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’sdownside. As such, as long as the stock
expires above $45, we will realize aprofit on this investment.
Visual Representation of Options Canceling Exposure
Let’stake alook again at our visual representation of the risk and reward
of astock:
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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 aput, expiring in 365 days
and struck at $50, on the same stock?
Because we are purchasing aput, we know that we are gaining expo-
sure to the downside. Any time we gain exposure, we shade the exposure

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20  •   The Intelligent Option Investor
Any time again 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 aforce 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 atypical 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
Astock 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:

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Option Fundamentals   • 21
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GREEN
GREEN
RED
RED
Going long astock (i.e., buying
astock).
 Going short astock (i.e., short
selling astock).
If you want to gain exposure to astock’supside potential by going
long (left-hand diagram), you also must simultaneously accept exposure to
the stock’sdownside risk. Similarly, if you want to gain exposure to astock’sdownside potential by going short (right-hand diagram), you also must ac-
cept exposure to the stock’supside 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 astock 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 acrazy structure to be built.

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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’stake alook at afew 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 acall op-
tion to gain exposure to astock’supside potential above $50 per share. Rather
than accepting exposure to the stock’sentire 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
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BE = $45
RED

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Option Fundamentals   • 23
Here an investor is bullish on the prospects of the stock, so he or she doesn’tmind accepting exposure to the stock’sdownside risk below $50. In return for
accepting this risk, the option investor receives apremium—let’ssay $5. This
$5 is income to the investor—kind of like ado-it-yourself dividend payment.
By the way, as you will discover later in this book, this is also the risk-
return profile of acovered call.
Buying a Put for Protection
50
100
150
200
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GREEN
REDGRAY
Above an investor wants to enjoy exposure to the stock’supside potential
while limiting his or her losses in case of amarket fall. By buying aput
option struck afew 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 again on the put contract. The investor can use
these gains to buy more of the stock at alower 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

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24  •   The Intelligent Option Investor
Here an investor is bullish on the prospects of the stock and is tailor -
ing where to gain and accept exposure by selling ashort-term put and
simultaneously buying alonger-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 Ihope you realized while looking at each of the preceding
diagrams is how similar each of them looks to aparticular part of our long
and short stock diagrams:
Buying astock.
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RED
GREEN
GREEN
RED
Short selling astock.
For example, doesn’tthe diagram labeled “Buying acall for growth”
in the preceding section look just like the top part of the buying stock
diagram?

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Option Fundamentals   • 25
In fact, many of the option strategies Iwill introduce in this book
simply represent acarving up of the risk-reward profile of along 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, Iwill actu-
ally use adifferent nomenclature from breakeven.
If adiagram has one or both of the elements of the risk-return profile
of buying astock, Iwill call the breakeven line the effective buy price and
abbreviate it EBP. For example, if we sell aput option, we accept downside
risk in the same way that we do when we buy astock:
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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
buyprice .”
Conversely, if adiagram has one or both of the elements of the risk-
return profile of short selling astock, Iwill call the breakeven line the
effective sell price and abbreviate it ESP. For example, if we buy aput option
anticipating afall in the stock, we would represent it graphically like this:

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26  •   The Intelligent Option Investor
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ESP = $45
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When ashort seller sells astock, he or she gets immediate profit exposure
to the stock’sdownside potential. The seller is selling at $50 and hopes to make
aprofit by buying the shares back later at alower price—let’ssay $35. When we
get profit exposure to astock’sdownside 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 anet 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 astock investor cannot. For example, here is the graphic representa-
tion of astrategy commonly called along strangle:
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BE 1 = $80.75
BE 2 = $19.25
GREEN
GREEN

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Option Fundamentals   • 27
Here we have astock 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 astock 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’srange of exposure) or down (into the put’srange 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 atotal loss, and vice versa. For this reason, we calculate both break-
even prices as the sum of both legs of our option structure (where aleg
is defined as asingle option in amultioption strategy). As long as the leg
that winds up ITM is ITM enough to cover the cost of the other leg, we
will make aprofit on this investment. The only way we can fail to make aprofit 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 Imentioned 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.
Ido not want to belabor the point, but Ido want to leave you with one
graphic illustration of a “typical” complex option strategy sometimes
called acondor :

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28  •   The Intelligent Option Investor
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BE 1
BE 2
RED
RED
There are afew important things to notice. First, notice how much shorter
the time frame is—we have moved from a 500-day time exposure to atwo-week
exposure. In general, afloor trader has no idea of what the long-term value of astock 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 aworse 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’smarket 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 agood 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 agood
sense of how options are priced in the open market. We cover the topic of
option pricing in Chapter 2.

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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 astock 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 afair price is for an option’srange 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 astep-by-step refutation
to the principles underlying the BSM. Intelligent investors should be very,
very happy that the BSM is such apoor tool for pricing options and pre-
dicting future stock prices. It is the BSM’sshortcomings and the general
market’sunwillingness 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
ahigh level of mathematical sophistication. Ihave interviewed candidates with
master’sdegrees in financial engineering who indeed had avery 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.

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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 astock 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. Arange of future prices determined mechanically by the option
market according to the BSM
2. Arationally 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 abig-picture sense of how the
BSM prices options that is put in terms of an everyday example. You will also
understand the assumptions underlying the BSM and how, when combined,
these assumptions provide aprediction of the likely future value of astock.
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 ageneral
idea of the theory of option prices. Imagine that you and your spouse or
significant other have reservations at anice 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,

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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 afixed number of inputs regarding the underlying asset and the contract itself.
Inputting these variables into the BSM generates arange 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 acertain price (that certain price being astrike 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 afeel for the BSM on aconceptual dining-
reservation level, let’sdig into aspecific 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 astock 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 anormal (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.

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49
Chapter 3
The InTellIgenT
InvesTor’sguIde 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
You will also learn about the three measures of volatility—forward, im-
plied, and statistical. You 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 aprecise 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 afair 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 aprice for agiven op-
tion. The BSM is designed to give aprecise 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.

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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 asense of how expensive it will
be to gain exposure to agiven 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 agiven 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 astock.
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 amoment, it is
clear that the flexibility of options must be avaluable thing. What would
it be worth to you to only gain upside to astock without having to worry
about losing capital as aresult of astock 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’sassume that we want to gain exposure to the upside poten-
tial of a $50 stock by buying acall option with astrike price of $70 and atime to expiration of 365 days. Here is the risk-return profile of this option
position merged with the image of the BSM cone:

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The Intelligent Investor’s Guide to Option Pricing  •  51
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Advanced Building Corp. (ABC)
Date/Day Count
Stock Price
GREEN
Notice that because this call option is struck at $70, the upside po-
tential we have gained lies completely outside the cone of values the BSM
sees as reasonably likely. This option, according to the BSM, is something
like the bet that aseven-year-old might make with another seven-year-
old: “If you can [insert practically impossible action here], I’ll pay you azillion 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 aphenomenal
return.
Off the playground and into the world of high finance, the way to
offer someone aphenomenal return is to set the price of arisky 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” abit 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’ssay 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).

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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’stry this
now by moving the strike price down to $60:
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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.

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The Intelligent Investor’s Guide to Option Pricing  •  53
Notice that by moving the strike down from an expected 5 percent chance
of success to an expected 20 percent chance of success, we have agreed that we
would pay four times the amount to play. What would happen if we lowered the
strike to $50 so that the exposure range started at the present price of the stock?
Obviously, this at-the-money (ATM) option would be more expensive still:
5/18/2012
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5/20/2013 249 499 749 999
Advanced Building Corp. (ABC)
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The range of upside exposure we have gained with this option is not only
well within the BSM probability cone, but in fact it lies across the dotted line in-
dicating the “most likely” future stock value as predicted by the BSM. In other
words, this option has abit better than a 50 percent chance of paying off, so it
should be proportionally more expensive than either of our previous options.
The payouts and probabilities Iprovided earlier are completely made
up in order to show the principles underlying the probabilistic pricing of
option contracts. However, by looking at an option pricing screen, it is very
easy to extrapolate annualized prices associated with each of the probabil-
ity levels Imentioned—5, 20, and 50 percent.
The following table lists the relative market prices of call options cor-
responding to each of the preceding diagrams.
1 The table also shows the
calculation of the call price as apercentage of the present price of the stock
($50) as well as the strike–stock price ratio , which shows how far above or
below the present stock price agiven strike price is.

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54  •   The Intelligent Option Investor
Strike Price Strike–Stock Price Ratio Call Price
Call Price as a Percent
of Stock Price
70 140% $0.25 0.5
60 120% $1.15 2.3
50 100% $4.15 8.3
Notice that each time we lowered the strike price in successive
examples, we lowered the ratio of the strike price to the stock price. This
relationship (sometimes abbreviated as K/S, where Kstands for strike price
and Sstands for stock price) and the change in option prices associated
with it are easy for stock investors to understand because of the obvious tie
to directionality. This is precisely the reason why we have used changes in
the strike–stock price ratio as avehicle to explain option pricing. There are
other variables that can cause option prices to change, and we will discuss
these in alater section.
Iwill not make such along-winded explanation, but, of course,
put options are priced in just the same way. In other words, this put
option,
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56  •   The Intelligent Option Investor
This is so because the area of the range of exposure for the option on
the left that is bounded by the BSM probability cone is much smaller than
the range of exposure for the option on the right that is bounded by the
same BSM probability cone.
Time Value versus Intrinsic Value
One thing that Ihope you will have noticed is that so far we have talked
about options that are either out of the money (OTM) or at the money
(ATM). In-the-money (ITM) options—options whose range of exposure
already contains the present stock price—may be bought and sold in just
the same way as ATM and OTM options, and the pricing principle is ex-
actly the same. That is, an ITM option is priced in proportion to how much
of its range of exposure is contained within the BSM probability cone.
However, if we think about the case of an OTM call option, we realize
that the price we are paying to gain access to the stock’supside potential
is based completely on potentiality. Contrast this case with the case of an
ITM call option, where an investor is paying not only for potential upside
exposure but also for actual upside as well.
It makes sense that when we think about pricing for an ITM call option,
we divide the total option price into one portion that represents the poten-
tial for future upside and another portion that represents the actual upside.
These two portions are known by the terms time value and intrinsic value,
respectively. It is easier to understand this concept if we look at aspecific
example, so let’sconsider the case of purchasing acall option struck at $40
and having it expire in one year for astock presently trading at $50 per share.
We know that acall option deals with the upside potential of astock
and that buying acall option allows an investor to gain exposure to that up-
side potential. As such, if we buy acall option struck at $40, we have access
to all the upside potential over that $40 mark. Because the stock is trading
at $50 right now, we are buying two bits of upside: the actual bit and the
potential bit. The actual upside we are buying is $10 worth (= $50 − $40)
and is termed the intrinsic value of the option.
Asimple way to think of intrinsic value that is valid for both call options
and put options is the amount by which an option is ITM. However, the option’scost will be greater than only the intrinsic value as long as there is still time

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The Intelligent Investor’s Guide to Option Pricing  •  57
before the option expires. The reason for this is that although the intrinsic value
represents the actual upside of the stock’sprice over the option strike price,
there is still the possibility that the stock price will move further upward in the
future. This possibility for the stock to move further upward is the potential bit
mentioned earlier. Formally, this is called the time value of an option.
Let us say that our one-year call option struck at $40 on a $50 stock
costs $11.20. Here is the breakdown of this example’soption price into in-
trinsic and time value:
 $10.00 Intrinsic value: the amount by which the option is ITM
+ $1.20 Time value: represents the future upside potential of the stock
= $11.20 Overall option price
Recall that earlier in this book Imentioned that it is almost always amis-
take to exercise acall option when it is ITM. The reason that it is almost always
amistake is the existence of time value. If we exercised the preceding option,
we would generate again of exactly the amount of intrinsic value—$10. How-
ever, if instead we sold the preceding option, we would generate again totaling
both the intrinsic value and the time value—$11.20 in this example—and then
we could use that gain to purchase the stock in the open market if we wanted.
Our way of representing the purchase of an ITM call option from arisk-reward perspective is as follows:
Advanced Building Corp. (ABC)
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EBP = $51.25
999
100
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GREEN
ORANGE

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58  •   The Intelligent Option Investor
Usually, our convention is to shade again of exposure in green, but
in the case of an ITM option, we will represent the range of exposure with
intrinsic value in orange. This will remind us that if the stock falls from its
present price of $50, we stand to lose the intrinsic value for which we have
already paid.
Notice also that our (two-tone) range of exposure completely over -
laps with the BSM probability cone. Recalling that each upper and lower
line of the cone represents about a 16 percent chance of going higher or
lower, respectively, we can tell that according to the option market, this
stock has alittle better than an 84 percent chance of trading for $40 or
above in one year’stime.
2
Again, the pricing used in this example is made up, but if we take alook at option prices in the market today and redo our earlier table to in-
clude this ITM option, we will get the following:
Strike Price ($)
Strike–Stock
Price Ratio (%) Call Price ($)
Call Price as a Percent
of Stock Price
70 140 $0.25 0.5
60 120 $1.15 2.3
50 100 $4.15 8.3
40 80 10.85 21.7
Again, it might seem confounding that anyone would want to use the
ITM strategy as part of their investment plan. After all, you end up paying
much more and being exposed to losses if the stock price drops. Iask you
to suspend your disbelief until we go into more detail regarding option
investment strategies in Part III of this book. For now, the important points
are (1) to understand the difference between time and intrinsic value,
(2) to see how ITM options are priced, and (3) to understand our convention
for diagramming ITM options.
From these diagrams and examples it is clear that moving the range
of exposure further and further into the BSM probability cone will increase
the price of the option. However, this is not the only case in which options
will change price. Every moment that time passes, changes can occur to

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The Intelligent Investor’s Guide to Option Pricing  •  59
the size of the BSM’sprobability cone itself. When the cone changes size,
the range-of-exposure area within the cone also changes. Let’sexplore this
concept more.
How Changing Market Conditions
Affect Option Prices
At the beginning of Chapter 2, Istarted with an intuitive example related
to afriendly bet on whether acouple would make it to arestaurant in time
for adinner reservation. Let’sgo back to that example now and see how the
inputs translate into the case of stock options.
Dinner Reservation Example Stock Option Equivalent
How long before seating time Tenor 3 of the option
Distance between home and restaurant Difference between strike price and
present market price (i.e., strike–stock
price ratio)
Amount of traffic/likelihood of getting caught
at astoplight
How much the stock returns are
thought likely to vary up and down
Average traveling speed Stock market drift
Gas expenditure Dividend payout
Looking at these inputs, it is clear that the only input that is not known
with certainty when we start for the restaurant is the amount of traffic/
number of stoplights measure.
Similarly, when the BSM is figuring arange of future stock prices,
the one input factor that is unknowable and that must be estimated is
how much the stock will vary over the time of the option contract. It is
no surprise, then, that expectations regarding this variable become the
single most important factor for determining the price of an option and
the factor that people talk most about when they talk about options—
volatility (vol).
This factor is properly known as forward volatility and is formally
defined as the expected one-standard-deviation fluctuation up and
down around the forward stock price. If this definition sounds familiar,

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60  •   The Intelligent Option Investor
it is because it is also the definition of the BSM cone. To the extent that
expectations are not directly observable, forward volatility can only be
guessed at.
The option market’sbest guess for the forward volatility, as expressed
through the option prices themselves, is known as implied volatility. We
will discuss implied volatility in more detail in the next section and will
see how to build a BSM cone using option market prices and the forward
volatility they imply in Part III.
The one other measure of volatility that is sometimes mentioned is sta-
tistical volatility (a.k.a. historical volatility). This is apurely descriptive statis-
tic that measures the amount the stock price actually fluctuated in the past.
Because it is simply abackward-looking statistic, it does not directly affect
option pricing. Although the effect of statistical volatility on option prices
is not direct, it can have an indirect effect, thanks to abehavioral bias called
anchoring. Volatility is ahard concept to understand, let alone aquantity to
attempt to predict. Rather than attempt to predict what forward volatility
should be, most market participants simply look at the recent past statistical
volatility and tack on some cushion to come to what they think is areason-
able value for implied volatility. In other words, they mentally anchor on the
statistical volatility and use that anchor as an aid to decide what forward vola-
tility should be. The amount of cushion people use to pad statistical volatility
differs for different types of stocks, but usually we can figure that the market’simplied volatility will be about 10 percentage points higher than statistical
volatility. It is important to realize that this is acompletely boneheaded way
of figuring what forward volatility will be (so don’temulate it yourself), but
people do boneheaded things in the financial markets all the time.
However people come to an idea of what forward volatility is rea-
sonable for agiven option, it is certain that changing perceptions about
volatility are one of the main drivers of option prices in the market. To
understand how this works, let’stake alook at what happens to the BSM
cone as our view of forward volatility changes.
Changing Volatility Assumptions
Let’ssay that we are analyzing an option that expires in two years, with astrike price of $70. Further assume that the market is expecting aforward

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The Intelligent Investor’s Guide to Option Pricing  •  61
volatility of 20 percent per year for this stock. Visually, our assumptions
yield the following:
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Aforward volatility of 20 percent per year suggests that after
three years, the most likely range for the stock’sprice according to the
BSM will be around $41 on the low side to around $82 on the high
side. Furthermore, we can tell from our investigations in Chapter 2 that
this option will be worth something, but probably not much—about the
same as or maybe alittle more than the one-year, $60 strike call option
we saw in Chapter 2.
4
Now let’sincrease our assumption for volatility over the life of the
contract to 40 percent per year. Increasing the volatility means that the
BSM probability cone becomes wider at each point. In simple terms, what
we are saying is that it is likely for there to be many more large swings in
price over the term of the option, so the range of the possible outcomes
is wider.
Here is what the graph looks like if we double our assumptions
regarding implied volatility from 20 to 40 percent:

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The Intelligent Investor’s Guide to Option Pricing  •  63
With this change in assumptions, we can see that the most likely
range for the stock’sprice three years in the future is between about $50 and
about $70. As such, the chance of the stock price hitting $70 in two years
moves from somewhat likely (20 percent volatility in the first example) to
very likely (40 percent volatility in the second example) to very unlikely
(10 percent volatility in the third example) in the eyes of the BSM. This
characterization of “very unlikely” is seen clearly by the fact that the BSM
probability cone contains not one whit of the call option’sexposure range.
In each of these cases, we have drawn the graphs by first picking an
assumed volatility rate and then checking the worth of an option at acer -
tain strike price. In actuality, option market participants operate in reverse
order to this. In other words, they observe the price of an option being
transacted in the marketplace and then use that price and the BSM model
to mathematically back out the percentage volatility implied by the option
price. This is what is meant by the term implied volatility and is the process
by which option prices themselves display the best guesses of the option
market’sparticipants regarding forward volatility.
Indeed, many short-term option speculators are not interested in the
range of stock prices implied by the BSM at all but rather the dramatic change in
price of the option that comes about with achange in the width of the volatility
cone. For example, atrader who saw the diagram representing 10 percent annu-
alized forward volatility earlier might assume that the company should be trad-
ing at 20 percent volatility and would buy options hoping that the price of the
options will increase as the implied volatility on the contracts return to normal.
This type of market participant talks about buying and selling volatility as if
implied volatility were acommodity in its own right. In this style of option trad-
ing, investors assume that option contracts for aspecific stock or index should
always trade at roughly the same levels of implied volatility.
5 When implied vola-
tilities change from the normal range—either by increasing or decreasing—an
option investor in this vein sells or buys options, respectively. Notice that this
style of option transaction completely ignores not only the ultimate value of the
underlying company but also the very price of the underlying stock.
It is precisely this type of strategy that gives rise to the complex short-
term option trading strategies we mentioned in Chapter 1—the ones that are
set up in such away as to shield the investor transacting options from any of
the directionality inherent in options. Our take on this kind of trading is that

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64  •   The Intelligent Option Investor
although it is indeed possible to make money using these types of strategies,
because multiple options must be transacted at one time (in order to control
directional risk), and because in the course of one year many similar trades
will need to be made, after you pay the transaction costs and assuming that
you will not be able to consistently win these bets, the returns you stand to
make using these strategies are low when one accounts for the risk undertaken.
Of course, because this style of option trading benefits brokers by
allowing them to profit from the bid-ask spread and from afee on each
transaction, they tend to encourage clients to trade in this way. What is
good for the goose is most definitely not good for the gander in the case of
brokers and investors, so, in general, strategies that will benefit the investor
relatively more than they benefit the investor’sbroker—like the intelligent
option investing we will discuss in Part III—are greatly preferable.
The two drivers that have the most profound day-to-day impact
on option prices are the ones we have already discussed: achange in the
strike–stock price ratio and achange in forward volatility expectations.
However, over the life of acontract, the most consistent driver of option
value change is time to expiration. We discuss this factor next.
Changing Time-to-Expiration Assumptions
To see why time to expiration is important to option pricing, let us leave
our volatility assumptions fixed at 20 percent per year and assume that we
are buying acall option struck at $60 and expiring in two years. First, let’slook at our base diagram—two years to expiration:
Advanced Building Corp. (ABC)
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Date/Day Count
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GREEN

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The Intelligent Investor’s Guide to Option Pricing  •  65
It is clear from the large area of the exposure range bordered by the
BSM probability cone that this option will be fairly expensive.
Let’snow look at an option struck at the same price on the same un-
derlying equity but with only one year until expiration:
Advanced Building Corp. (ABC)
5/18/2012 5/20/2013 249 499 749 999
100
90
80
70
60
50
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Date/Day Count
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GREEN
Consistent with our expectations, shortening the time to expiration
to 365 days from 730 days does indeed change the likelihood as calculated
by the BSM of acall option going above $60 from quite likely to just barely
likely. Again, this can be confirmed visually by noting the much smaller
area of the exposure range bounded by the BSM probability cone in the
case of the one-year option versus the two-year one.
Indeed, even without drawing two diagrams, we can see that the
chance of this stock rising above $60 decreases the fewer days until expira-
tion simply because the outline of the BSM probability cone cuts diagonal-
ly through the exposure range. As the cone’soutline gets closer to the edge
of the exposure range and finally falls below it, the perceived chance falls
to 16 percent and then lower. We would expect, just by virtue of the cone’sshape, that options would lose value with the passage of time.
This effect has aspecial name in the options world—time decay. Time
decay means that even if neither astock’sprice nor its volatility change very
much over the duration of an option contract, the value of that option will

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66  •   The Intelligent Option Investor
still fall slowly. Time decay is governed by the shape of the BSM cone and
the degree to which an option’srange of exposure is contained within the
BSM cone. The two basic rules to remember are:
1. Time decay is slowest when more than three months are left
before expiration and becomes faster the closer one moves toward
expiration.
2. Time decay is slowest for ITM options and becomes faster the
closer to OTM the option is.
Visually, we can understand the first rule—that time decay increases
as the option nears expiration—by observing the following:
Slope is shallow here...
But steep here...
The steepness of the slope of the curve at the two different points
shows the relative speed of time decay. Because the slope is steeper the less
time there is on the contract, time decay is faster at this point as well.
Visually, we can understand the second rule—that OTM options lose
value faster than ITM ones—by observing the following:
Time BT ime A Time BT ime A
GREEN
GREEN
ORANGE
OTM option ITM option

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The Intelligent Investor’s Guide to Option Pricing  •  67
At time Afor the OTM option, we see that there is abit of the range of
exposure contained within the cone; however, after some time has passed
and we are at time B, none of the range of exposure is contained within
the BSM cone. In contrast, at times Aand Bfor the ITM option, the entire
range of exposure is contained within the BSM cone. Granted, the area of
the range of exposure is not as great at time Bas it was at time A, but still,
what there is of the area is completely contained within the cone.
Theoretically, time decay is aconstant thing, but sometimes actual
market pricing does not conform well to theory, especially for thinly traded
options. For example, you might not see any change in the price of an option
for afew days and then see the quoted price suddenly fall by anickel even
though the stock price has not changed much. This is afunction of the way
prices are quoted—often moving in 5-cent increments rather than in 1-cent
increments—and lack of “interest” in the option as measured by liquidity.
Changing Other Assumptions
The other input assumptions for the BSM (stock market drift and dividend
yield) have very small effects on the range of predicted future outcomes in
what Iwould call “normal” economic circumstances. The reason for this is
that these assumptions do not change the width of the BSM cone but rather
change the tilt of the forward stock price line.
Remember that the effect of raising interest rates by afew points is
simply to tilt the forward stock price line up by afew degrees; increasing
your dividend assumptions has the opposite effect. As long as interest rates
and dividend yields stay within typical limits, you hardly see adifference in
predicted ranges (or option prices) on the basis of achange in these variables.
Simultaneous Changes in Variables
In all the preceding examples, we have held all variables but one constant
and seen how the option price changes with achange in the one “free”
variable. The thing that takes some time to get used to when one is first
dealing with options is that, in fact, the variables don’tall hold still when
another variable changes. The two biggest determinants of option price
are, as we’ve seen, the strike–stock price ratio and the forward volatility

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68  •   The Intelligent Option Investor
assumption. Because these are the two biggest determinants, let’stake alook at some common examples in which achange in one offsets or exac-
erbates achange in the other.
Following are afew examples of how interactions between the variables
sometimes appear. For each of these examples, Iam assuming ashorter
investment time horizon than Iusually do because most people who get hurt
by some adverse combination of variables exacerbate their pain by trading
short-term contracts, where the effect of time value is particularly severe.
Falling Volatility Offsets Accurate Directional Prediction
Let’ssay that we are expecting Advanced Building Corp. to announce that it
will release anew product and that we believe that this product announcement
will generate asignificant short-term boost in the stock price. We think that
the $50 stock price could pop up to $55, so we buy some short-dated calls
struck at $55, figuring that if the price does pop, we can sell the calls struck at
$55 for ahandsome profit. Here’sadiagram of what we are doing:
20
25
30
35
40Stock Price
45
50
55
60
Advanced Building Corp. (ABC)
65
GREEN
As you should be able to tell by this diagram, this call option should
be pretty cheap—there is alittle corner of the call option’srange of expo-
sure within the BSM cone, but not much.

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The Intelligent Investor’s Guide to Option Pricing  •  69
Now let’ssay that our analysis is absolutely right. Just after we buy the
call options, the company makes its announcement, and the shares pop up
by 5 percent. This changes the strike–stock price ratio from 1.05 to 1.00.
All things being held equal, this should increase the price of the option
because there would be alarger portion of the range of exposure contained
within the BSM cone.
However, as the stock price moves up, let’sassume that not everything
remains constant but that, instead, implied volatility falls. This does hap-
pen all the time in actuality; the option market is full of bright, insightful
people, and as they recognize that the uncertainty surrounding aproduct
announcement or whatever is growing, they bid up the price of the options
to try to profit in case of aswift stock price move.
In the preceding diagram, we’ve assumed an implied volatility of 35
percent per year. Let’ssay that the volatility falls dramatically to 15 percent
per year and see what happens to our diagram:
20
25
30
35
40Stock Price
45
50
55
60
Advanced Building Corp. (ABC)
65
Stock price jumps
Implied volatility drops
GREEN
The stock price moves up rapidly, but as you can see, the BSM cone shrinks
as the market reassesses the uncertainty of the stock’sprice range in the
short term. The tightening of the BSM cone is so drastic that it more than
offsets the rapid price change of the underlying stock, so now the option is
actually worth less!

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70  •   The Intelligent Option Investor
We, of course, know that it is worth less because after the announce-
ment, there is only the smallest sliver of the call’srange of exposure con-
tained within the BSM cone.
Volatility Rise Fails to Offset Inaccurate Directional Prediction
Let’ssay that we are bullish on the Antelope Bicycle Co. (ABC) and, noting
that the volatility looks “cheap, ” buy call options on the shares. In this case,
an investor would be expecting to make money on both the stock price and
the implied volatility increasing—asituation that would indeed create an
amplification of investor profits.
We buy a 10 percent OTM call on ABC that expires in 60 days when
the stock is trading for $50.
20
25
30
35
40Stock Price 45
50
55
Antelope Bicycle Corp. (ABC)
60
GREEN
The next morning, while checking our e-mail and stock alerts, we find
that ABC has been using ametal alloy in its crankshafts that spontaneously
combusts after acertain number of cranks. This process has led to severe
burn injuries to some of ABC’sriders, and the possibility of aclass-action
lawsuit is high. The market opens, and ABC’sshares crash by 10 percent. At
the same time, the volatility on the options skyrocket from 15 to 35 percent

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The Intelligent Investor’s Guide to Option Pricing  •  71
because of the added uncertainty surrounding product liability claims.
Here is what the situation looks like now:
20
25
30
35
40Stock Price 45
50
55
Antelope Bicycle Corp. (ABC)
60
GREEN
This time we were right that ABC’simplied volatility looked too cheap, but
because we were directionally wrong, our correct volatility prediction does us
no good financially. The stock has fallen heavily, and even with alarge increase
in the implied volatility, our option is likely worth less than it was when we
bought it. Also, because the option is now further OTM than it originally was,
time decay is more pronounced. Thus, to the extent that the stock price stays at
the new $45 level, our option’svalue will slip away quickly with each passing day.
Rise in Volatility Amplifies Accurate Directional Prediction
These examples have shown cases in which changes in option pricing
variables work to the investor’sdisadvantage, but it turns out that changes
can indeed work to an investor’sadvantage as well. For instance, let’ssay
that we find acompany—Agricultural Boron Co. (ABC)—that we think,
because of its patented method of producing agricultural boron com-
pounds, is relatively undervalued. We decide to buy 10 percent OTM calls
on it. Implied volatility is sitting at around 25 percent, but our option is far
enough OTM that it is not very expensive.

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The Intelligent Investor’s Guide to Option Pricing  •  73
With this happy news story, our call options went from nearly
worthless to worth quite abit—the increase in volatility amplified the
rising stock price and allowed us to profit from changes to two drivers of
option pricing.
There is an important follow-up to this happy story that is well worth
keeping in the back of your mind when you are thinking about investing
in possible takeover targets using options. That is, our BSM cone widened
agreat deal when the announcement was made because the market be-
lieved that there might be ahigher counteroffer or that the deal would fall
through. If instead the announcement from DuPont was that it had made
afriendly approach to the ABC board of directors and that its offer had
already been accepted, uncertainty surrounding the future of ABC would
fall to zero (i.e., the market would know that barring any antitrust con-
cerns, DuPont would close on this deal when it said it would). In this case,
implied volatility would simply fall away, and the call option’svalue would
become the intrinsic value (in other words, there is no potential or time
value left in the option). The situation would look like this:
20
30
40 Stock Price
50
60
70
Agricultural Boron Co. (ABC)
80
GREEN
We would still make $5 worth of intrinsic value on an invested base
that must have been very small (let’ssay $0.50 or so), but were the situation
to remain uncertain, we would make much more.

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75
Part II
Asound intellectuAl
frAmework for
Assessing vAlue
After reading Part I, you should have avery good theoretical grasp on
how options work and how option prices predict the future prices of stocks.
This takes us partway to the goal of becoming intelligent option investors.
The next step is to understand how to make intelligent, rational es-
timates of the value of acompany. It makes no sense at all for aperson to
invest his or her own capital buying or selling an option if he or she does not
have agood understanding of the value of the underlying stock.
The problem for most investors—both professional and individual—
is that they are confused about how to estimate the value of astock. As such,
even those who understand how the Black-Scholes-Merton model (BSM)
predicts future stock prices are not confident that they can do any better.
There is agood reason for the confusion among both professional and
private investors: they are not taught to pay attention to the right things.
Individual investors, by and large, do not receive training in the basic tools
of valuation analysis—discounted cash flows and how economic transac-
tions are represented in aset of financial statements. Professional investors
are exquisitely trained in these tools but too often spend time spinning
their wheels considering immaterial details simply because that is what
they have been trained to do and because their compensation usually relies
on short- rather than long-term performance. They have all the tools in the
world but are taught to apply them to answering the wrong questions.

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78  •   The Intelligent Option Investor
money and discount rates, but even being unacquainted with these terms
right now will not be ahandicap.
Business is essentially acollection of very simple transactions—pro-
ducing, selling, and investing excess profits. In my experience, one of the
biggest investing mistakes occurs when people forget to think about busi-
ness in terms of these simple transactions.
Having afirm grasp of valuation is an essential part of being an in-
telligent option investor. The biggest drawback of the BSM is its initial as-
sumption that all stock prices represent the true values of the stocks in
question. It follows that the best opportunity for investors comes when astock’spresent price is far from its true intrinsic value. In order to assess
how attractive an investment opportunity is, we must have agood under-
standing of the source of value for afirm and the factors that contribute to
it. These are the topics of this chapter and the next.
In terms of our intelligent option investing process, we need two
pieces of information:
1. Arange of future prices determined mechanically by the option
market according to the BSM
2. Arationally determined valuation range generated through an in-
sightful valuation analysis
This chapter and the next give the theoretical background necessary to de-
rive the latter.
Jargon to be introduced in this chapter is as follows:
Asset Structural constraints
Demand-side constraints Supply-side constraints
Owners’ cash profit (OCP) Expansionary cash flow
Free cash flow to owner(s) (FCFO) Working capital
The Value of an Asset
The meaning of asset , in financial terms, is different from the vernacular
meaning of “something I’ dbe upset about if it broke or was stolen. ” In
financial terms, an asset is anything that can be owned that (1) was created

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102  •   The Intelligent Option Investor
Another case in which the normal profit range of acompany may
change is through improvements in productivity. And although improve-
ments to productivity can take along time to play out, they can be ex-
tremely important. The reason for this is that even if acompany is in astage in which revenues do not grow very quickly, if profit margins are in-
creasing, profit that can flow to the owner(s) will grow at afaster rate than
revenues. You can see this very clearly in the following table:
Year 0 1 2 3 4 5 6 7 8 9 10
Revenues
($)
1,234 1,271 1,309 1,348 1,389 1,431 1,473 1,518 1,563 1,610 1,658
Revenue
growth (%)
— 3 3 3 3 3 3 3 3 3 3
OCP ($)
4 432 445 497 485 514 544 560 637 625 708 746
OCP
margin (%)
35 35 38 36 37 38 38 42 40 44 45
OCP
growth
rate (%)
— 3 12 –2 6 6 3 14 –2 13 5
Even though revenues grew by aconstant 3 percent per year over this
time, OCP margin (owner’scash profit/revenues) increased from 35 to
45 percent, and the compound annual growth in OCP was nearly twice
that of revenue growth—at 6 percent.
Thinking back to the earlier discussion of the life cycle of acompany,
recall that the rate at which acompany’scash flows grew was avery important
determinant of the value of the firm. The dynamic of acompany with arela-
tively slow-growing revenue line and an increasing profit margin is common.
Atypical scenario is that acompany whose revenues have been increasing
quickly may be more focused on meeting demand by any means possible rath-
er than in the most efficient way. As revenue growth slows, attention starts to
turn to increasing the efficiency of the production processes. As that efficiency
increases, so does the profit margin. As the profit margin increases, as long as
the revenue line has some positive growth, profit growth will be even faster.
This dynamic is worth keeping in mind when analyzing companies
and in the next section, where Idiscuss the next driver of company value—
investment level and efficacy.

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The Four Drivers of Value  •  105
Over this very long period, the nominal GDP growth in the United
States averaged just over 6 percent per year. If the investment projects
of acompany are generally successful, the company will be able to
dependably grow its profits at arate faster than this 6 percent (or so)
benchmark. The length of time it will be able to grow faster than this
benchmark will depend on various factors related to the competitive-
ness of the industry, the demand environment, and the investing skill
of its managers.
Seeing whether or not investments have been successful over time is
asimple matter of comparing OCP growth with nominal GDP . Let’slook at
afew actual examples. Here is agraph of my calculation of Walmart’s OCP
and OCP margin over the last 13 years:
2000 2005 2010
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
3.00%
3.50%
4.00%
4.50%
5.00%20,000
18,000
16,000
14,000
12,000
10,000
8,000
6,000
4,000
2,000
-
Estimated Owners’ Cash Proﬁt and OCP Margin for Walmart
Total Estimated OCP (LH) OCP Margin (RH)
As one might expect with such alarge, mature firm, OCP margin
(shown on the right-hand axis) is very steady—barely breaking from the
3.5 to 4.5 percent range over the last 10 years. At the same time, its to-
tal OCP (shown on the left-hand axis) grew nicely as aresult of increases
in revenues. Over the last seven years, Walmart has spent an average of
around 2 percent of its revenues on expansionary projects, implying that

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141
Part III
IntellIgent OptIOn
InvestIng
Now that you understand how options work and how to value companies,
it is time to move from the theoretical to the practical to see how to apply
this knowledge to investing in the market. With Part III of this book, we
make the transition from theoretical to practical, and by the time you finish
this part, you will be an intelligent option investor.
To invest in options, you must know how to transact them; this is the
subject of Chapter 7. In it, you will see how to interpret an option pricing
screen and to break down the information there so that you can under -
stand what the option market is predicting for the future price of astock. Ialso talk about the only one of the Greeks that an intelligent option investor
needs to understand well—delta.
Chapter 8 deals with asubject that is essential for option investors—
leverage. Not all option strategies are levered ones, but many are. As such,
without understanding what leverage is, how it can be measured and used,
and how it can be safely and sanely incorporated into aportfolio, you can-
not be said to truly understand options.
Chapters 9–11 deal with specific strategies to gain, accept, and mix
exposure. In these chapters Ioffer specific advice about what strike prices
are most effective to select and what tenors, what to do when the expected
outcomes of an investment materially change, and how to incorporate
each strategy into your portfolio. Chapter 11 also gives guidance on so-
called option overlay strategies, where aposition in astock is overlain by
an option to modify the stock’srisk-reward profile (e.g., protective puts for
hedging and covered calls for generating income).

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142  •   The Intelligent Option Investor
Unlike some books, this book includes only ahandful of strategies,
and most of those are very simple ones. Ishun complex positions for two
reasons. First, as you will see, transacting in options can be very expensive.
The more complex an option strategy is, the less attractive the potential
returns become. Second, the more complex astrategy is, the less the inher-
ent directionality of options can be used to an investor’sadvantage.
Simple strategies are best. If you understand these simple strategies
well, you can start modifying them yourself to meet specific investing sce-
narios when and if the need arises. Perhaps by using these simple strategies
you will not be able to chat with the local investment club option guru
about the “gamma on an iron condor, ” but that will be his or her loss and
not yours.
Chapter 12 looks at what it means to invest intelligently while under-
standing the two forms of risk you assume by selecting stocks in which to
invest: market risk and valuation risk.

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143
Chapter 7
FIndIng MIsprIced
OptIOns
All our option-related discussions so far have been theoretical. Now it
is time to delve into the practical to see how options work in the market.
After finishing this chapter, you should understand
1. How to read an option chain pricing screen
2. Option-specific pricing features such as awide bid-ask spread,
volatility smile, bid and ask volatility, and limited liquidity/
availability
3. What delta is and why it is important to intelligent option investors
4. How to compare what the option market implies about future
stock prices to an intelligently determined range
In terms of where this chapter fits into our goal of becoming intelligent
option investors, obviously, even if you have aperfect understanding of
option and valuation theory, if you do not understand the practical steps
you must take to find actual investment opportunities in the real world, all
the theory will do you no good.
New jargon introduced in this chapter includes the following:
Closing price Bid implied volatility
Settlement price Ask implied volatility
Contract size Volatility smile
Round-tripping Greeks
Bid-ask spread Delta

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144  •   The Intelligent Option Investor
Making Sense of Option Quotes
Let’sstart our practical discussion by taking alook at an actual option
pricing screen. These screens can seem intimidating at first, but by the end
of this chapter, they will be quite sensible.
Last
0.86 -0.23
-0.14
-0.04
-0.17
-0.14
-0.06
-0.13
-0.12
-0.07
-0.09
-0.14
-0.06
-0.20
-0.26
-0.10
+0.01
0.91 0.94 21.672% 24.733% 0.8387
0.4313
0.0631
0.0000
0.0000
0.0000
0.9580
0.9598
0.9620
0.7053
0.4743
0.2461
0.0357
0.0392
0.0482
21.722%
22.988%
62.849%
72.188%
81.286%
201.771%
192.670%
175.779%
20.098%
18.997%
18.491%
25.587%
29.201%
35.855%
55.427%
123.903%
64.054%
23.311%
22.407%
21.813%
21.147%
22.144%
23.409%
54.689%
66.920%
35.642%
23.656%
23.072%
22.553%
21.460%
21.374%
21.581%
32.597%
24.854%
23.426%
20.380%
19.627%
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
0.26
0.04
0.02
0.02
0.02
13.30
12.40
11.35
1.19
0.58
0.22
0.01
0.01
0.02
11.90
12.35
10.10
1.68
1.10
0.67
0.05
0.03
0.02
0.24
0.02
10.35
9.30
8.40
1.17 19.408%
18.405%
17.721%
0.56
0.20
11.75
10.70
9.50
1.65
1.08
0.65
0.04
0.01
0.01
11.55 12.30
12.00
10.00
2.48
1.93
1.48
0.41
0.29
0.21
12.20
3.60
1.75
10.05
9.85
2.44
1.91
1.45
0.39
0.27
0.18
12.10
3.50
1.70
0.00
0.23
0.02
C0.00
C0.00
C0.00
0.09
0.45
1.15
C4.99
C5.99
C6.99
C4.99
C5.99
C6.99
C12.01
C11.01
C10.01
1.16
0.54
0.22
C0.00
C0.00
C0.00
C0.00
C0.00
C0.00
0.33
0.76
1.40
C5.03
C6.00
C6.99
C0.00
C0.01
C0.03
0.84
1.23
1.88
C12.02
C11.03
C10.04
1.65
1.06
0.66
C0.06
0.03
0.02
C12.05
C11.07
C10.10
C2.58
1.93
12.10
3.40
1.69
0.68
4.25
C7.27
1.42
0.38
C0.30
C0.22
C0.11
C0.15
C0.19
1.80
2.27
2.73
C5.57
C6.43
C7.35
Chng Bid AskA skImpl.Impl.Bid Vol. Vol. Delta JUL 26 ´13
31
32
33
37
38
39
20
21
22
31
32
33
37
38
39
Description
Call
Last Chng Bid AskA skImpl.Impl.Bid Vol. Vol. Delta
Put
0.9897
0.9869
0.9834
0.6325
0.4997
0.3606
0.0463
0.0266
0.0155
0.9712
0.9628
0.9535
0.5890
0.5118
0.4324
0.1664
0.1258
0.0923
0.9064
0.5354
0.3336
+0.01
+0.10
+0.11
0.07 0.09 22.812%2 4.853% -0.1613
-0.5689
-0.9373
-1.0000
-1.0000
-1.0000
22.469%
24.612%
85.803%
203.970%
267.488%
20.456%
19.851%
N/A
N/A
N/A
0.42
1.20
5.25
7.25
8.90
0.39
1.17
4.90
4.85
5.40
+0.02
+0.09
+0.14
-0.0420
-0.0402
-0.0380
-0.2948
-0.5261
-0.7545
-0.9652
-0.9616
-0.9524
77.739%
70.681%
63.514%
20.303%
19.170%
19.011%
41.423%
61.602%
52.378%
N/A
N/A
N/A
N/A
N/A
N/A
0.02
0.02
0.02
0.34
0.73
1.38
5.30
6.55
7.30
0.33
0.71
1.35
4.95
19.958%
18.577%
17.954%
4.65
6.70
22.720%
22.019%
21.378%
20.455%
19.050%
21.354%
0.000%
23.193%
22.845%
22.218%
21.148%
20.913%
20.899%
+0.07
+0.05
+0.16
+0.09
+0.12
+0.04
50.831%
48.233%
46.993%
23.384%
22.672%
22.106%
36.111%
30.947%
44.342%
N/A
N/A
N/A
N/A
0.02
0.03
0.05
0.82
1.25
1.82
5.55
6.30
7.55
0.01
0.80
1.23
1.79
4.95
6.15
6.85
-0.0103
-0.0131
-0.0166
-0.3679
-0.5008
-0.6402
-0.9558
-0.9757
-0.9871
22.989%
22.284%
21.453%
17.134%
37.572%
38.919%
37.587%
35.246%
23.914%
23.485%
22.925%
22.967%
26.265%
28.715%
0.11 0.13
0.17
0.19
1.78
2.25
2.80
5.80
6.85
7.85
0.13
0.17
1.75
2.22
2.76
5.70
6.50
7.40
-0.0318
-0.0406
-0.0503
-0.4120
-0.4879
-0.5665
-0.8294
-0.8690
-0.9025
34.172%
23.567%
23.145%
22.479%
21.404%
19.420%
18.411%
37.790%
35.385%
30.523%
24.198%
23.081%
0.00
+0.09
33.497%
26.033%
24.745%
0.68
4.25
7.40
0.66
4.15
7.30
-0.0906
-0.4520
-0.6521
33.203%
25.378%
24.054%
AUG 16 ´13
20
21
22
31
32
33
37
38
39
SEP 20 ´13
20
21
22
31
32
33
37
38
39
20
32
37
JAN 17 ´14
JAN 16 ´15
Ipulled this screen—showing the prices for options on Oracle (ORCL)—
on the weekend of July 20–21, 2013, when the market was closed. The last
trade of Oracle’sstock on Friday, July 19, was at $31.86, down $0.15 from the
Thursday’sclose. Your brokerage screen may look different from this one, but
you should be able to pull back all the data columns shown here. Ihave limited
the data I’mpulling back on this screen in order to increase its readability.
More strikes were available, as well as more expiration dates. The expirations
shown here are 1 week and 26, 60, 180, and 544 days in the future—the
544-day expiry being the longest tenor available on the listed market.
Let’sfirst take alook at how the screen itself is set up without paying
attention to the numbers listed.

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Finding Mispriced Options    • 145
Calls are on the left, puts on the right.
Strike prices
and expirations
are listed here.
You can tell the stock was down on this day because most of the call
options are showing losses and all the put options are showing gains.
All the strikes for
each selected expiry
are listed grouped
together.
This query was set up
to pull back three
strikes at the three
moneyness regions
(20–22, 29–31, 37–39).
The 1-week options
and the LEAPS did
not have strikes at
each of the prices Irequested.
Now that you can see what the general setup is, let’sdrill down and
look at only the calls for one expiration to see what each column means.
Last
C12.02 11.75
10.70
9.50
1.65
1.08
0.65
0.04
0.01
0.01 0.02
0.03
0.05
0.67
1.10
1.68
10.10
12.35
11.90 N/A
N/A
N/A
22.720%
55.427% 20
SEP 20 ´13
21
22
31
32
33
37
38
39
0.9869
0.9834
0.6325
0.4997
0.3606
0.0463
0.0266
0.0155
123.903%
64.054%
23.311%
22.407%
21.813%
21.147%
22.144%
23.409%
22.019%
21.378%
20.455%
19.050%
21.354%
C11.03
C10.04
1.65
1.06
-0.13
-0.12
-0.07
0.00
+0.01
0.66
C0.06
0.03
0.02
Chnq Bid AskA skImpl.Impl.Bid Vol. Vol. Delta Description
Call
0.9897
Red
(loss) Green
(gain)

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146  •   The Intelligent Option Investor
Last
This is the last price at which the associated contract traded. Notice that
the last price associated with the far in-the-money (ITM) strikes ($20, $21,
$22) and one of the far out-of-the-money (OTM) strikes ($37) have the
letter “C” in front of them. This is just my broker’sway of showing that the
contract did not trade during that day’strading session and that the last
price listed was the closing price of the previous day. Closing prices are not
necessarily market prices. At the end of the day, if acontract has not traded,
the exchange will give an indicative closing price (or settlement price ) for
that day. The Oracle options expiring on August 16, 2013, and struck at
$20 may not have traded for six months or more, with the exchange simply
“marking” aclosing price every day.
One important fact to understand about option prices is that they
are quoted in per-share terms but must be transacted in contracts that rep-
resent control of multiple shares. The number of shares controlled by one
contract is called the contract size . In the U.S. market, one standard con-
tract represents control over 100 shares. Sometimes the number of shares
controlled by asingle contract differs (in the case of acompany that was
acquired through the exchange of shares), but these are not usually avail-
able to be traded. In general, one is safe remembering that the contract size
is 100 shares.
You cannot break acontract into smaller pieces or buy just part of acontract—transacting in options means you must do so with indivisible
contracts, with each contract controlling 100 shares. Period. As such, every
price you see on the preceding screenshot, if you were to transact in one of
those options, would cost you 100 times the amount shown. For example,
the last price for the $31-strike option was $1.65. The investor who bought
that contract paid $165 for it (plus fees, taxes, and commissions, which are
not included in the posted price). In the rest of this book, when Imake
calculations regarding money spent on acertain transaction, you will al-
ways see me multiply by 100.
Change
This is the change from the previous day’sclosing price. My broker shows
change only for contracts that were actively traded that day. It looks like

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Finding Mispriced Options    • 147
the near at-the-money (ATM) strikes were the most active because of the
two far OTM options that traded; one’sprice didn’tchange at all, and the
other went up by 1 cent. On aday in which the underlying stock fell, these
calls theoretically should have fallen in price as well (because the K/Sratio,
the ratio of strike price to stock price, was getting slightly larger). This just
shows that sometimes there is adisconnect between theory and practice
when it comes to options.
To understand what is probably happening, we should understand
something about market makers. Market makers are employees at bro-
ker-dealers who are responsible for ensuring aliquid, orderly securi-
ties market. In return for agreeing to provide aminimum liquidity of
10 contracts per strike price, market makers get the opportunity to earn
the bid-ask spread every time atrade is made (Iwill talk about bid-ask
spreads later). However, once amarket maker posts agiven price, he or
she is guaranteeing atrade at that price. If, in this case (because we’re
dealing with OTM call options), some unexpected positive news comes
out that will create ahuge rise in the stock price once it filters into the
market and an observant, quick investor sees it before the market maker
realizes it, the investor can get areally good price on those far OTM call
options (i.e., the investor could buy afar OTM call option for 1 cent and
sell it for 50 cents when the market maker realizes what has happened.
To provide alittle slack that prevents the market maker from losing too
much money if this happens, market makers usually post prices for far
OTM options or options on relatively illiquid stocks that are abit unrea-
sonable—at alevel where asmart investor would not trade with him or
her at that price. If someone trades at that price, fine—the market maker
has committed to provide liquidity, but the agreement does not stipulate
that the liquidity must be provided at areasonable price. For this reason,
frequently you will see prices on far OTM options that do not follow the
theoretical “rules” of options.
Bid-Ask
For astock investor, the difference between abid price and an ask price
is inconsequential. For option investors, though, it is afactor that must
be taken into consideration for reasons that Iwill detail in subsequent

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148  •   The Intelligent Option Investor
paragraphs. The easiest way to think of the bid-ask spread is to think in
terms of buying anew car. If you buy anew car, you pay, let’ssay, $20,000.
This is the ask price. You grab the keys, drive around the block, and
return to the showroom offering to sell the car back to the dealership. The
dealership buys it for $18,000. This is the bid price. The bid-ask spread is
$2,000 in this example.
Bid-ask spreads are proportionally much larger for options than
they are for stocks. For example, the options I’ve highlighted here are on
avery large, important, and very liquid stock. The bid-ask spread on the
$32-strike call option (which you will learn in the next section is exactly
ATM) is $0.02 on amidprice of $1.09. This works out to apercentage bid-
ask spread of 1.8 percent. Compare this with the bid-ask spread on Ora-
cle’sstock itself, which was $0.01 on amidprice of $31.855—apercentage
spread of 0.03 percent.
For smaller, less-liquid stocks, the percentage bid-ask spread is even
larger. For instance, here is the option chain for Mueller Water (MW A):
2.5
5
7.5
10
Last
C5.30
C2.80
0.55
C0.00
Change Bid AskI mpl. Bid Vol. Impl. Ask Vol. Impl. Bid Vol. Impl. Ask Vol.Delta
2.5
5
7.5
10
2.5
5
7.5
10
12.5
DescriptionCall
Last Change BidA sk Delta
Put
C0.00
C0.00
C0.25
C2.25
C0.00
C0.00
C0.55
C2.35
C0.00
C0.10
C0.85
C2.55
C4.80
5.20 5.50 N/A 340.099% 0.9978
0.9978
0.7330
0.1316
0.9347
0.8524
0.6103
0.1516
0.9933
0.9190
0.6070
0.2566
0.1024
142.171%
46.039%
76.652%
N/A
N/A
2.95
0.55
0.10
0.20
0.10 N/A
N/A
N/A
0.10
0.30
2.35
40.733%
N/A
N/A
N/A
N/A
36.550%
38.181%
35.520%
35.509%
35.664%
2.10
0.50
0.05
0.10
0.60
2.402.30
0.05
0.15
0.15
0.85
2.60
4.90
0.70
2.45
4.60
2.70
0.500.00
5.20 5.50
3.00
0.90
0.20
2.80
0.80
0.10
5.505.10
3.102.85
1.151.05
0.400.30
0.200.05
39.708%
N/A
N/A
36.722%
N/A
38.754%
38.318%
39.127%
36.347%
36.336%
292.169% 0.0000
-0.0000
-0.2778
-0.8663
-0.0616
-0.1447
-0.3886
-0.8447
-0.0018
-0.0787
-0.3890
-0.7375
-0.8913
128.711%
53.108%
88.008%
117.369%
60.675%
42.433%
44.802%
110.810%
50.757%
42.074%
43.947%
49.401%
163.282%
75.219%
42.610%
45.215%
122.894%
64.543%
42.697%
44.728%
50.218%
C5.30
C2.80
C0.85
C0.10
C5.30
C1.10
C0.35
C0.10
3.00 +0.15
AUG 16 ´13
NOV 15 ´13
FEB 21 ´14
Looking at the closest to ATM call options for the November expiration—
the ones struck at $7.50 and circled in the screenshot—you can see that
the bid-ask spread is $0.10 on amidprice of $0.85. This works out to 11.8
percent.
Because the bid-ask spread is so very large on option contracts,
round-tripping
1 an option contract creates alarge hurdle that the returns
of the security must get over before the investor makes any money. In the
case of Mueller Water, the options one buys would have to change in price
by 11.8 percent before the investor starts making any money at all. It is for
this reason that Iconsider day trading in options and/or using complex

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Finding Mispriced Options    • 149
strategies involving the simultaneous purchase and sale of multiple con-
tracts to be apoor investment strategy.
Implied Bid Volatility/Implied Ask Volatility
Because the price is so different between the bid and the ask, the range of fu-
ture stock prices implied by the option prices can be thought of as different
depending on whether you are buying or selling contracts. Employing the
graphic conventions we used earlier in this book, this effect is represented
as follows:
Implied price range implied
by ask price volatility of 23.4%
Implied price range implied
by bid price volatility of 21.4%
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Oracle (ORCL)
Price per Share
60
50
40
30
20
10
-
Because Oracle is such abig, liquid company, the difference between
the stock prices implied by the different bid-ask implied volatilities is not
large, but it can be substantial for smaller, less liquid companies. Looking
at the ask implied volatility column, you will notice the huge difference
between the far ITM options’ implied volatilities and those for ATM and
OTM options. The data in the preceding diagram are incomplete, but
if you were to graph all the implied volatility data, you would get the
following:

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150  •   The Intelligent Option Investor
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
Strike Price
Oracle (ORCL) Implied Volatility
Implied Volatility (Percent)
160
180
140
100
120
80
40
60
20
0
Thinking about what volatility means with regard to future stock
prices—namely, that it is aprediction of arange of likely values—it does not
make sense that options struck at different prices would predict such radi-
cally different stock price ranges. What the market is saying, in effect, is that it
expects different things about the likely future range of stock prices depending
on what option is selected. Clearly, this does not make much sense.
This “nonsensical” effect is actually proof that practitioners
understand that the Black-Scholes-Merton model’s (BSM’s) assumptions
are not correct and specifically that sudden downward jumps in astock
price can and do occur more often than would be predicted if returns fol-
lowed anormal distribution. This effect does occur and even has aname—
the volatility smile . Although this effect is extremely noticeable when
graphed in this way, it is not particularly important for the intelligent op-
tion investing strategies about which Iwill speak. Probably the most im-
portant thing to realize is that the pricing on far OTM and far ITM options
is alittle more informal and approximate than for ATM options, so if you
are thinking about transacting in OTM or ITM options, it is worth looking
for the best deal available. For example, notice that in the preceding dia-
gram, the $21-strike implied volatility is actually notably higher than the

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Finding Mispriced Options    • 151
$20-strike volatility. If you were interested in buying an ITM call option,
you would pay less time value for the $20-strike than for the $21-strike op-
tions—essentially the same investment. Iwill talk more about the volatility
smile in the next section when discussing delta.
In asimilar way, sometimes the implied volatility for puts is different
from the implied volatility for calls struck at the same price. Again, this is
one of the market frictions that arises in option markets. This effect also
has investing implications that Iwill discuss in the chapters detailing dif-
ferent option investing strategies.
The last column in this price display is delta , ameasure that is so
important that it deserves its own section—to which we turn now.
Delta: The Most Useful of the Greeks
Someone attempting to find out something about options will almost
certainly hear about how the Greeks are so important. In fact, Ithink that
they are so unimportant that Iwill barely discuss them in this book. If you
understand how options are priced—and after reading Part I, you do—the
Greeks are mostly common sense.
Delta, though, is important enough for intelligent option investors
to understand with abit more detail. Delta is the one number that gives
the probability of astock being above (for calls) or below (for puts) agiven
strike price at aspecific point in time.
Deltas for calls always carry apositive sign, whereas deltas for puts are
always negative, so, for instance, acall option on agiven stock whose delta is
exactly 0.50 will have aput delta of −0.50. The call delta of 0.50 means that there
is a 50 percent chance that the stock will expire above that strike, and the put
delta of −0.50 means that there is a 50 percent chance that the stock will expire
below that strike. In fact, this strike demonstrates the technical definition of
ATM—it is the most likely future price of the stock according to the BSM.
The reason that delta is so important is that it allows you one way
of creating the BSM probability cones that you will need to find option
investment opportunities. Recall that the straight dotted line in our BSM
cone diagrams meant the statistically most likely future price for the stock.
The statistically most likely future price for astock—assuming that stocks

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152  •   The Intelligent Option Investor
move randomly, which the BSM does—is the price level at which there is
an equal chance of the actual future stock price to be above or below. In
other words, the 50-delta mark represents the forward price of astock in
our BSM cones.
Recall now also that each line demarcating the cone represents roughly a
16 percent probability of the stock reaching that price at aparticular time in the
future. This means that if we find the call strike prices that have deltas closest to
0.16 and 0.84 (= 1.00 − 0.16) or the put strike prices that have deltas closest to
−0.84 and −0.16 for each expiration, we can sketch out the BSM cone at points
in the future (the data Iused to derive this graph are listed in tabular format at
the end of this section).
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Date
Oracle (ORCL)
Price per Share
45
40
35
30
25
20
5
10
15
-
Obviously, the bottom range looks completely distended compared
with the nice, smooth BSM cone shown in earlier chapters. This dis-
tension is simply another way of viewing the volatility smile. Like the
volatility smile, the distended BSM cone represents an attempt by partici-
pants in the options market to make the BSM more usable in real situa-
tions, where stocks really can and do fall heavily even though the efficient
market hypothesis (EMH) says that they should not. The shape is saying,

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