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A Complete Guide to the Futures mArket
 7. trading hours. Trading hours are listed in terms of the local times for the given exchange.
(all U.s. exchanges are currently located in either the eastern or Central time zones.)
 8. Daily price limit. exchanges normally specify a maximum amount by which the contract
price can change on a given day. For example, if the December corn contract closed at $4.10 on
the previous day, and the daily price limit is 25¢/bu, corn cannot trade above $4.35 or below
$3.85.
some markets employ formulas for increasing the daily limit after a specified number of
consecutive limit days.
in cases in which free market forces would normally seek an equilibrium price outside the
range boundaries implied by the limit, the market will simply move to the limit and virtually
cease to trade. For example, if after the market close the U.
s. Department of agriculture (UsDa)
releases a very bullish corn crop production estimate, which hypothetically would result in an
immediate 30¢/bu price rise in an unrestricted market, prices will be locked limit up (25¢/bu) the
next day. This means that the market will open and stay at the limit, with virtually no trading tak-
ing place. The reason for the absence of trading activity is that the limit rule restriction maintains
an artificially low price, leading to a deluge of buy orders at that price but few if any sell orders.
in the case of a very severe surprise event (e.g., sudden major crop damage), a market
could move several limits in succession, although such moves are less common than in the days
before near-24-hour electronic trading.
in such situations, traders on the wrong side of the
fence might not be able to liquidate their positions until the market trades freely. The new trader
should be aware of, but not be overly frightened by, this possibility, since such events of extreme
volatility rarely come as a complete surprise.
in most cases, markets vulnerable to such volatile
price action can be identified. some examples of such markets would include commodities in
which the UsDa is scheduled to release a major report, coffee or frozen concentrated orange
juice during their respective freeze seasons, and markets that have exhibited recent extreme
trading volatility. For some markets, the limit on the nearby contract is removed at some point
table 1.2 Contract Month Designations
Month ticker Designation
January F
February g
March H
april J
May K
June M
July n
august Q
september U
October V
november X
December Z

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9FOr Beginners Only
approaching expiration (frequently first notice day—see item 10). Daily price limits can change
frequently, so traders should consult the exchange on which their products trade to ensure they
are aware of current thresholds.
 9. Settlement type. Markets are designated either as physically deliverable or cash settled. in
Table 1.1, the e-mini s&P 500 futures are cash settled, while all the other markets can be physi-
cally delivered.
 10. First notice day. This is the first day on which a long can receive a delivery notice. First notice
day presents no problem for shorts, since they are not obligated to issue a notice until after the
last trading day. Furthermore, in some markets, first notice day occurs after last trading day,
presenting no problem to the long either, since all remaining longs at that point presumably
wish to take delivery. However, in markets in which first notice day precedes last trading day,
longs who do not wish to take delivery should be sure to offset their positions in time to avoid
receiving a delivery notice. (Brokerage firms routinely supply their clients with a list of these
important dates.)
although longs can pass on an undesired delivery notice by liquidating their
position, this transaction will incur extra transaction costs and should be avoided. Last notice
day is the final day a long can receive a delivery notice.
 11. last trading day. This is the last day on which positions can be offset before delivery becomes
obligatory for shorts and the acceptance of delivery obligatory for longs. as indicated previously,
the vast majority of traders will liquidate their positions before this day.
 12. Deliverable grade. This is the specific quality and type of the underlying commodity or finan-
cial instrument that is acceptable for delivery.
 ■ Volume and Open Interest
V olume is the total number of contracts traded on a given day. V olume figures are available for each
traded month in a market, but most traders focus on the total volume of all traded months.
Open interest is the total number of outstanding long contracts, or equivalently, the total number
of outstanding short contracts—in futures, the two are always the same. When a new contract begins
trading (typically about 12 to 18 months before its expiration date), its open interest is equal to zero.
if a buy order and sell order are matched, then the open interest increases to 1. Basically, open interest
increases when a new buyer purchases from a new seller and decreases when an existing long sells to
an existing short. The open interest will remain unchanged if a new buyer purchases from an existing
long or a new seller sells to an existing short.
V olume and open interest are very useful as indicators of a market’s liquidity.
not all listed futures mar-
kets are actively traded. some are virtually dormant, while others are borderline cases in terms of trading
activity. illiquid markets should be avoided, because the lack of an adequate order flow will mean that the
trader will often have to accept very poor trade execution prices if he wants to get in or out of a position.
generally speaking, markets with open interest levels below 5,000 contracts, or average daily
volume levels below 1,000 contracts, should be avoided, or at least approached very cautiously.
new markets will usually exhibit volume and open interest figures below these levels during their

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10a COMPleTe gUiDe TO THe FUTUres MarKeT
initial months (and sometimes even years) of trading. By monitoring the volume and open interest
fi gures, a trader can determine when the market’s level of liquidity is suffi cient to warrant participa-
tion. Figure 1.1 shows February 2016 gold (top) and april 2016 gold (bottom) prices, along with
their respective daily volume fi gures. February gold’s volume is negligible until november 2015,
at which point it increases rapidly into December and maintains a high level through January (the
February contract expires in late February). Meanwhile, april gold’s volume is minimal until Janu-
ary, at which point it increases steadily and becomes the more actively traded contract in the last
two days of January—even though the February gold contract is still a month from expiration at
that point.
 The breakdown of volume and open interest fi gures by contract month can be very useful in
determining whether a specifi c month is suffi ciently liquid. For example, a trader who prefers to
initiate a long position in a nine-month forward futures contract rather than in more nearby con-
tracts because of an assessment that it is relatively underpriced may be concerned whether its level
of trading activity is suffi cient to avoid liquidity problems. in this case, the breakdown of volume and
open interest fi gures by contract month can help the trader decide whether it is reasonable to enter
the position in the more forward contract or whether it is better to restrict trading to the nearby
contracts.
 Traders with short-term time horizons (e.g., intraday to a few days) should limit trading to the
most liquid contract, which is usually the nearby contract month.
 FIGURE  1.1 V olume shift in gold Futures
Chart created using Tradestation. ©Tradestation T echnologies, inc. all rights reserved.

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AN INTrOduCTION TO OPTIONS ON FuTureS
between the futures price and the strike price were less than the premium paid for the option, the
net result of the trade would still be a loss. In order for the call buyer to realize a net profit, the dif-
ference between the futures price and the strike price would have to exceed the premium at the time
the call was purchased (after adjusting for commission cost). The higher the futures price, the greater
the resulting profit. Of course, if the futures reach the desired objective, or the call buyer changes his
market opinion, he could sell his call prior to expiration.
4
The buyer of a put seeks to profit from an anticipated price decline by locking in a sales price.
Similar to the call buyer, his maximum possible loss is limited to the dollar amount of the premium
paid for the option. In the case of a put held until expiration, the trade would show a net profit if the
strike price exceeded the futures price by an amount greater than the premium of the put at purchase
(after adjusting for commission cost).
While the buyer of a call or put has limited risk and unlimited potential gain,
5 the reverse is true
for the seller. The option seller (“writer”) receives the dollar value of the premium in return for
undertaking the obligation to assume an opposite position at the strike price if an option is exercised.
For example, if a call is exercised, the seller must assume a short position in futures at the strike
price (since by exercising the call, the buyer assumes a long position at that price).
upon exercise,
the exchange’s clearinghouse will establish these opposite futures positions at the strike price. After
exercise, the call buyer and seller can either maintain or liquidate their respective futures positions.
The seller of a call seeks to profit from an anticipated sideways to modestly declining market. In
such a situation, the premium earned by selling a call will provide the most attractive trading oppor-
tunity. However, if the trader expected a large price decline, he would usually be better off going
short futures or buying a put—trades with open-ended profit potential. In a similar fashion, the seller
of a put seeks to profit from an anticipated sideways to modestly rising market.
Some novices have trouble understanding why a trader would not always prefer the buy side of an
option (call or put, depending on his market opinion), since such a trade has unlimited potential and
limited risk. Such confusion reflects the failure to take probability into account. Although the option
seller’s theoretical risk is unlimited, the price levels that have the greatest probability of occurring
(i.e., prices in the vicinity of the market price at the time the option trade occurs) would result in a net
gain to the option seller.
roughly speaking, the option buyer accepts a large probability of a small loss
in return for a small probability of a large gain, whereas the option seller accepts a small probability
of a large loss in exchange for a large probability of a small gain. In an efficient market, neither the
consistent option buyer nor the consistent option seller should have any advantage over the long run.
6
4 even if the call is held until the expiration date, it will usually still be easier to offset the position in the options
market rather than exercising the call.
5 T echnically speaking, the gains on a put would be limited, since prices cannot fall below zero; but for practical
purposes, it is entirely reasonable to speak of the maximum possible gain on a long put position as being unlimited.
6 T o be precise, this statement is not intended to imply that the consistent option buyer and consistent option seller
would both have the same expected outcome (zero excluding transactions costs). Theoretically, on average, it is rea-
sonable to expect the market to price options so there is some advantage to the seller to compensate option sellers for
providing price insurance—that is, assuming the highly undesirable exposure to a large, open-ended loss. So, in effect,
option sellers would have a more attractive return profile and a less attractive risk profile than option buyers, and it
is in this sense that the market will, on average, price options so that there is no net advantage to the buyer or seller.

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A Complete Guide to the Futures mArket
 ■ Factors That Determine Option Premiums
An option’s premium consists of two components:
Premiu mi ntri nsic v aluet imev alue=+
The intrinsic value of a call option is the amount by which the current futures price is above the strike
price. The intrinsic value of a put option is the amount by which the current futures price is below the
strike price. In effect, the intrinsic value is that part of the premium that could be realized if the option were
exercised and the futures contract offset at the current market price. For example, if July crude oil futures
were trading at $74.60, a call option with a strike price of $70 would have an intrinsic value of $4.60. The
intrinsic value serves as a floor price for an option. Why? Because if the premium were less than the intrinsic
value, a trader could buy and exercise the option, and immediately offset the resulting futures position,
thereby realizing a net gain (assuming this profit would at least cover the transaction costs).
Options that have intrinsic value (i.e., calls with strike prices below the current futures price and
puts with strike prices above the current futures price) are said to be in-the-money. Options with no
intrinsic value are called out-of-the-money options. An option whose strike price equals the futures
price is called an at-the-money option. The term at-the-money is also often used less restrictively to refer
to the specific option whose strike price is closest to the futures price.
An out-of-the-money option, which by definition has an intrinsic value of zero, nonetheless retains
some value because of the possibility the futures price will move beyond the strike price prior to the expi-
ration date. An in-the-money option will have a value greater than the intrinsic value because a position in
the option will be preferred to a position in the underlying futures contract.
reason: Both the option and
the futures contract will gain equally in the event of favorable price movement, but the option’s maximum
loss is limited. The portion of the premium that exceeds the intrinsic value is called the time value.
It should be emphasized that because the time value is almost always greater than zero, one should
avoid exercising an option before the expiration date. Almost invariably, the trader who wants to
offset his option position will realize a better return by selling the option, a transaction that will yield
the intrinsic value plus some time value, as opposed to exercising the option, an action that will yield
only the intrinsic value.
The time value depends on four quantifiable factors
7:
 1. the relationship between the strike price and the current futures price. As illus-
trated in Figure 34.1, the time value will decline as an option moves more deeply in-the-money
or out-of-the-money.
deeply out-of-the-money options will have little time value, since it is
unlikely the futures will move to (or beyond) the strike price prior to expiration. deeply in-
the-money options have little time value because these options offer very similar positions to
the underlying futures contracts—both will gain and lose equivalent amounts for all but an
extreme adverse price move. In other words, for a deeply in-the-money option, the fact that the
7 Theoretically, the time value will also be influenced by price expectations, which are a non-quantifiable factor.

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AN INTrOduCTION TO OPTIONS ON FuTureS
risk is limited is not worth very much, because the strike price is so far away from the prevailing
futures price. As Figure 34.1 shows, the time value will be at a maximum at the strike price.
 2. time remaining until expiration. The more time remaining until expiration, the greater
the time value of the option. This is true because a longer life span increases the probability
of the intrinsic value increasing by any specifi ed amount prior to expiration. In other words,
the more time until expiration, the greater the probable price range of futures. Figure 34.2
illustrates the standard theoretical assumption regarding the relationship between time value
and time remaining until expiration for an at-the-money option. Specifi cally, the time value is
 FIGURE  34.1 Theoretical Option Premium Curve
 Source: Chicago Board of Trade, Marketing department.
Call Option
Strike price
Intrinsic value
T -bond futures price130
132
134
136
138
140
Time value premium
8
6
4
2 Option premium
Strike price
Intrinsic
value
T-bond futures price
124
126
128
130
8
6
4
2 Option premium
Put Option
Time value premium
 FIGURE  34.2 Time Value decay
 Source: Options on Comex Gold Futures, published by Commodity
exchange, Inc. (COMeX), 1982.
Time value decay
94 10
Time remaining until expiration (months)
Time value premium

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A Complete Guide to the Futures mArket
table 34.2 Option prices as a Function of V olatility in
e-Mini S&p 500 Futures pricesa
annualized V olatility put or Call premium
10 22.88 ($1,144)
20 45.75 ($2,288)
30 68.62 ($3,431)
40 91.46 ($4,573)
50 114.29 ($5,715)
a At-the-money options at a strike price of 2000 with 30 days to expiration.
8 James Bowe, Option Strategies T rading Handbook (New Y ork, NY: Coffee, Sugar, and Cocoa exchange, 1983).
assumed to be a function of the square root of time. (This relationship is a consequence of the
typical assumption regarding the shape of the probability curve for prices of the underlying
futures contract.) Thus, an option with nine months until expiration would have 1.5 times the
time value of a four-month option with the same strike price
(; ;. )93 42 32 15== ÷=
and three times the time value of a one-month option (; ;)93 11 31 3== ÷= .
 3. V olatility. Time value will vary directly with the estimated volatility of the underlying futures
contract for the remaining lifespan of the option. This relationship is the result of the fact that
greater volatility raises the probability the intrinsic value will increase by any specified amount
prior to expiration. In other words, the greater the volatility, the larger the probable range of
futures prices. As Table 34.2 shows, volatility has a strong impact on theoretical option pre-
mium values.
Although volatility is an extremely important factor in determining option premium values,
it should be stressed that the future volatility of the underlying futures contract is never pre-
cisely known until after the fact. (In contrast, the time remaining until expiration and the rela -
tionship between the current price of futures and the strike price can be exactly specified at any
juncture.) Thus, volatility must always be estimated on the basis of historical volatility data. As
will be explained, this factor is crucial in explaining the deviation between theoretical and actual
premium values.
 4. Interest rates. The effect of interest rates on option premiums is considerably smaller than
any of the above three factors. The specific nature of the relationship between interest rates and
premiums was succinctly summarized by James Bowe
8:
The effect of interest rates is complicated because changes in rates affect not only the
underlying value of the option, but the futures price as well. Taking it in steps, a buyer
of any given option must pay the premium up front, and of course the seller receives
the money. If interest rates go up and everything else stays constant, the opportunity
cost to the option buyer of giving up the use of his money increases, and so he is will-
ing to bid less. Conversely, the seller of options can make more on the premiums by

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AN INTrOduCTION TO OPTIONS ON FuTureS
investing the cash received and so is willing to accept less; the value of the options fall.
However, in futures markets, part of the value of distant contracts in a carry market
reflects the interest costs associated with owning the commodity. An increase in the
interest rate might cause the futures price to increase, leading to the value of existing
calls going up. The net effect on calls is ambiguous, but puts should decline in value
with increasing interest rates, as the effects are reinforcing.
 ■ Theoretical versus Actual Option Premiums
There is a variety of mathematical models available that will indicate the theoretical “fair value” for an
option, given specific information regarding the four factors detailed in the previous section. Theoret-
ical values will approximate, but by no means coincide with, actual premiums.
does the existence of
such a discrepancy necessarily imply that the option is mispriced? definitely not. The model-implied
premium will differ from the actual premium for two reasons:
 1. The model’s assumption regarding the mathematical relationship between option prices (premi-
ums) and the factors that affect option prices may not accurately describe market behavior. This
is always true because, to some extent, even the best option-pricing models are only theoretical
approximations of true market behavior.
 2. The volatility figure used by an option-pricing model will normally differ somewhat from the
market’s expectation of future volatility. This is a critical point that requires further elaboration.
recall that although volatility is a crucial input in any option pricing formula, its value can
only be estimated. The theoretical “fair value” of an option will depend on the specific choice of a
volatility figure. Some of the factors that will influence the value of the volatility estimate are the
length of the prior period used to estimate volatility, the time interval in which volatility is mea-
sured, the weighting scheme (if any) used on the historical volatility data, and adjustments (if any)
to reflect relevant influences (e.g., the recent trend in volatility). It should be clear that any specific
volatility estimate will implicitly reflect a number of unavoidably arbitrary decisions.
different
assumptions regarding the best procedure for estimating future volatility from past volatility will
yield different theoretical premium values. Thus, there is no such thing as a single, well-defined fair
value for an option.
All that any option pricing model can tell you is what the value of the option should be given
the specific assumptions regarding expected volatility and the form of the mathematical relationship
between option prices and the key factors affecting them. If a given mathematical model provides a
close approximation of market behavior, a discrepancy between the theoretical value and the actual
premium means the market expectation for volatility, called the implied volatility, differs from the
historically based volatility estimate used in the model. The question of whether the volatility assump-
tions of a specific pricing model provide more accurate estimates of actual volatility than the implied
volatility figures (i.e., the future volatility suggested by actual premiums) can only be answered
empirically. A bias toward buying “underpriced” options (relative to the theoretical model fair value)

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OPTION TrAdINg STrATegIeS
 In most cases, it will make more sense for the trader simply to buy an in-the-money put since the
transaction costs will be lower. However, if a speculator is already short futures, the purchase of an
out-of-the-money call might present a viable alternative to liquidating this position and buying an
in-the-money put.
 tabLe 35.12b profit/Loss Calculations: Option-protected Short Futures—Short Futures + Long Out-
of-the-Money Call (Similar to Long In-the-Money put)
(1) (2) (3) (4) (5) (6)
Futures price at
expiration ($/oz)
premium of august $1,300
Call at Initiation ($/oz)
$ amount of
premium paid
profit/Loss on Short
Futures position
Call Value at
expiration
profit/Loss on position
[(4) + (5) – (3)]
1,000 9.1 $910 $20,000 $0 $19,090
1,050 9.1 $910 $15,000 $0 $14,090
1,100 9.1 $910 $10,000 $0 $9,090
1,150 9.1 $910 $5,000 $0 $4,090
1,200 9.1 $910 $0 $0 –$910
1,250 9.1 $910 –$5,000 $0 –$5,910
1,300 9.1 $910 –$10,000 $0 –$10,910
1,350 9.1 $910 –$15,000 $5,000 –$10,910
1,400 9.1 $910 –$20,000 $10,000 –$10,910
 FIGURE  35.12b Profi t/loss Profi le: Option-Protected Short Futures—Short Futures + long
Out-of-the-Money Call (Similar to long In-the-Money Put)
Price of August gold futures at option expiration ($/oz)
Futures price at time
of position initiation
Breakeven price = $1,190.90
Profit/loss at expiration ($)
1,000
10,000
15,000
20,000
5,000
−5,000
−10,000
−15,000
0
1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400
Strike price

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A Complete Guide to the Futures mArket
Strategy 13: Covered Call Write (Long Futures + Short Call)
example. Buy August gold futures at $1,200/oz and simultaneously sell an August $1,200 gold
futures call at a premium of $38.80/oz ($3,880). (See Table 35.13 and Figure 35.13.)
Comment. There has been a lot of nonsense written about covered call writing. In fact, even
the term is misleading. The implication is that covered call writing—the sale of calls against long
positions—is somehow a more conservative strategy than naked call writing—the sale of calls without
any offsetting long futures position. This assumption is absolutely false. Although naked call writing
implies unlimited risk, the same statement applies to covered call writing. As can be seen in Figure
35.13, the covered call writer merely exchanges unlimited risk in the event of a market advance (as is
the case for the naked call writer) for unlimited risk in the event of a market decline. In fact, the reader
can verify that this strategy is virtually equivalent to a “naked” short put position (see Strategy 35.6a).
One frequently mentioned motivation for covered call writing is that it allows the holder of a long
position to realize a better sales price. For example, if the market is trading at $1,200 and the holder
of a long futures contract sells an at-the-money call at a premium of $38.80/oz instead of liquidating
his position, he can realize an effective sales price of $1,238.80 if prices move higher (the $1,200
strike price plus the premium received for the sale of the call). And, if prices move down by no more
than $38.80/oz by option expiration, he will realize an effective sales price of at least $1,200. Pre-
sented in this light, this strategy appears to be a “heads you win, tails you win” proposition. However,
there is no free lunch. The catch is that if prices decline by more than $38.80, the trader will realize a
lower sales price than if he had simply liquidated the futures position. And, if prices rise substantially
higher, the trader will fail to participate fully in the move as he would have if he had maintained his
long position.
The essential point is that although many motivations are suggested for covered call writing, the
trader should keep in mind that this strategy is entirely equivalent to selling puts.
tabLe 35.13 profit/Loss Calculations: Covered Call Write—Long Futures + Short Call (Similar to
Short put)
(1) (2) (3) (4) (5) (6)
Futures price
at expiration
($/oz)
premium of
august $1,200 Call
at Initiation ($/oz)
$ amount of
premium received
profit/Loss on Long
Futures position
Call Value at
expiration
profit/Loss on position
[(3) + (4) – (5)]
1,000 38.8 $3,880 –$20,000 $0 –$16,120
1,050 38.8 $3,880 –$15,000 $0 –$11,120
1,100 38.8 $3,880 –$10,000 $0 –$6,120
1,150 38.8 $3,880 –$5,000 $0 –$1,120
1,200 38.8 $3,880 $0 $0 $3,880
1,250 38.8 $3,880 $5,000 $5,000 $3,880
1,300 38.8 $3,880 $10,000 $10,000 $3,880
1,350 38.8 $3,880 $15,000 $15,000 $3,880
1,400 38.8 $3,880 $20,000 $20,000 $3,880

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OPTION TrAdINg STrATegIeS
 Strategy 14: Covered put Write (Short Futures + Short put)
example . Sell August futures at $1,200 and simultaneously sell an August $1,200 gold futures put at
a premium of $38.70/oz ($3,870). (See Table 35.14 and Figure 35.14 .)
 FIGURE  35.13 Profi t/loss Profi le: Covered Call Write—long Futures + Short Call (Similar to
Short Put)
 Profi t/loss Profi le: Covered Call Write—long Futures + Short Call (Similar to
Price of August gold futures at option expiration ($/oz)
Profit/loss at expiration ($)
1,000
5,000
2,500
0
−2,500
−7 ,500
−10,000
−12,500
−15,000
−5,000
1,050 1,100 1,150 1,200 1,250
Futures price at time
of position initiation
and strike price
 Breakeven price
= $1,161 .20
1,300 1,350 1,400
−17 ,500
 tabLe 35.14 profit/Loss Calculations: Covered put Write—Short Futures + Short put (Similar to
Short Call)
(1) (2) (3) (4) (5) (6)
Futures price
at expiration
($/oz)
premium of
august $1,200 put
at Initiation ($/oz)
$ amount of
premium received
profit/Loss on Short
Futures position
put Value at
expiration
profit/Loss on position
[(3) + (4) – (5)]
1,000 38.7 $3,870 $20,000 $20,000 $3,870
1,050 38.7 $3,870 $15,000 $15,000 $3,870
1,100 38.7 $3,870 $10,000 $10,000 $3,870
1,150 38.7 $3,870 $5,000 $5,000 $3,870
1,200 38.7 $3,870 $0 $0 $3,870
1,250 38.7 $3,870 –$5,000 $0 –$1,130
1,300 38.7 $3,870 –$10,000 $0 –$6,130
1,350 38.7 $3,870 –$15,000 $0 –$11,130
1,400 38.7 $3,870 –$20,000 $0 –$16,130

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528A COMPleTe gUIde TO THe FUTUreS MArKeT
Comment. Comments analogous to those made for Strategy 13 would apply here. The sale of a put
against a short futures position is equivalent to the sale of a call. The reader can verify this by compar-
ing Figure 35.14 to Figure 35.4 a. The two strategies would be precisely equivalent (ignoring transac-
tion cost diff erences) if the put and call premiums were equal.
 Strategy 15: Synthetic Long Futures (Long Call + Short put)
example . Buy an August $1,150 gold futures call at a premium of $70.10/oz ($7,010) and simultane-
ously sell an August $1,150 gold futures put at a premium of $19.90/oz ($1,990). (See Table 35.15
and Figure 35.15 .)
Comment. A synthetic long futures position can be created by combining a long call and a short put
for the same expiration date and the same strike price. For example, as illustrated in Table 35.15 and Figure
 35.15 , the combined position of a long August $1,150 call and a short August $1,150 put is virtually
identical to a long August futures position. The reason for this equivalence is tied to the fact that the
diff erence between the premium paid for the call and the premium received for the put is approxi-
mately equal to the intrinsic value of the call. each $1 increase in price will raise the intrinsic value of
the call by an equivalent amount and each $1 decrease in price will reduce the intrinsic value of the
 FIGURE  35.14 Profi t/loss Profi le: Covered Put Write—Short Futures + Short Put (Similar
to Short Call)
Price of August gold futures at option expiration ($/oz)
1,000 1,050 1,100 1,150 1,200 1,250
Futures price at time
of position initiation
and strike price Breakeven price
= $1,238.70
1,300 1,350 1,400
Profit/loss at expiration ($)
5,000
2,500
0
−2,500
−7 ,500
−10,000
−12,500
−17 ,500
−15,000
−5,000

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529
OPTION TrAdINg STrATegIeS
 tabLe 35.15 profit/Loss Calculations: Synthetic Long Futures (Long Call + Short put)
(1) (2) (3) (4) (5) (6) (7) (8)
Futures price
at expiration
($/oz)
premium of
august $1,150
Call at Initiation
($/oz)
$ amount
of premium
paid
premium of
august $1,150
put at Initiation
($/oz)
$ amount
of premium
received
Call Value
at
expiration
put Value
at
expiration
profit/Loss on
position
[(5) − (3) + (6) − (7)]
1,000 70.1 $7,010 19.9 $1,990 $0 $15,000 −$20,020
1,050 70.1 $7,010 19.9 $1,990 $0 $10,000 −$15,020
1,100 70.1 $7,010 19.9 $1,990 $0 $5,000 −$10,020
1,150 70.1 $7,010 19.9 $1,990 $0 $0 −$5,020
1,200 70.1 $7,010 19.9 $1,990 $5,000 $0 −$20
1,250 70.1 $7,010 19.9 $1,990 $10,000 $0 $4,980
1,300 70.1 $7,010 19.9 $1,990 $15,000 $0 $9,980
1,350 70.1 $7,010 19.9 $1,990 $20,000 $0 $14,980
1,400 70.1 $7,010 19.9 $1,990 $25,000 $0 $19,980
 FIGURE  35.15 Profi t/loss Profi le: Synthetic long Futures (long Call + Short Put)
Price of August gold futures at option expiration ($/oz)
Profit/loss at expiration ($)
1,000
20,000
15,000
10,000
5,000
−5,000
−10,000
−15,000
−20,000
0
1,050 1,100 1,150 1,200 1,250
Futures price at time
of position initiation
Breakeven price
= $1,200.20
1,300 1,350 1,400

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56  •   The Intelligent Option Investor
This is so because the area of the range of exposure for the option on
the left that is bounded by the BSM probability cone is much smaller than
the range of exposure for the option on the right that is bounded by the
same BSM probability cone.
Time Value versus Intrinsic Value
One thing that I hope you will have noticed is that so far we have talked
about options that are either out of the money (OTM) or at the money
(ATM). In-the-money (ITM) options—options whose range of exposure
already contains the present stock price—may be bought and sold in just
the same way as ATM and OTM options, and the pricing principle is ex-
actly the same. That is, an ITM option is priced in proportion to how much
of its range of exposure is contained within the BSM probability cone.
However, if we think about the case of an OTM call option, we realize
that the price we are paying to gain access to the stock’s upside potential
is based completely on potentiality. Contrast this case with the case of an
ITM call option, where an investor is paying not only for potential upside
exposure but also for actual upside as well.
It makes sense that when we think about pricing for an ITM call option,
we divide the total option price into one portion that represents the poten-
tial for future upside and another portion that represents the actual upside.
These two portions are known by the terms time value and intrinsic value,
respectively. It is easier to understand this concept if we look at a specific
example, so let’s consider the case of purchasing a call option struck at $40
and having it expire in one year for a stock presently trading at $50 per share.
We know that a call option deals with the upside potential of a stock
and that buying a call option allows an investor to gain exposure to that up-
side potential. As such, if we buy a call option struck at $40, we have access
to all the upside potential over that $40 mark. Because the stock is trading
at $50 right now, we are buying two bits of upside: the actual bit and the
potential bit. The actual upside we are buying is $10 worth (= $50 − $40)
and is termed the intrinsic value of the option.
A simple way to think of intrinsic value that is valid for both call options
and put options is the amount by which an option is ITM. However, the option’s
cost will be greater than only the intrinsic value as long as there is still time

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The Intelligent Investor’s Guide to Option Pricing  •  57
before the option expires. The reason for this is that although the intrinsic value
represents the actual upside of the stock’s price over the option strike price,
there is still the possibility that the stock price will move further upward in the
future. This possibility for the stock to move further upward is the potential bit
mentioned earlier. Formally, this is called the time value of an option.
Let us say that our one-year call option struck at $40 on a $50 stock
costs $11.20. Here is the breakdown of this example’s option price into in-
trinsic and time value:
 $10.00 Intrinsic value: the amount by which the option is ITM
+ $1.20 Time value: represents the future upside potential of the stock
= $11.20 Overall option price
Recall that earlier in this book I mentioned that it is almost always a mis-
take to exercise a call option when it is ITM. The reason that it is almost always
a mistake is the existence of time value. If we exercised the preceding option,
we would generate a gain of exactly the amount of intrinsic value—$10. How-
ever, if instead we sold the preceding option, we would generate a gain totaling
both the intrinsic value and the time value—$11.20 in this example—and then
we could use that gain to purchase the stock in the open market if we wanted.
Our way of representing the purchase of an ITM call option from a
risk-reward perspective is as follows:
Advanced Building Corp. (ABC)
5/18/2012 5/20/2013 249 499 749
EBP = $51.25
999
100
90
80
70
60
50
40
30
20
Date/Day Count
Stock Price
GREEN
ORANGE

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

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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

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Finding Mispriced Options    • 151
$20-strike volatility. If you were interested in buying an ITM call option,
you would pay less time value for the $20-strike than for the $21-strike op-
tions—essentially the same investment. 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

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152  •   The Intelligent Option Investor
move randomly, which the BSM does—is the price level at which there is
an equal chance of the actual future stock price to be above or below. In
other words, the 50-delta mark represents the forward price of 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,

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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 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!

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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 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

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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 0.84 +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’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
-
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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 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

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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 (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

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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

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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.

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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. ” 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 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.

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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. 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.

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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 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

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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

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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’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

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214  •   The Intelligent Option Investor
from a portfolio of short puts with the yield I might generate from a cor -
porate bond portfolio. With this consideration, and keeping in mind that
these investments are unlevered, 2 the name of the game is to generate as
high a percentage return as possible over the investing time horizon while
minimizing the amount of real downside risk you are accepting.
T enor Selection
To maximize percentage return, in general, it is better to sell options with
relatively short-term expirations (usually tenors of from three to nine
months before expiration). This is just the other side of the coin of the
rule to buy long-tenor options: the longer the time to expiration, the less
time value there is on a per-day basis. The rule to sell shorter-tenor options
implies that you will make a higher absolute return by chaining together
two back-to-back 6-month short puts than you would by selling a single
12-month option at the beginning of the period.
During normal market conditions, selling shorter-tenor options is
the best tactical choice, but during large market downdrafts, when there
is terror in the marketplace and implied volatilities increase enormously
for options on all companies, you might be able to make more by sell-
ing a longer-tenor option than by chaining together a series of shorter-
tenor ones (because, presumably, the implied volatilities of options will
drop as the market stabilizes, and this drop means that you will make
less money on subsequent put sales). At these times of extreme market
stress, there are situations where you can find short-put opportunities
on long-tenor options that defy economic logic and should be invested
in opportunistically.
For example, during the terrible market drops in 2009, I found a
company whose slightly ITM put long-term equity anticipation securities
(LEAPS) were trading at such a high price that the effective buy price of
the stock was less than the amount of cash the firm had on its balance
sheet. Obviously, for a firm producing positive cash flows, the stock should
not trade at less than the value of cash presently on the balance sheet! I ef-
fectively got the chance to buy a firm with $6 of cash on the balance sheet
and the near certainty of generating about $2 more over the economic life
of the options for $5.50. The opportunity to buy $6–$8 worth of cash for

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Accepting Exposure   • 215
$5.50 does not come along very often, so you should take advantage of it
when you see it.
Of course, the absolute value of premium you will receive by writing
(jargon that means selling an option) a short-term put is less than the ab-
solute value of the premium you will receive by writing a long-term one.
3
As such, an investor must balance the effective buy price of the stock (the
strike price of the option less the amount of premium to be received) in
which he or she is investing in the short-put strategy with the percentage
return he or she will receive if the put expires OTM.
I will talk more about effective buy price in the next section, but keep
in mind that we would like to generate the highest percentage return pos-
sible and that this usually means choosing shorter-tenor options.
Strike Price Selection
In general, the best policy is to sell options at as close to the 50-delta [at-
the-money (ATM)] mark as one can because that is where time value for
any option is at its absolute maximum. Our expectation is that the option’s
time value will be worthless at expiration, and if that is indeed the case,
we will be selling time value at its maximum and “closing” our time value
position at zero—its minimum. In this way, we are obeying (in reverse
order) the old investing maxim “Buy low, sell high. ” Selling ATM puts
means that our effective buy price will be the strike price at which we sold
less the amount of the premium we received. It goes without saying that
an intelligent investor would not agree to accept the downside exposure
to a stock if he or she were not prepared to buy the stock at the effective
buy price.
Some people want to sell OTM puts, thereby making the effective buy
price much lower than the present market price. This is an understandable
impulse, but simply attempting to minimize the effective buy price means
that you must ignore the other element of a successful short put strategy:
maximizing the return generated. There are times when you might like to
sell puts on a company but only at a lower strike price. Rather than accept-
ing a lower return for accepting that risk, I find that the best strategy is
simply to wait awhile until the markets make a hiccup and knock down the
price of the stock to your desired strike price.

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216  •   The Intelligent Option Investor
Portfolio Management
As we have discussed, the best percentage returns on short-put investments
come from the sale of short-tenor ATM options. I find that each quarter there
are excellent opportunities to find a fairly constant stream of this type of short-
term bet that, when strung together in a portfolio, can generate annualized
returns in the high-single-digit to low-teens percentage range. This level of
returns—twice or more the yield recently found on a high-quality corporate
bond portfolio and closer to the bond yield on highly speculative small com-
panies with low credit ratings—is possible by investing in strong, high-quality
blue chip stocks. In my mind, it is difficult to allocate much money to corpo-
rate bonds when this type of alternative is available.
Some investors prefer to sell puts on stocks that are not very vola-
tile or that have had a significant run-up in price,
4 but if you think about
how options are priced, it is clear that finding stocks that the market
perceives as more volatile will allow you to generate higher returns. Y ou
can confirm this by looking at the diagrams of a short-put investment
given two different volatility scenarios. First, a diagram in which implied
volatility is low:
Advanced Building Corp. (ABC)
80
70
60
50
40
30
20
5/18/2012 5/20/2013 249 499 749 999
Date/Day Count
Stock Price
RED

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Mixing Exposure  •  243
ignore the fact that most people simply want to generate a bit of extra in-
come out of the holdings they already have and so are psychologically re-
sistant to both selling ATM (because this makes it more likely for their
shares to be called away) and selling at a time when the stock price sud-
denly drop (because they want to reap the benefit of the shares recovering).
Although I understand these sentiments, it is important to realize
that options are financial instruments and not magical ones. It would be
nice if we could simply find an investment tool that we could bolt onto
our present stock holdings that would increase the dividend a nice amount
but that wouldn’t put us at risk of having to deliver our beloved stocks to a
complete stranger; unfortunately, this is not the case for options.
For example, let’s say that you own stock in a company that is paying out
a very nice dividend yield of 5 percent at present prices. This is a mature firm
that has tons of cash flow but few opportunities for growth, so management
has made the welcome choice to return cash to shareholders. The stock is trad-
ing at $50 per share, but because the dividend is attractive to you, you are loathe
to part with the stock. As such, you would prefer to write the covered call at a
$55 or even a $60 strike price. A quick look at the BSM cone tells us why you
should not be expecting a big boost in yield from selling the covered calls:
80
Sold call
range of
exposure
70
60
50
40
30
20
5/18/2012 5/20/2013 249 499 749 999
Cash Flows R Us, Inc. (CASH)
Date/Day Count
Stock Price
GREEN
LIGHT GREENGRAY
LIGHT REDRED

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244  •   The Intelligent Option Investor
Clearly, the range of exposure for the $55-strike call is well above the
BSM cone. The BSM cone is pointing downward because the dividend rate
is 5 percent—higher than the risk-free rate. This means that BSM drift will
be lower. In addition, because this is an old, mature, steady-eddy kind of
company, the expected forward volatility is low. Basically, this is a perfect
storm for a low option price.
My suggestion is to either write calls on stocks you don’t mind de-
livering to someone else—stocks for which you are very confident in the
valuation range and are now at or above the upper bound—or simply to
look for a portfolio of short-put/covered-call investments and treat it like
a high-yield bond portfolio, as I described in Chapter 10 when explaining
short puts. It goes without saying that if you think that a stock has a lot of
unappreciated upside potential, it’s not a good idea to sell that exposure
away!
One other note about execution: as I have said, short puts and cov-
ered calls are the same thing, but a good many investors do not realize this
fact or their brokerages prevent them from placing any trade other than a
covered call. This leads to a situation in which there is a tremendous sup-
ply of calls. Any time there is a lot of supply, the price goes down, and you
will indeed find covered calls on some companies paying a lot less than
the equivalent short put. Because you will be accepting the same downside
exposure, it is better to get paid more for it, so my advice is to write the put
rather than the covered call in such situations.
To calculate returns for covered calls, I carry out the following steps:
1. Assume that you buy the underlying stock at the market price.
2. Deduct the money you will receive from the call sale as well as
any projected dividends—these are the two elements of your cash
inflow—from the market price of the stock. The resulting figure is
your effective buy price (EBP).
3. Divide your total cash inflow by the EBP .
I always include the projected dividend payment as long as I am writ-
ing a short-tenor covered call and there are no issues with the company
that would prevent it from paying the dividend. Owners of record have a
right to receive dividends, even after they have written a covered call on the

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Mixing Exposure  •  245
stock, so it makes sense to count the dividend inflow as one element that
reduces your EBP . In formula form, this turns out to be
−−Coveredc allr eturn= premiumr eceivedf romc all+ projectedd ividends
stockp rice premiumf romc allp rojected dividends
For a short put, you have no right to receive the dividend, so I find the
return using the following formula:
−Shortp ut return= premiumr eceivedf roms hort put
strikepricep remium from shortp ut
Common Pitfalls
Taking Profit
One mistake I hear people make all the time is saying that they are going
to “take profit” using a covered call. Writing a covered call is taking profit
in the sense that you no longer enjoy capital gains from the stock’s appre-
ciation, but it is certainly not taking profit in the sense of being immune
to falls in the market price of the stock. The call premium you receive will
cushion a stock price drop, but it will certainly not shield you from it. If
you want to take profits on a successful stock trade, hit the “Sell” button.
Locking in a Loss
A person sent me an e-mail telling me that she had bought a stock at $17,
sold covered calls on it when it got to $20 (in order to “take profits”), and
now that the stock was trading for $11, she wanted to know how she could
“repair” her position using options. Unfortunately, options are not magical
tools and cannot make up for a prior decision to buy a stock at $17 and ride
it down to $11.
If you are in such a position, don’t panic. It will be tempting to write
a new call at the lower ATM price ($11 in this example) because the cash
inflow from that covered call will be the most. Don’t do it. By writing a
covered call at the lower price, you are—if the shares are called away—
locking in a realized loss on the position. Y ou can see this clearly if you list
each transaction in the example separately.

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246  •   The Intelligent Option Investor
No. Buy/Sell Instrument
Price of
Instrument
Effective
Buy (Sell)
Price of
Stock Note
1 Buy Stock $17/share $17/share Original purchase
2 Sell Call option $1/share $16/share Selling a covered call
to take profits when
stock reaches $20/
share leaves the
investor with down-
side exposure and $1
in premium income.
3 Sell Call option $0.75 ($11.75/
share)
Stock falls to $11, and
investor sells another
covered call to
generate income to
ameliorate the loss.
In transaction 1, the investor buys the shares for $17. In transaction 2,
when the stock hits $20 per share, the investor sells a covered call and receives
$1 in premium. This reduces the effective buy price to $16 per share and
means that the investor will have to deliver the shares if the stock is trad-
ing at $20 or above at expiration. When the stock instead falls to $11, the
investor—wanting to cushion the pain of the loss—sells another ATM cov-
ered call for $0.75. This covered call commits the investor to sell the shares
for $11.75. No matter how you look at it, buying at $16 per share and sell-
ing at $11.75 per share is not a recipe for investing success.
The first step in such a situation as this—when the price of a stock
on which you have accepted downside exposure falls—is to look back
to your valuation. If the value of the firm has indeed dropped because
of some material negative news and the position no longer makes sense
from an economic perspective, just sell the shares and take the lumps.
If, however, the stock price has dropped but the valuation still makes
for a compelling investment, stay in the position; if the investment is

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Mixing Exposure  •  247
compelling enough, this is the time to figure out a clever way to get more
exposure to it.
Y ou can write calls as long as they are at least at the same strike
price as your previous purchase price or EBP; this just means that you
are buying at $16 and agreeing to sell at at least $16, in other words. Also
keep in mind that any dividend payment you receive you can also think
of as a reduction of your EBP—that cash inflow is offsetting the cost of
the shares. Factoring in dividends and the (very small) cash inflow as-
sociated with writing far OTM calls will, as long as you are right about
the valuation, eventually reduce your EBP enough so that you can make
a profit on the investment.
Over-/Underexposure
Options are transacted in contract sizes of 100 shares. If you hold a number
of shares that is not evenly divisible by 100, you must decide whether you
are going to sell the next number down of contracts or the next number
up. For example, let’s say that you own 250 shares of ABC. Y ou can either
choose to sell two call contracts (in which case you will not be receiving
yield on 50 of your shares) or sell three call contracts (in which case you
will be effectively shorting 50 shares). My preference is to sell fewer con-
tracts controlling fewer shares than I hold, and in fact, your broker may or
may not insist that you do so as well. If not, it is an unpleasant feeling to get
a call from a broker saying that you have a margin call on a position that
you didn’t know you had.
Getting Assigned
If you write covered calls, you live with the risk that you will have to deliver
your beloved shares to a stranger. Y ou can deliver your shares and use the
proceeds from that sale (the broker will deposit an amount equal to the
strike price times the contract multiplier into your account, and you get
to keep the premium you originally received) to buy the shares again, but
there is no way around delivering the shares if assigned.

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