of the security must get over before the investor makes any money. In the 
case of Mueller Water, the options one buys would have to change in price 
by 11.8 percent before the investor starts making any money at all. It is for 
this reason that I consider day trading in options and/or using complex 
Finding Mispriced Options    • 149
strategies involving the simultaneous purchase and sale of multiple con-
tracts to be a poor investment strategy.
Implied Bid Volatility/Implied Ask Volatility
Because the price is so different between the bid and the ask, the range of fu-
ture stock prices implied by the option prices can be thought of as different 
depending on whether you are buying or selling contracts. Employing the 
graphic conventions we used earlier in this book, this effect is represented 
as follows:
Implied price range implied
by ask price volatility of 23.4%
Implied price range implied
by bid price volatility of 21.4%
6/21/201612/24/20156/27/201512/29/20147/2/20141/3/20147/7/20131/8/20131/12/2012
Oracle (ORCL)
Price per Share
60
50
40
30
20
10
-
Because Oracle is such a big, liquid company, the difference between 
the stock prices implied by the different bid-ask implied volatilities is not 
large, but it can be substantial for smaller, less liquid companies. Looking 
at the ask implied volatility column, you will notice the huge difference 
between the far ITM options’ implied volatilities and those for ATM and 
OTM options. The data in the preceding diagram are incomplete, but 
if you were to graph all the implied volatility data, you would get the 
following:
150  •   The Intelligent Option Investor
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
Strike Price
Oracle (ORCL) Implied Volatility
Implied Volatility (Percent)
160
180
140
100
120
80
40
60
20
0
Thinking about what volatility means with regard to future stock 
prices—namely, that it is a prediction of a range of likely values—it does not 
make sense that options struck at different prices would predict such radi-
cally different stock price ranges. What the market is saying, in effect, is that it 
expects different things about the likely future range of stock prices depending 
on what option is selected. Clearly, this does not make much sense.
This “nonsensical” effect is actually proof that practitioners 
understand that the Black-Scholes-Merton model’s (BSM’s) assumptions 
are not correct and specifically that sudden downward jumps in a stock 
price can and do occur more often than would be predicted if returns fol-
lowed a normal distribution. This effect does occur and even has a name—
the volatility smile . Although this effect is extremely noticeable when 
graphed in this way, it is not particularly important for the intelligent op-
tion investing strategies about which I will speak. Probably the most im-
portant thing to realize is that the pricing on far OTM and far ITM options 
is a little more informal and approximate than for ATM options, so if you 
are thinking about transacting in OTM or ITM options, it is worth looking 
for the best deal available. For example, notice that in the preceding dia-
gram, the $21-strike implied volatility is actually notably higher than the 
Finding Mispriced Options    • 151
$20-strike volatility. If you were interested in buying an ITM call option, 
you would pay less time value for the $20-strike than for the $21-strike op-
tions—essentially the same investment. I will talk more about the volatility 
smile in the next section when discussing delta.
In a similar way, sometimes the implied volatility for puts is different 
from the implied volatility for calls struck at the same price. Again, this is 
one of the market frictions that arises in option markets. This effect also 
has investing implications that I will discuss in the chapters detailing dif-
ferent option investing strategies.
The last column in this price display is delta , a measure that is so 
important that it deserves its own section—to which we turn now.
Delta: The Most Useful of the Greeks
Someone attempting to find out something about options will almost 
certainly hear about how the Greeks are so important. In fact, I think that 
they are so unimportant that I will barely discuss them in this book. If you 
understand how options are priced—and after reading Part I, you do—the 
Greeks are mostly common sense. 
Delta, though, is important enough for intelligent option investors 
to understand with a bit more detail. Delta is the one number that gives 
the probability of a stock being above (for calls) or below (for puts) a given 
strike price at a specific point in time.
Deltas for calls always carry a positive sign, whereas deltas for puts are 
always negative, so, for instance, a call option on a given stock whose delta is 
exactly 0.50 will have a put delta of −0.50. The call delta of 0.50 means that there 
is a 50 percent chance that the stock will expire above that strike, and the put 
delta of −0.50 means that there is a 50 percent chance that the stock will expire 
below that strike. In fact, this strike demonstrates the technical definition of 
ATM—it is the most likely future price of the stock according to the BSM.
The reason that delta is so important is that it allows you one way 
of creating the BSM probability cones that you will need to find option 
investment opportunities. Recall that the straight dotted line in our BSM 
cone diagrams meant the statistically most likely future price for the stock. 
The statistically most likely future price for a stock—assuming that stocks 
152  •   The Intelligent Option Investor
move randomly, which the BSM does—is the price level at which there is 
an equal chance of the actual future stock price to be above or below. In 
other words, the 50-delta mark represents the forward price of a stock in 
our BSM cones.
Recall now also that each line demarcating the cone represents roughly a 
16 percent probability of the stock reaching that price at a particular time in the 
future. This means that if we find the call strike prices that have deltas closest to 
0.16 and 0.84 (= 1.00 − 0.16) or the put strike prices that have deltas closest to 
−0.84 and −0.16 for each expiration, we can sketch out the BSM cone at points 
in the future (the data I used to derive this graph are listed in tabular format at 
the end of this section).
6/21/201612/24/20156/27/201512/29/20147/2/20141/3/20147/7/20131/8/20137/12/2012
Date
Oracle (ORCL)
Price per Share
45
40
35
30
25
20
5
10
15
-
Obviously, the bottom range looks completely distended compared 
with the nice, smooth BSM cone shown in earlier chapters. This dis-
tension is simply another way of viewing the volatility smile. Like the 
volatility smile, the distended BSM cone represents an attempt by partici-
pants in the options market to make the BSM more usable in real situa-
tions, where stocks really can and do fall heavily even though the efficient 
market hypothesis (EMH) says that they should not. The shape is saying, 
Finding Mispriced Options    • 153
“We think that these prices far below the current price are much more 
likely than they would be assuming normal percentage returns. ” (Or, in a 
phrase, “We’re scared!”)
If we compare the delta-derived “cone” with a theoretically derived 
BSM cone, here is what we would see:
Oracle (ORCL)
Date
Price per Share
60
50
40
30
20
10
-
6/21/201612/24/20156/27/201512/29/20147/2/20141/3/20147/7/20131/8/20137/12/2012
Of course, we did not need the BSM cone to tell us that the points 
associated with the downside strikes look too low. But it is interesting to see 
that the upside and most likely values are fairly close to what the BSM projects. 
Note also that the downside point on the farthest expiration is nearly 
fairly priced according to the BSM, contrary to the shorter-tenor options. 
This effect could be because no one is trading the far ITM call long-term 
equity anticipation securities (LEAPS), so the market maker has simply 
posted his or her bid and ask prices using the BSM as a base. In the market, 
this is what usually happens—participants start out with a mechanically 
generated price (i.e., using the BSM or some other computational option 
pricing model) and make adjustments based on what feels right, what 
arbitrage opportunities are available, and so on.
154  •   The Intelligent Option Investor
One important thing to note is that although we are using the delta 
figure to get an idea of the probability that the market is assigning to a certain 
stock price outcome, we are also using deltas for options that nearly no one 
ever trades. Most option volume is centered around the 50-delta mark and a 
10 to 20 percentage point band around it (i.e., from 30- to 40-delta to 60- to 
70-delta). It is doubtful to me that these thinly traded options contain much 
real information about market projections of future stock prices.
Another problem with using the deltas to get an idea about market 
projections is that we are limited in the length of time we can project out 
to only the number of strikes available. For this example, I chose an impor-
tant tech company with a very liquid stock, so it has plenty of expirations 
and many strikes available so that we can get a granular look at deltas. 
However, what if we were looking at Mueller Water’s option chain and try-
ing to figure out what the market is saying?
2.5
5
7.5
10
Last
C5.30
C2.80
0.55
C0.00
Change Bid Ask Impl. Bid Vol. Impl. Ask Vol. Delta AUG 16 ´13
2.5
5
7.5
10
NOV 15 ´13
2.5
5
7.5
10
12.5
FEB 21 ´14
DescriptionCall
5.20 5.50 N/A 340.099% 0.9978
0.9978
0.7330
0.1316
0.9347
0.8524
0.6103
0.1516
0.9933
0.9190
0.6070
0.2566
0.1024
142.171%
46.039%
76.652%
N/A
N/A
2.95
0.55
0.10
2.70
0.500.00
5.20 5.50
3.00
0.90
0.20
2.80
0.80
0.10
5.505.10
3.102.85
1.151.05
0.400.30
0.200.05
39.708%
N/A
N/A
36.722%
N/A
38.754%
38.318%
39.127%
36.347%
36.336%
163.282%
75.219%
42.610%
45.215%
122.894%
64.543%
42.697%
44.728%
50.218%
C5.30
C2.80
C0.85
C0.10
C5.30
C1.10
C0.35
C0.10
3.00 +0.15
Here you can see that we only have three expirations: 26, 117, and 
215 days from when these data were taken. In addition, there are hardly 
any strikes that are reasonably close to our crucial 84-delta, 50-delta, and 
16-delta strikes, which means that we have to do a lot of extrapolation to 
try to figure out where the market’s idea of the BSM cone lies.
To get a better picture of what the market is saying, I recommend 
looking at options that are the most heavily traded and assuming that the 
implied volatility on these strikes gives true information about the mar -
ket’s assumptions about the future price range of a stock. Using the im-
plied volatility on heavily traded contracts as the true forward volatility 
expected by the market allows us to create a theoretical BSM cone that we 
Finding Mispriced Options    • 155
can extend indefinitely into the future and that is probably a lot closer to 
representing actual market expectations for the forward volatility (and, by 
extension, the range of future prices for a stock). Once we have this BSM 
cone—with its high-low ranges spelled out for us—we can compare it with 
the best- and worst-case valuations we derived as part of the company 
analysis process.
Let’s look at this process in the next section, where I spell out, step by 
step, how to compare an intelligent valuation range with that implied by 
the option market.
Note: Data used for Oracle graphing example:
Expiration Date Lower Middle Upper
7/25/2013 29.10 31.86 32.75
8/16/2013 22.00 32.00 33.50
9/20/2013 19.00 32.00 35.00
12/20/2013 20.00 32.50 37.00
1/17/2014 19.00 32.50 37.20
1/16/2015 23.00 32.30 42.00
Here I have eyeballed (and sometimes done a quick extrapolation) to try 
to get the price that is closest to the 84-delta, 50-delta, and 16-delta marks, 
respectively. Of course, you could calculate these more carefully and get 
exact numbers, but the point of this is to get a general idea of how likely the 
market thinks a particular future stock price is going to be.
Comparing an Intelligent Valuation  
Range with a BSM Range
The point of this book is to teach you how to be an intelligent option investor 
and not how to do stochastic calculus or how to program a computer to 
calculate the BSM. As such, I’m not going to explain how to mathematically 
derive the BSM cone. Instead, on my website I have an application that will 
allow you to plug in a few numbers and create a graphic representation of a 
BSM cone and carry out the comparison process described in this section. 
The only thing you need to know is what numbers to plug into this web 
application! 
156  •   The Intelligent Option Investor
I’ll break the process into three steps:
1. Create a BSM cone.
2. Overlay your rational valuation range on the BSM cone.
3. Look for discrepancies.
Create a BSM Cone
The heart of a BSM cone is the forward volatility number. As we have seen, 
as forward volatility increases, the range of future stock prices projected by 
the BSM (and expected by the market) also increases. However, after hav-
ing looked at the market pricing of options, we also know that a multitude 
of volatility numbers is available. Which one should we look at? Each strike 
price has its own implied volatility number. What strike price’s volatility 
should we use? There are also multiple tenors. What tenor options should 
we look at? Should we look at implied volatility at the bid price? At the ask 
price? Perhaps we should take the “kitchen sink” approach and just average 
all the implied volatilities listed!
The answer is, in fact, easy if you use some simplifying assumptions 
to pick a single volatility number. I am not an academic, so I don’t neces-
sarily care if these simplifying assumptions are congruent with theory. 
Also, I am not an arbitrageur, so I don’t much care about very precise 
numbers, and this attitude also lends itself well to the use of simplifying 
assumptions. All we have to make sure of is that the simplifying as-
sumptions don’t distort our perception to the degree that we make bad 
economic choices.
Here are the assumptions that we will make:
1. The implied volatility on a contract one or two months from expi-
ration that is ATM or at least within the 40- to 60-delta band and 
that is the most heavily traded will contain the market’s best idea 
of the true forward volatility of the stock. 
2. If a big announcement is scheduled for the near future, implied 
volatility numbers may be skewed, so their information might 
not be reliable. In this case, try to find a heavily traded near ATM 
strike at an expiry after the announcement will be made. If the 
announcement will be made in about four months or more, just try 
Finding Mispriced Options    • 157
to eyeball the ATM volatility for the one- and two-month contracts.
3. If there is a large bid-ask spread, the relevant forward volatility 
to use is equal to the implied volatility we want to transact. In 
other words, use the ask implied volatility if you are thinking 
about gaining exposure and the bid implied volatility if you are 
thinking about accepting exposure (the online application shows 
cones for both the bid implied volatility and the ask implied 
volatility).
Basically, these rules are just saying, “If you want to know what the 
option market is expecting the future price range of a stock to be, find a 
nice, liquid near ATM strike’s implied volatility and use that. ” Most op-
tion trading is done in a tight band around the present ATM mark and for 
expirations from zero to three months out. By looking at the most heavily 
traded implied volatility numbers, we are using the market’s price-discov-
ery function to the fullest. Big announcements sometimes can throw off  
the true volatility picture, which is why we try to avoid gathering infor -
mation from options in these cases (e.g., legal decisions, Food and Drug 
Administration trial decisions, particularly impactful quarterly earnings 
announcements, and so on). 
If I was looking at Oracle, I would probably choose the $32-strike 
options expiring in September. These are the 50-delta options with  
61 days to expiration, and there is not much of a difference between 
calls and puts or between the bid and ask. The August expiration op-
tions look a bit suspicious to me considering that their implied volatility 
is a couple of percentage points below that of the others. It probably 
doesn’t make a big difference which you use, though. We are trying to 
find opportunities that are severely mispriced, not trying to split hairs 
of a couple of percentage points. All things considered, I would prob-
ably use a number somewhere around 22 percent for Oracle’s forward 
volatility.
C12.02 11.75 N/A 55.427% 0.9897 C0.00 0.02 N/A 50.831%- 0.01032011.90
C11.03 10.70 N/A 123.903% 0.9869 C0.01 0.03 N/A 48.233%- 0.01312112.35
C10.04 9.50 N/A 64.054% 0.9834 C0.03 0.05 37.572% 46.993%- 0.01660.012210.10
C0.06 0.04 20.455% 21.147% 0.0463 C5.03 5.55 N/A 36.111%- 0.95584.95370.05
1.65 1.65 22.720% 23.311% 0.6325 0.84 +0.07 0.82 22.989% 23.384%- 0.36790.80311.68-0.13
1.06 1.08 22.019% 22.407% 0.4997 1.23 +0.05 1.25 22.284% 22.672%- 0.50081.23321.10-0.12
0.66 0.65 21.378% 21.813% 0.3606 1.88 +0.16 1.82 21.453% 22.106%- 0.64021.79330.67-0.07
0.02 0.01 21.354% 23.409% 0.0155 C6.99 7.55 N/A 44.342%- 0.98716.85390.02+0.01
0.03 0.01 19.050% 22.144% 0.0266 C6.00 6.30 17.134% 30.947%- 0.97576.15380.030.00
SEP 20 ´13
158  •   The Intelligent Option Investor
For Mueller Water, it’s a little trickier:
2.5
5
7.5
10
Last
C5.30
C2.80
0.55
C0.00
Change BidA sk Delta AUG 16 ´13
2.5
5
7.5
10
NOV 15 ´13
2.5
5
7.5
10
12.5
FEB 21 ´14
DescriptionCall
Last Change BidA sk Impl. Bid Vol. Impl. Ask Vol.Impl. Bid Vol. Impl. Ask Vol. Delta
Put
C0.00
C0.00
C0.25
C2.25
C0.00
C0.00
C0.55
C2.35
C0.00
C0.10
C0.85
C2.55
C4.80
5.20 5.50N /A 340.099% 0.9978
0.9978
0.7330
0.1316
0.9347
0.8524
0.6103
0.1516
0.9933
0.9190
0.6070
0.2566
0.1024
142.171%
46.039%
76.652%
N/A
N/A
2.95
0.55
0.10
0.20
0.10 N/A
N/A
N/A
0.10
0.30
2.35
40.733%
N/A
N/A
N/A
N/A
36.550%
38.181%
35.520%
35.509%
35.664%
2.10
0.50
0.05
0.10
0.60
2.402.30
0.05
0.15
0.15
0.85
2.60
4.90
2.70
0.500.00
5.20 5.50
3.00
0.90
0.20
2.80
0.80
0.10
5.505.10
3.102.85
1.151.05
0.400.30
0.200.05
39.708%
N/A
N/A
36.722%
N/A
38.754%
38.318%
39.127%
36.347%
36.336%
292.169% 0.0000
-0.0000
-0.2778
-0.8663
-0.0616
-0.1447
-0.3886
-0.8447
-0.0018
-0.0787
-0.3890
-0.7375
-0.8913
128.711%
53.108%
88.008%
117.369%
60.675%
42.433%
44.802%
110.810%
50.757%
42.074%
43.947%
49.401%
163.282%
75.219%
42.610%
45.215%
122.894%
64.543%
42.697%
44.728%
50.218%
C5.30
C2.80
C0.85
C0.10
C5.30
C1.10
C0.35
C0.10
3.00 +0.15
0.70
2.45
4.60
In the end, I would probably end up picking the implied volatility 
associated with the options struck at $7.50 and expiring in August 2013 
(26 days until expiration). I was torn between these and the same strike 
expiring in November, but the August options are at least being actively 
traded, and the percentage bid-ask spread on the call side is lower for them 
than for the November options. Note, though, that the August 2013 put 
options are so far OTM that the bid-ask spread is very wide. In this case, 
I would probably look closer at the call options’ implied volatilities. In the 
end, I would have a bid volatility of around 39 percent and an ask volatility 
of around 46 percent. Because the bid-ask spread is large, I would probably 
want to see a cone for both the bid and ask.
Plugging in the 22.0/22.5 for Oracle,
2 I would come up with this cone:
Date
Oracle (ORCL)
Price per Share
60
40
50
30
10
20
-
6/21/201612/24/20156/27/201512/29/20147/2/20141/3/20147/7/20131/8/20137/12/2012
Finding Mispriced Options    • 159
Plugging in the 39/46 for Mueller Water, I would get the following:
6/21/201612/24/20156/27/201512/29/20147/2/20141/3/20147/7/20131/8/20137/12/2012
Date
Mueller Water (MWA)
Price per Share
25
20
15
5
10
-
Y ou can see with Mueller Water just how big a 7 percentage point dif-
ference can be for the bid and ask implied volatilities in terms of projected 
outcomes. The 39 percent bid implied volatility generates an upper range 
at just around $15; the 46 percent ask implied volatility generates an upper 
range that is 20 percent or so higher than that!
Overlay an Intelligent Valuation Range on the BSM Cone
This is simple and exactly the same for a big company or a small one, 
so I’ll just keep going with the Oracle example. After having done a full 
valuation as shown in the exam valuation of Oracle on the IOI website, 
you’ve got a best-case valuation, a worst-case valuation, and probably 
an idea about what a likely valuation is. Y ou simply draw those numbers 
onto a chart like this:
160  •   The Intelligent Option Investor
6/21/201612/24/20156/27/201512/29/20147/2/20141/3/20147/7/20131/8/20137/12/2012
Date
Oracle (ORCL)
Price per Share
60
Best Case
Likely Case
Worst Case
40
50
30
10
20
-
$52
$43
$30
Once this step is done, we are ready to go onto the next and final step.
Look for Discrepancies
The last step is also easy. Because options split a stock’s returns into upside 
and downside exposure, we need to take a look at both the upside and 
downside to see where our projections differ from those of the market.
6/21/201612/24/20156/27/201512/29/20147/2/20141/3/20147/7/20131/8/20137/12/2012
Date
Oracle (ORCL)
Price per Share
60
Best Case
Likely Case
Worst Case
40
50
30
10
20
Downside
Upside
-
$52
$43
$30
A
B
Finding Mispriced Options    • 161
On the upside, we can see that our likely case valuation is $43 per share, 
whereas the BSM’s most likely value is a bit less than $35—a difference of 
more than 20 percent. This is the area on the graph labeled “ A. ” The BSM 
prices options based on the likelihood of the stock hitting a certain price 
level. The BSM considers the $43 price level to be relatively unlikely, whereas 
I consider it relatively likely. As such, I believe that options that allow me to 
gain exposure to the upside potential of Oracle—call options—are underval-
ued. In keeping with the age-old rule of investing to buy low, I will want to 
gain exposure to Oracle’s upside by buying low-priced call options.
On the downside, I notice that there is a fairly large discrepancy 
between my worst-case valuation ($30) and the lower leg of the BSM cone 
(approximately $24)—this is the region of the graph labeled “B, ” and the 
separation between the two values is again (just by chance) about 20 percent. 
The BSM is pricing options granting exposure to the downside—put 
options—struck at $24 as if they were fairly likely to occur; something that 
is fairly likely to occur will be priced expensively by the BSM. My analysis, 
on the other hand, makes me think that the BSM’s valuation outcome is  
very unlikely. The discrepancy implies that I believe the put options to be 
overvalued—the BSM sees a $24 valuation as likely, with expensive options, 
whereas I see it as unlikely, with nearly valueless options. In this case, we 
should consider the other half of the age-old investing maxim and sell high.
In a graphic representation, this strategy might look like this:
6/21/201612/24/20156/27/201512/29/20147/2/20141/3/20147/7/20131/8/20137/12/2012
Date
Oracle (ORCL)
Price per Share
60
Best Case
Likely Case
Worst Case
40
50
30
10
20
Downside
Upside
-
$52
$43
$30
GREEN
RED
162  •   The Intelligent Option Investor
Why would I select such a short-term put option to sell? Why would 
I pick an OTM call option to buy? These are the kinds of questions I will 
cover in Chapters 9–11, which look at the specifics of different option 
strategies.
Before we look at strategies, though, an option investor cannot be 
said to be intelligent without understanding what leverage is and how to 
use it safely and effectively in a portfolio. We turn to this in Chapter 8.
163
Chapter 8
Understanding and 
managing Leverage
In the media, the word leverage seems like it usually occurs alongside such 
words as dangerous, speculative, or even irresponsible, so most people have 
internalized the message that leverage is morally wrong; options—levered 
instruments that they are—are, by extension, viewed as morally wrong as 
well. In fact, nearly everyone uses leverage every day of their lives without 
incident and presumably without incurring a moral stain. In my opinion, 
it is not leverage that is the problem but rather an ignorance of how lever-
age works, coupled with overleverage and the inherent human belief that 
disasters only happen to someone else, that is the problem. 
Leverage is a powerful tool, but like all powerful tools, if used recklessly 
and without understanding, it can bring its user to unpleasant outcomes. 
Certainly a discussion of gaining and accepting exposure using option con-
tracts would be incomplete without a good explanation of leverage.
I like to think of leverage coming in three flavors: operational, financial, 
and investment—the first two of which I mentioned in an earlier chapter and 
go into more detail in Appendix B. This chapter delves specifically into in-
vestment leverage, but to the extent that investment leverage is similar to the 
other forms of leverage, referring to Appendix B to learn about those forms 
will help deepen your understanding of investment leverage. In this chapter, 
I first define investment leverage, discuss how it can be gained by using either 
debt or options, look at common ways to measure it, and introduce a unique 
method of measuring and managing leverage in an investment portfolio.
Leverage is not something to be taken lightly. Many very highly 
trained, well-educated, and well-capitalized investors have gone bankrupt 
164  •   The Intelligent Option Investor
because of their lack of appreciation for the fact that the sword of lever -
age cuts both ways. Certainly an option investor cannot be considered an 
intelligent investor without having an understanding and a deep sense 
of respect for the simultaneous power and danger that leverage conveys.
New jargon introduced in this chapter includes the following:
Lambda
Notional exposure
Investment Leverage
Commit the following definition to memory:
Investment leverage is the boosting of investment returns calcu-
lated as a percentage by altering the amount of one’s own capital 
at risk in a single investment.
Investment leverage is inextricably linked to borrowing money—this 
is what I mean by the phrase “altering the amount of one’s own capital at 
risk. ” In this way, it is very similar to financial leverage. In fact, in my mind, 
the difference between financial and investment leverage is that a company 
uses financial leverage to fund projects that will produce goods or provide 
services, whereas in the case of investing leverage, it is used not to produce 
goods or services but to amplify the effects of a speculative position.
Frequently people think of investing leverage as simply borrowing 
money to invest. However, as I mentioned earlier, you can invest in options 
for a lifetime and never explicitly borrow money in the process. I believe 
that the preceding definition is broad enough to handle both the case of 
investment leverage generated through explicit borrowing and the case of 
leverage generated by options.
Let’s take a look at a few example investments—unlevered, levered 
using debt, and levered using options.
Unlevered Investment
Let’s say that you buy a stock for exactly $50 per share, expecting that its intrinsic 
value is closer to $85 per share. Over the next year, the stock increases by $5, 
or 10 percent in value. Y our unrealized percentage gain on this investment is 
Understanding and Managing Leverage    • 165
obviously 10 percent. If instead the stock declines to $45 per share over that 
year, you would be sitting on an unrealized percentage loss of 10 percent.
Of course, this is very straightforward. Let’s now look at the purchase 
of a share of common stock using borrowed capital.
Levered Investment Using Debt
Let’s say that to buy a $50 share, you borrow $45 from a bank at an inter -
est rate of 5 percent per year, put in $5 of your own cash, and buy that 
same share of stock. Again, let’s assume that the stock increases in value by 
$5 over one year, closing at $55 per share. At the end of the year, you sell the 
stock and pay back the bank loan with interest (a total of $47.25). Doing so, 
you realize gross proceeds of $7.75 on an original investment of $5 of your 
own capital, which equates to $2.75 in gross profits and implies a percent-
age investment return of 55 percent.
There are three important things to note by comparing the levered 
and unlevered examples:
1. The percentage return is much higher for the levered investment 
(55 versus 10 percent) because you have reduced the amount of 
your own capital at risk much more than you have reduced the 
dollar return in the numerator.
2. The actual dollar amount gained is lower in the levered example 
($2.75 versus $10). If your investment mandate would have been 
“Generate at least $10 worth of investment returns, ” a single unit 
of the levered investment would have failed to meet this mandate. 
3. Obviously, the underlying asset and its returns are the same in both 
levered and unlevered scenarios—we are changing our profit expo-
sure to the underlying, not altering its volatility or other behavior. 
To fully understand leverage’s effects, however, we should also con-
sider the loss scenario. Again, let’s assume that we borrow $45 and spend 
$5 of our own money to buy the $50 per share stock. We wake the next 
morning to news that the company has discovered accounting irregulari-
ties in an important foreign subsidiary that has caused it to misstate reve-
nues and profits for the last three years. The shares suddenly fall 10 percent 
on the news. The unrealized loss is $5—the 10 percent fall in stock value 
has wiped out 100 percent of our investment capital. 
166  •   The Intelligent Option Investor
And herein lies the painful lesson learned by many a soul in the 
financial markets: leverage cuts both ways. The profits happily roll in dur-
ing the good times, but the losses inexorably crash down during bad times.
Levered Investment Using Options
Discussing option-based investing leverage is much easier if we focus on 
the perspective of gaining exposure. Because most people are more com-
fortable thinking about the long side of investing, let’s look at an example 
of gaining upside exposure on a company.
Let’s assume we see a $50 per share stock that we believe is worth $85 (in 
this example, I am assuming that we only have a point estimate of the intrinsic 
value of the company so as to simplify the following diagram—normally, it is 
much more helpful to think about fair value ranges, as explained in Part II of 
this book and demonstrate in the online example). We are willing to buy the 
share all the way up to a price of $68 (implying a 25 percent return if bought 
at $68 and sold at $85) and can get call options struck at $65 per share for only 
$1.50. Graphically, this prospective investment looks like this:
Fair Value Estimate
5/18/2012 5/20/2013 249 499 749 999
-
10
20
30
40
50
60
70
80
90
EBP = $66.50
Date/Day Count
Advanced Building Corp. (ABC)
Stock Price
GREEN
Understanding and Managing Leverage    • 167
In two years, you are obligated to pay your counterparty $65 if you 
want to hold the stock, but the decision as to whether to take possession 
of the stock in return for payment is solely at your discretion. In essence, 
then, you can look at buying a call option as a conditional borrowing of 
funds sometime in the future. Buying the call option, you are saying, “I 
may want to borrow $65 two years from now. I will pay you some interest 
up front now, and if I decide to borrow the $65 in two years, I’ll pay you 
that principal then. ”
In graphic terms, we can think about this transaction like this:
5/18/2012 5/20/2013 249 499 749 999
-
10
20
30
40
50
60
70
80
90
$1.50 “prepaid interest”
Contingent loan, the future repayment
of principal is made solely at the
investor’s own discretion.
Fair Value Estimate
Advanced Building Corp. (ABC)
Date/Day Count
Stock Price
GREEN
If the stock does indeed hit the $85 mark just at the time our option 
expires, we will have realized a gross profit of $20 (=  $85 −  $65) on an 
investment of $1.50, for a percentage return of 1,233 percent! Obviously, 
the call option works very much like a loan in terms of altering the 
investor’s capital at risk and boosting subsequent investment returns. 
However, although the leverage looks very similar, there are two impor -
tant differences:
168  •   The Intelligent Option Investor
1. As shown and mentioned earlier, when using an option, payment 
on the principal amount of $65 in this case is conditional and com-
pletely discretionary. For an option, the interest payment is made 
up front and is a sunk cost.
2. Because repayment is discretionary in the case of an option, you 
do not have any financial risk over and above the prepayment of 
interest in the form of an option premium. Repayment of a con-
ventional loan is mandatory, so you have a large financial risk if 
you cannot repay the principal at maturity in this case.
Regarding the first difference, not only is the loan conditional 
and discretionary, the loan also has value and can be transferred to 
another for a profit. What I mean is this: if the stock rises quickly, the 
value of that option in the open market will increase, and rather than 
holding the “loan” to maturity, you can simply sell it with your profits 
offsetting the original cost of the prepaid interest plus giving you a 
nice profit. 
Regarding the second difference, consider this: if you are using bor -
rowed money to invest and your stock drops heavily, the broker will make 
a margin call (i.e., ask you to deposit more capital into the account), and 
if you cannot make the margin call, the broker will liquidate the position 
(most brokers shoot first and ask questions later, simply closing out the 
position and selling other assets to cover the loss at the first sign margin 
requirements will not be met). If this happens, you can be 100 percent 
correct on your valuation long term but still fail to benefit economically 
because the position has been forcibly closed. In the case of options, the 
underlying stock can lose 20 percent in a single day, and the owner of a 
call option will never receive a margin call. The flip side of this benefit 
is that although you are not at risk of losing a position to a margin call, 
option ownership does not guarantee that you will receive an economic 
reward either. 
For example, if the option mentioned in the preceding example ex-
pires in two years when the stock is trading at $64.99 and the stock has paid 
$2.10 in dividends over the previous two years, the option holder ends up 
with neither the stock nor the dividend check.
Understanding and Managing Leverage    • 169
Simple Ways of Measuring Option 
Investment Leverage
There are several single-point, easily calculable numbers to measure 
option-based investment leverage. There are uses for these simple measures 
of leverage, but unfortunately, for reasons I will discuss, the simple num-
bers are not enough to help an investor intelligently manage a portfolio 
containing option positions. 
The two simple measures are lambda and notional exposure. Both are 
explained in the following sections.
Lambda
The standard measure investors use to determine the leverage in an option 
position is one called lambda . Lambda—sometimes known as percent 
delta—is a derivative of the delta
1 factor we discussed in Chapter 7 and is 
found using the following equation:
= ×Lambda deltas tock price
optionprice
Let’s look at an actual example. The other day, I bought a deep in-
the-money (ITM) long-tenor call option struck at $20 when the stock 
was trading at $30.50. The delta of the option at that time was 0.8707, 
and the price was $11. The leverage in my option position was calculated 
as follows:
= × = × =Lambda deltas tock price
optionprice
0.87 30.50
11 2.40
 
What this figure of 2.4 is telling us is that when I bought that option, if the 
price of the underlying moved by 1 percent, the value of my position would 
move by about 2.4 percent. This is not a hard and fast number—a change in 
price of either the stock or the option (as a result of a change in volatility or 
time value or whatever) will change the delta, and the lambda will change 
based on those things. 
170  •   The Intelligent Option Investor
Because investment leverage comes about by changing the amount 
of your own capital that is at risk vis-à-vis the total size of the investment, 
you can imagine that moneyness has a large influence on lambda. Let’s 
take a look at how investment leverage changes for in-the-money (ITM), 
at-the-money (ATM), and out-of-the-money (OTM) options. The stock 
underlying the following options was trading at $31.25 when these data 
were taken, so I’m showing the $29 and $32 strikes as ATM: 
Strike Price K /S Ratio Call Price Delta Lambda
15.00 0.48 17.30 0.91 1.64
20.00 0.64 11.50 0.92 2.50 ITM
21.00 0.67 11.30 0.86 2.38
22.00 0.70 9.60 0.89 2.90
… 
…
…
…
…
29.00 0.93 3.40 0.68 6.25
30.00 0.96 2.74 0.61 6.96 ATM
31.00 0.99 2.16 0.54 7.81
…
…
…
…
…
39.00 1.25 0.18 0.09 15.63
40.00 1.28 0.13 0.06 14.42 OTM
41.00 1.31 0.09 0.05 17.36
When an option is deep ITM, as in the case of the $20-strike call, we 
are making a significant expenditure of our own capital compared with 
the size of the investment. Buying a call option struck at $20, we are—
as explained in the preceding section—effectively borrowing an amount 
equal to the $20 strike price. In addition to this, we are spending $11.50 in 
premium. Of this amount, $11.25 is intrinsic value, and $0.25 is time value. 
We can look at the time value portion as the prepaid interest we discussed 
in the preceding section, and we can even calculate the interest rate im-
plied by this price (this option had 189 days left before expiration, implying 
an annual interest charge of 2.4 percent, for example). This prepaid interest 
can be offset partially or fully by profit realized on the position, but it can 
never be recaptured so must be considered a sunk cost. Time value always 
decays independent of the price changes of the underlying, so although an 
Understanding and Managing Leverage    • 171
upward movement in the stock will offset the money spent on time value, 
the amount spent on time value is never recoverable.
The remaining $11.25 of the premium paid for a $20-strike call op-
tion is intrinsic value . Buying intrinsic value means that we are exposing 
our own capital to the risk of an unrealized loss if the stock falls below 
$31.25. Lambda is directly related to the amount of capital we are exposing 
to an unrealized loss versus the size of the “loan” from the option, so be-
cause we are risking $11.25 of our own capital and borrowing $20 with the 
option (a high capital-to-loan proportion), our investment leverage meas-
ured by lambda is a relatively low 2.50.
Now direct your attention to a far OTM call option—the one struck 
at $39. If we invest in the $39-strike option, we are again effectively 
taking out a $39 contingent loan to buy the shares. Again, we take the 
time-value portion of the option’s price—in this case the entire premi-
um of $1.28—to be the prepaid interest (an implied annualized rate of  
6.3 percent) and note that we are exposing none of our own capital to 
the risk of an unrealized loss. Because we are subjecting none of our 
own capital in this investment and taking out a large loan, our invest-
ment leverage soars to a very high value of 15.63. This implies that a  
1 percentage point move in the underlying stock will boost our invest-
ment return by over 15 percent!
Obviously, these calculations tell us that our investment returns are 
going to be much more volatile for small changes in the underlying’s price 
when buying far OTM options than when buying far ITM options. This is 
fine information for someone interested in more speculative strategies—if 
a speculator has the sense that a stock will rise quickly, he or she could, 
rather than buying the stock, buy OTM options, and if the stock went up 
fast enough and soon enough offset any drop of implied volatility and time 
decay, he or she would pocket a nice, highly levered profit.
However, there are several factors that limit the usefulness of lambda. 
First, because delta is not a constant, the leverage factor does not stay put 
as the stock moves around. For someone who intends to hold a position for 
a longer time, then, lambda provides little information regarding how the 
position will perform over their investment horizon. 
In addition, reading the preceding descriptions of lambda, it is ob-
vious that this measure deals exclusively with the percentage change in 
172  •   The Intelligent Option Investor
the option’s value. Although everyone (especially fly-by-night investment 
newsletter editors) likes to tout their percentage returns, we know from 
our earlier investigations of leverage that percentage returns are only part 
of the story of successful investing. Let’s see why using the three invest-
ments I mentioned earlier—an ITM call struck at $20, an OTM call struck 
at $39, and a long stock position at $31. 
I believe that there is a good chance that this stock is worth north of 
$40—in the $43 range, to be precise (my worst-case valuation was $30, and 
my best-case valuation was in the mid-$50 range). If I am right, and if this 
stock hits the $43 mark just as my options expire,
2 what do I stand to gain 
from each of these investments?
Let’s take a look. 
Spent Gross Profit Net Profit Percent Profit
$39-strike call 0.18 4.00 3.82 2,122
$20-strike call 11.50 23.00 11.50 100
Shares 31.25 43.00 11.75 38
This table means that in the case of the $20-strike call, we spent 
$11.50 to win gross proceeds of $23.00 (= $43 − $20) and a profit net of 
investment of $11.50. Netting $11.50 on an $11.50 investment generates a 
percentage profit of 100 percent.
Looking at this chart, the first thing you are liable to notice is the 
“Percent Profit” column. That 2,122 percent return looks like something 
you might see advertised on an option tout service, doesn’t it? Y es, that 
percentage return is wonderful, until you realize that the absolute value 
of your dollar winnings will not allow you to buy a latte at Starbuck’s. 
Likewise, the 100 percent return on the $20-strike options looks heads and 
shoulders better than the measly 38 percent on the shares, until you again 
realize that the latter is still giving you more money by a quarter.
Recall the definition of leverage as a way of “boosting investment re-
turns calculated as a percentage, ” and recall that in my previous discussion 
of financial leverage, I mentioned that the absolute dollar value is always 
highest in the unlevered case. The fact is that many people get excited about 
stratospheric percentage returns, but stratospheric percentage returns only 
Understanding and Managing Leverage    • 173
matter if a significant chunk of your portfolio is exposed to those returns!
Lambda is a good measure to show how sensitive percentage returns are to 
a move in the stock price, but it is useless when trying to understand what 
the portfolio effects of those returns will be on an absolute basis.
Notional Exposure
Look back at the preceding table. Let’s say that we wanted to make 
lambda more useful in understanding portfolio effects by seeing how 
many contracts we would need to buy to match the absolute return of 
the underlying stock. Because our expected dollar return of one of the 
$39-strike calls only makes up about a third of the absolute return of the 
straight stock investment ($3.82 / $11.75 = 32.5% ≈ 1/3), it follows that if 
we wanted to make the same dollar return by investing in these call options 
that we expect to make by buying the shares, we would have to buy three 
of the call options for every share we wanted to buy. Recalling that op-
tions are transacted in contract sizes of 100 shares, we know that if we were 
willing to buy 100 shares of Oracle’s stock, we would have to buy options 
implying control over 300 shares to generate the same absolute profit for 
our portfolio.
I call this implied control figure notional exposure. Continuing with 
the $39-strike example, we can see that the measure of our leverage on the 
basis of notional exposure is 3:1. The value of the notional exposure is cal-
culated by multiplying it by the strike; in this case, the notional exposure 
of 300 shares multiplied by the strike price of $39 gives a notional value 
for the contracts of $11,700. This value is called the notional amount of the 
option position. 
Some people calculate a leverage figure by dividing the notional amount 
by the total cost of the options. In our example, we would pay $18 per con-
tract for three contracts, so leverage measured in this way would work out to 
be 217 (= $11,700 ÷ $54). I actually do not believe this last measure of lever-
age to be very helpful, but notional control will become important when we 
talk about the leverage of short-call spreads later in this chapter.
These simple methods of measuring leverage have their place in ana-
lyzing option investment strategies, but in order to really master leverage, 
you must understand leverage in the context of portfolio management.
174  •   The Intelligent Option Investor
Understanding Leverage’s Effects on a Portfolio
Looking at leverage from a lambda or notional control perspective gives 
some limited information about leverage, but I believe that the best way 
to think about option-based investment leverage is to think about the ef-
fect of leverage on an actual portfolio allocation basis. This gives a richer, 
more nuanced view of how leverage stands to help or hurt our portfolio 
and allows us more insight into how we can intelligently structure a mixed 
option-stock portfolio.
Let’s start our discussion of leverage in a portfolio context by thinking 
about how to select investments into a portfolio. We will assume that we 
have $100 in cash and want to use some or all of that cash to invest in risky 
securities. Cash is riskless (other than inflation risk, but let’s ignore that 
for a moment), so the risk we take on in the portfolio will be dampened 
by keeping cash, and the returns we will win from the portfolio will be 
similarly dampened.
We have a limited amount of capital and want to allocate that capital 
to risky investments in proportion to two factors:
1. The amount we think we can gain from the investment
2. Our conviction in the investment, which is a measure of our per -
ception of the riskiness of the investment
We might see a potential investment that would allow us to reap a profit 
of $9 for every $1 invested (i.e., we would gain a great deal), but if our 
conviction in that investment is low (i.e., we think the chance of winning 
$9 for every $1 invested is very low), we would likely not allocate much of 
our portfolio to it.
In constructing a portfolio, most people set a limit on the proportion 
of their portfolio they want to allocate to any one investment. I personally 
favor more concentrated positions, but let’s say that you paid better atten-
tion to your finance professor in school than I did and figure that you want 
to limit your risk exposure to any one security to a maximum of $5 of your 
$100 portfolio. 
An unlevered portfolio means that each $5 allocation would be made 
by spending $5 of your own capital. Y ou would know that if the value of 
the underlying security decreases by $2.50, the value of the allocation will 
Understanding and Managing Leverage    • 175
also fall to $2.50. If, instead, the value of the underlying security increases 
by $2.50, the value of that allocation will rise to $7.50.
In a levered portfolio, each $5 allocation uses some proportion of 
capital that is not yours—borrowed in the case of a margin loan and con-
tingently borrowed in the case of an option. This means that for every 
$1 increase or decrease in the value of the underlying security, the lev-
ered allocation increases or decreases by more than $1. Leverage, in this 
context, represents the rate at which the value of the allocation increases 
or decreases for every one-unit change in the value of the underlying 
security.
When thinking about the risk of leverage, we must treat different types 
of losses differently. A realized loss represents a permanent loss of capital—a 
sunk cost for which future returns can offset but never undo. An unrealized 
loss may affect your psychology but not your wealth (unless you need to 
realize the loss to generate cash flow for something else—I talk about this 
in Chapter 11 when I address hedging). For this reason, when we measure 
how much leverage we have when the underlying security declines, we will 
measure it on the basis of how close we are to suffering a realized loss rather 
than on the basis of the unrealized value of the loss. Leverage on the profit 
side will be handled the same way: we will treat our fair value estimate as the 
price at which we will realize a gain. Because the current market price of a 
security may not sit exactly between our fair value estimate and the point at 
which we suffer a realized loss, our upside and downside leverage may be 
different.
Let’s see how this comes together with an actual example. For this ex-
ample, I looked at the price of Intel’s (INTC) shares and options when the 
former were trading at $22.99. Let’s say that we want to commit 5 percent 
of our portfolio value to an investment in Intel, which we believe is worth 
$30 per share. For every $100,000 in our portfolio, this would mean buying 
217 shares. This purchase would cost us $4,988.83 (neglecting taxes and 
fees, of course) and would leave us with $11.17 of cash in reserve. After we 
made the buy, the stock price would fluctuate, and depending on what its 
price was at the end of 540 days [I’m using as an investment horizon the 
days to expiration of the longest-tenor long-term equity anticipation secu-
rities (LEAPS)], the allocation’s profit and loss profile would be represented 
graphically like this:
176  •   The Intelligent Option Investor
02468 10 12 14 16 18 20 22 24
Stock Price
Unlevered Investment (Full Allocation)
Gain (Loss) on Allocation
26 28 30 32 34 36 38 40 42 44 46 48 50(6,000)
(4,000)
(2,000)
-
2,000
4,000
6,000
8,000
Unrealized Gain
Unrealized Loss
Cash Value
Net Gain (Loss) - Unlevered
Realized Loss
Here the future stock price is listed from 0 to 50 on the horizontal axis, 
and the net profit or loss to this position is listed on the vertical axis. Obvious-
ly, any gain or loss would be unrealized unless Intel’s stock price went to zero, 
at which point the total position would only be worth whatever spare cash we 
had. The black profit and loss line is straight—the position will lose or gain on 
a one-for-one basis with the price of the stock, so our leverage is 1.0.
Now that we have a sense of what the graph for a straight stock 
position looks like, let’s take a look at a few different option positions. 
When I drew the data for this example, the following 540-day expiration 
call options were available:
Strike Price Ask Price Delta
15 8.00 0.79
22 2.63 0.52
25 1.43 0.35
Let’s start with the ITM option and construct a simple-minded posi-
tion that attempts to buy as many of these option contracts as possible with 
the $5,000 we have reserved for this investment. We will pay $8 per share 
Understanding and Managing Leverage    • 177
or $800 per contract, which would allow us to buy six contracts in all for 
$4,800. There is only $0.01 worth of time value (= $15.00 + $8.00 − $22.99) 
on these options because they are so far ITM. This means that we are pay-
ing $1 per contract worth of time value that is never recoverable, so we 
shall treat it as a realized loss. If we were to graph our potential profit and 
loss profile using this option, assuming that we are analyzing the position 
just as the 540-day options expire, we would get the following
3:
Net Gain (Loss) - Levered
0246810 12 14 16 18 20 22 24
Stock Price
Levered Strategy Overview
Gain (Loss) on Allocation
26 28 30 32 34 36 38 40 42 44 46 48 50(10,000)
(5,000)
-
5,000
10,000
Unrealized Gain
Unrealized Loss
Cash Value
Realized Loss
15,000
20,000
The most obvious differences from the diagram of the unlevered po-
sition are (1) that the net gain/loss line is kinked at the strike price and 
(2) that we will realize a total loss of invested capital—$4,800 in all—if 
Intel’s stock price closes at $15 or below. The kinked line demonstrates the 
meaning of the first point made earlier regarding option-based investment 
leverage—an asymmetrical return profile for profits and losses. Note that 
this kinked line is just the hockey-stick representation of option profit and 
loss at expiration that one sees in every book about options except this 
one. Although I don’t believe that hockey-stick diagrams are terribly useful 
for understanding individual option transactions, at a portfolio level, they 
do represent the effect of leverage very well. This black line represents a 
178  •   The Intelligent Option Investor
levered position, and its slope is much steeper than that of an equivalent 
line showing net profit and loss on an unlevered position. A comparison of 
the two net profit lines on the same graph shows this clearly:
02468 10 12 14 16 18 20 22 24
Stock Price
Profit and Loss Profile for Levered and Unlevered Investments
Gain (Loss) on Allocation
26 28 30 32 34 36 38 40 42 44 46 48 50
(10,000)
(5,000)
-
5,000
10,000
15,000
20,000
Net Gain (Loss) - Unlevered
Net Gain (Loss) - Levered
Looking at this diagram, you will notice the following things about 
the risk and return characteristics of the two positions:
Investment Maximum Loss Price
Net Profit at Fair 
Value Estimate
Stock $0 $1,472
Option $15 (2.8 × stock loss) $4,200 (3.0 × stock profit)
The leverage on the stock loss and the leverage on the stock profit are 
nearly equal in this instance because the point at which we realize a loss 
($15) is just about the same distance below the market price as our pre-
sumed fair value ($30) is above. The leverage to loss is calculated as
=Loss leverage realized loss as ap ercent of allocation
percents tock declinet or ealizedl oss
Understanding and Managing Leverage    • 179
In this example, we suffer a realized loss of 96 percent (= $4,800 ÷ 
$5,000) if the stock falls 35 percent, so the equation becomes
= − =− ×Lossleverage 96%
35% 2.8
 
(By convention, I’ll always write the loss leverage as a negative.) This 
equation just means that it takes a drop of 35 percent to realize a loss on 
96 percent of the allocation.
The profit leverage is simply a ratio of the levered portfolio’s net profit 
to the unlevered portfolio’s net profit at the fair value estimate. For this 
example, we have
== ×Profitleverage $4,200
$1,472 3.0
 
Let’s do the same exercise for the ATM and OTM options and see 
what fully levered portfolios with each of these options would look like 
from a risk-return perspective. If we bought as many $22-strike options as 
a $5,000 position size would allow (19 contracts in all), our profit and loss 
graph and table would look like this:
02468 10 12 14 16 18 20 22 24
Stock Price
Levered Strategy Overview
Gain (Loss) on Allocation
26 28 30 32 34 36 38 40 42 44 46 48 50(20,000)
-
40,000
60,000
80,000
100,000
20,000
Unrealized Gain
Unrealized Loss
Cash Value
Net Gain (Loss) - Levered
Realized Loss
180  •   The Intelligent Option Investor
Instrument Maximum-Loss Price Net Profit at Fair Value Estimate
Stock $0 $1,472
Option $22 (23.2 × stock loss) $10,203 (6.9 × stock profit)
This is quite a handsome potential profit—6.9 times higher than we 
could earn using a straight stock position—but at an enormous risk. Each 
$1 drop in the stock price equates to a $23.20 drop in the value of the posi-
tion. Note that the realized loss shows a step up from $22 to $23. This just 
shows that above the strike price, our only realized loss is the money we 
spent on time value.
The last example is that of the fully levered OTM call options. Here is 
the table illustrating this case:
Instrument Maximum-Loss Price Net Profit at Fair Value Estimate
Stock $0 $1,472
Option $25 (IRL 5 percent) $12,495 (8.5 × stock profit)
There is no intrinsic value to this option, so the entire cost of  
the option is treated as an immediate realized loss (IRL) from inception. 
The “IRL 5 percent” notation means that there is an immediate realized 
loss of 5 percent of the total portfolio. The maximum net loss is again at 
the strike price of $25. The leverage factor at our fair value estimate price 
is 8.5, but again this leverage comes at the price of having to realize a  
5 percent loss on your portfolio—500 basis points of performance—and 
there is no certainty that you will have enough or any profits to offset this 
realized loss.
Of course, investing choices are not as black and white as what I have 
presented here. If you want to commit 5 percent of your portfolio to a 
straight stock idea, you have to spend 5 percent of your portfolio value on 
stock, but this is not true for options. For example, I might choose to spend 
2.5 percent of my portfolio’s worth on ATM calls (nine contracts in this ex-
ample), considering the position in terms of a 5 percent stock investment, 
and then leave the rest as cash reserve. Here is what this investment would 
look like from a leverage perspective:
Understanding and Managing Leverage    • 181
02468 10 12 14 16 18 20 22 24
Stock Price
Levered Strategy Overview
Gain (Loss) on Allocation
26 28 30 32 34 36 38 40 42 44 46 48 50(5,000)
-
15,000
10,000
20,000
25,000
30,000
5,000
Unrealized Gain
Unrealized Loss
Cash Value
Net Gain (Loss) - Levered
Realized Loss
Instrument Maximum-Loss Price Net Profit at Fair Value Estimate
Stock $0 $1,472
Option $22 (11 × stock loss) $4,833 (5.1 × stock profit)
The 11 times loss figure was calculated in the following way: there is a 
total of 47.3 percent of my allocation to this investment that is lost if the price 
of the stock goes down by 4.3 percent, so −47.3 percent/4.3 percent = −11.0. 
Obviously, this policy of keeping some cash in reserve represents a sensible ap-
proach to portfolio management when leverage is used. An investor in straight 
stock who makes 20 investments that do not hit his or her expected fair value 
within the investment horizon might have a few bad years of performance, but 
an investor who uses maximum option leverage and allocates 5 percent to 20 
ideas will end up bankrupt if these don’t work out by expiration time!
Similar to setting a cash reserve, you also might decide to make an 
investment that combines cash, stock, and options. For example, I might 
buy 100 shares of Intel, three ITM option contracts, and leave the rest of 
my 5 percent allocation in cash. Here is what that profit and loss profile 
would look like:
182  •   The Intelligent Option Investor
0 24681 01 21 41 61 82 02 22 4
Stock Price
Levered Strategy Overview
Gain (Loss) on Allocation
26 28 30 32 34 36 38 40 42 44 46 48 50(6,000)
(4,000)
(2,000)
-
4,000
2,000
6,000
10,000
12,000
8,000 Unrealized Gain
Unrealized Loss
Cash Value
Net Gain (Loss) - Levered
Realized Loss
Instrument Maximum-Loss Price Net Profit at Fair Value Estimate
Stock $0 $1,472
Option $15 (1.8 × stock loss) $3,803 (2.6 × stock profit)
Three $800 option contracts represent $2,400 of capital or 48 percent of 
this allocation’s capital. Thus 48 percent of the capital was lost with a 34.8 per-
cent move downward in the stock, generating a −1.4 times value for the options 
plus we add another −0.4 times value to represent the loss on the small stock 
allocation; together these generate the −1.8 times figure you see on the loss side. 
Of course, if the option loss is realized, we still own 100 shares, so the maximum 
loss will not be felt until the shares hit $0, as shown in the preceding diagram.
For the remainder of this book I will describe leverage positions us-
ing the two following terms: loss leverage and profit leverage . I will write 
these in the following way: 
− X.x
Y.y
where the first number will be the loss leverage ratio, and the second 
number will be the profit leverage ratio based on the preceding rules that 
Understanding and Managing Leverage    • 183
I’ve used for calculation. All OTM options will be marked with an IRL fol-
lowed by the percentage of the total portfolio used in the option purchase 
(not the percentage of the individual allocation but the total percentage 
amount of your investment capital). On my website, you’ll find an online 
leverage tool that allows you to calculate these numbers yourself.
Managing Leverage
A realized loss is, to me, serious business. There are times when an inves-
tor must take a realized loss—specifically when his or her view of the fair 
value or fair value range of a company changes materially enough that an 
investment position becomes unattractive. However, if you find yourself 
taking realized losses because of material changes in valuation too often, 
you should either figure out where you are going wrong in the valuation 
process or just put your money into a low-load mutual fund and spend 
your time doing something more productive.
The point is that taking a realized loss is not something you have to do 
too often if you are a good investor, and hopefully, when those losses are taken, 
they are small. As such, I believe that there are two ways to successfully manage 
leverage. First is to use leverage sparingly by investing in combinations of ITM 
options and stocks. ITM option prices mainly represent intrinsic value, and be-
cause the time-value component is that which represents a realized loss right out 
of the gate, buying ITM options means that you are minimizing realized losses.
The second method for managing leverage when you cannot resist 
taking a higher leverage position is spending as little as possible of your 
investment capital on it. This means that when you see that there is a com-
pany that has a material chance of being worth a lot more or a lot less than 
it is traded for at present but that material chance is still much less likely 
than other valuation scenarios, you should invest your capital in the idea 
sparingly. By making smaller investments with higher leverage, you will 
not realize a loss on too much of your capital at one time, and if you are 
right at least some of the time on these low-probability, high-potential-
reward bets, you will come out ahead in the end.
Of course, you also can use a combination of these two methods. For 
example, I have found it helpful to take the main part of a position using a 
184  •   The Intelligent Option Investor
combination of stock and ITM call options but also perhaps buying a few 
OTM call options as well. As the investment ages and more data about the 
company’s operations come in, if this information leads me to be more 
bullish about the prospects of the stock, I may again increase my leverage 
using OTM call options—especially when I see implied volatility trading at 
a particularly low level or if the stock price itself is depressed because of a 
generally weak market. 
I used to be of the opinion that if you are confident in your valuation 
and your valuation implies a big enough unlevered return, it is irrational 
not to get exposure to that investment with as much leverage as possible. 
A few large and painful losses of capital have convinced me that where-
as levering up on high-conviction investments is theoretically a rational 
investment regime, practically, it is a sucker’s game that is more likely to 
deplete your investment capital than it is to allow you to hit home runs.
Y ounger investors, who still have a long investing career ahead of 
them and plenty of time to make up for mistakes early on, probably can 
feel more comfortable using more leverage, but as you grow closer to the 
time when you need to use your investments (e.g., paying for retirement, 
kids’ college expenses, or whatever), using lower leverage is better.
Looking back at the preceding tables, one row in one table in particular 
should stand out to you. This is the last row of the last table, where the leverage is 
−1.8/2.6. To me, this is a very attractive leverage ratio because of the asymmetry 
in the risk-reward balance. This position is levered, but the leverage is lopsided 
in the investor’s favor, so the investor stands to win more than he or she loses. 
This asymmetry is the key to successful investing—not only from a 
leverage standpoint but also from an economic standpoint as well. I believe 
an intelligent, valuation-centric method for investing in companies such as 
the ones outlined in this book that allow investors an edge up by allowing 
them to identify cases in which the valuation simply does not line up with 
the market price. This in itself presents an asymmetrical profit opportunity, 
and the real job of an intelligent investor is to find as large an asymmetry 
as possible and courageously invest in that company. If you can also tailor 
your leverage such that your payout is asymmetrical in your favor as well, 
this only adds potential for outsized returns, in my opinion.
The other reason that the −1.8/2.6 leverage ratio investment interests 
me is because of the similarity it has to the portfolio of Warren Buffett’s 
Understanding and Managing Leverage    • 185
Berkshire Hathaway (BRK.A). In a recent academic paper written by re-
searchers at AQR Capital titled, “Buffett’s Alpha, ”4 the researchers found 
that a significant proportion of Buffett’s legendary returns can be attributed 
to finding firms that have low valuation risk and investing in them using a 
leverage ratio of roughly 1.8. The leverage comes from the float from his in-
surance companies (the monies paid in premium by clients over and above 
that required to pay out claims). As individual investors, we do not have a 
captive insurance company from which we can receive continual float, but 
by buying options and using leverage prudently, it is possible to invest in a 
manner similar to a master investor.
In this section, we have only discussed leverage considerations when 
we gain exposure by buying options. There is a good reason to ignore the 
case where we are accepting exposure by selling options that we will dis-
cuss when we talk about margining in Chapter 10. We now continue with 
chapters on gaining, accepting, and mixing exposure. In these chapters, we 
will use all of what we have learned about option pricing, valuation, and 
leverage to discuss practical option investment strategies.
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187
Chapter 9
GaininG ExposurE
This chapter is designed as an encyclopedic listing of the main strategies 
for gaining exposure (i.e., buying options) that an intelligent option inves-
tor should understand. Gaining exposure seems easy in the beginning be-
cause it is straightforward—simply pay your premium up front, then if the 
stock moves into your option’s range of exposure by expiration time, you 
win. However, the more you use these strategies in investing exposure, the 
more nuances arise.
What tenor should I choose? What strike price should I choose? 
Should I exercise early if my option is in the money (ITM)? How much 
capital should I commit to a given trade? If the stock price goes in the 
opposite direction from my option’s range of exposure, should I close 
my option position? All these questions are examples of why gaining 
exposure by buying options is not as straightforward a process as it 
may seem at first and are all the types of questions I will cover in the 
following pages.
Gaining exposure means buying options, and the one thing that an 
option buyer must never lose sight of is that time is always working against 
him or her. Options expire. If your options expire out of the money (OTM), 
the capital you spent on premiums on those options is a realized loss. No 
matter how confident you are about your valuation call, you should al-
ways keep this immutable truth of option buying in mind. Indeed, there 
are ways to reduce the risk of this happening or to manage a portfolio in 
188  •   The Intelligent Option Investor
such a way that such a loss of capital becomes just a cost of doing business 
that will be made up for in another investment down the line.
For each of the strategies mentioned in this chapter, I present 
a stylized graphic representing the Black-Scholes-Merton model 
(BSM) cone and the option’s range of exposure plus best- and worst-
case valuation scenarios. These are two of the required inputs for an 
intelligent option investing strategy—an intelligently determined valu-
ation range and the mechanically determined BSM forecast range. I will 
also provide a summary of the relative pricing of upside and downside 
exposure vis-à-vis an intelligent valuation range (e.g., “Upside expo-
sure is undervalued”), the steps taken to execute the strategy, and its 
potential risks and return.
After this summary section, I provide textual discussions of tenor se-
lection, strike price selection, portfolio management (i.e., rolling, exercise, 
etc.), and any miscellaneous items of interest to note. Understanding the 
strategies well and knowing how to use the tools at your disposal to tilt 
the balance of risk and reward in your favor are the hallmark and pinnacle 
of intelligent option investing. Intelligent option investors gain exposure 
when the market underestimates the likelihood of a valuation that the in-
vestor believes is a rational outcome. In graphic terms, this means that ei-
ther one or both of the investor’s best- and worst-case valuation scenarios 
lie outside the BSM cone.
Simple (one-option) strategies to gain exposure include
•	Long calls
•	Long puts
Complex (multioption) strategies to gain exposure include
•	Long strangles
•	Long straddles
Jargon introduced in this chapter includes the following:
Roll
Ratio(ing)
Gaining Exposure 	 	•	 189
Long Call
GREEN
Downside: Fairly priced
Upside: Undervalued
Execute: Buy a call option
Risk: Amount equal to premium paid
Reward: Unlimited less amount of premium paid
The Gist
An investor uses this strategy when he or she believes that there is a material 
chance that the value of a company is much higher than the present market price. 
The investor must pay a premium to initiate the position, and the proportion of 
the premium that represents time value should be recognized as a realized loss 
because it cannot be recovered. If the stock fails to move into the area of exposure 
before option expiration, there will be no profit to offset this realized loss.
In economic terms, this transaction allows an investor to go long an 
undervalued company without accepting an uncertain risk of loss if the 
stock falls. Instead of the uncertain risk of loss, one must pay the fixed pre-
mium. This strategy obeys the same rules of leverage as discussed earlier 
in this book, with in-the-money (ITM) call options offering less leverage 
but being much more forgiving regarding timing than are at-the-money 
(ATM) or especially out-of-the-money (OTM) options. 
190  •   The Intelligent Option Investor
T enor Selection
In general, the rule for gaining exposure is to buy as long a tenor as is 
available. If a stock moves up faster than you expected, the option will still 
have time value left on it, and you can sell it to recoup the extra money you 
spent to buy the longer-tenor option. In addition, long-tenor options are 
usually proportionally less expensive than shorter-tenor ones. Y ou can see 
this through the following table. These ask prices are for call options on 
Google (GOOG) struck at whatever price was closest to the 50-delta mark 
for every tenor available.
Days to Expiration Ask Price Marginal Price/Day Delta
3 6.00 2.00 52
10 10.30 0.61 52
17 12.90 0.37 52
24 15.50 0.37 52
31 17.70 0.31 52
59 22.40 0.17 49
87 34.40 0.43 50
150 42.60 0.13 50
178 47.30 0.17 50
241 56.00 0.14 50
542 86.40 0.10 50
The “Marginal Price/Day” column is simply the extra that you pay to get 
the extra days on the contract. For example, the contract with three days left is 
$6.00. For seven more days of exposure, you pay a total of $4.30 extra, which 
works out to a per-day rate of $0.61. We see blips in the marginal price per 
day field as we go from 59 to 87 to 150 days, but these are just artifacts of data 
availability; the closest strikes did not have the same delta for each expiration.
The preceding chart, it turns out, is just the inverse of the rule we 
already learned in Chapter 3: “time value slips away fastest as we get closer 
to expiration. ” If time value slips away more quickly nearer expiration, it 
must mean that the time value nearer expiration is proportionally worth 
more than the time value further away from expiration. The preceding 
table simply illustrates this fact.
Gaining Exposure 	 	•	 191
Value investors generally like bargains and to buy in bulk, so we 
should also buy our option time value “in bulk” by buying the longest 
tenor available and getting the lowest per-day price for it. It follows that if 
long-term equity anticipation securities (LEAPS) are available on a stock, 
it is usually best to buy one of those. LEAPS are wonderful tools because, 
aside from the pricing of time value illustrated in the preceding table, if 
you find a stock that has undervalued upside potential, you can win from 
two separate effects:
1. The option market prices options as if underlying stocks were ef-
ficiently priced when they may not be (e.g., the market thinks that 
the stock is worth $50 when it’s worth $70). This discrepancy gives 
rise to the classic value-investor opportunity.
2. As long as interest rates are low, the drift term understates the ac-
tual, probable drift of the stock market of around 10 percent per 
year. This effect tends to work for the benefit of a long-tenor call 
option whether or not the pricing discrepancy is as profound as 
originally thought.
There are a couple of special cases in which this “buy the longest 
tenor possible” rule of thumb should not be used. First, if you believe 
that a company may be acquired, it is best to spend as little on time value 
as possible. I will discuss this case again when I discuss selecting strike 
prices, but when a company agrees to be acquired by another (and the 
market does not think there will be another offer and regulatory approv-
als will go through), the time value of an option drops suddenly because 
the expected life of the stock as an independent entity has been short-
ened by the acquiring company. This situation can get complicated for 
stock-based acquisitions (i.e., those that use stocks as the currency of 
acquisition either partly or completely) because owners of the acquiree’s 
options receive a stake in the acquirer’s options with strike price adjusted 
in proportion to the acquisition terms. In this case, the time value on 
your acquiree options would not disappear after the acquisition but be 
transferred to the acquirer’s company’s options. The real point is that it 
is impossible, as far as I know, to guess whether an acquisition will be 
made in cash or in shares, so the rule of thumb to buy as little time value 
as possible still holds.
192  •   The Intelligent Option Investor
In general, attempting to profit from potential mergers is dif-
ficult using options because you have to get both the timing of the 
suspected transaction and the acquisition price correct. I will discuss 
a possible solution to this situation in the next section about picking 
strike prices.
The second case in which it is not necessary to buy as long a tenor as 
possible is when you are trading in expectation of a particular company 
announcement. In general, this game of anticipating stock price move-
ments is a hard one to win and one that value investors usually steer clear 
of, but if you are sure that some announcement scheduled for a particular 
day or week is likely to occur but do not want to make a long-term invest-
ment on the company, you can buy a shorter-tenor option that obviously 
must include the anticipated announcement date. It is probably not a bad 
idea to build in a little cushion between your expiration and the anticipated 
date of the announcement because sometimes announcements are pushed 
back and rescheduled.
Strike Price Selection 
From the discussion regarding leverage in the preceding section, it is 
clear that selecting strike prices has a lot to do with selecting what level 
of leverage you have on any given bet. Ultimately, then, strike selec-
tion—the management of leverage, in other words—is intimately tied 
to your own risk profile and the degree to which you are risk averse or 
risk seeking.
My approach, which I will talk more about in the following section 
on portfolio management, may be too conservative for others, but I put it 
forward as one alternative among many that I have found over time to be 
sensible. Any investment has risk to the extent that there is never perfect 
certainty regarding a company’s valuation. Some companies have a fairly 
tight valuation range—meaning that the confluence of their revenue stream, 
profit stream, and investment efficacy does not vary a great deal from best to 
worst case. Other companies’ valuation ranges are wide, with a few clumps 
of valuation scenarios far apart or with just one or two outlying valuation 
scenarios that, although not the most likely, are still materially probable.
Gaining Exposure 	 	•	 193
On the rare occasion in which we find a company that has a valuation 
range that is far different from the present market price (either tight 
or wide), I would rather commit more capital to the idea, and for me, 
committing more capital to a single idea means using less leverage. In other 
words, I would prefer to buy an ITM call and lever at a reasonable rate (e.g., 
the −1.8 × /2.6 × level we saw in the Intel example earlier). Graphically, my 
approach would look like this:
Advanced Building Corp. (ABC)
110
100
90
80
70
60
50
40
30
20
5/18/2012 5/20/2013 249 499 749 999
Date/Day Count
Stock Price
GREEN
ORANGE
Here I have bought a deep ITM call option LEAPS that gives me lev-
erage of about −1.5/2.0. I have maximized my tenor and minimized my 
leverage ratio with the ITM call. This structure will allow me to profit as 
long as the stock goes up by the time my option expires, even if the stock 
price does not hit a certain OTM strike price.
In the more common situation, in which we find a company that is 
probably about fairly valued in most scenarios but that has an outlying 
valuation scenario or two that doesn’t seem to be priced in properly by 
the market, I will commit less capital to the idea but use more leverage. 
Graphically, my approach would look more like this:
194  •   The Intelligent Option Investor
Advanced Building Corp. (ABC)
100
90
80
70
60
50
40
30
20
5/18/2012 5/20/2013 249 499 749 999
Date/Day Count
Stock Price
GREEN
Here I have again maximized my tenor by buying LEAPS, but this 
time I increase my leverage to something like an “IRL/10.0” level in case 
the stars align and the stock price sales to my outlier valuation. 
Some people would say that the IIM approach is absolutely the op-
posite of a rational one. If you are—the counterargument goes—confident 
in your valuation range, you should try to get as much leverage on that idea 
as possible; buying an ITM option is stupid because you are not using the 
leverage of options to their fullest potential. This counterargument has its 
point, but I find that there is just too much uncertainty in the markets to be 
too bold with the use of leverage. 
Options are time-dependent instruments, and if your option expires 
worthless, you have realized a loss on whatever time value you original-
ly spent on it. Economies, now deeply intertwined all over the globe, are 
phenomenally complex things, so it is the height of hubris to claim that 
I can perfectly know what the future value of a firm is and how long it will 
take for the market price to reflect that value. In addition, I as a human 
decision maker am analyzing the world and investments through a con-
genital filter based on behavioral biases.
Retaining my humility in light of the enormous complexity of the 
marketplace and my ingrained human failings and expressing this humility 
Gaining Exposure 	 	•	 195
by using relatively less leverage when I want to commit a significant amount 
of capital to an idea constitute, I have found, given my risk tolerance and 
experience, the best path for me for a general investment.
In contrast, we all have special investment loves or wild hares or 
whatever, and sometimes we must express ourselves with a commitment 
of capital. For example, “If XYZ really can pull it off and come up with a 
cure for AIDS, its stock will soar. ” In instances such as these, I would rather 
commit less capital and express my doubt in the outcome with a smaller 
but more highly levered bet. If, on average, my investment wild hares come 
true every once in a while and, when they do, the options I’ve bought on 
them pay off big enough to more than cover my realized losses on all those 
that did not, I am net further ahead in the end.
These rules of thumb are my own for general investments. In the spe-
cial situation of investing in a possible takeover target, there are a few extra 
considerations. A company is likely to be acquired in one of two situations: 
(1) it is a sound business with customers, product lines, or geographic 
exposure that another company wants, or (2) it is a bad business, either 
because of management incompetence, a secular decline in the business, or 
something else, but it has some valuable asset(s) such as intellectual prop-
erty that a company might want to have.
If you think that a company of the first sort may be acquired, I be-
lieve that it is best to buy ITM call options to attempt to minimize the time 
value spent on the investment (you could also sell puts, and I will discuss 
this approach in Chapter 10). In this case, you want to minimize the time 
value spent because you know that the time value you buy will drain away 
when a takeover is announced and accepted. By buying an ITM contract, 
you are mainly buying intrinsic value, so you lose little time value if and 
when the takeover goes through. If you think that a company of the second 
sort (a bad company in decline) may be acquired, I believe that it is best to 
minimize the time value spent on the investment by not buying a lot of call 
contracts and by buying them OTM. In this case, you want to minimize the 
time value spent using OTM options by limiting the number of contracts 
bought because you do not want to get stuck losing too much capital if 
and when the bad company’s stock loses value while you are holding the 
options. Typical buyout premiums are in the 30 percent range, so buy-
ing call options 20 percent OTM or so should generate a decent profit if 
196  •   The Intelligent Option Investor
the company is taken out. Just keep in mind that the buyout premium is 
30 percent over the last price, not 30 percent over the price at which you 
decided to make your investment. If you buy 20 percent OTM call options 
and the stock decreases by 10 percent before a 30 percent premium buyout 
is announced, you will end up with nothing, as shown in the following 
timeline:
$12-Strike Options Bought When the Stock Is Trading for $10
•	Stock falls to $9.
•	Buyout is announced at 30 percent above last price—$11.70.
•	12-strike call owner’s profit = $0.
However, there is absolutely no assurance that an acguirer will pay some-
thing for a prospective acguiree. Depending on how keen the acquirer is to get 
its hands on the assets of the target, it may actually allow the target company 
to go bankrupt and then buy its assets at $0.30 on the dollar or whatever. It is 
precisely this uncertainty that makes it unwise to commit too much capital to 
an idea involving a bad company—even if you think it may be taken out.
Portfolio Management
I like to think of intelligent option investing as a meal. In our investment 
meal, the underlying instrument—the stock—should, in most cases, form 
the main course. 
People have different ideas about diversification in a securities portfolio 
and about the maximum percentage of a portfolio that should be allocated to 
a specific idea. Clearly, most people are more comfortable allocating a greater 
percentage of their portfolio to higher-confidence ideas, but this is normal-
ly framed in terms of relative levels (i.e., for some people, a high-conviction 
idea will make up 5 percent of their portfolio and a lower-conviction one  
2.5 percent; for others, a high-conviction idea will make up 20 percent of their 
portfolio and a lower-conviction one 5 percent). Rather than addressing what 
size of investment meal is best to eat, let’s think about the meal’s composition.
Considering the underlying stock as the main course, I consider the 
leverage as sauces and side dishes. ITM options positions are the main 
Gaining Exposure 	 	•	 197
sauce to make the main course more interesting and flavorful. Y ou can 
layer ITM options onto the stock to increase leverage to a level with which 
you feel comfortable. This does not have to be Buffett’s 1.8:1 leverage of 
course. Levering more lightly will provide less of a kick when a company 
performs according to your best-case scenario, but also carries less risk 
of a severe loss if the company’s performance is mediocre or worse. OTM 
option positions (and “long diagonals” to be discussed in Chapter 11) can 
be thought of as a spicy side dish to the main meal. They can be added 
opportunistically (when and if the firm in which you are investing has a 
bad quarter and its stock price drops for temporary reasons involving sen-
timent rather than substance) for extra flavor. OTM options can also be 
used as a snack to be nibbled on between proper meals. Snack, in this case, 
means a smaller sized position in firms that have a small but real upside 
potential but a greater chance that it is fairly valued as is, or in a company 
in which you don’t have the conviction in its ability to create much value 
for you, the owner. 
Another consideration regarding the appropriate level of investment 
leverage one should apply to a given position is how much operational 
and financial leverage (both are discussed in detail in Appendix B) a firm 
has. A firm that is highly levered will have a much wider valuation range 
and will be much more likely to be affected by macroeconomic considera-
tions that are out of the control of the management team and inscrutable 
to the investor. In these cases, I think the best response is to adjust one’s 
investment leverage according to the principles of “margin of safety” and 
contrarianism. 
By creating a valuation range, rather than thinking only of a single point-
estimate for the value of the firm, we have unwittingly allowed ourselves to 
become very skillful at picking appropriate margins of safety. For example, I 
recently looked at the value of a company whose stock was trading for around 
$16 per share. The company had very high operational and financial lever-
age, so my valuation range was also very large—from around $6 per share 
worst case to around $37 per share best case with a most likely value of around  
$25 per share. The margin of safety is 36 percent (=  ($25 −  $16)/ $25). 
While some might think this is a reasonable margin of safety to take a bold, 
concentrated position, I elected instead to take a small, unlevered one because 
to me, the $9 margin of safety for this stock is still not wide enough. The best 
198  •   The Intelligent Option Investor
time to take a larger position and to use more leverage is when the market is 
pricing a stock as if it were almost certain that a company will face a worst-case 
future when you consider this worst-case scenario to be relatively unlikely. In 
this illustration, if the stock price were to fall by 50 percent—to the $8 per share 
level—while my assessment of the value of the company remained unchanged 
(worst, likely, and best case of $6, $25, and $37, respectively), I would think I 
had the margin of safety necessary to commit a larger proportion of my portfo-
lio to the investment and add more investment leverage. With the stock sitting 
at $8 per share, my risk ($8 − $6 = $2) is low and unlikely to be realized while 
my potential return is large and much closer to being assured. With the stock’s 
present price of $16 per share, my risk ($16 − $6 = $10) is large and when bad-
case scenarios are factored in along with the worst-case scenario, more likely 
to occur.
Thinking of margins of safety from this perspective, it is obvious that 
one should not frame them in terms of arbitrary levels (e.g., “I have a rule 
to only buy stocks that are 30% or lower than my fair value estimate. ”), but 
rather in terms informed by an intelligent valuation range. In this example, 
a 36 percent margin of safety is sufficient for me to commit a small 
proportion of my portfolio to an unlevered investment, but not to go “all 
in. ” For a concentrated, levered position in this investment, I would need a 
margin of safety approaching 76 percent (= ($25 − $6)/$25) and at least over  
60 percent (= ($25 - $10)/$25).
When might such a large margin of safety present itself? Just when 
the market has lost all hope and is pricing in disaster for the company. 
This is where the contrarianism comes into play. The best time to make 
a levered investment in a company with high levels of operational lever -
age is when the rest of the market is mainly concerned about the possible 
negative effects of that operational leverage. For example, during a reces-
sion, consumer demand drops and idle time at factories increases. This 
has a quick and often very negative effect on profitability for companies 
that own the idle factories, and if conditions are bad enough or look to 
have no near-term (i.e., within about six months) resolution, the price of 
those companies’ stocks can plummet. Market prices often fall so low as to 
imply, from a valuation perspective, that the factories are likely to remain 
idled forever. In these cases, I believe that not using investment leverage in 
this case may carry with it more real risk than using  investment leverage 
Gaining Exposure 	 	•	 199
(see my discussion of risk in Chapter 12 after reading the paragraphs below 
about financial leverage).
In boom times, just the opposite is true. Factories are nearing full 
capacity and demand is strong. Most of the market is thinking only of the 
extra percentage points of profit that can be squeezed out of the opera-
tions when continuing strong demand pushes factory capacity even higher. 
As every contrarian knows, this is precisely the wrong time to fall in love 
with the stock of an operationally levered company; it is also precisely the 
wrong time to use investment leverage to gain exposure to the stock of an 
operationally levered company.
Financial leverage is more dangerous and requires a much more care-
ful consideration of valuation scenarios, especially if the economy is in or is 
going into recession. In recessions, consumer demand for products slows, 
but banks’ and bondholders’ demand for interest and principal payments 
continues unabated. If demand is so low that a company is not generating 
enough cash flow to pay interest on its debt, or if it can pay interest on its 
debt but does not have enough cash on hand to pay an entire principal pay-
ment (and banks refuse to finance that payment), the equity of the com-
pany will be worth nothing. As Buffett has so eloquently wrote in the 2010 
annual letter to Berkshire Hathaway shareholders, “[A]ny series of positive 
numbers, however impressive the numbers may be, evaporates when mul-
tiplied by a single zero. ” It doesn’t matter how great a given business may 
be during boom times; if its equity value falls to zero during bad times, the 
owner of the company’s stock will lose his or her entire investment.
One sad fact of life is that in many cases, companies with great op-
erational leverage (e.g., those that own factories) have funded this leverage 
through the issuance of debt—hereby layering financial leverage onto oper-
ational leverage. Because financial leverage represents such a severe risk to 
equity investors during bust times, and because it is devilishly hard to know 
when the next bust time might come, I personally think that using less in-
vestment leverage on companies fitting this profile is generally prudent.
Let us assume that you have decided on the composition of an investment 
meal and dug in using your chosen allocation size and leverage level. How do 
you know when to stop “eating” and close all or part of your position? Or con-
versely, what should you do when you realize that the meal is more delicious 
than you had originally imagined? These are natural questions to ask. 
200  •   The Intelligent Option Investor
After you enter a position and some time passes, it becomes clearer 
what valuation scenario the company is tending toward. In some cases, 
a bit of information will come out that is critical to your valuation of the 
company on which other market participants may not be focused. Obvi-
ously, if a bit of information comes out that has a big, positive or negative 
impact on your assessment of the company’s value, you should adjust your 
position size accordingly. If you believe the impact is positive, it makes 
sense to build to a position by increasing your shares owned and/or by 
adding “spice” to that meal by adjusting your target leverage level. If the 
impact is negative, it makes sense to start by reducing leverage (or you 
can think of it as increasing the proportion of cash supporting a particular 
position), even if this reduction means realizing a loss. If the impact of the 
news is so negative that the investment is no longer attractive from a risk-
reward perspective, I believe that it should be closed and the lumps taken 
sooner rather than later. Considering what we know about prospect theory, 
this is psychologically a difficult thing to do, but in my experience, waiting 
to close a position in which you no longer have confidence seldom does 
you any good.
Obviously, the risk/reward equation of an investment is also influ-
enced by a stock’s market price. If the market price starts scraping against 
the upper edge of your valuation range, again, it is time to reduce leverage 
and/or close the position.
If your options are in danger of expiring before a stock has reached 
your fair value estimate, you may roll your position by selling your option 
position and using the proceeds to buy another option position at a more 
distant tenor. At this time, you must again think about your target leverage 
and adjust the strikes of your options accordingly. If the price of the stock 
has decreased over the life of the option contract, this will mean that you 
realize a loss, which is not an easy thing to do psychologically, but consid-
ering the limitations imposed by time for all option investments, this is an 
unavoidable situation in this case.
One of the reasons I dislike investing in non-LEAPS call options is 
that rolling means that not only do we have to pay another set of bro-
ker and exchange fees, but we also must pay both sides of the bid-ask 
spread. Keeping in mind how wide the bid-ask spread can be with options 
and what an enormous drag this can be on returns, you should carefully 
Gaining Exposure 	 	•	 201
consider whether the prospective returns justify entering a long call posi-
tion that will likely have to be rolled multiple times before the stock hits 
your fair value estimate.
By the way, it goes without saying that to the extent that an option 
you want to roll has a significant amount of time value on it, it is better 
to roll before time decay starts to become extreme. This usually occurs at 
around three months before expiration. It turns out that option liquidity 
increases in the last three months before expiration, and rolling is made 
easier with the greater liquidity.
Having discussed gaining bullish exposure with this section about 
long calls, let’s now turn to gaining bearish exposure in the following sec-
tion on long puts.
Long Put
GREEN
Downside: Undervalued
Upside: Fairly priced
Execute: Buy a put option
Risk: Amount of premium paid
Reward: Amount equal to strike price—premium
The Gist
An investor uses this strategy when he or she believes that it is very likely 
that the value of a company is much lower than the present market price. 
The investor must pay a premium to initiate the position, and the propor-
tion of the premium that represents time value should be recognized as a 
202  •   The Intelligent Option Investor
realized loss because it cannot be recovered. If the stock fails to move into 
the area of exposure before option expiration, there will be no profit to 
offset this realized loss.
In economic terms, this transaction allows an investor to sell short 
an overvalued company without accepting an uncertain risk of loss if the 
stock rises. Instead of the uncertain risk of loss, the investor must pay the 
fixed premium. This strategy obeys the same rules of leverage as discussed 
earlier in this book, with ITM put options offering less leverage but a great-
er cushion before realizing a loss than do ATM or OTM put options.
T enor Selection
Shorting stocks, which is what you are doing when you buy put op-
tions, is hard work, not for the faint of heart. There are a couple of 
reasons for this:
1. Markets generally go up, and for better or worse, a rising tide usu-
ally does lift all boats.
2. Even when a company is overvalued, it is hard to know what cata-
lyst will make that fact obvious to the rest of the market and when.
In the words of Jim Chanos, head of the largest short-selling hedge fund 
in the world, the market is a “giant positive reinforcement machine. ”
1 
It is psychologically difficult to hold a bearish position when it seems 
like the whole world disagrees with you. All these difficulties in taking 
bearish positions are amplified by options because options are levered 
instruments, and losses feel all the more acute when they occur on a 
levered position.
My rule for gaining bullish exposure is to pick the longest-tenor op-
tion possible. I made the point that by buying LEAPS, you can enjoy a 
likely upward drift that exceeds the drift assumed by option pricing. When 
buying puts, you are on the opposite side of this drift factor (i.e., the “ris-
ing tide lifts all boats” factor), and every day that the stock does not fall is 
another day of time value that has decayed without you enjoying a profit. 
On the other hand, if you decide not to spend as much on time value and 
buy a shorter-tenor put option, unless the market realizes that the stock is 
Gaining Exposure 	 	•	 203
overvalued and it drops before the shorter option expires, you must pay the 
entire bid-ask spread and the broker and exchange fees again when you roll 
your put option.
The moral of the story is that when selecting tenors for puts, you need 
to balance the existence of upward market drift (which lends weight to the 
argument for choosing shorter tenors) with bid-ask spreads and other fees 
(which lends weight to the argument for longer tenors). If you can iden-
tify a catalyst, you can plan the tenor of the option investment based on 
the expected catalyst. However, it’s unfortunate but mysteriously true that 
bearish catalysts have a tendency to be ignored by the market’s “happy ma-
chine” until the instant when suddenly they are not and the shares collapse. 
The key for a short seller is to be in the game when the market realizes the 
stock’s overvaluation.
Strike Price Selection
When it comes to strike prices, short sellers find themselves fighting drift  
in much the same way as they did when selecting tenors. A short seller with 
a position in stocks can be successful if the shares he or she is short go up 
less than other stocks in the market. The short exposure acts as a hedge to 
the portfolio as a whole, and if it loses less money than the rest of the port-
folio gains, it can be thought of as a successful investment.
However, the definition for success is different for buyers of a put 
option, who must not only see their bearish bets not go up by much but 
rather must see their bearish bets fall if they are to enjoy a profit. If the 
investor wanting bearish exposure decides to gain it by buying OTM puts, 
he or she must—as we learned in the section about leverage—accept a 
realized loss as soon as the put is purchased. If, on the other hand, the 
investor wants to minimize the realized loss accepted up front, he or she 
must accept that he or she is in a levered bearish position so that every 
1 percent move to the upside for the stock generates a loss larger than 1 
percent for the position.
There is another bearish strategy that you can use by accepting 
exposure that I will discuss in the next section, but for investors who are 
gaining bearish exposure, there is no way to work around the dilemma of 
the option-based short seller just mentioned.
204  •   The Intelligent Option Investor
Portfolio Management
There is certainly no way around the tradeoff between OTM and ITM 
risk—the rules of leverage are immutable whether in a bullish or a bear -
ish investment—but there are some ways of framing the investment that 
will allow intelligent investors to feel more comfortable with making 
these types of bearish bets. First, I believe that losses associated with a 
bearish position are treated differently within our own minds than those 
associated with bullish positions. The reason for this might be the fact 
that if you decide to proactively invest in the market, you must buy se-
curities, but you need not sell shares short. The fact that you are losing 
when you are engaged in an act that you perceive as unnecessary just 
adds to a sense of regret and self-doubt that is necessarily part of the 
investing process.
In addition, investors seem to be able to accept underperform-
ing bullish investments in a portfolio context (e.g., “XYZ is losing, but 
it’s only 5 percent of my holdings, and the rest of my portfolio is up, so 
it’s okay”) but look at underperforming bearish investments as if they 
were the only investments they held (e.g., “I’m losing 5 percent on that 
damned short. Why did I ever short that stock in the first place?”). In gen-
eral, people have a hard time looking at investments in a portfolio con-
text (I will discuss this more when I talk about hedging in Chapter 11),  
but this problem seems to be orders of magnitude worse in the case of a 
bearish position.
My solution to this dilemma—perhaps not the best or most rational 
from a performance standpoint but most manageable to me from a psy-
chological one—is to buy OTM puts with much smaller position sizes than 
I might for bullish bets with the same conviction level. This means that I 
have smaller, more highly levered positions. The reason this works for me 
is that once I spend the premium on the put option, I consider the money 
gone—a sunk cost—and do not even bother to look at the mark-to-market 
value of the option after that unless there is a large drop in the stock price. 
Somehow this acknowledgment of a realized loss up front is easier to han-
dle psychologically than watching my ITM put position suffer unrealized 
losses of 1.5 times the rise of the stock every day.
This strategy may well be proof that I simply am not a natural-born 
short seller, and you are encouraged, now that you understand the issues 
Gaining Exposure 	 	•	 205
involved, to devise a method for gaining bearish exposure that fits your own 
risk profile. 
Strangle
GREEN
GREEN
Downside: Undervalued
Upside: Undervalued
Execute: Buy an OTM call option simultaneously with buying an 
OTM put option
Risk: Amount of premium paid
Reward: Unlimited on upside, limited to strike less total (two-leg) 
premium on the downside
The Gist
The strangle is used when the market is undervaluing the likelihood that a 
stock’s value is significantly above or below the present market price. It is a 
more speculative position and, because both legs are OTM, a highly lever-
aged one. It can sometimes be useful for companies such as smaller drug 
companies whose value hinges on the success or failure of a particular drug 
or for companies that have a material chance of bankruptcy but if they can 
206  •   The Intelligent Option Investor
avoid this extreme downside are worth much more than they are presently 
trading at.
The entire premium paid must be treated as a realized loss because 
it can never be recovered. If the stock fails to move into one of the areas 
of exposure before option expiration, there will be no profit to offset this 
realized loss.
There is no reason why you have to buy puts and calls in equal num-
bers. If you believe that both upside and downside scenarios are materially 
possible but believe that the downside scenario is more plausible, you can 
buy more puts than calls. This is called ratioing a position. 
T enor Selection
Because the strangle is a combination of two strategies we have already 
discussed, the considerations regarding tenor are the same as for each of 
the components—that is, using the drift advantage in long-term equity an-
ticipating securities (LEAPS) and buying them or the longest-tenor calls 
available and balancing the fight against drift and the cost of rolling and 
buying perhaps shorter-tenor puts.
Strike Price Selection
A strangle is slightly different in nature from its two components—long 
calls and long puts. A strangle is an option investor’s way of expressing 
the belief that the market in general has underestimated the intrinsic 
uncertainty in the valuation of a firm. Options are directional instru-
ments, but a strangle is a strategy that acknowledges that the investor 
has no clear idea of which direction a stock will move but only that 
its future value under different scenarios is different from its present 
market price.
Because both purchased options are OTM ones, this implies, in my 
mind, a more speculative investment and one that lends itself to taking 
profit on it before expiration. Nonetheless, my conservatism forces me to 
select strike prices that would allow a profit on the entire position if the 
stock price is at one of the two strikes at expiration. Because I am buying 
exposure to both the upside and the downside, I always like to make sure 
Gaining Exposure 	 	•	 207
that if the option expires when the stock price is at either edge of my valu-
ation range, it is far enough in-the-money to pay me back for both legs of 
the investment (plus an attractive return).
Portfolio Management
As mentioned earlier, this is naturally a more speculative style of option 
investment, and it may well be more beneficial to close the successful leg of 
the strategy before expiration than to hold the position to expiration. Com-
pared with the next strategy presented here (the straddle), the strangle ac-
tually generates worse returns if held to expiration, so if you are happy with 
your returns midway through the investment, you should close the posi-
tion rather than waiting for expiration. The exception to this rule is that if 
news comes out that convinces you that the value of the firm is materially 
higher or lower than what you had originally forecast and uncertainty in 
the other direction has been removed, you should assess the possibility of 
making a more substantial investment in the company.
One common problem with investors—even experienced and sophis-
ticated ones—is that they check the past price history of a stock and decide 
whether the stock has “more room” to move in a particular direction. The 
most important two things to know when considering an investment are its 
value and the uncertainty surrounding that value. Whether the stock was 
cheaper three years ago or much more expensive does not matter—these are 
backward-looking measures, and you cannot invest with a rear-view mirror.
One final note regarding this strategy is what to do with the unused 
leg. If the stock moves up strongly and you take profits on the call, what 
should you do with the put, in other words. Unfortunately, the unused leg is 
almost always worthless, and often it will cost more than it’s worth to close 
it. I usually keep this leg open because you never know what may happen, 
and perhaps before it expires, you will be able to close it at a better price.
This is a speculative strategy—a bit of spice or an after-dinner mint 
in the meal of investing. Don’t expect to get rich using it (if you do get rich 
using it, it means that you were lucky because you would have had to have 
used a lot of leverage in the process), but you may be pleasantly surprised 
with the boost you get from these every once in a while.
Let’s now turn briefly to a related strategy—the straddle.
208  •   The Intelligent Option Investor
Straddle
GREEN
Downside: Undervalued
Upside: Undervalued
Execute: Simultaneously buy an ATM put and an ATM call
Risk: Amount of premium paid
Reward: Unlimited?
The Gist
I include the straddle here for completeness sake. I have not included a 
lot of the fancier multioption strategies in this book because I have found 
them to be more expensive than they are worth, especially for someone 
with a definite directional view on a security. However, the straddle is re-
ferred to commonly and is deceptively attractive, so I include it here to 
warn investors against its use, if for no other reason.
The straddle shares many similarities with the strangle, of course, but 
straddles are enormously expensive because you are paying for every pos-
sible price the stock will move to over the term of the options. For example, 
I just looked up option prices for BlackBerry (BBRY), whose stock was 
trading at $9.00. For the 86 days to expiry, $9-strike calls (delta = 0.56) and 
$9-strike puts (delta = –0.44) were priced at $1.03 and $1.13, respectively.  
Gaining Exposure 	 	•	 209
The total premium of $2.16 represents 24 percent of the stock’s price, which 
means that if the implied volatility (around 60 percent) remains constant, 
the stock would have to move 24 percent before an investor even breaks 
even. It is true that during sudden downward stock price moves, implied 
volatility usually rises, so it might take a little less of a stock price move-
ment to the downside to break even. However, during sudden upside 
moves, implied volatility often drops, which would make it more difficult 
to break even to the upside.
Despite this expense, a straddle will still give an investor a lower 
breakeven point than a strangle on the same stock if held to expiration. 
The key is that a strangle will almost always generate a higher profit than 
a straddle if it is closed before expiration simply because the initial cost of 
the strangle is lower and the relative leverage of each of its legs is higher. 
This is yet another reason to consider closing a strangle  early if and when 
you are pleased with the profits made. 
If you do not know whether a stock will move up or down, the best 
you can hope for is to make a speculative bet on the company. When you 
make speculative bets, it is best to reduce the amount spent on it or you will 
whittle down all your capital on what amounts to a roulette wheel. Reduc-
ing the amount spent on a single bet is the reason an intelligent investor 
should stay away from straddles.
With all the main strategies for gaining exposure covered, let’s now 
turn to accepting exposure by selling options.
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211
Chapter 10
Accepting exposure
Brokerages and exchanges treat the acceptance of exposure by counter -
parties in a very different way from counterparties who want to gain expo-
sure. There is a good reason for this: although an investor gaining exposure 
has an option to transact in the future, his or her counterparty—an investor 
accepting exposure—has a commitment to transact in the future at the sole 
discretion of the option buyer. If the investor accepting exposure does not 
have the financial wherewithal to carry out the committed transaction, the 
broker or exchange is on the hook for the liability.
1
For example, an investor selling a put option struck at $50 per share 
is committing to buy the stock in question for $50 a share at some point 
in the future—this is the essence of accepting exposure. If, however, 
the investor does not have enough money to buy the stock at $50 at 
some point in the future, the investor’s commitment to buy the shares is 
economically worthless.
To guard against this eventuality, brokers require exposure-accepting 
investors to post a security deposit called margin that will fully cover the fi-
nancial obligation to which the investor is committing. In the preceding ex-
ample, for instance, the investor would have to keep $5,000 (= $50 per share × 
100 shares/contract) in reserve and would not be able to spend those reserved 
funds for stock or option purchases until the contract has expired worthless.
Because of this margin requirement, it turns out that one of our strat-
egies for accepting leverage—short puts—always carries with it a loss lev-
erage of –1.0—exactly the same as the loss leverage of a stock. Think about 
it this way: what difference is there between using $50 to buy a stock and 
212  •   The Intelligent Option Investor
setting $50 aside in an escrow account you can’t touch and promising that 
you will buy the stock with the escrow funds in the future if requested to 
do so? From a risk perspective, “very little” is the answer. 
Short calls are more complicated, but I will discuss the leverage car -
ried by them using elements of the structure I set forth in Chapter 8. In the 
following overviews, I add one new line item to the tables that details the 
margin requirements of the positions.
Intelligent option investors accept exposure when the market over -
estimates the likelihood of a valuation that the investor believes is not a 
rational outcome. In graphic terms, this means that either one or both of 
the investor’s best- and worst-case valuation scenarios lie well within the 
Black-Scholes-Merton model (BSM) cone.
Simple (one-option) strategies to accept exposure include 
1. Short put
2. Short call (call spread)
Complex (multioption) strategies to accept exposure include the following:
1. Short straddle
2. Short strangle
Jargon introduced in this chapter includes the following:
Margin Put-call parity
Early exercise Cover (a position)
Writing (an option)
Short Put
RED
Accepting Exposure   • 213
Downside: Overvalued
Upside: Fairly valued
Execute: Sell a put contract
Risk: Strike price minus premium received [same as stock inves-
tor at the effective buy price (EBP)]
Reward: Limited to premium received
Margin: Notional amount of position
The Gist
The market is pricing in a relatively high probability that the stock price 
will fall. An investor, from a longer investment time frame perspective, 
believes that the value of the stock is likely worth at least the present mar-
ket value and perhaps more. The investor agrees to accept the downside 
risk perceived by the market and, in return, receives a premium for doing 
so. The premium cannot be fully realized unless the option expires out-  
of-the money (OTM). If the option expires in-the-money (ITM), the 
investor pays an amount equal to the strike price for the stock but can 
partially offset the cost of the stock by the premium received. The inves-
tor thus promises to buy the stock in question at a price of the strike 
price of the option less the premium received—what I call the effective 
buy price.
I think of the short-put strategy as being very similar to buying cor -
porate bonds and believe that the two investment strategies share many 
similarities. A bond investor is essentially looking to receive a specific 
monetary return (in the form of interest) in exchange for accepting 
the risk of the business failing. The only time a bond investor owns a 
company’s assets is after the value of the firm’s equity drops to zero, and 
the assets revert to the control of the creditors. Similarly, a short-put in-
vestor is looking to receive a specific monetary return (in the form of an 
option premium) in exchange for accepting the risk that the company’s 
stock will decrease in value. The only time a short-put investor owns a 
company’s shares is after the market value of the shares expires below the 
preagreed strike price.
Because the strategies are conceptually similar, I usually think of short-
put exposure in similar terms and compare the “yield” I am generating 
214  •   The Intelligent Option Investor
from a portfolio of short puts with the yield I might generate from a cor -
porate bond portfolio. With this consideration, and keeping in mind that 
these investments are unlevered, 2 the name of the game is to generate as 
high a percentage return as possible over the investing time horizon while 
minimizing the amount of real downside risk you are accepting.
T enor Selection
To maximize percentage return, in general, it is better to sell options with 
relatively short-term expirations (usually tenors of from three to nine 
months before expiration). This is just the other side of the coin of the 
rule to buy long-tenor options: the longer the time to expiration, the less 
time value there is on a per-day basis. The rule to sell shorter-tenor options 
implies that you will make a higher absolute return by chaining together 
two back-to-back 6-month short puts than you would by selling a single 
12-month option at the beginning of the period.
During normal market conditions, selling shorter-tenor options is 
the best tactical choice, but during large market downdrafts, when there 
is terror in the marketplace and implied volatilities increase enormously 
for options on all companies, you might be able to make more by sell-
ing a longer-tenor option than by chaining together a series of shorter-
tenor ones (because, presumably, the implied volatilities of options will 
drop as the market stabilizes, and this drop means that you will make 
less money on subsequent put sales). At these times of extreme market 
stress, there are situations where you can find short-put opportunities 
on long-tenor options that defy economic logic and should be invested 
in opportunistically. 
For example, during the terrible market drops in 2009, I found a 
company whose slightly ITM put long-term equity anticipation securities 
(LEAPS) were trading at such a high price that the effective buy price of 
the stock was less than the amount of cash the firm had on its balance 
sheet. Obviously, for a firm producing positive cash flows, the stock should 
not trade at less than the value of cash presently on the balance sheet! I ef-
fectively got the chance to buy a firm with $6 of cash on the balance sheet 
and the near certainty of generating about $2 more over the economic life 
of the options for $5.50. The opportunity to buy $6–$8 worth of cash for 
Accepting Exposure   • 215
$5.50 does not come along very often, so you should take advantage of it 
when you see it.
Of course, the absolute value of premium you will receive by writing 
(jargon that means selling an option) a short-term put is less than the ab-
solute value of the premium you will receive by writing a long-term one.
3 
As such, an investor must balance the effective buy price of the stock (the 
strike price of the option less the amount of premium to be received) in 
which he or she is investing in the short-put strategy with the percentage 
return he or she will receive if the put expires OTM.
I will talk more about effective buy price in the next section, but keep 
in mind that we would like to generate the highest percentage return pos-
sible and that this usually means choosing shorter-tenor options.
Strike Price Selection
In general, the best policy is to sell options at as close to the 50-delta [at-
the-money (ATM)] mark as one can because that is where time value for 
any option is at its absolute maximum. Our expectation is that the option’s 
time value will be worthless at expiration, and if that is indeed the case, 
we will be selling time value at its maximum and “closing” our time value 
position at zero—its minimum. In this way, we are obeying (in reverse 
order) the old investing maxim “Buy low, sell high. ” Selling ATM puts 
means that our effective buy price will be the strike price at which we sold 
less the amount of the premium we received. It goes without saying that 
an intelligent investor would not agree to accept the downside exposure 
to a stock if he or she were not prepared to buy the stock at the effective 
buy price.
Some people want to sell OTM puts, thereby making the effective buy 
price much lower than the present market price. This is an understandable 
impulse, but simply attempting to minimize the effective buy price means 
that you must ignore the other element of a successful short put strategy: 
maximizing the return generated. There are times when you might like to 
sell puts on a company but only at a lower strike price. Rather than accept-
ing a lower return for accepting that risk, I find that the best strategy is 
simply to wait awhile until the markets make a hiccup and knock down the 
price of the stock to your desired strike price.
216  •   The Intelligent Option Investor
Portfolio Management
As we have discussed, the best percentage returns on short-put investments 
come from the sale of short-tenor ATM options. I find that each quarter there 
are excellent opportunities to find a fairly constant stream of this type of short-
term bet that, when strung together in a portfolio, can generate annualized 
returns in the high-single-digit to low-teens percentage range. This level of 
returns—twice or more the yield recently found on a high-quality corporate 
bond portfolio and closer to the bond yield on highly speculative small com-
panies with low credit ratings—is possible by investing in strong, high-quality 
blue chip stocks. In my mind, it is difficult to allocate much money to corpo-
rate bonds when this type of alternative is available.
Some investors prefer to sell puts on stocks that are not very vola-
tile or that have had a significant run-up in price,
4 but if you think about 
how options are priced, it is clear that finding stocks that the market 
perceives as more volatile will allow you to generate higher returns. Y ou 
can confirm this by looking at the diagrams of a short-put investment 
given two different volatility scenarios. First, a diagram in which implied 
volatility is low:
Advanced Building Corp. (ABC)
80
70
60
50
40
30
20
5/18/2012 5/20/2013 249 499 749 999
Date/Day Count
Stock Price
RED
Accepting Exposure   • 217
Now a diagram when implied volatility is higher:
RED
Advanced Building Corp. (ABC)
80
70
60
50
40
30
20
5/18/2012 5/20/2013 249 499 749 999
Date/Day Count
Stock Price
Obviously, there is much more of the put option’s range of exposure 
bounded by the BSM cone in the second, high-volatility scenario, and this 
means that the price received for accepting the same downside risk will be 
substantially higher when implied volatility is elevated.
The key to setting up a successful allocation of short puts is to find 
companies that have relatively low downside valuation risk but that also 
have a significant amount of perceived price risk (as seen by the market)—
even if this risk is only temporary in nature. Quarterly earnings seasons are 
nearly custom made for this purpose. Sell-side analysts (and the market 
in general) mainly use multiples of reported earnings to generate a target 
price for a stock. As such, a small shortfall in reported earnings as a result 
of a transitory and/or nonmaterial accounting technicality can cause sell-
side analysts and other market participants to bring down their short-term 
target price estimates sharply and can cause stock prices to drop sharply 
as well.
5
These times, when a high-quality company drops sharply as a re-
sult of perceived risk by other investors, are a wonderful time to replen-
ish a portfolio of short puts. If you time the tenors well, your short-put 
218  •   The Intelligent Option Investor
investment will be expiring just about the time another short-put invest-
ment is becoming attractive, so you can use the margin that has until re-
cently been used to support the first position to support the new one.
Obviously, this strategy only works when markets are generally trend-
ing upward or at least sideways over the investment horizon of your short 
puts. If the market is falling, short-put positions expire ITM, so you are left 
with a position in the underlying stocks. For an option trader (i.e., a short-
term speculator), being put a stock is a nightmare because he or she has 
no concept of the underlying value of the firm. However, for an intelligent 
option investor, being put a stock simply means the opportunity to receive 
a dividend and enjoy capital appreciation in a strong stock with very little 
downside valuation risk.
The biggest problem arises when an investor sells a put and then re-
vises down his or her lowest-case valuation scenario at a later time. For in-
stance, the preceding diagram shows a worst-case scenario of $55 per share. 
What if new material information became known to you that changed your 
lower valuation range to $45 per share just as the market price for the stock 
dropped, as in the following diagram?
Advanced Building Corp. (ABC)
80
70
60
50 EBP = $47.50
Overvaluation of
downside exposure
40
30
20
5/18/2012 5/20/2013 249 499 749 999
Date/Day Count
Stock Price
RED
Accepting Exposure   • 219
Looking at this diagram closely, you should be able to see several 
things:
1. The investor who is short this put certainly has a notable unrealized 
loss on his or her position. Y ou can tell this because the put the 
investor sold is now much more valuable than at the time of 
the original sale (more of the range of exposure is carved out by 
the BSM cone now). When you sell something at one price and the 
value of that thing goes up in the future, you suffer an opportunity 
loss on your original sale.
2. With the drop in price and the cut in fair value, the downside ex-
posure on this stock still looks overvalued.
3. If the company were to perform so that its share price eventually 
hit the new, reduced best-case valuation mark, the original short-
put position would generate a profit—albeit a smaller profit than 
the one originally envisioned.
At this point, there are a couple of choices open to the investor:
1. Convert the unrealized loss on the short-put position to a realized 
one by buying $50-strike puts to close the position (a.k.a. cover the 
position).
2. Leave the position open and manage it in the same way that the 
investor would manage a struggling stock position.
It is rarely a sound idea to close a short put immediately after the re-
lease of information that drives down the stock price (the first choice above, 
in other words). At these times, investors are generally panicked, and this 
panic will cause the price of the option you buy to cover to be more expen-
sive than justified. Waiting a few days or weeks for the fear to drain out of 
the option prices (i.e., for the BSM cone to narrow) and for the stock price 
to stabilize some will usually allow you to close the option position at a more 
favorable price. There is one exception to this rule: if your new valuation 
suggests a fair value at or below the present market price, it is better to close 
the position immediately and realize those losses. If you do not close the 
position, you are simply gambling (as opposed to investing) because you no 
longer have a better than even chance of making money on the investment.
220  •   The Intelligent Option Investor
The decision to leave the position open must depend on what other 
potential investments you are able to make and how the stock position that 
will likely be put to you at expiration of the option contract stacks up on a 
relative basis. For instance, let’s assume that you had received a premium 
of $2.50 for writing the puts struck at $50. This gives you an effective buy 
price of $47.50. The stock is now trading at $43 per share, so you can think 
of your position as an unlevered, unrealized loss of $4.50, or a little under 
10 percent of your EBP . Y our new worst-case valuation is $55 per share, 
which implies a gain of about 15 percent on your EBP; your new best-case 
valuation is $65 per share, which implies a gain of 37 percent.
How do these numbers compare with other investments in your port-
folio? How much spare capacity does your portfolio have for additional 
investments? (That is, do you have enough spare cash to increase the size 
of this investment by selling more puts at the new market price or buying 
shares of stock? And if so, would your portfolio be weighted too heavily on a 
single industry or sector?) By answering these questions and understanding 
how this presently losing investment compares with other existing or poten-
tial investments should govern your portfolio management of the position.
An investor cannot change the price at which he or she transacted 
in a security. The best he or she can do is to develop a rational view of the 
value of a security and judge that security by its relative merit versus other 
possible investments. Whether you ever make an option transaction, this 
is a good rule to keep in mind.
Let us now take a look at short calls and short-call spreads—the 
strategy used for accepting upside exposure.
Short Call (Call Spread)
RED
Accepting Exposure   • 221
Downside: Fairly valued
Upside: Overvalued
Execute: Sell a call contract (short call); sell a call contract while 
simultaneously buying a call contract at a higher strike 
price (short-call spread)
Risk: Unlimited for short call; difference between strike prices 
and premium received (short-call spread)
Reward: Limited to the amount of premium received
Margin: Variable for a short call; dollar amount equal to the differ-
ence between strike prices for a short-call spread
The Gist
The market overestimates the likelihood that the value of a firm is above its pre-
sent market price. An investor accepts the overvalued upside exposure in return 
for a fixed payment of premium. The full amount of the premium will only flow 
through to the investor if the price of the stock falls and the option expires OTM.
There are two variations of this investment—the short call and the 
short-call spread. This book touches on the former but mainly addresses 
the latter. A short call opens up the investor to potentially unlimited capital 
losses (because stocks theoretically do not have an upper bound for their 
price), and a broker will not allow you to invest using this strategy except 
for the following conditions:
1. Y ou are a hedge fund manager and have the ability to borrow 
stocks through your broker and sell them short.
2. Y ou are short calls not on a stock but on a diversified index (such 
as the Dow Jones Industrial Index or the Standard and Poor’s 500 
Index) through an exchange-traded fund (ETF) or a futures con-
tract and hold a diversified stock portfolio.
For investors fitting the first condition, short calls are margined in the 
same way as the rest of your short portfolio. That is, you must deposit initial 
margin on the initiation of the investment, and if the stock price goes up, you 
must pay in variance margin to support the position. Obviously, as the stock 
price falls, this margin account is settled in your favor. For investors fitting the 
second condition, when you originally sell the call option, your broker should 
222  •   The Intelligent Option Investor
indicate on your statements that a certain proportion of your account effec-
tively will be treated as margin. This means that you stand to receive the eco-
nomic benefit from your diversified portfolio of securities but will not be able 
to liquidate all of it. If the market climbs higher, a larger proportion of your 
portfolio will be considered as margin; if it falls lower, a smaller proportion 
of your portfolio will be considered as margin. Basically, a proportion of any 
gains from your diversified stock portfolio will be reapportioned to serve as 
collateral for your short call when the market is rising, and a proportion of any 
losses from your diversified stock portfolio will be offset by a freeing of margin 
related to your profits on the short call when the market is falling.
Most brokers restrict the ability of individual investors to write un-
covered calls on individual stocks, so the rest of this discussion will cover 
the short-call spread strategy for individual stocks.
T enor Selection
Tenors for short-call spreads should be fairly short under the same reason-
ing as that for short puts—one receives more time value per day for short-
er-tenor options. Look for calls in the three- to nine-month tenor range. 
The tenor of the purchased call (at the higher strike price) should be the 
same as the tenor of the sold calls (at the lower strike price). Theoretically, 
the bought calls could be longer, but it is hard to think of a valuation justifi-
cation for such a structure. By buying a longer-tenor call for the upside leg 
of the investment, you are expressing an investment opinion that the stock 
will likely rise over the long term—this exactly contradicts the purpose of 
this strategy: expressing a bearish investment opinion.
Strike Price Selection
Theoretically, you can choose any two strike prices, sell the call at the lower 
price, and buy the call at the higher price and execute this investment. If you 
sold an ITM call, you would receive premium that consists of both time and 
intrinsic value. If the stock fell by expiration, you would realize all the wasted 
time value plus the difference between the intrinsic value at initiation and the 
intrinsic value at expiration.
Despite the theory, however, in practice, the lower strike option is usually 
sold ATM or OTM because of the threat of assignment. Assignment is the pro-
cess the exchange goes through when investors choose to exercise the option 
Accepting Exposure   • 223
they own rather than trade them away for a profit. Recall from Chapter 2  
that experienced option investors do not do this most of the time; they 
know that because of the existence of time value, it is usually more beneficial 
for them to sell their option in the market and use the proceeds to buy the stock 
if they want to hold the underlying. Inexperienced investors, however, often are 
not conscious of the time-value nuance and sometimes elect to exercise their 
option. In this case, the exchange randomly pairs the option holders who wish 
to exercise with an option seller who has promised to sell at that exercise price.
There is one case in which a sophisticated investor might chose to 
exercise an ITM call option early, related to a principle in option pricing 
called put-call parity. This rule, which was used to price options before 
advent of the BSM, simply states that a certain relationship must exist be-
tween the price of a put at one strike price, the price of a call at that same 
strike price, and the market price of the underlying stock. Put-call parity 
is discussed in Appendix C. In this appendix, you can learn what the exact 
put-call parity rule is (it is ridiculously simple) and then see how it can be 
used to determine when it is best to exercise early in case you are long a 
call and when your short-call (spread) position is in danger of early exercise 
because of a trading strategy known as dividend arbitrage.
The assignment process is random, but obviously, the more contracts 
you sell, the better the chance is that you will be assigned on some part or all 
of your sold contracts. Even if you hold until expiration, there is still a chance 
that you may be assigned to fulfill a contract that was exercised on settlement.
Clearly, from the standpoint of option sale efficiency, an ATM call is the 
most sensible to sell for the same reason that a short put also was most efficient 
ATM. As such, the discussion that follows assumes that you are selling the 
ATM strike and buying back a higher strike to cover.
In a call-spread strategy, the capital you have at risk is the difference be-
tween the two strike prices—this is the amount that must be deposited into 
margin. Depending on which strike price you use to cover, the net premium 
received differs because the cost of the covering call is cheaper the further 
OTM you cover. As the covering call becomes more and more OTM, the ratio 
of premium received to capital at risk changes. Put in these terms, it seems 
that the short-call spread is a levered strategy because leverage has to do with 
altering the capital at risk in order to change the percentage return. This con-
trasts with the short-call spread’s mirror strategy on the put side—short puts—
in that the short-put strategy is unlevered. 
224  •   The Intelligent Option Investor
For instance, here are data from ATM and OTM call options on IBM 
(IBM) expiring in 80 days. I took these data when IBM’s shares were trad-
ing at $196.80 per share.
Sell a Call at 195
Cover at ($) Net Premium Received ($) Percent Return Capital at Risk ($)
200 2.40 48 5
205 4.26 43 10
210 5.47 36 15
215 6.17 31 20
220 6.51 26 25
225 6.70 22 30
230 6.91 20 35
235 6.90 17 40
240 6.96 15 45
In this table, net premium received was calculated by selling at the $195 
strike’s bid price and buying at each of the listed strike price’s ask prices. Percent 
return is the proportion of net premium received as a percentage of the capital 
at risk—the width of the spread. This table clearly shows that accepting expo-
sure with a call spread is a levered strategy. The potential return on a percent-
age basis can be raised simply by lowering the amount of capital at risk.
However, although accepting exposure with a call spread is un-
deniably levered from this perspective, there is one large difference: un-
like the leverage discussed earlier in this book for a purchase of call op-
tions—in which your returns were potentially unlimited—the short-call 
spread investor receives premium up front that represents the maximum 
return possible on the investment. As such, in the sense of the investor’s 
potential gains being limited, the short-call spread position appears to be 
an unlevered investment.
Considering the dual nature of a short-call spread, it is most help-
ful to think about managing these positions using a two-step process with 
both tactical and strategic aspects. We will investigate the tactical aspect 
of leverage in the remainder of this section and the strategic aspect in the 
portfolio management section.
Accepting Exposure   • 225
Tactically, once an investor has decided to accept exposure to a stock’s 
upside potential using a call spread, he or she has a relatively limited choice 
of investments. Let’s assume that we sell the ATM strike; in the IBM ex-
ample shown earlier, there is a choice of nine strike prices at which we 
can cover. The highest dollar amount of premium we can receive—what I 
will call the maximum return—is received by covering at the most distant 
strike. Every strike between the ATM and the most distant strike will at 
most generate some percentage of this maximum return.
Now let’s look at the risk side. Let’s say that we sell the $195-strike call 
and cover using the $210-strike call. Now assume that some bit of good 
news about IBM comes out, and the stock suddenly moves to exactly $210. 
If the option expires when IBM is trading at $210, we will have lost the 
entire amount of margin we posted to support this investment—$15 in all. 
This $15 loss will be offset by the amount of premium we received from 
selling the call spread—$5.47 in the IBM example—generating a net loss of 
$9.53 (= $5.47 − $15). Compare this with the loss that we would suffer if we 
had covered using the most distant call strike. In this case, we would have 
received $6.96 in premium, so if the option expires when IBM is trading at 
the same $210 level as earlier, our net loss would be $8.04 (= $6.96 − $15). 
Because our maximum return is generated with the widest spread, it fol-
lows that our minimum loss for the stock going to any intermediate strike 
price also will be generated with the widest spread.
At the same time, if we always select the widest spread, we face an 
entirely different problem. That is, the widest spread exposes us to the great-
est potential loss. If the stock goes only to $210, it is true that the widest 
spread will generate a smaller loss than the $195–$210 spread. However, in 
the extreme, if the stock moves up strongly to $240, we would lose the $45 
gross amount supporting the margin account and a net amount of $38.04 
(= $45 – $6.96). Contrast this with a net loss of $9.53 for the $195–$210 
spread. Put simply, if the stock moves up only a bit, we will do better with 
the wider spread; if it moves up a lot, it is better to choose a narrower 
spread. 
In short, when thinking about call spreads, we must balance our 
amount of total exposure against the exposure we would have for an inter-
mediate outcome against the total amount of premium we are receiving. If 
we are too protective and initiate the smallest spread possible, our chance 
226  •   The Intelligent Option Investor
of losing the entire margin amount is higher, but the margin amount lost 
is smaller. On the other hand, if we attempt to maximize our winnings 
and initiate the widest spread possible, our total exposure is greatest, even 
though the chance of losing all of it is lower.
Plotting these three variables on a graph, here is what we get:
200 (11%)
0%
20%
40%
60%
80%
106% 102%
94%89%
100%
120%
140%
160%
180%
200%
205 (22%) 210 (33%) 215 (44%) 220 (56%) 225 (67%) 230 (78%) 235 (89%) 240 (100%)
Strike (% of Total Exposure)
Risk & Return of Call Spreads vs. Maximum Spread
Risk Comparison Return Comparison
Here, on the horizontal axis, we have the value of the covering strike and 
the size of the corresponding spread as a percentage of the widest spread. 
This shows how much proportional capital is at risk (e.g., at the $215-strike, 
we are risking a total of $20 of margin; $20 is 44 percent of total exposure 
of $45 if we covered at the $240-strike level). The top line shows how much 
greater the loss would be if we used that strike to cover rather than the 
maximum strike and the option expired at that strike price (e.g., if we cover 
at the $215-strike and the option expires when the stock is trading at $215, 
our loss would be 6 percent greater than the loss we would suffer if we 
covered at the $240-strike). The bottom line shows the premium we will 
realize as income if the stock price declines as a percentage of the total pre-
mium possible if we covered at the maximum strike price. Here are the val-
ues from the graph in tabular format so that you can see the numbers used:
Strike 
Price
Dollar 
Spread
Percent of 
Maximum 
Spread (a)
Bid 
Price
Ask 
Price
Covering at Strike
Covering at Maximum 
Strike
Difference
Risk 
Comparison 
(%) (b)
Return 
Comparison  
(%) (c)
Potential 
Gain
Worst-Case 
(Loss)
Potential 
Gain
Worst-Case 
Gain (Loss)
195 — — 7.05 7.10 — — — — — — —
200 5 11 4.55 4.65 2.40 (2.60) 6.96 1.96 (3.55) N.C. 34
205 10 22 2.75 2.79 4.26 (5.74) 6.96 (3.04) 2.29 189 61
210 15 33 1.54 1.58 5.47 (9.53) 6.96 (8.04) 0.87 119 79
215 20 44 0.84 0.88 6.17 (13.83) 6.96 (13.04) 0.53 106 89
220 25 56 0.38 0.54 6.51 (18.49) 6.96 (18.04) 0.39 102 94
225 30 67 0.12 0.35 6.70 (23.30) 6.96 (23.04) 0.30 101 96
230 35 78 0.11 0.14 6.91 (28.09) 6.96 (28.04) 0.25 100 99
235 40 89 0.03 0.15 6.90 (33.10) 6.96 (33.04) 0.21 100 99
240 45 100 0.02 0.09 6.96 (38.04) 6.96 (38.04) 0.18 100 100
227
228  •   The Intelligent Option Investor
With a table like this, you can balance, on the one hand, the degree 
you are reducing your overall exposure in a worst-case scenario (by look-
ing at column a) against how much risk you are taking on for a bad-case 
(intermediary upward move of the stock) scenario (by looking at column 
b) against how much less premium you stand to earn if the stock does go 
down as expected (by looking at column c). 
There are no hard and fast rules for which is the correct covering strike to 
select—that will depend on your confidence in the valuation and timing, your 
risk profile, and the position size—but looking at the table, I tend to be drawn 
to the $215 and $220 strikes. With both of those strikes, you are reducing your 
worst-case exposure by about half, increasing your bad-case exposure just 
marginally, and taking only a small haircut on the premium you are receiving.
6
Now that we have an idea of how to think about the potential risk and 
return on a per-contract basis, let’s turn to leverage in the strategic sense—
figuring out how much capital to commit to a given bearish idea.
Portfolio Management
When we thought about leverage from a call buyer’s perspective, we 
thought about how large of an allocation we wanted to make to the idea 
itself and changed our leverage within that allocation to modify the profits 
we stood to make. Let’s do this again with IBM—again assuming that we are 
willing to allocate 5 percent of our portfolio to an investment in the view 
that this company’s stock price will not go higher. At a price of $196.80, a 
5 percent allocation would mean controlling a little more than 25 shares for 
every $100,000 of portfolio value.
7 Because options have a contract size of 
100 shares, an unlevered 5 percent allocation to this investment would 
require a portfolio size of $400,000.
The equation to calculate the leverage ratio on the basis of notional 
exposure is
× =Notional valueo fo ne contract
Dollarv alue of allocation number of contractsl everager atio
So, for instance, if we had a $100,000 portfolio of which we were willing to 
commit 5 percent to this short-call spread on IBM, our position would have a 
leverage ratio of
Accepting Exposure   • 229
×= ≈$19,500
$5,000 13 .9 4: 1leverage
Selling the $195/$220 call spread will generate $651 worth of pre-
mium income and put at risk $2,500 worth of capital. Nothing can change 
these two numbers—in this sense, the short-call spread has no leverage. 
The 4:1 leverage figure merely means that the percentage  return will ap-
pear nearly four times as large on a given allocation as a 1:1 allocation 
would appear. The following table—assuming the sale of one contract of 
the $195/$220 call spread—shows this in detail:
Winning Case Losing Case
Premium 
Received 
($)
Target 
Allocation 
($) Leverage
Stock 
Move ($)
Percent 
Return on 
Allocation
Stock 
Move 
($)
Dollar 
Return
Percent 
Return on 
Allocation
651 20,000 1:1 –2 3.3 +25 –1,849 –9.2
651 10,000 2:1 –2 6.5 +25 –1,849 –18.5
651 5,000 4:1 –2 13.0 +25 –1,849 –37.0
Note: The dollar return in the losing case is calculated as the loss of the $2,500 of margin 
per contract less than the premium received of $651.
Notice that the premium received never changes, nor does the worst-
case return. Only the perception of the loss changes with the size of our 
target allocation.
Now that we have a sense of how to calculate what strategic leverage 
we are using, let’s think about how to size the position and about how much 
risk we are willing to take. When we are selling a call or call spread, we are 
committing to sell a stock at the strike price. If we were actually selling the 
stock at that price rather than committing to do so, where would we put 
our stop loss—in other words, when would we close the position, assuming 
that our valuation or our timing was not correct?
Let’s say that for this stock, if the price rose to $250, you would be 
willing to admit that you were wrong and would realize a loss of $55 per share, 
or $5,500 per hundred shares. This figure—the $5,500 per hundred shares 
you would be willing to lose in an unlevered short stock position—can be 
used as a guide to select the size of your levered short-call spread.
230  •   The Intelligent Option Investor
In this case, you might choose to sell a single $195–$240 call spread, in 
which case your maximum exposure would be $4,500 [= 1 × (240 – 195) × 100] 
at the widest spread. This investment would have a leverage ratio of approxi-
mately 1:1. Alternatively, you could choose to sell two $195–$220 spreads, in 
which case your maximum exposure would be $5,000 [= 2 × (220 − 195) × 
100], with a leverage ratio of approximately 2:1. Which choice you select will 
depend on your assessment of the valuation of the stock, your risk tolerance, 
and the composition of your portfolio (i.e., how much of your portfolio is al-
located to the tech sector, in this example of an investment in IBM). Because 
the monetary returns from a short-call or call-spread strategy are fixed and 
the potential for losses are rather high, I prefer to execute bearish investments 
using the long-put strategy discussed in the “Gaining Exposure” section.
With this explanation of the short-call spread complete, we have all the 
building blocks necessary to understand all the other strategies mentioned 
in this book. Let’s now turn to two nonrecommended complex strategies 
for accepting exposure—the short straddle and the short strangle—both of 
which are included not because they are good strategies but rather for the 
sake of completeness.
Short Straddle/Short Strangle
Short Straddle
RED
Downside: Overvalued
Upside: Overvalued
Execute: Sell an ATM put; simultaneously sell an ATM call spread
Accepting Exposure   • 231
Risk: Amount equal to upper strike price minus premium received
Reward: Limited to premium received
Margin: Dollar amount equal to upper strike price
Short Strangle
RED
RED
Downside: Overvalued
Upside: Overvalued
Execute: Sell an OTM put; simultaneously sell an OTM call spread
Risk: Call-spread leg: Amount equal to difference between 
strikes and premium received. Put leg: Amount equal to 
strike price minus premium received. Total exposure is 
the sum of both legs.
Reward: Limited to premium received
Margin: Call-spread leg: Amount equal to difference between 
strikes. Put leg: Amount equal to strike price. Total mar -
gin is the sum of both legs.
The Gist
In my opinion, these are short-term trades rather than investments. Even 
though a short put uses a short-tenor option, the perspective of the inves-
tor is that he or she is buying shares. These strategies are a way to express 
the belief that the underlying stock price will not move over a short time. 
In my experience, there is simply no way to develop a rational view of how 
a single stock will move over a short time frame. In the short term, markets 
232  •   The Intelligent Option Investor
fluctuate based on animal spirits, fads, and various other insanities. Why 
subject yourself to the torture of trying to figure out these insanities and 
profit from them when there are easier, more intelligent ways of doing so? 
Of the two strategies, the short straddle is preferable because it yields 
the greatest amount of premium. Use this strategy at your own peril, 
however.
Let’s turn now to a discussion of how to mix exposure—simultane-
ously gaining and accepting exposure and overlaying options on stock po-
sitions.
233
Chapter 11
Mixing ExposurE
Mixing exposure uses combinations of gaining and accepting exposure, 
employing strategies that we already discussed to create what amounts to 
sort of a short-term synthetic position in a stock (either long or short). 
These strategies, nicknamed “diagonals” can be extremely attractive and 
extremely financially rewarding in cases where stocks are significantly mis-
priced (in which case, exposure to one direction is overvalued, whereas the 
other is extremely undervalued). 
Frequently, using one of these strategies, an investor can enter a po-
sition in a levered out-of-the-money (OTM) option for what, over time, 
becomes zero cost (or can even net a cash inflow) and zero downside expo-
sure. This is possible because the investor uses the sale of one shorter-tenor 
at-the-money (ATM) option to subsidize the purchase of another longer-
tenor OTM one. Once the sold option expires, another can be sold again, 
and whatever profit is realized from that sale goes to further subsidize the 
position.
This strategy works well because of a couple of rules of option pricing 
that we have already discussed:
1. ATM options are more expensive than OTM options of the same 
tenor.
2. Short-tenor options are worth less than long-tenor options, but 
the value per day is higher for the short-tenor options.
234  •   The Intelligent Option Investor
I provide actual market examples of these strategies in this chapter and will 
point out the effect of both these points in those examples.
Because these strategies are a mix of exposures, it makes sense 
that they are just complex (i.e., multioption) positions. I will discuss the 
following:
1. Long diagonal
2. Short diagonal
Note that the nomenclature I use here is a bit different from what others 
in the market may use. What I term a diagonal in this book is what others 
might call a “spit-strike synthetic stock. ” Since Bernie Madoff ’s infamous 
“split-strike conversion” fraud, this term doesn’t have a very good ring to 
it. For other market participants, a diagonal means simultaneously buying 
and selling options of the same type (i.e calls or puts). In this book, it means 
selling an option of one kind and buying the other kind.
I will also talk about what is known in the options world as overlays. One 
of the most useful things about options is the way that they can be grafted or 
overlain onto an existing common stock position in a way that alters the port-
folio’s overall risk-reward profile. The strategies I will review here are as follows:
1. Covered calls
2. Protective puts
3. Collars
These strategies are popular but often misunderstood ways to alter your 
portfolio’s risk-reward profile.
Coming this far in this book, you already have a good understand-
ing about how options work, so the concepts presented here will not be 
difficult, but I will discuss some nuances that will help you to evaluate 
investment choices and make sound decisions regarding the use of these 
strategies. I will refer to strike selection and tenor selection in the following 
pages, but for these, along with “The Gist” section, I’ll include an “Execu-
tion” section and a “Common Pitfalls” section.
Covered calls are an easy strategy to understand once you understand 
short puts, so I will discuss those first. Protective puts share a lot of simi-
larities with in-the-money (ITM) call options, and I will discuss those next. 
Mixing Exposure  •  235
Collars are just a combination of the other two overlay strategies and so are 
easiest left to the end.
Long Diagonal
GREEN
RED
Downside: Overvalued
Upside: Undervalued
Execute: Sell an ATM put option (short put) and simultaneously 
buy an OTM call option (long call)
Risk: Sum of put’s strike price and net premium paid for call
Reward: Unlimited
Margin: Amount equal to put’s strike price
The Gist
Other than the blank space in the middle of the diagram and the disparity 
between the lengths of the tenors, the preceding diagram looks very much like 
the risk-return profile diagram for a long stock—accepting downside exposure 
in return for gaining upside exposure. As you can see from the diagram, the 
range of exposure for the short put lies well within the Black-Scholes-Merton 
model (BSM) cone, but the range of exposure for the long call is well outside 
the cone. It is often possible to find short-put–long-call combinations that al-
low for an immediate net credit when setting up this investment.
236  •   The Intelligent Option Investor
Because we must fully margin a short-put investment, that leg of 
the long diagonal carries with it a loss leverage ratio of –1.0. However, the 
OTM call leg represents an immediate realized loss coupled with a very 
high lambda value for gains. As such, if the put option expires ITM, the 
long diagonal is simply a levered strategy; if the put option expires OTM, 
the investment is a very highly levered one because the unlevered put 
ceases to influence the leverage equation. Another short put may be written  
after the previous short put expires; this further subsidizes the cost of the 
calls and so greatly increases the leverage on the strategy.
If the stock moves quickly toward the upper valuation range, this 
structure becomes extremely profitable on an unrealized basis. If the put 
option expires ITM, the investor is left with a levered long investment in 
the stock in addition to the long position in the OTM. As in any other 
complex structure, the investment may be ratioed—for instance, by buying 
one call for every two puts sold or vice versa.
Strike Price Selection
The put should be sold ATM or close to ATM in order to maximize the time 
value sold, as explained earlier in the short-put summary. The call strike may be 
bought at any level depending on the investor’s appetite for leverage but is usu-
ally purchased OTM. The following table shows the net debit or credit associated 
with the long diagonal between the ATM put ($55 strike price, delta of –0.42, 
priced at the bid price) with an expiration of 79 days and each call strike (at the 
ask price) listed, all of which are long-term equity anticipated securities (LEAPS) 
having expirations in 534 days. The lambda figure for the OTM calls is also given 
to provide an idea of the comparative leverage of each call option. For this exam-
ple, I am using JP Morgan Chase (JPM) when its stock was trading for $56.25.
Strike Delta (Debit) Credit Call Lambda (%)
57.50 0.43 (2.52) 5.6
60.00 0.37 (1.57) 6.1
62.50 0.31 (0.76) 6.7
65.00 0.26 (0.25) 7.0
70.00 0.16 0.78 8.4
75.00 0.10 1.28 9.5
80.00 0.06 1.56 10.5
Mixing Exposure  •  237
Here we can see that for a long diagonal using 79-day ATM puts 
and 594-day LEAPS that are OTM by just over 15 percent, we are 
paying a net of only $25 per contract for notional control of 100 
shares. On a per-contract basis, at the following settlement prices, 
we would generate the following profits (or losses, in the case of the 
first row):
Settlement Price ($) Dollar Profit per Contract
Percentage Return on Original 
Investment (%)
65 0 –100
66 100 300
67 200 700
68 300 1,100
69 400 1,500
70 500 1,900
71 600 2,300
72 700 2,700
73 800 3,100
74 900 3,500
75 1,000 3,900
If the stock price moves up very quickly, it might be more beneficial 
to close the position or some portion of the position before expiration. Let’s 
say that my upper-range estimate for this stock was $75. From the preced-
ing table, I can see that my profit per contract if the stock settles at my fair 
value range is $1,000. If there is enough time value on a contract when 
the stock is trading in the upper $60 range to generate a realized profit of 
$1,000, I am likely to take at least some profits at that time rather than wait-
ing for the calls to expire.
In Chapter 9, I discussed portfolio composition and likened the use 
of leverage as a side dish to a main course. This is an excellent side dish that 
can be entered into when we see a chance to supplement the main meal of 
a long stock–ITM call option position with a bit more spice. Let’s now turn 
to its bearish mirror—the short diagonal.
238  •   The Intelligent Option Investor
Short Diagonal
RED
GREEN
Downside: Undervalued
Upside: Overvalued
Execute: Sell an ATM call option while buying one to cover at a 
higher price (short-call spread) and simultaneously buy 
an OTM put option (long put)
Risk: Sum of put’s strike price and net premium paid for call
Reward:  Amount equal to the put’s strike price minus any net 
premium paid for it 
Margin: Amount equal to spread between call options
The Gist
The diagram for a short diagonal is just the inverse of the long diagonal and, of 
course, looks very similar to the risk-return profile diagram for a short stock—
accepting upside exposure in return for gaining downside exposure. The gist 
of this strategy is simply the short-exposure equivalent to the long diagonal, so 
the comments about the long diagonal are applicable to this strategy as well. 
The one difference is that because you must spend money to cover the short 
call on the upside, the subsidy that the option sale leg provides to the option 
purchase leg is less than in the case of the long diagonal. Also, of course, a stock 
price cannot turn negative, so your profit upside is capped at an amount equal 
to the effective sell price. This investment also may be ratioed (e.g., by using 
one short-call spread to subsidize two long puts).
Mixing Exposure  •  239
Strike Price Selection
Strike price selection for a short diagonal is more difficult because there 
are three strikes to price this time. Looking at the current pricing for a 
call spread with the short call struck at $55, I get the following selection of 
credits:
Upper Call Strike ($)
Call Spread 
Net Credit ($)
Percent Total 
Risk Percent Total Return
57.50 1.27 17 49
60.00 2.14 33 83
62.50 2.44 50 94
65.00 2.51 67 97
70.00 2.59 100 100
Looking at this, let’s say we decide to go with the $55.00/$62.50 call 
spread. Doing so, we would receive a net credit of $2.44. Now selecting the 
put to purchase is a matter of figuring out the leverage of the position with 
which you are comfortable.
Strike ($) Delta (Debit) Credit ($) Put Lambda (%)
20.00 –0.02 2.20 –4.5
23.00 –0.02 2.11 –4.6
25.00 –0.03 2.05 –4.6
28.00 –0.04 1.91 –4.8
30.00 –0.05 1.78 –4.8
33.00 –0.07 1.57 –4.8
35.00 –0.09 1.38 –4.8
38.00 –0.12 0.99 –4.8
40.00 –0.15 0.67 –4.7
42.00 –0.17 0.30 –4.7
45.00 –0.23 (0.43) –4.5
47.00 –0.26 (1.01) –4.4
50.00 –0.33 (1.91) –4.4
52.50 –0.39 (3.11) –4.0
240  •   The Intelligent Option Investor
Notice that there is much less leverage on the long-put side than on 
the long-call side. This is a function of the volatility smile and the abnor -
mally high pricing on the far OTM put side. It turns out that the $20-strike 
puts have an implied volatility of 43.3 percent compared to an ATM im-
plied volatility of 22.0 percent.
Obviously, the lower level of leverage will make closing before expira-
tion less attractive, so it is important to select a put strike price between the 
present market price and your worst-case fair value estimate. In this way, 
if the option does expire when the stock is at that level, you will at least be 
able to realize the profit of the intrinsic value.
With these explanations of the primary mixed-exposure strategies, 
now let’s turn to overlays—where an option position is added to a stock 
position to alter the risk-return characteristics of the investor’s portfolio.
Covered Call
Contingent Upside Exposure
Contingent Downside Exposure
LIGHT GREEN
RED
LIGHT RED
Downside: Overvalued
Upside: Fairly valued or undervalued
Mixing Exposure  •  241
Execute: Buy common stock and simultaneously sell a call option
Risk: Strike price minus premium received
Reward: Limited to premium and, as long as the shares are not called, 
the dividends received during the tenor of the option
Margin:  None as long as stock and option positions are evenly 
matched—long stock position serves as collateral for the 
sold call
The Gist
If you look just as far as the option tenor lasts on the preceding diagram, 
you will see that the risk-return profile is identical to that of a short put. As 
evidence, please compare the following two diagrams:
We have sold
away the upside
exposure so are
left with only
the acceptance
of downside
exposure here.
RED
Covered call
242  •   The Intelligent Option Investor
We accepted
downside
exposure when
we sold this
put, so have no
exposure to the
upside here.
RED
The top of the “Covered call” diagram is grayed out because we have 
sold away the upside exposure to the stock by selling the call option, and 
we are left only with the acceptance of the stock’s downside exposure. The 
pictures are slightly different, but the economic impact is the same.
The other difference you will notice is that after the option expires, in the 
case of the covered call, we have represented the graphic as though there is some 
residual exposure. This is represented in this way because if the option expires 
ITM, you will have to deliver your stock to the counterparty who bought your 
call options. As such, your future exposure to the stock is contingent on another 
investor’s actions and the price movement of the stock. This is an important point 
to keep in mind, and I will discuss it more in the “Common Pitfalls” section.
Execution
Because this strategy is identical from a risk-reward perspective to short 
puts, the execution details should be the same as well. Indeed, covered 
calls should—like short puts—be executed ATM to get the most time value 
possible and preferably should be done on a stock that has had a recent fall 
and whose implied volatility has spiked. However, these theoretical points 
Short put
Mixing Exposure  •  243
ignore the fact that most people simply want to generate a bit of extra in-
come out of the holdings they already have and so are psychologically re-
sistant to both selling ATM (because this makes it more likely for their 
shares to be called away) and selling at a time when the stock price sud-
denly drop (because they want to reap the benefit of the shares recovering).
Although I understand these sentiments, it is important to realize 
that options are financial instruments and not magical ones. It would be 
nice if we could simply find an investment tool that we could bolt onto 
our present stock holdings that would increase the dividend a nice amount 
but that wouldn’t put us at risk of having to deliver our beloved stocks to a 
complete stranger; unfortunately, this is not the case for options.
For example, let’s say that you own stock in a company that is paying out 
a very nice dividend yield of 5 percent at present prices. This is a mature firm 
that has tons of cash flow but few opportunities for growth, so management 
has made the welcome choice to return cash to shareholders. The stock is trad-
ing at $50 per share, but because the dividend is attractive to you, you are loathe 
to part with the stock. As such, you would prefer to write the covered call at a 
$55 or even a $60 strike price. A quick look at the BSM cone tells us why you 
should not be expecting a big boost in yield from selling the covered calls:
80
Sold call
range of
exposure
70
60
50
40
30
20
5/18/2012 5/20/2013 249 499 749 999
Cash Flows R Us, Inc. (CASH)
Date/Day Count
Stock Price
GREEN
LIGHT GREENGRAY
LIGHT REDRED
244  •   The Intelligent Option Investor
Clearly, the range of exposure for the $55-strike call is well above the 
BSM cone. The BSM cone is pointing downward because the dividend rate 
is 5 percent—higher than the risk-free rate. This means that BSM drift will 
be lower. In addition, because this is an old, mature, steady-eddy kind of 
company, the expected forward volatility is low. Basically, this is a perfect 
storm for a low option price.
My suggestion is to either write calls on stocks you don’t mind de-
livering to someone else—stocks for which you are very confident in the 
valuation range and are now at or above the upper bound—or simply to 
look for a portfolio of short-put/covered-call investments and treat it like 
a high-yield bond portfolio, as I described in Chapter 10 when explaining 
short puts. It goes without saying that if you think that a stock has a lot of 
unappreciated upside potential, it’s not a good idea to sell that exposure 
away!
One other note about execution: as I have said, short puts and cov-
ered calls are the same thing, but a good many investors do not realize this 
fact or their brokerages prevent them from placing any trade other than a 
covered call. This leads to a situation in which there is a tremendous sup-
ply of calls. Any time there is a lot of supply, the price goes down, and you 
will indeed find covered calls on some companies paying a lot less than 
the equivalent short put. Because you will be accepting the same downside 
exposure, it is better to get paid more for it, so my advice is to write the put 
rather than the covered call in such situations.
To calculate returns for covered calls, I carry out the following steps:
1. Assume that you buy the underlying stock at the market price.
2. Deduct the money you will receive from the call sale as well as 
any projected dividends—these are the two elements of your cash 
inflow—from the market price of the stock. The resulting figure is 
your effective buy price (EBP).
3. Divide your total cash inflow by the EBP .
I always include the projected dividend payment as long as I am writ-
ing a short-tenor covered call and there are no issues with the company 
that would prevent it from paying the dividend. Owners of record have a 
right to receive dividends, even after they have written a covered call on the 
Mixing Exposure  •  245
stock, so it makes sense to count the dividend inflow as one element that 
reduces your EBP . In formula form, this turns out to be
−−Coveredc allr eturn= premiumr eceivedf romc all+ projectedd ividends
stockp rice premiumf romc allp rojected dividends
For a short put, you have no right to receive the dividend, so I find the  
return using the following formula:
−Shortp ut return= premiumr eceivedf roms hort put
strikepricep remium from shortp ut
Common Pitfalls
Taking Profit
One mistake I hear people make all the time is saying that they are going 
to “take profit” using a covered call. Writing a covered call is taking profit 
in the sense that you no longer enjoy capital gains from the stock’s appre-
ciation, but it is certainly not taking profit in the sense of being immune 
to falls in the market price of the stock. The call premium you receive will 
cushion a stock price drop, but it will certainly not shield you from it. If 
you want to take profits on a successful stock trade, hit the “Sell” button.
Locking in a Loss
A person sent me an e-mail telling me that she had bought a stock at $17, 
sold covered calls on it when it got to $20 (in order to “take profits”), and 
now that the stock was trading for $11, she wanted to know how she could 
“repair” her position using options. Unfortunately, options are not magical 
tools and cannot make up for a prior decision to buy a stock at $17 and ride 
it down to $11.
If you are in such a position, don’t panic. It will be tempting to write 
a new call at the lower ATM price ($11 in this example) because the cash 
inflow from that covered call will be the most. Don’t do it. By writing a 
covered call at the lower price, you are—if the shares are called away—
locking in a realized loss on the position. Y ou can see this clearly if you list 
each transaction in the example separately.
246  •   The Intelligent Option Investor
No. Buy/Sell Instrument
Price of 
Instrument
Effective 
Buy (Sell) 
Price of 
Stock Note
1 Buy Stock $17/share $17/share Original purchase
2 Sell Call option $1/share $16/share Selling a covered call 
to take profits when 
stock reaches $20/
share leaves the 
investor with down-
side exposure and $1 
in premium income.
3 Sell Call option $0.75 ($11.75/
share)
Stock falls to $11, and 
investor sells another 
covered call to 
generate income to 
ameliorate the loss.
In transaction 1, the investor buys the shares for $17. In transaction 2, 
when the stock hits $20 per share, the investor sells a covered call and receives 
$1 in premium. This reduces the effective buy price to $16 per share and 
means that the investor will have to deliver the shares if the stock is trad-
ing at $20 or above at expiration. When the stock instead falls to $11, the 
investor—wanting to cushion the pain of the loss—sells another ATM cov-
ered call for $0.75. This covered call commits the investor to sell the shares 
for $11.75. No matter how you look at it, buying at $16 per share and sell-
ing at $11.75 per share is not a recipe for investing success.
The first step in such a situation as this—when the price of a stock 
on which you have accepted downside exposure falls—is to look back 
to your valuation. If the value of the firm has indeed dropped because 
of some material negative news and the position no longer makes sense 
from an economic perspective, just sell the shares and take the lumps. 
If, however, the stock price has dropped but the valuation still makes 
for a compelling investment, stay in the position; if the investment is 
Mixing Exposure  •  247
compelling enough, this is the time to figure out a clever way to get more 
exposure to it. 
Y ou can write calls as long as they are at least at the same strike 
price as your previous purchase price or EBP; this just means that you 
are buying at $16 and agreeing to sell at at least $16, in other words. Also 
keep in mind that any dividend payment you receive you can also think 
of as a reduction of your EBP—that cash inflow is offsetting the cost of 
the shares. Factoring in dividends and the (very small) cash inflow as-
sociated with writing far OTM calls will, as long as you are right about 
the valuation, eventually reduce your EBP enough so that you can make 
a profit on the investment.
Over-/Underexposure
Options are transacted in contract sizes of 100 shares. If you hold a number 
of shares that is not evenly divisible by 100, you must decide whether you 
are going to sell the next number down of contracts or the next number 
up. For example, let’s say that you own 250 shares of ABC. Y ou can either 
choose to sell two call contracts (in which case you will not be receiving 
yield on 50 of your shares) or sell three call contracts (in which case you 
will be effectively shorting 50 shares). My preference is to sell fewer con-
tracts controlling fewer shares than I hold, and in fact, your broker may or 
may not insist that you do so as well. If not, it is an unpleasant feeling to get 
a call from a broker saying that you have a margin call on a position that 
you didn’t know you had.
Getting Assigned
If you write covered calls, you live with the risk that you will have to deliver 
your beloved shares to a stranger. Y ou can deliver your shares and use the 
proceeds from that sale (the broker will deposit an amount equal to the 
strike price times the contract multiplier into your account, and you get 
to keep the premium you originally received) to buy the shares again, but 
there is no way around delivering the shares if assigned.
248  •   The Intelligent Option Investor
Now that you understand covered calls, let’s turn to protective 
puts.
Protective Puts
LIGHT GREEN
RED
GRAY
Downside: Irrelevant
Upside: Undervalued
Execute: Buy common stock and simultaneously buy a put op-
tion (the diagram shows the purchase of an OTM put 
option)
Risk: Purchase price of stock minus strike price of put option 
minus premium paid
Reward: Unlimited, less premium paid for put option, which can-
not be recovered
Margin: None because this is a purchase of an option
The Gist
If you look just as far as the option tenor lasts in the preceding diagram, 
you will see that the risk-return profile is identical to that of a short put. As 
evidence, please compare the following two diagrams:
Mixing Exposure  •  249
GREEN
RED
GRAY
GREEN
ORANGE
Protective put
ITM call
250  •   The Intelligent Option Investor
The graphic conventions are a little different, but both diagrams show 
the acceptance of a narrow band of downside exposure offset by a bound-
less gain of upside exposure. The area below the protective put’s strike price 
shows that economic exposure has been neutralized, and the area below 
the ITM call shows no economic exposure. The pictures are slightly differ-
ent, but the economic impact is the same.
The objective of a protective put is obvious—allow yourself the 
economic benefits from gaining upside exposure while shielding yourself 
from the economic harm of accepting downside exposure. The problem is 
that this protection comes at a price. I will provide more infromation about 
this in the next section.
Execution
Everyone understands the concept of protective puts—it’s just like the 
home insurance you buy every year to insure your property against dam-
age. If you buy an OTM protective put (let’s say one struck at 90 percent of 
the current market price of the stock), the exposed amount from the stock 
price down to the put strike can be thought of as your “deductible” on your 
home insurance policy. The premium you pay for your put option can be 
thought of as the “premium” you pay on your home insurance policy.
Okay—let’s go shopping for stock insurance. Apple (AAPL) is trad-
ing for $452.53 today, so I’ll price both ATM and OTM put insurance for 
these shares with an expiration of 261 days in the future. I’ll also annualize 
that rate.
Strike ($) “Deductible” ($) “Premium” ($)
Premium as 
Percent of 
Stock Price
Annualized 
Premium (%)
450 2.53 40.95 9.1 12.9
405 47.53 20.70 4.6 6.5
360 92.53 8.80 1.9 2.7
Now, given these rates and assuming that you are insuring a $500,000 
house, the following table shows what equivalent deductibles, annual 
premiums, and total liability to a home owner would be for deductibles 
equivalent to the strike prices I’ve picked for Apple: 
Mixing Exposure  •  251
Equivalent 
AAPL Strike ($) Deductible ($)  Annual Premium ($)
Total Liability to Home 
Owner ($)
450 2,795 64,500 67,295
405 52,516 32,500 85,016
360 102,236 13,500 115,736
I know that I would not be insuring my house at these rates and under 
those conditions! In light of these prices, the first thing you must consider 
is whether protecting a particular asset from unrealized price declines is 
worth the huge realized losses you must take to buy put premium. Buying 
ATM put protection on AAPL is setting up a 12.9 percent hurdle rate that 
the stock must surpass in one year just for you to start making a profit on 
the position, and 13 percent per year is quite a hurdle rate!
If there is some reason why you believe that you need to pay for insurance, 
a better option—cheaper from a realized loss perspective—would be to sell 
the shares and use part of the proceeds to buy call options as an option-based 
replacement for the stock position. This approach has a few benefits:
1. The risk-reward profile is exactly the same between the two 
structures.
2. Any ATM or ITM call will be more lightly levered than any OTM 
put, meaning a lower realized loss on initiation.
3. For dividend-paying stocks, call owners do not have the right to 
receive dividends, but the amount of the projected dividend is de-
ducted from the premium (as part of the drift calculation shown 
in the section on covered calls). As such, although not being paid 
dividends over time, you are getting what amounts to a one-time 
upfront dividend payment.
4. If you do not like the thought of leverage in your portfolio, you can 
self-margin the position (i.e., keep enough cash in reserve such that 
you are not “borrowing” any money through the call purchase).
I do not hedge individual positions, but I do like the ITM call op-
tion as an alternative for people who feel the need to do so. For hedg-
ing of a general portfolio, rather than hedging of a particular holding in 
a portfolio, options on sector or index exchange-traded funds (ETFs) are 
more reasonably priced. Here are the ask prices for put options on the SPX 
252  •   The Intelligent Option Investor
ETF [tracking the Standard and Poor’s 500 Index (S&P 500), which closed 
at 1,685.73 when these data were retrieved] expiring in about 10 months:
Strike/Stock ($) Ask Price ($) Premium as  Percent of Stock Price
0.99 106.60 6.3
0.89 50.90 3.0
0.80 25.80 1.5
This is still a hefty chunk of change to pay for protection on an index but 
much less than the price of protection on individual stocks.
1
Common Pitfalls
Hedge Timing
Assume that you had talked to me a year ago and decided to take my ad-
vice and avoid buying protective puts on single-name options. Instead, you 
took a protective put position on the S&P 500. Good for you. 
Setting aside for a moment how much of your portfolio to hedge, let’s 
take a look at what happened since you bought the downside protection:
S&P 500
1,800
1,700
1,600
1,500
1,400
1,300
1,200
1,100
1,000
8/1/20129/1/201210/1/201211/1/201212/1/20121/1/20132/1/20133/1/20134/1/20135/1/20136/1/20137/1/2013
GREEN
Mixing Exposure  •  253
When you bought the protection, the index was trading at 1,375, so 
you bought one-year puts about 5 percent OTM at $1,300. If the market 
had fallen heavily or even moderately during the first five months of the 
contract, your puts would have served you very well. However, now the 
puts are not 5 percent OTM anymore but 23 percent OTM, and it would 
take another Lehman shock for the market to make it down to your put 
strike.
Keeping in mind that buying longer-tenor options gives you a better 
annualized cost than shorter-tenor options, you should be leery of entering 
into a hedging strategy such as the one pictured here:
S&P 500
1,800
1,700
1,600
1,500
1,400
1,300
1,200
1,100
1,000
8/1/20129/1/201210/1/201211/1/201212/1/20121/1/20132/1/20133/1/20134/1/20135/1/20136/1/20137/1/2013
GREEN
Buying short-tenor puts helps in terms of providing nearer to 
ATM protection, but the cost is higher, and it gets irritating to keep 
buying expensive options and never benefiting from them (funny—
no one ever says this about home insurance). Although there are no 
perfect solutions to this quandary, I believe the following approach 
has merit:
254  •   The Intelligent Option Investor
S&P 500
1,800
1,700
1,600
1,500
1,400
1,300
1,200
1,100
1,000
8/1/20129/1/201210/1/201211/1/201212/1/20121/1/20132/1/20133/1/20134/1/20135/1/20136/1/20137/1/2013
GREEN GREENLIGHT GREEN
LIGHT GREEN
LIGHT GREEN
Here I bought fewer long-term put contracts at the outset and then add-
ed put contracts at higher strikes opportunistically as time passed. I have left 
myself somewhat more exposed at certain times, and my protection doesn’t all 
pick up at a single strike price, so the insurance coverage is spotty, but I have 
likely reduced my hedging cost a great deal while still having a potential source 
of investible cash on hand in the form of options with time value on them.
The Unhappy Case of a Successful Hedge
Markets are down across the board. Y our brokerage screen is awash in red. 
The only bright spot is the two or three lines of your screen showing your 
S&P 500 puts, which are strongly positive. Y ou bought your protection 
when the market was going up, so it was very cheap to purchase. Now, with 
the market in a terror, the implied volatilities have shot up, and you are sit-
ting on a huge positive unrealized value.
Now what?
The psychological urge to keep that hedge on will be strong. Such a po-
sition is safe after all, and with the rest of the world falling apart, it feels nice to 
have somewhere safe to go. What should you do with this unrealized profit?
Mixing Exposure  •  255
Step one is always assessing the value of securities in your portfolio 
and securities that might be on your watch list. Does the news driving the 
markets down have a material effect on the value of any of your holdings? 
Certainly, if the market believes that the economy is going into a recession, 
the next few years’ worth of revenue growth and profits may be those that 
you projected for your explicit-period worst-case scenarios, but that will 
likely be offset by faster medium-term growth as the economy bounces 
back. Think about the valuations you have for your holdings objectively and 
with as little passion as possible. It’s better not to have your brokerage screen 
or a price chart of the financial markets or whatever up while you do this.
Are there securities whose present prices are significantly different from 
your worst-case valuation range? Do the prices imply an unlevered return of 30, 
40, or 50 percent or more? Is there a stock that has been on your watch list for a 
long time but until now has never been at a price at which you wanted to buy it?
This is where you must resist the urge to take the safe path and close the 
hedge and then turn around the cash and increase your position size on your 
best investments or on investments that you have always wanted to make but 
haven’t had the chance. This will be a hard thing to do psychologically. The 
world is telling you to run and hide. This is the time to remember the maxim, 
“Be bold when others are scared and scared when others are bold. ” Times of 
stress are those that set great investors apart from the rest of the crowd.
Not Having a Plan
Finally, we get to the question of how to size our hedge. If we look at the in-
dicative prices for S&P 500 puts shown earlier, we can see that if we choose 
to hedge the entire amount of our portfolio, we set up at least a 6 percent-
age point drag on our portfolio every 10 months or so, and that is a lot of 
potentially dead weight to be carrying around.
In daily life, I believe that people are prone to overinsure (e.g., 
extended warrantees for consumer electronic items and so on), and this 
is a good habit to keep away from in investing. Risk is not a temporary 
unrealized loss caused by market panic. Usually risk is not the inability to 
invest more capital when you want to invest more capital (unless by not 
investing it you will have a shortfall in capital in the future). Risk is usually 
not any of the things TV pundits talk about as being risk.
256  •   The Intelligent Option Investor
I will discuss risk in greater detail in Chapter 12, but a sensible defini-
tion of risk is not having the capital resources to pay for something when 
you need to pay for it. In this sense, risk can be talked about in terms of 
liquidity—a short-term lack of spending power—and solvency—a funda-
mental lack of capital assets. For example, let’s say that you have commit-
ted to pay a restaurant and entertainers the remainder of their $50,000 fee 
for your son’s bar mitzvah or your daughter’s wedding, and you only have 
$20,000 in net worth. Y ou are in a position of risk because of problems of 
solvency but not necessarily liquidity (i.e., you could borrow the money to 
pay for these things). However, if you have a net worth of $3 million—all of 
it unrealized gains on real estate holdings—and you have the same $50,000 
bill to pay, you may be in a position of risk because of problems in liquidity 
but not solvency.
Risk that stems from issues of liquidity usually can be controlled 
through intelligent asset allocation. For example, the millionaire father in 
the preceding bar mitzvah/wedding example can realize $50,000 worth 
of his unrealized investment gains to meet his immediate cash need. A 
79-year-old with 85 percent of her net worth of $2.5 million invested in 
tech sector initial public offerings (IPOs) or companies in the Chinese in-
frastructure supply chain can ameliorate her risk of not being able to pay 
for necessary healthcare and living expenses by shifting more of her assets 
into bonds and CDs. Usually, in cases such as this—which, I believe, make 
up the majority of cases people are trying to “hedge”—there are much 
better ways of controlling risk than buying puts on the S&P 500 or the 
Russell 2000! 
However, there is a more subtle instance of risk—not maximizing re-
turns on one’s invested capital and, because of this, not having the capital 
adequacy to meet unforeseen cash-flow needs in the future. This instance 
of risk deals with solvency, rather than liquidity.
This type of risk cannot be ameliorated through a defensive strategy 
but must be controlled through an offensive one. Setting aside savings, in-
vesting those savings wisely and consistently in good times, and having the 
courage to invest when it is hardest to do so (i.e., when the market is crash-
ing) are all elements of this risk-control strategy. Put options can only help 
with the third case here—investing when it is hardest to do so—but they 
cannot help without the put owner’s input of personal courage.
Mixing Exposure  •  257
This topic brings us back to the last section—investing the proceeds 
in a successful hedge in undervalued assets. I believe that portfolio hedges 
should be set up with a particular cost and investing goal in mind. For 
example, “I am willing to allocate as much as 1 percentage point of my 
investment performance this year to have an extra 5 percent of cash on 
hand to invest in case the market drops by 10 to 20 percent. ” This is the 
rough outline of a hedging plan. It specifies the maximum you are will-
ing to spend and a target for how much cash you want in case of a certain 
market downdraft.
This plan does not mean that you always have to spend 1 percent 
of your net worth on hedges. There are times when it is more sensible to 
spend more on hedges—because of building macroeconomic uncertainty 
or whatever—and other times when it is more sensible to spend less—when 
the economy is just coming out of a recession for instance.
Also note that the plan specifies a cash level. If you are not fully in-
vested in your securities portfolio, you are already hedged to the degree 
that your cash assets are not subject to direct security price risk (cash is 
subject to inflation risk, but this is another topic). The cash you have on 
reserve will allow you to purchase if and when the market falls. As such, 
I don’t believe that people holding a significant allocation of cash should 
think about hedging per se. Y ou may believe that the market is ready to fall, 
in which case, you can make a bearish bet on the level of the index using a 
long put, a short-call spread, or a short diagonal, but this is a proactive in-
vestment that expresses your opinion about the level of the market vis-à-vis 
the state of the economy.
What it does not specify is what you will spend the cash on. This is 
where an understanding of the value of the companies in your portfolio 
or on your watch list comes into play. If you had an extra 5 percent (or 
$50,000 or however you want to think about it) in cash, in what securities 
would you invest? Of course, the answer will change depending on the 
price of the securities vis-à-vis what you know to be a sensible valuation 
range because the expected returns on the investments will change with 
the market price. 
So this is the last step in a sensible hedging plan—having an idea of 
what companies you would want to invest in were you to have the extra 
capital and if you could be reasonably assured of a good return. Having a 
258  •   The Intelligent Option Investor
plan like this in place will allow you to size and time your hedges appropri-
ately and will help you to make the most out of whatever temporary crisis 
might come your way.
2
Now that you have a good understanding of protective puts and 
hedging, let’s turn to the last overlay strategy—the collar.
Collar
Contingent Exposure
Contingent Exposure
Contingent Exposure
GREEN
LIGHT GREEN
LIGHT ORANGE
LIGHT RED
ORANGE
RED
Downside: Irrelevant
Upside: Undervalued
Execute: Sell a call option on a stock or index that you own and on 
which you have a gain, and use the proceeds from the call 
sale to buy an OTM put 
Risk: Flexible, depending on selection of strikes
Reward: Limited to level of sold call strike
Margin: None because the long position in the hedged security 
serves as collateral for the sold call option, and the OTM 
put option is purchased, so it does not require margining
Mixing Exposure  •  259
The Gist
This structure is really much simpler and has a much more straightfor -
ward investment purpose than it may seem when you look at the preceding 
diagram. When people talk about “taking profits” using a covered call, the 
collar is actually the strategy they should be using.
Imagine that you bought a stock some time ago and have a nice 
unrealized gain on it. The stock is about where you think its likely fair 
value is, but you do not want to sell it for whatever reason (e.g., it is 
paying a nice dividend or you bought it less than a year ago and do not 
want to be taxed on short-term capital gains or whatever). Although you 
do not want to sell it, you would like to protect yourself from downside 
exposure.
Y ou can do this cheaply using a collar. The collar is a covered call, 
which we have already discussed, whose income subsidizes the purchase of 
a protective put at some level that will allow you to keep some of the unre-
alized gains on your securities position. The band labeled “Orange” on the 
diagram shows an unrealized gain (or, conversely, a potential unrealized 
loss). If you buy a put that is within this orange band or above, you will be 
guaranteed of making at least some realized profit on your original stock 
or index investment. Depending on how much you receive for the covered 
call and what strike you select for the protective put, this collar may rep-
resent completely “free” downside protection or you might even be able to 
realize a net credit.
Execution
The execution of this strategy depends a great deal on personal prefer -
ence and on the individual investor’s situation. For example, an investor 
can sell a short-tenor covered call and use those proceeds to buy a longer-
tenor protective put. He or she can sell the covered call ATM and buy a 
protective put that is close to ATM; this means the maximum and mini-
mum potential return on the previous security purchase is in a fairly tight 
band. Conversely, the investor might sell an OTM covered call and buy 
a protective put that is also OTM. This would lock in a wider range of 
guaranteed profits over the life of the option.
260  •   The Intelligent Option Investor
I show a couple of examples below that give you the flavor of the 
possibilities of the collar strategy. With these examples, you can experi-
ment yourself with a structure that fits your particular needs. Look on 
my website for a collar scenario calculator that will allow you to visualize 
the collar and understand the payoff structure given different conditions. 
For these examples, I am assuming that I bought Qualcomm stock at  
$55 per share. Qualcomm is now trading for $64.71—an unrealized gain 
of 17.7 percent.
Collar 1: 169 Days to Expiration
Strike Price ($) Bid (Ask) Price ($)
Sold call 65.00  3.40
Purchased put 60.00 (2.14)
Net credit $1.26
This collar yields the following best- and worst-case effective sell prices 
(ESPs) and corresponding returns (assuming a $55 buy price):
ESP ($) Return (%)
Best case 66.26 20.5
Worst case 61.26 11.4
Here we sold the $65-strike calls for $3.40 and used those proceeds to 
buy the $60-strike put options at $2.14. This gave us a net credit of $1.26, 
which we simply add to both strike prices to calculate our ESP . We add the 
net credit to the call strike because if the stock moves above the call strike, 
we will end up delivering the stock at the strike price while still keeping the 
net credit. We add the net credit to the put strike because if the stock closes 
below the put strike, we have the right to sell the shares at the strike price 
and still keep the net credit. The return numbers are calculated on the basis 
of a $55 purchase price and the ESPs listed. Thus, by setting up this collar in 
Mixing Exposure  •  261
this way, we have locked in a worst possible gain of 11.4 percent and a best 
possible gain of 20.5 percent for the next five and a half months.
Let’s look at another collar with a different profit and loss profile:
Collar 2: 78 Days to Expiration
Strike Price ($) Bid (Ask) Price ($)
Sold call 70  0.52
Purchased put 62.50 (1.55)
Net debit (1.03)
This collar yields the following best- and worst-case ESPs and corresponding 
returns (assuming a $55 buy price):
ESP ($) Return (%)
Best case 68.97 25.4
Worst case 61.47 11.8
This shows a shorter-tenor collar—about two and a half months be-
fore expiration—that allows for more room for capital gains. This might be 
the strategy of a hedge fund manager who is long the stock and uncertain 
about the next quarterly earnings report. For his or her own business rea-
sons, the manager does not want to show an unrealized loss in case Qual-
comm’s report is not good, but he or she also doesn’t want to restrict the 
potential capital gains much either.
Calculating the ESPs and the returns in the same way as described 
here, we get a guaranteed profit range from around 12 to over 25 percent. 
One thing to note as well is that the protection is provided by a put, and 
a put option can be sold any time before expiry to generate a cash inflow 
from time value. Let’s say then that when Qualcomm reports its quarterly 
earnings, the stock price drops to $61—a mild drop that the hedge fund 
manager considers a positive sign. Now that the manager is less worried 
about the downside exposure, he or she can sell the put for a profit.  
262  •   The Intelligent Option Investor
The cash inflow from selling the put for a profit may even change the net 
debit on the collar to a net credit, or the manager can use some of the cash 
flow to buy back the sold call option if he or she is worried about the upside 
being limited. 
These are just two examples, but they show the kind of flexibility that 
makes collars very useful investing instruments. With this chapter com-
plete, you have all the tools required to be an intelligent option investor. 
Let’s finish with an important discussion—an investigation of risk and in-
telligent option investing. This is the topic of Chapter 12.
263
Chapter 12
Risk and the intelligent 
OptiOn investOR
The preceding 11 chapters have given you a great deal of information about 
the mechanics of option investing and stock valuation. In this last chapter, 
let’s look at a subject that I have mentioned throughout this book—risk—
and see how an intelligent option investor conceives of it. 
There are many forms of risk—some of which we discussed earlier 
(e.g., the career risk of an investment business agent, solvency risk of a 
retiree looking to maintain a good quality of life, and liquidity risk of a 
parent needing to make a big payment for a child’s wedding). The two risks 
I discuss here are those that are most applicable to an owner of capital 
making potentially levered investments in complex, uncertain assets such 
as stocks. These two risks are market risk and valuation risk.
Market Risk
Market risk is unavoidable for anyone investing capital. Markets fluctuate, and 
in the short term, these fluctuations often have little to do with the long-term 
value of a given stock. Short term, it must be noted, is also relative. In words 
attributed to John Maynard Keynes, but which is more likely an anonymous 
aphorism, “The market can remain irrational longer than you can remain sol-
vent. ” Indeed, it is this observation and my own painful experience of the truth 
of it that has brought me to my appreciation for in-the-money (ITM) options 
as a way to preserve my capital and cushion the blow of timing uncertainty.

264  •   The Intelligent Option Investor
Market risk is a factor that investors in levered instruments must 
always keep in mind. Even an ITM call long-term equity anticipated 
security (LEAPS) in the summer of 2007 might have become a short-tenor 
out-of-the-money (OTM) call by the fall of 2008 after the Lehman shock 
because of the sharp decline in stock prices in the interim. Unexpected 
things can and do happen. A portfolio constructed oblivious to this fact is 
a dangerous thing.
As long as market fluctuations only cause unrealized losses, market 
risk is manageable. But if a levered loss must be realized, either because of 
an option expiration or in order to fund another position, it has the poten-
tial to materially reduce your available investment capital. Y ou cannot ma-
terially reduce your investment capital too many times before running out.
A Lehman shock is a worst-case scenario, and some investors live 
their entire lives without experiencing such severe and material market 
risk. In most cases, rather than representing a material threat, market risk 
represents a wonderful opportunity to an intelligent investor.
Most human decision makers in the market are looking at either 
technical indicators—which are short term by nature—or some sort of 
multiple value (e.g., price-to-something ratio). These kinds of measures are 
wonderful for brokers because they encourage brokerage clients to make 
frequent trades and thus pay the brokerages frequent fees. 
The reaction of short-term traders is also wonderful for intelligent 
investors. This is so because a market reaction that might look sensible or 
rational to someone with an investment time horizon measured in days or 
months will often look completely ridiculous to an investor with a longer-
term perspective. For example, let’s say that a company announces that its 
earnings will be lower next quarter because of a delay in the release of a 
new product. Investors who are estimating a short-term value for the stock 
based on an earnings multiple will sell the stock when they see that earn-
ings will likely fall. Technical traders see that the stock has broken through 
some line of “resistance” or that one moving average has crossed another 
moving average, so they sell it as well. Perhaps an algorithmic trading 
engine recognizes the sharp drop and places a series of sell orders that are 
covered almost as soon as they are filled. In the meantime, someone who 
has held the stock for a while and has a gain on it gets protective of this gain 
and decides to buy a put option to protect his or her gains.

Risk and the Intelligent Option Investor   • 265
For an intelligent option investor who has a long-term worst-case 
valuation that is now 20 percent higher than the market price, there is a 
wonderful opportunity to sell a put and receive a fat premium (with the 
possibility of owning the stock at an attractive discount to the likely fair 
value), sell a put and use the proceeds to buy an OTM call LEAPS, or sim-
ply buy the stock to open a position.
Indeed, this strategy is perfectly in keeping with the dictum, “Be fear-
ful when others are greedy and greedy when others are fearful. ” This strat-
egy is also perfectly reasonable but obviously rests on the ability of the 
investor to accurately estimate the actual intrinsic value of a stock. This 
brings us to the next form of risk—valuation risk.
Valuation Risk
Although valuation is not a difficult process, it is one that necessarily in-
cludes unknowable elements. In our own best- and worst-case valuation 
methodology, we have allowed for these unknowns by focusing on plausi-
ble ranges rather than precise point estimates. Of course, our best- or worst-
case estimates might be wrong. This could be due to our misunderstanding 
of the economic dynamics of the business in which we have invested or 
may even come about because of the way we originally framed the problem. 
Thinking back to how we defined our ranges, recall that we were focusing 
on one-standard-deviation probabilities—in other words, scenarios that 
might plausibly be expected to materialize two times out of three. Obvi-
ously, even if we understand the dynamics of the business very well, one 
time out of three, our valuation process will generate a fair value range that 
is, in fact, materially different from the actual intrinsic value of the stock.
In contrast to market risk, which most often is a nonmaterial and tem-
porary issue, misestimating the fair value of a stock represents a material 
risk to capital, whether our valuation range is too low or too high. If we esti-
mate a valuation range that is too low, we are likely to end up not allocating 
enough capital to the investment or using inappropriately light leverage. 
This means that we will have missed the opportunity to generate as much 
return on this investment as we may have. If we estimate a valuation range 
that is too high, we are likely to end up allocating too much capital to the 

266  •   The Intelligent Option Investor
investment or using inappropriately high leverage. In the best case, we allo-
cate too much capital to an idea that generates low returns when we might 
have allocated it to a higher-return investment. In the worst case, we suffer 
a loss of capital when the market price falls and we realize that our original 
estimates were overly optimistic.
One of the best ways to protect against valuation risk is to invest in 
only the most compelling, most clearly mispriced securities. A friend who 
worked for years advising companies on mergers and acquisitions has a 
wonderful way of visualizing valuation risk that I have found particularly 
helpful.
1 In his conception, a company’s stock price can be represented  
by layers. At the bottom layer is the value of the company’s net assets if they 
were all sold today. The next layer assumes that, for instance, the company 
will cease to exist as a going concern after 10 years and will sell its net 
assets then. The next layer assumes that, for instance, the company exists 
perpetually as a going concern, but its free cash flow to owner(s) (FCFO) 
doesn’t grow again. On and on, each layer represents a more aggressive 
assumption about the growth of its cash flows until we are assuming, for 
instance, that the company’s FCFO will grow at an average of 50 percent 
per year for the next 15 years and then 6 percent for every year after that in 
perpetuity. We can visualize this in the following graphic:
Value of cash flows growing at 50 percent per year for 15 years and 
then at 6 percent per year after that—$52 per share.
Value of cash flows growing at 20 percent per year for 15 years and 
then at 6 percent per year after that—$27/share.
Value of cash flows not growing but continuing on into 
perpetuity—$9 per share.
Value of cash flows not growing and lasting 20 years—$7 per  
share.
Market value of hard assets—$2 to $4 per share.

Risk and the Intelligent Option Investor   • 267
Let’s assume that the present market value of the shares is $16 per 
share. This share price assumes a growth in FCFO of 8 percent per year for 
the next 5 years and 5 percent per year in perpetuity after that—roughly  
equal to what we consider our most likely operational performance 
scenario. We see the possibility of faster growth but realize that this faster 
growth is unlikely—the valuation layer associated with this faster growth 
is the $18 to $20 level. We also see the possibility of a slowdown, and the 
valuation layer associated with this worst-case growth rate is the $11 to 
$13 level.
Now let’s assume that because of some market shock, the price of the 
shares falls to the $10 range. At the same time, let’s assume that the likely 
economic scenario, even after the stock price fall, is still the same as before—
most likely around $16 per share; the best case is $20 per share, and the worst 
case is $11 per share. Let’s also say that you can sell a put option, struck at 
$10, for $1 per share—giving you an effective buy price of $9 per share.
In this instance, the valuation risk is indeed small as long as we are 
correct about the relative levels of our valuation layers. Certainly, in this 
type of scenario, it is easier to commit capital to your investment idea than 
it would be, say, to sell puts struck at $16 for $0.75 per share!
Thinking of stock prices in this way, it is clear that when the market 
price of a stock is within a valuation layer that implies unrealistic economic 
assumptions, you will more than likely be able to use a combination of 
stocks and options to tilt the balance of risk and reward in your own 
favor—the very definition of intelligent option investing.
Intelligent Option Investing
In my experience, most stocks are mostly fairly priced most of the time. 
There may be scenarios at one tail or the other that might be inappropriately 
priced by the option market (and, by extension, by the stock market), but 
by and large, it is difficult to find profoundly mispriced assets—an asset 
whose market price is significantly different from its most likely valuation 
layer.
Opportunities tend to be most compelling when the short-term pic-
ture is the most uncertain. Short-term uncertainties make investing boldly 

268  •   The Intelligent Option Investor
a psychologically difficult process, but indeed, it is those times that make 
the difference between a successful investor and an investor who nurtures 
many regrets.
In the end, an intelligent option investor is not one who has a much 
better knowledge of some sector, industry, or even company. It is not the 
investor who takes the biggest risks in the hope of realizing the biggest 
return. It is not the investor who attempts always to be the investing 
“hero” and make the most complex, theoretically beautiful, laboriously 
researched argument to justify an investment. Rather, the intelligent op-
tion investor is the one who has a sound, repeatable process for estimat-
ing the value of stocks, an understanding of the pitfalls that can limit an 
investor’s potential, and a firm understanding of the tools that can be 
used to invest. It is the investor who understands the limits to his or her 
own expertise but who also understands that market risk does not equal 
valuation risk and has the courage to act boldly when the two deviate 
the most.
In short, the intelligent option investor is you.

269
Appendix A
Choose Your Battles 
WiselY
I discuss specific option investment strategies in great detail in Part III 
of this book. However, after reading Chapters 2 and 3, you should have a 
good understanding of how options are priced, so it is a good time to see 
in what circumstances the Black-Scholes-Merton model (BSM) works best 
and where it works worst. An intelligent investor looks to avoid the condi-
tions where the BSM works best like the plague and seek out the conditions 
where it works worst because those cases offer the best opportunities to tilt 
the risk-reward balance in the investor’s favor.
Jargon introduced in this appendix includes
Front month
Fungible
Idiosyncratic assets
Where the BSM Works Best
The following are the situations in which the BSM works best and are the 
conditions you should most avoid:
1. Short investment time horizons
2. Fungible investment assets
270  •   The Intelligent Option Investor
Short Investment Time Horizons
When the scholars developing the BSM were researching financial 
markets for the purpose of developing their model, the longest-tenor 
options had expirations only a few months distant. Most market partic-
ipants tended to trade in the front-month  contracts (i.e., the contracts 
that will expire first), as is still mainly the case. Indeed, thinking back 
to our preceding discussion about price randomness, over short time 
horizons, it is very difficult to prove that asset price movements are not 
random.
As such, the BSM is almost custom designed to handle short time 
horizons well.
Perhaps not unsurprisingly, agents
1 are happy to encourage clients to 
trade options with short tenors because
1. It gives them more opportunities per year to receive fees and com-
missions from their clients. 
2. They are mainly interested in reliably generating income on the 
basis of the bid-ask spread, and bid-ask spreads differ on the basis 
of liquidity, not time to expiration. 
3. Shorter time frames offer fewer chances for unexpected price 
movements in the underlying that the market makers have a hard 
time hedging.
In essence, a good option market maker is akin to a used car sales-
man. He knows that he can buy at a low price and sell at a high one, so his 
main interest is in getting as many customers to transact as possible. With 
this perspective, the market maker is happy to use the BSM, which seems 
to give reasonable enough option valuations over the time period about 
which he most cares.
In the case of short-term option valuations, the theory describes 
reality accurately enough, and structural forces (such as wide bid-ask 
spreads) make it hard to exploit mispricings if and when they occur. 
To see an example of this, let’s take a look at what the BSM assumes is 
a reasonable range of prices for a company with assumed 20 percent 
volatility over a period of 30 days.
Appendix A: Choose Your Battles Wisely   • 271
10
-
20
30
40
50
60
70
The range of prices implied over the next 30 days goes from around 
$47 per share to around $53 per share. If we translate what the BSM con-
siders the reasonable range into percentage terms, it works out to a loss 
or gain of around 6 percent. Just thinking about this in terms of one’s 
personal experience for a moment, this is actually not a bad guess for a 
range for a large-capitalization firm (the forward volatility assumption of  
20 percent is consistent with a large-cap firm’s “typical” implied volatility). 
I certainly would have no confidence in trying to guess the upper and 
lower stock price boundaries any better than the BSM on such a short 
time frame. 
It is funny, then, that most investors insist on speculating in options 
on a short-term basis—usually at tenors of a month or shorter. Again, these 
seem like the kinds of bets you might get betting on red at a roulette wheel 
in Vegas. Sure, it makes one feel like James Bond the 50 percent of the time 
that the marble falls on red, but anyone who is the least bit thoughtful 
would, after a time, step back and wonder how far ahead he or she is getting 
by playing such a game.
2
272  •   The Intelligent Option Investor
It is important to realize that the fact that options are usually 
efficiently priced in the short term does not prevent us from transacting 
in short-tenor options. In fact, some strategies discussed in Part III are 
actually more attractive when an investor uses shorter-tenor options or 
combines short- and long-tenor options into a single strategy.
Hopefully, the distinction between avoiding short-tenor option 
strategies and making long-term investments in short-tenor options is 
clear after reading through Part III.
Fungible Underlying Assets
Again, returning for a moment to the foundation of the BSM, the scholars built 
their mathematical models by studying short-term agricultural commodity 
markets. A commodity is, by definition, a fungible or interchangeable asset; 
one bushel of corn of a certain quality rating is completely indistinguishable 
from any other bushel of corn of the same quality rating.
Stocks, on the other hand, are idiosyncratic assets. They are intangible 
markers of value for incredibly complex systems called companies, no two 
of which is exactly alike (e.g., GM and Ford—the pair that illustrates the 
idea of “paired” investments in many people’s minds—are both American 
car companies, but as operating entities, they have some significant differ-
ences. For example, GM has a much larger presence in China and has a 
different capital and governance structure since going bankrupt than Ford, 
which avoided bankruptcy during the mortgage crisis).
The academics who built the BSM were not hesitant to apply a model 
that would value idiosyncratic assets such as stocks because they had as-
sumed from the start that financial markets are efficient—meaning that 
every idiosyncratic feature for a given stock was already fully “priced in” 
by the market. This allowed them to overlook the complexity of individual 
companies and treat them as interchangeable, homogeneous entities.
The BSM, then, did not value idiosyncratic, multidimensional 
companies; rather, it valued single-dimensional entities that the scholars 
assumed had already been “standardized” or commoditized in some sense 
by the communal wisdom of the markets. Y ou will see in the next sec-
tion that the broad, implicit assumption by option market participants 
that markets are efficient actually brings about the greatest opportunity 
Appendix A: Choose Your Battles Wisely   • 273
to derive low-risk profits for intelligent investors. The point I make here 
is simply how difficult it is to invest in options on commodities or in fact 
any asset that you cannot analyze using fundamental valuation techniques.
For investors who simply cannot resist making commodity investments, 
I offer the following case study: I personally believe that climate change will 
make it harder for the world to feed its burgeoning population. Among 
exchange-traded funds (ETFs), futures, and options, it is very easy these days 
to express an investment opinion on such a belief, and I have done just that—
put my money where my mouth is. While I have made such investments,  
I must admit that I have absolutely no basis for my valuation of the agricul-
tural commodities in question and have no way to know if I have received my 
bullish exposure to these commodities at a reasonable or unreasonable price.
Such speculative investments satisfy some psychological need, but they are 
not investments in the strict “intelligent investor” sense because it is very hard to 
rationally calculate a fair value for the asset. Should these types of investments 
not be made, then? A strict adherent to rational investment principles might 
say, “No, they should not be. ” However, considering the irrational ways people 
find to spend money, it would seem that we have been somehow hardwired to 
do things in a way that an economist would not consider totally rational. Rather 
than fight that primitive urge, I prefer to give into it—but only with very small 
parts of my portfolio. This strategy is akin to taking only $50 to the casino floor 
and promising that once that money is gone, you won’t spend any more. 
Y ou may have a gut feeling about the price of oil, the level of interest 
rates, the price of cotton, or whatever. Do yourself a favor, and if you chose 
to make a financial bet on the basis of your hunch, do as I do and make 
it a small one. While a small investment means different things to differ -
ent people, a good way to judge is to imagine the capital being completely 
gone. If you have heart palpitations at that thought, keep cutting the pro-
spective investment in half until you feel better.
Where the BSM Works Worst
Now that we know where not to look for intelligent option investments, 
let’s look at conditions in which the BSM works worst—these are the best 
places for us to tilt the balance of risk and return in our favor.
274  •   The Intelligent Option Investor
1. Grossly mispriced assets
2. Bimodal outcomes
3. Long investment time horizons
Grossly Mispriced Assets
The main assumption of the BSM is that there are no grossly mispriced as-
sets. I believe that this contention is wrong on the basis of behavioral and 
structural factors that are covered briefly in Part II of this book but would 
require another book to fully cover. 
Just imagine, though, that, for some reason, a stock is dramatically 
undervalued. For right now, I will not discuss why this situation could 
come about, but let’s say that rather than being worth $50 per share, 
a company is worth, best case, closer to $110 per share and, worst case, 
$70 per share. Let’s further say that we had some sort of a hazy crystal 
ball that would give us a very high degree of certainty that these best- and 
worst-case values represent the real future range of values.
Here is what a diagram of that situation would look like:
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Date/Day Count
Advanced Building Corp. (ABC)
Stock Price
Best Case, 110
Worst Case, 70
-
Now look at the following diagrams of a put and a call option and, 
based on what you know about the way the BSM prices options, think 
about the answers to the following questions.
Appendix A: Choose Your Battles Wisely   • 275
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Advanced Building Corp. (ABC)
Stock Price
-
GREEN
Put option
If someone were worried about this stock’s downside potential below $50, 
what would likely be the price that investor would pay to buy this put option?
a. Almost nothing
b. A little
c. A good bit
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Advanced Building Corp. (ABC)
Stock Price
-
RED
Call option
276  •   The Intelligent Option Investor
If someone wanted to make extra income by selling calls to accept expo-
sure to the stock’s upside, what price would they likely charge for someone 
wanting to buy this call option?
a. Almost nothing
b. A little
c. A good bit
Obviously, the correct answer to the put option question is c. This option 
would be pretty expensive because its range of exposure overlaps with so 
much of the BSM cone. Conversely, the answer to the call option question 
is a. This option would be really cheap because its range of exposure is well 
above the BSM cone.
Remember, though, that we have our crystal ball, and we know 
that this stock will likely be somewhere between $70 and $110 per share  
in a few years. With this confidence, wouldn’t it make sense to take the 
opposite side of both the preceding trades? Doing so would look like 
this:
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110
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5/20/2013 249 499 749 999
Date/Day Count
Advanced Building Corp. (ABC)
Stock Price
Best Case, 110
Worst Case, 70
-
GREEN
RED
In this investment, which I explain in detail in Chapter 11, we are 
receiving a good bit of money by selling an expensive put and paying 
Appendix A: Choose Your Battles Wisely   • 277
very little money to buy a cheap call. It may happen that the money we 
receive for selling the put actually may be greater than the money we 
pay for the call, so we actually get paid a net fee when we make this 
transaction!
We can sell the put confidently because we know that our worst-case 
valuation is $70 per share; as long as we are confident in our valuation—a 
topic covered in Part II of this book—we need not worry about the price 
declining. We do not mind spending money on the call because we think 
that the chance is very good that at expiration or before the call will be 
worth much, much more than we paid for it.
Truly, the realization that the BSM is pricing options on inefficiently 
priced stocks as if they were efficiently priced is the most profound and 
compelling source of profits for intelligent investors. Furthermore, finding 
grossly mispriced stocks and exploiting the mispricing using options rep-
resents the most compelling method for tilting the risk-reward equation in 
our direction.
The wonderful thing about investing is that it does not require you to 
swing at all the pitches. Individual investors have a great advantage in that 
they may swing at only the pitches they know they can hit. The process of 
intelligent investing is simply one of finding the right pitches, and intel-
ligent option investing simply uses an extremely powerful bat to hit that 
sweet pitch.
Bimodal Outcomes
Some companies are speculative by nature—for instance, a drug company 
doing cancer research. The company has nothing but some intangible as-
sets (the ideas of the scientists working there) and a great deal of costs 
(the salaries going to those scientists, the payments going to patent attor -
neys, and the considerable costs of paying for clinical trials). If the research 
proves fruitful, the company’s value is great—let’s say $500 per share. If 
the clinical trials show low efficacy or dangerous side effects, however, the 
company’s worth goes to virtually nil. What’s more, it may take years before 
it is clear which of these alternatives is true.
278  •   The Intelligent Option Investor
Given what you know about the BSM, does this seem like the kind of 
situation conducive to accurate option pricing? This example certainly does 
not sound like the pricing scenario of a short-term agricultural commodity, 
after all. If this hypothetical drug company’s stock price was sitting at $50 per 
share, what is the value of the upper range the option market might be 
pricing in? Let’s assume that this stock is trading with a forward volatility of 
100 percent per year (on the day I am writing this, there are only four stocks 
with options trading at a price that implies a forward volatility of greater than 
100 percent). What price range does this 100 percent per year volatility imply, 
and can we design an option structure that would allow us to profit from a big 
move in either direction? Here is a diagram of this situation:
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Advanced Biotechnology Co. (ABC)
Stock Price
749 999
GREEN
GREEN
Indeed, even boosting volatility assumptions to a very high level, 
it seems that we can still afford to gain exposure to both the upside and 
downside of this stock at a very reasonable price. Y ou can see from the pre-
ceding diagram that both regions of exposure on the put side and the call 
side are outside the BSM cone, meaning that they will be relatively cheap. 
The options market is trying to boost the price of the options enough so 
that the calls and puts are fairly priced, but for various reasons (including 
behavioral biases), most of the time it fails miserably. 
Appendix A: Choose Your Battles Wisely   • 279
Long Investment Time Horizons
This is simply a corollary to the rule that the BSM is generally good at 
pricing short-time-horizon investments. The BSM is built on the prem-
ise that stocks will only rise by as much as the risk-free rate. If you ask a 
finance professor or a market maker, he or she will be able to give you an 
elegant and logically consistent reason why this must be so.
However, as you saw in Chapter 3, this situation has never been so—
the return on stocks is sometimes negative but often much more positive 
than risk-free bonds. If we average the returns out, stocks still generate 
returns that are heads and shoulders above bonds.
Over short time horizons, the difference simply isn’t material. For in-
stance, let’s say that we assume that a given stock should generate around 
10 percent compound annual returns over the next three to five years com-
pared with a 5 percent assumption for the risk-free rate. If we are looking at 
very short time horizons—such as 60 days—and assume that our stock will 
grow at exactly that 10 percent rate over that short time, then we should 
compare our expectations with those of the option market. Here is the dia-
gram we would get:
Advanced Building Corp. (ABC)
30
20
40
50
60
70
60 days
80Stock Price
280  •   The Intelligent Option Investor
Clearly, there is not much of a difference between the BSM expected 
value (shown by the dotted line) and the dot representing a 10 percent 
upward drift in the stock. However, if we extend this analysis out for three 
years, look what happens:
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Advanced Building Corp. (ABC)
749 999
20
30
40
50
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70Stock Price
80
With the longer time horizon, our assumed stock price is significantly 
higher than what the BSM calculates as its expected price. If we take “assumed 
future stock price” to mean the price at which we think there is an equal chance 
that the true stock price will be above or below that mark, we can see that the 
difference, marked by the double-headed arrow in the preceding diagram, is the 
advantage we have over the option market.
3 This advantage again means that 
downside exposure will be overvalued and upside exposure will be undervalued.
How, you may ask, can this discrepancy persist? Shouldn’t someone 
figure out that these options are priced wrong and take advantage of an 
arbitrage opportunity? The two reasons why these types of opportunities 
tend to persist are
1. Most people active in the option market are trading on a very 
short-term basis. Long-term equity anticipated securities 
(LEAPS)—options with tenors of a year or more—do exist, but 
Appendix A: Choose Your Battles Wisely   • 281
generally the volumes are light because the people in the option 
markets generally are not willing to wait longer than 60 days for 
their “investment” to work out. Because the time to expiration for 
most option contracts is so short, the difference between the BSM’s 
expected price based on a 5 percent risk-free rate and an expected 
price based on a 10 percent equity return is small, so no one real-
izes that it’s there (as seen on the first diagram).
2. The market makers are generally able to hedge out what little ex-
posure they have to the price appreciation of LEAPS. They don’t 
care about the price of the underlying security, only about the size 
of the bid-ask spread, and they always price the bid-ask spread on 
LEAPS in as advantageous a way as they can. Also, the career of an 
equity option trader on the desk of a broker-dealer can change a 
great deal in a single year. As discussed in Part II, market makers 
are not incentivized in such a way that they would ever care what 
happened over the life of a LEAPS.
Congratulations. After reading Part I of this book and this appendix, 
you have a better understanding of the implications of option investing 
for fundamental investors than most people working on Wall Street. 
There are many more nuances to options that I discuss in Part III of this 
book—especially regarding leverage and the sensitivity of options to input 
changes—but for now, simply understanding how the BSM works puts you 
at a great advantage over other market participants.
282
Appendix B
THe MAny FAceS OF 
LeverAGe
An intelligent option investor must understand investing leverage in 
order to make sense of option investing strategies. Investing leverage is, 
however, not the only form of leverage, and to have a well-rounded and 
well-educated view of investing leverage, you should understand the other 
forms as well. In addition, when assessing the value of companies, it is im-
portant to understand leverage because leverage often is the root cause of 
rapid changes in profitability during times of changing consumer demand 
such as inflection points in the business cycle.
Operational Leverage
Operational leverage is the acceptance of fixed operating costs in order to 
make a higher per-unit profit, such as when a company decides to build a 
factory rather than contracting for its products to be made by a third party. 
When a company spends cash to build a factory, that expenditure is not 
treated as an immediate cost on the income statement. Rather, the cost 
of the new factory is spread over future periods as the noncash expense 
known as depreciation.
1
Let us take a look at two companies, both of which produce the same 
items, but one of which outsources production to a third party (Unlevered 
Co.) and the other of which has built a factory to manufacture its products 
Appendix B: The Many Faces of Leverage  • 283
(Levered Co.). In reality, there are methods used by companies to front-
load depreciation expenses in order to minimize taxable income for new 
projects, but let’s assume that Levered Co. is using what is called straight-
line depreciation so that the charge is identical each quarter.
Unlevered Co. Levered Co.
Revenues 100.0 100.0
Fixed depreciation expense 0.0 −65.0
Variable operating expenses −85.0 −15.0
Operating profit 15.0 20.0
Pretax profit 15.0 20.0
Tax −4.5 −6.0
Net profit 10.5 14.0
As you can see here, Levered Co. ’s profits are a bit better than those 
of Unlevered Co. because the former is not paying a supplier and can 
produce the items at a lower cost. Note also that both companies have 
variable costs. For Unlevered Co., these variable costs include the costs 
of the items it has produced by the third party plus whatever salaries it 
has to pay to salespeople and administrative staff; for Levered Co., vari-
able costs include the costs of raw materials plus the cost of any salaries 
paid to production, sales, and administrative staff. This is our base case—
representing midcycle economic conditions (i.e., not boom or not bust).
Now let’s look at the two companies during a trough in the business 
cycle—or bust conditions.
Unlevered Co. Levered Co.
Revenues 70.0 70.0
Fixed depreciation expense 0.0 −65.0
Variable operating expenses −59.5 −10.5
Operating profit 10.5 −5.5
Pretax profit 10.5 −5.5
Tax −3.2 +1.6
Net profit 7.3 −3.9
284  •   The Intelligent Option Investor
Costs at Unlevered Co. decrease proportionally to the decrease in 
revenues, so the operating profit margin is the same in its case. However, 
for Levered Co., even though the variable costs decrease proportionally to 
the decrease in revenues, the cost of depreciation stays fixed, causing a loss 
that is only slightly ameliorated through a small tax benefit.
Thus, obviously, in business-cycle trough conditions, profitability is 
hurt through the assumption of operational leverage. Let’s take a look at 
what happens to both companies in peak conditions.
2
Unlevered Co. Levered Co.
Revenues 130.0 130.0
Fixed depreciation expense 0.0 −65.0
Variable operating expenses −110.5 −19.5
Operating profit 19.5 45.5
Pretax profit 19.5 45.5
Tax −5.9 −13.6
Net profit 13.6 31.9
Obviously, having the operational leverage during peak times is a 
wonderful thing. After the fixed-cost hurdle of depreciation is cleared, each 
extra widget produced allows the company to generate profits that are gov-
erned solely by variable costs. Unlevered Co. is in a better position when 
there is a downturn, but its profitability falls behind Levered Co. ’s more and 
more the better economic conditions are.
When thinking about the valuation of companies, we must remember 
what a large effect operational leverage can have on operations. Financial 
markets usually underestimate the effects of operational leverage both 
when the business cycle is at its peak and when it is at its trough. At the 
peak, analysts are wont to extrapolate high margins out forever and ignore 
the possibility that the sword of leverage swings both ways. At the trough, 
analysts are overly pessimistic and forget that a small improvement in de-
mand can have a very large impact on financial results. 
Operational leverage is neither good nor bad—it is merely a strategic busi-
ness choice that has different implications during different parts of the business 
cycle and under different revenue conditions. An intelligent investor under-
stands this fact and is happy to invest when the rest of the market has forgotten it.
Financial Leverage
Financial leverage involves the acceptance of fixed financial costs such 
as a loan or a lease contract to fund a business. Considering the expense 
of building factories, usually operational and financial leverage occur 
simultaneously, but to understand financial leverage itself, let’s look at two 
companies that, other than the amount of debt on their balance sheets, are 
exactly the same in terms of revenues and profit margin. Our base case 
shows that the unlevered company will generate a higher absolute profit 
because it does not have the fixed financing costs.
Unlevered Co. Levered Co.
Revenues 100.0 100.0
Operating expenses −80.0 −80.0
Operating profit 20.0 20.0
Interest expense 0.0 −15.0
Pretax profit 20.0 5.0
Tax −6.0 −1.5
Net profit 14.0 3.5
Now let’s increase revenues for both companies by 50 percent and see 
what happens.
Unlevered Co. Levered Co.
Revenues 150.0 150.0
Operating expenses −120.0 −120.0
Operating profit 30.0 30.0
Interest expense 0.0 −15.0
Pretax profit 30.0 15.0
Tax −9.0 −4.5
Net profit 21.0 11.5
The absolute profit is still higher for the unlevered company, but the 
percentage change from the first case to the second shows a big difference. 
The unlevered company’s profits increased by 50 percent (from 14.0 to 
21.0) with a 50 percent rise in revenues. However, the levered company’s 
profits increased by a whopping 229 percent (from 3.5 to 11.5) with the 
same 50 percent rise in revenues. 
Appendix B: The Many Faces of Leverage  • 285
286  •   The Intelligent Option Investor
Here we see an example of a defining characteristic of financial and 
investment leverage; that is, these sorts of leverage affect percentage calcu-
lations, but in absolute terms, unlevered transactions always generate more 
for a fixed level of exposure. We explore this concept in great detail when 
we discuss investment leverage in Chapter 8.
To see the dangerous side of leverage’s double-edged sword, let’s look 
at a case where revenues drop 50 percent from the original baseline.
Unlevered Co. Levered Co.
Revenues 50.0 50.0
Operating expenses −40.0 −40.0
Operating profit 10.0 10.0
Interest expense 0.0 −15.0
Pretax profit 10.0 −5.0
Tax −3.0 +1.5
Net profit 7.0 −3.5
Here we see that even with the tax benefit for the levered company, 
it is still running at a loss because of the fixed financial costs, whereas the 
unlevered company is still realizing a gain. In a worst-case scenario, fixed 
financial costs can exceed the cash coming into the business, leading to 
debt default and, depending on the situation, bankruptcy.
Thinking about the best and worst cases from an investment perspec-
tive for a moment, you can see why some equity investors actually prefer a 
highly levered firm: the higher the leverage, the greater is the incremental 
profit for equity holders when times are good. For a levered company that 
is in transition from bad to good—whether due to an upturn in economic 
conditions during a business cycle or a company-specific issue such as the 
introduction of a new product line boosting a flagging legacy business—
a small improvement in business conditions creates a big improvement 
in profits available to shareholders. The flip side is that when business 
conditions turn downward—a transition from good to bad—a levered 
company’s fall from profitability to loss is sudden, and its stock price fall 
can be even worse. The fact is that just in the case of operational lever -
age, financial leverage is not good or bad—it is simply a strategic business 
choice that has different implications in different situations. 
287
Appendix c
PUT-cALL PArITy
Before the Black-Scholes-Merton model (BSM), there was no way to 
directly calculate the value of an option, but there was a way to triangulate 
put and call prices as long as one had three pieces of data:
1. The stock’s price
2. The risk-free rate
3. The price of a call option to figure the fair price of the put, and vice 
versa
In other words, if you know the price of either the put or a call, as long 
as you know the stock price and the risk-free rate, you can work out the 
price of the other option. These four prices are all related by a specific rule 
termed put-call parity.
Put-call parity is only applicable to European options, so it is not ter-
ribly important to stock option investors most of the time. The one time it 
becomes useful is when thinking about whether to exercise early in order 
to receive a stock dividend—and that discussion is a bit more technical. I’ll 
delve into those technical details in a moment, but first, let’s look at the big 
picture. Using the intelligent option investor’s graphic format employed in 
this book, the big picture is laughably trivial.
Direct your attention to the following diagrams. What is the differ -
ence between the two?
288  •   The Intelligent Option Investor
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20
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GREENGREEN
REDRED
If you say, “Nothing, ” you are practically right but technically 
wrong. The image on the left is actually the risk-reward profile of a pur -
chased call option struck at $50 paired with a sold put option struck at 
$50. The image on the right is the risk-reward profile of a stock trading 
at $50 per share.
This simple comparison is the essence of put-call parity. The parity  
part of put-call parity just means that accepting downside exposure by sell-
ing a put while gaining upside exposure by buying a call is basically the 
same thing as accepting downside exposure and gaining upside exposure 
by buying a stock.
What did I say? It is laughably trivial. Now let’s delve into the details 
of how the put-call parity relationship can be used to help decide whether 
to exercise a call option or not (or whether the call option you sold is likely 
to be exercised or not).
Dividend Arbitrage and Put-call Parity
Any time you see the word arbitrage , the first thing that should jump to 
mind is “small differences. ” Arbitrage is the science of observing small dif-
ferences between two prices that should be the same (e.g., the price of IBM 
Appendix C: Put-Call Parity   • 289
traded on the New Y ork Stock Exchange and the price of IBM traded in 
Philadelphia) but are not. An arbitrageur, once he or she spots the small 
difference, sells the more expensive thing and buys the less expensive one 
and makes a profit without accepting any risk. 
Because we are going to investigate dividend arbitrage, even a big-
picture guy like me has to get down in the weeds because the differences we 
are going to try to spot are small ones. The weeds into which we are wading 
are mathematical ones, I’m afraid, but never fear—we’ll use nothing more 
than a little algebra. We’ll use these variables in our discussion:
K = strike price
C
K = call option struck at K
PK = put option struck at K
Int = interest on a risk-free instrument 
Div = dividend payment
S = stock price
Because we are talking about arbitrage, it makes sense that we are 
going to look at two things, the value of which should be the same. We 
are going to take a detailed look at the preceding image, which means that 
we are going to compare a position composed of options with a position 
composed of stock.
Let’s say that the stock at which we were looking to build a position is 
trading at $50 per share and that options on this stock expire in exactly one 
year. Further, let’s say that this stock is expected to yield $0.25 in dividends 
and that the company will pay these dividends the same day that the op-
tions expire.
Let’s compare the two positions in the same way as we did in the 
preceding big-picture image. As we saw in that image, a long call and a 
short put are the same as a stock. Mathematically, we would express this 
as follows:
C
K − PK = SK
Although this is simple and we agreed that it’s about right, it is not 
technically so.
The preceding equation is not technically right because we know that 
a stock is an unlevered instrument and that options are levered ones. In the 
290  •   The Intelligent Option Investor
preceding equation, we can see that the left side of the equation is levered 
(because it contains only options, and options are levered instruments), 
and the right side is unlevered. Obviously, then, the two cannot be exactly 
the same.
We can fix this problem by delevering the left side of the preceding 
equation. Any time we sell a put option, we have to place cash in a mar -
gin account with our broker. Recall that a short put that is fully margined 
is an unlevered instrument, so margining the short put should delever 
the entire option position. Let’s add a margin account to the left side and 
put $K in it:
C
K − PK + K = S
This equation simply says that if you sell a put struck at K and put $K 
worth of margin behind it while buying a call option, you’ll have the same 
risk, return, and leverage profile as if you bought a stock—just as in our 
big-picture diagram.
But this is not quite right if one is dealing with small differences. 
First, let’s say that you talk your broker into funding the margin ac-
count using a risk-free bond fund that will pay some fixed amount of 
interest over the next year. To fund the margin account, you tell your 
broker you will buy enough of the bond account that one year from 
now, when the put expires, the margin account’s value will be exactly 
the same as the strike price. In this way, even by placing an amount less 
than the strike price in your margin account originally, you will be able 
to fulfill the commitment to buy the stock at the strike price if the put 
expires in the money (ITM). The amount that will be placed in margin 
originally will be the strike price less the amount of interest you will 
receive from the risk-free bond. In mathematical terms, the preceding 
equation becomes 
C
K − PK + (K – Int) = S
Now all is right with the world. For a non-dividend-paying stock, this fully 
expresses the technical definition of put-call parity.
However, because we are talking about dividend arbitrage, we have to 
think about how to adjust our equation to include dividends. We know that 
a call option on a dividend-paying stock is worth less because the dividend 
Appendix C: Put-Call Parity   • 291
acts as a “negative drift” term in the BSM. When a dividend is paid, theory 
says that the stock price should drop by the amount of the dividend. Be-
cause a drop in price is bad for the holder of a call option, the price of a call 
option is cheaper by the amount of the expected dividend.
Thus, for a dividend-paying stock, to establish an option-based position 
that has exactly the same characteristics as a stock portfolio, we have to keep 
the expected amount of the dividend in our margin account.
1 This money 
placed into the option position will make up for the dividend that will be 
paid to the stock holder. Here is how this would look in our equation:
C
K − PK + (K − Int) + Div = S
With the dividend payment included, our equation is complete.
Now it is time for some algebra. Let’s rearrange the preceding equa-
tion to see what the call option should be worth:
CK = PK + Int − Div + (S − K)
Taking a look at this, do you notice last term (S  – K )? A stock’s price 
minus the strike price of a call is the intrinsic value. And we know that 
the value of a call option consists of intrinsic value and time value. This 
means that
/dncurlybracketleft/dncurlybracketmid/horizcurlybracketext/horizcurlybracketext/dncurlybracketright/horizcurlybracketext/horizcurlybracketext/dncurlybracketleft/dncurlybracketmid/dncurlybracketright=+ −−CP SKKK IntD iv + ()
Time valueI ntrinsic value
So now let’s say that time passes and at the end of the year, the stock 
is trading at $70—deep ITM for our $50-strike call option. On the day 
before expiration, the time value will be very close to zero as long as the op-
tion is deep ITM. Building on the preceding equation, we can put the rule 
about the time value of a deep ITM option in the following mathematical 
equation:
P
K + Int − Div ≈ 0
If the time value ever falls below 0, the value of the call would trade for less 
than the intrinsic value. Of course, no one would want to hold an option 
that has negative time value. In mathematical terms, that scenario would 
look like this:
P
K + Int − Div < 0
292  •   The Intelligent Option Investor
From this equation, it follows that if
PK + Int < Div
your call option has a negative implied time value, and you should sell the 
option in order to collect the dividend. 
This is what is meant by dividend arbitrage . But it is hard to get the 
flavor for this without seeing a real-life example of it. The following table 
shows the closing prices for Oracle’s stock and options on January 9, 2014, 
when they closed at $37.72. The options had an expiration of 373 days in 
the future—as close as I could find to one year—the one-year risk-free rate 
was 0.14 percent, and the company was expected to pay $0.24 worth of 
dividends before the options expired.
Calls Puts
Bid Ask Delta Strike Bid Ask Delta
19.55 19.85 0.94 18 0.08 0.13 −0.02
17.60 17.80 0.94 20 0.13 0.15 −0.03
14.65 14.85 0.92 23 0.25 0.28 −0.05
12.75 12.95 0.91 25 0.36 0.39 −0.07
10.00 10.25 0.86 28 0.66 0.69 −0.12
8.30 8.60 0.81 30 0.97 1.00 −0.17
6.70 6.95 0.76 32 1.40 1.43 −0.23
4.70 4.80 0.65 35 2.33 2.37 −0.34
3.55 3.65 0.56 37 3.15 3.25 −0.43
2.22 2.26 0.42 40 4.80 4.90 −0.57
1.55 1.59 0.33 42 6.15 6.25 −0.65
0.87 0.90 0.22 45 8.25 8.65 −0.75
0.31 0.34 0.10 50 12.65 13.05 −0.87
In the theoretical option portfolio, we are short a put, so its value to 
us is the amount we would have to pay if we tried to flatten the position by 
buying it back—the ask price. Conversely, we are long a call, so its value to 
us is the price we could sell it for—the bid price.
Let’s use these data to figure out which calls we might want to exercise 
early if a dividend payment was coming up.
Appendix C: Put-Call Parity   • 293
Strike Call
Put
(a)
Interest2
(b)
Put + Interest
(a + b) Dividend P + I − D Notes
18 19.55 0.13 0.03 0.16 0.24 (0.08) P + I < D, 
arbitrage
20 17.60 0.15 0.03 0.18 0.24 (0.06) P + I < D, 
arbitrage
23 14.65 0.28 0.03 0.31 0.24 0.07 No arbitrage
25 12.75 0.39 0.04 0.43 0.24 0.19 No arbitrage
28 10.00 0.69 0.04 0.73 0.24 0.49 No arbitrage
30 8.30 1.00 0.04 1.04 0.24 0.80 No arbitrage
32 6.70 1.43 0.05 1.48 0.24 1.24 No arbitrage
35 4.70 2.37 0.05 2.42 0.24 2.18 No arbitrage
37 3.55 3.25 0.05 3.30 0.24 3.06 No arbitrage
40 2.22 4.90 0.06 4.96 0.24 4.72 No arbitrage
42 1.55 6.25 0.06 6.31 0.24 6.07 No arbitrage
45 0.87 8.65 0.06 8.71 0.24 8.47 No arbitrage
50 0.31 13.05 0.07 13.12 0.24 12.88 No arbitrage
There are only two strikes that might be arbitraged for the 
dividends—the two furthest ITM call options. In order to realize the 
arbitrage opportunity, you would wait until the day before the ex-dividend 
date, exercise the stock option, receive the dividend, and, if you didn’t want 
to keep holding the stock, sell it and realize the profit.
This page intentionally left blank 
295
Notes
Introduction
1. Options, Futures, and Other Derivatives  by John C. Hull (New Y ork: 
Prentice Hall, Eighth Edition, February 12, 2011), is considered the 
Bible of the academic study of options.
2. Option Volatility and Pricing by Sheldon Natenberg (New Y ork: 
McGraw-Hill, Updated and Expanded Edition, August 1, 1994), is 
considered the Bible of professional option traders.
3. The Greeks are measures of option sensitivity used by traders to man-
age risk in portfolios of options. They are named after the Greek 
symbols used in the Black-Scholes-Merton option pricing model.
4. “To invest successfully over a lifetime does not require a stratospheric 
IQ, unusual business insights, or inside information. What’s needed 
is a sound intellectual framework for making decisions and the abil-
ity to keep emotions from corroding that framework. ” Preface to The 
Intelligent Investor by Benjamin Graham (New Y ork: Collins Business, 
Revised Edition, February 21, 2006). 
Chapter 1
1. In other words, if all option contracts were specific and customized, 
every time you wanted to trade an option contract as an individual in-
vestor, you would have to first find a counterparty to take the other side 
of the trade and then do due diligence on the counterparty to make 
sure that he or she would be able to fulfill his or her side of the bargain. 
It is hard to imagine small individual investors being very interested in 
the logistical headaches that this process would entail!
296 •   N o t e s
2. One more bit of essential but confusing jargon when investing in 
options is related to exercise. There are actually two styles of exercise; 
one can be exercised at any time before expiration—these are termed 
American style—and the other can only be exercised at expiration—
termed European style. Confusingly, these styles have nothing to do 
about the home country of a given stock or even on what exchange 
they are traded. American-style exercise is normal for all single-stock 
options, whereas European-style exercise is normal for index futures. 
Because this book deals almost solely with single-stock options (i.e., 
options on IBM or GOOG, etc.), I will not make a big deal out of this 
distinction. There is one case related to dividend-paying stocks where 
American-style exercise is beneficial. This is discussed in Appendix C. 
Most times, exercise style is not a terribly important thing.
3. Just like going to Atlantic City, even though the nominal odds for rou-
lette are 50:50, you end up losing money in the long run because you 
have to pay—the house at Atlantic City or the broker on Wall Street—
just to play the game.
Chapter 3
1. We adjusted and annualized the prices of actual option contracts so 
that they would correspond to the probability levels we mentioned 
earlier. It would be almost impossible to find a stock trading at exactly 
$50 and with the option market predicting exactly the range of future 
price that we have shown in the diagrams. This table is provided simply 
to give you an idea of what one might pay for call options of different 
moneyness in the open market.
2. Eighty-four percent because the bottom line marks the price at which 
there is only a 16 percent chance that the stock will go any lower. If 
there is a 16 percent chance that the stock will be lower than $40 in 
one year’s time, this must mean that there is an 84 percent chance 
that the stock will be higher than $40 in one year’s time. We write 
“a little better than 84 percent chance” because you’ll notice that the 
stock price corresponding to the bottom line of the cone is around 
$42—a little higher than the strike price. The $40 mark might corre-
spond to a chance of, let’s say, 13 percent that the stock will be lower; 
Notes  • 297
this would, in turn, imply an 87 percent  chance of being higher than 
$40 in a year.
3. Tenor is just a specialty word used for options and bonds to mean the 
remaining time before expiration/maturity. We will see later that op-
tion tenors usually range from one month to one year and that special 
long-term options have tenors of several years.
4. We’re not doing any advanced math to figure this out. We’re just eye-
balling the area of the exposure range within the cone in this diagram 
and recalling that the area within the cone of the $60 strike, one-year 
option was about the same.
5. In other words, in this style of trading, people are anchoring on recent 
implied volatilities—rather than on recent statistical volatilities—to 
predict future implied volatilities.
6. Note that even though this option is now ITM, we did not pay for any 
intrinsic value when we bought the option. As such, we are shading the 
entire range of exposure in green.
Chapter 4
1. The “capital” we have discussed so far is strategic capital. There is an-
other form of tactical capital that is vital to companies, termed working 
capital. Working capital consists of the short-term assets essential for 
running a business (e.g., inventory and accounts receivables) less the 
short-term liabilities accrued during the course of running the busi-
ness (e.g., accounts payable). Working capital is tactical in the sense 
that it is needed for day-to-day operation of the business. A company 
may have the most wonderful productive assets in the world, but if it 
does not have the money to buy the inventory of raw materials that will 
allow it to produce its widgets, it will not be able to generate revenues 
because it will not be able to produce anything.
2. The law of large numbers is actually a law of statistics, but when most 
people in the investing world use this phrase, it is the colloquial version 
to which they are referring. 
3. Apple Computer, for instance, was a specialized maker of computers 
mainly used by designers and artists in the late 1990s. Through some 
298 •   N o t e s
inspired leadership and a large capital infusion from Microsoft to keep 
it afloat in its darkest days, Apple Computer changed its name to just 
Apple and began producing handheld music devices, smartphones, and 
other media appliances (including computers). By the late 1990s, Apple 
was facing severe structural constraints. The market in which it com-
peted—the market for personal computers—had been commoditized, 
and prices did nothing but go down. It was clinging to a niche market 
of a few educational institutions and creative professionals—not a very 
robust or quickly growing market. However, the company was able to 
reinvent itself as a media technology company and media content pro-
vider using its investments and know-how in personal computing as a 
base. Doing so, Apple jumped from a mature company into a virtual 
startup and once again became a supply-constrained company in a 
very short period of time. This is a rare twist, but not unheard of.
4. Don’t waste your time remembering this formula unless you already 
know it. Y ou can always look up the exact equation when you need to use 
it. Just remember, “ A dollar today is worth more than a dollar tomorrow. ”
5. If you are curious about the CAPM or any of the other related aca-
demic methods for determining discount rates, you have no further 
to go than your local library or various sources online. The CAPM is 
one of the pillars of modern finance, and there are plenty of resources 
to learn about it. In the end, though, the “proper” discount rate you 
will calculate will not be far off from these values. There are plenty 
of more important things on which to concentrate in a valuation, so 
my suggestion is to spend time on those and save learning about the 
CAPM.
Chapter 5
1. Note that, even though it may feel like it from a shareholder perspective, 
the period during which a company is making poor investments and 
generating substructural profit growth will only last for a limited time. 
Sooner or later, an activist investor or another company will acquire all 
or part of the capital stock of the underperforming company and run 
the enterprise in a more rational way.
Notes  • 299
2. For the structural stage, I usually only use one scenario. When I start-
ed in the business of valuation, I used 6 percent growth of cash flows 
in perpetuity. Recently, convinced by PIMCO’s argument that we are 
entering an extended “new normal” period, I tend to use 5 percent 
instead.
3. For instance, a company may have only six very large and important 
customers, each of which it picked up in subsequent years. If it loses 
one of those customers, rather than +35 percent revenue growth over 
the next year, the revenue may decline by 20 percent. Or even if the 
company does not lose a customer, if it does not gain another, its 
revenue growth may be trivial—3 percent, let’s say.
4. Please see the online materials for the specific formulas used for OCP 
and FCFO.
5. A person with a 100-share stake in Exxon—an investment worth just 
under $10,000—has a proportional stake of 0.000006 percent in the 
company. No wonder investors usually do not have a strong sense of 
being an owner of the companies in which they are invested.
6. In a counterexample, IBM’s management should be commended for 
selling off the dying, undifferentiated PC business to Lenovo and rea-
ligning the tech giant as primarily a provider of software and services.
7. Networking behemoth Cisco Systems’ (CSCO) purchase of Pure 
Digital (a company that made Flip video cameras) springs immedi-
ately to mind.
Chapter 6
1. The fact that a consensus of opinion is reached is an interesting social be-
havioral bias called herding. This bias, one that I will not go into great de-
tail about here, is the tendency for people to be influenced by the actions 
or opinions of others when making a decision as a member of a group.
2. Paul Slovic, “Behavioral Problems of Adhering to a Decision Policy, ” 
paper presented at the Institute for Quantitative Research in Finance, 
Napa, CA, May 1, 1973.
3. This research report was quoted and summarized on the following site: 
http://www.valuewalk.com/2013/07/hedge-fund-alpha-negative/.
300 •   N o t e s
4. The original academic paper discussing prospect theory was published 
in Econometrica, Volume 47, Number 2, in March 1979 under the title: 
“Prospect Theory: An Analysis of Decision Under Risk. ”
5. Over the years, the paradigm for broker-dealers has changed, so some 
of what is written here is a bit dated. Broker-dealers have one part of 
its business dedicated to increasing customer “flow” as is described 
here. Over the last 20 years or so, however, they have additionally 
begun to capitalize what amounts to in-house hedge funds, called 
“proprietary trading desks” or “prop traders. ” While the prop traders 
are working on behalf of corporations that were historically known as 
broker-dealers (e.g., Goldman Sachs, Morgan Stanley), they are in fact 
buy-side institutions. In the interest of clarity in this chapter, I treat 
broker-dealers as purely sell-side entities even though they in fact have 
elements of both buy- and sell-sides.
Chapter 7
1. Round-tripping means buying a security and selling it later.
2. This bit of shorthand just means a bid volatility of 22.0 and an ask 
volatility of 22.5.
Chapter 8
1. This is one of the reasons why I called delta the most useful of the 
Greeks.
2. When I pulled these data, I pulled the 189-day options, so my chance 
of this stock hitting that high a price in this short time period is slim, 
but the point I am making here about percentage versus absolute re-
turns still holds true.
3. A tool to calculate all the downside and upside leverage figures shown 
in this chapter is available on the intelligent option investor website.
4. “Buffett’s Alpha, ” Andrea Frazzini, David Kabiller, and Lasse H. Ped-
ersen, 2012, National Bureau of Economic Research, NBER Working 
Paper No. 19681.
Notes  • 301
Chapter 9
1. Yale Alumni Magazine, “The Fraud Detective, ” September/October 
2013 Issue, http://www.yalealumnimagazine.com/articles/3737.
Chapter 10
1. This is, in fact, the crux of why U.S. taxpayers all got the opportunity 
to own a piece of AIG. One of the subsidiaries of AIG made 
commitments to carry out transactions that, with the collapse of the 
mortgage bubble, it had no ability to do. In this case, it was not a bro-
ker or exchange that had to bear the exposure to AIG’s failure—the 
contracts AIG were trading were over-the-counter and thus not regu-
lated by an exchange—it was the financial system at large and U.S. 
taxpayers in particular.
2. The fact that this strategy is unlevered means that percentage returns 
provide an accurate representation of the absolute wealth generated 
with the strategy. As we saw earlier, levered investments can show very 
high percentage returns, whereas absolute returns are not as great. This 
is not the case for short puts.
3. Writing an option means selling an option.
4. This is especially true for people investing in covered calls—a strategy 
I will discuss in Chapter 11 and that has the same risk-return profile as 
the short-put strategy.
5. Of course, there are other reasons for increased volatility during 
earnings seasons, and some of the volatility reflects issues that are ma-
terial to valuation. In my opinion, though, the vast majority of infor -
mation given at these times is helpful for understanding only a few 
months’ worth of prospective business results and, as such, should not 
cause a material change in an intelligent investor’s perception of long-
run company value.
6. I am speaking here about the most attractive calls from a math-
ematical perspective, not a valuation one. I have not valued IBM 
and am most definitely not making an investment recommenda-
tion here. I used IBM because it is a liquid option with a good 
302 •   N o t e s
many OTM strikes, not because I believe it’s a bearish investment 
opportunity.
7. $100,000 × 5% = $5,000; $5,000/$196.80 per share = 25.4 shares.
Chapter 11
1. This is due to a statistical property known as dispersion . Dispersion—
the fact that prices on many things do not usually move in lockstep 
with one another—is the root of all diversification strategies.
2. This assumes that crises are only temporary. Of course, structural or 
secular downturns are a different matter, and the whole process of 
investing must be done in a different way. In particular, conceptions of 
sensible terminal growth rates become vital during these times.
Chapter 12
1. I am indebted to Brent Farler for this image, which I think is really 
brilliant.
Appendix A
1. Refer to the discussion of investing agents and principals in Chapter 6. 
2. It is only the nominal odds that are 50:50 anyway. The player always 
has to pay the house (and if you’re James Bond, you must tip the dealer 
a cool million dollars), just as an investor must pay the broker. As such, 
the net odds are always against the owner of capital.
3. Remember that the dotted line in the BSM cone shows that 50:50 
“expected” value. Because our expected value dot is much higher, this 
means that we are assigning a higher probability of that price occurring 
than is the option market as a whole.
Notes  • 303
Appendix B
1. The idea behind this process is to match the timing of the costs of 
equipment with revenues from the items produced with that equip-
ment. This is a key principle of accountancy called matching.
2. The problem is that troughs, by definition, follow peaks. Usually, just 
like the timing of large acquisitions, companies decide to spend huge 
amounts to build new production capacity at just about the same time 
that economic conditions peak, and the factories come online just as 
the economy is starting to sputter and fail.
Appendix C
1. A penny saved is a penny earned. We can think of the option being 
cheaper by the amount of the dividend, so we will place the amount 
that we save on the call option in savings.
2. This is calculated using the following equation:
Interest = strike × r × percent of 1 year
In the case of the $18 strike, interest = 18 × 0.14% × (373 days/365 days 
per year) = $0.03.
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305
A
Absolute dollar value of returns, 
172–173
Accuracy, confidence vs., 119–121
Acquisitions (see Mergers and 
acquisitions)
Activist investors, 110
Against the Gods (Peter Bernstein), 9
Agents:
buy-side, 132–136
defined, 131
investment strategies of, 137–138
principals vs., 131–132
sell-side, 136–137
AIG, 301n1
Allocation:
and leverage in portfolios,  
174–183
and liquidity risk, 256
and portfolio management with 
short-call spreads, 228–229
Alpha, 134
American-style options, 296n2 
(Chapter 1)
Analysis paralysis, 120
Anchoring, 60, 97
Announcements:
and creating BSM cones, 156, 157
market conditions following, 68–69, 
72–73
tenor and trading in expectation  
of, 192
AOL, 103
Apple Computer, 101, 250–251,  
297–298n3
Arbitrage:
defined, 288–289
dividend, 223, 288–293
Ask price, 147
Asset allocation, liquidity risk  
and, 256
Assets:
defined, 78–79
fungible, 272–273
in golden rule of valuation, 77
hidden, 110, 111
idiosyncratic, 272
interchangeable, 272–273
mispriced, 274–277
operating, 110
price vs. value of, 79–80
underlying, 33–34, 272–273
Assets under management (AUM), 132
Assignment:
with covered calls, 247–248
defined, 222–223
Assumptions:
BSM model, 32–33, 40–47, 78, 150
dividend yield, 67
with forward volatility number, 
156–157
time-to-expiration, 64–67
volatility, 60–64
At-the-money (ATM) options:
BSM cone for, 53
collars, 259
covered calls, 242–243, 245, 246
defined, 13, 16, 17
long calls, 189
long diagonals, 235–237
Index
306  •   Index
At-the-money (ATM) options: (continued)
long straddles, 208–209
OTM options vs., 233–234
protective puts, 250–251, 253
short diagonals, 238, 240
short puts, 215, 216
short straddles, 230
short-call spreads, 222–225
AUM (assets under management), 132
B
Balance-sheet effects, 92, 108–111
Behavior, efficient market hypothesis 
as model for, 41–42
Behavioral biases, 114–130
overconfidence, 118–122
pattern recognition, 114–118
perception of risk, 123–130
Behavioral economics, 42, 114
Bentley, 97–98
Berkshire Hathaway, 185
Bernstein, Peter, 9
Biases, behavioral (see Behavioral 
biases)
Bid price, 147
Bid-ask spreads, 147–149
Bimodal outcomes, companies with, 
277–278
Black, Fischer, 8–9
BlackBerry, 208–209
Black-Scholes-Merton (BSM) model, 9
assumptions of, 32–33, 40–47, 78, 150
conditions favoring, 269–273
conditions not favoring, 273–281
incorrect facets of, 29
predicting future stock prices from, 
32–39
ranges of exposure and price 
predictions from, 50–56
theory of, 32
(See also BSM cone)
Bonds, investing in short puts vs., 
213–214
Booms, leverage during, 199
Breakeven line, 25
for call options, 15, 16
for long strangle, 26–27
for put options, 17, 18
(See also Effective buy price [EBP])
Broker-dealers, 137, 299–300n5
Brokers, benefits of short-term trading 
for, 64
BSM cone:
for call options, 50–55
for collars, 258
for covered calls, 240–244
creating, 156–160
defined, 38–39
delta-derived, 151–155
discrepancies between valuation and, 
160–162
for ITM options, 57–58
for long calls, 189
for long diagonals, 235
for long puts, 201
for long strangles, 205
overlaying valuation range on, 160
for protective puts, 248, 249
for put options, 54–55
for short diagonals, 238
for short puts, 212, 216, 217
for short straddles, 230
for short strangles, 231
for short-call spreads, 220
with simultaneous changes in variables, 
68–74
and time-to-expiration assumptions, 
64–67
and volatility assumptions,  
60–64
BSM model (see Black-Scholes-Merton 
(BSM) model)
Bubbles, 42–43
Buffett, Warren, xv, 184–185
Buying options (see Exposure-gaining 
strategies)
Buy-side structural impediments, 
132–136
Index   • 307
C
CAGR (compound annual growth 
rate), 46
Call options (calls):
BSM cone for, 50–55
buying, for growth, 22
covered, 240–248
defined, 11
delta for, 151
dividend arbitrage with, 292–293
leverage with, 167–168
on quotes, 145
short, 14, 221
tailoring exposure with, 24
visual representation of, 12–16
and volatility, 68–74
(See also Covered calls; Long calls; 
Short-call spreads)
Capital:
investment, 183–184
strategic vs. working, 297n1 
(Chapter 4)
Capital asset pricing model (CAPM), 
88, 298n4
Capital expense, 80
Career risk, 263
Cash, hedge size and, 257
Cash flows:
on behalf of owners, 80–82
expansionary, 82, 104–108 
in golden rule of valuation, 77
present value of future, 87–89
summing, from different time periods, 
87–89
(See also Free cash flow to owners 
[FCFO])
“Catalysts, ” 137
CBOE (see Chicago Board Options 
Exchange)
Central counterparties, 8
Change (option quotes), 146–147
Chanos, Jim, 202
Chicago Board Options Exchange 
(CBOE), 4, 8, 47
Chicago Mercantile Exchange, 8
China, joint ventures in, 84
Cisco Systems, 299n6 (Chapter 5)
Closet indexing, 133
Closing prices:
change in, 146–147
defined, 146
Collars, 258–262
Commitment, counterparties’ , 211
Commodities, options on, 6–7
Companies:
with bimodal outcomes,  
277–278
drivers of value for (see Value 
drivers)
economic life of, 82–86, 93–94
economic value of, 137–139
operational details of, xiii–xiv, 
110–111
Complex investment strategies, 142
Compound annual growth rate 
(CAGR), 46
Condors, 27–28
Confidence, accuracy vs., 119–121
Contingent loans, call options as, 
167–168
Contract size, 146
Counterparties:
central, 8
commitments of, 211
for options contracts, 295n1 
(Chapter 1)
Counterparty risk, 7–8
Covered calls, 23, 240–248,  
301n4
about, 241–242
BSM cone, 240–244
execution of, 242–245
pitfalls with, 245–248
with protective puts, 259–262
Covering positions, 219, 228
Cremers, Martijn, 133
C-system, 115–118
Customer “flow, ” 299n5 (Chapter 6)
308  •   Index
d
Debt, investment leverage from, 165–166
Dell, 101
Delta, 151–155, 300n1 (Chapter 8)
Demand-side constraints, 84–86
Depreciation, 282–284
Diagonals, 233
long, 235–237
short, 238–240
Directionality of options, 9–20
calls, 12–16
and exposure, 18–20
importance of, 27–28
puts, 16–18
and stock, 10–11
volatility and predications about, 
68–74
Discount rate, 87–89, 298n5
Dispersion, 302n1 (Chapter 11)
Distribution of returns:
fat-tailed, 45
leptokurtic, 45
lognormal, 36–37
normal, 32, 36, 40, 43–45
Dividend arbitrage, 223, 288–293
Dividend yield, 67
Dividend-paying stocks, prices of, 
35–36
Dividends, 86
Downturns, short puts during, 214–215
Drift:
assumptions about, 32, 35–36
effects of, 67
and long calls, 202–203
and long puts, 191
and long strangles, 206
Drivers of value (see Value drivers)
e
Early exercise, 223
Earnings before interest, taxes, 
depreciation, and amortization 
(EBITDA), 99
Earnings before interest and taxes 
(EBIT), 99
Earnings per share (EPS), 99
Earnings seasons:
and tenor of short puts, 217–218
volatility in, 301n5
EBIT (earnings before interest and 
taxes), 99
EBITDA (earnings before interest, 
taxes, depreciation, and 
amortization), 99
EBP (see Effective buy price)
Economic environment, profitability 
and, 101
Economic life of companies:
and golden rule of valuation,  
82–86
improving valuations by 
understanding, 93–94
Economic value of companies,  
137–139
Effective buy price (EBP), 24–25,  
213, 244
Effective sell price (ESP), 25–26
Efficacy (see Investing level and 
efficacy)
Efficient market hypothesis (EMH), 
33, 34, 40–43
Endowments, 135, 136
Enron, 110
EPS (earnings per share), 99
ESP (effective sell price), 25–26
European-style options, 296n2 
(Chapter 1)
Exchange-traded funds (ETFs), 
options on, 251–252
Execution of option overlay strategies:
collars, 259–262
covered calls, 242–245
protective puts, 250–252
Exercising options, 13,  
296n2 (Chapter 1)
Expansionary cash flows, 82, 104–108
Index   • 309
Expiration of options, 187
Explicit forecast stage, 93–96
Exposure:
accepting, 14, 18–20
canceling out, 18–20
gaining, 13, 18–20
notional, 173
tailoring level of, 24
(See also Ranges of exposure)
Exposure-accepting strategies,  
211–232
margin requirements for, 211–212
short call, 220–230
short put, 212–220
short straddle, 230–232
short strangle, 231–232
Exposure-gaining strategies, 187–209
and expiration of options, 187
long call, 189–201
long put, 201–205
straddle, 208–209
strangle, 205–207
Exposure-mixing strategies, 233–262
collar, 258–262
covered call, 240–248
long diagonal, 235–237
and OTM vs. ATM options, 233–234
protective put, 248–258
short diagonal, 238–240
Exxon, 299n4 (Chapter 5)
F
False precision, 93, 96–97
Fama, Eugene, 42
Fat-tailed distribution, 45
FCFO (see Free cash flow to owners)
“Fight or flight” response, 118
Financial crises, 302n2 (Chapter 11)
Financial leverage:
defined, 285–286
investment vs., 164
and level of investment leverage, 
197–199
Financial statements, xv
Flexibility (with option investing), 20–28
Float, 185
Ford, 103, 272
Forward prices:
adding ranges to, 36–39
calculating, 34–36
defined, 35–36
ranges of exposure and, 50–56
Forward volatility:
choosing forward volatility number, 
156–160
defined, 59–61
and strike–stock price ratio, 67–74
Free cash flow to owners (FCFO):
defined, 82
and drivers of value, 111–112
in joint ventures, 84
and supply-side constraints, 83
Front-month contracts, 270
Fungible assets, 272–273
G
Gains, levered vs. unlevered, 165
Gaussian distribution (see Normal 
distribution)
GDP (gross domestic product), 
104–108
Gillette Razors, 84
GM, 272
Goals, for hedges, 257
“Going long, ” 10, 21
“Going short, ” 21
Golden rule of valuation, 77–89
cash flows generated on behalf of 
owners in, 80–82
and definition of assets, 78–80
and drivers of value, 91–92
and economic life of company, 82–86
and summing cash flows from 
different time periods, 87–89
Google, 84, 127–130, 190
“Greeks, ” xiv, 295n3
310  •   Index
Gross domestic product (GDP), 104–108
Growth:
buying call options for, 22
nominal GDP , 104–108
revenue, 92, 97–99
structural growth stage, 94, 95
H
Hedge funds, 132–134, 136
Hedge funds of funds (HFoF), 134
Hedges:
reinvesting profit from, 254–255
size of, 255–258
timing of, 252–254
Hedging:
planning for, 255–258
for portfolios, 251–252
Herding, 138, 299n1
HFoF (hedge funds of funds), 134
Historical volatility, 60
Hostile takeovers, 110
The Human Face of Big Data (Rick 
Smolan), 114
I
IBM, 224–230, 299n5 (Chapter 5), 
301n6
Idiosyncratic assets, 272
Immediate realized loss (IRL), 180, 183
Implied volatility:
bid/ask, 149–151
changing assumptions about, 60–64
and short puts, 216–217
Income, selling put options for, 23
Indexing, closet, 133
Insurance, 5, 250
Insurance companies, 135, 136
Intel, 175
Interchangeable assets, 272–273
Interest:
calculating, 303n2
options and payment on, 168
prepaid, 170
Interest rates, 67
In-the-money (ITM) options:
calls vs. puts, 27
covered calls, 242
defined, 13, 16, 17
investment leverage for, 170–172
levered strategy with, 176–180
long calls, 189, 193–197
long diagonals, 236
long puts, 204
managing leverage with, 183–184
and market risk, 263–264
pricing of, 56–59, 150
protective puts, 249–251
short puts, 213–215
short-call spread, 222, 223
time decay for, 66–67
Intrinsic value, 56–59, 171
Investing level and efficacy, 92,  
103–108
Investment capital, leverage and, 
183–184
Investment leverage, 163–185
from debt, 165–166
defined, 164
managing, 183–185
margin of safety for, 197–199
measuring, 169–173
from options, 166–168
and portfolio management,  
196–197
in portfolios, 174–183
unlevered investments, 164–165
Investment phase (investment stage), 
86, 93–96
Investors:
activist, 110
risk-averse, 123, 125–127
risk-neutral, 124–126
risk-seeking, 123, 125–127
IRL (immediate realized loss),  
180, 183
ITM (see In-the-money options)
Index   • 311
J
Jaguar, 103
Joint ventures (JVs), 84–85
JP Morgan Chase, 236–237
K
Kahneman, Daniel, 42, 123, 126
Keen, Steven, 43
Keynes, John Maynard, 263
Kroger, 100
K/S (see Strike–stock price ratio)
L
Lambda, 169–173
Large numbers, law of, 85, 297n2 
(Chapter 4)
Last (option quotes), 146
LEAPS (see Long-term equity 
anticipated securities)
Legs (option structure), 27
Lehman Brothers, 264
Lenovo, 299n5 (Chapter 5)
Leptokurtic distribution, 45
Leverage, 163, 282–286
financial, 164, 197–199, 285–286
operating (operational), 101,  
197–199, 282–284
(See also Investment leverage)
Leverage ratio, 228–229
Levered investments, portfolios with, 
176–183
Liabilities, hidden, 110–111
Life insurance companies, 135
Liquidity risk, 256, 263
Listed look-alike option market, 6
Literary work, options on, 5–6
Lo, Andrew, 42
Load, 132, 134
Loans, call options as,  
167–168
Lognormal curve, 37
Lognormal distribution,  
36–37
Long calls, 13, 189–201
about, 189
BSM cone, 189
in long diagonals, 235–237
portfolio management with,  
196–201
strike price for, 192–196
tenor for, 190–192
Long diagonals, 235–237
Long puts, 201–205
about, 201–202
BSM cone, 201
portfolio management with,  
204–205
in short diagonals, 238–240
strike price for, 203
tenor for, 202–203
Long straddles, 208–209
Long strangles, 26–27, 205–207, 209
Long-term equity anticipated 
securities (LEAPS), 153, 191, 
280–281
Loss leverage:
conventions for, 182–183
formula, 178–179
with short puts, 211–212
Losses:
with levered vs. unlevered 
instruments, 165–166
locking in, 245–247
on range of exposure, 15
unrealized, 175–176
(See also Realized losses)
M
MacKinlay, Craig, 42
Margin calls, 168
Margin of safety, 197–199
Margin requirements, 211–212
Market conditions, 59–74
assumptions about drift and 
dividend yield, 67
simultaneous changes in, 67–74
312  •   Index
Market conditions (continued)
time-to-expiration assumptions, 64–67
and types of volatility, 59–60
volatility assumptions, 60–64
Market efficiency, 32–34, 40–43
Market makers, 147, 281
Market risk, 263–265
Matching, 302n1 (Appendix B)
Maximum return, 225
Mergers and acquisitions:
strike prices selection and, 195–196
tenor and, 191–192
Merton, Robert, 8–9
Miletus, 6–7
Mispriced assets, 274–277
Mispriced options, 143–162
deltas of, 151–155
reading option quotes, 144–151
and valuation risk, 266
and valuation vs. BSM range, 155–162
Moneyness of options:
calls, 13–14
puts, 16–17
Morningstar, 132
Most likely (term), 38
Motorola Mobility Systems, 84
Mueller Water, 148–149, 154, 158–160
Multiples-based valuation, 99–100
Mutual funds, 132–133, 136
n
Nominal GDP growth:
owners’ cash profit vs., 104–108
as structural constraint, 104
Normal distribution, 32, 36, 40, 43–45
Notional amount of position, 173
Notional exposure, 173
O
OCC (Options Clearing  
Corporation), 8
OCP (see Owners’ cash profit)
Operating assets, 110
Operating leverage (operational 
leverage):
defined, 282–284
and level of investment leverage, 
197–199
and profitability, 101
Operational details of companies,  
xiii–xiv, 110–111
Option investing:
choices in, 22–24
conditions favoring BSM, 269–273
conditions not favoring BSM, 273–281
flexibility in, 20–28
long-term strategies, 1
misconceptions about, 1
risk in, 268
shortcuts for valuation in, 93–97
stock vs., 21–22
strategies for, 142 (See also specific 
types of strategies)
structural impediments in, 131–139
three-step process, xiv
valuation in, 75
Option pricing, 29–47, 49–74
and base assumptions of BSM, 40–47
market conditions in, 59–74
predicting future stock prices from, 
32–39
and ranges of exposure, 50–56
theory of, 30–32
time vs. intrinsic value in, 56–59
Option pricing models:
base assumptions of, 40–47
history of, 8–9
operational details of companies in, 
xiii–xiv
predicting future stock prices with, 
32–39
ranges of exposure and price 
predictions from, 50–56
(See also Black-Scholes-Merton 
[BSM] model)
Option quotes, 144–151
Index   • 313
Optionality, 4
Options, 3–28
buying (see Exposure-gaining 
strategies)
characteristics of, 4
defined, 4
directionality of, 9–20
examples of, 5–6
expiration of, 187
history of, 6–9
investment leverage from, 166–168
misconceptions about, 1
mispriced, 143–162
(See also specific types)
Options Clearing Corporation (OCC), 8
Options contracts:
counterparties for, 295n1 (Chapter 1)
examples of, 5–6
front-month, 270
private, 6–8
Oracle, 107–108, 144, 146, 148–153, 
155, 157, 159–162
Organic revenue growth, 97
Out-of-the-money (OTM) options:
ATM options vs., 233–234
call vs. put, 27
collars, 258–262
defined, 13, 16, 17
investment leverage for, 171–172
levered strategy with, 180, 181
long calls, 193, 195–197
long diagonals, 235–237
long puts, 203, 204
long strangles, 205–207
and market makers, 147
pricing of, 150
protective puts, 248, 250–253
realized losses and, 187
rising volatility and, 70–74
short diagonals, 238–240
short puts, 213, 215
short strangles, 231
short-call spreads, 221–224
time decay for, 66–67
unrealized losses, 187
Overconfidence, 118–122
Overexposure, 247
Overlays, 23, 234
Owners:
cash flows generated on behalf of, 
80–82
free cash flow to (see Free cash flow 
to owners (FCFO))
Owners’ cash profit (OCP):
defined, 82
nominal GDP growth vs., 104–108
profitability as, 99–102
P
Parity, 288
Pattern recognition, 114–118
Peaks (business-cycle):
operational leverage in, 284
and troughs, 302–303n2
Pension funds, 135, 136
Percent delta, 169–173
Percent profit, 172–173
Percentage return, 229
Portfolio management:
for long calls, 196–201
for long puts, 204–205
for long strangles, 207
for short puts, 216–220
for short-call spreads, 228–230
Portfolios:
hedging, 251–252
investment leverage in, 174–183
Precision, false, 93, 96–97
Premium, 13
Prepaid interest, 170
Present value of future cash flows, 87–89
Pricing power, 98
Principal (financial), 168
Principals, agents vs., 131–132
Problem solving, X- vs. C-system, 
115–118
314  •   Index
Procter & Gamble, 84
Productivity, 102
Profit:
from covered calls, 245
from hedging, 254–255
owners’ cash, 82
percent, 172–173
Profit leverage, 179–180, 182–183
Profitability:
and financial leverage, 285–286
and operational leverage,  
283–284
as value driver, 92, 99–102
Proprietary trading desks (prop 
traders), 300n5
Prospect theory, 123–127
Protective puts, 248–258
about, 248–250
BSM cone, 248, 249
with covered calls, 259–262
execution of, 250–252
pitfalls with, 252–258
Pure Digital, 299n6 (Chapter 5)
Put options (puts):
BSM cone for, 54–55
buying, for protection, 23
defined, 11
delta for, 151
on quotes, 145
selling, for income, 23
tailoring exposure with, 24
visual representation of, 16–18
(See also Long puts; Protective puts; 
Short puts)
Put-call parity, 223, 287–293
defined, 287–288
and dividend arbitrage, 288–293
for non-dividend-paying stock, 
289–290
Q
Qualcomm, 260–262
Quotes, option, 144–151
R
Random-walk principal, 41
Ranges of exposure, 3
for call options, 12–13, 15
for ITM options, 58–59
and option pricing, 50–56
Rankine, Graeme, 41–42
Ratioing, 206, 238
Realized losses:
and buying puts, 203
immediate, 180, 183
managing leverage to minimize, 
183–185
and option buying, 187–188
unrealized vs., 175–176
Recessions, leverage during, 198, 199
Reflective thought processes, 116–118
Reflexive thought processes, 116–118
Return(s):
absolute dollar value of, 172–173
for covered calls, 244–245
maximum, 225
percentage, 229
for short puts, 245
(See also Distribution of returns)
Revenue growth, 92, 97–99
Risk, 263–268
career, 263
counterparty, 7–8
liquidity, 256, 263
market, 263–265
in option investing, 267–268
perception of, 123–130
and size of hedges, 255–256
solvency, 256, 263
valuation, 265–267
Risk-averse investors, 123, 125–127
Risk-free rate:
borrowing at, 32, 40, 46
BSM model assumption about, 32, 
35–36, 40, 45–46
Risk-neutral investors, 124–126
Risk-seeking investors, 123, 125–127
Index   • 315
Rolling, 200–201
Round-tripping, 148–149, 300n1 
(Chapter 7)
S
Safeway, 100
Schiller, Robert, 43
Scholes, Myron, 8–9
Secular downturns, 302n2 (Chapter 11)
Secular shifts, profitability and,  
101–102
Sell-side structural impediments, 
136–137
Settlement prices, 146
Shiller, Robert, 42
Short calls, 14, 221
Short diagonal, 238–240
Short puts, 211–220
about, 213–214
BSM cone, 212
covered calls and, 241–244
in long diagonals, 235–237
loss leverage with, 211–212
portfolio management with, 216–220
protective puts vs., 248–250
returns for, 245
strike price for, 215
tenor for, 214–215
Short straddles, 230–232
Short strangles, 231–232
Short-call spreads, 220–230
about, 221–222
BSM cone, 220
portfolio management with,  
228–230
in short diagonals, 238–240
strike price for, 222–228
tenor for, 222
Short-term trading strategies:
implied volatility in, 63–64
intelligent investing vs., 267–268
and market risk, 264–265
Slovic, Paul, 119
Smolan, Rick, 114
Solvency risk, 256, 263
S&P 500 (see Standard & Poor’s 500 
Index)
Special-purpose vehicles, 110
Spreads:
bid-ask, 147–149
short-call (see Short-call spreads)
SPX ETF , 251–252
Standard & Poor’s 500 Index (S&P 
500):
correlation of hedge funds and, 134
distribution of returns, 44–46
protective puts on, 252–254
Startup stage, 86
Statistical volatility, 60
Stock investing, xiii
choices in, 20–22
visual representation of, 10–11
Stock prices:
BSM model assumption about, 32, 
34–35, 40–47
directional predictions of, 68–74
of dividend-paying stocks, 35–36
predicting, with BSM model, 32–39
(See also Forward prices; strike–
stock price ratio [K/S])
Stock-split effect, 42
Stop loss, 229
Straddles:
long, 208–209
short, 230–232
Straight-line depreciation, 283
Strangles:
long, 26–27, 205–207, 209
short, 231–232
Strategic capital, 297n1 (Chapter 4)
Strike prices:
and BSM cone, 52–54
defined, 12
long call, 192–196
long diagonal, 236–237
long put, 203
316  •   Index
Strike prices: (continued )
long strangle, 206–207
short diagonal, 239–240
short put, 215
short-call spread, 222–228
Strike–stock price ratio (K/S):
and change in closing price,  
146–147
defined, 53–54
and forward volatility, 67–74
Structural constraints, 86, 104
Structural downturns, 302n2  
(Chapter 11)
Structural growth stage, 94, 95
Structural impediments, 131–139
buy-side, 132–136
and investment strategies,  
137–139
principals vs. agents, 131–132
sell-side, 136–137
Sun Microsystems, 108
Supply-side constraints, 83
Symmetry, bias associated with, 
114–118
T
“Taking profit” with covered calls, 245
Taxes, BSM model assumption about, 
32, 40, 46
Technical analysis, 115
Tenor, 297n3 (Chapter 3)
defined, 59
for long calls, 190–192
for long puts, 202–203
for long strangles, 206
for protective puts, 252–254
for short puts, 214–215
for short-call spreads, 222
Terminal phase, 86
Time decay, 65–67
Time horizons:
long, 279–281
short, 270–272
Time value:
intrinsic vs., 56–59
of money, 87, 93–95
Time Warner, 103
Time-to-expiration assumptions,  
64–67
Toyota, 97
Trading restrictions, 32, 40, 46
Troughs (business-cycle):
operational leverage in, 283–284
and peaks, 302–303n2
Tversky, Amos, 123, 126
“2-and-20” arrangements, 134
U
Uncertainty, 118–119
Underexposure, 247
Underlying assets:
fungible, 272–273
and future stock price, 33–34
University of Chicago, 41
Unlevered investments:
levered vs., 164–165
in portfolios, 175–176, 178
Unrealized losses, 175–176
Unrealized profit, 254–255
Unused leg, long strangle, 207
U.S. Treasury bonds, 45–46
Utility curves, 124–126
V
Valuation:
golden rule of, 77–89
multiples-based, 99–100
shortcuts for, 93–97
value drivers in, 91–97
Valuation range:
BSM cone vs., 160–162
creating, 122
and margins of safety, 197–199
overlaying BSM cone with, 160
and strike price selection, 192–194
Valuation risk, 265–267
Index   • 317
Value:
of companies, 137–139
intrinsic, 56–59, 171
time, 56–59, 87, 93–95
Value drivers, 91–112
balance-sheet effects, 108–111
investing level and efficacy, 103–108
profitability, 99–103
revenue growth, 97–99
in valuation process, 91–97
Value investing, 79
Volatility (vol.):
amplifying directional predictions 
with, 71–74
changing assumptions about, 60–64
in earnings season, 301n5
failing to offset directional 
predictions with, 70–71
historical, 60
offsetting directional predictions 
with, 68–70
statistical, 60
types of, 59–60
(See also Forward volatility; Implied 
volatility)
Volatility smile, 45, 150, 152
W
Walmart, 105–108
Whole Foods Market, 100, 101
Working capital, 297n1  
(Chapter 4)
Writing options, 215, 301n3
x
X-system, 115–118
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ABOUT THE AUTHOR 
erik Kobayashi-Solomon, a veteran from the investment banking and 
hedge fund world, is the founder and principal of IOI, LLC a financial 
consultancy for individual and institutional investors. In addition to 
publishing an institutional investor-focused subscription product, Erik 
runs option and investment “boot camps” and consults on risk control, 
option strategies, and stock valuations for individual and institutional 
investors. 
Before starting IOI, Erik worked for Morningstar in its stock research 
department for over six years. At Morningstar, he first managed a team of 
semiconductor industry analysts before becoming the coeditor and driv-
ing force of Morningstar’s OptionInvestor newsletter and serving as the 
company’s Market Strategist. 
In addition to coauthoring a guide to fundamental investing and 
option strategies used in the Morningstar Investor Training Options 
Course and popular weekly articles about using options as a tool for in-
vestment portfolios, Erik was the host of several popular webinars such as 
“Covered Calls A to Z” and “Hedging 101. ” His video lecture about avoid-
ing behavioral and structural pitfalls called “Making Better Investment 
Decisions” was so popular that he was invited to be the featured speaker at 
several investment conferences throughout the United States. In addition, 
he represented Morningstar on television and radio, was interviewed by 
magazines and newspapers from Dallas to Tokyo to New Delhi, and was 
a frequent guest contributor to other Morningstar/Ibbotson publications.
Erik started his career in the world of finance at Morgan Stanley 
Japan, where he ultimately headed Morgan’s listed derivatives operations 
in Tokyo. After returning to the United States, Erik founded a small hedge 
fund based on his original research in the field of Behavioral Finance and 
later became the Risk Manager for a larger investment fund. There, he de-
signed option hedges for the fund’s $800 million global equity portfolio 
and advised the portfolio manager on quantitative investment strategies 
and Japanese stock market investments.
Erik, the son of a NASA scientist father and a concert violin-
ist mother, graduated Magna Cum Laude  and Phi Beta Kappa from the 
University of Texas at Austin, where he majored in Asian Studies and 
Japanese. After working in Japan for several years as a teacher, translator, 
and television actor, he won a full-ride scholarship to study business at 
the number one ranked school for international business in the United 
States—Thunderbird—in Glendale, Arizona. There, he worked as a research 
assistant to Dr. Anant Sundaram (Finance, presently at Dartmouth) from 
whom he gained a love for finance and economics, Dr. Graeme Rankine 
(Accounting) who introduced him to Behavioral Finance, and Dr. Charles 
Neilson (Marketing) who taught him the importance of strategic thinking. 
Erik graduated Summa Cum Laude  and was selected as the outstanding 
student of his graduating class.
Erik lives in Chicago, Illinois with his family and enjoys long distance 
running and reading. In his spare time, he volunteers at the local Japanese 
school to teach children Kendo—the Japanese art of swordsmanship.