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 aphrase, “We’re scared!”)
If we compare the delta-derived “cone” with atheoretically 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 abase. In the market,
this is what usually happens—participants start out with amechanically
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.

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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 acertain
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, Ichose an impor-
tant tech company with avery liquid stock, so it has plenty of expirations
and many strikes available so that we can get agranular look at deltas.
However, what if we were looking at Mueller Water’soption 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 alot of extrapolation to
try to figure out where the market’sidea of the BSM cone lies.
To get abetter picture of what the market is saying, Irecommend
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’sassumptions about the future price range of astock. Using the im-
plied volatility on heavily traded contracts as the true forward volatility
expected by the market allows us to create atheoretical BSM cone that we

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Finding Mispriced Options    • 155
can extend indefinitely into the future and that is probably alot closer to
representing actual market expectations for the forward volatility (and, by
extension, the range of future prices for astock). 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’slook at this process in the next section, where Ispell 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 Ihave eyeballed (and sometimes done aquick 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 ageneral idea of how likely the
market thinks aparticular 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 acomputer to
calculate the BSM. As such, I’mnot going to explain how to mathematically
derive the BSM cone. Instead, on my website Ihave an application that will
allow you to plug in afew numbers and create agraphic 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!

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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 amultitude
of volatility numbers is available. Which one should we look at? Each strike
price has its own implied volatility number. What strike price’svolatility
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 asingle volatility number. Iam not an academic, so Idon’tneces-
sarily care if these simplifying assumptions are congruent with theory.
Also, Iam not an arbitrageur, so Idon’tmuch 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’tdistort our perception to the degree that we make bad
economic choices.
Here are the assumptions that we will make:
1. The implied volatility on acontract 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’sbest idea
of the true forward volatility of the stock.
2. If abig 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 aheavily 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

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Finding Mispriced Options    • 157
to eyeball the ATM volatility for the one- and two-month contracts.
3. If there is alarge 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 astock to be, find anice, liquid near ATM strike’simplied volatility and use that. ” Most op-
tion trading is done in atight 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’sprice-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 Iwas looking at Oracle, Iwould 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 adifference between
calls and puts or between the bid and ask. The August expiration op-
tions look abit suspicious to me considering that their implied volatility
is acouple of percentage points below that of the others. It probably
doesn’tmake abig difference which you use, though. We are trying to
find opportunities that are severely mispriced, not trying to split hairs
of acouple of percentage points. All things considered, Iwould prob-
ably use anumber somewhere around 22 percent for Oracle’sforward
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

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158  •   The Intelligent Option Investor
For Mueller Water, it’salittle 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, Iwould probably end up picking the implied volatility
associated with the options struck at $7.50 and expiring in August 2013
(26 days until expiration). Iwas 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,
Iwould probably look closer at the call options’ implied volatilities. In the
end, Iwould have abid volatility of around 39 percent and an ask volatility
of around 46 percent. Because the bid-ask spread is large, Iwould probably
want to see acone for both the bid and ask.
Plugging in the 22.0/22.5 for Oracle,
2 Iwould 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

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Finding Mispriced Options    • 159
Plugging in the 39/46 for Mueller Water, Iwould 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
-
You 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 abig company or asmall one,
so I’ll just keep going with the Oracle example. After having done afull
valuation as shown in the exam valuation of Oracle on the IOI website,
you’ve got abest-case valuation, aworst-case valuation, and probably
an idea about what alikely valuation is. You simply draw those numbers
onto achart like this:

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Finding Mispriced Options    • 161
On the upside, we can see that our likely case valuation is $43 per share,
whereas the BSM’smost likely value is abit less than $35—adifference 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 acertain price
level. The BSM considers the $43 price level to be relatively unlikely, whereas
Iconsider it relatively likely. As such, Ibelieve 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, Iwill want to
gain exposure to Oracle’supside by buying low-priced call options.
On the downside, Inotice that there is afairly large discrepancy
between my worst-case valuation ($30) and the lower leg of the BSM cone
(approximately $24)—this is the region of the graph labeled “B, ” and the
separation between the two values is again (just by chance) about 20 percent.
The BSM is pricing options granting exposure to the downside—put
options—struck at $24 as if they were fairly likely to occur; something that
is fairly likely to occur will be priced expensively by the BSM. My analysis,
on the other hand, makes me think that the BSM’svaluation outcome is
very unlikely. The discrepancy implies that Ibelieve the put options to be
overvalued—the BSM sees a $24 valuation as likely, with expensive options,
whereas Isee 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 agraphic 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

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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 adeep 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 apercentage by altering the amount of one’sown capital
at risk in asingle investment.
Investment leverage is inextricably linked to borrowing money—this
is what Imean by the phrase “altering the amount of one’sown 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 acompany
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 aspeculative position.
Frequently people think of investing leverage as simply borrowing
money to invest. However, as Imentioned earlier, you can invest in options
for alifetime and never explicitly borrow money in the process. Ibelieve
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’stake alook at afew example investments—unlevered, levered
using debt, and levered using options.
Unlevered Investment
Let’ssay that you buy astock 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. Your unrealized percentage gain on this investment is

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166  •   The Intelligent Option Investor
And herein lies the painful lesson learned by many asoul 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’slook at an example
of gaining upside exposure on acompany.
Let’sassume we see a $50 per share stock that we believe is worth $85 (in
this example, Iam assuming that we only have apoint 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 aprice 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

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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 acall option as aconditional borrowing of
funds sometime in the future. Buying the call option, you are saying, “Imay want to borrow $65 two years from now. Iwill pay you some interest
up front now, and if Idecide 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’sown 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 agross profit of $20 (= $85 − $65) on an
investment of $1.50, for apercentage return of 1,233 percent! Obviously,
the call option works very much like aloan in terms of altering the
investor’scapital at risk and boosting subsequent investment returns.
However, although the leverage looks very similar, there are two impor -
tant differences:

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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 asunk 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 acon-
ventional loan is mandatory, so you have alarge 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 aprofit. What Imean 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 anice 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
amargin 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 asingle day, and the owner of acall option will never receive amargin call. The flip side of this benefit
is that although you are not at risk of losing aposition to amargin 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.

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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 Iwill discuss, the simple num-
bers are not enough to help an investor intelligently manage aportfolio
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 aderivative of the delta
1 factor we discussed in Chapter 7 and is
found using the following equation:
= ×Lambda deltas tock price
optionprice
Let’slook at an actual example. The other day, Ibought adeep 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 Ibought 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 ahard and fast number—achange in
price of either the stock or the option (as aresult of achange in volatility or
time value or whatever) will change the delta, and the lambda will change
based on those things.

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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 alarge influence on lambda. Let’stake alook 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’mshowing 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 asignificant expenditure of our own capital compared with
the size of the investment. Buying acall 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 asunk cost. Time value always
decays independent of the price changes of the underlying, so although an

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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 (ahigh capital-to-loan proportion), our investment leverage meas-
ured by lambda is arelatively low 2.50.
Now direct your attention to afar 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’sprice—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 alarge loan, our invest-
ment leverage soars to avery 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’sprice
when buying far OTM options than when buying far ITM options. This is
fine information for someone interested in more speculative strategies—if
aspeculator has the sense that astock 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 anice, highly levered profit.
However, there are several factors that limit the usefulness of lambda.
First, because delta is not aconstant, the leverage factor does not stay put
as the stock moves around. For someone who intends to hold aposition for
alonger 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

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172  •   The Intelligent Option Investor
the option’svalue. 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’ssee why using the three invest-
ments Imentioned earlier—an ITM call struck at $20, an OTM call struck
at $39, and along stock position at $31.
Ibelieve that there is agood 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 Iam right, and if this
stock hits the $43 mark just as my options expire,
2 what do Istand to gain
from each of these investments?
Let’stake alook.
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 aprofit net of
investment of $11.50. Netting $11.50 on an $11.50 investment generates apercentage 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’tit? Yes, that
percentage return is wonderful, until you realize that the absolute value
of your dollar winnings will not allow you to buy alatte 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 aquarter.
Recall the definition of leverage as away of “boosting investment re-
turns calculated as apercentage, ” and recall that in my previous discussion
of financial leverage, Imentioned 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

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Understanding and Managing Leverage    • 173
matter if asignificant chunk of your portfolio is exposed to those returns!
Lambda is agood measure to show how sensitive percentage returns are to
amove 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’ssay 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 athird 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’sstock, we would have to buy options
implying control over 300 shares to generate the same absolute profit for
our portfolio.
Icall 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 anotional value
for the contracts of $11,700. This value is called the notional amount of the
option position.
Some people calculate aleverage 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). Iactually 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.

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174  •   The Intelligent Option Investor
Understanding Leverage’s Effects on a Portfolio
Looking at leverage from alambda or notional control perspective gives
some limited information about leverage, but Ibelieve 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 aricher,
more nuanced view of how leverage stands to help or hurt our portfolio
and allows us more insight into how we can intelligently structure amixed
option-stock portfolio.
Let’sstart our discussion of leverage in aportfolio context by thinking
about how to select investments into aportfolio. 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’signore that
for amoment), 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 alimited 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 ameasure of our per -
ception of the riskiness of the investment
We might see apotential investment that would allow us to reap aprofit
of $9 for every $1 invested (i.e., we would gain agreat 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 aportfolio, most people set alimit on the proportion
of their portfolio they want to allocate to any one investment. Ipersonally
favor more concentrated positions, but let’ssay that you paid better atten-
tion to your finance professor in school than Idid and figure that you want
to limit your risk exposure to any one security to amaximum of $5 of your
$100 portfolio.
An unlevered portfolio means that each $5 allocation would be made
by spending $5 of your own capital. You would know that if the value of
the underlying security decreases by $2.50, the value of the allocation will

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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 alevered portfolio, each $5 allocation uses some proportion of
capital that is not yours—borrowed in the case of amargin 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. Arealized loss represents apermanent loss of capital—asunk 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—Italk about this
in Chapter 11 when Iaddress 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 arealized 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 again. Because the current market price of asecurity may not sit exactly between our fair value estimate and the point at
which we suffer arealized loss, our upside and downside leverage may be
different.
Let’ssee how this comes together with an actual example. For this ex-
ample, Ilooked at the price of Intel’s (INTC) shares and options when the
former were trading at $22.99. Let’ssay 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’musing as an investment horizon the
days to expiration of the longest-tenor long-term equity anticipation secu-
rities (LEAPS)], the allocation’sprofit and loss profile would be represented
graphically like this:

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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’sstock 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
aone-for-one basis with the price of the stock, so our leverage is 1.0.
Now that we have asense of what the graph for astraight stock
position looks like, let’stake alook at afew different option positions.
When Idrew 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’sstart with the ITM option and construct asimple-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

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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 arealized 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 atotal loss of invested capital—$4,800 in all—if
Intel’sstock 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 Idon’tbelieve that hockey-stick diagrams are terribly useful
for understanding individual option transactions, at aportfolio level, they
do represent the effect of leverage very well. This black line represents a

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Understanding and Managing Leverage    • 179
In this example, we suffer arealized 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 anegative.) This
equation just means that it takes adrop of 35 percent to realize aloss on
96 percent of the allocation.
The profit leverage is simply aratio of the levered portfolio’snet profit
to the unlevered portfolio’snet profit at the fair value estimate. For this
example, we have
== ×Profitleverage $4,200
$1,472 3.0

Let’sdo the same exercise for the ATM and OTM options and see
what fully levered portfolios with each of these options would look like
from arisk-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

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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 ahandsome potential profit—6.9 times higher than we
could earn using astraight 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 astep 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 Ihave
presented here. If you want to commit 5 percent of your portfolio to astraight stock idea, you have to spend 5 percent of your portfolio value on
stock, but this is not true for options. For example, Imight choose to spend
2.5 percent of my portfolio’sworth 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 aleverage perspective:

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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 atotal 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 asensible 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 afew 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’twork out by expiration time!
Similar to setting acash reserve, you also might decide to make an
investment that combines cash, stock, and options. For example, Imight
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:

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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’scapital. 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 Iwill describe leverage positions us-
ing the two following terms: loss leverage and profit leverage . Iwill write
these in the following way:
− X.x
Y.ywhere 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

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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
Arealized loss is, to me, serious business. There are times when an inves-
tor must take arealized loss—specifically when his or her view of the fair
value or fair value range of acompany 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 alow-load mutual fund and spend
your time doing something more productive.
The point is that taking arealized loss is not something you have to do
too often if you are agood investor, and hopefully, when those losses are taken,
they are small. As such, Ibelieve 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 arealized 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 ahigher leverage position is spending as little as possible of your
investment capital on it. This means that when you see that there is acom-
pany that has amaterial chance of being worth alot more or alot 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 aloss 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 acombination of these two methods. For
example, Ihave found it helpful to take the main part of aposition using a

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184  •   The Intelligent Option Investor
combination of stock and ITM call options but also perhaps buying afew
OTM call options as well. As the investment ages and more data about the
company’soperations come in, if this information leads me to be more
bullish about the prospects of the stock, Imay again increase my leverage
using OTM call options—especially when Isee implied volatility trading at
aparticularly low level or if the stock price itself is depressed because of agenerally weak market.
Iused to be of the opinion that if you are confident in your valuation
and your valuation implies abig enough unlevered return, it is irrational
not to get exposure to that investment with as much leverage as possible.
Afew large and painful losses of capital have convinced me that where-
as levering up on high-conviction investments is theoretically arational
investment regime, practically, it is asucker’sgame that is more likely to
deplete your investment capital than it is to allow you to hit home runs.
Younger investors, who still have along 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 avery attractive leverage ratio because of the asymmetry
in the risk-reward balance. This position is levered, but the leverage is lopsided
in the investor’sfavor, so the investor stands to win more than he or she loses.
This asymmetry is the key to successful investing—not only from aleverage standpoint but also from an economic standpoint as well. Ibelieve
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

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Understanding and Managing Leverage    • 185
Berkshire Hathaway (BRK.A). In arecent academic paper written by re-
searchers at AQR Capital titled, “Buffett’s Alpha, ”4 the researchers found
that asignificant proportion of Buffett’slegendary returns can be attributed
to finding firms that have low valuation risk and investing in them using aleverage 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 acaptive insurance company from which we can receive continual float, but
by buying options and using leverage prudently, it is possible to invest in amanner similar to amaster investor.
In this section, we have only discussed leverage considerations when
we gain exposure by buying options. There is agood reason to ignore the
case where we are accepting exposure by selling options that we will dis-
cuss when we talk about margining in Chapter 10. We now continue with
chapters on gaining, accepting, and mixing exposure. In these chapters, we
will use all of what we have learned about option pricing, valuation, and
leverage to discuss practical option investment strategies.

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187
Chapter 9
GaininG ExposurE
This chapter is designed as an encyclopedic listing of the main strategies
for gaining exposure (i.e., buying options) that an intelligent option inves-
tor should understand. Gaining exposure seems easy in the beginning be-
cause it is straightforward—simply pay your premium up front, then if the
stock moves into your option’srange of exposure by expiration time, you
win. However, the more you use these strategies in investing exposure, the
more nuances arise.
What tenor should Ichoose? What strike price should Ichoose?
Should Iexercise early if my option is in the money (ITM)? How much
capital should Icommit to agiven trade? If the stock price goes in the
opposite direction from my option’srange of exposure, should Iclose
my option position? All these questions are examples of why gaining
exposure by buying options is not as straightforward aprocess as it
may seem at first and are all the types of questions Iwill 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 arealized 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 aportfolio in

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188  •   The Intelligent Option Investor
such away that such aloss of capital becomes just acost of doing business
that will be made up for in another investment down the line.
For each of the strategies mentioned in this chapter, Ipresent
astylized graphic representing the Black-Scholes-Merton model
(BSM) cone and the option’srange 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. Iwill
also provide asummary 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, Iprovide 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 avaluation that the in-
vestor believes is arational outcome. In graphic terms, this means that ei-
ther one or both of the investor’sbest- 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)

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Gaining Exposure • 189
Long Call
GREEN
Downside: Fairly priced
Upside: Undervalued
Execute: Buy acall 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 amaterial
chance that the value of acompany is much higher than the present market price.
The investor must pay apremium to initiate the position, and the proportion of
the premium that represents time value should be recognized as arealized 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.

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190  •   The Intelligent Option Investor
Tenor Selection
In general, the rule for gaining exposure is to buy as long atenor as is
available. If astock 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. You 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 atotal of $4.30 extra, which
works out to aper-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.

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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 astock,
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 astock 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’sworth $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 along-tenor call
option whether or not the pricing discrepancy is as profound as
originally thought.
There are acouple of special cases in which this “buy the longest
tenor possible” rule of thumb should not be used. First, if you believe
that acompany may be acquired, it is best to spend as little on time value
as possible. Iwill discuss this case again when Idiscuss selecting strike
prices, but when acompany 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’soptions receive astake in the acquirer’soptions 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’scompany’soptions. The real point is that it
is impossible, as far as Iknow, 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.

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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. Iwill discuss
apossible 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 atenor as
possible is when you are trading in expectation of aparticular company
announcement. In general, this game of anticipating stock price move-
ments is ahard one to win and one that value investors usually steer clear
of, but if you are sure that some announcement scheduled for aparticular
day or week is likely to occur but do not want to make along-term invest-
ment on the company, you can buy ashorter-tenor option that obviously
must include the anticipated announcement date. It is probably not abad
idea to build in alittle 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 alot 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 Iwill talk more about in the following section
on portfolio management, may be too conservative for others, but Iput it
forward as one alternative among many that Ihave found over time to be
sensible. Any investment has risk to the extent that there is never perfect
certainty regarding acompany’svaluation. Some companies have afairly
tight valuation range—meaning that the confluence of their revenue stream,
profit stream, and investment efficacy does not vary agreat deal from best to
worst case. Other companies’ valuation ranges are wide, with afew 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.

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Gaining Exposure • 193
On the rare occasion in which we find acompany that has avaluation
range that is far different from the present market price (either tight
or wide), Iwould rather commit more capital to the idea, and for me,
committing more capital to asingle idea means using less leverage. In other
words, Iwould prefer to buy an ITM call and lever at areasonable 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 Ihave bought adeep ITM call option LEAPS that gives me lev-
erage of about −1.5/2.0. Ihave 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 acertain OTM strike price.
In the more common situation, in which we find acompany that is
probably about fairly valued in most scenarios but that has an outlying
valuation scenario or two that doesn’tseem to be priced in properly by
the market, Iwill commit less capital to the idea but use more leverage.
Graphically, my approach would look more like this:

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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 Ihave again maximized my tenor by buying LEAPS, but this
time Iincrease 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 arational 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 Ifind 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 aloss 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
Ican perfectly know what the future value of afirm is and how long it will
take for the market price to reflect that value. In addition, Ias ahuman
decision maker am analyzing the world and investments through acon-
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

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Gaining Exposure • 195
by using relatively less leverage when Iwant to commit asignificant amount
of capital to an idea constitute, Ihave found, given my risk tolerance and
experience, the best path for me for ageneral investment.
In contrast, we all have special investment loves or wild hares or
whatever, and sometimes we must express ourselves with acommitment
of capital. For example, “If XYZ really can pull it off and come up with acure for AIDS, its stock will soar. ” In instances such as these, Iwould rather
commit less capital and express my doubt in the outcome with asmaller
but more highly levered bet. If, on average, my investment wild hares come
true every once in awhile 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, Iam net further ahead in the end.
These rules of thumb are my own for general investments. In the spe-
cial situation of investing in apossible takeover target, there are afew extra
considerations. Acompany is likely to be acquired in one of two situations:
(1) it is asound business with customers, product lines, or geographic
exposure that another company wants, or (2) it is abad business, either
because of management incompetence, asecular decline in the business, or
something else, but it has some valuable asset(s) such as intellectual prop-
erty that acompany might want to have.
If you think that acompany of the first sort may be acquired, Ibe-
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 Iwill 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 atakeover 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 acompany of the second
sort (abad company in decline) may be acquired, Ibelieve that it is best to
minimize the time value spent on the investment by not buying alot 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’sstock 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 adecent profit if

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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’sprofit = $0.
However, there is absolutely no assurance that an acguirer will pay some-
thing for aprospective 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 abad company—even if you think it may be taken out.
Portfolio Management
Ilike to think of intelligent option investing as ameal. In our investment
meal, the underlying instrument—the stock—should, in most cases, form
the main course.
People have different ideas about diversification in asecurities portfolio
and about the maximum percentage of aportfolio that should be allocated to
aspecific idea. Clearly, most people are more comfortable allocating agreater
percentage of their portfolio to higher-confidence ideas, but this is normal-
ly framed in terms of relative levels (i.e., for some people, ahigh-conviction
idea will make up 5 percent of their portfolio and alower-conviction one
2.5 percent; for others, ahigh-conviction idea will make up 20 percent of their
portfolio and alower-conviction one 5 percent). Rather than addressing what
size of investment meal is best to eat, let’sthink about the meal’scomposition.
Considering the underlying stock as the main course, Iconsider the
leverage as sauces and side dishes. ITM options positions are the main

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Gaining Exposure • 197
sauce to make the main course more interesting and flavorful. You can
layer ITM options onto the stock to increase leverage to alevel 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 akick when acompany
performs according to your best-case scenario, but also carries less risk
of asevere loss if the company’sperformance is mediocre or worse. OTM
option positions (and “long diagonals” to be discussed in Chapter 11) can
be thought of as aspicy side dish to the main meal. They can be added
opportunistically (when and if the firm in which you are investing has abad 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 asnack to be nibbled on between proper meals. Snack, in this case,
means asmaller sized position in firms that have asmall but real upside
potential but agreater chance that it is fairly valued as is, or in acompany
in which you don’thave 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 agiven position is how much operational
and financial leverage (both are discussed in detail in Appendix B) afirm
has. Afirm that is highly levered will have amuch 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, Ithink the best response is to adjust one’sinvestment leverage according to the principles of “margin of safety” and
contrarianism.
By creating avaluation range, rather than thinking only of asingle 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, Irecently looked at the value of acompany 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 amost likely value of around
$25 per share. The margin of safety is 36 percent (= ($25 − $16)/ $25).
While some might think this is areasonable margin of safety to take abold,
concentrated position, Ielected instead to take asmall, unlevered one because
to me, the $9 margin of safety for this stock is still not wide enough. The best

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198  •   The Intelligent Option Investor
time to take alarger position and to use more leverage is when the market is
pricing astock as if it were almost certain that acompany will face aworst-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), Iwould think Ihad the margin of safety necessary to commit alarger 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’spresent 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., “Ihave arule
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 asmall
proportion of my portfolio to an unlevered investment, but not to go “all
in. ” For aconcentrated, levered position in this investment, Iwould need amargin of safety approaching 76 percent (= ($25 − $6)/$25) and at least over
60 percent (= ($25 - $10)/$25).
When might such alarge margin of safety present itself? Just when
the market has lost all hope and is pricing in disaster for the company.
This is where the contrarianism comes into play. The best time to make
alevered investment in acompany with high levels of operational lever -
age is when the rest of the market is mainly concerned about the possible
negative effects of that operational leverage. For example, during areces-
sion, consumer demand drops and idle time at factories increases. This
has aquick and often very negative effect on profitability for companies
that own the idle factories, and if conditions are bad enough or look to
have no near-term (i.e., within about six months) resolution, the price of
those companies’ stocks can plummet. Market prices often fall so low as to
imply, from avaluation perspective, that the factories are likely to remain
idled forever. In these cases, Ibelieve that not using investment leverage in
this case may carry with it more real risk than using investment leverage

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200  •   The Intelligent Option Investor
After you enter aposition and some time passes, it becomes clearer
what valuation scenario the company is tending toward. In some cases,
abit of information will come out that is critical to your valuation of the
company on which other market participants may not be focused. Obvi-
ously, if abit of information comes out that has abig, positive or negative
impact on your assessment of the company’svalue, you should adjust your
position size accordingly. If you believe the impact is positive, it makes
sense to build to aposition by increasing your shares owned and/or by
adding “spice” to that meal by adjusting your target leverage level. If the
impact is negative, it makes sense to start by reducing leverage (or you
can think of it as increasing the proportion of cash supporting aparticular
position), even if this reduction means realizing aloss. If the impact of the
news is so negative that the investment is no longer attractive from arisk-
reward perspective, Ibelieve that it should be closed and the lumps taken
sooner rather than later. Considering what we know about prospect theory,
this is psychologically adifficult thing to do, but in my experience, waiting
to close aposition in which you no longer have confidence seldom does
you any good.
Obviously, the risk/reward equation of an investment is also influ-
enced by astock’smarket price. If the market price starts scraping against
the upper edge of your valuation range, again, it is time to reduce leverage
and/or close the position.
If your options are in danger of expiring before astock has reached
your fair value estimate, you may roll your position by selling your option
position and using the proceeds to buy another option position at amore
distant tenor. At this time, you must again think about your target leverage
and adjust the strikes of your options accordingly. If the price of the stock
has decreased over the life of the option contract, this will mean that you
realize aloss, which is not an easy thing to do psychologically, but consid-
ering the limitations imposed by time for all option investments, this is an
unavoidable situation in this case.
One of the reasons Idislike investing in non-LEAPS call options is
that rolling means that not only do we have to pay another set of bro-
ker and exchange fees, but we also must pay both sides of the bid-ask
spread. Keeping in mind how wide the bid-ask spread can be with options
and what an enormous drag this can be on returns, you should carefully

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Gaining Exposure • 201
consider whether the prospective returns justify entering along call posi-
tion that will likely have to be rolled multiple times before the stock hits
your fair value estimate.
By the way, it goes without saying that to the extent that an option
you want to roll has asignificant amount of time value on it, it is better
to roll before time decay starts to become extreme. This usually occurs at
around three months before expiration. It turns out that option liquidity
increases in the last three months before expiration, and rolling is made
easier with the greater liquidity.
Having discussed gaining bullish exposure with this section about
long calls, let’snow turn to gaining bearish exposure in the following sec-
tion on long puts.
Long Put
GREEN
Downside: Undervalued
Upside: Fairly priced
Execute: Buy aput option
Risk: Amount of premium paid
Reward: Amount equal to strike price—premium
The Gist
An investor uses this strategy when he or she believes that it is very likely
that the value of acompany is much lower than the present market price.
The investor must pay apremium to initiate the position, and the propor-
tion of the premium that represents time value should be recognized as a

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202  •   The Intelligent Option Investor
realized loss because it cannot be recovered. If the stock fails to move into
the area of exposure before option expiration, there will be no profit to
offset this realized loss.
In economic terms, this transaction allows an investor to sell short
an overvalued company without accepting an uncertain risk of loss if the
stock rises. Instead of the uncertain risk of loss, the investor must pay the
fixed premium. This strategy obeys the same rules of leverage as discussed
earlier in this book, with ITM put options offering less leverage but agreat-
er cushion before realizing aloss than do ATM or OTM put options.
Tenor Selection
Shorting stocks, which is what you are doing when you buy put op-
tions, is hard work, not for the faint of heart. There are acouple of
reasons for this:
1. Markets generally go up, and for better or worse, arising tide usu-
ally does lift all boats.
2. Even when acompany is overvalued, it is hard to know what cata-
lyst will make that fact obvious to the rest of the market and when.
In the words of Jim Chanos, head of the largest short-selling hedge fund
in the world, the market is a “giant positive reinforcement machine. ”
1
It is psychologically difficult to hold abearish position when it seems
like the whole world disagrees with you. All these difficulties in taking
bearish positions are amplified by options because options are levered
instruments, and losses feel all the more acute when they occur on alevered position.
My rule for gaining bullish exposure is to pick the longest-tenor op-
tion possible. Imade the point that by buying LEAPS, you can enjoy alikely upward drift that exceeds the drift assumed by option pricing. When
buying puts, you are on the opposite side of this drift factor (i.e., the “ris-
ing tide lifts all boats” factor), and every day that the stock does not fall is
another day of time value that has decayed without you enjoying aprofit.
On the other hand, if you decide not to spend as much on time value and
buy ashorter-tenor put option, unless the market realizes that the stock is

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Gaining Exposure • 203
overvalued and it drops before the shorter option expires, you must pay the
entire bid-ask spread and the broker and exchange fees again when you roll
your put option.
The moral of the story is that when selecting tenors for puts, you need
to balance the existence of upward market drift (which lends weight to the
argument for choosing shorter tenors) with bid-ask spreads and other fees
(which lends weight to the argument for longer tenors). If you can iden-
tify acatalyst, you can plan the tenor of the option investment based on
the expected catalyst. However, it’sunfortunate but mysteriously true that
bearish catalysts have atendency to be ignored by the market’s “happy ma-
chine” until the instant when suddenly they are not and the shares collapse.
The key for ashort seller is to be in the game when the market realizes the
stock’sovervaluation.
Strike Price Selection
When it comes to strike prices, short sellers find themselves fighting drift
in much the same way as they did when selecting tenors. Ashort seller with
aposition in stocks can be successful if the shares he or she is short go up
less than other stocks in the market. The short exposure acts as ahedge to
the portfolio as awhole, and if it loses less money than the rest of the port-
folio gains, it can be thought of as asuccessful investment.
However, the definition for success is different for buyers of aput
option, who must not only see their bearish bets not go up by much but
rather must see their bearish bets fall if they are to enjoy aprofit. If the
investor wanting bearish exposure decides to gain it by buying OTM puts,
he or she must—as we learned in the section about leverage—accept arealized loss as soon as the put is purchased. If, on the other hand, the
investor wants to minimize the realized loss accepted up front, he or she
must accept that he or she is in alevered bearish position so that every
1 percent move to the upside for the stock generates aloss larger than 1
percent for the position.
There is another bearish strategy that you can use by accepting
exposure that Iwill discuss in the next section, but for investors who are
gaining bearish exposure, there is no way to work around the dilemma of
the option-based short seller just mentioned.

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204  •   The Intelligent Option Investor
Portfolio Management
There is certainly no way around the tradeoff between OTM and ITM
risk—the rules of leverage are immutable whether in abullish or abear -
ish investment—but there are some ways of framing the investment that
will allow intelligent investors to feel more comfortable with making
these types of bearish bets. First, Ibelieve that losses associated with abearish position are treated differently within our own minds than those
associated with bullish positions. The reason for this might be the fact
that if you decide to proactively invest in the market, you must buy se-
curities, but you need not sell shares short. The fact that you are losing
when you are engaged in an act that you perceive as unnecessary just
adds to asense of regret and self-doubt that is necessarily part of the
investing process.
In addition, investors seem to be able to accept underperform-
ing bullish investments in aportfolio context (e.g., “XYZ is losing, but
it’sonly 5 percent of my holdings, and the rest of my portfolio is up, so
it’sokay”) but look at underperforming bearish investments as if they
were the only investments they held (e.g., “I’mlosing 5 percent on that
damned short. Why did Iever short that stock in the first place?”). In gen-
eral, people have ahard time looking at investments in aportfolio con-
text (Iwill discuss this more when Italk about hedging in Chapter 11),
but this problem seems to be orders of magnitude worse in the case of abearish position.
My solution to this dilemma—perhaps not the best or most rational
from aperformance standpoint but most manageable to me from apsy-
chological one—is to buy OTM puts with much smaller position sizes than
Imight for bullish bets with the same conviction level. This means that Ihave smaller, more highly levered positions. The reason this works for me
is that once Ispend the premium on the put option, Iconsider the money
gone—asunk cost—and do not even bother to look at the mark-to-market
value of the option after that unless there is alarge drop in the stock price.
Somehow this acknowledgment of arealized loss up front is easier to han-
dle psychologically than watching my ITM put position suffer unrealized
losses of 1.5 times the rise of the stock every day.
This strategy may well be proof that Isimply am not anatural-born
short seller, and you are encouraged, now that you understand the issues

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206  •   The Intelligent Option Investor
avoid this extreme downside are worth much more than they are presently
trading at.
The entire premium paid must be treated as arealized loss because
it can never be recovered. If the stock fails to move into one of the areas
of exposure before option expiration, there will be no profit to offset this
realized loss.
There is no reason why you have to buy puts and calls in equal num-
bers. If you believe that both upside and downside scenarios are materially
possible but believe that the downside scenario is more plausible, you can
buy more puts than calls. This is called ratioing aposition.
Tenor Selection
Because the strangle is acombination of two strategies we have already
discussed, the considerations regarding tenor are the same as for each of
the components—that is, using the drift advantage in long-term equity an-
ticipating securities (LEAPS) and buying them or the longest-tenor calls
available and balancing the fight against drift and the cost of rolling and
buying perhaps shorter-tenor puts.
Strike Price Selection
Astrangle is slightly different in nature from its two components—long
calls and long puts. Astrangle is an option investor’sway of expressing
the belief that the market in general has underestimated the intrinsic
uncertainty in the valuation of afirm. Options are directional instru-
ments, but astrangle is astrategy that acknowledges that the investor
has no clear idea of which direction astock will move but only that
its future value under different scenarios is different from its present
market price.
Because both purchased options are OTM ones, this implies, in my
mind, amore speculative investment and one that lends itself to taking
profit on it before expiration. Nonetheless, my conservatism forces me to
select strike prices that would allow aprofit on the entire position if the
stock price is at one of the two strikes at expiration. Because Iam buying
exposure to both the upside and the downside, Ialways like to make sure

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