gent 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


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, bu

eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf


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


ho 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 exposur


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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GREEN
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


ice (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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OTM
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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
499
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749 999
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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GREEN
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


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
RED
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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200
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20
40
60
80
100
120
140
160
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GREEN
GREEN
RED
RED
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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50
100
150
200
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


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
-
50
100
150
200
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
50
100
150
200
-
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
100
150
200
-
GREEN
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
RED
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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RED
GREEN
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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1


x-
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 defici


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


ut 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.
Advanced Building Corp. (ABC)
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30
20
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:
Advanced Building Corp. (ABC)
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100
90
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.
Advanced Building Corp. (ABC)
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100
90
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


ercent
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:
Advanced Building Corp. (ABC)
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90
80
70
60
50
40
30
20
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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9


ow 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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90
100
80
70
60
50
40
30
20
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
profes


ism 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


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.


ices 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
5/20/2013 249 499 999749
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 I