large on option contracts,
round-tripping
1 an option contract creates a large hurdle that the returns
of the security must get over before the investor makes any money. In the
case of Mueller Water, the options one buys would have to change in price
by 11.8 percent before the investor starts making any money at all. It is for
this reason that I consider day trading in options and/or using complex
Finding Mispriced Options    • 149
strategies involving the simultaneous purchase and sale of multiple con-
tracts to be a poor investment strategy.
Implied Bid Volatility/Implied Ask Volatility
Because the price is so different between the bid and the ask, the range of fu-
ture stock prices implied by the option prices can be thought of as different
depending on whether you are buying or selling contracts. Employing the
graphic conventions we used earlier in this book, this effect is represented
as follows:
Implied price range implied
by ask price volatility of 23.4%
Implied price range implied
by bid price volatility of 21.4%
6/21/201612/24/20156/27/201512/29/20147/2/20141/3/20147/7/20131/8/20131/12/2012
Oracle (ORCL)
Price per Share
60
50
40
30
20
10
-
Because Oracle is such a big, liquid company, the difference between
the stock prices implied by the different bid-ask implied volatilities is not
large, but it can be substantial for smaller, less liquid companies. Looking
at the ask implied volatility column, you will notice the huge difference
between the far ITM options’ implied volatilities and those for ATM and
OTM options. The data in the preceding diagram are incomplete, but
if you were to graph all the implied volatility data, you would get the
following:
150  •   The Intelligent Option Investor
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
Strike Price
Oracle (ORCL) Implied Volatility
Implied Volatility (Percent)
160
180
140
100
120
80
40
60
20
0
Thinking about what volatility means with regard to future stock
prices—namely, that it is a prediction of a range of likely values—it does not
make sense that options struck at different prices would predict such radi-
cally different stock price ranges. What the market is saying, in effect, is that it
expects different things about the likely future range of stock prices depending
on what option is selected. Clearly, this does not make much sense.
This “nonsensical” effect is actually proof that practitioners
understand that the Black-Scholes-Merton model’s (BSM’s) assumptions
are not correct and specifically that sudden downward jumps in a stock
price can and do occur more often than would be predicted if returns fol-
lowed a normal distribution. This effect does occur and even has a name—
the volatility smile . Although this effect is extremely noticeable when
graphed in this way, it is not particularly important for the intelligent op-
tion investing strategies about which I will speak. Probably the most im-
portant thing to realize is that the pricing on far OTM and far ITM options
is a little more informal and approximate than for ATM options, so if you
are thinking about transacting in OTM or ITM options, it is worth looking
for the best deal available. For example, notice that in the preceding dia-
gram, the $21-strike implied volatility is actually notably higher than the
Finding Mispriced Options    • 151
$20-strike volatility. If you were interested in buying an ITM call option,
you would pay less time value for the $20-strike than for the $21-strike op-
tions—essentially the same investment. I will talk more about the volatility
smile in the next section when discussing delta.
In a similar way, sometimes the implied volatility for puts is different
from the implied volatility for calls struck at the same price. Again, this is
one of the market frictions that arises in option markets. This effect also
has investing implications that I will discuss in the chapters detailing dif-
ferent option investing strategies.
The last column in this price display is delta , a measure that is so
important that it deserves its own section—to which we turn now.
Delta: The Most Useful of the Greeks
Someone attempting to find out something about options will almost
certainly hear about how the Greeks are so important. In fact, I think that
they are so unimportant that I will barely discuss them in this book. If you
understand how options are priced—and after reading Part I, you do—the
Greeks are mostly common sense.
Delta, though, is important enough for intelligent option investors
to understand with a bit more detail. Delta is the one number that gives
the probability of a stock being above (for calls) or below (for puts) a given
strike price at a specific point in time.
Deltas for calls always carry a positive sign, whereas deltas for puts are
always negative, so, for instance, a call option on a given stock whose delta is
exactly 0.50 will have a put delta of −0.50. The call delta of 0.50 means that there
is a 50 percent chance that the stock will expire above that strike, and the put
delta of −0.50 means that there is a 50 percent chance that the stock will expire
below that strike. In fact, this strike demonstrates the technical definition of
ATM—it is the most likely future price of the stock according to the BSM.
The reason that delta is so important is that it allows you one way
of creating the BSM probability cones that you will need to find option
investment opportunities. Recall that the straight dotted line in our BSM
cone diagrams meant the statistically most likely future price for the stock.
The statistically most likely future price for a stock—assuming that stocks
152  •   The Intelligent Option Investor
move randomly, which the BSM does—is the price level at which there is
an equal chance of the actual future stock price to be above or below. In
other words, the 50-delta mark represents the forward price of a stock in
our BSM cones.
Recall now also that


re price for the stock.
The statistically most likely future price for a stock—assuming that stocks
152  •   The Intelligent Option Investor
move randomly, which the BSM does—is the price level at which there is
an equal chance of the actual future stock price to be above or below. In
other words, the 50-delta mark represents the forward price of a stock in
our BSM cones.
Recall now also that each line demarcating the cone represents roughly a
16 percent probability of the stock reaching that price at a particular time in the
future. This means that if we find the call strike prices that have deltas closest to
0.16 and 0.84 (= 1.00 − 0.16) or the put strike prices that have deltas closest to
−0.84 and −0.16 for each expiration, we can sketch out the BSM cone at points
in the future (the data I used to derive this graph are listed in tabular format at
the end of this section).
6/21/201612/24/20156/27/201512/29/20147/2/20141/3/20147/7/20131/8/20137/12/2012
Date
Oracle (ORCL)
Price per Share
45
40
35
30
25
20
5
10
15
-
Obviously, the bottom range looks completely distended compared
with the nice, smooth BSM cone shown in earlier chapters. This dis-
tension is simply another way of viewing the volatility smile. Like the
volatility smile, the distended BSM cone represents an attempt by partici-
pants in the options market to make the BSM more usable in real situa-
tions, where stocks really can and do fall heavily even though the efficient
market hypothesis (EMH) says that they should not. The shape is saying,
Finding Mispriced Options    • 153
“We think that these prices far below the current price are much more
likely than they would be assuming normal percentage returns. ” (Or, in a
phrase, “We’re scared!”)
If we compare the delta-derived “cone” with a theoretically derived
BSM cone, here is what we would see:
Oracle (ORCL)
Date
Price per Share
60
50
40
30
20
10
-
6/21/201612/24/20156/27/201512/29/20147/2/20141/3/20147/7/20131/8/20137/12/2012
Of course, we did not need the BSM cone to tell us that the points
associated with the downside strikes look too low. But it is interesting to see
that the upside and most likely values are fairly close to what the BSM projects.
Note also that the downside point on the farthest expiration is nearly
fairly priced according to the BSM, contrary to the shorter-tenor options.
This effect could be because no one is trading the far ITM call long-term
equity anticipation securities (LEAPS), so the market maker has simply
posted his or her bid and ask prices using the BSM as a base. In the market,
this is what usually happens—participants start out with a mechanically
generated price (i.e., using the BSM or some other computational option
pricing model) and make adjustments based on what feels right, what
arbitrage opportunities are available, and so on.
154  •   The Intelligent Option Investor
One important thing to note is that although we are using the delta
figure to get an idea of the probability that the market is assigning to a certain
stock price outcome, we are also using deltas for options that nearly no one
ever trades. Most option volume is centered around the 50-delta mark and a
10 to 20 percentage point band around it (i.e., from 30- to 40-delta to 60- to
70-delta). It is doubtful to me that these thinly traded options contain much
real information about market projections of future stock prices.
Another problem with using the deltas to get an idea about market
projections is that we are limited in the length of time we can project out
to only the number of strikes available. For this example, I chose an impor-
tant tech company with a very liquid stock, so it has plenty of expirations
and many strikes available so that we can get a granular look at deltas.
However, what if we were looking at Mueller Water’s option chain and try-
ing to figure out what the market is saying?
2.5
5
7.5
10
Last
C5.30
C2.80
0.55
C0.00
Change Bid Ask Impl. Bid Vol. Impl. Ask Vol. Delta AUG 16 ´13
2.5
5
7.5
10
NOV 15 ´13
2.5
5
7.5
10
12.5
FEB 21 ´14
DescriptionCall
5.20 5.50 N/A 340.099% 0.9978
0.9978
0.7330
0.1316
0.9347
0.8524
0.6103
0.1516
0.9933
0.9190
0.6070
0.2566
0.1024
142.171%
46.039%
76.652%
N/A
N/A
2.95
0.55
0.10
2.70
0.500.00
5.20 5.50
3.00
0.90
0.20
2.80
0.80
0.10
5.505.10
3.102.85
1.151.05
0.400.30
0.200.05
39.708%
N/A
N/A
36.722%
N/A
38.754%
38.318%
39.127%
36.347%
36.336%
163.282%
75.219%
42.610%
45.215%
122.894%
64.543%
42.697%
44.728%
50.218%
C5.30
C2.80
C0.85
C0.10
C5.30
C1.10
C0.35
C0.10
3.00 +0.15
Here you can see that we only have three expirations: 26, 117, and
215 days from when these data were taken. In addition, there are hardly
any strikes that are reasonably close to our crucial 84-delta, 50-delta, and
16-delta strikes, which means that we have to do a lot of extrapolation to
try to figure out where the market’s idea of the BSM cone lies.
To get a better picture of what the market is saying, I recommend
looking at options that are the most heavily traded and assuming that the
implied volatility on these strikes gives true information about the mar -
ket’s assumptions about the future price range of a stock. Using the im-
plied volatility on heavily traded contracts as the true forward volatility
expected by the market allows us to create a theoretical BSM cone that we
Finding Mispriced Options    • 155
can extend indefinitely into the future and that is probably a lot closer to
representing actual market expectations for the forward volatility (and, by
extension, the range of future prices for a stock). Once we have this BSM
cone—with its high-low ranges spelled out for us—we can compare it with
the best- and worst-case valuations we derived as part of the company
analysis process.
Let’s look at this process in the next section, where I spell out, step by
step, how to compare an intelligent valuation range with that implied by
the option market.
Note: Data used for Oracle graphing exampl

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


k). Once we have this BSM
cone—with its high-low ranges spelled out for us—we can compare it with
the best- and worst-case valuations we derived as part of the company
analysis process.
Let’s look at this process in the next section, where I spell out, step by
step, how to compare an intelligent valuation range with that implied by
the option market.
Note: Data used for Oracle graphing example:
Expiration Date Lower Middle Upper
7/25/2013 29.10 31.86 32.75
8/16/2013 22.00 32.00 33.50
9/20/2013 19.00 32.00 35.00
12/20/2013 20.00 32.50 37.00
1/17/2014 19.00 32.50 37.20
1/16/2015 23.00 32.30 42.00
Here I have eyeballed (and sometimes done a quick extrapolation) to try
to get the price that is closest to the 84-delta, 50-delta, and 16-delta marks,
respectively. Of course, you could calculate these more carefully and get
exact numbers, but the point of this is to get a general idea of how likely the
market thinks a particular future stock price is going to be.
Comparing an Intelligent Valuation
Range with a BSM Range
The point of this book is to teach you how to be an intelligent option investor
and not how to do stochastic calculus or how to program a computer to
calculate the BSM. As such, I’m not going to explain how to mathematically
derive the BSM cone. Instead, on my website I have an application that will
allow you to plug in a few numbers and create a graphic representation of a
BSM cone and carry out the comparison process described in this section.
The only thing you need to know is what numbers to plug into this web
application!
156  •   The Intelligent Option Investor
I’ll break the process into three steps:
1. Create a BSM cone.
2. Overlay your rational valuation range on the BSM cone.
3. Look for discrepancies.
Create a BSM Cone
The heart of a BSM cone is the forward volatility number. As we have seen,
as forward volatility increases, the range of future stock prices projected by
the BSM (and expected by the market) also increases. However, after hav-
ing looked at the market pricing of options, we also know that a multitude
of volatility numbers is available. Which one should we look at? Each strike
price has its own implied volatility number. What strike price’s volatility
should we use? There are also multiple tenors. What tenor options should
we look at? Should we look at implied volatility at the bid price? At the ask
price? Perhaps we should take the “kitchen sink” approach and just average
all the implied volatilities listed!
The answer is, in fact, easy if you use some simplifying assumptions
to pick a single volatility number. I am not an academic, so I don’t neces-
sarily care if these simplifying assumptions are congruent with theory.
Also, I am not an arbitrageur, so I don’t much care about very precise
numbers, and this attitude also lends itself well to the use of simplifying
assumptions. All we have to make sure of is that the simplifying as-
sumptions don’t distort our perception to the degree that we make bad
economic choices.
Here are the assumptions that we will make:
1. The implied volatility on a contract one or two months from expi-
ration that is ATM or at least within the 40- to 60-delta band and
that is the most heavily traded will contain the market’s best idea
of the true forward volatility of the stock.
2. If a big announcement is scheduled for the near future, implied
volatility numbers may be skewed, so their information might
not be reliable. In this case, try to find a heavily traded near ATM
strike at an expiry after the announcement will be made. If the
announcement will be made in about four months or more, just try
Finding Mispriced Options    • 157
to eyeball the ATM volatility for the one- and two-month contracts.
3. If there is a large bid-ask spread, the relevant forward volatility
to use is equal to the implied volatility we want to transact. In
other words, use the ask implied volatility if you are thinking
about gaining exposure and the bid implied volatility if you are
thinking about accepting exposure (the online application shows
cones for both the bid implied volatility and the ask implied
volatility).
Basically, these rules are just saying, “If you want to know what the
option market is expecting the future price range of a stock to be, find a
nice, liquid near ATM strike’s implied volatility and use that. ” Most op-
tion trading is done in a tight band around the present ATM mark and for
expirations from zero to three months out. By looking at the most heavily
traded implied volatility numbers, we are using the market’s price-discov-
ery function to the fullest. Big announcements sometimes can throw off
the true volatility picture, which is why we try to avoid gathering infor -
mation from options in these cases (e.g., legal decisions, Food and Drug
Administration trial decisions, particularly impactful quarterly earnings
announcements, and so on).
If I was looking at Oracle, I would probably choose the $32-strike
options expiring in September. These are the 50-delta options with
61 days to expiration, and there is not much of a difference between
calls and puts or between the bid and ask. The August expiration op-
tions look a bit suspicious to me considering that their implied volatility
is a couple of percentage points below that of the others. It probably
doesn’t make a big difference which you use, though. We are trying to
find opportunities that are severely mispriced, not trying to split hairs
of a couple of percentage points. All things considered, I would prob-
ably use a number somewhere around 22 percent for Oracle’s forward
volatility.
C12.02 11.75 N/A 55.427% 0.9897 C0.00 0.02 N/A 50.831%- 0.01032011.90
C11.03 10.70 N/A 123.903% 0.9869 C0.01 0.03 N/A 48.233%- 0.01312112.35
C10.04 9.50 N/A 64.054% 0.9834 C0.03 0.05 37.572% 46.993%- 0.01660.012210.10
C0.06 0.04 20.455% 21.147% 0.0463 C5.03 5.55 N/A 36.111%- 0.95584.95370.05
1.65 1.65 22.720% 23.311% 0.6325 0.8


a number somewhere around 22 percent for Oracle’s forward
volatility.
C12.02 11.75 N/A 55.427% 0.9897 C0.00 0.02 N/A 50.831%- 0.01032011.90
C11.03 10.70 N/A 123.903% 0.9869 C0.01 0.03 N/A 48.233%- 0.01312112.35
C10.04 9.50 N/A 64.054% 0.9834 C0.03 0.05 37.572% 46.993%- 0.01660.012210.10
C0.06 0.04 20.455% 21.147% 0.0463 C5.03 5.55 N/A 36.111%- 0.95584.95370.05
1.65 1.65 22.720% 23.311% 0.6325 0.84 +0.07 0.82 22.989% 23.384%- 0.36790.80311.68-0.13
1.06 1.08 22.019% 22.407% 0.4997 1.23 +0.05 1.25 22.284% 22.672%- 0.50081.23321.10-0.12
0.66 0.65 21.378% 21.813% 0.3606 1.88 +0.16 1.82 21.453% 22.106%- 0.64021.79330.67-0.07
0.02 0.01 21.354% 23.409% 0.0155 C6.99 7.55 N/A 44.342%- 0.98716.85390.02+0.01
0.03 0.01 19.050% 22.144% 0.0266 C6.00 6.30 17.134% 30.947%- 0.97576.15380.030.00
SEP 20 ´13
158  •   The Intelligent Option Investor
For Mueller Water, it’s a little trickier:
2.5
5
7.5
10
Last
C5.30
C2.80
0.55
C0.00
Change BidA sk Delta AUG 16 ´13
2.5
5
7.5
10
NOV 15 ´13
2.5
5
7.5
10
12.5
FEB 21 ´14
DescriptionCall
Last Change BidA sk Impl. Bid Vol. Impl. Ask Vol.Impl. Bid Vol. Impl. Ask Vol. Delta
Put
C0.00
C0.00
C0.25
C2.25
C0.00
C0.00
C0.55
C2.35
C0.00
C0.10
C0.85
C2.55
C4.80
5.20 5.50N /A 340.099% 0.9978
0.9978
0.7330
0.1316
0.9347
0.8524
0.6103
0.1516
0.9933
0.9190
0.6070
0.2566
0.1024
142.171%
46.039%
76.652%
N/A
N/A
2.95
0.55
0.10
0.20
0.10 N/A
N/A
N/A
0.10
0.30
2.35
40.733%
N/A
N/A
N/A
N/A
36.550%
38.181%
35.520%
35.509%
35.664%
2.10
0.50
0.05
0.10
0.60
2.402.30
0.05
0.15
0.15
0.85
2.60
4.90
2.70
0.500.00
5.20 5.50
3.00
0.90
0.20
2.80
0.80
0.10
5.505.10
3.102.85
1.151.05
0.400.30
0.200.05
39.708%
N/A
N/A
36.722%
N/A
38.754%
38.318%
39.127%
36.347%
36.336%
292.169% 0.0000
-0.0000
-0.2778
-0.8663
-0.0616
-0.1447
-0.3886
-0.8447
-0.0018
-0.0787
-0.3890
-0.7375
-0.8913
128.711%
53.108%
88.008%
117.369%
60.675%
42.433%
44.802%
110.810%
50.757%
42.074%
43.947%
49.401%
163.282%
75.219%
42.610%
45.215%
122.894%
64.543%
42.697%
44.728%
50.218%
C5.30
C2.80
C0.85
C0.10
C5.30
C1.10
C0.35
C0.10
3.00 +0.15
0.70
2.45
4.60
In the end, I would probably end up picking the implied volatility
associated with the options struck at $7.50 and expiring in August 2013
(26 days until expiration). I was torn between these and the same strike
expiring in November, but the August options are at least being actively
traded, and the percentage bid-ask spread on the call side is lower for them
than for the November options. Note, though, that the August 2013 put
options are so far OTM that the bid-ask spread is very wide. In this case,
I would probably look closer at the call options’ implied volatilities. In the
end, I would have a bid volatility of around 39 percent and an ask volatility
of around 46 percent. Because the bid-ask spread is large, I would probably
want to see a cone for both the bid and ask.
Plugging in the 22.0/22.5 for Oracle,
2 I would come up with this cone:
Date
Oracle (ORCL)
Price per Share
60
40
50
30
10
20
-
6/21/201612/24/20156/27/201512/29/20147/2/20141/3/20147/7/20131/8/20137/12/2012
Finding Mispriced Options    • 159
Plugging in the 39/46 for Mueller Water, I would get the following:
6/21/201612/24/20156/27/201512/29/20147/2/20141/3/20147/7/20131/8/20137/12/2012
Date
Mueller Water (MWA)
Price per Share
25
20
15
5
10
-
Y ou can see with Mueller Water just how big a 7 percentage point dif-
ference can be for the bid and ask implied volatilities in terms of projected
outcomes. The 39 percent bid implied volatility generates an upper range
at just around $15; the 46 percent ask implied volatility generates an upper
range that is 20 percent or so higher than that!
Overlay an Intelligent Valuation Range on the BSM Cone
This is simple and exactly the same for a big company or a small one,
so I’ll just keep going with the Oracle example. After having done a full
valuation as shown in the exam valuation of Oracle on the IOI website,
you’ve got a best-case valuation, a worst-case valuation, and probably
an idea about what a likely valuation is. Y ou simply draw those numbers
onto a chart like this:
160  •   The Intelligent Option Investor
6/21/201612/24/20156/27/201512/29/20147/2/20141/3/20147/7/20131/8/20137/12/2012
Date
Oracle (ORCL)
Price per Share
60
Best Case
Likely Case
Worst Case
40
50
30
10
20
-
$52
$43
$30
Once this step is done, we are ready to go onto the next and final step.
Look for Discrepancies
The last step is also easy. Because options split a stock’s returns into upside
and downside exposure, we need to take a look at both the upside and
downside to see where our projections differ from those of the market.
6/21/201612/24/20156/27/201512/29/20147/2/20141/3/20147/7/20131/8/20137/12/2012
Date
Oracle (ORCL)
Price per Share
60
Best Case
Likely Case
Worst Case
40
50
30
10
20
Downside
Upside
-
$52
$43
$30
A
B
Finding Mispriced Options    • 161
On the upside, we can see that our likely case valuation is $43 per share,
whereas the BSM’s most likely value is a bit less than $35—a difference of
more than 20 percent. This is the area on the graph labeled “ A. ” The BSM
prices options based on the likelihood of the stock hitting a certain price
level. The BSM considers the $43 price level to be relatively unlikely, whereas
I consider it relatively likely. As such, I believe that options that allow me to
gain exposure to the upside potential of Oracle—call options—are underval-
ued. In keeping with the age-old rule of investing to buy low, I will want to
gain exposure to Oracle’s upside by buying low-priced call options.
On the downside, I notice that there is a fairly large discrepancy
between my worst-case valuation ($30) and the lower leg of the BSM cone
(approximately $24)—this is the region of the graph labeled “B, ” and the
separation between the two values is again (just by chance) about 20 percent.
The BSM is pricing options granting exposure to the downside—put
options—struck at $24 as if they were fairly likely to occur; something that
is fairly like


e discrepancy
between my worst-case valuation ($30) and the lower leg of the BSM cone
(approximately $24)—this is the region of the graph labeled “B, ” and the
separation between the two values is again (just by chance) about 20 percent.
The BSM is pricing options granting exposure to the downside—put
options—struck at $24 as if they were fairly likely to occur; something that
is fairly likely to occur will be priced expensively by the BSM. My analysis,
on the other hand, makes me think that the BSM’s valuation outcome is
very unlikely. The discrepancy implies that I believe the put options to be
overvalued—the BSM sees a $24 valuation as likely, with expensive options,
whereas I see it as unlikely, with nearly valueless options. In this case, we
should consider the other half of the age-old investing maxim and sell high.
In a graphic representation, this strategy might look like this:
6/21/201612/24/20156/27/201512/29/20147/2/20141/3/20147/7/20131/8/20137/12/2012
Date
Oracle (ORCL)
Price per Share
60
Best Case
Likely Case
Worst Case
40
50
30
10
20
Downside
Upside
-
$52
$43
$30
GREEN
RED
162  •   The Intelligent Option Investor
Why would I select such a short-term put option to sell? Why would
I pick an OTM call option to buy? These are the kinds of questions I will
cover in Chapters 9–11, which look at the specifics of different option
strategies.
Before we look at strategies, though, an option investor cannot be
said to be intelligent without understanding what leverage is and how to
use it safely and effectively in a portfolio. We turn to this in Chapter 8.
163
Chapter 8
Understanding and
managing Leverage
In the media, the word leverage seems like it usually occurs alongside such
words as dangerous, speculative, or even irresponsible, so most people have
internalized the message that leverage is morally wrong; options—levered
instruments that they are—are, by extension, viewed as morally wrong as
well. In fact, nearly everyone uses leverage every day of their lives without
incident and presumably without incurring a moral stain. In my opinion,
it is not leverage that is the problem but rather an ignorance of how lever-
age works, coupled with overleverage and the inherent human belief that
disasters only happen to someone else, that is the problem.
Leverage is a powerful tool, but like all powerful tools, if used recklessly
and without understanding, it can bring its user to unpleasant outcomes.
Certainly a discussion of gaining and accepting exposure using option con-
tracts would be incomplete without a good explanation of leverage.
I like to think of leverage coming in three flavors: operational, financial,
and investment—the first two of which I mentioned in an earlier chapter and
go into more detail in Appendix B. This chapter delves specifically into in-
vestment leverage, but to the extent that investment leverage is similar to the
other forms of leverage, referring to Appendix B to learn about those forms
will help deepen your understanding of investment leverage. In this chapter,
I first define investment leverage, discuss how it can be gained by using either
debt or options, look at common ways to measure it, and introduce a unique
method of measuring and managing leverage in an investment portfolio.
Leverage is not something to be taken lightly. Many very highly
trained, well-educated, and well-capitalized investors have gone bankrupt
164  •   The Intelligent Option Investor
because of their lack of appreciation for the fact that the sword of lever -
age cuts both ways. Certainly an option investor cannot be considered an
intelligent investor without having an understanding and a deep sense
of respect for the simultaneous power and danger that leverage conveys.
New jargon introduced in this chapter includes the following:
Lambda
Notional exposure
Investment Leverage
Commit the following definition to memory:
Investment leverage is the boosting of investment returns calcu-
lated as a percentage by altering the amount of one’s own capital
at risk in a single investment.
Investment leverage is inextricably linked to borrowing money—this
is what I mean by the phrase “altering the amount of one’s own capital at
risk. ” In this way, it is very similar to financial leverage. In fact, in my mind,
the difference between financial and investment leverage is that a company
uses financial leverage to fund projects that will produce goods or provide
services, whereas in the case of investing leverage, it is used not to produce
goods or services but to amplify the effects of a speculative position.
Frequently people think of investing leverage as simply borrowing
money to invest. However, as I mentioned earlier, you can invest in options
for a lifetime and never explicitly borrow money in the process. I believe
that the preceding definition is broad enough to handle both the case of
investment leverage generated through explicit borrowing and the case of
leverage generated by options.
Let’s take a look at a few example investments—unlevered, levered
using debt, and levered using options.
Unlevered Investment
Let’s say that you buy a stock for exactly $50 per share, expecting that its intrinsic
value is closer to $85 per share. Over the next year, the stock increases by $5,
or 10 percent in value. Y our unrealized percentage gain on this investment is
Understanding and Managing Leverage    • 165
obviously 10 percent. If instead the stock declines to $45 per share over that
year, you would be sitting on an unrealized percentage loss of 10 percent.
Of course, this is very straightforward. Let’s now look at the purchase
of a share of common stock using borrowed capital.
Levered Investment Using Debt
Let’s say that to buy a $50 share, you borrow $45 from a bank at an inter -
est rate of 5 percent per year, put in $5 of your own cash, and buy that
same share of stock. Again, let’s assume that the stock increases in value by
$5 over one


cent.
Of course, this is very straightforward. Let’s now look at the purchase
of a share of common stock using borrowed capital.
Levered Investment Using Debt
Let’s say that to buy a $50 share, you borrow $45 from a bank at an inter -
est rate of 5 percent per year, put in $5 of your own cash, and buy that
same share of stock. Again, let’s assume that the stock increases in value by
$5 over one year, closing at $55 per share. At the end of the year, you sell the
stock and pay back the bank loan with interest (a total of $47.25). Doing so,
you realize gross proceeds of $7.75 on an original investment of $5 of your
own capital, which equates to $2.75 in gross profits and implies a percent-
age investment return of 55 percent.
There are three important things to note by comparing the levered
and unlevered examples:
1. The percentage return is much higher for the levered investment
(55 versus 10 percent) because you have reduced the amount of
your own capital at risk much more than you have reduced the
dollar return in the numerator.
2. The actual dollar amount gained is lower in the levered example
($2.75 versus $10). If your investment mandate would have been
“Generate at least $10 worth of investment returns, ” a single unit
of the levered investment would have failed to meet this mandate.
3. Obviously, the underlying asset and its returns are the same in both
levered and unlevered scenarios—we are changing our profit expo-
sure to the underlying, not altering its volatility or other behavior.
To fully understand leverage’s effects, however, we should also con-
sider the loss scenario. Again, let’s assume that we borrow $45 and spend
$5 of our own money to buy the $50 per share stock. We wake the next
morning to news that the company has discovered accounting irregulari-
ties in an important foreign subsidiary that has caused it to misstate reve-
nues and profits for the last three years. The shares suddenly fall 10 percent
on the news. The unrealized loss is $5—the 10 percent fall in stock value
has wiped out 100 percent of our investment capital.
166  •   The Intelligent Option Investor
And herein lies the painful lesson learned by many a soul in the
financial markets: leverage cuts both ways. The profits happily roll in dur-
ing the good times, but the losses inexorably crash down during bad times.
Levered Investment Using Options
Discussing option-based investing leverage is much easier if we focus on
the perspective of gaining exposure. Because most people are more com-
fortable thinking about the long side of investing, let’s look at an example
of gaining upside exposure on a company.
Let’s assume we see a $50 per share stock that we believe is worth $85 (in
this example, I am assuming that we only have a point estimate of the intrinsic
value of the company so as to simplify the following diagram—normally, it is
much more helpful to think about fair value ranges, as explained in Part II of
this book and demonstrate in the online example). We are willing to buy the
share all the way up to a price of $68 (implying a 25 percent return if bought
at $68 and sold at $85) and can get call options struck at $65 per share for only
$1.50. Graphically, this prospective investment looks like this:
Fair Value Estimate
5/18/2012 5/20/2013 249 499 749 999
-
10
20
30
40
50
60
70
80
90
EBP = $66.50
Date/Day Count
Advanced Building Corp. (ABC)
Stock Price
GREEN
Understanding and Managing Leverage    • 167
In two years, you are obligated to pay your counterparty $65 if you
want to hold the stock, but the decision as to whether to take possession
of the stock in return for payment is solely at your discretion. In essence,
then, you can look at buying a call option as a conditional borrowing of
funds sometime in the future. Buying the call option, you are saying, “I
may want to borrow $65 two years from now. I will pay you some interest
up front now, and if I decide to borrow the $65 in two years, I’ll pay you
that principal then. ”
In graphic terms, we can think about this transaction like this:
5/18/2012 5/20/2013 249 499 749 999
-
10
20
30
40
50
60
70
80
90
$1.50 “prepaid interest”
Contingent loan, the future repayment
of principal is made solely at the
investor’s own discretion.
Fair Value Estimate
Advanced Building Corp. (ABC)
Date/Day Count
Stock Price
GREEN
If the stock does indeed hit the $85 mark just at the time our option
expires, we will have realized a gross profit of $20 (= $85 − $65) on an
investment of $1.50, for a percentage return of 1,233 percent! Obviously,
the call option works very much like a loan in terms of altering the
investor’s capital at risk and boosting subsequent investment returns.
However, although the leverage looks very similar, there are two impor -
tant differences:
168  •   The Intelligent Option Investor
1. As shown and mentioned earlier, when using an option, payment
on the principal amount of $65 in this case is conditional and com-
pletely discretionary. For an option, the interest payment is made
up front and is a sunk cost.
2. Because repayment is discretionary in the case of an option, you
do not have any financial risk over and above the prepayment of
interest in the form of an option premium. Repayment of a con-
ventional loan is mandatory, so you have a large financial risk if
you cannot repay the principal at maturity in this case.
Regarding the first difference, not only is the loan conditional
and discretionary, the loan also has value and can be transferred to
another for a profit. What I mean is this: if the stock rises quickly, the
value of that option in the open market will increase, and rather than
holding the “loan” to maturity, you can simply sell it with your profits
offsetting the original cost of the prepaid interest plus giving you a
nice profit.
Regarding the second difference, consider this: if you are using bor -
rowed money to invest and your stock drops heavily, the broker will mak


stock rises quickly, the
value of that option in the open market will increase, and rather than
holding the “loan” to maturity, you can simply sell it with your profits
offsetting the original cost of the prepaid interest plus giving you a
nice profit.
Regarding the second difference, consider this: if you are using bor -
rowed money to invest and your stock drops heavily, the broker will make
a margin call (i.e., ask you to deposit more capital into the account), and
if you cannot make the margin call, the broker will liquidate the position
(most brokers shoot first and ask questions later, simply closing out the
position and selling other assets to cover the loss at the first sign margin
requirements will not be met). If this happens, you can be 100 percent
correct on your valuation long term but still fail to benefit economically
because the position has been forcibly closed. In the case of options, the
underlying stock can lose 20 percent in a single day, and the owner of a
call option will never receive a margin call. The flip side of this benefit
is that although you are not at risk of losing a position to a margin call,
option ownership does not guarantee that you will receive an economic
reward either.
For example, if the option mentioned in the preceding example ex-
pires in two years when the stock is trading at $64.99 and the stock has paid
$2.10 in dividends over the previous two years, the option holder ends up
with neither the stock nor the dividend check.
Understanding and Managing Leverage    • 169
Simple Ways of Measuring Option
Investment Leverage
There are several single-point, easily calculable numbers to measure
option-based investment leverage. There are uses for these simple measures
of leverage, but unfortunately, for reasons I will discuss, the simple num-
bers are not enough to help an investor intelligently manage a portfolio
containing option positions.
The two simple measures are lambda and notional exposure. Both are
explained in the following sections.
Lambda
The standard measure investors use to determine the leverage in an option
position is one called lambda . Lambda—sometimes known as percent
delta—is a derivative of the delta
1 factor we discussed in Chapter 7 and is
found using the following equation:
= ×Lambda deltas tock price
optionprice
Let’s look at an actual example. The other day, I bought a deep in-
the-money (ITM) long-tenor call option struck at $20 when the stock
was trading at $30.50. The delta of the option at that time was 0.8707,
and the price was $11. The leverage in my option position was calculated
as follows:
= × = × =Lambda deltas tock price
optionprice
0.87 30.50
11 2.40

What this figure of 2.4 is telling us is that when I bought that option, if the
price of the underlying moved by 1 percent, the value of my position would
move by about 2.4 percent. This is not a hard and fast number—a change in
price of either the stock or the option (as a result of a change in volatility or
time value or whatever) will change the delta, and the lambda will change
based on those things.
170  •   The Intelligent Option Investor
Because investment leverage comes about by changing the amount
of your own capital that is at risk vis-à-vis the total size of the investment,
you can imagine that moneyness has a large influence on lambda. Let’s
take a look at how investment leverage changes for in-the-money (ITM),
at-the-money (ATM), and out-of-the-money (OTM) options. The stock
underlying the following options was trading at $31.25 when these data
were taken, so I’m showing the $29 and $32 strikes as ATM:
Strike Price K /S Ratio Call Price Delta Lambda
15.00 0.48 17.30 0.91 1.64
20.00 0.64 11.50 0.92 2.50 ITM
21.00 0.67 11.30 0.86 2.38
22.00 0.70 9.60 0.89 2.90
…
…
…
…
…
29.00 0.93 3.40 0.68 6.25
30.00 0.96 2.74 0.61 6.96 ATM
31.00 0.99 2.16 0.54 7.81
…
…
…
…
…
39.00 1.25 0.18 0.09 15.63
40.00 1.28 0.13 0.06 14.42 OTM
41.00 1.31 0.09 0.05 17.36
When an option is deep ITM, as in the case of the $20-strike call, we
are making a significant expenditure of our own capital compared with
the size of the investment. Buying a call option struck at $20, we are—
as explained in the preceding section—effectively borrowing an amount
equal to the $20 strike price. In addition to this, we are spending $11.50 in
premium. Of this amount, $11.25 is intrinsic value, and $0.25 is time value.
We can look at the time value portion as the prepaid interest we discussed
in the preceding section, and we can even calculate the interest rate im-
plied by this price (this option had 189 days left before expiration, implying
an annual interest charge of 2.4 percent, for example). This prepaid interest
can be offset partially or fully by profit realized on the position, but it can
never be recaptured so must be considered a sunk cost. Time value always
decays independent of the price changes of the underlying, so although an
Understanding and Managing Leverage    • 171
upward movement in the stock will offset the money spent on time value,
the amount spent on time value is never recoverable.
The remaining $11.25 of the premium paid for a $20-strike call op-
tion is intrinsic value . Buying intrinsic value means that we are exposing
our own capital to the risk of an unrealized loss if the stock falls below
$31.25. Lambda is directly related to the amount of capital we are exposing
to an unrealized loss versus the size of the “loan” from the option, so be-
cause we are risking $11.25 of our own capital and borrowing $20 with the
option (a high capital-to-loan proportion), our investment leverage meas-
ured by lambda is a relatively low 2.50.
Now direct your attention to a far OTM call option—the one struck
at $39. If we invest in the $39-strike option, we are again effectively
taking out a $39 contingent loan to buy the shares. Again, we take the
time-value portion of the option’s price—in this case the entire premi-
um


ption (a high capital-to-loan proportion), our investment leverage meas-
ured by lambda is a relatively low 2.50.
Now direct your attention to a far OTM call option—the one struck
at $39. If we invest in the $39-strike option, we are again effectively
taking out a $39 contingent loan to buy the shares. Again, we take the
time-value portion of the option’s price—in this case the entire premi-
um of $1.28—to be the prepaid interest (an implied annualized rate of
6.3 percent) and note that we are exposing none of our own capital to
the risk of an unrealized loss. Because we are subjecting none of our
own capital in this investment and taking out a large loan, our invest-
ment leverage soars to a very high value of 15.63. This implies that a
1 percentage point move in the underlying stock will boost our invest-
ment return by over 15 percent!
Obviously, these calculations tell us that our investment returns are
going to be much more volatile for small changes in the underlying’s price
when buying far OTM options than when buying far ITM options. This is
fine information for someone interested in more speculative strategies—if
a speculator has the sense that a stock will rise quickly, he or she could,
rather than buying the stock, buy OTM options, and if the stock went up
fast enough and soon enough offset any drop of implied volatility and time
decay, he or she would pocket a nice, highly levered profit.
However, there are several factors that limit the usefulness of lambda.
First, because delta is not a constant, the leverage factor does not stay put
as the stock moves around. For someone who intends to hold a position for
a longer time, then, lambda provides little information regarding how the
position will perform over their investment horizon.
In addition, reading the preceding descriptions of lambda, it is ob-
vious that this measure deals exclusively with the percentage change in
172  •   The Intelligent Option Investor
the option’s value. Although everyone (especially fly-by-night investment
newsletter editors) likes to tout their percentage returns, we know from
our earlier investigations of leverage that percentage returns are only part
of the story of successful investing. Let’s see why using the three invest-
ments I mentioned earlier—an ITM call struck at $20, an OTM call struck
at $39, and a long stock position at $31.
I believe that there is a good chance that this stock is worth north of
$40—in the $43 range, to be precise (my worst-case valuation was $30, and
my best-case valuation was in the mid-$50 range). If I am right, and if this
stock hits the $43 mark just as my options expire,
2 what do I stand to gain
from each of these investments?
Let’s take a look.
Spent Gross Profit Net Profit Percent Profit
$39-strike call 0.18 4.00 3.82 2,122
$20-strike call 11.50 23.00 11.50 100
Shares 31.25 43.00 11.75 38
This table means that in the case of the $20-strike call, we spent
$11.50 to win gross proceeds of $23.00 (= $43 − $20) and a profit net of
investment of $11.50. Netting $11.50 on an $11.50 investment generates a
percentage profit of 100 percent.
Looking at this chart, the first thing you are liable to notice is the
“Percent Profit” column. That 2,122 percent return looks like something
you might see advertised on an option tout service, doesn’t it? Y es, that
percentage return is wonderful, until you realize that the absolute value
of your dollar winnings will not allow you to buy a latte at Starbuck’s.
Likewise, the 100 percent return on the $20-strike options looks heads and
shoulders better than the measly 38 percent on the shares, until you again
realize that the latter is still giving you more money by a quarter.
Recall the definition of leverage as a way of “boosting investment re-
turns calculated as a percentage, ” and recall that in my previous discussion
of financial leverage, I mentioned that the absolute dollar value is always
highest in the unlevered case. The fact is that many people get excited about
stratospheric percentage returns, but stratospheric percentage returns only
Understanding and Managing Leverage    • 173
matter if a significant chunk of your portfolio is exposed to those returns!
Lambda is a good measure to show how sensitive percentage returns are to
a move in the stock price, but it is useless when trying to understand what
the portfolio effects of those returns will be on an absolute basis.
Notional Exposure
Look back at the preceding table. Let’s say that we wanted to make
lambda more useful in understanding portfolio effects by seeing how
many contracts we would need to buy to match the absolute return of
the underlying stock. Because our expected dollar return of one of the
$39-strike calls only makes up about a third of the absolute return of the
straight stock investment ($3.82 / $11.75 = 32.5% ≈ 1/3), it follows that if
we wanted to make the same dollar return by investing in these call options
that we expect to make by buying the shares, we would have to buy three
of the call options for every share we wanted to buy. Recalling that op-
tions are transacted in contract sizes of 100 shares, we know that if we were
willing to buy 100 shares of Oracle’s stock, we would have to buy options
implying control over 300 shares to generate the same absolute profit for
our portfolio.
I call this implied control figure notional exposure. Continuing with
the $39-strike example, we can see that the measure of our leverage on the
basis of notional exposure is 3:1. The value of the notional exposure is cal-
culated by multiplying it by the strike; in this case, the notional exposure
of 300 shares multiplied by the strike price of $39 gives a notional value
for the contracts of $11,700. This value is called the notional amount of the
option position.
Some people calculate a leverage figure by dividing the notional amount
by the total cost of the options. In our example, we would pay $18 p


is cal-
culated by multiplying it by the strike; in this case, the notional exposure
of 300 shares multiplied by the strike price of $39 gives a notional value
for the contracts of $11,700. This value is called the notional amount of the
option position.
Some people calculate a leverage figure by dividing the notional amount
by the total cost of the options. In our example, we would pay $18 per con-
tract for three contracts, so leverage measured in this way would work out to
be 217 (= $11,700 ÷ $54). I actually do not believe this last measure of lever-
age to be very helpful, but notional control will become important when we
talk about the leverage of short-call spreads later in this chapter.
These simple methods of measuring leverage have their place in ana-
lyzing option investment strategies, but in order to really master leverage,
you must understand leverage in the context of portfolio management.
174  •   The Intelligent Option Investor
Understanding Leverage’s Effects on a Portfolio
Looking at leverage from a lambda or notional control perspective gives
some limited information about leverage, but I believe that the best way
to think about option-based investment leverage is to think about the ef-
fect of leverage on an actual portfolio allocation basis. This gives a richer,
more nuanced view of how leverage stands to help or hurt our portfolio
and allows us more insight into how we can intelligently structure a mixed
option-stock portfolio.
Let’s start our discussion of leverage in a portfolio context by thinking
about how to select investments into a portfolio. We will assume that we
have $100 in cash and want to use some or all of that cash to invest in risky
securities. Cash is riskless (other than inflation risk, but let’s ignore that
for a moment), so the risk we take on in the portfolio will be dampened
by keeping cash, and the returns we will win from the portfolio will be
similarly dampened.
We have a limited amount of capital and want to allocate that capital
to risky investments in proportion to two factors:
1. The amount we think we can gain from the investment
2. Our conviction in the investment, which is a measure of our per -
ception of the riskiness of the investment
We might see a potential investment that would allow us to reap a profit
of $9 for every $1 invested (i.e., we would gain a great deal), but if our
conviction in that investment is low (i.e., we think the chance of winning
$9 for every $1 invested is very low), we would likely not allocate much of
our portfolio to it.
In constructing a portfolio, most people set a limit on the proportion
of their portfolio they want to allocate to any one investment. I personally
favor more concentrated positions, but let’s say that you paid better atten-
tion to your finance professor in school than I did and figure that you want
to limit your risk exposure to any one security to a maximum of $5 of your
$100 portfolio.
An unlevered portfolio means that each $5 allocation would be made
by spending $5 of your own capital. Y ou would know that if the value of
the underlying security decreases by $2.50, the value of the allocation will
Understanding and Managing Leverage    • 175
also fall to $2.50. If, instead, the value of the underlying security increases
by $2.50, the value of that allocation will rise to $7.50.
In a levered portfolio, each $5 allocation uses some proportion of
capital that is not yours—borrowed in the case of a margin loan and con-
tingently borrowed in the case of an option. This means that for every
$1 increase or decrease in the value of the underlying security, the lev-
ered allocation increases or decreases by more than $1. Leverage, in this
context, represents the rate at which the value of the allocation increases
or decreases for every one-unit change in the value of the underlying
security.
When thinking about the risk of leverage, we must treat different types
of losses differently. A realized loss represents a permanent loss of capital—a
sunk cost for which future returns can offset but never undo. An unrealized
loss may affect your psychology but not your wealth (unless you need to
realize the loss to generate cash flow for something else—I talk about this
in Chapter 11 when I address hedging). For this reason, when we measure
how much leverage we have when the underlying security declines, we will
measure it on the basis of how close we are to suffering a realized loss rather
than on the basis of the unrealized value of the loss. Leverage on the profit
side will be handled the same way: we will treat our fair value estimate as the
price at which we will realize a gain. Because the current market price of a
security may not sit exactly between our fair value estimate and the point at
which we suffer a realized loss, our upside and downside leverage may be
different.
Let’s see how this comes together with an actual example. For this ex-
ample, I looked at the price of Intel’s (INTC) shares and options when the
former were trading at $22.99. Let’s say that we want to commit 5 percent
of our portfolio value to an investment in Intel, which we believe is worth
$30 per share. For every $100,000 in our portfolio, this would mean buying
217 shares. This purchase would cost us $4,988.83 (neglecting taxes and
fees, of course) and would leave us with $11.17 of cash in reserve. After we
made the buy, the stock price would fluctuate, and depending on what its
price was at the end of 540 days [I’m using as an investment horizon the
days to expiration of the longest-tenor long-term equity anticipation secu-
rities (LEAPS)], the allocation’s profit and loss profile would be represented
graphically like this:
176  •   The Intelligent Option Investor
02468 10 12 14 16 18 20 22 24
Stock Price
Unlevered Investment (Full Allocation)
Gain (Loss) on Allocation
26 28 30 32 34 36 38 40 42 44 46 48 50(6,000)
(4,000)
(2,000)
-
2,000
4,000
6,000
8,000
U


on of the longest-tenor long-term equity anticipation secu-
rities (LEAPS)], the allocation’s profit and loss profile would be represented
graphically like this:
176  •   The Intelligent Option Investor
02468 10 12 14 16 18 20 22 24
Stock Price
Unlevered Investment (Full Allocation)
Gain (Loss) on Allocation
26 28 30 32 34 36 38 40 42 44 46 48 50(6,000)
(4,000)
(2,000)
-
2,000
4,000
6,000
8,000
Unrealized Gain
Unrealized Loss
Cash Value
Net Gain (Loss) - Unlevered
Realized Loss
Here the future stock price is listed from 0 to 50 on the horizontal axis,
and the net profit or loss to this position is listed on the vertical axis. Obvious-
ly, any gain or loss would be unrealized unless Intel’s stock price went to zero,
at which point the total position would only be worth whatever spare cash we
had. The black profit and loss line is straight—the position will lose or gain on
a one-for-one basis with the price of the stock, so our leverage is 1.0.
Now that we have a sense of what the graph for a straight stock
position looks like, let’s take a look at a few different option positions.
When I drew the data for this example, the following 540-day expiration
call options were available:
Strike Price Ask Price Delta
15 8.00 0.79
22 2.63 0.52
25 1.43 0.35
Let’s start with the ITM option and construct a simple-minded posi-
tion that attempts to buy as many of these option contracts as possible with
the $5,000 we have reserved for this investment. We will pay $8 per share
Understanding and Managing Leverage    • 177
or $800 per contract, which would allow us to buy six contracts in all for
$4,800. There is only $0.01 worth of time value (= $15.00 + $8.00 − $22.99)
on these options because they are so far ITM. This means that we are pay-
ing $1 per contract worth of time value that is never recoverable, so we
shall treat it as a realized loss. If we were to graph our potential profit and
loss profile using this option, assuming that we are analyzing the position
just as the 540-day options expire, we would get the following
3:
Net Gain (Loss) - Levered
0246810 12 14 16 18 20 22 24
Stock Price
Levered Strategy Overview
Gain (Loss) on Allocation
26 28 30 32 34 36 38 40 42 44 46 48 50(10,000)
(5,000)
-
5,000
10,000
Unrealized Gain
Unrealized Loss
Cash Value
Realized Loss
15,000
20,000
The most obvious differences from the diagram of the unlevered po-
sition are (1) that the net gain/loss line is kinked at the strike price and
(2) that we will realize a total loss of invested capital—$4,800 in all—if
Intel’s stock price closes at $15 or below. The kinked line demonstrates the
meaning of the first point made earlier regarding option-based investment
leverage—an asymmetrical return profile for profits and losses. Note that
this kinked line is just the hockey-stick representation of option profit and
loss at expiration that one sees in every book about options except this
one. Although I don’t believe that hockey-stick diagrams are terribly useful
for understanding individual option transactions, at a portfolio level, they
do represent the effect of leverage very well. This black line represents a
178  •   The Intelligent Option Investor
levered position, and its slope is much steeper than that of an equivalent
line showing net profit and loss on an unlevered position. A comparison of
the two net profit lines on the same graph shows this clearly:
02468 10 12 14 16 18 20 22 24
Stock Price
Profit and Loss Profile for Levered and Unlevered Investments
Gain (Loss) on Allocation
26 28 30 32 34 36 38 40 42 44 46 48 50
(10,000)
(5,000)
-
5,000
10,000
15,000
20,000
Net Gain (Loss) - Unlevered
Net Gain (Loss) - Levered
Looking at this diagram, you will notice the following things about
the risk and return characteristics of the two positions:
Investment Maximum Loss Price
Net Profit at Fair
Value Estimate
Stock $0 $1,472
Option $15 (2.8 × stock loss) $4,200 (3.0 × stock profit)
The leverage on the stock loss and the leverage on the stock profit are
nearly equal in this instance because the point at which we realize a loss
($15) is just about the same distance below the market price as our pre-
sumed fair value ($30) is above. The leverage to loss is calculated as
=Loss leverage realized loss as ap ercent of allocation
percents tock declinet or ealizedl oss
Understanding and Managing Leverage    • 179
In this example, we suffer a realized loss of 96 percent (= $4,800 ÷
$5,000) if the stock falls 35 percent, so the equation becomes
= − =− ×Lossleverage 96%
35% 2.8

(By convention, I’ll always write the loss leverage as a negative.) This
equation just means that it takes a drop of 35 percent to realize a loss on
96 percent of the allocation.
The profit leverage is simply a ratio of the levered portfolio’s net profit
to the unlevered portfolio’s net profit at the fair value estimate. For this
example, we have
== ×Profitleverage $4,200
$1,472 3.0

Let’s do the same exercise for the ATM and OTM options and see
what fully levered portfolios with each of these options would look like
from a risk-return perspective. If we bought as many $22-strike options as
a $5,000 position size would allow (19 contracts in all), our profit and loss
graph and table would look like this:
02468 10 12 14 16 18 20 22 24
Stock Price
Levered Strategy Overview
Gain (Loss) on Allocation
26 28 30 32 34 36 38 40 42 44 46 48 50(20,000)
-
40,000
60,000
80,000
100,000
20,000
Unrealized Gain
Unrealized Loss
Cash Value
Net Gain (Loss) - Levered
Realized Loss
180  •   The Intelligent Option Investor
Instrument Maximum-Loss Price Net Profit at Fair Value Estimate
Stock $0 $1,472
Option $22 (23.2 × stock loss) $10,203 (6.9 × stock profit)
This is quite a handsome potential profit—6.9 times higher than we
could earn using a straight stock position—but at an enormous risk. Each
$1 drop in the stock price equates to a $23.20 drop in the value of the posi-
tion. Note that the realized loss shows a step up from $22 to


s Price Net Profit at Fair Value Estimate
Stock $0 $1,472
Option $22 (23.2 × stock loss) $10,203 (6.9 × stock profit)
This is quite a handsome potential profit—6.9 times higher than we
could earn using a straight stock position—but at an enormous risk. Each
$1 drop in the stock price equates to a $23.20 drop in the value of the posi-
tion. Note that the realized loss shows a step up from $22 to $23. This just
shows that above the strike price, our only realized loss is the money we
spent on time value.
The last example is that of the fully levered OTM call options. Here is
the table illustrating this case:
Instrument Maximum-Loss Price Net Profit at Fair Value Estimate
Stock $0 $1,472
Option $25 (IRL 5 percent) $12,495 (8.5 × stock profit)
There is no intrinsic value to this option, so the entire cost of
the option is treated as an immediate realized loss (IRL) from inception.
The “IRL 5 percent” notation means that there is an immediate realized
loss of 5 percent of the total portfolio. The maximum net loss is again at
the strike price of $25. The leverage factor at our fair value estimate price
is 8.5, but again this leverage comes at the price of having to realize a
5 percent loss on your portfolio—500 basis points of performance—and
there is no certainty that you will have enough or any profits to offset this
realized loss.
Of course, investing choices are not as black and white as what I have
presented here. If you want to commit 5 percent of your portfolio to a
straight stock idea, you have to spend 5 percent of your portfolio value on
stock, but this is not true for options. For example, I might choose to spend
2.5 percent of my portfolio’s worth on ATM calls (nine contracts in this ex-
ample), considering the position in terms of a 5 percent stock investment,
and then leave the rest as cash reserve. Here is what this investment would
look like from a leverage perspective:
Understanding and Managing Leverage    • 181
02468 10 12 14 16 18 20 22 24
Stock Price
Levered Strategy Overview
Gain (Loss) on Allocation
26 28 30 32 34 36 38 40 42 44 46 48 50(5,000)
-
15,000
10,000
20,000
25,000
30,000
5,000
Unrealized Gain
Unrealized Loss
Cash Value
Net Gain (Loss) - Levered
Realized Loss
Instrument Maximum-Loss Price Net Profit at Fair Value Estimate
Stock $0 $1,472
Option $22 (11 × stock loss) $4,833 (5.1 × stock profit)
The 11 times loss figure was calculated in the following way: there is a
total of 47.3 percent of my allocation to this investment that is lost if the price
of the stock goes down by 4.3 percent, so −47.3 percent/4.3 percent = −11.0.
Obviously, this policy of keeping some cash in reserve represents a sensible ap-
proach to portfolio management when leverage is used. An investor in straight
stock who makes 20 investments that do not hit his or her expected fair value
within the investment horizon might have a few bad years of performance, but
an investor who uses maximum option leverage and allocates 5 percent to 20
ideas will end up bankrupt if these don’t work out by expiration time!
Similar to setting a cash reserve, you also might decide to make an
investment that combines cash, stock, and options. For example, I might
buy 100 shares of Intel, three ITM option contracts, and leave the rest of
my 5 percent allocation in cash. Here is what that profit and loss profile
would look like:
182  •   The Intelligent Option Investor
0 24681 01 21 41 61 82 02 22 4
Stock Price
Levered Strategy Overview
Gain (Loss) on Allocation
26 28 30 32 34 36 38 40 42 44 46 48 50(6,000)
(4,000)
(2,000)
-
4,000
2,000
6,000
10,000
12,000
8,000 Unrealized Gain
Unrealized Loss
Cash Value
Net Gain (Loss) - Levered
Realized Loss
Instrument Maximum-Loss Price Net Profit at Fair Value Estimate
Stock $0 $1,472
Option $15 (1.8 × stock loss) $3,803 (2.6 × stock profit)
Three $800 option contracts represent $2,400 of capital or 48 percent of
this allocation’s capital. Thus 48 percent of the capital was lost with a 34.8 per-
cent move downward in the stock, generating a −1.4 times value for the options
plus we add another −0.4 times value to represent the loss on the small stock
allocation; together these generate the −1.8 times figure you see on the loss side.
Of course, if the option loss is realized, we still own 100 shares, so the maximum
loss will not be felt until the shares hit $0, as shown in the preceding diagram.
For the remainder of this book I will describe leverage positions us-
ing the two following terms: loss leverage and profit leverage . I will write
these in the following way:
− X.x
Y.y
where the first number will be the loss leverage ratio, and the second
number will be the profit leverage ratio based on the preceding rules that
Understanding and Managing Leverage    • 183
I’ve used for calculation. All OTM options will be marked with an IRL fol-
lowed by the percentage of the total portfolio used in the option purchase
(not the percentage of the individual allocation but the total percentage
amount of your investment capital). On my website, you’ll find an online
leverage tool that allows you to calculate these numbers yourself.
Managing Leverage
A realized loss is, to me, serious business. There are times when an inves-
tor must take a realized loss—specifically when his or her view of the fair
value or fair value range of a company changes materially enough that an
investment position becomes unattractive. However, if you find yourself
taking realized losses because of material changes in valuation too often,
you should either figure out where you are going wrong in the valuation
process or just put your money into a low-load mutual fund and spend
your time doing something more productive.
The point is that taking a realized loss is not something you have to do
too often if you are a good investor, and hopefully, when those losses are taken,
they are small. As such, I believe that there are two ways to successfully manage
leverage. Fir


are going wrong in the valuation
process or just put your money into a low-load mutual fund and spend
your time doing something more productive.
The point is that taking a realized loss is not something you have to do
too often if you are a good investor, and hopefully, when those losses are taken,
they are small. As such, I believe that there are two ways to successfully manage
leverage. First is to use leverage sparingly by investing in combinations of ITM
options and stocks. ITM option prices mainly represent intrinsic value, and be-
cause the time-value component is that which represents a realized loss right out
of the gate, buying ITM options means that you are minimizing realized losses.
The second method for managing leverage when you cannot resist
taking a higher leverage position is spending as little as possible of your
investment capital on it. This means that when you see that there is a com-
pany that has a material chance of being worth a lot more or a lot less than
it is traded for at present but that material chance is still much less likely
than other valuation scenarios, you should invest your capital in the idea
sparingly. By making smaller investments with higher leverage, you will
not realize a loss on too much of your capital at one time, and if you are
right at least some of the time on these low-probability, high-potential-
reward bets, you will come out ahead in the end.
Of course, you also can use a combination of these two methods. For
example, I have found it helpful to take the main part of a position using a
184  •   The Intelligent Option Investor
combination of stock and ITM call options but also perhaps buying a few
OTM call options as well. As the investment ages and more data about the
company’s operations come in, if this information leads me to be more
bullish about the prospects of the stock, I may again increase my leverage
using OTM call options—especially when I see implied volatility trading at
a particularly low level or if the stock price itself is depressed because of a
generally weak market.
I used to be of the opinion that if you are confident in your valuation
and your valuation implies a big enough unlevered return, it is irrational
not to get exposure to that investment with as much leverage as possible.
A few large and painful losses of capital have convinced me that where-
as levering up on high-conviction investments is theoretically a rational
investment regime, practically, it is a sucker’s game that is more likely to
deplete your investment capital than it is to allow you to hit home runs.
Y ounger investors, who still have a long investing career ahead of
them and plenty of time to make up for mistakes early on, probably can
feel more comfortable using more leverage, but as you grow closer to the
time when you need to use your investments (e.g., paying for retirement,
kids’ college expenses, or whatever), using lower leverage is better.
Looking back at the preceding tables, one row in one table in particular
should stand out to you. This is the last row of the last table, where the leverage is
−1.8/2.6. To me, this is a very attractive leverage ratio because of the asymmetry
in the risk-reward balance. This position is levered, but the leverage is lopsided
in the investor’s favor, so the investor stands to win more than he or she loses.
This asymmetry is the key to successful investing—not only from a
leverage standpoint but also from an economic standpoint as well. I believe
an intelligent, valuation-centric method for investing in companies such as
the ones outlined in this book that allow investors an edge up by allowing
them to identify cases in which the valuation simply does not line up with
the market price. This in itself presents an asymmetrical profit opportunity,
and the real job of an intelligent investor is to find as large an asymmetry
as possible and courageously invest in that company. If you can also tailor
your leverage such that your payout is asymmetrical in your favor as well,
this only adds potential for outsized returns, in my opinion.
The other reason that the −1.8/2.6 leverage ratio investment interests
me is because of the similarity it has to the portfolio of Warren Buffett’s
Understanding and Managing Leverage    • 185
Berkshire Hathaway (BRK.A). In a recent academic paper written by re-
searchers at AQR Capital titled, “Buffett’s Alpha, ”4 the researchers found
that a significant proportion of Buffett’s legendary returns can be attributed
to finding firms that have low valuation risk and investing in them using a
leverage ratio of roughly 1.8. The leverage comes from the float from his in-
surance companies (the monies paid in premium by clients over and above
that required to pay out claims). As individual investors, we do not have a
captive insurance company from which we can receive continual float, but
by buying options and using leverage prudently, it is possible to invest in a
manner similar to a master investor.
In this section, we have only discussed leverage considerations when
we gain exposure by buying options. There is a good reason to ignore the
case where we are accepting exposure by selling options that we will dis-
cuss when we talk about margining in Chapter 10. We now continue with
chapters on gaining, accepting, and mixing exposure. In these chapters, we
will use all of what we have learned about option pricing, valuation, and
leverage to discuss practical option investment strategies.
This page intentionally left blank
187
Chapter 9
GaininG ExposurE
This chapter is designed as an encyclopedic listing of the main strategies
for gaining exposure (i.e., buying options) that an intelligent option inves-
tor should understand. Gaining exposure seems easy in the beginning be-
cause it is straightforward—simply pay your premium up front, then if the
stock moves into your option’s range of exposure by expiration time, you
win.


9
GaininG ExposurE
This chapter is designed as an encyclopedic listing of the main strategies
for gaining exposure (i.e., buying options) that an intelligent option inves-
tor should understand. Gaining exposure seems easy in the beginning be-
cause it is straightforward—simply pay your premium up front, then if the
stock moves into your option’s range of exposure by expiration time, you
win. However, the more you use these strategies in investing exposure, the
more nuances arise.
What tenor should I choose? What strike price should I choose?
Should I exercise early if my option is in the money (ITM)? How much
capital should I commit to a given trade? If the stock price goes in the
opposite direction from my option’s range of exposure, should I close
my option position? All these questions are examples of why gaining
exposure by buying options is not as straightforward a process as it
may seem at first and are all the types of questions I will cover in the
following pages.
Gaining exposure means buying options, and the one thing that an
option buyer must never lose sight of is that time is always working against
him or her. Options expire. If your options expire out of the money (OTM),
the capital you spent on premiums on those options is a realized loss. No
matter how confident you are about your valuation call, you should al-
ways keep this immutable truth of option buying in mind. Indeed, there
are ways to reduce the risk of this happening or to manage a portfolio in
188  •   The Intelligent Option Investor
such a way that such a loss of capital becomes just a cost of doing business
that will be made up for in another investment down the line.
For each of the strategies mentioned in this chapter, I present
a stylized graphic representing the Black-Scholes-Merton model
(BSM) cone and the option’s range of exposure plus best- and worst-
case valuation scenarios. These are two of the required inputs for an
intelligent option investing strategy—an intelligently determined valu-
ation range and the mechanically determined BSM forecast range. I will
also provide a summary of the relative pricing of upside and downside
exposure vis-à-vis an intelligent valuation range (e.g., “Upside expo-
sure is undervalued”), the steps taken to execute the strategy, and its
potential risks and return.
After this summary section, I provide textual discussions of tenor se-
lection, strike price selection, portfolio management (i.e., rolling, exercise,
etc.), and any miscellaneous items of interest to note. Understanding the
strategies well and knowing how to use the tools at your disposal to tilt
the balance of risk and reward in your favor are the hallmark and pinnacle
of intelligent option investing. Intelligent option investors gain exposure
when the market underestimates the likelihood of a valuation that the in-
vestor believes is a rational outcome. In graphic terms, this means that ei-
ther one or both of the investor’s best- and worst-case valuation scenarios
lie outside the BSM cone.
Simple (one-option) strategies to gain exposure include
• Long calls
• Long puts
Complex (multioption) strategies to gain exposure include
• Long strangles
• Long straddles
Jargon introduced in this chapter includes the following:
Roll
Ratio(ing)
Gaining Exposure • 189
Long Call
GREEN
Downside: Fairly priced
Upside: Undervalued
Execute: Buy a call option
Risk: Amount equal to premium paid
Reward: Unlimited less amount of premium paid
The Gist
An investor uses this strategy when he or she believes that there is a material
chance that the value of a company is much higher than the present market price.
The investor must pay a premium to initiate the position, and the proportion of
the premium that represents time value should be recognized as a realized loss
because it cannot be recovered. If the stock fails to move into the area of exposure
before option expiration, there will be no profit to offset this realized loss.
In economic terms, this transaction allows an investor to go long an
undervalued company without accepting an uncertain risk of loss if the
stock falls. Instead of the uncertain risk of loss, one must pay the fixed pre-
mium. This strategy obeys the same rules of leverage as discussed earlier
in this book, with in-the-money (ITM) call options offering less leverage
but being much more forgiving regarding timing than are at-the-money
(ATM) or especially out-of-the-money (OTM) options.
190  •   The Intelligent Option Investor
T enor Selection
In general, the rule for gaining exposure is to buy as long a tenor as is
available. If a stock moves up faster than you expected, the option will still
have time value left on it, and you can sell it to recoup the extra money you
spent to buy the longer-tenor option. In addition, long-tenor options are
usually proportionally less expensive than shorter-tenor ones. Y ou can see
this through the following table. These ask prices are for call options on
Google (GOOG) struck at whatever price was closest to the 50-delta mark
for every tenor available.
Days to Expiration Ask Price Marginal Price/Day Delta
3 6.00 2.00 52
10 10.30 0.61 52
17 12.90 0.37 52
24 15.50 0.37 52
31 17.70 0.31 52
59 22.40 0.17 49
87 34.40 0.43 50
150 42.60 0.13 50
178 47.30 0.17 50
241 56.00 0.14 50
542 86.40 0.10 50
The “Marginal Price/Day” column is simply the extra that you pay to get
the extra days on the contract. For example, the contract with three days left is
$6.00. For seven more days of exposure, you pay a total of $4.30 extra, which
works out to a per-day rate of $0.61. We see blips in the marginal price per
day field as we go from 59 to 87 to 150 days, but these are just artifacts of data
availability; the closest strikes did not have the same delta for each expiration.
The preceding chart, it turns out, is just the inverse of the rule we
already learned in Chapter 3: “time value slips away fastest as we get closer
to expiration. ”


a per-day rate of $0.61. We see blips in the marginal price per
day field as we go from 59 to 87 to 150 days, but these are just artifacts of data
availability; the closest strikes did not have the same delta for each expiration.
The preceding chart, it turns out, is just the inverse of the rule we
already learned in Chapter 3: “time value slips away fastest as we get closer
to expiration. ” If time value slips away more quickly nearer expiration, it
must mean that the time value nearer expiration is proportionally worth
more than the time value further away from expiration. The preceding
table simply illustrates this fact.
Gaining Exposure • 191
Value investors generally like bargains and to buy in bulk, so we
should also buy our option time value “in bulk” by buying the longest
tenor available and getting the lowest per-day price for it. It follows that if
long-term equity anticipation securities (LEAPS) are available on a stock,
it is usually best to buy one of those. LEAPS are wonderful tools because,
aside from the pricing of time value illustrated in the preceding table, if
you find a stock that has undervalued upside potential, you can win from
two separate effects:
1. The option market prices options as if underlying stocks were ef-
ficiently priced when they may not be (e.g., the market thinks that
the stock is worth $50 when it’s worth $70). This discrepancy gives
rise to the classic value-investor opportunity.
2. As long as interest rates are low, the drift term understates the ac-
tual, probable drift of the stock market of around 10 percent per
year. This effect tends to work for the benefit of a long-tenor call
option whether or not the pricing discrepancy is as profound as
originally thought.
There are a couple of special cases in which this “buy the longest
tenor possible” rule of thumb should not be used. First, if you believe
that a company may be acquired, it is best to spend as little on time value
as possible. I will discuss this case again when I discuss selecting strike
prices, but when a company agrees to be acquired by another (and the
market does not think there will be another offer and regulatory approv-
als will go through), the time value of an option drops suddenly because
the expected life of the stock as an independent entity has been short-
ened by the acquiring company. This situation can get complicated for
stock-based acquisitions (i.e., those that use stocks as the currency of
acquisition either partly or completely) because owners of the acquiree’s
options receive a stake in the acquirer’s options with strike price adjusted
in proportion to the acquisition terms. In this case, the time value on
your acquiree options would not disappear after the acquisition but be
transferred to the acquirer’s company’s options. The real point is that it
is impossible, as far as I know, to guess whether an acquisition will be
made in cash or in shares, so the rule of thumb to buy as little time value
as possible still holds.
192  •   The Intelligent Option Investor
In general, attempting to profit from potential mergers is dif-
ficult using options because you have to get both the timing of the
suspected transaction and the acquisition price correct. I will discuss
a possible solution to this situation in the next section about picking
strike prices.
The second case in which it is not necessary to buy as long a tenor as
possible is when you are trading in expectation of a particular company
announcement. In general, this game of anticipating stock price move-
ments is a hard one to win and one that value investors usually steer clear
of, but if you are sure that some announcement scheduled for a particular
day or week is likely to occur but do not want to make a long-term invest-
ment on the company, you can buy a shorter-tenor option that obviously
must include the anticipated announcement date. It is probably not a bad
idea to build in a little cushion between your expiration and the anticipated
date of the announcement because sometimes announcements are pushed
back and rescheduled.
Strike Price Selection
From the discussion regarding leverage in the preceding section, it is
clear that selecting strike prices has a lot to do with selecting what level
of leverage you have on any given bet. Ultimately, then, strike selec-
tion—the management of leverage, in other words—is intimately tied
to your own risk profile and the degree to which you are risk averse or
risk seeking.
My approach, which I will talk more about in the following section
on portfolio management, may be too conservative for others, but I put it
forward as one alternative among many that I have found over time to be
sensible. Any investment has risk to the extent that there is never perfect
certainty regarding a company’s valuation. Some companies have a fairly
tight valuation range—meaning that the confluence of their revenue stream,
profit stream, and investment efficacy does not vary a great deal from best to
worst case. Other companies’ valuation ranges are wide, with a few clumps
of valuation scenarios far apart or with just one or two outlying valuation
scenarios that, although not the most likely, are still materially probable.
Gaining Exposure • 193
On the rare occasion in which we find a company that has a valuation
range that is far different from the present market price (either tight
or wide), I would rather commit more capital to the idea, and for me,
committing more capital to a single idea means using less leverage. In other
words, I would prefer to buy an ITM call and lever at a reasonable rate (e.g.,
the −1.8 × /2.6 × level we saw in the Intel example earlier). Graphically, my
approach would look like this:
Advanced Building Corp. (ABC)
110
100
90
80
70
60
50
40
30
20
5/18/2012 5/20/2013 249 499 749 999
Date/Day Count
Stock Price
GREEN
ORANGE
Here I have bought a deep ITM call option LEAPS that gives me lev-
erage of a


, I would prefer to buy an ITM call and lever at a reasonable rate (e.g.,
the −1.8 × /2.6 × level we saw in the Intel example earlier). Graphically, my
approach would look like this:
Advanced Building Corp. (ABC)
110
100
90
80
70
60
50
40
30
20
5/18/2012 5/20/2013 249 499 749 999
Date/Day Count
Stock Price
GREEN
ORANGE
Here I have bought a deep ITM call option LEAPS that gives me lev-
erage of about −1.5/2.0. I have maximized my tenor and minimized my
leverage ratio with the ITM call. This structure will allow me to profit as
long as the stock goes up by the time my option expires, even if the stock
price does not hit a certain OTM strike price.
In the more common situation, in which we find a company that is
probably about fairly valued in most scenarios but that has an outlying
valuation scenario or two that doesn’t seem to be priced in properly by
the market, I will commit less capital to the idea but use more leverage.
Graphically, my approach would look more like this:
194  •   The Intelligent Option Investor
Advanced Building Corp. (ABC)
100
90
80
70
60
50
40
30
20
5/18/2012 5/20/2013 249 499 749 999
Date/Day Count
Stock Price
GREEN
Here I have again maximized my tenor by buying LEAPS, but this
time I increase my leverage to something like an “IRL/10.0” level in case
the stars align and the stock price sales to my outlier valuation.
Some people would say that the IIM approach is absolutely the op-
posite of a rational one. If you are—the counterargument goes—confident
in your valuation range, you should try to get as much leverage on that idea
as possible; buying an ITM option is stupid because you are not using the
leverage of options to their fullest potential. This counterargument has its
point, but I find that there is just too much uncertainty in the markets to be
too bold with the use of leverage.
Options are time-dependent instruments, and if your option expires
worthless, you have realized a loss on whatever time value you original-
ly spent on it. Economies, now deeply intertwined all over the globe, are
phenomenally complex things, so it is the height of hubris to claim that
I can perfectly know what the future value of a firm is and how long it will
take for the market price to reflect that value. In addition, I as a human
decision maker am analyzing the world and investments through a con-
genital filter based on behavioral biases.
Retaining my humility in light of the enormous complexity of the
marketplace and my ingrained human failings and expressing this humility
Gaining Exposure • 195
by using relatively less leverage when I want to commit a significant amount
of capital to an idea constitute, I have found, given my risk tolerance and
experience, the best path for me for a general investment.
In contrast, we all have special investment loves or wild hares or
whatever, and sometimes we must express ourselves with a commitment
of capital. For example, “If XYZ really can pull it off and come up with a
cure for AIDS, its stock will soar. ” In instances such as these, I would rather
commit less capital and express my doubt in the outcome with a smaller
but more highly levered bet. If, on average, my investment wild hares come
true every once in a while and, when they do, the options I’ve bought on
them pay off big enough to more than cover my realized losses on all those
that did not, I am net further ahead in the end.
These rules of thumb are my own for general investments. In the spe-
cial situation of investing in a possible takeover target, there are a few extra
considerations. A company is likely to be acquired in one of two situations:
(1) it is a sound business with customers, product lines, or geographic
exposure that another company wants, or (2) it is a bad business, either
because of management incompetence, a secular decline in the business, or
something else, but it has some valuable asset(s) such as intellectual prop-
erty that a company might want to have.
If you think that a company of the first sort may be acquired, I be-
lieve that it is best to buy ITM call options to attempt to minimize the time
value spent on the investment (you could also sell puts, and I will discuss
this approach in Chapter 10). In this case, you want to minimize the time
value spent because you know that the time value you buy will drain away
when a takeover is announced and accepted. By buying an ITM contract,
you are mainly buying intrinsic value, so you lose little time value if and
when the takeover goes through. If you think that a company of the second
sort (a bad company in decline) may be acquired, I believe that it is best to
minimize the time value spent on the investment by not buying a lot of call
contracts and by buying them OTM. In this case, you want to minimize the
time value spent using OTM options by limiting the number of contracts
bought because you do not want to get stuck losing too much capital if
and when the bad company’s stock loses value while you are holding the
options. Typical buyout premiums are in the 30 percent range, so buy-
ing call options 20 percent OTM or so should generate a decent profit if
196  •   The Intelligent Option Investor
the company is taken out. Just keep in mind that the buyout premium is
30 percent over the last price, not 30 percent over the price at which you
decided to make your investment. If you buy 20 percent OTM call options
and the stock decreases by 10 percent before a 30 percent premium buyout
is announced, you will end up with nothing, as shown in the following
timeline:
$12-Strike Options Bought When the Stock Is Trading for $10
• Stock falls to $9.
• Buyout is announced at 30 percent above last price—$11.70.
• 12-strike call owner’s profit = $0.
However, there is absolutely no assurance that an acguirer will pay some-
thing for a prospective acguiree. Depending on how keen the acquirer is to get
its hands on the assets of the target, it may actually allow


line:
$12-Strike Options Bought When the Stock Is Trading for $10
• Stock falls to $9.
• Buyout is announced at 30 percent above last price—$11.70.
• 12-strike call owner’s profit = $0.
However, there is absolutely no assurance that an acguirer will pay some-
thing for a prospective acguiree. Depending on how keen the acquirer is to get
its hands on the assets of the target, it may actually allow the target company
to go bankrupt and then buy its assets at $0.30 on the dollar or whatever. It is
precisely this uncertainty that makes it unwise to commit too much capital to
an idea involving a bad company—even if you think it may be taken out.
Portfolio Management
I like to think of intelligent option investing as a meal. In our investment
meal, the underlying instrument—the stock—should, in most cases, form
the main course.
People have different ideas about diversification in a securities portfolio
and about the maximum percentage of a portfolio that should be allocated to
a specific idea. Clearly, most people are more comfortable allocating a greater
percentage of their portfolio to higher-confidence ideas, but this is normal-
ly framed in terms of relative levels (i.e., for some people, a high-conviction
idea will make up 5 percent of their portfolio and a lower-conviction one
2.5 percent; for others, a high-conviction idea will make up 20 percent of their
portfolio and a lower-conviction one 5 percent). Rather than addressing what
size of investment meal is best to eat, let’s think about the meal’s composition.
Considering the underlying stock as the main course, I consider the
leverage as sauces and side dishes. ITM options positions are the main
Gaining Exposure • 197
sauce to make the main course more interesting and flavorful. Y ou can
layer ITM options onto the stock to increase leverage to a level with which
you feel comfortable. This does not have to be Buffett’s 1.8:1 leverage of
course. Levering more lightly will provide less of a kick when a company
performs according to your best-case scenario, but also carries less risk
of a severe loss if the company’s performance is mediocre or worse. OTM
option positions (and “long diagonals” to be discussed in Chapter 11) can
be thought of as a spicy side dish to the main meal. They can be added
opportunistically (when and if the firm in which you are investing has a
bad quarter and its stock price drops for temporary reasons involving sen-
timent rather than substance) for extra flavor. OTM options can also be
used as a snack to be nibbled on between proper meals. Snack, in this case,
means a smaller sized position in firms that have a small but real upside
potential but a greater chance that it is fairly valued as is, or in a company
in which you don’t have the conviction in its ability to create much value
for you, the owner.
Another consideration regarding the appropriate level of investment
leverage one should apply to a given position is how much operational
and financial leverage (both are discussed in detail in Appendix B) a firm
has. A firm that is highly levered will have a much wider valuation range
and will be much more likely to be affected by macroeconomic considera-
tions that are out of the control of the management team and inscrutable
to the investor. In these cases, I think the best response is to adjust one’s
investment leverage according to the principles of “margin of safety” and
contrarianism.
By creating a valuation range, rather than thinking only of a single point-
estimate for the value of the firm, we have unwittingly allowed ourselves to
become very skillful at picking appropriate margins of safety. For example, I
recently looked at the value of a company whose stock was trading for around
$16 per share. The company had very high operational and financial lever-
age, so my valuation range was also very large—from around $6 per share
worst case to around $37 per share best case with a most likely value of around
$25 per share. The margin of safety is 36 percent (= ($25 − $16)/ $25).
While some might think this is a reasonable margin of safety to take a bold,
concentrated position, I elected instead to take a small, unlevered one because
to me, the $9 margin of safety for this stock is still not wide enough. The best
198  •   The Intelligent Option Investor
time to take a larger position and to use more leverage is when the market is
pricing a stock as if it were almost certain that a company will face a worst-case
future when you consider this worst-case scenario to be relatively unlikely. In
this illustration, if the stock price were to fall by 50 percent—to the $8 per share
level—while my assessment of the value of the company remained unchanged
(worst, likely, and best case of $6, $25, and $37, respectively), I would think I
had the margin of safety necessary to commit a larger proportion of my portfo-
lio to the investment and add more investment leverage. With the stock sitting
at $8 per share, my risk ($8 − $6 = $2) is low and unlikely to be realized while
my potential return is large and much closer to being assured. With the stock’s
present price of $16 per share, my risk ($16 − $6 = $10) is large and when bad-
case scenarios are factored in along with the worst-case scenario, more likely
to occur.
Thinking of margins of safety from this perspective, it is obvious that
one should not frame them in terms of arbitrary levels (e.g., “I have a rule
to only buy stocks that are 30% or lower than my fair value estimate. ”), but
rather in terms informed by an intelligent valuation range. In this example,
a 36 percent margin of safety is sufficient for me to commit a small
proportion of my portfolio to an unlevered investment, but not to go “all
in. ” For a concentrated, levered position in this investment, I would need a
margin of safety approaching 76 percent (= ($25 − $6)/$25) and at least over
60 percent (= ($25 - $10)/$25).
When might such a