tion, and 13 percent per year is quite a hurdle rate!
If there is some reason why you believe that you need to pay for insurance,
a better option—cheaper from a realized loss perspective—would be to sell
the shares and use part of the proceeds to buy call options as an option-based
replacement for the stock position. This approach has a few benefits:
1. The risk-reward profile is exactly the same between the two
structures.
2. Any ATM or ITM call will be more lightly levered than any OTM
put, meaning a lower realized loss on initiation.
3. For dividend-paying stocks, call owners do not have the right to
receive dividends, but the amount of the projected dividend is de-
ducted from the premium (as part of the drift calculation shown
in the section on covered calls). As such, although not being paid
dividends over time, you are getting what amounts to a one-time
upfront dividend payment.
4. If you do not like the thought of leverage in your portfolio, you can
self-margin the position (i.e., keep enough cash in reserve such that
you are not “borrowing” any money through the call purchase).
I do not hedge individual positions, but I do like the ITM call op-
tion as an alternative for people who feel the need to do so. For hedg-
ing of a general portfolio, rather than hedging of a particular holding in
a portfolio, options on sector or index exchange-traded funds (ETFs) are
more reasonably priced. Here are the ask prices for put options on the SPX
252  •   The Intelligent Option Investor
ETF [tracking the Standard and Poor’s 500 Index (S&P 500), which closed
at 1,685.73 when these data were retrieved] expiring in about 10 months:
Strike/Stock ($) Ask Price ($) Premium as Percent of Stock Price
0.99 106.60 6.3
0.89 50.90 3.0
0.80 25.80 1.5
This is still a hefty chunk of change to pay for protection on an index but
much less than the price of protection on individual stocks.
1
Common Pitfalls
Hedge Timing
Assume that you had talked to me a year ago and decided to take my ad-
vice and avoid buying protective puts on single-name options. Instead, you
took a protective put position on the S&P 500. Good for you.
Setting aside for a moment how much of your portfolio to hedge, let’s
take a look at what happened since you bought the downside protection:
S&P 500
1,800
1,700
1,600
1,500
1,400
1,300
1,200
1,100
1,000
8/1/20129/1/201210/1/201211/1/201212/1/20121/1/20132/1/20133/1/20134/1/20135/1/20136/1/20137/1/2013
GREEN
Mixing Exposure  •  253
When you bought the protection, the index was trading at 1,375, so
you bought one-year puts about 5 percent OTM at $1,300. If the market
had fallen heavily or even moderately during the first five months of the
contract, your puts would have served you very well. However, now the
puts are not 5 percent OTM anymore but 23 percent OTM, and it would
take another Lehman shock for the market to make it down to your put
strike.
Keeping in mind that buying longer-tenor options gives you a better
annualized cost than shorter-tenor options, you should be leery of entering
into a hedging strategy such as the one pictured here:
S&P 500
1,800
1,700
1,600
1,500
1,400
1,300
1,200
1,100
1,000
8/1/20129/1/201210/1/201211/1/201212/1/20121/1/20132/1/20133/1/20134/1/20135/1/20136/1/20137/1/2013
GREEN
Buying short-tenor puts helps in terms of providing nearer to
ATM protection, but the cost is higher, and it gets irritating to keep
buying expensive options and never benefiting from them (funny—
no one ever says this about home insurance). Although there are no
perfect solutions to this quandary, I believe the following approach
has merit:
254  •   The Intelligent Option Investor
S&P 500
1,800
1,700
1,600
1,500
1,400
1,300
1,200
1,100
1,000
8/1/20129/1/201210/1/201211/1/201212/1/20121/1/20132/1/20133/1/20134/1/20135/1/20136/1/20137/1/2013
GREEN GREENLIGHT GREEN
LIGHT GREEN
LIGHT GREEN
Here I bought fewer long-term put contracts at the outset and then add-
ed put contracts at higher strikes opportunistically as time passed. I have left
myself somewhat more exposed at certain times, and my protection doesn’t all
pick up at a single strike price, so the insurance coverage is spotty, but I have
likely reduced my hedging cost a great deal while still having a potential source
of investible cash on hand in the form of options with time value on them.
The Unhappy Case of a Successful Hedge
Markets are down across the board. Y our brokerage screen is awash in red.
The only bright spot is the two or three lines of your screen showing your
S&P 500 puts, which are strongly positive. Y ou bought your protection
when the market was going up, so it was very cheap to purchase. Now, with
the market in a terror, the implied volatilities have shot up, and you are sit-
ting on a huge positive unrealized value.
Now what?
The psychological urge to keep that hedge on will be strong. Such a po-
sition is safe after all, and with the rest of the world falling apart, it feels nice to
have somewhere safe to go. What should you do with this unrealized profit?
Mixing Exposure  •  255
Step one is always assessing the value of securities in your portfolio
and securities that might be on your watch list. Does the news driving the
markets down have a material effect on the value of any of your holdings?
Certainly, if the market believes that the economy is going into a recession,
the next few years’ worth of revenue growth and profits may be those that
you projected for your explicit-period worst-case scenarios, but that will
likely be offset by faster medium-term growth as the economy bounces
back. Think about the valuations you have for your holdings objectively and
with as little passion as possible. It’s better not to have your brokerage screen
or a price chart of the financial markets or whatever up while you do this.
Are there securities whose present prices are significantly different from
your worst-case valuation range? Do the prices imply an unlevered retur


economy bounces
back. Think about the valuations you have for your holdings objectively and
with as little passion as possible. It’s better not to have your brokerage screen
or a price chart of the financial markets or whatever up while you do this.
Are there securities whose present prices are significantly different from
your worst-case valuation range? Do the prices imply an unlevered return of 30,
40, or 50 percent or more? Is there a stock that has been on your watch list for a
long time but until now has never been at a price at which you wanted to buy it?
This is where you must resist the urge to take the safe path and close the
hedge and then turn around the cash and increase your position size on your
best investments or on investments that you have always wanted to make but
haven’t had the chance. This will be a hard thing to do psychologically. The
world is telling you to run and hide. This is the time to remember the maxim,
“Be bold when others are scared and scared when others are bold. ” Times of
stress are those that set great investors apart from the rest of the crowd.
Not Having a Plan
Finally, we get to the question of how to size our hedge. If we look at the in-
dicative prices for S&P 500 puts shown earlier, we can see that if we choose
to hedge the entire amount of our portfolio, we set up at least a 6 percent-
age point drag on our portfolio every 10 months or so, and that is a lot of
potentially dead weight to be carrying around.
In daily life, I believe that people are prone to overinsure (e.g.,
extended warrantees for consumer electronic items and so on), and this
is a good habit to keep away from in investing. Risk is not a temporary
unrealized loss caused by market panic. Usually risk is not the inability to
invest more capital when you want to invest more capital (unless by not
investing it you will have a shortfall in capital in the future). Risk is usually
not any of the things TV pundits talk about as being risk.
256  •   The Intelligent Option Investor
I will discuss risk in greater detail in Chapter 12, but a sensible defini-
tion of risk is not having the capital resources to pay for something when
you need to pay for it. In this sense, risk can be talked about in terms of
liquidity—a short-term lack of spending power—and solvency—a funda-
mental lack of capital assets. For example, let’s say that you have commit-
ted to pay a restaurant and entertainers the remainder of their $50,000 fee
for your son’s bar mitzvah or your daughter’s wedding, and you only have
$20,000 in net worth. Y ou are in a position of risk because of problems of
solvency but not necessarily liquidity (i.e., you could borrow the money to
pay for these things). However, if you have a net worth of $3 million—all of
it unrealized gains on real estate holdings—and you have the same $50,000
bill to pay, you may be in a position of risk because of problems in liquidity
but not solvency.
Risk that stems from issues of liquidity usually can be controlled
through intelligent asset allocation. For example, the millionaire father in
the preceding bar mitzvah/wedding example can realize $50,000 worth
of his unrealized investment gains to meet his immediate cash need. A
79-year-old with 85 percent of her net worth of $2.5 million invested in
tech sector initial public offerings (IPOs) or companies in the Chinese in-
frastructure supply chain can ameliorate her risk of not being able to pay
for necessary healthcare and living expenses by shifting more of her assets
into bonds and CDs. Usually, in cases such as this—which, I believe, make
up the majority of cases people are trying to “hedge”—there are much
better ways of controlling risk than buying puts on the S&P 500 or the
Russell 2000!
However, there is a more subtle instance of risk—not maximizing re-
turns on one’s invested capital and, because of this, not having the capital
adequacy to meet unforeseen cash-flow needs in the future. This instance
of risk deals with solvency, rather than liquidity.
This type of risk cannot be ameliorated through a defensive strategy
but must be controlled through an offensive one. Setting aside savings, in-
vesting those savings wisely and consistently in good times, and having the
courage to invest when it is hardest to do so (i.e., when the market is crash-
ing) are all elements of this risk-control strategy. Put options can only help
with the third case here—investing when it is hardest to do so—but they
cannot help without the put owner’s input of personal courage.
Mixing Exposure  •  257
This topic brings us back to the last section—investing the proceeds
in a successful hedge in undervalued assets. I believe that portfolio hedges
should be set up with a particular cost and investing goal in mind. For
example, “I am willing to allocate as much as 1 percentage point of my
investment performance this year to have an extra 5 percent of cash on
hand to invest in case the market drops by 10 to 20 percent. ” This is the
rough outline of a hedging plan. It specifies the maximum you are will-
ing to spend and a target for how much cash you want in case of a certain
market downdraft.
This plan does not mean that you always have to spend 1 percent
of your net worth on hedges. There are times when it is more sensible to
spend more on hedges—because of building macroeconomic uncertainty
or whatever—and other times when it is more sensible to spend less—when
the economy is just coming out of a recession for instance.
Also note that the plan specifies a cash level. If you are not fully in-
vested in your securities portfolio, you are already hedged to the degree
that your cash assets are not subject to direct security price risk (cash is
subject to inflation risk, but this is another topic). The cash you have on
reserve will allow you to purchase if and when the market falls. As such,
I don’t believe that people holding a significant allocation of cash shou

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


you are not fully in-
vested in your securities portfolio, you are already hedged to the degree
that your cash assets are not subject to direct security price risk (cash is
subject to inflation risk, but this is another topic). The cash you have on
reserve will allow you to purchase if and when the market falls. As such,
I don’t believe that people holding a significant allocation of cash should
think about hedging per se. Y ou may believe that the market is ready to fall,
in which case, you can make a bearish bet on the level of the index using a
long put, a short-call spread, or a short diagonal, but this is a proactive in-
vestment that expresses your opinion about the level of the market vis-à-vis
the state of the economy.
What it does not specify is what you will spend the cash on. This is
where an understanding of the value of the companies in your portfolio
or on your watch list comes into play. If you had an extra 5 percent (or
$50,000 or however you want to think about it) in cash, in what securities
would you invest? Of course, the answer will change depending on the
price of the securities vis-à-vis what you know to be a sensible valuation
range because the expected returns on the investments will change with
the market price.
So this is the last step in a sensible hedging plan—having an idea of
what companies you would want to invest in were you to have the extra
capital and if you could be reasonably assured of a good return. Having a
258  •   The Intelligent Option Investor
plan like this in place will allow you to size and time your hedges appropri-
ately and will help you to make the most out of whatever temporary crisis
might come your way.
2
Now that you have a good understanding of protective puts and
hedging, let’s turn to the last overlay strategy—the collar.
Collar
Contingent Exposure
Contingent Exposure
Contingent Exposure
GREEN
LIGHT GREEN
LIGHT ORANGE
LIGHT RED
ORANGE
RED
Downside: Irrelevant
Upside: Undervalued
Execute: Sell a call option on a stock or index that you own and on
which you have a gain, and use the proceeds from the call
sale to buy an OTM put
Risk: Flexible, depending on selection of strikes
Reward: Limited to level of sold call strike
Margin: None because the long position in the hedged security
serves as collateral for the sold call option, and the OTM
put option is purchased, so it does not require margining
Mixing Exposure  •  259
The Gist
This structure is really much simpler and has a much more straightfor -
ward investment purpose than it may seem when you look at the preceding
diagram. When people talk about “taking profits” using a covered call, the
collar is actually the strategy they should be using.
Imagine that you bought a stock some time ago and have a nice
unrealized gain on it. The stock is about where you think its likely fair
value is, but you do not want to sell it for whatever reason (e.g., it is
paying a nice dividend or you bought it less than a year ago and do not
want to be taxed on short-term capital gains or whatever). Although you
do not want to sell it, you would like to protect yourself from downside
exposure.
Y ou can do this cheaply using a collar. The collar is a covered call,
which we have already discussed, whose income subsidizes the purchase of
a protective put at some level that will allow you to keep some of the unre-
alized gains on your securities position. The band labeled “Orange” on the
diagram shows an unrealized gain (or, conversely, a potential unrealized
loss). If you buy a put that is within this orange band or above, you will be
guaranteed of making at least some realized profit on your original stock
or index investment. Depending on how much you receive for the covered
call and what strike you select for the protective put, this collar may rep-
resent completely “free” downside protection or you might even be able to
realize a net credit.
Execution
The execution of this strategy depends a great deal on personal prefer -
ence and on the individual investor’s situation. For example, an investor
can sell a short-tenor covered call and use those proceeds to buy a longer-
tenor protective put. He or she can sell the covered call ATM and buy a
protective put that is close to ATM; this means the maximum and mini-
mum potential return on the previous security purchase is in a fairly tight
band. Conversely, the investor might sell an OTM covered call and buy
a protective put that is also OTM. This would lock in a wider range of
guaranteed profits over the life of the option.
260  •   The Intelligent Option Investor
I show a couple of examples below that give you the flavor of the
possibilities of the collar strategy. With these examples, you can experi-
ment yourself with a structure that fits your particular needs. Look on
my website for a collar scenario calculator that will allow you to visualize
the collar and understand the payoff structure given different conditions.
For these examples, I am assuming that I bought Qualcomm stock at
$55 per share. Qualcomm is now trading for $64.71—an unrealized gain
of 17.7 percent.
Collar 1: 169 Days to Expiration
Strike Price ($) Bid (Ask) Price ($)
Sold call 65.00 3.40
Purchased put 60.00 (2.14)
Net credit $1.26
This collar yields the following best- and worst-case effective sell prices
(ESPs) and corresponding returns (assuming a $55 buy price):
ESP ($) Return (%)
Best case 66.26 20.5
Worst case 61.26 11.4
Here we sold the $65-strike calls for $3.40 and used those proceeds to
buy the $60-strike put options at $2.14. This gave us a net credit of $1.26,
which we simply add to both strike prices to calculate our ESP . We add the
net credit to the call strike because if the stock moves above the call strike,
we will end up delivering the stock at the strike price while still keeping the
net credit. We add the net credit to the put strike because if the stock closes
below the put strike, we have the right to


This gave us a net credit of $1.26,
which we simply add to both strike prices to calculate our ESP . We add the
net credit to the call strike because if the stock moves above the call strike,
we will end up delivering the stock at the strike price while still keeping the
net credit. We add the net credit to the put strike because if the stock closes
below the put strike, we have the right to sell the shares at the strike price
and still keep the net credit. The return numbers are calculated on the basis
of a $55 purchase price and the ESPs listed. Thus, by setting up this collar in
Mixing Exposure  •  261
this way, we have locked in a worst possible gain of 11.4 percent and a best
possible gain of 20.5 percent for the next five and a half months.
Let’s look at another collar with a different profit and loss profile:
Collar 2: 78 Days to Expiration
Strike Price ($) Bid (Ask) Price ($)
Sold call 70 0.52
Purchased put 62.50 (1.55)
Net debit (1.03)
This collar yields the following best- and worst-case ESPs and corresponding
returns (assuming a $55 buy price):
ESP ($) Return (%)
Best case 68.97 25.4
Worst case 61.47 11.8
This shows a shorter-tenor collar—about two and a half months be-
fore expiration—that allows for more room for capital gains. This might be
the strategy of a hedge fund manager who is long the stock and uncertain
about the next quarterly earnings report. For his or her own business rea-
sons, the manager does not want to show an unrealized loss in case Qual-
comm’s report is not good, but he or she also doesn’t want to restrict the
potential capital gains much either.
Calculating the ESPs and the returns in the same way as described
here, we get a guaranteed profit range from around 12 to over 25 percent.
One thing to note as well is that the protection is provided by a put, and
a put option can be sold any time before expiry to generate a cash inflow
from time value. Let’s say then that when Qualcomm reports its quarterly
earnings, the stock price drops to $61—a mild drop that the hedge fund
manager considers a positive sign. Now that the manager is less worried
about the downside exposure, he or she can sell the put for a profit.
262  •   The Intelligent Option Investor
The cash inflow from selling the put for a profit may even change the net
debit on the collar to a net credit, or the manager can use some of the cash
flow to buy back the sold call option if he or she is worried about the upside
being limited.
These are just two examples, but they show the kind of flexibility that
makes collars very useful investing instruments. With this chapter com-
plete, you have all the tools required to be an intelligent option investor.
Let’s finish with an important discussion—an investigation of risk and in-
telligent option investing. This is the topic of Chapter 12.
263
Chapter 12
Risk and the intelligent
OptiOn investOR
The preceding 11 chapters have given you a great deal of information about
the mechanics of option investing and stock valuation. In this last chapter,
let’s look at a subject that I have mentioned throughout this book—risk—
and see how an intelligent option investor conceives of it.
There are many forms of risk—some of which we discussed earlier
(e.g., the career risk of an investment business agent, solvency risk of a
retiree looking to maintain a good quality of life, and liquidity risk of a
parent needing to make a big payment for a child’s wedding). The two risks
I discuss here are those that are most applicable to an owner of capital
making potentially levered investments in complex, uncertain assets such
as stocks. These two risks are market risk and valuation risk.
Market Risk
Market risk is unavoidable for anyone investing capital. Markets fluctuate, and
in the short term, these fluctuations often have little to do with the long-term
value of a given stock. Short term, it must be noted, is also relative. In words
attributed to John Maynard Keynes, but which is more likely an anonymous
aphorism, “The market can remain irrational longer than you can remain sol-
vent. ” Indeed, it is this observation and my own painful experience of the truth
of it that has brought me to my appreciation for in-the-money (ITM) options
as a way to preserve my capital and cushion the blow of timing uncertainty.

264  •   The Intelligent Option Investor
Market risk is a factor that investors in levered instruments must
always keep in mind. Even an ITM call long-term equity anticipated
security (LEAPS) in the summer of 2007 might have become a short-tenor
out-of-the-money (OTM) call by the fall of 2008 after the Lehman shock
because of the sharp decline in stock prices in the interim. Unexpected
things can and do happen. A portfolio constructed oblivious to this fact is
a dangerous thing.
As long as market fluctuations only cause unrealized losses, market
risk is manageable. But if a levered loss must be realized, either because of
an option expiration or in order to fund another position, it has the poten-
tial to materially reduce your available investment capital. Y ou cannot ma-
terially reduce your investment capital too many times before running out.
A Lehman shock is a worst-case scenario, and some investors live
their entire lives without experiencing such severe and material market
risk. In most cases, rather than representing a material threat, market risk
represents a wonderful opportunity to an intelligent investor.
Most human decision makers in the market are looking at either
technical indicators—which are short term by nature—or some sort of
multiple value (e.g., price-to-something ratio). These kinds of measures are
wonderful for brokers because they encourage brokerage clients to make
frequent trades and thus pay the brokerages frequent fees.
The reaction of short-term traders is also wonderful for intelligent
investors. This is so because a market reaction that might look sensible or
rational to som


by nature—or some sort of
multiple value (e.g., price-to-something ratio). These kinds of measures are
wonderful for brokers because they encourage brokerage clients to make
frequent trades and thus pay the brokerages frequent fees.
The reaction of short-term traders is also wonderful for intelligent
investors. This is so because a market reaction that might look sensible or
rational to someone with an investment time horizon measured in days or
months will often look completely ridiculous to an investor with a longer-
term perspective. For example, let’s say that a company announces that its
earnings will be lower next quarter because of a delay in the release of a
new product. Investors who are estimating a short-term value for the stock
based on an earnings multiple will sell the stock when they see that earn-
ings will likely fall. Technical traders see that the stock has broken through
some line of “resistance” or that one moving average has crossed another
moving average, so they sell it as well. Perhaps an algorithmic trading
engine recognizes the sharp drop and places a series of sell orders that are
covered almost as soon as they are filled. In the meantime, someone who
has held the stock for a while and has a gain on it gets protective of this gain
and decides to buy a put option to protect his or her gains.

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

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

Risk and the Intelligent Option Investor   • 267
Let’s assume that the present market value of the shares is $16 per
share. This share price assumes a growth in FCFO of 8 percent per year for
the next 5 years and 5 percent per year in perpetuity after that—roughly
equal to what we consider our


lows not growing and lasting 20 years—$7 per
share.
Market value of hard assets—$2 to $4 per share.

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

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

269
Appendix A
Choose Your Battles
WiselY
I discuss specific option investment strategies in great detail in Part III
of this book. However, after reading Chapters 2 and 3, you should have a
good understanding of how options are priced, so it is a good time to see
in what circumstances the Black-Scholes-Merton model (BSM) works best
and where it works worst. An intelligent investor looks to avoid the condi-
tions where the BSM works best like the plague and seek out the conditions
where it works worst because those cases offer the best opportunities to tilt
the risk-reward balance in the investor’s favor.
Jargon introduced in this appendix includes
Front month
Fungible
Idiosyncratic assets
Where the BSM Works Best
The following are the situations in which the BSM works best and are the
conditions you should most avoid:
1. Short investment time horizons
2. Fungible investment assets
270  •   The Intelligent Option Investor
Short Investment Time Horizons
When the scholars developing the BSM were researching financial
markets for the purpose of developing their model, the longest-tenor
options had expirations only a few months distant. Most market partic-
ipants tended to trade in the front-month contracts (i.e., the contracts
that will expire first), as is still mainly the case. Indeed, thinking back
to our preceding discussion about price randomness, over short time
horizons, it is very difficult to prove that asset price movements are not
random.
As such, the BSM is almost custom designed to handle short time
horizons well.
Perhaps not unsurprisingly, agents
1 are happy to encourage clients to
trade options with short tenors because
1. It gives them more opportunities per year to receive fees and com-
missions from their clients.
2. They are mainly interested in reliably generating income on the
basis of the bid-ask spread, and bid-ask spreads differ on the basis
of liquidity, not time to expiration.
3. Shorter time frames offer fewer chances for unexpected price
movements in the underlying that the market makers have a hard
time hedging.
In essence, a good option market maker is akin to a used car sales-
man. He knows that he can buy at a low price and sell at a high one, so his
main interest is in getting as many customers to transact as possible. With
this perspective, the market maker is happy to use the BSM, which seems
to give reasonable enough


movements in the underlying that the market makers have a hard
time hedging.
In essence, a good option market maker is akin to a used car sales-
man. He knows that he can buy at a low price and sell at a high one, so his
main interest is in getting as many customers to transact as possible. With
this perspective, the market maker is happy to use the BSM, which seems
to give reasonable enough option valuations over the time period about
which he most cares.
In the case of short-term option valuations, the theory describes
reality accurately enough, and structural forces (such as wide bid-ask
spreads) make it hard to exploit mispricings if and when they occur.
To see an example of this, let’s take a look at what the BSM assumes is
a reasonable range of prices for a company with assumed 20 percent
volatility over a period of 30 days.
Appendix A: Choose Your Battles Wisely   • 271
10
-
20
30
40
50
60
70
The range of prices implied over the next 30 days goes from around
$47 per share to around $53 per share. If we translate what the BSM con-
siders the reasonable range into percentage terms, it works out to a loss
or gain of around 6 percent. Just thinking about this in terms of one’s
personal experience for a moment, this is actually not a bad guess for a
range for a large-capitalization firm (the forward volatility assumption of
20 percent is consistent with a large-cap firm’s “typical” implied volatility).
I certainly would have no confidence in trying to guess the upper and
lower stock price boundaries any better than the BSM on such a short
time frame.
It is funny, then, that most investors insist on speculating in options
on a short-term basis—usually at tenors of a month or shorter. Again, these
seem like the kinds of bets you might get betting on red at a roulette wheel
in Vegas. Sure, it makes one feel like James Bond the 50 percent of the time
that the marble falls on red, but anyone who is the least bit thoughtful
would, after a time, step back and wonder how far ahead he or she is getting
by playing such a game.
2
272  •   The Intelligent Option Investor
It is important to realize that the fact that options are usually
efficiently priced in the short term does not prevent us from transacting
in short-tenor options. In fact, some strategies discussed in Part III are
actually more attractive when an investor uses shorter-tenor options or
combines short- and long-tenor options into a single strategy.
Hopefully, the distinction between avoiding short-tenor option
strategies and making long-term investments in short-tenor options is
clear after reading through Part III.
Fungible Underlying Assets
Again, returning for a moment to the foundation of the BSM, the scholars built
their mathematical models by studying short-term agricultural commodity
markets. A commodity is, by definition, a fungible or interchangeable asset;
one bushel of corn of a certain quality rating is completely indistinguishable
from any other bushel of corn of the same quality rating.
Stocks, on the other hand, are idiosyncratic assets. They are intangible
markers of value for incredibly complex systems called companies, no two
of which is exactly alike (e.g., GM and Ford—the pair that illustrates the
idea of “paired” investments in many people’s minds—are both American
car companies, but as operating entities, they have some significant differ-
ences. For example, GM has a much larger presence in China and has a
different capital and governance structure since going bankrupt than Ford,
which avoided bankruptcy during the mortgage crisis).
The academics who built the BSM were not hesitant to apply a model
that would value idiosyncratic assets such as stocks because they had as-
sumed from the start that financial markets are efficient—meaning that
every idiosyncratic feature for a given stock was already fully “priced in”
by the market. This allowed them to overlook the complexity of individual
companies and treat them as interchangeable, homogeneous entities.
The BSM, then, did not value idiosyncratic, multidimensional
companies; rather, it valued single-dimensional entities that the scholars
assumed had already been “standardized” or commoditized in some sense
by the communal wisdom of the markets. Y ou will see in the next sec-
tion that the broad, implicit assumption by option market participants
that markets are efficient actually brings about the greatest opportunity
Appendix A: Choose Your Battles Wisely   • 273
to derive low-risk profits for intelligent investors. The point I make here
is simply how difficult it is to invest in options on commodities or in fact
any asset that you cannot analyze using fundamental valuation techniques.
For investors who simply cannot resist making commodity investments,
I offer the following case study: I personally believe that climate change will
make it harder for the world to feed its burgeoning population. Among
exchange-traded funds (ETFs), futures, and options, it is very easy these days
to express an investment opinion on such a belief, and I have done just that—
put my money where my mouth is. While I have made such investments,
I must admit that I have absolutely no basis for my valuation of the agricul-
tural commodities in question and have no way to know if I have received my
bullish exposure to these commodities at a reasonable or unreasonable price.
Such speculative investments satisfy some psychological need, but they are
not investments in the strict “intelligent investor” sense because it is very hard to
rationally calculate a fair value for the asset. Should these types of investments
not be made, then? A strict adherent to rational investment principles might
say, “No, they should not be. ” However, considering the irrational ways people
find to spend money, it would seem that we have been somehow hardwired to
do things in a way that an economist would not consider totally rational. Rather
th


tionally calculate a fair value for the asset. Should these types of investments
not be made, then? A strict adherent to rational investment principles might
say, “No, they should not be. ” However, considering the irrational ways people
find to spend money, it would seem that we have been somehow hardwired to
do things in a way that an economist would not consider totally rational. Rather
than fight that primitive urge, I prefer to give into it—but only with very small
parts of my portfolio. This strategy is akin to taking only $50 to the casino floor
and promising that once that money is gone, you won’t spend any more.
Y ou may have a gut feeling about the price of oil, the level of interest
rates, the price of cotton, or whatever. Do yourself a favor, and if you chose
to make a financial bet on the basis of your hunch, do as I do and make
it a small one. While a small investment means different things to differ -
ent people, a good way to judge is to imagine the capital being completely
gone. If you have heart palpitations at that thought, keep cutting the pro-
spective investment in half until you feel better.
Where the BSM Works Worst
Now that we know where not to look for intelligent option investments,
let’s look at conditions in which the BSM works worst—these are the best
places for us to tilt the balance of risk and return in our favor.
274  •   The Intelligent Option Investor
1. Grossly mispriced assets
2. Bimodal outcomes
3. Long investment time horizons
Grossly Mispriced Assets
The main assumption of the BSM is that there are no grossly mispriced as-
sets. I believe that this contention is wrong on the basis of behavioral and
structural factors that are covered briefly in Part II of this book but would
require another book to fully cover.
Just imagine, though, that, for some reason, a stock is dramatically
undervalued. For right now, I will not discuss why this situation could
come about, but let’s say that rather than being worth $50 per share,
a company is worth, best case, closer to $110 per share and, worst case,
$70 per share. Let’s further say that we had some sort of a hazy crystal
ball that would give us a very high degree of certainty that these best- and
worst-case values represent the real future range of values.
Here is what a diagram of that situation would look like:
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100
110
120
5/20/2013 249 499 749 999
Date/Day Count
Advanced Building Corp. (ABC)
Stock Price
Best Case, 110
Worst Case, 70
-
Now look at the following diagrams of a put and a call option and,
based on what you know about the way the BSM prices options, think
about the answers to the following questions.
Appendix A: Choose Your Battles Wisely   • 275
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5/20/2013 249 499 749 999
Date/Day Count
Advanced Building Corp. (ABC)
Stock Price
-
GREEN
Put option
If someone were worried about this stock’s downside potential below $50,
what would likely be the price that investor would pay to buy this put option?
a. Almost nothing
b. A little
c. A good bit
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Date/Day Count
Advanced Building Corp. (ABC)
Stock Price
-
RED
Call option
276  •   The Intelligent Option Investor
If someone wanted to make extra income by selling calls to accept expo-
sure to the stock’s upside, what price would they likely charge for someone
wanting to buy this call option?
a. Almost nothing
b. A little
c. A good bit
Obviously, the correct answer to the put option question is c. This option
would be pretty expensive because its range of exposure overlaps with so
much of the BSM cone. Conversely, the answer to the call option question
is a. This option would be really cheap because its range of exposure is well
above the BSM cone.
Remember, though, that we have our crystal ball, and we know
that this stock will likely be somewhere between $70 and $110 per share
in a few years. With this confidence, wouldn’t it make sense to take the
opposite side of both the preceding trades? Doing so would look like
this:
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50
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70
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90
100
110
120
5/20/2013 249 499 749 999
Date/Day Count
Advanced Building Corp. (ABC)
Stock Price
Best Case, 110
Worst Case, 70
-
GREEN
RED
In this investment, which I explain in detail in Chapter 11, we are
receiving a good bit of money by selling an expensive put and paying
Appendix A: Choose Your Battles Wisely   • 277
very little money to buy a cheap call. It may happen that the money we
receive for selling the put actually may be greater than the money we
pay for the call, so we actually get paid a net fee when we make this
transaction!
We can sell the put confidently because we know that our worst-case
valuation is $70 per share; as long as we are confident in our valuation—a
topic covered in Part II of this book—we need not worry about the price
declining. We do not mind spending money on the call because we think
that the chance is very good that at expiration or before the call will be
worth much, much more than we paid for it.
Truly, the realization that the BSM is pricing options on inefficiently
priced stocks as if they were efficiently priced is the most profound and
compelling source of profits for intelligent investors. Furthermore, finding
grossly mispriced stocks and exploiting the mispricing using options rep-
resents the most compelling method for tilting the risk-reward equation in
our direction.
The wonderful thing about investing is that it does not require you to
swing at all the pitches. Individual investors have a great advantage in that
they may swing at only the pitches they know they can hit. The process of
intelligent investing is simply one of finding the right pitches, and intel-
ligent option investing simply uses an extremely powerful bat to hit that
sweet pitch.
Bimodal Outcomes
Some companies are speculative by nature—for instance, a drug company
doing cance


itches. Individual investors have a great advantage in that
they may swing at only the pitches they know they can hit. The process of
intelligent investing is simply one of finding the right pitches, and intel-
ligent option investing simply uses an extremely powerful bat to hit that
sweet pitch.
Bimodal Outcomes
Some companies are speculative by nature—for instance, a drug company
doing cancer research. The company has nothing but some intangible as-
sets (the ideas of the scientists working there) and a great deal of costs
(the salaries going to those scientists, the payments going to patent attor -
neys, and the considerable costs of paying for clinical trials). If the research
proves fruitful, the company’s value is great—let’s say $500 per share. If
the clinical trials show low efficacy or dangerous side effects, however, the
company’s worth goes to virtually nil. What’s more, it may take years before
it is clear which of these alternatives is true.
278  •   The Intelligent Option Investor
Given what you know about the BSM, does this seem like the kind of
situation conducive to accurate option pricing? This example certainly does
not sound like the pricing scenario of a short-term agricultural commodity,
after all. If this hypothetical drug company’s stock price was sitting at $50 per
share, what is the value of the upper range the option market might be
pricing in? Let’s assume that this stock is trading with a forward volatility of
100 percent per year (on the day I am writing this, there are only four stocks
with options trading at a price that implies a forward volatility of greater than
100 percent). What price range does this 100 percent per year volatility imply,
and can we design an option structure that would allow us to profit from a big
move in either direction? Here is a diagram of this situation:
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50
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350
400
450
5/20/2013 249 499
Date/Day Count
Advanced Biotechnology Co. (ABC)
Stock Price
749 999
GREEN
GREEN
Indeed, even boosting volatility assumptions to a very high level,
it seems that we can still afford to gain exposure to both the upside and
downside of this stock at a very reasonable price. Y ou can see from the pre-
ceding diagram that both regions of exposure on the put side and the call
side are outside the BSM cone, meaning that they will be relatively cheap.
The options market is trying to boost the price of the options enough so
that the calls and puts are fairly priced, but for various reasons (including
behavioral biases), most of the time it fails miserably.
Appendix A: Choose Your Battles Wisely   • 279
Long Investment Time Horizons
This is simply a corollary to the rule that the BSM is generally good at
pricing short-time-horizon investments. The BSM is built on the prem-
ise that stocks will only rise by as much as the risk-free rate. If you ask a
finance professor or a market maker, he or she will be able to give you an
elegant and logically consistent reason why this must be so.
However, as you saw in Chapter 3, this situation has never been so—
the return on stocks is sometimes negative but often much more positive
than risk-free bonds. If we average the returns out, stocks still generate
returns that are heads and shoulders above bonds.
Over short time horizons, the difference simply isn’t material. For in-
stance, let’s say that we assume that a given stock should generate around
10 percent compound annual returns over the next three to five years com-
pared with a 5 percent assumption for the risk-free rate. If we are looking at
very short time horizons—such as 60 days—and assume that our stock will
grow at exactly that 10 percent rate over that short time, then we should
compare our expectations with those of the option market. Here is the dia-
gram we would get:
Advanced Building Corp. (ABC)
30
20
40
50
60
70
60 days
80Stock Price
280  •   The Intelligent Option Investor
Clearly, there is not much of a difference between the BSM expected
value (shown by the dotted line) and the dot representing a 10 percent
upward drift in the stock. However, if we extend this analysis out for three
years, look what happens:
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Date/Day Count
Advanced Building Corp. (ABC)
749 999
20
30
40
50
60
70Stock Price
80
With the longer time horizon, our assumed stock price is significantly
higher than what the BSM calculates as its expected price. If we take “assumed
future stock price” to mean the price at which we think there is an equal chance
that the true stock price will be above or below that mark, we can see that the
difference, marked by the double-headed arrow in the preceding diagram, is the
advantage we have over the option market.
3 This advantage again means that
downside exposure will be overvalued and upside exposure will be undervalued.
How, you may ask, can this discrepancy persist? Shouldn’t someone
figure out that these options are priced wrong and take advantage of an
arbitrage opportunity? The two reasons why these types of opportunities
tend to persist are
1. Most people active in the option market are trading on a very
short-term basis. Long-term equity anticipated securities
(LEAPS)—options with tenors of a year or more—do exist, but
Appendix A: Choose Your Battles Wisely   • 281
generally the volumes are light because the people in the option
markets generally are not willing to wait longer than 60 days for
their “investment” to work out. Because the time to expiration for
most option contracts is so short, the difference between the BSM’s
expected price based on a 5 percent risk-free rate and an expected
price based on a 10 percent equity return is small, so no one real-
izes that it’s there (as seen on the first diagram).
2. The market makers are generally able to hedge out what little ex-
posure they have to the price appreciation of LEAPS. They don’t
care about the price of the underlying security, only about the size
of the


expected price based on a 5 percent risk-free rate and an expected
price based on a 10 percent equity return is small, so no one real-
izes that it’s there (as seen on the first diagram).
2. The market makers are generally able to hedge out what little ex-
posure they have to the price appreciation of LEAPS. They don’t
care about the price of the underlying security, only about the size
of the bid-ask spread, and they always price the bid-ask spread on
LEAPS in as advantageous a way as they can. Also, the career of an
equity option trader on the desk of a broker-dealer can change a
great deal in a single year. As discussed in Part II, market makers
are not incentivized in such a way that they would ever care what
happened over the life of a LEAPS.
Congratulations. After reading Part I of this book and this appendix,
you have a better understanding of the implications of option investing
for fundamental investors than most people working on Wall Street.
There are many more nuances to options that I discuss in Part III of this
book—especially regarding leverage and the sensitivity of options to input
changes—but for now, simply understanding how the BSM works puts you
at a great advantage over other market participants.
282
Appendix B
THe MAny FAceS OF
LeverAGe
An intelligent option investor must understand investing leverage in
order to make sense of option investing strategies. Investing leverage is,
however, not the only form of leverage, and to have a well-rounded and
well-educated view of investing leverage, you should understand the other
forms as well. In addition, when assessing the value of companies, it is im-
portant to understand leverage because leverage often is the root cause of
rapid changes in profitability during times of changing consumer demand
such as inflection points in the business cycle.
Operational Leverage
Operational leverage is the acceptance of fixed operating costs in order to
make a higher per-unit profit, such as when a company decides to build a
factory rather than contracting for its products to be made by a third party.
When a company spends cash to build a factory, that expenditure is not
treated as an immediate cost on the income statement. Rather, the cost
of the new factory is spread over future periods as the noncash expense
known as depreciation.
1
Let us take a look at two companies, both of which produce the same
items, but one of which outsources production to a third party (Unlevered
Co.) and the other of which has built a factory to manufacture its products
Appendix B: The Many Faces of Leverage  • 283
(Levered Co.). In reality, there are methods used by companies to front-
load depreciation expenses in order to minimize taxable income for new
projects, but let’s assume that Levered Co. is using what is called straight-
line depreciation so that the charge is identical each quarter.
Unlevered Co. Levered Co.
Revenues 100.0 100.0
Fixed depreciation expense 0.0 −65.0
Variable operating expenses −85.0 −15.0
Operating profit 15.0 20.0
Pretax profit 15.0 20.0
Tax −4.5 −6.0
Net profit 10.5 14.0
As you can see here, Levered Co. ’s profits are a bit better than those
of Unlevered Co. because the former is not paying a supplier and can
produce the items at a lower cost. Note also that both companies have
variable costs. For Unlevered Co., these variable costs include the costs
of the items it has produced by the third party plus whatever salaries it
has to pay to salespeople and administrative staff; for Levered Co., vari-
able costs include the costs of raw materials plus the cost of any salaries
paid to production, sales, and administrative staff. This is our base case—
representing midcycle economic conditions (i.e., not boom or not bust).
Now let’s look at the two companies during a trough in the business
cycle—or bust conditions.
Unlevered Co. Levered Co.
Revenues 70.0 70.0
Fixed depreciation expense 0.0 −65.0
Variable operating expenses −59.5 −10.5
Operating profit 10.5 −5.5
Pretax profit 10.5 −5.5
Tax −3.2 +1.6
Net profit 7.3 −3.9
284  •   The Intelligent Option Investor
Costs at Unlevered Co. decrease proportionally to the decrease in
revenues, so the operating profit margin is the same in its case. However,
for Levered Co., even though the variable costs decrease proportionally to
the decrease in revenues, the cost of depreciation stays fixed, causing a loss
that is only slightly ameliorated through a small tax benefit.
Thus, obviously, in business-cycle trough conditions, profitability is
hurt through the assumption of operational leverage. Let’s take a look at
what happens to both companies in peak conditions.
2
Unlevered Co. Levered Co.
Revenues 130.0 130.0
Fixed depreciation expense 0.0 −65.0
Variable operating expenses −110.5 −19.5
Operating profit 19.5 45.5
Pretax profit 19.5 45.5
Tax −5.9 −13.6
Net profit 13.6 31.9
Obviously, having the operational leverage during peak times is a
wonderful thing. After the fixed-cost hurdle of depreciation is cleared, each
extra widget produced allows the company to generate profits that are gov-
erned solely by variable costs. Unlevered Co. is in a better position when
there is a downturn, but its profitability falls behind Levered Co. ’s more and
more the better economic conditions are.
When thinking about the valuation of companies, we must remember
what a large effect operational leverage can have on operations. Financial
markets usually underestimate the effects of operational leverage both
when the business cycle is at its peak and when it is at its trough. At the
peak, analysts are wont to extrapolate high margins out forever and ignore
the possibility that the sword of leverage swings both ways. At the trough,
analysts are overly pessimistic and forget that a small improvement in de-
mand can have a very large impact on financial results.
Operational leverage is neither good nor bad—it is merely a strategic busi-
ness choice that has differe


h. At the
peak, analysts are wont to extrapolate high margins out forever and ignore
the possibility that the sword of leverage swings both ways. At the trough,
analysts are overly pessimistic and forget that a small improvement in de-
mand can have a very large impact on financial results.
Operational leverage is neither good nor bad—it is merely a strategic busi-
ness choice that has different implications during different parts of the business
cycle and under different revenue conditions. An intelligent investor under-
stands this fact and is happy to invest when the rest of the market has forgotten it.
Financial Leverage
Financial leverage involves the acceptance of fixed financial costs such
as a loan or a lease contract to fund a business. Considering the expense
of building factories, usually operational and financial leverage occur
simultaneously, but to understand financial leverage itself, let’s look at two
companies that, other than the amount of debt on their balance sheets, are
exactly the same in terms of revenues and profit margin. Our base case
shows that the unlevered company will generate a higher absolute profit
because it does not have the fixed financing costs.
Unlevered Co. Levered Co.
Revenues 100.0 100.0
Operating expenses −80.0 −80.0
Operating profit 20.0 20.0
Interest expense 0.0 −15.0
Pretax profit 20.0 5.0
Tax −6.0 −1.5
Net profit 14.0 3.5
Now let’s increase revenues for both companies by 50 percent and see
what happens.
Unlevered Co. Levered Co.
Revenues 150.0 150.0
Operating expenses −120.0 −120.0
Operating profit 30.0 30.0
Interest expense 0.0 −15.0
Pretax profit 30.0 15.0
Tax −9.0 −4.5
Net profit 21.0 11.5
The absolute profit is still higher for the unlevered company, but the
percentage change from the first case to the second shows a big difference.
The unlevered company’s profits increased by 50 percent (from 14.0 to
21.0) with a 50 percent rise in revenues. However, the levered company’s
profits increased by a whopping 229 percent (from 3.5 to 11.5) with the
same 50 percent rise in revenues.
Appendix B: The Many Faces of Leverage  • 285
286  •   The Intelligent Option Investor
Here we see an example of a defining characteristic of financial and
investment leverage; that is, these sorts of leverage affect percentage calcu-
lations, but in absolute terms, unlevered transactions always generate more
for a fixed level of exposure. We explore this concept in great detail when
we discuss investment leverage in Chapter 8.
To see the dangerous side of leverage’s double-edged sword, let’s look
at a case where revenues drop 50 percent from the original baseline.
Unlevered Co. Levered Co.
Revenues 50.0 50.0
Operating expenses −40.0 −40.0
Operating profit 10.0 10.0
Interest expense 0.0 −15.0
Pretax profit 10.0 −5.0
Tax −3.0 +1.5
Net profit 7.0 −3.5
Here we see that even with the tax benefit for the levered company,
it is still running at a loss because of the fixed financial costs, whereas the
unlevered company is still realizing a gain. In a worst-case scenario, fixed
financial costs can exceed the cash coming into the business, leading to
debt default and, depending on the situation, bankruptcy.
Thinking about the best and worst cases from an investment perspec-
tive for a moment, you can see why some equity investors actually prefer a
highly levered firm: the higher the leverage, the greater is the incremental
profit for equity holders when times are good. For a levered company that
is in transition from bad to good—whether due to an upturn in economic
conditions during a business cycle or a company-specific issue such as the
introduction of a new product line boosting a flagging legacy business—
a small improvement in business conditions creates a big improvement
in profits available to shareholders. The flip side is that when business
conditions turn downward—a transition from good to bad—a levered
company’s fall from profitability to loss is sudden, and its stock price fall
can be even worse. The fact is that just in the case of operational lever -
age, financial leverage is not good or bad—it is simply a strategic business
choice that has different implications in different situations.
287
Appendix c
PUT-cALL PArITy
Before the Black-Scholes-Merton model (BSM), there was no way to
directly calculate the value of an option, but there was a way to triangulate
put and call prices as long as one had three pieces of data:
1. The stock’s price
2. The risk-free rate
3. The price of a call option to figure the fair price of the put, and vice
versa
In other words, if you know the price of either the put or a call, as long
as you know the stock price and the risk-free rate, you can work out the
price of the other option. These four prices are all related by a specific rule
termed put-call parity.
Put-call parity is only applicable to European options, so it is not ter-
ribly important to stock option investors most of the time. The one time it
becomes useful is when thinking about whether to exercise early in order
to receive a stock dividend—and that discussion is a bit more technical. I’ll
delve into those technical details in a moment, but first, let’s look at the big
picture. Using the intelligent option investor’s graphic format employed in
this book, the big picture is laughably trivial.
Direct your attention to the following diagrams. What is the differ -
ence between the two?
288  •   The Intelligent Option Investor
-
20
5/18/2012 5/20/2013
40
60
80
100
120Stock Price
140
160
180
200
-
20
5/18/2012 5/20/2013
40
60
80
100
120Stock Price
140
160
180
200
GREENGREEN
REDRED
If you say, “Nothing, ” you are practically right but technically
wrong. The image on the left is actually the risk-reward profile of a pur -
chased call option struck at $50 paired with a sold put option struck at
$50. The image on the right is the risk-reward profile of a stock trading
at $50 per share.
This simple comparison is the essence of


120Stock Price
140
160
180
200
GREENGREEN
REDRED
If you say, “Nothing, ” you are practically right but technically
wrong. The image on the left is actually the risk-reward profile of a pur -
chased call option struck at $50 paired with a sold put option struck at
$50. The image on the right is the risk-reward profile of a stock trading
at $50 per share.
This simple comparison is the essence of put-call parity. The parity
part of put-call parity just means that accepting downside exposure by sell-
ing a put while gaining upside exposure by buying a call is basically the
same thing as accepting downside exposure and gaining upside exposure
by buying a stock.
What did I say? It is laughably trivial. Now let’s delve into the details
of how the put-call parity relationship can be used to help decide whether
to exercise a call option or not (or whether the call option you sold is likely
to be exercised or not).
Dividend Arbitrage and Put-call Parity
Any time you see the word arbitrage , the first thing that should jump to
mind is “small differences. ” Arbitrage is the science of observing small dif-
ferences between two prices that should be the same (e.g., the price of IBM
Appendix C: Put-Call Parity   • 289
traded on the New Y ork Stock Exchange and the price of IBM traded in
Philadelphia) but are not. An arbitrageur, once he or she spots the small
difference, sells the more expensive thing and buys the less expensive one
and makes a profit without accepting any risk.
Because we are going to investigate dividend arbitrage, even a big-
picture guy like me has to get down in the weeds because the differences we
are going to try to spot are small ones. The weeds into which we are wading
are mathematical ones, I’m afraid, but never fear—we’ll use nothing more
than a little algebra. We’ll use these variables in our discussion:
K = strike price
C
K = call option struck at K
PK = put option struck at K
Int = interest on a risk-free instrument
Div = dividend payment
S = stock price
Because we are talking about arbitrage, it makes sense that we are
going to look at two things, the value of which should be the same. We
are going to take a detailed look at the preceding image, which means that
we are going to compare a position composed of options with a position
composed of stock.
Let’s say that the stock at which we were looking to build a position is
trading at $50 per share and that options on this stock expire in exactly one
year. Further, let’s say that this stock is expected to yield $0.25 in dividends
and that the company will pay these dividends the same day that the op-
tions expire.
Let’s compare the two positions in the same way as we did in the
preceding big-picture image. As we saw in that image, a long call and a
short put are the same as a stock. Mathematically, we would express this
as follows:
C
K − PK = SK
Although this is simple and we agreed that it’s about right, it is not
technically so.
The preceding equation is not technically right because we know that
a stock is an unlevered instrument and that options are levered ones. In the
290  •   The Intelligent Option Investor
preceding equation, we can see that the left side of the equation is levered
(because it contains only options, and options are levered instruments),
and the right side is unlevered. Obviously, then, the two cannot be exactly
the same.
We can fix this problem by delevering the left side of the preceding
equation. Any time we sell a put option, we have to place cash in a mar -
gin account with our broker. Recall that a short put that is fully margined
is an unlevered instrument, so margining the short put should delever
the entire option position. Let’s add a margin account to the left side and
put $K in it:
C
K − PK + K = S
This equation simply says that if you sell a put struck at K and put $K
worth of margin behind it while buying a call option, you’ll have the same
risk, return, and leverage profile as if you bought a stock—just as in our
big-picture diagram.
But this is not quite right if one is dealing with small differences.
First, let’s say that you talk your broker into funding the margin ac-
count using a risk-free bond fund that will pay some fixed amount of
interest over the next year. To fund the margin account, you tell your
broker you will buy enough of the bond account that one year from
now, when the put expires, the margin account’s value will be exactly
the same as the strike price. In this way, even by placing an amount less
than the strike price in your margin account originally, you will be able
to fulfill the commitment to buy the stock at the strike price if the put
expires in the money (ITM). The amount that will be placed in margin
originally will be the strike price less the amount of interest you will
receive from the risk-free bond. In mathematical terms, the preceding
equation becomes
C
K − PK + (K – Int) = S
Now all is right with the world. For a non-dividend-paying stock, this fully
expresses the technical definition of put-call parity.
However, because we are talking about dividend arbitrage, we have to
think about how to adjust our equation to include dividends. We know that
a call option on a dividend-paying stock is worth less because the dividend
Appendix C: Put-Call Parity   • 291
acts as a “negative drift” term in the BSM. When a dividend is paid, theory
says that the stock price should drop by the amount of the dividend. Be-
cause a drop in price is bad for the holder of a call option, the price of a call
option is cheaper by the amount of the expected dividend.
Thus, for a dividend-paying stock, to establish an option-based position
that has exactly the same characteristics as a stock portfolio, we have to keep
the expected amount of the dividend in our margin account.
1 This money
placed into the option position will make up for the dividend that will be
paid to the stock holder. Here is how this would look i


by the amount of the expected dividend.
Thus, for a dividend-paying stock, to establish an option-based position
that has exactly the same characteristics as a stock portfolio, we have to keep
the expected amount of the dividend in our margin account.
1 This money
placed into the option position will make up for the dividend that will be
paid to the stock holder. Here is how this would look in our equation:
C
K − PK + (K − Int) + Div = S
With the dividend payment included, our equation is complete.
Now it is time for some algebra. Let’s rearrange the preceding equa-
tion to see what the call option should be worth:
CK = PK + Int − Div + (S − K)
Taking a look at this, do you notice last term (S – K )? A stock’s price
minus the strike price of a call is the intrinsic value. And we know that
the value of a call option consists of intrinsic value and time value. This
means that
/dncurlybracketleft/dncurlybracketmid/horizcurlybracketext/horizcurlybracketext/dncurlybracketright/horizcurlybracketext/horizcurlybracketext/dncurlybracketleft/dncurlybracketmid/dncurlybracketright=+ −−CP SKKK IntD iv + ()
Time valueI ntrinsic value
So now let’s say that time passes and at the end of the year, the stock
is trading at $70—deep ITM for our $50-strike call option. On the day
before expiration, the time value will be very close to zero as long as the op-
tion is deep ITM. Building on the preceding equation, we can put the rule
about the time value of a deep ITM option in the following mathematical
equation:
P
K + Int − Div ≈ 0
If the time value ever falls below 0, the value of the call would trade for less
than the intrinsic value. Of course, no one would want to hold an option
that has negative time value. In mathematical terms, that scenario would
look like this:
P
K + Int − Div < 0
292  •   The Intelligent Option Investor
From this equation, it follows that if
PK + Int < Div
your call option has a negative implied time value, and you should sell the
option in order to collect the dividend.
This is what is meant by dividend arbitrage . But it is hard to get the
flavor for this without seeing a real-life example of it. The following table
shows the closing prices for Oracle’s stock and options on January 9, 2014,
when they closed at $37.72. The options had an expiration of 373 days in
the future—as close as I could find to one year—the one-year risk-free rate
was 0.14 percent, and the company was expected to pay $0.24 worth of
dividends before the options expired.
Calls Puts
Bid Ask Delta Strike Bid Ask Delta
19.55 19.85 0.94 18 0.08 0.13 −0.02
17.60 17.80 0.94 20 0.13 0.15 −0.03
14.65 14.85 0.92 23 0.25 0.28 −0.05
12.75 12.95 0.91 25 0.36 0.39 −0.07
10.00 10.25 0.86 28 0.66 0.69 −0.12
8.30 8.60 0.81 30 0.97 1.00 −0.17
6.70 6.95 0.76 32 1.40 1.43 −0.23
4.70 4.80 0.65 35 2.33 2.37 −0.34
3.55 3.65 0.56 37 3.15 3.25 −0.43
2.22 2.26 0.42 40 4.80 4.90 −0.57
1.55 1.59 0.33 42 6.15 6.25 −0.65
0.87 0.90 0.22 45 8.25 8.65 −0.75
0.31 0.34 0.10 50 12.65 13.05 −0.87
In the theoretical option portfolio, we are short a put, so its value to
us is the amount we would have to pay if we tried to flatten the position by
buying it back—the ask price. Conversely, we are long a call, so its value to
us is the price we could sell it for—the bid price.
Let’s use these data to figure out which calls we might want to exercise
early if a dividend payment was coming up.
Appendix C: Put-Call Parity   • 293
Strike Call
Put
(a)
Interest2
(b)
Put + Interest
(a + b) Dividend P + I − D Notes
18 19.55 0.13 0.03 0.16 0.24 (0.08) P + I < D,
arbitrage
20 17.60 0.15 0.03 0.18 0.24 (0.06) P + I < D,
arbitrage
23 14.65 0.28 0.03 0.31 0.24 0.07 No arbitrage
25 12.75 0.39 0.04 0.43 0.24 0.19 No arbitrage
28 10.00 0.69 0.04 0.73 0.24 0.49 No arbitrage
30 8.30 1.00 0.04 1.04 0.24 0.80 No arbitrage
32 6.70 1.43 0.05 1.48 0.24 1.24 No arbitrage
35 4.70 2.37 0.05 2.42 0.24 2.18 No arbitrage
37 3.55 3.25 0.05 3.30 0.24 3.06 No arbitrage
40 2.22 4.90 0.06 4.96 0.24 4.72 No arbitrage
42 1.55 6.25 0.06 6.31 0.24 6.07 No arbitrage
45 0.87 8.65 0.06 8.71 0.24 8.47 No arbitrage
50 0.31 13.05 0.07 13.12 0.24 12.88 No arbitrage
There are only two strikes that might be arbitraged for the
dividends—the two furthest ITM call options. In order to realize the
arbitrage opportunity, you would wait until the day before the ex-dividend
date, exercise the stock option, receive the dividend, and, if you didn’t want
to keep holding the stock, sell it and realize the profit.
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295
Notes
Introduction
1. Options, Futures, and Other Derivatives by John C. Hull (New Y ork:
Prentice Hall, Eighth Edition, February 12, 2011), is considered the
Bible of the academic study of options.
2. Option Volatility and Pricing by Sheldon Natenberg (New Y ork:
McGraw-Hill, Updated and Expanded Edition, August 1, 1994), is
considered the Bible of professional option traders.
3. The Greeks are measures of option sensitivity used by traders to man-
age risk in portfolios of options. They are named after the Greek
symbols used in the Black-Scholes-Merton option pricing model.
4. “To invest successfully over a lifetime does not require a stratospheric
IQ, unusual business insights, or inside information. What’s needed
is a sound intellectual framework for making decisions and the abil-
ity to keep emotions from corroding that framework. ” Preface to The
Intelligent Investor by Benjamin Graham (New Y ork: Collins Business,
Revised Edition, February 21, 2006).
Chapter 1
1. In other words, if all option contracts were specific and customized,
every time you wanted to trade an option contract as an individual in-
vestor, you would have to first find a counterparty to take the other side
of the trade and then do due diligence on the counterparty to make
sure that he or she would be able to fulfill his or her side of the bargain.
It is hard to imagine small individual investors being very interested in
the logistical hea


customized,
every time you wanted to trade an option contract as an individual in-
vestor, you would have to first find a counterparty to take the other side
of the trade and then do due diligence on the counterparty to make
sure that he or she would be able to fulfill his or her side of the bargain.
It is hard to imagine small individual investors being very interested in
the logistical headaches that this process would entail!
296 •   N o t e s
2. One more bit of essential but confusing jargon when investing in
options is related to exercise. There are actually two styles of exercise;
one can be exercised at any time before expiration—these are termed
American style—and the other can only be exercised at expiration—
termed European style. Confusingly, these styles have nothing to do
about the home country of a given stock or even on what exchange
they are traded. American-style exercise is normal for all single-stock
options, whereas European-style exercise is normal for index futures.
Because this book deals almost solely with single-stock options (i.e.,
options on IBM or GOOG, etc.), I will not make a big deal out of this
distinction. There is one case related to dividend-paying stocks where
American-style exercise is beneficial. This is discussed in Appendix C.
Most times, exercise style is not a terribly important thing.
3. Just like going to Atlantic City, even though the nominal odds for rou-
lette are 50:50, you end up losing money in the long run because you
have to pay—the house at Atlantic City or the broker on Wall Street—
just to play the game.
Chapter 3
1. We adjusted and annualized the prices of actual option contracts so
that they would correspond to the probability levels we mentioned
earlier. It would be almost impossible to find a stock trading at exactly
$50 and with the option market predicting exactly the range of future
price that we have shown in the diagrams. This table is provided simply
to give you an idea of what one might pay for call options of different
moneyness in the open market.
2. Eighty-four percent because the bottom line marks the price at which
there is only a 16 percent chance that the stock will go any lower. If
there is a 16 percent chance that the stock will be lower than $40 in
one year’s time, this must mean that there is an 84 percent chance
that the stock will be higher than $40 in one year’s time. We write
“a little better than 84 percent chance” because you’ll notice that the
stock price corresponding to the bottom line of the cone is around
$42—a little higher than the strike price. The $40 mark might corre-
spond to a chance of, let’s say, 13 percent that the stock will be lower;
Notes  • 297
this would, in turn, imply an 87 percent chance of being higher than
$40 in a year.
3. Tenor is just a specialty word used for options and bonds to mean the
remaining time before expiration/maturity. We will see later that op-
tion tenors usually range from one month to one year and that special
long-term options have tenors of several years.
4. We’re not doing any advanced math to figure this out. We’re just eye-
balling the area of the exposure range within the cone in this diagram
and recalling that the area within the cone of the $60 strike, one-year
option was about the same.
5. In other words, in this style of trading, people are anchoring on recent
implied volatilities—rather than on recent statistical volatilities—to
predict future implied volatilities.
6. Note that even though this option is now ITM, we did not pay for any
intrinsic value when we bought the option. As such, we are shading the
entire range of exposure in green.
Chapter 4
1. The “capital” we have discussed so far is strategic capital. There is an-
other form of tactical capital that is vital to companies, termed working
capital. Working capital consists of the short-term assets essential for
running a business (e.g., inventory and accounts receivables) less the
short-term liabilities accrued during the course of running the busi-
ness (e.g., accounts payable). Working capital is tactical in the sense
that it is needed for day-to-day operation of the business. A company
may have the most wonderful productive assets in the world, but if it
does not have the money to buy the inventory of raw materials that will
allow it to produce its widgets, it will not be able to generate revenues
because it will not be able to produce anything.
2. The law of large numbers is actually a law of statistics, but when most
people in the investing world use this phrase, it is the colloquial version
to which they are referring.
3. Apple Computer, for instance, was a specialized maker of computers
mainly used by designers and artists in the late 1990s. Through some
298 •   N o t e s
inspired leadership and a large capital infusion from Microsoft to keep
it afloat in its darkest days, Apple Computer changed its name to just
Apple and began producing handheld music devices, smartphones, and
other media appliances (including computers). By the late 1990s, Apple
was facing severe structural constraints. The market in which it com-
peted—the market for personal computers—had been commoditized,
and prices did nothing but go down. It was clinging to a niche market
of a few educational institutions and creative professionals—not a very
robust or quickly growing market. However, the company was able to
reinvent itself as a media technology company and media content pro-
vider using its investments and know-how in personal computing as a
base. Doing so, Apple jumped from a mature company into a virtual
startup and once again became a supply-constrained company in a
very short period of time. This is a rare twist, but not unheard of.
4. Don’t waste your time remembering this formula unless you already
know it. Y ou can always look up the exact equation when you need to use
it. Just remember, “ A dollar today is worth more than a dollar tomorr


Apple jumped from a mature company into a virtual
startup and once again became a supply-constrained company in a
very short period of time. This is a rare twist, but not unheard of.
4. Don’t waste your time remembering this formula unless you already
know it. Y ou can always look up the exact equation when you need to use
it. Just remember, “ A dollar today is worth more than a dollar tomorrow. ”
5. If you are curious about the CAPM or any of the other related aca-
demic methods for determining discount rates, you have no further
to go than your local library or various sources online. The CAPM is
one of the pillars of modern finance, and there are plenty of resources
to learn about it. In the end, though, the “proper” discount rate you
will calculate will not be far off from these values. There are plenty
of more important things on which to concentrate in a valuation, so
my suggestion is to spend time on those and save learning about the
CAPM.
Chapter 5
1. Note that, even though it may feel like it from a shareholder perspective,
the period during which a company is making poor investments and
generating substructural profit growth will only last for a limited time.
Sooner or later, an activist investor or another company will acquire all
or part of the capital stock of the underperforming company and run
the enterprise in a more rational way.
Notes  • 299
2. For the structural stage, I usually only use one scenario. When I start-
ed in the business of valuation, I used 6 percent growth of cash flows
in perpetuity. Recently, convinced by PIMCO’s argument that we are
entering an extended “new normal” period, I tend to use 5 percent
instead.
3. For instance, a company may have only six very large and important
customers, each of which it picked up in subsequent years. If it loses
one of those customers, rather than +35 percent revenue growth over
the next year, the revenue may decline by 20 percent. Or even if the
company does not lose a customer, if it does not gain another, its
revenue growth may be trivial—3 percent, let’s say.
4. Please see the online materials for the specific formulas used for OCP
and FCFO.
5. A person with a 100-share stake in Exxon—an investment worth just
under $10,000—has a proportional stake of 0.000006 percent in the
company. No wonder investors usually do not have a strong sense of
being an owner of the companies in which they are invested.
6. In a counterexample, IBM’s management should be commended for
selling off the dying, undifferentiated PC business to Lenovo and rea-
ligning the tech giant as primarily a provider of software and services.
7. Networking behemoth Cisco Systems’ (CSCO) purchase of Pure
Digital (a company that made Flip video cameras) springs immedi-
ately to mind.
Chapter 6
1. The fact that a consensus of opinion is reached is an interesting social be-
havioral bias called herding. This bias, one that I will not go into great de-
tail about here, is the tendency for people to be influenced by the actions
or opinions of others when making a decision as a member of a group.
2. Paul Slovic, “Behavioral Problems of Adhering to a Decision Policy, ”
paper presented at the Institute for Quantitative Research in Finance,
Napa, CA, May 1, 1973.
3. This research report was quoted and summarized on the following site:
http://www.valuewalk.com/2013/07/hedge-fund-alpha-negative/.
300 •   N o t e s
4. The original academic paper discussing prospect theory was published
in Econometrica, Volume 47, Number 2, in March 1979 under the title:
“Prospect Theory: An Analysis of Decision Under Risk. ”
5. Over the years, the paradigm for broker-dealers has changed, so some
of what is written here is a bit dated. Broker-dealers have one part of
its business dedicated to increasing customer “flow” as is described
here. Over the last 20 years or so, however, they have additionally
begun to capitalize what amounts to in-house hedge funds, called
“proprietary trading desks” or “prop traders. ” While the prop traders
are working on behalf of corporations that were historically known as
broker-dealers (e.g., Goldman Sachs, Morgan Stanley), they are in fact
buy-side institutions. In the interest of clarity in this chapter, I treat
broker-dealers as purely sell-side entities even though they in fact have
elements of both buy- and sell-sides.
Chapter 7
1. Round-tripping means buying a security and selling it later.
2. This bit of shorthand just means a bid volatility of 22.0 and an ask
volatility of 22.5.
Chapter 8
1. This is one of the reasons why I called delta the most useful of the
Greeks.
2. When I pulled these data, I pulled the 189-day options, so my chance
of this stock hitting that high a price in this short time period is slim,
but the point I am making here about percentage versus absolute re-
turns still holds true.
3. A tool to calculate all the downside and upside leverage figures shown
in this chapter is available on the intelligent option investor website.
4. “Buffett’s Alpha, ” Andrea Frazzini, David Kabiller, and Lasse H. Ped-
ersen, 2012, National Bureau of Economic Research, NBER Working
Paper No. 19681.
Notes  • 301
Chapter 9
1. Yale Alumni Magazine, “The Fraud Detective, ” September/October
2013 Issue, http://www.yalealumnimagazine.com/articles/3737.
Chapter 10
1. This is, in fact, the crux of why U.S. taxpayers all got the opportunity
to own a piece of AIG. One of the subsidiaries of AIG made
commitments to carry out transactions that, with the collapse of the
mortgage bubble, it had no ability to do. In this case, it was not a bro-
ker or exchange that had to bear the exposure to AIG’s failure—the
contracts AIG were trading were over-the-counter and thus not regu-
lated by an exchange—it was the financial system at large and U.S.
taxpayers in particular.
2. The fact that this strategy is unlevered means that percentage returns
provide an accurate representation of the absolute wealth gene


. In this case, it was not a bro-
ker or exchange that had to bear the exposure to AIG’s failure—the
contracts AIG were trading were over-the-counter and thus not regu-
lated by an exchange—it was the financial system at large and U.S.
taxpayers in particular.
2. The fact that this strategy is unlevered means that percentage returns
provide an accurate representation of the absolute wealth generated
with the strategy. As we saw earlier, levered investments can show very
high percentage returns, whereas absolute returns are not as great. This
is not the case for short puts.
3. Writing an option means selling an option.
4. This is especially true for people investing in covered calls—a strategy
I will discuss in Chapter 11 and that has the same risk-return profile as
the short-put strategy.
5. Of course, there are other reasons for increased volatility during
earnings seasons, and some of the volatility reflects issues that are ma-
terial to valuation. In my opinion, though, the vast majority of infor -
mation given at these times is helpful for understanding only a few
months’ worth of prospective business results and, as such, should not
cause a material change in an intelligent investor’s perception of long-
run company value.
6. I am speaking here about the most attractive calls from a math-
ematical perspective, not a valuation one. I have not valued IBM
and am most definitely not making an investment recommenda-
tion here. I used IBM because it is a liquid option with a good
302 •   N o t e s
many OTM strikes, not because I believe it’s a bearish investment
opportunity.
7. $100,000 × 5% = $5,000; $5,000/$196.80 per share = 25.4 shares.
Chapter 11
1. This is due to a statistical property known as dispersion . Dispersion—
the fact that prices on many things do not usually move in lockstep
with one another—is the root of all diversification strategies.
2. This assumes that crises are only temporary. Of course, structural or
secular downturns are a different matter, and the whole process of
investing must be done in a different way. In particular, conceptions of
sensible terminal growth rates become vital during these times.
Chapter 12
1. I am indebted to Brent Farler for this image, which I think is really
brilliant.
Appendix A
1. Refer to the discussion of investing agents and principals in Chapter 6.
2. It is only the nominal odds that are 50:50 anyway. The player always
has to pay the house (and if you’re James Bond, you must tip the dealer
a cool million dollars), just as an investor must pay the broker. As such,
the net odds are always against the owner of capital.
3. Remember that the dotted line in the BSM cone shows that 50:50
“expected” value. Because our expected value dot is much higher, this
means that we are assigning a higher probability of that price occurring
than is the option market as a whole.
Notes  • 303
Appendix B
1. The idea behind this process is to match the timing of the costs of
equipment with revenues from the items produced with that equip-
ment. This is a key principle of accountancy called matching.
2. The problem is that troughs, by definition, follow peaks. Usually, just
like the timing of large acquisitions, companies decide to spend huge
amounts to build new production capacity at just about the same time
that economic conditions peak, and the factories come online just as
the economy is starting to sputter and fail.
Appendix C
1. A penny saved is a penny earned. We can think of the option being
cheaper by the amount of the dividend, so we will place the amount
that we save on the call option in savings.
2. This is calculated using the following equation:
Interest = strike × r × percent of 1 year
In the case of the $18 strike, interest = 18 × 0.14% × (373 days/365 days
per year) = $0.03.
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305
A
Absolute dollar value of returns,
172–173
Accuracy, confidence vs., 119–121
Acquisitions (see Mergers and
acquisitions)
Activist investors, 110
Against the Gods (Peter Bernstein), 9
Agents:
buy-side, 132–136
defined, 131
investment strategies of, 137–138
principals vs., 131–132
sell-side, 136–137
AIG, 301n1
Allocation:
and leverage in portfolios,
174–183
and liquidity risk, 256
and portfolio management with
short-call spreads, 228–229
Alpha, 134
American-style options, 296n2
(Chapter 1)
Analysis paralysis, 120
Anchoring, 60, 97
Announcements:
and creating BSM cones, 156, 157
market conditions following, 68–69,
72–73
tenor and trading in expectation
of, 192
AOL, 103
Apple Computer, 101, 250–251,
297–298n3
Arbitrage:
defined, 288–289
dividend, 223, 288–293
Ask price, 147
Asset allocation, liquidity risk
and, 256
Assets:
defined, 78–79
fungible, 272–273
in golden rule of valuation, 77
hidden, 110, 111
idiosyncratic, 272
interchangeable, 272–273
mispriced, 274–277
operating, 110
price vs. value of, 79–80
underlying, 33–34, 272–273
Assets under management (AUM), 132
Assignment:
with covered calls, 247–248
defined, 222–223
Assumptions:
BSM model, 32–33, 40–47, 78, 150
dividend yield, 67
with forward volatility number,
156–157
time-to-expiration, 64–67
volatility, 60–64
At-the-money (ATM) options:
BSM cone for, 53
collars, 259
covered calls, 242–243, 245, 246
defined, 13, 16, 17
long calls, 189
long diagonals, 235–237
Index
306  •   Index
At-the-money (ATM) options: (continued)
long straddles, 208–209
OTM options vs., 233–234
protective puts, 250–251, 253
short diagonals, 238, 240
short puts, 215, 216
short straddles, 230
short-call spreads, 222–225
AUM (assets under management), 132
B
Balance-sheet effects, 92, 108–111
Behavior, efficient market hypothesis
as model for, 41–42
Behavioral biases, 114–130
overconfidence, 118–122
pattern recognition, 114–118
perception of risk, 123–130
Behavioral economics, 42, 114
Bentley, 97–98
Berkshire Hathaway, 185
Bernstein, Peter, 9
Biases, behavioral (see Behavioral
biases)
Bid price, 147
Bid-ask spreads, 147–149
Bimodal outcomes, companies with,
277