884 Part VI: Measuring and Trading VolatiHty
To answer the question, one must create two equations in two unknowns, xand
y. The unknowns represent the quantities of options to be bought and sold, respec
tively. The constants in the equations are taken from the table above.
The first equation represents gamma neutral:
0.045 X + 0.026 y = 0,
where
xis the number of April 50'sin the spread and yis the number of April 60's. Note
that the constants in the equation are the gammas of the two calls involved.
The second equation represents the desired vega risk of making 2.5 points, or $250,
if the volatility decreases:
0.08 X + 0.06 y = - 2.5,
where
xand yare the same quantities as in the first equation, and the constants in this equa
tion are the gammas of the options. Furthermore, note that the vega risk is negative,
since the spreader wants to profit if volatility decreases.
Solving the two equations in two unknowns by algebraic methods yields the fol
lowing results:
Equations:
0.045 X + 0.026 y = 0
0.08 X + 0.06 Y = - 2.5
Solutions:
X = 104.80
y = -181.45
This means that one would buy 105 April 50 calls, since xbeing positive means that
the options would be bought. He would also sell 181 April 60 calls (yis negative,
which implies that the calls would be sold). This is nearly the same ratio determined
in the previous example. The quantities are slightly higher, since the vega here is
-$250 instead of the -$238 achieved in the previous example.
Finally, one would again determine the amount of stock to buy or sell to neu
tralize the delta by computing the position delta:
Position delta = 105 x 0.47 - 181 x 0.17 = 18.58
Thus 1,858 shares of XYZ would be shorted to neutralize the position.

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Chapter 40: Advanced Concepts 885
Note: All the equations cannot be set equal to zero, or the solution will be all
zeros. This is easily handled by setting at least one equation equal to asmall, nonzero
quantity, such as 0.1. As long as at least one of the risk factors is nonzero, one can
determine the neutral ratio for all other factors merely by solving these simultaneous
equations. There are plenty of low-cost computer programs that can solve simultane
ous equations such as these.
This concept can be carried to greater lengths in order to determine the best
spread to create in order to achieve the desired results. One might even try to use
three different options, using the third option to neutralize delta, so that he wouldn'thave to neutralize with stock. The third equation would use deltas as constants and
would be set to equal zero, representing delta neutral. Solving this would require
solving three equations in three unknowns, asimple matter for acomputer.
As long as at least one of the risk factors is nonzero, one can determine the neu
tral ratio for all other factors merely by solving these simultaneous equations. Even
more importantly, the computer can scan many combinations of options that produce
aposition that is both gamma and delta neutral and has aspecific position vega
(-$238, for example). One would then choose the "best" spread of the available pos
sibilities by logical methods including, if possible, choosing one with positive theta,
so time is working in his favor.
To summarize, one can neutralize all variables, or he can specify the risk that he
wants to accept in any of them. Merely write the equations and solve them. It is best
to use acomputer to do this, but the fact that it can be done adds an entirely new,
broad dimension to option spreading and risk-reducing strategies.
EVALUATING A POSITION USING THE RISK MEASURES
The previous sections have dealt with establishing anew position and determining its
neutrality or lack thereof. However, the most important use of these risk measures is
to predict how aposition will perform into the future. At aminimum, aserious strate
gist should use acomputer to print out aprojection of the profits and losses and posi
tion risk at future expected prices. Moreover, this type of analysis should be done for
several future times in order to give the strategist an idea of how the passage of time
and the resultant larger movements by the underlying security would affect the posi
tion.
First, one would choose an appropriate time period - say, 7 days hence - for the
first analysis. Then he should use the statistical projection of stock prices (see Chapter
28 on mathematical applications) to determine probable prices for the underlying
security at that time. Obviously, this stock price projection needs to use volatility, and

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886 Part VI: Measuring and Trading Volatility
that is somewhat variable. But, for the purposes of such aprojection, it is acceptable
to use the current volatility. The results of as many as 9 stock prices might be dis
played: every one-half standard deviation from -2 through + 2 (-2.0, -1.5, -1.0,
-0.5, 0, 0.5, 1.0, 1.5, 2.0).
Example: XYZ is at 60 and has avolatility of 35%. Adistribution of stock prices 7
days into the future would be determined using the equation:
Future Price = Current Price xeav-ft
where
acorresponds to the constants in the following table: (-2.0 ... 2.0):
# Standard Deviations
-2.0
- 1.5
- 1.0
-0.5
0
0.5
1.0
1.5
2.0
Projected Stack Price
54.46
55.79
57.16
58.56
60.00
61.47
62.98
64.52
66.11
Again, refer to Chapter 28 on mathematical applications for amore in-depth
discussion of this price determination equation.
Note that the formula used to project prices has time as one of its components.
This means that as we look further out in time, the range of possible stock prices will
expand - anecessary and logical component of this analysis. For example, if the
prices were being determined 14 days into the future, the range of prices would be
from 52.31 to 68.82. That is, XYZ has the same probability of being at 54.46 in 7 days
that it has of being at 52.31 in 14 days. At expiration, some 90 days hence, the range
would be quite abit wider still. Do not make the mistake of trying to evaluate the
position at the same prices for each time period (7 days, 14 days, 1 rnonth, expiration,
etc.). Such an analysis would be wrong.
Once the appropriate stock prices have been determined, the following quanti
ties would be calculated for each stock price: profit or loss, position delta, position
gamma, position theta, and position vega. (Position rho is generally aless important
risk measure for stock and futures short-term options.) Armed with this information,
the strategist can be prepared to face the future. An important item to note: Amodel

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Chapter 40: Advanced Concepts 887
will necessarily be used to make these projections. As was shown earlier, if there is adistortion in the current implied volatilities of the options involved in the position,
the strategist should use the current implieds as input to the model for future option
price projections. If he does not, the position may look overly attractive if expensive
options are being sold or cheap ones are being bought. Atruer profit picture is
obtained by propagating the current implied volatility structure into the near future.
Using an example similar to the previous one aratio spread using short stock
to make it delta neutral - the concepts will be described.
Initial Position. XYZ is at 60. The January 70 calls, which have three months
until expiration, are expensive with respect to the January 60 calls. Astrategist
expects this discrepancy to disappear when the implied volatility of XYZ options
decreases. He therefore established the following position, which is both gamma
and delta neutral.
Position Delta Gamma
Long 100 January 60 calls 0.57 0.0723
Short 240 January 70 calls 0.20 0.0298
Short 800 XYZ
The risk measures for the entire position are:
Position delta: -38 shares (virtually delta neutral)
Position gamma: + 7 shares (gamma neutral)
Position theta: + $263
Position vega: -$827
Theta Vega
-0.020 0.109
-0.019 0.080
Thus, the position is both gamma and delta neutral. Moreover, it has the attrac
tive feature of making $263 per day because of the positive theta. Finally, as was the
intention of the spreader, it will make money if the volatility of XYZ declines: $827
for each percentage point decrease in implied volatility. Two equations in two
unknowns (gamma and vega) were solved to obtain the quantities to buy and sell. The
resulting position delta was neutralized by selling 800 XYZ.
The following analyses will assume that the relative expensiveness of the April
70 calls persists. These are the calls that were sold in the position. If that overpricing
should disappear, the spread would look more favorable, but there is no guarantee
that they will cheapen - especially over ashort time period such as one or two weeks.
How would the position look in 7 days at the stock prices determined above?

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888 Part VI: Measuring and Trading Vo/atillty
Stock
Price P&L Delta Gamma Theta Vega
54.46 1905 - 7.40 1.62 0.94 - 1.57
55.79 1077 - 4.90 2.07 1.18 - 1.96
57.16 606 1.97 2.13 1.53 - 2.90
58.56 528 0.74 1.65 2.00 -4.62
60.00 771 2.38 0.56 2.63 -7.22
61.47 1127 2.07 - 1.01 3.38 -10.63
62.98 1252 - 0.87 - 2.85 4.22 -14.56
64.52 702 - 6.73 - 4.67 5.07 -18.61
66.11 - 1019 -15.42 - 6.21 5.85 -22.31
In asimilar manner, the position would have the following characteristics after
14 days had passed:
Stock
Price P&L Delto Gamma Theta Vega
52.31 4221 - 9.10 0.69 0.55 - 0.98
54.14 2731 - 6.93 1.69 0.75 - 0.89
56.02 1782 - 2.87 2.51 1.06 - 1.21
57.98 1717 2.17 2.44 1.61 - 2.69
60.00 2577 5.85 1.00 2.51 -6.00
62.09 3839 5.29 - 1.63 3.73 -11.05
64.26 4361 - 1.55 - 4.61 5.09 -16.90
66.50 2631 -14.80 - 7.02 6.31 -22.17
68.82 - 2799 -32.83 - 8.32 7.18 -25.72
The same information will be presented graphically in Figure 40-13 so that
those who prefer pictures instead of columns of numbers can follow the discussions
easily.
First, the profitability of the spread can be examined. This profit picture
assumes that the volatility of XYZ remains unchanged. Note that in 7 days, there is asmall profit if the stock remains unchanged. This is to be expected, since theta was
positive, and therefore time is working in favor of this spread. Likewise, in 14 days,
there is an even bigger profit if XYZ remains relatively unchanged - again due to the
positive theta. Overall, there is an expected profit of $800 in 7 days, or $2,600 in 14
days, from this position. This indicates that it is an attractive situation statistically, but,
of course, it does not mean that one cannot lose money.

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Chapter 40: Advanced Concepts 889
Continuing to look at the profit picture, the downside is favorable to the spread
since the short stock in the position would contribute to ever larger profits in the case
that XYZ tumbles dramatically (see Figure 40-12). The upside is where problems
could develop. In 7 days, the position breaks even at about 65 on the upside; in 14
days, it breaks even at about 67.50.
The reader may be asking, "Why is there such adramatic risk to the upside? Ithought the position was delta neutral and gamma neutral." True, the position was
originally neutral with respect to both those variables. That neutrality explains the
flatness of the profit curves about the current stock price of 60. However, once the
stock has moved 1.50 standard deviations to the upside, the neutrality begins to dis
appear. To see this, let us look at Figures 40-13 and 40-14 that show both the posi
tion delta and position gamma 7 days and 14 days after the spread was established.
Again, these are the same numbers listed in the previous tables.
First, look at the position delta in 7 days (Figure 40-13). Note that the position
remains relatively delta neutral with XYZ between 57 and 63. This is because the
gamma was initially neutral. However, the position begins to get quite delta short if
XYZ rises above 63 or falls below 57 in 7 days. What is happening to gamma while
this is going on? Since we just observed that the delta eventually changes, that has to
mean that the position is acquiring some gamma.
FIGURE 40-12.
XYZ ratio spread, gamma and delta neutral.
4300
3400
2500
1600
~ 700 a..
0
-200 53 55 57 59 61 63
.-1100
-2000
Stock Price

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Chapter 40: Advanced Concepts 891
Figure 40-14 depicts the fact that gamma is not very stable, considering that it
started at nearly zero. If XYZ falls, gamma increases alittle, reflecting the fact that
the position will get somewhat shorter as XYZ falls. But since there are only calls cou
pled with short stock in this position, there is no risk to the downside. Positive
gamma, even asmall positive gamma like this one, is beneficial to stock movement.
The upside is another matter entirely. The gamma begins to become seriously
negative above astock price of 63 in 7 days. Recall that negative gamma means that
one'sposition is about to react poorly to price changes in the market - the position
will soon be "fighting the market." As the stock goes even higher, the gamma
becomes even more negative. These observations apply to stock price movements in
either 7 days or 14 days; in fact, the effect on gamma does not seem to be particu
larly dependent on time in this example, since the two lines on Figure 40-15 are very
close to each other.
The above information depicts in detailed form the fact that this position will
not behave well if the stock rises too far in too short atime. However, stable stock
prices will produce profits, as will falling prices. These are not earth-shattering con
clusions since, by simple observation, one can see that there are extra short calls plus
some short stock in the position. However, the point of calculating this information
in advance is to be able to anticipate where to make adjustments and how much to
adjust.
Follow-Up Action. How should the strategist use this information? Asim
plistic approach is to adjust the delta as it becomes non-neutral. This won'tdo
anything for gamma, however, and may therefore not necessarily be the best
approach. If one were to adjust only the delta, he would do it in the following
manner: The chart of delta (Figure 40-13) shows that the position will be
approximately delta short 800 shares if XYZ rises to 64.50 in aweek. One sim
ple plan would be to cover the 800 shares of XYZ that are short if the stock rises
to 64.50. Covering the 800 shares would return the position to delta neutral at
that time. Note that if the stock rises at aslower pace, the point at which the
strategist would cover the 800 shares moves higher. For example, the delta in 14
days (again in Figure 40-13) shows that XYZ would have to be at about 65.50 for
the position to be delta short 800 shares. Hence, if it took two weeks for XYZ to
begin rising, one could wait until 65.50 before covering the 800 shares and
returning the position to delta neutral.
In either case, the purchase of the 800 shares does not take care of the negative
gamma that is creeping into the position as the stock rises. The only way to counter
negative gamma is to buy options, not stock. To return aposition to neutrality with

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892 Part VI: Measuring and Trading Volatility
respect to more than one risk variable requires one to approach the problem as he
did when the position was established: Neutralize the gamma first, and then use stock
to adjust the delta. Note the difference between this approach and the one described
in the previous paragraph. Here, we are trying to adjust gamma first, and will get to
delta later.
In order to add some positive gamma, one might want to buy back (cover) some
of the January 70 calls that are currently short. Suppose that the decision is made to
cover when XYZ reaches 65.50 in 14 days. From the graph above, one can see that
the position would be approximately gamma short 700 shares at the time. Suppose
that the gamma of the January 70 calls is 0.07. Then, one would have to cover 100
January 70 calls to add 700 shares of positive gamma to the position, returning it to
gamma neutral. This purchase would, of course, make the position delta long, so
some stock would have to be sold short as well in order to make the position delta
neutral once again.
Thus, the procedure for follow-up action is somewhat similar to that for estab
lishing the position: First, neutralize the gamma and then eliminate the resulting
delta by using the common stock. The resulting profit graph will not be shown for
this follow-up adjustment, since the process could go on and on. However, afew
observations are pertinent. First, the purchase of calls to reduce the negative gamma
hurts the original thesis of the position - to have negative vega and positive theta, if
possible. Buying calls will add vega to and subtract theta from the position, which is
not desirable. However, it is more desirable than letting losses build up in the posi
tion as the stock continues to run to the upside. Second, one might choose to rerrwve
the position if it is profitable. This might happen if the volatility did decrease as
expected. Then, when the stock rallies, producing negative gamma, one might actu
ally have aprofit, because his assumption concerning volatility had been right. If he
does not see much further potential gains from decreasing volatility, he might use the
point at which negative gamma starts to build up as the exit point from his position.
Third, one might choose to accept the acquired gamma risk. Rather than jeopardize
his initial thesis, one may just want to adjust the delta and let the gamma build up.
This is no longer aneutral strategy, but one may have reasons for approaching the
position this way. At least he has calculated the risk and is aware of it. If he chooses
to accept it rather than eliminate it, that is his decision.
Finally, it is obvious that the process is dynamic. As factors change (stock price,
volatility, time), the position itself changes and the strategist is presented with new
choices. There is no absolutely correct adjustment. The process is more of an art than
ascience at times. Moreover, the strategist should continue to recalculate these prof
it pictures and risk measures as the stock moves and time passes, or if there is a

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Chapter 40: Advanced Concepts 893
change in the securities involved in the position. There is one absolute truism and
that is that the serious strategist should be aware of the risk his position has with
respect to at least the four basic measures of delta, gamma, theta, and vega. To be
ignorant of the risk is to be delinquent in the management of the position.
TRADING GAMMA FROM THE LONG SIDE
The strategist who is selling overpriced options and hedging that purchase with other
options or stock will often have aposition similar to the one described earlier. Large
stock movements - at least in one direction will typically be aproblem for such
positions. The opposite of this strategy would be to have aposition that is long
gamma. That is, the position does better if the stock moves quickly in one direction.
While this seems pleasing to the psyche, these types of positions have their own
brand of risk.
The simplest position with long gamma is along straddle, or abackspread
(reverse ratio spread). Another way to construct aposition with long gamma is to
invert acalendar spread - to buy the near-term option and to sell alonger-term one.
Since anear-term option has ahigher gamma than alonger-term one with the same
strike, such aposition has long gamma. In fact, traders who expect violent action in
astock often construct such aposition for the very reason that the public will come
in behind them, bid up the short-term calls (increasing their implied volatility), and
make the spread more profitable for the trader.
Unfortunately, all of these positions often involve being long just about every
thing else, including theta and vega as well. This means that time is working against
the position, and that swings in implied volatility can be helpful or harmful as well.
Can one construct aposition that is long gamma, but is not so subject to the other
variables? Of course he can, but what would it look like? The answer, as one might
suspect, is not an ironclad one.
For the following examples, assume these prices exist:
XYZ: 60
Option
March 60 call
June 60 call
Price
3.25
5.50
Delta
0.54
0.57
Gamma
0.0510
0.0306
Theta
0.033
0.021
Vega
0.089
0.147
Example: Suppose that astrategist wants to create aposition that is gamma long, but
is neutral with respect to both delta and vega. He thinks the stock will move, but is
not sure of the price direction, and does not want to have any risk with respect to

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894 Part VI: Measuring and Trading Volatility
quick changes in volatility. In order to quantify the statement that he "wants to be
gamma long," let us assume that he wants to be gamma long 1,000 shares or 10 con
tracts.
It is known that delta can always be neutralized last, so let us concentrate on the
other two variables first. The two equations below are used to determine the quanti
ties to buy in order to make gamma long and vega neutral:
0.0510x + 0.0306y = 10 (gamma, expressed in# of contracts)
0.089x + 0.147y = 0 (vega)
The solution to these equations is:
X = 308, y = -186
Thus, one would buy 308 March 60 calls and would sell 186 June 60 calls. This is the
reverse calendar spread that was discussed: Near-term calls are bought and longer
term calls are sold.
Finally, the delta must be neutralized. To do this, calculate the position delta
using the quantities just determined:
Position delta= 0.54 x 308 - 0.57 x 186 = 60.30
So, the position is long 60 contracts, or 6,000 shares. It can be made delta neutral by
selling short 6,000 shares of XYZ.
The overall position would look like this:
Position
Short 6,000 XYZ
Long 308 March 60 calls
Short 186 June 60 calls
Its risk measurements are:
Delta
1.00
0.54
0.57
Position delta: long 30 shares (neutral)
Position vega: $7 (neutral)
Position gamma: long 1,001 shares
Gamma
0
0.0510
0.0306
Vega
0
0.089
0.147
This position then satisfies the initial objectives of wanting to be gamma long
1,000 shares, but delta and vega neutral.
Finally, note that theta = -$625. The position will lose $625 per day from time
decay.
The strategist must go further than this analysis, especially if one is dealing with
positions that are not simple constructions. He should calculate aprofit picture as

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Chapter 40: Advanced Concepts 895
well as look at how the risk measures behave as time passes and the stock price
changes.
Figure 40-15 (see Tables 40-10, 40-11, and 40-12) shows the profit potential in
7 days, in 14 days, and at March expiration. Figure 40-16 shows the position vega at
the 7- and 14-day time intervals. Before discussing these items, the data will be pre
sented in tabular form at three different times: in 7 days, in 14 days, and at March
expiration.
The data in Table 40-10 depict the position in 7 days.
Table 40-11 represents the results in 14 days.
Finally, the position as it looks at March expiration should be known as well (see
Table 40-12).
In each case, note that the stock prices are calculated in accordance with the
statistical formula shown in the last section. The more time that passes, the further it
is possible for the stock to roam from the current price.
The profit picture (Figure 40-15) shows that this position looks much like along
straddle would: It makes large, symmetric profits if the stock goes either way up or
way down. Moreover, the losses if the stock remains relatively unchanged can be
large. These losses tend to mount right away, becoming significant even in 14 days.
Hence, if one enters this type of position, he had better get the desired stock move
ment quickly, or be prepared to cut his losses and exit the position.
The most startling thing to note about the entire position is the devastating effect
of time on the position. The profit picture shows that large losses will result if the stock
movement that is expected does not materialize. These losses are completely due to
time decay. Theta is negative in the initial position ($625 of losses per day), and
remains negative and surprisingly constant - until March expiration ( when the long
calls expire). Time also affects vega. Notice how the vega begins to get negative right
away and keeps getting much more negative as time passes. Simply, it can be seen that
as time passes, the position becomes vulnerable to increases in implied volatility.
This relationship between time and volatility might not be readily apparent to
the strategist unless he takes the time to calculate these sorts of tables or figures. In
fact, one may be somewhat confounded by this observation. What is happening is
that as time passes, the options that are owned are less explosive if volatility increas
es, but the options that were sold have alot of time remaining, and are therefore apt
to increase violently if volatility spurts upward.
Figures 40-17 and 40-18 provide less enlightening information about delta and
gamma. Since gamma was positive to start with, the delta increases dramatically as
the stock rises, and decreases just as fast if the stock falls (Figure 40-18). This is stan
dard behavior for positions with long gamma; along straddle would look very similar.

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Chapter 40: Advanced Concepts
FIGURE 40-16.
Trading long gamma, position vega.
55 60
0
-2
-4
al
0)
~
-6
-8
-10
Stock Price
TABLE 40-11.
65
Risk measures of long gamma position in 14 days.
Stock
Price P&L Delta Gamma
52.31 24945 - 79.34 4.75
54.14 11445 - 67.68 8.00
56.02 277 -49.79 10.79
57.98 - 7263 -26.87 12.42
60.00 - 10141 - 1.44 12.47
62.09 - 7784 23.32 10.99
64.26 347 44.47 8.45
66.50 11491 60.12 5.55
68.82 26672 69.81 2.92
891
Theta Vega
2.10 - 9.91
3.91 - 7.87
5.76 - 5.56
7.21 - 3.73
7.88 - 3.04
7.60 - 3.78
6.47 - 5.71
4.82 - 8.20
3.09 -10.48
So, is this agood position? That is adifficult question to answer unless one
knows what is going to happen to the underlying stock. Statistically, this type of posi
tion has anegative expected return and would generally produce losses over the long
run. However, in situations in which the near-term options are destined to get over
heated - perhaps because of atakeover rumor or just aleak of material information

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898 Part VI: Measuring and Trading Volatility
TABLE 40-12.
Risk measures of long gamma position at March expiration.
Stock
Price P&L Delta
46.19 81327 - 75.69
49.31 55628 - 89.84
52.64 22378 -110.50
56.20 - 21523 -136.65
60.00 78907 144.68
64.06 - 25946 117.44
68.39 19787 95.03
73.01 59732 79.05
77.95 96062 69.19
FIGURE 40-17.
Trading long gamma, position gamma.
(J)
(I)
1200
1000
800
~ 600 .c
(/)
400
200
55 60
Stock Price
Gamma Theta Vega
- 3.65 -1.32 - 6.88
- 5.39 -2.25 -11.43
- 6.89 -3.33 -16.50
- 7.62 -4.28 -20.67
- 7.29 -4.79 -22.49
- 6.03 -4.70 -21.26
- 4.31 -4.10 -17.44
- 2.67 -3.24 -12.43
- 1.43 -2.41 - 7.69
65
about acompany - many sophisticated traders establish this type of position to take
advantage of the expected explosion in stock price.
Other Variations. Without going into as much detail, it is possible to com
pare the above position with similar ones. The purpose in doing so is to illustrate
how achange in the strategist'sinitial requirements would alter the established

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Chapter 40: Advanced Concepts
FIGURE 40-1 8.
Trading long gamma, position delta.
6000
4000
2000
"' ~ 01---------,-----~rr------,,-----
.s::.
(J)
-2000
-4000
-8000
-8000
55 65
Stock Price
899
position. In the preceding position, the strategist wanted to be gamma long, but
neutral with respect to delta and volatility. Suppose he not only expects price
movement (meaning he wants positive gamma), but also expects an increase in
volatility. If that were the case, he would want positive vega as well. Suppose he
quantifies that desire by deciding that he wants to make $1,000 for every one
percentage increase in volatility. The simultaneous equations would then be:
0.050lx + 0.0306y = 10 (gamma)
0.089x + 0.147y = 10 (vega)
The solution to these equations is:
X = 243, y = -80
Furthermore, 8,500 shares would have to be sold short in order to make the position
delta neutral. The resulting position would then be:
Short 8,500 XYZ
Long 243 March 60 calls
Short 80 June 60 calls
Delta: neutral
Gamma: long 1,000 shares
Vega: long $1,000
Theta: long $630

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900 Part VI: Measuring and Trading VolatiHty
Recall that the position discussed in the last section was vega neutral and was:
Short 6,000 XYZ
Long 308 March 60 calls
Short 186 June 60 calls
Delta: neutral
Gamma: long 1,000 shares
Vega: neutral
Theta: long $625
Notice that in the new position, there are over three times as many long March
60 calls as there are short June 60 calls. This is amuch larger ratio than in the vega
neutral position, in which about 1.6 calls were bought for each one sold. This even
greater preponderance of near-term calls that are purchased means the newer posi
tion has an even larger exposure to time decay than did the previous one. That is, in
order to acquire the positive vega, one is forced to take on even more risk with
respect to time decay. For that reason, this is aless desirable position than the first
one; it seems overly risky to want to be both long gamma and long volatility.
This does not necessarily mean that one would never want to be long volatility.
In fact, if one expected volatility to increase, he might want to establish aposition that
was delta neutral and gamma neutral, but had positive vega. Again, using the same
prices as in the previous examples, the following position would satisfy these criteria:
Short 2,600 XYZ
Short 64 March 60 calls
Long 106 June 60 calls
Delta: neutral
Gamma: neutral
Vega: long $1,000
Theta: long $11
This position has amore conventional form. It is acalendar spread, except that
more long calls are purchased. Moreover, the theta of this position is only $11- it will
only lose $11 per day to time decay. At first glance it might seem like the best of the
three choices. Unfortunately, when one draws the profit graph (Figure 40-19), he
finds that this position has significant downside risk: The short stock cannot com
pensate for the large quantity of June 60 calls. Still, the position does make money on
the upside, and will also make money if volatility increases. If the near-term March
calls were overpriced with respect to the June calls at the time the position was estab
lished, it would make it even more desirable.
To summarize, defining the risks one wants to take or avoid specifies the con
struction of the eventual position. The strategist should examine the potential risks
and rewards, especially the profit picture. If the potential risks are not desirable, the
strategist should rethink his requirements and try again. Thus, in the example pre
sented, the strategist felt that he initially wanted to be long gamma, but it involved too

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Chapter 40: Advanced Concepts
FIGURE 40-19.
Trading long gamma, 11 conventional" calendar.
7500
5000
2500
fJ)
fJ)
.3 :;:, 0 '§ 45 50 Q.
-2500
-5000 At March Expiration
-7500
Stock Price
901
75
much risk of time decay. Asecond attempt was made, introducing positive volatility
into the situation, but that didn'tseem to help much. Finally, athird analysis was gen
erated involving only long volatility and not long gamma. The resulting position has lit
tle time risk, but has risk if the stock drops in price. It is probably the best of the three.
The strategist arrives at this conclusion through alogical process of analysis.
ADVANCED MATHEMATICAL CONCEPTS
The remainder of this chapter is ashort adjunct to Chapter 28 on mathematical
applications. It is quite technical. Those who desire to understand the basic concepts
behind the risk measures and perhaps to utilize them in more advanced ways will be
interested in what follows.
CALCULATING THE "'GREEKS"
It is known that the equation for delta is adirect byproduct of the Black-Scholes
model calculation:
~ = N(dl)

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902 Part VI: Measuring and Trading Volatility
Each of the risk measures can be derived mathematically by taking the partial
derivative of the model. However, there is ashortcut approximation that works just
as well. For example, the formula for gamma is as follows:
x=ln[ P ]/v-ft+v-ft
s X (1 + r)t 2
r - e(-x212)
- pv ✓ 27tt
There is asimpler, yet correct, way to arrive at the gamma. The delta is the par
tial derivative of the Black-Scholes model with respect to stock price - that is, it is
the amount by which the option'sprice changes for achange in stock price. The
gamma is the change in delta for the same change in stock price. Thus, one can
approximate the gamma by the following steps:
1. Calculate the delta with p = Current stock price.
2. Set p = p + 1 and recalculate the delta.
3. Gamma = delta from step 1 - delta from step 2.
The same procedure can be used for the other "greeks":
Vega: 1. Calculate the option price with aparticular volatility.
2.
3.
Theta: 1.
2.
3.
Rho: 1.
2.
3.
Calculate another option price with volatility increased by 1 %.
Vega = difference of the prices in steps 1 and 2.
Calculate the option price with the current time to expiration.
Calculate the option price with 1 day less time remaining to expiration.
Theta = difference of the prices in steps 1 and 2.
Calculate the option price with the current risk-free interest rate.
Calculate the option price with the rate increased by 1 % .
Rho = difference of the prices in steps 1 and 2.
THE GAMMA OF THE GAMMA
The discussion of this concept was deferred from earlier sections because it is some
what difficult to grasp. It is included now for those who may wish to use it at some
time. Those readers who are not interested in such matters may skip to the next sec
tion.

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Chapter 40: Advanced Concepts 903
Recall that this is the sixth risk measurement of an option position. The gamma
of the gamma is the anwunt by which the gamma will change when the stock price
changes.
Recall that in the earlier discussion of gamma, it was noted that gamma
changes. This example is based on the same example used earlier.
Example: With XYZ at 49, assume the January 50 call has adelta of 0.50 and agamma of 0.05. If XYZ moves up 1 point to 50, the delta of the call will increase by
the amount of the gamma: It will increase from 0.50 to 0.55. Simplistically, if XYZ
moves up another point to 51, the delta will increase by another 0.05, to 0.60.
Obviously, the delta cannot keep increasing by 0.05 each time XYZ gains anoth
er point in price, for it will eventually exceed 1.00 by that calculation, and it is known
that the delta has amaximum of 1.00. Thus, it is obvious that the gamma changes.
In reality, the gamma decreases as the stock moves away from the strike. Thus,
with XYZ at 51, the gamma might only be 0.04. Therefore, if XYZ moved up to 52,
the call'sdelta would only increase by 0.04, to 0.64. Hence, the gamma of the gamma
is -0.01, since the gamma decreased from .05 to .04 when the stock rose by one
point.
As XYZ moves higher and higher, the gamma will get smaller and smaller.
Eventually, with XYZ in the low 60's, the delta will be nearly 1.00 and the gamma
nearly 0.00.
This change in the gamma as the stock moves is called the gamma of the
gamma. It is probably referred to by other names, but since its use is limited to only
the most sophisticated traders, there is no standard name. Generally, one would use
this measure on his entire portfolio to gauge how quickly the portfolio would be
responding to the position gamma.
Example: With XYZ at 31. 75 as in some of the previous examples, the following risk
measures exist:
Option Option Option Position
Position Delta Gamma Gamma/Gamma Gamma/Gamma
Short 4,500 XYZ 1.00 0.00 0.0000 0
Short 100 XYZ April 25 calls 0.89 0.01 -0.0015 -15
Long 50 XYZ April 30 calls 0.76 0.03 -0.0006 - 3
Long 139 XYZ July 30 calls 0.74 0.02 -0.0003 - 4
Total Gamma of Gamma: -22

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904 Part VI: Measuring and Trading Volatility
Recall that, in the same example used to describe gamma, the position was delta
long 686 shares and had apositive gamma of 328 shares. Furthermore, we now see
that the gamma itself is going to decrease as the stock moves up ( it is negative) or will
increase as the stock moves down. In fact, it is expected to increase or decrease by
22 shares for each point XYZ moves.
So, if XYZ moves up by 1 point, the following should happen:
a. Delta increases from 686 to 1,014, increasing by the amount of the gamma.
b. Gamma decreases from 328 to 306, indicating that afurther upward move by
XYZ will result in asmaller increase in delta.
One can build ageneral picture of how the gamma of the gamma changes over
different situations - in- or out-of-the-money, or with more or less time remaining
until expiration. The following table of two index calls, the January 350 with one
month of life remaining and the December 350 with eleven months of life remain
ing, shows the delta, gamma, and gamma of the gamma for various stock prices.
Index January 350 call December 350 call
Price Delta Gamma Gamma/Gamma Delta Gamma Gamma/Gamma
310 .0006 .0001 .0000 .3203 .0083 .0000
320 .0087 .0020 .0004 .3971 .0082 .0000
330 .0618 .0100 .0013 .4787 .0080 -.0000
340 .2333 .0744 .0013 .5626 .0078 -.0001
350 .5241 .0309 -.0003 .6360 .0073 -.0001
360 .7957 .0215 -.0014 .6984 .0067 -.0001
370 .9420 .0086 -.0010 .7653 .0060 -.0001
380 .9892 .0021 -.0003 .8213 .0052 -.0001
Several conclusions can be drawn, not all of which are obvious at first glance.
First of all, the gamma of the gamma for long-term options is very small. This should
be expected, since the delta of along-term option changes very slowly. The next fact
can best be observed while looking at the shorter-term January 350 table. The
gamma of the gamma is near zero for deeply out-of-the-money options. But, as the
option comes closer to being in-the-money, the gamma of the gamma becomes apos
itive number, reaching its maximum while the option is still out-of-the-money. By the
time the option is at-the-money, the gamma of the gamma has turned negative. It
then remains negative, reaching its most negative point when slightly in-the-money.
From there on, as the option goes even deeper into-the-money, the gamma of the
gamma remains negative but gets closer and closer to zero, eventually reaching
(minus) zero when the option is very far in-the-money.

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Chapter 40: Advanced Concepts 905
Can one possibly reason this risk measurement out without making severe
mathematical calculations? Well, possibly. Note that the delta of an option starts as asmall number when the option is out-of-the-money. It then increases, slowly at first,
then more quickly, until it is just below 0.60 for an at-the-money option. From there
on, it will continue to increase, but much more slowly as the option becomes in-the
money. This movement of the delta can be observed by looking at gamma: It is the
change in the delta, so it starts slowly, increases as the stock nears the strike, and then
begins to decrease as the option is in-the-money, always remaining apositive num
ber, since delta can only change in the positive direction as the stock rises. Finally,
the gamma of the gamma is the change in the gamma, so it in tum starts as apositive
number as gamma grows larger; but then when gamma starts tapering off, this is
reflected as anegative gamma of the gamma.
In general, the gamma of the gamma is used by sophisticated traders on large
option positions where it is not obvious what is going to happen to the gamma as the
stock changes in price. Traders often have some feel for their delta. They may even
have some feel for how that delta is going to change as the stock moves (i.e., they
have afeel for gamma). However, sophisticated traders know that even positions that
start out with zero delta and zero gamma may eventually acquire some delta. The
gamma of the gamma tells the trader how much and how soon that eventual delta will
be acquired.
MEASURING THE DIFFERENCE OF IMPLIED VOLATILITIES
Recall that when the topic of implied volatility was discussed, it was shown that if one
could identify situations in which the various options on the same underlying securi
ty had substantially different implied volatilities, then there might be an attractive
neutral spread available. The strategist might ask how he is to determine if the dis
crepancies between the individual options are significantly large to warrant attention.
Furthermore, is there aquick way (using acomputer, of course) to determine this?
Alogical way to approach this is to look at each individual implied volatility and
compute the standard deviation of these numbers. This standard deviation can be
converted to apercentage by dividing it by the overall implied volatility of the stock.
This percentage, if it is large enough, alerts the strategist that there may be opportu
nities to spread the options of this underlying security against each other. An exam
ple should clarify this procedure.
Example: XYZ is trading at 50, and the following options exist with the indicated
implied volatilities. We can calculate astandard deviation of these implieds, called
implied deviation, via the formula:

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906 Part VI: Measuring and Trading Volatility
Implied deviation = sqrt (sum of differences from mean) 2/(# options - 1)
XYZ:50
Implied
Option Volatility
October 45 call 21%
November 45 call 21%
January 45 call 23%
October 50 call 32%
November 50 call 30%
January 50 call 28%
October 55 call 40%
November 55 call 37%
January 55 call 34%
Average: 30.44%
Sum of ( difference from avg)2 = 389.26
Implied deviation = sqrt (sum of diff)2/(# options - 1)
= sqrt (389.26 I 8)
= 6.98
Difference
from Average
-9.44
-9.44
-7.44
+ 1.56
-0.44
-2.44
+9.56
+6.56
+3.56
This figure represents the raw standard deviation of the implied volatilities. To
convert it into auseful number for comparisons, one must divide it by the average
implied volatility.
Pd . . Implied deviation ercent eV1at10n = A . 1. dverage imp ie
= 6.98/30.44
= 23%
This "percent deviation" number is usually significant if it is larger than 15%.
That is, if the various options have implied volatilities that are different enough from
each other to produce aresult of 15% or greater in the above calculation, then the
strategist should take alook at establishing neutral spreads in that security or futures
contract.
The concept presented here can be refined further by using aweighted average
of the implieds ( taking into consideration such factors as volume and distance from the
striking price) rather than just using the raw average. That task is left to the reader.

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Chapter 40: Advanced Concepts 907
Recall that acomputer can perform alarge number of Black-Scholes calcula
tions in ashort period of time. Thus, the computer can calculate each option'simplied volatility and then perform the "percent deviation" calculation even faster.
The strategist who is interested in establishing this type of neutral spread would only
have to scan down the list of percent deviations to find candidates for spreading. On
agiven day, the list is usually quite short - perhaps 20 stocks and 10 futures contracts
will qualify.
SUMMARY
In today'shighly competitive and volatile option markets, neutral traders must be
extremely aware of their risks. That risk is not just risk at expiration, but also the cur
rent risk in the market. Furthermore, they should have an idea of how the risk will
increase or decrease as the underlying stock or futures contract moves up and down
in price. Moreover, the passage of time or the volatility that the options are being
assigned in the marketplace - the implied volatility - are important considerations.
Even changes in short-term interest rates can be of interest, especially iflonger-term
options (LEAPS) are involved.
Once the strategist understands these concepts, he can use them to select new
positions, to adjust existing ones, and to formulate specific strategies to take advan
tage of them. He can select aspecific criteria that he wants to exploit - selling high
volatility, for example and use the other measures to construct aposition that has
little risk with respect to any of the other variables. Furthermore, the market-maker
or specialist, who does not want to acquire any market risk if he can help it, will use
these techniques to attempt to neutralize all of the current risk, if possible.

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Taxes
In this chapter, the basic tax treatment of listed options will be outlined and sev
eral tax strategies will be presented. The reader should be aware of the fact that tax
laws change, and therefore should consult tax counsel before actually implementing
any tax-oriented strategy. The interpretation of certain tax strategies by the Internal
Revenue Service is subject to reclarification or change, as well.
An option is acapital asset and any gains or losses are capital gains or losses.
Differing tax consequences apply, depending on whether the option trade is acomplete transaction by itself, or whether it becomes part of astock transaction via
exercise or assignment. Listed option transactions that are closed out in the options
market or are allowed to expire worthless are capital transactions. The holding period
for option transactions to qualify as long-term is always the same as for stocks ( cur
rently, it'sone year). Gains from option purchases could possibly be long-term gains if
the holding period of the option exceeds the long-term capital gains holding period.
Gains from the sale of options are short-term capital gains. In addition, the tax
treatment of futures options and index options and other listed nonequity options
may differ from that of equity options. We will review these points individually.
HISTORY
In the short life of listed option trading. there have been several major changes in the
tax rules. When options were first listed in 1973, the tax laws treated the gains and
losses from writing options as ordinary income. That is, the thinking was that only
professionals or those people in the business actually wrote over-the-counter options,
and thus their gains and losses represented their ordinary income, or means of mak
ing aliving. This rule presented some interesting strategies involving spreads,
because the long side of the spread could be treated as long-term gain (if held for
908

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Chapter 41: Taxes 909
more than 6 months, which was the required holding period for along-term gain at
that time), and the short side of the spread could be ordinary loss. Of course, the
stock would have had to move in the desired direction in order to obtain this result.
In 1976, the tax laws changed. The major changes affecting option traders were
that the long-term holding period was extended to one year and also that gains or
losses from writing options were considered to be capital gains. The extension of the
long-term period essentially removed all possibilities of listed option holders ever
obtaining along-term gain, because the listed option market'slongest-term options
had only 9 months of life.
All through this period there were awide array of tax strategies that were avail
able, legally, to allow investors to defer capital gains from one year to the next, there
by avoiding payment of taxes. Essentially, one would enter into aspread involving
deep in-the-money options that would expire in the next calendar year. Perhaps the
spread would be established during October, using January options. Then one would
wait for the underlying stock to move. Once amove had taken place, the spread
would have aprofit on one side and aloss on the other. The loss would be realized
by rolling the losing option into another deep in-the-money option. The realized loss
could thus be claimed on that year'staxes. The remaining spread - now an unrealized
profit - would be left in place until expiration, in the next calendar year. At that time,
the spread would be removed and the gain would be realized. Thus, the gain was
moved from one year to the next. Then, later in that year, the gain would again be
rolled to the next calendar year, and so on.
These practices were effectively stopped by the new tax ruling issued in 1984.
Two sweeping changes were made. First, the new rules stated that, in any spread
position involving offsetting options - as the two deep in-the-money options in the
previous example - the losses can be taken only to the extent that they exceed the
unrealized gain on the other side of the spread. (The tax literature insists on calling
these positions "straddles" after the old commodity term, but for options purposes
they are really spreads or covered writes.) As aby-product of this rule, the holding
period of stock can be terminated or eliminated by writing options that are too deeply
in-the-money. Second, the new rules required that all positions in nonequity options
and all futures be marked to market at the end of the tax year, and that taxes be paid
on realized and unrealized gains alike. The tax rate for nonequity options was low
ered from that of equity options. Then, in 1986, the long-term and short-term capi
tal gains rates were made equal to the lowest ordinary rate. All of these points will be
covered in detail.

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910 Part VI: Measuring and Trading Volatility
BASIC TAX TREATMENT
Listed options that are exercised or assigned fall into adifferent category for tax pur
poses. The original premium of the option transaction is combined into the stock
transaction. There is no tax liability on this stock position until the stock position itself
is closed out. There are four different combinations of exercising or assigning puts or
calls. Table 41-1 summarizes the method of applying the option premium to the stock
cost or sale price.
Examples of how to treat these various transactions are given in the following
sections. In addition to examples explaining the basic tax treatment, some supple
mentary strategies are included as well.
CALL BUYER
If acall holder subsequently sells the call or allows it to expire worthless, he has acapital gain or loss. For equity options, the holding period of the option determines
whether the gain or loss is long-term or short-term. As mentioned previously, along
term gain would be possible if held for more than one year. For tax purposes, an
option that expires worthless is considered to have been sold at zero dollars on the
expiration date.
Example: An investor purchases an XYZ October 50 call for 5 points on July l. He
sells the call for 9 points on September 1. That is, he realizes acapital gain via aclos
ing transaction. His taxable gain would be computed as shown in Table 41-1, assum
ing that a $25 commission was paid on both the purchase and the sale.
TABLE 41-1.
Applying the option premium to the stock cost or sale price.
Action
Call buyer exercises
Put buyer exercises
Call writer assigned
Put writer assigned
Net proceeds of sale ($900 - $25)
Net cost ($500 + $25)
Short-term gain:
Tax Treatment
Add call premium to stock cost
Subtract put premium from stock sale price
Add call premium to stock sale price
Subtract put premium from stock cost
$875
-525
$350

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Chapter 41: Taxes 911
Alternatively, if the stock had fallen in price by October expiration and the October
50 call had expired worthless, the call buyer would have lost $525 - his entire net
cost. If he had held the call until it expired worthless, he would have ashort-term
capital loss of $525 to report among his taxable transactions.
PUT BUYER
The holder of aput has much the same tax consequences as the holder of acall, pro
vided that he is not also long the underlying stock. This initial discussion of tax con
sequences to the put holder will assume that he does not simultaneously own the
underlying stock. If the put holder sells his put in the option market or allows it to
expire worthless, the gain or loss is treated as capital gain, long-term for equity puts
held more than one year. Historically, the purchase of aput was viewed as perhaps
the only way an investor could attain along-term gain in adeclining market.
Example: An investor buys an XYZ April 40 put for 2 points with the stock at 43.
Later, the stock drops in price and the put is sold for 5 points. The commissions were
$25 on each option trade, so the tax consequences would be:
Net sale proceeds ($500 - $25)
Net cost ($200 + $25)
Short-term capital gain:
$475
-225
$250
Alternatively, if he had sold the put at aloss, perhaps in arising market, he would
have ashort-term capital loss. Furthermore, if he allowed the put to expire totally
worthless, his short-term loss would be equal to the entire net cost of $225.
CALL WRITER
Written calls that are bought back in the listed option market or are allowed to expire
worthless are short-term capital gains. Awritten call cannot produce along-term
gain, regardless of the holding period. This treatment of awritten call holds true even
if the investor simultaneously owned the underlying stock (that is, he had acovered
write). As long as the call is bought back or allowed to expire worthless, the gain or
loss on the call is treated separately from the underlying stock for tax purposes.
Example: Atrader sells naked an XYZ July 30 call for 3 points and buys it back three
months later at aprice of 1. The commissions were $25 for each trade, so the tax gain
would be:

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912
Net sale proceeds ($300 - $25)
Net cost ($100 + $25)
Short-term gain:
Part VI: Measuring and Trading Volatility
$275
-125
$150
If the investor had not bought the call back, but had been fortunate enough to be
able to allow it to expire worthless, his gain for tax purposes would have been the
entire $275, representing his net sale proceeds. The purchase cost is considered to
be zero for an option that expires worthless.
PUT WRITER
The tax treatment of written puts is quite similar to that of written calls. If the put is
bought back in the open market or is allowed to expire worthless, the transaction is
ashort-term capital item.
Example: An investor writes an XYZ July 40 put for 4 points, and later buys it back
for 2 points after arally by the underlying stock. The commissions were $25 on each
option trade, so the tax situation would be:
Net put sale price ($400 - $25)
Net put cost ($100 + $25)
Short-term gain:
$375
-125
$250
If the put were allowed to expire worthless, the investor would have anet gain of
$375, and this gain would be short-term.
THE 60/40 RULE
As mentioned earlier, nonequity option positions and future positions must be
marked to market at the end of the tax year and taxes paid on both the unrealized and
realized gains and losses. This same rule applies to futures positions. The tax rate on
these gains and losses is lower than the equity options rate. Regardless of the actual
holding period of the positions, one treats 60% of his tax liability as long-term and
40% as short-term. This ruling means that even gains made from extremely short
term activity such as day-trading can qualify partially as long-term gains.
Since 1986, long-term and short-term capital gains rates have been equal. If
long-term rates should drop, then the rule would again be more meaningful.
Example: Atrader in nonequity options has made three trades during the tax year.
It is now the end of the tax year and he must compute his taxes. First, he bought S&P

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Chapter 41: Taxes 913
500 calls for $1,500 and sold them 6 weeks later for $3,500. Second, he bought an
OEX January 160 call for 3.25 seven months ago and still holds it. It currently is trad
ing at 11.50. Finally, he sold 5 SPX February 250 puts for 1.50 three days ago. They
are currently trading at 2. The net gain from these transactions should be computed
without regard to holding period.
Nonequity Original Current Gain/
Contract Price Price Cost Proceeds Loss
S&Pcalls $1,500 $3,500 +$2,000 realized
OEX January 160 3.25 11.50 $ 325 $1,150 + 825 unrealized
SPX February 250 1.50 2.00 $1,000 $ 750 250 unrealized
Total caeital gains +$2,575
The total taxable amount is $2,575, regardless of holding period and regardless of
whether the item is realized or unrealized. Of this total taxable amount, 60% ($1,545)
is subject to long-term treatment and 40% ($1,030) is subject to short-term treat
ment.
In practice, one computes these figures on aseparate form (Section 1256) and
merely enters the two final figures - $1,545 and $1,030- on the tax schedule for cap
ital gains and losses. Note that if one loses money in nonequity options, he actually
has atax disadvantage in comparison to equity options, because he must take some
of his loss as along-term loss, while the equity option trader can take all of his loss as
short-term.
EXERCISE AND ASSIGNMENT
Except for aspecified situation that we will discuss later, exercise and assignment do
not have any tax effect for nonequity options because everything is marked to mar
ket at the end of the year. However, since equity options are subject to holding peri
od considerations, the following discussion pertains to them.
CALL EXERCISE
An equity call holder who has an in-the-money call might decide to exercise the call
rather than sell it in the options market. If he does this, there are no tax consequences
on the option trade itself. Rather, the cost of the stock is increased by the net cost of
the original call option. Moreover, the holding period begins on the day the stock is

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914 Part VI: Measuring and Trading Volatility
purchased (the day after the call was exercised). The option'sholding period has no
bearing on the stock position that resulted from the exercise.
Example: An XYZ October 50 call was bought for 5 points on July 1. The stock had
risen by October expiration, and the call holder decided to exercise the call on
October 20th. The option commission was $25 and the stock commission was $85.
The cost basis for the stock would be computed as follows:
Buy 1 00 XYZ at 50 via exercise
($5,000 plus $85 commission)
Original call cost ($500 plus $25)
Total tax basis of stock
Holding period of stock begins on October 21.
$5,085
525
$5,610
When this stock is eventually sold, it will be again or aloss, depending on the stock'ssale price as compared to the tax basis of $5,610 for the stock. Furthermore, it will
be ashort-term transaction unless the stock is held until October 21st of the follow
ing year.
CALL ASSIGNMENT
If awritten call is not closed out, but is instead assigned, the call'snet sale proceeds
are added to the sale proceeds of the underlying stock. The call'sholding period is
lost, and the stock position is considered to have been sold on the date of the assign
ment.
Example: Anaked writer sells an XYZ July 30 call for 3 points, and is later assigned
rather than buying back the option when it was in-the-money near expiration. The
stock commission is $75. His net sale proceeds for the stock would be computed as
follows:
Net call sale proceeds ($300 - $25)
Net stock proceeds from assignment
of 100 shares at 30 ($3,000 - $75)
Net stock sale proceeds
$ 275
2,925
$3,200
In the case in which the investor writes anaked, or uncovered, call, he sells
stock short upon assignment. He may, of course, cover the short sale by purchasing
stock in the open market for delivery. Such ashort sale of stock is governed by the

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Chapter 41: Taxes 915
applicable tax rules pertaining to short sales that any gains or losses from the short
sale of stock are short-term gains or losses.
Tax Treatment for the Covered Writer. If, on the other hand, the
investor was assigned on acovered call - that is, he was operating the covered
writing strategy and he elects to deliver the stock that he owns against the
assignment notice, he has acomplete stock transaction. The net cost of the stock
was determined by its purchase price at an earlier date and the net sale proceeds
are, of course, determined by the assignment in accordance with the preceding
example.
Determining the proceeds from the stock purchase and sale is easy, but deter
mining the tax status of the transaction is not. In order to prevent stockholders from
using deeply in-the-money calls to protect their stock while letting it become along
term item, some complicated tax rules have been passed. They can be summarized
as follows:
1. If the equity option was out-of-the-money when first written, it has no effect on
the holding period of the stock.
2. If the equity option was too deeply in-the-money when first written and the stock
was not yet held long-term, then the holding period of the stock is eliminated.
3. If the equity option was in-the-money, but not too deeply, then the holding peri
od of the stock is suspended while the call is in place.
These rules are complicated and merit further explanation. The first rule mere
ly says that one can write out-of-the-money calls without any problem. If the stock
later rises and is called away, the sale proceeds for the stock include the option pre
mium, and the transaction is long-term or short-term depending on the holding peri
od of the stock.
Example: Assume that on September 1st of aparticular year, an investor buys 100
XYZ at 35. He holds the stock for awhile, and then on July 15th of the following year
- after the stock has risen to 43 - he sells an October 45 call for 3 points.
Net call sale proceeds ($300 - $25)
Net stock proceeds from
assignment ($4,500 - $75)
Net stock sale proceeds
Net stock cost ($3,500 + $75)
Net long-term gain
$ 275
$4,425
$4,700 $4,700
$3,575
+$1, 125

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916 Part VI: Measuring and Trading Volatllity
Thus, this covered writer has anet gain of $1,125 and it is along-term gain because
the stock was held for more than one year (from September 1st of the year in which
he bought it, to October expiration of the next year, when the stock was called away).
Note that in asimilar situation in which the stock had been held for less than
one year before being called away, the gain would be short-term.
Let us now look at the other two rules. They are related in that their differen
tiation relies on the definition of "too deeply in-the-money." They come into play
only if the stock was not already held long-term when the call was written. If the writ
ten call is too deeply in-the-money, it can eliminate the holding period of short-term
stock. Otherwise, it can suspend it. If the call is in-the-money, but not too deeply in
the-money, it is referred to as aqualified covered call. There are several rules regard
ing the determination of whether an in-the-money call is qualified or not. Before
actually getting to that definition, which is complicated, let us look at two examples
to show the effect of the call being qualified or not qualified.
Example: Qualified Covered Write: On March 1st, an investor buys 100 XYZ at 35.
He holds the stock for 3% months, and, on July 15th, the stock has risen to 43. This
time he sells an in-the-money call, the October 40 call for 6. By October expiration,
the stock has declined and the call expires worthless.
He would now have the following situation: a $575 short-term gain from the
sale of the call, plus he is long 100 XYZ with aholding period of only 3% months.
Thus, the sale of the October call suspended his holding period, but did not elimi
nate it.
He could now hold the stock for another 8½ months and then sell it as along
term item.
If the stock in this example had stayed above 40 and been called away, the net
result would have been that the option proceeds would have been added to the stock
sale price as in previous examples, and the entire net gain would have been short
term due to the fact that the writing of the qualified covered call had suspended the
holding period of the stock at 3½ months.
That example was one of writing acall which was not too deeply in-the-money.
If, however, one writes acall on stock that is not yet held long-term and the call is too
deeply in-the-money, then the holding period of the stock is eliminated. That is, if the
call is subsequently bought back or expires worthless, the stock must then be held for
another year in order to qualify as along-term investment. This rule can work to an
investor'sadvantage. If one buys stock and it goes down and he is in jeopardy of hav
ing along-term loss, but he really does not want to sell the stock, he can sell acall

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Chapter 41: Taxes 917
that is too deeply in-the-money (if one exists), and eliminate the holding period on
the stock
Qualified Covered Call. The preceding examples and discussion summa
rize the covered writing rules. Let us now look at what is aqualified covered call.
The following rules are the literal interpretation. Most investors work from
tables that are built from these rules. Such atable may be found in Appendix E.
(Be aware that these rules may change, and consult atax advisor for the latest
figures.) Acovered call is qualified if:
1. the option has more than 30 days of life remaining when it is written, and
2. the strike of the written call is not lower than the following benchmarks:
a. First determine the applicable stock price (ASP). That is normally the closing
price of the stock on the previous day. However, if the stock opens more than
ll0% higher than its previous close, then the applicable stock price is that
higher opening.
b. If the ASP is less than $25, then the benchmark strike is 85% of ASP. So any
call written with astrike lower than 85% of ASP would not be qualified. (For
example, if the stock was at 12 and one wrote acall with astriking price of 10,
it would not be qualified- it is too deeply in-the-money.)
c. If the ASP is between 25.13 and 60, then the benchmark is the next lowest
strike. Thus, if the stock were at 39 and one wrote acall with astrike of 35, it
would be qualified.
d. If the ASP is greater than 60 and not higher than 150, and the call has more
than 90 days of life remaining, the benchmark is two strikes below the ASP.
There is afurther condition here that the benchmark cannot be more than 10
points lower than the ASP. Thus, if astock is trading at 90, one could write acall with astrike of 80 as long as the call had more than 90 days remaining
until expiration, and still be qualified.
e. If the ASP is greater than 150 and the call has more than 90 days of life remain
ing, the benchmark is two strikes below the ASP. Thus, if there are 10-point
striking price intervals, then one could write acall that was 20 points in-the
money and still be qualified. Of course, if there are 5-point intervals, then one
could not write acall deeper than 10 points in-the-money and still be qualified.
These rules are complicated. That is why they are summarized in Appendix E.
In addition, they are always subject to change, so if an investor is considering writing
an in-the-money covered call against stock that is still short-term in nature, he should
check with his tax advisor and/or broker to determine whether the in-the-money call
is qualified or not.

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918 Part VI: Measuring and Trading Volatility
There is one further rule in connection with qualified calls. Recall that we stat
ed that the above rules apply only if the stock is not yet held long-term when the call
is written. If the stock is already long-term when the call is written, then it is consid
ered long-term when called away, regardless of the position of the striking price when
the call was written. However, if one sells an in-the-money call on stock already held
long-term, and then subsequently buys that call back at aloss, the loss on the call
must be taken as along-term loss because the stock was long-term.
Overall, arising market is the best, taxwise, for the covered call writer. If he
writes out-of-the-money calls and the stock rises, he could have ashort-term loss on
the calls plus along-term gain on the stock.
Example: On January 2nd of aparticular year, an investor bought 100 shares of XYZ
at 32, paying $75 in commissions, and simultaneously wrote a July 35 call for 2 points.
The July 35 expired worthless, and the investor then wrote an October 35 call for 3
points. In October, with XYZ at 39, the investor bought back the October 35 call for
6 points (it was in-the-money) and sold a January 40 call for 4 points. In January, on
the expiration day, the stock was called away at 40. The investor would have along
term capital gain on his stock, because he had held it for more than one year. He
would also have two short-term capital transactions from the July 35 and October 35
calls. Tables 41-2 and 41-3 show his net tax treatment from operating this covered
writing strategy. The option commission on each trade was $25.
Things have indeed worked out quite well, both profit-wise and tax-wise, for this
covered call writer. Not only has he made anet profit of $850 from his transactions on
the stock and options over the period of one year, but he has received very favorable
tax treatment. He can take ashort-term loss of $175 from the combined July and
October option transactions, and is able to take the $1,025 gain as along-term gain.
TABLE 41-2.
Summary of trades.
January 2
July
October
January
Bought 100 XYZ at 32
Sold 1 July 35 call at 2
July call expired worthless (XYZ at 32)
Sold 1 October 35 call at 3
Bought back October 35 call for 6 points (XYZ at 39)
Sold 1 January 40 call for 4 points
(of the following year)
1 00 XYZ called away at 40

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Chapter 41: Taxes
TABLE 41-3.
Tax treatment of trades.
Short-term capital items:
July 35 call: Net proceeds ($200 - $25)
Net cost {expired worthless)
Short-term capital gain
October 35 call: Net proceeds ($300 - $25)
Net cost ($600 + $25)
Short-term capital loss
919
$175
0
$175
$275
- 625
($350)
Long-term capital item:
100 shares XYZ: Purchased January 2 of one year and sold at January
expiration of the following year. Therefore, held for
more than one year, qualifying for long-term treatment.
Net sale proceeds of stock {assigned call):
January 40 call sale proceeds
($400 - $25)
Sold 1 00 XYZ at 40 strike
{$4,000 $75)
Net cost of stock (January 2 trade):
Bought 100 at 32 {$3,200 + $75)
Long-term capital gain
$375
+ 3,925
$4,300
- 3,275
$1,025
This example demonstrates an important tax consequence for the covered call
writer: His optimum scenario tax-wise is arising market, for he may be able to
achieve along-term gain on the underlying stock if he holds it for at least one year,
while simultaneously subtracting short-term losses from written calls that were
closed out at higher prices. Unfortunately, in adeclining market, the opposite result
could occur: short-term option gains coupled with the possibility of along-term loss
on the underlying stock. There are ways to avoid long-term stock losses, such as buy
ing aput ( discussed later in the chapter) or going short against the box before the
stock becomes long-term. However, these maneuvers would interrupt the covered
writing strategy, which may not be awise tactic.
In summary, then, the covered call writer who finds himself with an in-the
money call written and expiration date drawing near may have several alternatives
open to him. If the stock is not yet held long-term, he might elect to buy back the
written call and to write another call whose expiration date is beyond the date
required for along-term holding period on the stock. This is apparently what the
hypothetical investor in the preceding example did with his October 35 call. Since

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920 Part VI: Measuring and Trading VolatiRty
that call was in-the-money, he could have elected to let the call be assigned and to
take his profit on the position at that time. However, this would have produced ashort-term gain, since the stock had not yet been held for one year, so he elected
instead to terminate the October 35 call through aclosing purchase transaction and
to simultaneously write acall whose expiration date exceeded the one year period
required to make the stock along-term item. He thus wrote the January 40 call,
expiring in the next year. Note that this investor not only decided to hold the stock
for along-term gain, but also decided to try for more potential profits: He rolled the
call up to ahigher striking price. This lets the holding period continue. An in-the
money write would have suspended it.
DELIVERING .,.,NEW" STOCK TO AVOID A LARGE LONG· TERM GAIN
Some covered call writers may not want to deliver the stock that they are using to
cover the written call, if that call is assigned. For example, if acovered writer were
writing against stock that had an extremely low cost basis, he might not be willing to
take the tax consequences of selling that particular stock holding. Thus, the writer of
acall that is assigned may sometimes wish to buy stock in the open market to deliv
er against his assignment, rather than deliver the stock he already owns. Recall that
it is completely in accordance with the Options Clearing Corporation rules for acall
writer to buy stock in the open market to deliver against an assignment. For tax pur
poses, the confirmation that the investor receives from his broker for the sale of the
stock via assignment should clearly specify which particular shares of stock are being
sold. This is usually accomplished by having the confirmation read "Versus Purchase"
and listing the purchase date of the stock being sold. This is done to clearly identify
that the "new" stock, and not the older long-term stock, is being delivered against the
assignment. The investor must give these instructions to his broker, so that the
brokerage firm puts the proper notation on the confirmation itself. If the investor
realizes that his stock might be in danger of being called away and he wants to avail
himself of this procedure, he should discuss it with his broker beforehand, so that the
proper procedures can be enacted when the stock is actually called away.
Example: An investor owns 100 shares ofXYZ and his cost basis, after multiple stock
splits and stock dividends over the years, is $2 per share. With XYZ at 50, this investor
decides to sell an XYZ July 50 call for 5 points to bring in some income to his port
folio. Subsequently, the call is assigned, but the investor does not want to deliver his
XYZ, which he owns at acost basis of $2 per share, because he would have to pay cap
ital gains on alarge profit. He may go into the open market and buy another 100
shares of XYZ at its current market price for delivery against the assignment notice.

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Chapter 41: Taxes 921
Suppose he does this on July 20th, the day he receives the assignment notice on his
XYZ July 50 call. The confirmation that he receives from his broker for the sale of
100 XYZ at 50 - that is, the confirmation for the call assignment - should be marked
"Versus Purchase July 20th." The year of the sale date should be noted on the con
firmation as well. This long-term holder of XYZ stock must, of course, pay for the
additional XYZ bought in the open market for delivery against the assignment notice.
Thus, it is imperative that such an investor have areserve of funds that he can fall
back on if he thinks that he must ever implement this sort of strategy to avoid the tax
consequences of selling his low-cost-basis stock.
PUT EXERCISE
If the put holder does not choose to liquidate the option in the listed market, but
instead exercises the put - thereby selling stock at the striking price - the net cost of
the put is subtracted from the net sale proceeds of the underlying stock.
Example: Assume an XYZ April 45 put was bought for 2 points. XYZ had declined in
price below 45 by April expiration, and the put holder decides to exercise his in-the
money put rather than sell it in the option market. The commission on the stock sale
is $85, so the net sale proceeds for the underlying stock would be:
Sale of 100 XYZ at 45 strike ($4,500 - $85)
Net cost of put ($200 + 25)
Net sale proceeds on stock for tax purposes:
$4,415
- 225
$4,190
If the stock sale represents anew position - that is, the investor has shorted the
underlying stock - it will eventually be ashort-term gain or loss, according to pres
ent tax rules governing short sales. If the put holder already owns the underlying
stock and is using the put exercise as ameans of selling that stock, his gain or loss on
the stock transaction is computed, for tax purposes, by subtracting his original net
stock cost from the sale proceeds as determined above.
PUT ASSIGNMENT
If awritten put is assigned, stock is bought at the striking price. The net cost of this
purchased stock is reduced by the amount of the original put premium received.
Example: If one initially sold an XYZ July 40 put for 4 points, and it was assigned,
the net cost of the stock would be determined as follows, assuming a $75 commission
charge on the stock purchase:

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922
Cost of 100 XYZ assigned at 40 ($4,000 + $75)
Net proceeds of put sale ($400 - $25)
Net cost basis of stock
Part VI: Measuring and Trading Volatility
$4,075
- 375
$3,700
The holding period for stock purchased via aput assignment begins on the day of the
put assignment. The period during which the investor was short the put has no bear
ing on the holding period of the stock. Obviously, the put transaction itself does not
become acapital item; it becomes part of the stock transaction.
SPECIAL TAX PROBLEMS
THE WASH SALE RULE
The call buyer should be aware of the wash sale rule. In general, the wash sale rule
denies atax deduction for asecurity sold at aloss if asubstantially identical security,
or an option to acquire that security, is purchased within 30 days before or 30 days
after the original sale. This means that one cannot sell XYZ to take atax loss and also
purchase XYZ within the 61-day period that extends 30 days before and 30 days after
the sale. Of course, an investor can legally make such atrade, he just cannot take the
tax loss on the sale of the stock. Acall option is certainly an option to acquire the
security. It would thus invoke the wash sale rule for an investor to sell XYZ stock to
take aloss and also purchase any XYZ call within 30 days before or after the stock
sale.
Various series of call options are not generally considered to be substantially
identical securities, however. If one sells an XYZ January 50 call to take aloss, he may
then buy any other XYZ call option without jeopardizing his tax loss from the sale of
the January 50. It is not clear whether he could repurchase another January 50 call
that is, an identical call - without jeopardizing the taxable loss on the original sale of
the January 50.
It would also be acceptable for an investor to sell acall to take aloss and then
immediately buy the underlying security. This would not invoke the wash sale rule.
Avoiding a Wash Sale. It is generally held that the sale of aput is not the
acquisition of an option to buy stock, even though that is the effect of assign
ment of the written put. This fact may be useful in certain cases. If an investor
holds astock at aloss, he may want to sell that stock in order to take the loss on
his taxes for the current year. The wash sale rule prevents him from repurchas
ing the same stock, or acall option on that stock, within 30 days after the sale.
Thus, the investor will be "out of" the stock for amonth; that is, he will not be

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Chapter 41: Taxes 923
able to participate in any rally in the stock in the next 30 days. If the underlying
stock has listed put options, the investor may be able to partially offset this neg
ative effect. By selling an in-the-money put at the same time that the stock is
sold, the investor will be able to take his stock loss on the current year'staxes
and also will be able to participate in price movements on the underlying stock.
If the stock should rally, the put will decrease in price. However, if the stock ral
lies above the striking price of the put, the investor will not make as much from the
put sale as he would have from the ownership of the stock. Still, he does realize some
profits if the stock rallies.
Conversely, if the stock falls in price, the investor will lose on the put sale. This
certainly represents arisk although no more of arisk than owning the stock did. An
additional disadvantage is that the investor who has sold aput will not receive the div
idends, if any are paid by the underlying stock.
Once 30 days have passed, the investor can cover the put and repurchase the
underlying stock. The investor who utilizes this tactic should be careful to select aput
sale in which early assignment is minimal. Therefore, he should sell along-term, in
the-money put when utilizing this strategy. (He needs the in-the-money put in order
to participate heavily in the stock'smovements.) Note that if stock should be put to
the investor before 30 days had passed, he would thus be forced to buy stock, and the
wash sale rule would be invoked, preventing him from taking the tax loss on the stock
at that time. He would have to postpone taking the loss until he makes asale that
does not invoke the wash sale rule.
Finally, this strategy must be employed in amargin account, because the put
sale will be uncovered. Obviously, the money from the sale of the stock itself can be
used to collateralize the sale of the put. If the stock should drop in value, it is always
possible that additional collateral will be required for the uncovered put.
THE SHORT-SALE RULE - PUT HOLDER'S PROBLEM
Aput purchase made by an investor who also owns the underlying stock may have an
effect on the holding period of the stock. If astock holder buys aput, he would nor
mally do so to eliminate some of the downside risk in case the stock falls in price.
However, if aput option is purchased to protect stock that is not yet held long enough
to qualify for long-term capital gains treatment, the entire holding period of the stock
is wiped out. Furthermore, the holding period for the stock will not begin again until
the put is disposed of. For example, if an investor has held XYZ for 11 months - not
quite long enough to qualify as along-term holding - and then buys aput on XYZ,
he will wipe out the entire accrued holding period on the stock. Furthermore, when
he finally disposes of the put, the holding period for the stock must begin all over

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924 Part VI: Measuring and Trading VolatHity
again. The previous 11-month holding period is lost, as is the holding period during
which the stock and put were held together. This tax consequence of aput purchase
is derived from the general rules governing short sales, which state that the acquisi
tion of an option to sell property at afixed price (that is, aput) is treated as ashort
sale. This ruling has serious tax consequences for an investor who has bought aput
to protect stock that is still in ashort-term tax status.
✓,,Married" Put and Stock. There are two cases in which the put purchase
does not affect the holding period of the underlying stock. First, if the stock has
already been held long enough to qualify for long-term capital treatment, the
purchase of aput has no bearing on the holding period of the underlying stock.
Second, if the put and the stock that it is intended to protect are bought at the
same time, and the investor indicates that he intends to exercise that particular
put to sell those particular shares of stock, the put and the stock are considered
to be "married" and the normal tax rulings for astock holding would apply. The
investor must actually go through with the exercise of the put in order for the
"married" status to remain valid. If he instead should allow the put to expire
worthless, he could not take the tax loss on the put itself but would be forced to
add the put' scost to the net cost of the underlying stock. Finally, if the investor
neither exercises the put nor allows it to expire worthless but sells both the put
and the stock in their respective markets, it would appear that the short sale
rules would come back into effect.
This definition of "married" put and stock, with its resultant ramifications, is
quite detailed. What exactly are the consequences? The "married" rule was original
ly intended to allow an investor to buy stock, protect it, and still have achance of real
izing along-term gain. This is possible with options with more than one year of life
remaining. The reader must be aware of the fact that, if he initially "marries" stock
and alisted 3-month put, for example, there is no way that he can replace that put at
its expiration with another put and still retain the "married" status. Once the original
"married" put is disposed of - through sale, exercise, or expiration - no other put may
be considered to be "married" to the stock.
Protecting a Long· Term Gain or Avoiding a Long-Term Loss. The
investor may be able, at times, to use the short-sale aspect of put purchases to
his advantage. The most obvious use is that he can protect along-term gain with
aput purchase. He might want to do this if he has decided to take the long-term
gain, but would prefer to delay realizing it until the following tax year. Apur
chase of aput with amaturity date in the following year would accomplish that
purpose.

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Chapter 41: Taxes 92S
Another usage of the put purchase, for tax purposes, might be to avoid along
term loss on astock position. If an investor owns astock that has declined in price
and also is about to become along-term holding, he can buy aput on that stock to
eliminate the holding period. This avoids having to take along-term loss. Once the
put is removed, either by its sale or by its expiring worthless, the stock holding peri
od would begin all over again and it would be ashort-term position. In addition, if
the investor should decide to exercise the put that he purchased, the result would be
ashort-term loss. The sale basis of the stock upon exercise of the put would be equal
to the striking price of the put less the amount of premium paid for the put, less all
commission costs. Furthermore, note that this strategy does not lock in the loss on
the underlying stock. If the stock rallies, the investor would be able to participate in
that rally, although he would probably lose all of the premium that he paid for the
put. Note that both of these long-term strategies can be accomplished via the sale of
adeeply in-the-money call as well.
SUMMARY
This concludes the section of the tax chapter dealing with listed option trades and
their direct consequences on option strategies. In addition to the basic tax treatment
for option traders of liquidation, expiring worthless, or assignment or exercise, sev
eral other useful tax situations have been described. The call buyer should be aware
of the wash sale rule. The put buyer must be aware of the short sale rules involving
both put and stock ownership. The call writer should realize the beneficial effects of
selling an in-the-money call to protect the underlying stock, while waiting for areal
ization of profit in the following tax year. The put writer may be able to avoid awash
sale by utilizing an in-the-money put write, while still retaining profit potential from
arally by the underlying stock.
TAX PLANNING STRATEGIES FOR EQUITY OPTIONS
DEFERRING A SHORT· TERM CALL GAIN
The call holder may be interested in either deferring again until the following year
or possibly converting ashort-term gain on the call into along-term gain on the stock.
It is much easier to do the former than the latter. Aholder of aprofitable call that is
due to expire in the following year can take any of three possible actions that might
let him retain his profit while deferring the gain until the following tax year. One way
in which to do this would be to buy aput option. Obviously, he would want to buy an

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926 Part VI: Measuring and Trading Volatillty
in-the-money put for this purpose. By so doing, he would be spending as little as pos
sible in the way of time value premium for the put option and he would also be lock
ing in his gain on the call. The gains and losses from the put and call combination
would nearly equal each other from that time forward as the stock moves up or down,
unless the stock rallies strongly, thereby exceeding the striking price of the put. This
would be ahappy event, however, since even larger gains would accrue. The combi
nation could be liquidated in the following tax year, thus achieving again.
Example: On September 1st, an investor bought an XYZ January 40 call for 3 points.
The call is due to expire in the following year. XYZ has risen in price by December
1st, and the call is selling for 6 points. The call holder might want to take his 3-point
gain on the call, but would also like to defer that gain until the following year. He
might be able to do this by buying an XYZ January 50 put for 5 points, for example.
He would then hold this combination until after the first of the new year. At that
time, he could liquidate the entire combination for at least 10 points, since the strik
ing price of the put is 10 points greater than that of the call. In fact, if the stock should
have climbed to or above 50 by the first of the year, or should have fallen to or below
40 by the first of the year, he would be able to liquidate the combination for more
than 10 points. The increase in time value premium at either strike would also be abenefit. In any case, he would have again - his original cost was 8 points (3 for the
call and 5 for the put). Thus, he has effectively deferred taking the gain on the orig
inal call holding until the next tax year. The risk that the call holder incurs in this type
of transaction is the increased commission charges of buying and selling the put as
well as the possible loss of any time value premium in the put itself. The investor
must decide for himself whether these risks, although they may be relatively small,
outweigh the potential benefit from deferring his tax gain into the next year.
Another way in which the call holder might be able to defer his tax gain into the
next year would be to sell another XYZ call against the one that he currently holds.
That is, he would create aspread. To assure that he retains as much of his current
gain as possible, he should sell an in-the-money call. In fact, he should sell an in-the
money call with alower striking price than the call held long, if possible, to ensure
that his gain remains intact even if the underlying stock should collapse substantial
ly. Once the spread has been established, it could be held until the following tax year
before being liquidated. The obvious risk in this means of deferring gain is that one
could receive an assignment notice on the short call. This is not aremote possibility,
necessarily, since an in-the-money call should be used as protection for the current
gain. Such an assignment would result in large commission costs on the resultant pur
chase and sale of the underlying stock, and could substantially reduce one'sgain.

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