Chapter 41: Taxes 927
Thus, the risk in this strategy is greater than that in the previous one (buying aput),
but it may be the only alternative available if puts are not traded on the underlying
stock in question.
Example: An investor bought an XYZ February 50 call for 3 points in August. In
December, the stock is at 65 and the call is at 15. The holder would like to "lock in"
his 12-point call profit, but would prefer deferring the actual gain into the following
tax year. He could sell an XYZ February 45 call for approximately 20 points to do this.
If no assignment notice is received, he will be able to liquidate the spread at acost
of 5 points with the stock anywhere above 50 at February expiration. Thus, in the end
he would still have a 12-point gain - having received 20 points for the sale of the
February 45 and having paid out 3 points for the February 50 plus 5 points to liqui
date the spread to take his gain. If the stock should fall below 50 before February
expiration, his gain would be even larger, since he would not have to pay out the
entire 5 points to liquidate the spread.
The third way in which acall holder could lock in his gain and still defer the gain
into the following tax year would be to sell the stock short while continuing to hold
the call. This would obviously lock in the gain, since the short sale and the call pur
chase will offset each other in profit potential as the underlying stock moves up or
down. In fact, if the stock should plunge downward, large profits could accrue.
However, there is risk in using this strategy as well. The commission costs of the short
sale will reduce the call holder'sprofit. Furthermore, if the underlying stock should
go ex-dividend during the time that the stock is held short, the strategist will be liable
for the dividend as well. In addition, more margin will be required for the short stock.
The three tactics discussed above showed how to defer aprofitable call gain into
the following tax year. The gain would still be short-term when realized. The only way
in which acall holder could hope to convert his gain into along-term gain would be
to exercise the call and then hold the stock for more than one year. Recall that the
holding period for stock acquired through exercise begins on the day of exercise - the
option'sholding period is lost. If the investor chooses this alternative, he of course is
spending some of his gains for the commissions on the stock purchase as well as sub
jecting himself to an entire year'sworth of market risk. There are ways to protect astock holding while letting the holding period accrue - for example, writing out-of
the-money calls - but the investor who chooses this alternative should carefully
weigh the risks involved against the possible benefits of eventually achieving along
term gain. The investor should also note that he will have to advance considerably
more money to hold the stock.

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928 Part VI: Measuring and Trading Volatility
DEFERRING A PUT HOLDER'S SHORT· TERM GAIN
Without going into as much detail, there are similar ways in which aput holder who
has ashort-term gain on aput due to expire in the following tax year can attempt to
defer the realization of that gain into the following tax year. One simple way in which
he could protect his gain would be to buy acall option to protect his profitable put.
He would want to buy an in-the-money call for this purpose. This resulting combina
tion is similar in nature to the one described for the call buyer in the previous section.
Asecond way that he could attempt to protect his gain and still defer its real
ization into the following tax year would be to sell another XYZ put option against the
one that he holds long. This would create avertical spread. This put holder should
attempt to sell an in-the-money put, if possible. Of course, he would not want to sell
aput that was so deeply in-the-money that there is risk of early assignment. The
results of such aspread are analogous to the call spread described in detail in the last
section.
Finally, the put holder could buy the underlying stock if he had enough avail
able cash or collateral to finance the stock purchase. This would lock in the profit, as
the stock and the put would offset each other in terms of gains or losses while the
stock moved up or down. In fact, if the stock should experience alarge rally, rising
above the striking price of the put, even larger profits would become possible.
In each of the tactics described, the position would be removed in the follow
ing tax year, thereby realizing the gain that was deferred.
DIFFICULTY OF DEFERRING GAINS FROM WRITING
As afinal point in this section on deferring gains from option transactions, it might
be appropriate to describe the risks associated with the strategy of attempting to
defer gains from uncovered option writing into the following tax year. Recall that in
the previous sections, it was shown that acall or put holder who has an unrealized
profit in an option that is due to expire in the following tax year could attempt to "lock
in" the gain and defer it. The dollar risks to aholder attempting such atax deferral
were mainly commission costs and/or small amounts of time value premium paid for
options. However, the option writer who has an unrealized profit may have amore
difficult time finding away to both "lock in" the gain and also defer its realization into
the following tax year. It would seem, at first glance, that the call writer could mere
ly take actions opposite to those that the call buyer takes: buying the underlying
stock, buying another call option, or selling aput. Unfortunately, none of these
actions "locks in" the call writer'sprofit. In fact, he could lose substantial investment
dollars in his attempt to defer the gain into the following year.

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Chapter 41: Taxes 929
Example: An investor has written an uncovered XYZ January 50 call for 5 points and
the call has dropped in value to 1 point in early December. He might want to take
the 4-point gain, but would prefer to defer realization of the gain until the following
tax year. Since the call write is at aprofit, the stock must have dropped and is prob
ably selling around 45 in early December. Buying the underlying stock would not
accomplish his purpose, because if the stock continued to decline through year-end,
he could lose asubstantial amount on the stock purchase and could make only 1 more
point on the call write. Similarly, acall purchase would not work well. Acall with alower striking price - for example, the XYZ January 45 or the January 40- could lose
substantial value if the underlying stock continued to drop in price. An out-of-the
money call - the XYZ January 60 - is also unacceptable, because if the underlying
stock rallied to the high 50's, the writer would lose money both on his January 50 call
write and on his January 60 call purchase at expiration. Writing aput option would
not "lock in" the profit either. If the underlying stock continued to decline, the loss
es on the put write would certainly exceed the remaining profit potential of 1 point
in the January 50 call. Alternatively, if the stock rose, the losses on the January 50 call
could offset the limited profit potential provided by aput write. Thus, there is no rel
atively safe way for an uncovered call writer to attempt to "lock in" an unrealized gain
for the purpose of deferring it to the following tax year. The put writer seeking to
defer his gains faces similar problems.
UNEQUAL TAX TREATMENT ON SPREADS
There are two types of spreads in which the long side may receive different tax treat
ment than the short side. One is the normal equity option spread that is held for more
than one year. The other is any spread between futures, futures options, or cash
based options and equity options.
With equity options, if one has aspread in place for more than one year and if
the movement of the underlying stock is favorable, one could conceivably have along-term gain on the long side and ashort-term loss on the short side of the spread.
Example: An investor establishes an XYZ bullish call spread in options that have 15
months of life remaining: In October of one year, he buys the January 70 LEAPS call
expiring just over ayear in the future. At the same time, he sells the January 80
LEAPS call, again expiring just over ayear hence. Suppose he pays 13 for the January
70 call and receives 7 for the January 80 call. In December of the following year, he
decides to remove the spread, after he has held it for more than one year - specifi
cally, for 14 months in this case. XYZ has advanced by that time, and the spread is
worth 9. With XYZ at 90, the January 70 call is trading at 20 and the January 80 call
is trading at 11. The capital gain and loss results for tax purposes are summarized in
the following table (commissions are omitted from this example):

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930
Option
XYZ January 70 LEAPS call
XYZ January 80 LEAPS call
Cost
$1,300
$1,100
Part VI: Measuring and Trading Volatllity
Proceeds
$2,000
$ 700
Goin/Loss
$700 long-term gain
$400 short-term loss
No taxes would be owed on this spread since one-half of the long-term gain is
less than the short-term loss. The investor with this spread could be in afavorable
position since, even though he actually made money in the spread - buying it at a 6-
point debit and selling it at a 9-point credit - he can show aloss on his taxes due to
the disparate treatment of the two sides of the spread.
The above spread requires that the stock move in afavorable direction in order
for the tax advantage to materialize. If the stock were to move in the opposite direc
tion, then one should liquidate the spread before the long side of the spread had
reached aholding period of one year. This would prevent taking along-term loss.
Another type of spread may be even more attractive in this respect. That is aspread in which nonequity options are spread against equity options. In this case, the
trader would hope to make aprofit on the nonequity or futures side, because part of
that gain is automatically long-term gain. He would simultaneously want to take aloss
on the equity option side, because that would be entirely short-term loss.
There is no riskless way to do this, however. For example, one might buy apack
age of puts on stocks and hedge them by selling an index put on an index that per
forms more or less in line with the chosen stocks. If the index rises in price, then one
would have short-term losses on his stock options, and part of the gain on his index
puts would be treated as long-term. However, if the index were to fall in price, the
opposite would be true, and long-term losses would be generated - not something
that is normally desirable. Moreover, the spread itself has risk, especially the tracking
risk between the basket of stocks and the index itself.
This brings out an important point: One should be cautious about establishing
spreads merely for tax purposes. He might wind up losing money, not to mention that
there could be unfavorable tax consequences. As always, atax advisor should be con
sulted before any tax-oriented strategy is attempted.
SUMMARY
Options can be used for many tax purposes. Short-term gains can be deferred into
the next tax year, or can be partially protected with out-of-the-money options until
they mature into long-term gains. Long-term losses can be avoided with the purchase
of aput or sale of adeeply in-the-money call. Wash sales can be avoided without giv
ing up the entire ownership potential of the stock. There are risks as well as rewards

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Chapter 41: Taxes 931
in any of the strategies. Commission costs and the dissipation of time value premium
in purchased options will both work against the strategist.
Atax advisor should be consulted before actually implementing any tax strate
gy, whether that strategy employs options or not. Tax rules change from time to time.
It is even possible that acertain strategy is not covered by awritten rule, and only atax advisor is qualified to give consultation on how such astrategy might be inter
preted by the IRS.
Finally, the options strategist should be careful not to confuse tax strategies with
his profit-oriented strategies. It is generally agood idea to separate profit strategies
from tax strategies. That is, if one finds himself in aposition that conveniently lends
itself to tax applications, fine. However, one should not attempt to stay in aposition
too long or to close it out at an illogical time just to take advantage of atax break. The
tax consequences of options should never be considered to be more important than
sound strategy management.

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Chapter 42: The Best Strategy? 933
is generally called volatility trading. If the net change in the market is small over aperiod of time, these strategies should perform well: ratio writing, ratio spreading
(especially "delta neutral spreads"), straddle and strangle writing, neutral calendar
spreading, and butterfly spreads. On the other hand, if options are cheap and the
market is expected to be volatile, then these would be best: straddle and strangle
buys, backspreads, and reverse hedges and spreads.
Certain other strategies overlap into more than one of the three broad
categories. For example, the bullish or bearish calendar spread is initially aneutral
position. It only assumes abullish or bearish bias after the near-term option expires.
In fact, any of the diagonal or calendar strategies whose ultimate aim is to generate
profits on the sale of shorter-term options are similar in nature. If these near-term
profits are generated, they can offset, partially or completely, the cost oflong options.
Thus, one might potentially own options at areduced cost and could profit from adefinitive move in his favor at the right time. It was shown in Chapters 14, 23, and
24 that diagonalizing aspread can often be very attractive.
This brief grouping into three broad categories, does not cover all the strategies
that have been discussed. For example, some strategies are generally to be avoided
by most investors: high-risk naked option writing (selling options for fractional prices)
and covered or ratio put writing. In essence, the investor will normally do best with
aposition that has limited risk and the potential of large profits. Even if the profit
potential is alow-probability event, one or two successful cases may be able to over
come aseries of limited losses. Complex strategies that fit this description are the
diagonal put and call combinations described in Chapters 23 and 24. The simplest
strategy fitting this description is the T-bill/option purchase program described in
Chapter 26.
Finally, many strategies may be implemented in more than one way. The
method of implementation may not alter the profit potential, but the percentage risk
levels can be substantially different. Equivalent strategies fit into this category.
Example: Buying stock and then protecting the stock purchase with aput purchase
is an equivalent strategy in profit potential to buying acall. That is, both have limit
ed dollar risk and large potential dollar profit if the stock rallies. However, they are
substantially different in their structure. The purchase of stock and aput requires
substantially more initial investment dollars than does the purchase of acall, but the
limited dollar risk of the strategy would normally be arelatively small percentage of
the initial investment. The call purchase, on the other hand, involves amuch small
er capital outlay; in addition, while it also has limited dollar risk, the l~ss may easily
represent the entire initial investment. The stockholder will receive cash dividends
while the call holder will not. Moreover, the stock will not expire as the call will. This

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934 Part VI: Measuring and Trading Volatility
provides the stock/put holder with an additional alternative of choosing to extend his
position for alonger period of time by buying another put or possibly by just contin
uing to hold the stock after the original put expires.
Many equivalent positions have similar characteristics. The straddle purchase
and the reverse hedge (short stock and buy calls) have similar profit and loss poten
tial when measured in dollars. Their percentage risks are substantially different, how
ever. In fact, as was shown in Chapter 20, another strategy is equivalent to both of
these-buying stock and buying several puts. That is, buying astraddle is equivalent
to buying 100 shares of stock and simultaneously buying two puts. The "buy stock and
puts" strategy has alarger initial dollar investment, but the percentage risk is small
er and the stockholder will receive any dividends paid by the common stock.
In summary, the investor must know two things well: the strategy that he is con
templating using, and his own attitude toward risk and reward. His own attitude
represents suitability, atopic that is discussed more fully in the following section.
Every strategy has risk. It would not be proper for an investor to pursue the best
strategy in the universe (such astrategy does not exist, of course) if the risks of that
strategy violated the investor'sown level of financial objectives or accepted investment
methodology. On the other hand, it is also not sufficient for the investor to merely feel
that astrategy is suitable for his investment objectives. Suppose an investor felt that
the T-bill/option strategy was suitable for him because of the profit and risk levels.
Even if he understands the philosophies of option purchasing, it would not be proper
for him to utilize the strategy unless he also understands the mechanics of buying
Treasury bills and, more important, the concept of annualized risk.
WHAT IS BEST FOR ME MIGHT NOT BE BEST FOR YOU
It is impossible to classify any one strategy as the best one. The conservative investor
would certainly not want to be an outright buyer of options. For him, covered call
writing might be the best strategy. Not only would it accomplish his financial aims
moderate profit potential with reduced risk-but it would be much more appealing
to him psychologically. The conservative investor normally understands and accepts
the risks of stock ownership. It is only asmall step from that understanding to the
covered call writing strategy. The aggressive investor would most likely not consider
covered call writing to be the best strategy, because he would consider the profit
potential too small. He is willing to take larger risks for the opportunity to make larg
er profits. Outright option purchases might suit him best, and he would accept, by
his aggressive stature, that he could lose nearly all his money in arelatively short time

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Chapter 42: The Best Strategy? 935
period. ( Of course, one would hope that he uses only 15 to 20% of his assets for spec
ulative option buying.)
Many investors fit somewhere in between the conservative description and the
aggressive description. They might want to have the opportunity to make large prof
its, but certainly are not willing to risk alarge percentage of their available funds in
ashort period of time. Spreads might therefore appeal to this type of investor, espe
cially the low-debit bullish or bearish calendar spreads. He might also consider occa
sional ventures into other types of strategies-bullish or bearish spreads, straddle
buys or writes, and so on-but would generally not be into awide range of these
types of positions. The T-bill/option strategy might work well for this investor also.
The wealthy aggressive investor may be attracted by strategies that offer the
opportunity to make money from credit positions, such as straddle or combination
writing. Although ratio writing is not acredit strategy, it might also appeal to this type
of investor because of the large amounts of time value premium that are gathered in.
These are generally strategies for the wealthier investor because he needs the "stay
ing power" to be able to ride out adverse cycles. If he can do this, he should be able
to operate the strategy for asufficient period of time in order to profit from the con
stant selling of time value premiums.
In essence, the answer to the question of "which strategy is best" again revolves
around that familiar word, "suitability." The financial needs and investment objectives
of the individual investor are more important than the merits of the strategy itself. It
sounds nice to say that he would like to participate in strategies with limited risk and
potentially large profits. Unfortunately, if the actual mechanics of the strategy involve
risk that is not suitable for the investor, he should not use the strategy, no matter how
attractive it sounds.
Example: The T-bill/option strategy seems attractive: limited risk because only 10%
of one'sassets are subjected to risk annually; the remaining 90% of one'sassets earn
interest; and if the option profits materialize, they could be large. What if the worst
scenario unfolds? Suppose that poor option selections are continuously made and
there are three or four years of losses, coupled with adeclining rate of interest earned
from the Treasury bills (not to mention the commission charges for trading the secu
rities). The portfolio might have lost 15 or 20% of its assets over those years. Agood
test of suitability is for the investor to ask himself, in advance: "How will Ireact if the
worst case occurs?" If there will be sleepless nights, pointing of fingers, threats, and
so forth, the strategy is unsuitable. If, on the other hand, the investor believes that he
would be disappointed (because no one likes to lose money), but that he can with
stand the risk, the strategy may indeed be suitable.

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936 Part VI: Measuring and Trading Volatility
MATHEMATICAL RANKING
The discussion above demonstrates that it is not possible to ultimately define the best
strategy when one considers the background, both financial and psychological, of the
individual investor. However, the reader may be interested in knowing which strate
gies have the best mathematical chances of success, regardless of the investor'sper
sonal feelings. Not unexpectedly, strategies that take in large amounts of time value
premium have high mathematical expectations. These include ratio writing, ratio
spreading, straddle writing, and naked call writing (but only if the "rolling for cred
its" follow-up strategy is adhered to). The ratio strategies would have to be operated
according to adelta-neutral ratio in order to be mathematically optimum. Unfor
tunately, these strategies are not for everyone. All involve naked options, and also
require that the investor have asubstantial amount of money ( or collateral) available
to make the strategies work properly. Moreover, naked option writing in any form is
not suitable for some investors, regardless of their protests to the contrary.
Another group of strategies that rank high on an expected profit basis are those
that have limited risk with the potential of occasionally attaining large profits. The Thill/option strategy is aprime example of this type of strategy. The strategies in which
one attempts to reduce the cost of longer-term options through the sale of near-term
options fit in this broad category also, although one should limit his dollar commit
ment to 15 to 20% of his portfolio. Calendar spreads such as the combinations
described in Chapter 23 (calendar combination, calendar straddle, and diagonal but
terfly spread) or bullish call calendar spreads or bearish put calendar spreads are all
examples of such strategies. These strategies may have arather frequent probability
of losing asmall amount of money, coupled with alow probability of earning large
profits. Still, afew large profits may be able to more than overcome the frequent, but
small, losses. Ranking behind these strategies are the ones that offer limited profits
with areasonable probability of attaining that profit. Covered call writing, large debit
bull or bear spreads (purchased option well in-the-money and possible written option
as well), neutral calendar spreads, and butterfuly spreads fit into this category.
Unfortunately, all these strategies involve relatively large commission costs.
Even though these are not strategies that normally require alarge investment, the
investor who wants to reduce the percentage effect of commissions must take larger
positions and will therefore be advancing asizable amount of money.
Speculative buying and spreading strategies rank the lowest on amathematical
basis. The T-bill/option strategy is not aspeculative buying strategy. In-the-money
purchases, including the in-the-money combination, generally outrank out-of-the
money purchases. This is because one has the possibility of making alarge percent
age profit but has decreased the chance of losing all his investment, since he starts

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Chapter 42: The Best Strategy? 937
out in-the-money. In general, however, the constant purchase of time value premi
ums, which must waste away by the time the options expire, will have aburdensome
negative effect. The chances of large profits and large losses are relatively equal on amathematical basis, and thus become subsidiary to the time premium effect in the
long run. This mathematical outlook, of course, precludes those investors who are
able to predict stock movements with an above-average degree of accuracy. Although
the true mathematical approach holds that it is not possible to accurately predict the
market, there are undoubtedly some who can and many who try.
SUMMARY
Mathematical expectations for astrategy do not make it suitable even if the expect
ed returns are good, for the improbable may occur. Profit potentials also do not
determine suitability; risk levels do. In the final analysis, one must determine the
suitability of astrategy by determining if he will be able to withstand the inherent
risks if the worst scenario should occur. For this reason, no one strategy can be des
ignated as the best one, because there are numerous attitudes regarding the degree
of risk that is acceptable.

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Postscript
Option strategies cannot be unilaterally classified as aggressive or conservative.
There are certainly many aggressive applications, the simplest being the outright pur
chase of calls or puts. However, options can also have conservative applications, most
notably in reducing some of the risks of common stock ownership. In addition, there
are less polarized applications, particularly spreading techniques, that allow the
investor to take amiddle-of-the-road approach.
Consequently, the investor himself-not options--becomes the dominant force
in determining whether an option strategy is too risky. It is imperative that the
investor understand what he is trying to accomplish in his portfolio before actually
implementing an option strategy. Not only should he be cognizant of the factors that
go into determining the initial selection of the position, but he must also have in mind
aplan of follow-up action. If he has thought out, in advance, what action he will take
if the underlying entity rises or falls, he will be in aposition to make amore rational
decision when and if it does indeed make amove. The investor must also determine
if the risk of the strategy is acceptable according to his financial means and objec
tives. If the risk is too high, the strategy is not suitable.
Every serious investor owes it to himself to acquire an understanding of listed
option strategies. Since various options strategies are available for amultitude of pur
poses, alrrwst every money manager or dedicated investor will be able to use options
in his strategies at one time or another. For astock-oriented investor to ignore the
potential advantages of using options would be as serious amistake as it would be for
alarge grain company to ignore the hedging properties available in the futures mar
ket, or as it would be for an income-oriented investor to concentrate only in utilities
and Treasury bills while ignoring less well known, but equally compatible, alterna
tives such as GNMAs.
938

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Strategy Sullllllary
Except for arbitrage strategies and tax strategies, the strategies we have described
deal with risk of market movement. It is therefore often convenient to summarize
option strategies by their risk and reward characteristics and by their market out
look-bullish, bearish, or neutral. Table A-1 lists all the risk strategies that were dis
cussed and gives ageneral classification of their risks and rewards. If astrategist has
adefinite attitude about the market'soutlook or about his own willingness to accept
risks, he can scan Table A-1 and select the strategies that most closely resemble his
thinking. The number in parentheses after the strategy name indicates the chapter in
which the strategy was discussed.
Table A-1 gives abroad classification of the various risk and reward potentials
of the strategies. For example, abullish call calendar spread does not actually have
unlimited profit potential unless its near-tenn call expires worthless. In fact, all cal
endar spread or diagonal spread positions have limited profit potential at best until
the near-term options expire.
Also, the definition of limited risk can vary widely. Some strategies do have arisk that is truly limited to arelatively small percentage of the initial investment-the
protected stock purchase, for example. In other cases, the risk is limited but is also
equal to the entire initial investment. That is, one could lose 100% of his investment
in ashort time period. Option purchases and bull, bear, or calendar spreads are
examples.
Thus, although Table A-1 gives abroad perspective on the outlook for various
strategies, one must be aware of the differences in reward, risk, and market outlook
when actually implementing one of the strategies.
943

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944
TABLE A-1.
General strategy summary.
Strategy (Chapter)
Bullish strategies
Call purchase (3)
Synthetic long stock (short put/long call) (21)
Bull spread-puts or calls (7 and 22)
Protected stock purchase (long stock/long put) ( 17)
Bullish call calendar spread (9)
Covered call writing (2)
Uncovered put write ( 19)
Bearish Strategies
Put purchase ( 16)
Protected short sale (synthetic put) (4 and 16)
Synthetic short sale (long put/short call) (21)
Bear spread-put or call (and 22)
Covered put write ( 19)
Bearish put calendar spread (22)
Naked call write (5)
Neutral strategies
Straddle purchase ( 1 8)
Reverse hedge (simulated straddle buy) (4)
Fixed income + option purchase (25)
Diagonal spread (14, 23, and 24)
Neutral calendar spread-puts or calls (9 and 22)
Butterfly spread ( 10 and 23)
Calendar straddle or combination (23)
Reverse spread ( 13)
Ratio write-put or call (6 and 19)
Straddle or combination write (20)
Ratio spread-put or call ( 11 and 24)
Ratio calendar spread-put or call (12 and 24)
Risk
Limited
Unlimited 0
Limited
Limited
Limited
Unlimited 0
Unlimited 0
Limited
Limited
Unlimited
Limited
Unlimited
Limited
Unlimited
Limited
Limited
Limited
Limited
Limited
Limited
Limited
Limited
Unlimited
Unlimited
Unlimited
Unlimited
Appendix A
Reward
Unlimited
Unlimited
Limited
Unlimited
Unlimited
Limited
Limited
Unlimited 0
Unlimited 0
Unlimited 0
Limited
Limited
Unlimited 0
Limited
Unlimited
Unlimited
Unlimited
Unlimited
Limited
Limited
Unlimited
Unlimited
Limited
Limited
Limited
Unlimited
0 Wherever the risk or reword is limited only by the fact that ostock cannot foll below zero in price,
the entry is marked. Obviously, although the potential may technically be limited, it could still be quite
large if the underlying stock did foll alarge distance.

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946
TABLE B-1.
Equivalent strategies.
This Strategy is equivalent to
Call purchase
Put purchase
Long stock
Short stock
Naked call write
Naked put write
Bullish call spread
(long call at lower strike/
short call at higher strike)
Bearish call spread
(long call at higher strike/
short call at lower strike)
Ratio call write
(long stock/short calls)
... and is also equivalent to ...
Straddle buy (long call/long put)
Appendix B
This Strategy
Long stock/long put
Short stock/long call (synthetic put)
Long call/ short put (synthetic stock)
Long put/ short call (synthetic short sale)
Short stock/short put
Covered call write (long stock/ short call)
Bullish put spread
(long put at lower strike/
short put at higher strike)
Bearish put spread
(long put at higher strike/
short put at lower strike)
Straddle write (short put/short call)
Ratio put write (short stock/ short puts)
Reverse hedge (short stock/long calls)
or buy stock/buy puts
Butterfly call spread Butterfly put spread
(long 1 call at each outside strike/ (long one put at each outer strike/
short 2 calls at middle strike) short two calls at middle strike)
All four of these "butterfly" strategies are equivalent
Butterfly combination Protected straddle write
(bullish call spread at two (short straddle at middle strike/
lower strikes/bearish put spread
at two higher strikes)
long call at highest strike/
long put at lowest strike

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948
Annualized Risk (Ch. 26)
Annualized risk = L INV 360
i
1
Hi
where INVi = percent of total assets invested in options
with holding periods, Hi
length of holding period in days
Bear Spread
-Calls (Ch. 8)
-Puts (Ch. 22)
p = Cl - C2
R = s2 - s1 - P
B = s1 + P
R = P2 - Pl
p = S2 - S1 - R
B = s1 + P = s2 + Pl - P2
Black Model (Ch. 34):
Xs
Cpr
Theoretical futures call price= e-rt x BSM[r = 0%]
where BSM[r = O) is the Black-Scholes Model
using r = 0% as the short-term interest rate
Put price = Call price - e-rt x (f - s)
where f = futures price
current stock price
striking price
call price
put price
interest rate
time (in years)
Bu
Dp
Rbreak-even point
upside break-even point
downside break-even point
maximum profit potential
maximum risk potential
ffutures price
Appendix C
Subscripts indicate multiple items. For example s1, s2, s3 would designate three striking prices in aformula.
The formulae are arranged alphabetically by title or by strategy.

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952
Ntlt. Delta of long option eu ra ra 10 = -----=---=--Delta of short option
Equivalent Futures Position (Ch. 34)
EFP = Delta x Number of options
Equivalent Stock Position (Ch. 28)
ESP = Unit of trading x Delta xnumber of options
Appendix Cwhere unit of trading is the number of shares of the underlying stock that
can be bought or sold with the option (normally 100).
Futures Contract Fair Value (Ch. 29)
-Stock index futures
Index value x (1 + rt) + Present worth (dividends)
Also see Present worth.
Future Stock Price (Ch. 28)
where
-lognormal distribution, assuming amovement of afixed number of stan
dard deviations
q = future stock price
Vt = volatility for the time period
a = number of standard deviations of movement
(normally-3.0::; a::; 3.0)
Gamma (Ch. 40)
Xs
Cprlet z = In [ x ] /v --ft + v --ft
S X (1 + r)t 2
Then (-x212)
r- __ e-===--
- xv ✓ 2nt
current stock price Bstriking price
call price
put price
interest rate
time (in years)
u
Dp
Rbreak-even point
upside break-even point
downside break-even point
maximum profit potential
maximum risk potential
Subscripts indicate multiple items. For example s1, s2, s3 would designate three striking prices in aformula.
The formulae are arranged alphabetically by title or by strategy.

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954 Appendix C
Ratio Spread
-Calls (Ch. 11): buy n1 calls at lower strike, s1, and sell n2 calls at higher
strike, s2
S1 < s2
n1 < n2
R = n1c1 - n2c2
P = (s2-s1)n1 -Rp
U=s2+ --n2-n1
Break-even cost of long calls for follow-up action (Ch. 11)
Break-even cost = n2(s2 - si) - Rn2 n1
-Puts (Ch. 24): buy n2 puts at higher strike, s2, and sell n1 puts at lower
strike, s1
S1 < S2
n2 < n1
R = n2p2 - n1p1
P = n2(s2 - s1) - Rp
D =S1 ----n1 -n2
Reversal-See Conversion and Reversal Profit
Reverse Hedge (Ch. 4)-simulated straddle purchase
General case: short mround lots of stock and long ncalls
R = m(s -x) + nc
U=s+-R-n-m
R D=s--m
Xs
Ccurrent stock price
striking price
call price
pput price
rinterest rate
t = time (in years)
Bu
Dp
Rbreak-even point
upside break-even point
downside break-even point
maximum profit potential
maximum risk potential
Subscripts indicate multiple items. For example s1, s2, s3 would designate three striking prices in aformula.
The formulae are arranged alphabetically by title or by strategy.

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954 Appendix C
Ratio Spread
-Calls (Ch. 11): buy n1 calls at lower strike, s1, and sell n2 calls at higher
strike, s2
s1 < s2
n1 < n2
R = n1c1 - n2c2
P = (s2 - s1)n1 -Rp
U=s 2 +--n2-n1
Break-even cost oflong calls for follow-up action (Ch. 11)
Break-even cost = n2(s2 - si) - Rn2-n1
-Puts (Ch. 24): buy n2 puts at higher strike, s2, and sell n1 puts at lower
strike, s1
S1 < S2
n2 < n1
R = n2p2 - n1p1
P = n2(s2 - s1) - Rp D =S1----
n1 -n2
Reversed-See Conversion and Reversal Profit
Reverse Hedge (Ch. 4)-simulated straddle purchase
General case: short mround lots of stock and long ncalls
R = m(s -x) + nc
U=s+-R-n-m
R D=s--m
Xs
Ccurrent stock price
striking price
call price
pput price
rinterest rate
t = time (in years)
Bu
Dp
Rbreak-even point
upside break-even point
downside break-even point
maximum profit potential
maximum risk potential
Subscripts indicate multiple items. For example s1, s2, s3 would designate three striking prices in aformula.
The formulae are arranged alphabetically by title or by strategy.

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TABLE E-1. ~
Qualified covered call options.
~
Call is not "deep-in-the-money" Call is not
II
deep-in-the-money"
Applicable if Strike Price2 is at least: Applicable if Strike Price2 is at least:
Stock More than Stock More than
Price1 31-90-Day Call 90-Day Call Price1 31-90-Day Call 90-Day Call
5.13-5.88 5 5 75.13-80 75 70
6-10 None None 80.13-85 80 75
10.13-11.75 10 10 85.13-90 85 80
11.88-15 None None 90.13-95 90 85
15.13-17.63 15 15 95.13-100 95 90
17.75-20 None None 100.13-105 100 95
20.13-23.50 20 20 105.13-110 100 100
23.63-25 None None 110.13-120 110 110
25.13-30 25 25 120.13-130 120 120
30.13-35 30 30 130.13-140 130 130
35.13-40 35 35 140.13-150 140 140
40.13-45 40 40 150.13-160 150 140
45.13-50 45 45 160.13-170 160 150
50.13-55 50 50 170.13-180 170 160
55.13-60 55 55 180.13-190 180 170
60.13-65 60 55 190.13-200 190 180
65.13-70 65 60 200.13-210 200 190
70.13-75 70 65 210.13-220 210 200
1 Applicable stock price is either the closing price of the stock on the day preceding the date the option was granted, or the opening price on
tthe day the option is granted if such price is greater than 100% of the preceding day'sclosing price.
2Assumption is that strike prices are only at $5 intervals up to $ 100 and $10 intervals over $100. Note: If the stock splits, option strike prices 5:c·
will have smaller intervals for aperiod of time. ""'

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Glossary
American Exercise: afeature of an option that indicates it may be exercised at any
time. Therefore, it is subject to early assignment.
Arbitrage: the process in which professional traders simultaneously buy and sell the
same or equivalent securities for ariskless profit. See also Risk Arbitrage.
Assign: to designate an option writer for fulfillment of his obligation to sell stock (call
option writer) or buy stock (put option writer). The writer receives an assignment
notice from the Options Clearing Corporation. See also Early Exercise.
Assignment Notice: see Assign.
Automatic Exercise: aprotection procedure whereby the Options Clearing
Corporation attempts to protect the holder of an expiring in-the-money option by
automatically exercising the option on behalf of the holder.
Average Down: to buy more of asecurity at alower price, thereby reducing the
holder'saverage cost. (Average Up: to buy more at ahigher price.)
Backspread: see Reverse Strategy.
Bear Spread: an option strategy that makes its maximum profit when the underly
ing stock declines and has its maximum risk if the stock rises in price. The strate
gy can be implemented with either puts or calls. In either case, an option with ahigher striking price is purchased and one with alower striking price is sold, both
options generally having the same expiration date. See also Bull Spread.
Bearish: an adjective describing an opinion or outlook that expects adecline in
price, either by the general market or by an underlying stock, or both. See also
Bullish.
963

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964 Glossary
Beta: ameasure of how astock'smovement correlates to the movement of the entire
stock market. The beta is not the same as volatility. See also Standard Deviation,
Volatility.
Black Model: amodel used to predict futures option prices; it is amodified version
of the Black-Scholes model. See Model.
Board Broker: the exchange member in charge of keeping the book of public
orders on exchanges utilizing the "market-maker" system, as opposed to the "spe
cialist system," of executing orders. See also Market-Maker, Specialist.
Box Spread: atype of option arbitrage in which both abull spread and abear spread
are established for ariskless profit. One spread is established using put options and
the other is established using calls. The spreads may both be debit spreads ( call
bull spread vs. put bear spread), or both credit spreads (call bear spread vs. put
bull spread).
Break-Even Point: the stock price (or prices) at which aparticular strategy neither
makes nor loses money. It generally pertains to the result at the expiration date of
the options involved in the strategy. A "dynamic" break-even point is one that
changes as time passes.
Broad-Based: generally referring to an index, it indicates that the index is composed
of asufficient number of stocks or of stocks in avariety of industry groups. Broad
based indices are subject to more favorable treatment for naked option writers.
See also Narrow- Based.
Bull Spread: an option strategy that achieves its maximum potential if the underly
ing security rises far enough, and has its maximum risk if the security falls far
enough. An option with alower striking price is bought and one with ahigher strik
ing price is sold, both generally having the same expiration date. Either puts or
calls may be used for the strategy. See also Bear Spread.
Bullish: describing an opinion or outlook in which one expects arise in price, either
by the general market or by an individual security. See also Bearish.
Butterfly Spread: an option strategy that has both limited risk and limited profit
potential, constructed by combining abull spread and abear spread. Three strik
ing prices are involved, with the lower two being utilized in the bull spread and the
higher two in the bear spread. The strategy can be established with either puts or
calls; there are four different ways of combining options to construct the same
basic position.
Calendar Spread: an option strategy in which ashort-term option is sold and alonger-term option is bought, both having the same striking price. Either puts or

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Glossary 965
calls may be used. Acalendar combination is astrategy that consists of acall cal
endar spread and aput calendar spread at the same time. The striking prices of
the calls would be higher than the striking prices of the puts. Acalendar straddle
consists of selling anear-term straddle and buying alonger-term straddle, both
with the same striking price.
Calendar Straddle or Combination: see Calendar spread.
Call: an option that gives the holder the right to buy the underlying security at aspecified price for acertain, fixed period of time. See also Put.
Call Price: the price at which abond or preferred stock may be called in by the issu
ing corporation; see Redemption Price.
Capitalization-Weighted Index: astock index that is computed by adding the cap
italizations (float times price) of each individual stock in the index, and then divid
ing by the divisor. The stocks with the largest market values have the heaviest
weighting in the index. See also Divisor, Float, Price-Weighted Index.
Carrying Cost: the interest expense on adebit balance created by establishing aposition.
Cash- Based: Referring to an option or future that is settled in cash when exercised
or assigned. No physical entity, either stock or commodity, is received or delivered.
CBOE: the Chicago Board Options Exchange; the first national exchange to trade
listed stock options.
Circuit Breaker: alimit applied to the trading of index futures contracts designed
to keep the stock market from crashing.
Class: aterm used to refer to all put and call contracts on the same underlying secu
rity.
Closing Transaction: atrade that reduces an investor'sposition. Closing buy trans
actions reduce short positions and closing sell transactions reduce long positions.
See also Opening Transaction.
Collateral: the loan value of marginable securities; generally used to finance the
writing of uncovered options.
Combination: (1) any position involving both put and call options that is not astrad
dle. See also Straddle. (2) the name given to the trade at expiration whereby an
arbitrageur rolls his options from one month to the next. For example, if he sells
his synthetic long stock position in June and reestablishes it by buying asynthetic
long stock position in September, the entire four-sided trade is called acombina
tion by floor traders. See also Straddle, Strangle.

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966 Glossary
Commodities: see Futures Contract.
Contingent Order: an order whose execution or price is dependent on the align
ment or price of the underlying security and/or its options. Most commonly it is an
order to buy stock and sell acovered call option that is given as one order to the
trading desk of abrokerage firm. Also called a "net order." This is a "not held"
order. See also Market Not Held Order.
Conversion Arbitrage: ariskless transaction in which the arbitrageur buys the
underlying security, buys aput, and sells acall. The options have the same terms.
See also Reversal Arbitrage.
Conversion Ratio: see Convertible Security.
Converted Put: see Synthetic Put.
Convertible Security: asecurity that is convertible into another security. Generally,
aconvertible bond or convertible preferred stock is convertible into the underly
ing stock of the same corporation. The rate at which the shares of the bond or pre
ferred stock are convertible into the common is called the conversion ratio.
Cover: to buy back as aclosing transaction an option that was initially written, or
stock that was initially sold short.
Covered: awritten option is considered to be covered if the writer also has an oppos
ing market position on ashare-for-share basis in the underlying security. That is, ashort call is covered if the underlying stock is owned, and ashort put is covered
(for margin purposes) if the underlying stock is also short in the account. In addi
tion, ashort call is covered if the account is also long another call on the same secu
rity, with astriking price equal to or less than the striking price of the short call. Ashort put is covered if there is also along put in the account with astriking price
equal to or greater than the striking price of the short put.
Covered Call Write: astrategy in which one writes call options while simultane
ously owning an equal number of shares of the underlying stock.
Covered Put Write: astrategy in which one sells put options and simultaneously is
short an equal number of shares of the underlying security.
Covered Straddle Write: the term used to describe the strategy in which an
investor owns the underlying security and also writes astraddle on that security.
This is not really acovered position.
Credit: money received in an account. Acredit transaction is one in which the net
sale proceeds are larger than the net buy proceeds ( cost), thereby bringing money
into the account. See also Debit.

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Glossary 967
Cycle: the expiration dates applicable to various classes of options. There are three
cycles: January/April/July/October, February/May/ August/November, and
March/June/Septem ber/Decem ber.
Debit: an expense, or money paid out from an account. Adebit transaction is one in
which the net cost is greater than the net sale proceeds. See also Credit.
Deliver: to take securities from an individual or firm and transfer them to another
individual or firm. Acall writer who is assigned must deliver stock to the call hold
er who exercised. Aput holder who exercises must deliver stock to the put writer
who is assigned.
Delivery: the process of satisfying an equity call assignment or an equity put exer
cise. In either case, stock is delivered. For futures, the process of transferring the
physical commodity from the seller of the futures contract to the buyer.
Equivalent delivery refers to asituation in which delivery may be made in any of
various, similar entities that are equivalent to each other (for example, Treasury
bonds with differing coupon rates).
Delta: (1) the amount by which an option'sprice will change for acorresponding 1-
point change in price by the underlying entity. Call options have positive deltas,
while put options have negative deltas. Technically, the delta is an instantaneous
measure of the option'sprice change, so that the delta will be altered for even frac
tional changes by the underlying entity. Consequently, the terms "up delta" and
"down delta" may be applicable. They describe the option'schange after afull 1-
point change in price by the underlying security, either up or down. The "up delta"
may be larger than the "down delta" for acall option, while the reverse is true for
put options. (2) the percent probability of acall being in-the-money at expiration.
See also Hedge Ratio.
Delta Neutral Spread: aratio spread that is established as aneutral position by uti
lizing the deltas of the options involved. The neutral ratio is determined by divid
ing the delta of the purchased option by the delta of the written option. See also
Delta, Ratio Spread.
Depository Trust Corporation (OTC): acorporation that will hold securities for
member institutions. Generally used by option writers, the DTC facilitates and
guarantees delivery of underlying securities when assignment is made against
securities held in DTC.
Diagonal Spread: any spread in which the purchased options have alonger matu
rity than do the written options, as well as having different striking prices. Typical

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968 Glossary
types of diagonal spreads are diagonal bull spreads, diagonal bear spreads, and
diagonal butterfly spreads.
Discount: an option is trading at adiscount if it is trading for less than its intrinsic
value. Afuture is trading at adiscount if it is trading at aprice less than the cash
price of its underlying index or commodity. See also Intrinsic Value, Parity.
Discount Arbitrage: ariskless arbitrage in which adiscount option is purchased
and an opposite position is taken in the underlying security. The arbitrageur may
either buy acall at adiscount and simultaneously sell the underlying security
(basic call arbitrage), or buy aput at adiscount and simultaneously buy the under
lying security (basic put arbitrage). See also Discount.
Discretion: see Limit Order, Market Not Held Order.
Dividend Arbitrage: in the riskless sense, an arbitrage in which aput is purchased
and so is the underlying stock. The put is purchased when it has time value pre
mium less than the impending dividend payment by the underlying stock. The
transaction is closed after the stock goes ex-dividend. Also used to denote aform
of risk arbitrage in which asimilar procedure is followed, except that the amount
of the impending dividend is unknown and therefore risk is involved in the trans
action. See also Ex-Dividend, Time Value Premium.
Divisor: amathematical quantity used to compute an index. It is initially an arbitrary
number that reduces the index value to asmall, workable number. Thereafter the
divisor is adjusted for stock splits (price-weighted index) or additional issues of
stock (capitalization-weighted index).
Downside Protection: generally used in connection with covered call writing, this
is the cushion against loss, in case of aprice decline by the underlying security, that
is afforded by the written call option. Alternatively, it may be expressed in terms
of the distance the stock could fall before the total position becomes aloss (an
amount equal to the option premium), or it can be expressed as percentage of the
current stock price. See also Covered Call Write.
Dynamic: for option strategies, describing analyses made during the course of
changing security prices and during the passage of time. This is as opposed to an
analysis made at expiration of the options used in the strategy. Adynamic break
even point is one that changes as time passes. Adynamic follow-up action is one
that will change as either the security price changes or the option price changes or
time passes. See also Break-Even Point, Follow-Up Action.
Early Exercise (assignment): the exercise or assignment of an option contract
before its expiration date.

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Glossary 969
Equity Option: an option that has common stock as its underlying security. See also
Non-Equity Option.
Equity Requirement: arequirement that aminimum amount of equity must be
present in amargin account. Normally, this requirement is $2,000, but some bro
kerage firms may impose higher equity requirements for uncovered option writing.
Equivalent Positions: positiohs that have similar profit potential, when measured
in dollars, but are constructed with differing securities. Equivalent positions have
the same profit graph. Acovered call write is equivalent to an uncovered put write,
for example. See also Profit Graph.
Escrow Receipt: areceipt issued by abank in order to verify that acustomer ( who has
written acall) in fact owns the stock and therefore the call is considered covered.
European Exercise: afeature of an option that stipulates that the option may be
exercised only at its expiration. Therefore, there can be no early assignment with
this type of option.
Exchange-Traded Fund (ETF): an index fund that is listed on astock exchange.
Options are listed on some ETFs. See also Index Fund.
Ex-Dividend: the process whereby astock'sprice is reduced when adividend is
paid. The ex-dividend date (ex-date) is the date on which the price reduction takes
place. Investors who own stock on the ex-date will receive the dividend, and those
who are short stock must pay out the dividend.
Exercise: to invoke the right granted under the terms of alisted options contract.
The holder is the one who exercises. Call holders exercise to buy the underlying
security, while put holders exercise to sell the underlying security.
Exercise Limit: the limit on the number of contracts aholder can exercise in afixed
period of time. Set by the appropriate option exchange, it is designed to prevent
an investor or group of investors from "cornering" the market in astock.
Exercise Price: the price at which the option holder may buy or sell the underlying
security, as defined in the terms of his option contract. It is the price at which the
call holder may exercise to buy the underlying security or the put holder may exer
cise to sell the underlying security. For listed options, the exercise price is the
same as the striking price. See also Exercise.
Expected Return: arather complex mathematical analysis involving statistical dis
tribution of stock prices, it is the return an investor might expect to make on an
investment if he were to make exactly the same investment many times through
out history.

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970 Glossary
Expiration Date: the day on which an option contract becomes void. The expiration
date for listed stock options is the Saturday after the third Friday of the expiration
month. All holders of options must indicate their desire to exercise, if they wish to
do so, by this date. See also Expiration Time.
Expiration Time: the time of day by which all exercise notices must be received on
the expiration date. Technically, the expiration time is currently 5:00 P.M. on the
expiration date, but public holders of option contracts must indicate their desire
to exercise no later than 5:30 P.M. on the business day preceding the expiration
date. The times are Eastern Time. See also Expiration Date.
Facilitation: the process of providing amarket for asecurity. Normally, this refers
to bids and offers made for large blocks of securities, such as those traded by insti
tutions. Listed options may be used to offset part of the risk assumed by the trad
er who is facilitating the large block order. See also Hedge Ratio.
Fair Value: normally, aterm used to describe the worth of an option or futures con
tract as determined by amathematical model. Also sometimes used to indicate
intrinsic value. See also Intrinsic Value, Model.
First Notice Day: the first day upon which the buyer of afutures contract can be
called upon to take delivery. See also Notice Period.
Float: the number of shares outstanding of aparticular common stock.
Floor Broker: atrader on the exchange floor who executes the orders of public cus
tomers or other investors who do not have physical access to the trading area.
Follow-Up Action: any trading in an option position after the position is established.
Generally, to limit losses or to take profits.
Fundamental Analysis: amethod of analyzing the prospects of asecurity by observ
ing accepted accounting measures such as earnings, sales, assets, and so on. See
also Technical Analysis.
Futures Contract: astandardized contract calling for the delivery of aspecified
quantity of acommodity at aspecified date in the future.
Gamma: ameasure of risk of an option that measures the amount by which the delta
changes for a I-point change in the stock price; alternatively, when referring to an
entire option position, the amount of change of the delta of the entire position
when the stock changes in price by one point.
Gamma of the Gamma: amathematical measure of risk that measures by how
much the gamma will change for a I-point move in the stock price. See Gamma.

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Glossary 971
Good Until Canceled (GTC): adesignation applied to some types of orders, mean
ing that the order remains in effect until it is either filled or canceled. See also
Limit, Stop-Limit Order, Stop Order.
Hedge Ratio: the mathematical quantity that is equal to the delta of an option. It is
useful in facilitation in that atheoretically riskless hedge can be established by tak
ing offsetting positions in the underlying stock and its call options. See also Delta,
Facilitation.
Historic Volatility: See Volatility.
Holder: the owner of asecurity.
Horizontal Spread: an option strategy in which the options have the same striking
price, but different expiration dates.
Implied Volatility: aprediction of the volatility of the underlying stock, it is deter
mined by using prices currently existing in the option market at the time, rather
than using historical data on the price changes of the underlying stock See also
Volatility.
Incremental Return Concept: astrategy of covered call writing in which the
investor is striving to earn an additional return from option writing against astock
position that he is targeted to sell, possibly at substantially higher prices.
Index: acompilation of the prices of several common entities into asingle number.
See also Capitalization-Weighted Index, Price-Weighted Index.
Index Arbitrage: aform of arbitraging index futures against stock If futures are
trading at prices significantly higher than fair value, the arbitrager sells futures and
buys the exact stocks that make up the index being arbitraged; if futures are at adiscount to fair value, the arbitrage entails buying futures and selling stocks.
Index Fund: amutual fund whose components exactly match the stocks that make
up awidely disseminated index, such as the S&P 500, Dow-Jones, Russell 2000, or
NASDAQ-100. See also Exchange-Traded Fund.
Index Option: an option whose underlying entity is an index. Most index options are
cash-based.
Institution: an organization, probably very large, engaged in investing in securities.
Normally abank, insurance company, or mutual fund.
Intermarket Spread: afutures spread in which futures contracts in one market are
spread against futures contracts trading in another market. Examples: Currency
spreads (yen vs. deutsche mark) or TED spread (T-Bills vs. Eurodollars).

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972 Glossary
In-the-Money: aterm describing any option that has intrinsic value. Acall option is
in-the-money if the underlying security is higher than the striking price of the call.
Aput option is in-the-money if the security is below the striking price. See also
Intrinsic Value, Out-of-the-Money.
Intramarket Spread: afutures spread in which futures contracts are spread against
other futures contracts in the same market; example, buy May soybeans, sell
March soybeans.
Intrinsic Value: the value of an option if it were to expire immediately with the
underlying stock at its current price; the amount by which an option is in-the
money. For call options, this is the difference between the stock price and the
striking price, if that difference is apositive number, or zero otherwise. For put
options it is the difference between the striking price and the stock price, if that
difference is positive, and zero otherwise. See also In-the-Money, Parity, Time
Value Premium.
Last Trading Day: the third Friday of the expiration month. Options cease trading
at 3:00 P.M. Eastern Time on the last trading day.
LEAPS: Long-term Equity Anticipation Securities. These are long-term listed
options, currently having maturities as long as two and one-half years.
Leg: arisk-oriented method of establishing atwo-sided position. Rather than enter
ing into asimultaneous transaction to establish the position (aspread, for exam
ple), the trader first executes one side of the position, hoping to execute the other
side at alater time and abetter price. The risk materializes from the fact that abetter price may never be available, and aworse price must eventually be accept
ed.
Letter of Guarantee: aletter from abank to abrokerage firm stating that acus
tomer (who has written acall option) does indeed own the underlying stock and
the bank will guarantee delivery if the call is assigned. Thus, the call can be con
sidered covered. Not all brokerage firms accept letters of guarantee.
Leverage: in investments, the attainment of greater percentage profit and risk
potential. Acall holder has leverage with respect to astockholder-the former will
have greater percentage profits and losses than the latter, for the same movement
in the underlying stock.
Limit: see Trading Limit.
Limit Order: an order to buy or sell securities at aspecified price (the limit). Alimit
order may also be placed "with discretion" -afixed; usually small, amount such as
1/sor ¼ of apoint. In this case, the floor broker executing the order may use his

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Glossary 973
discretion to buy or sell at 1/sor ¼ of apoint beyond the limit if he feels it is nec
essary to fill the order.
Listed Option: aput or call option that is traded on anational option exchange.
Listed options have fixed striking prices and expiration dates. See also Over-the
Counter Option.
Local: atrader on afutures exchange who buys and sells for his own account and
may fill public orders.
Lognormal Distribution: astatistical distribution that is often applied to the move
ment of the stock prices. It is aconvenient and logical distribution because it
implies that stock prices can theoretically rise forever but cannot fall below zero-
afact which is, of course, true.
Margin: to buy asecurity by borrowing funds from abrokerage house. The margin
requirement-the maximum percentage of the investment that can be loaned by
the broker firm-is set by the Federal Reserve Board.
Market Basket: aportfolio of common stocks whose performance is intended to
simulate the performance of aspecific index. See Index.
Market-Maker: an exchange member whose function is to aid in the making of amarket, by making bids and offers for his account in the absence of public buy or
sell orders. Several market-makers are normally assigned to aparticular security.
The market-maker system encompasses the market-makers and the board bro
kers. See also Board Broker, Specialist.
Market Not Held Order: also amarket order, but the investor is allowing the floor
broker who is executing the order to use his own discretion as to the exact timing
of the execution. If the floor broker expects adecline in price and he is holding a
"market not held" buy order, he may wait to buy, figuring that abetter price will
soon be available. There is no guarantee that a "market not held" order will be
filled.
Market Order: an order to buy or sell securities at the current market. The order
will be filled as long as there is amarket for the security.
Married Put and Stock: aput and stock are considered to be married if they are
bought on the same day, and the position is designated at that time as ahedge.
Model: amathematical formula designed to price an option as afunction of certain
variables-generally stock price, striking price, volatility, time to expiration, divi
dends to be paid, and the current risk-free interest rate. The Black
Scholes model is one of the more widely used models.

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974 Glossary
Monte Carlo Simulation: amodel designed to simulate areal-world event that can
not be approximated merely with amathematical formula. The Monte Carlo sim
ulation approximates such an event (the movement of the stock market, for exam
ple) and then it is simulated agreat number of times. The net result of all the sim
ulations is then interpreted as the result, generally expressed as aprobability of
occurrence. For example, a Monte Carlo simulation can be used to determine how
stocks might behave under certain stock price distributions that are different from
the lognormal distribution.
Naked Option: see Uncovered Option.
Narrow-Based: Generally referring to an index, it indicates that the index is com
posed of only afew stocks, generally in aspecific industry group. Narrow-based
indices are not subject to favorable treatment for naked option writers. See also
Broad-Based.
"Net" Order: see Contingent Order.
Neutral: describing an opinion that is neither bearish or bullish. Neutral option
strategies are generally designed to perform best if there is little nor no net change
in the price of the underlying stock. See also Bearish, Bullish.
Non-Equity Option: an option whose underlying entity is not common stock; typi
cally refers to options on physical commodities, but may also be extended to
include index options.
"Not Held": see Market Not Held Order.
Notice Period: the time during which the buyer of afutures contract can be called
upon to accept delivery. Typically, the 3 to 6 weeks preceding the expiration of the
contract.
Open Interest: the net total of outstanding open contracts in aparticular option
series. An opening transaction increases the open interest, while any closing trans
action reduces the open interest.
Opening Transaction: atrade that adds to the net position of an investor. An open
ing buy transaction adds more long securities to the account. An opening sell
transaction adds more short securities. See also Closing Transaction.
Option Pricing Curve: agraphical representation of the projected price of an
option at afixed point in time. It reflects the amount of time value premium in the
option for various stock prices, as well. The curve is generated by using amathe
matical model. The delta ( or hedge ratio) is the slope of atangent line to the curve
at afixed stock price. See also Delta, Hedge Ratio, Model.

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Glossary 975
Options Clearing Corporation (OCC): the issuer of all listed option contracts that
are trading on the national option exchanges.
Original Issue Discount (O1D): the initial price of azero-coupon bond. The owner
owes taxes on the theoretical interest, or phantom income, generated by the annu
al appreciation of the bond toward maturity. In reality, no interest is paid by the
zero-coupon bond, but the government is taxing the appreciation of the bond as if
it were interest.
Out-of-the-Money: describing an option that has no intrinsic value. Acall option is
out-of-the-money if the stock is below the striking price of the call, while aput
option is out-of-the-money if the stock is higher than the striking price of the put.
See also In-the-Money, Intrinsic Value.
Over-the-Counter Option (OTC): an option traded over-the-counter, as opposed
to alisted stock option. The OTC option has adirect link between buyer and sell
er, has no secondary market, and has no standardization of striking prices and expi
ration dates. See a'lso Listed Option, Secondary Market.
Overvalued: describing asecurity trading at ahigher price than it logically should.
Normally associated with the results of option price predictions by mathematical
models. If an option is trading in the market for ahigher price than the model indi
cates, the option is said to be overvalued. See a'/so Fair Value, Undervalued.
Pairs Trading: ahedging technique in which one buys aparticular stock and sells
short another stock. The two stocks are theoretically linked in their price history,
and the hedge is established when the historical relationship is out of line, in hopes
that it will return to its former correlation.
Parity: describing an in-the-money option trading for its intrinsic value: that is, an
option trading at parity with the underlying stock. Also used as apoint of refer
ence-an option is sometimes said to be trading at ahalf-point over parity or at aquarter-point under parity, for example. An option trading under parity is adis
count option. See a'/so Discount, Intrinsic Value.
PERCS: Preferred Equity Redemption Cumulative Stock. Issued by acorporation,
this preferred stock pays ahigher dividend than the common and has aprice at
which it can be called in for redemption by the issuing corporation. As such, it is
really acovered call write, with the call premium being given to the holder in the
form of increased dividends. See Call Price, Covered Call Write, Redemption Price.
Physical Option: an option whose underlying security is aphysical commodity that
is not stock or futures. The physical commodity itself, typically acurrency or

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976 Glossary
Treasury debt issue, underlies that option contract. See also Equity Option, Index
Option.
Portfolio Insurance: amethod of selling index futures or buying index put options
to protect aportfolio of stocks.
Position: as anoun, specific securities in an account or strategy. Acovered call writ
ing position might be long 1,000 XYZ and short 10 XYZ January 30 calls. As averb,
to facilitate; to buy or sell-generally ablock of securities-thereby establishing aposition. See also Facilitation, Strategy.
Position Limit: the maximum number of put or call contracts on the same side of
the market that can be held in any one account or group of related accounts. Short
puts and long calls are on the same side of the market. Short calls and long puts
are on the same side of the market.
Premium: for options, the total price of an option contract. The sum of the intrinsic
value and the time value premium. For futures, the difference between the
futures price and the cash price of the underlying index or commodity.
Present Worth: amathematical computation that determines how much money
would have to be invested today, at aspecified rate, in order to produce adesig
nated amount at some time in the future. For example, at 10% for one year, the
present worth of $ll0 is $100.
Price-Weighted Index: astock index that is computed by adding the prices of each
stock in the index, and then dividing by the divisor. See also Capitalization
Weighted Index, Divisor.
Profit Graph: agraphical representation of the potential outcomes of astrategy.
Dollars of profit or loss are graphed on the vertical axis, and various stock prices
are graphed on the horizontal axis. Results may be depicted at any point in time,
although the graph usually depicts the results at expiration of the options involved
in the strategy.
Profit Range: the range within which aparticular position makes aprofit. Generally
used in reference to strategies that have two break-even points-an upside break
even and adownside break-even. The price range between the two break-even
points would be the profit range. See also Break-Even Point.
Profit Table: atable of results of aparticular strategy at some point in time. This is
usually atabular compilation of the data drawn on aprofit graph. See also Profit
Graph.

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Glossary 917
Program Trading: the act of buying or selling aparticular portfolio of stocks and
hedging with an offsetting position in index futures. The portfolio of stocks may be
small or large, but it is not the makeup of any stock index. See also Index Arbitrage.
Protected Strategy: aposition that has limited risk. Aprotected short sale (short
stock, long call) has limited risk, as does aprotected straddle write ( short straddle,
long out-of-the-money combination). See also Combination, Straddle.
Public Book (of orders): the orders to buy or sell, entered by the public, that are
away from the current market. The board broker or specialist keeps the public
book. Market-makers on the CBOE can see the highest bid and lowest offer at any
time. The specialist'sbook is closed ( only he knows at what price and in what quan
tity the nearest public orders are). See also Board Broker, Market-Maker,
Specialist.
Put: an option granting the holder the right to sell the underlying security at acer
tain price for aspecified period of time. See also Call.
Put-Call Ratio: the ratio of put trading volume divided by call trading volume;
sometime~ calculated with open interest or total dollars instead of trading volume.
Can be calculated daily, weekly, monthly, etc. Moving averages are often used to
smooth out short-term, daily figures.
Ratio Calendar Combination: astrategy consisting of asimultaneous position of aratio calendar spread using calls and asimilar position using puts, where the strik
ing price of the calls is greater than the striking price of the puts.
Ratio Calendar Spread: selling more near-term options than longer-term ones
purchased, all with the same strike, either puts or calls.
Ratio Spread: constructed with either puts or calls, the strategy consists of buying acertain amount of options and then selling alarger quantity of out-of-the-money
options.
Ratio Strategy: astrategy in which one has an unequal number of long securities
and short securities. Normally, it implies apreponderance of short options over
either long options or long stock.
Ratio Write: buying stock and selling apreponderance of calls against the stock that
is owned. ( Occasionally constructed as shorting stock and selling puts.)
Redemption Price: the price at which astructured product may be redeemed for
cash. This is distinctly different from a "call price," which is the price at which an
issue may be called away by the issuer. See also Call Price, PERCS, Structured
Product.

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978 Glossary
Resistance: aterm in technical analysis indicating aprice area higher than the cur
rent stock price where an abundance of supply exists for the stock, and therefore
the stock may have trouble rising through the price. See also Support.
Return (on investment): the percentage profit that one makes, or might make, on
his investment.
Return if Exercised: the return that acovered call writer would make if the under
lying stock were called away.
Return if Unchanged: the return that an investor would make on aparticular posi
tion if the underlying stock were unchanged in price at the expiration of the
options in the position.
Reversal Arbitrage: ariskless arbitrage that involves selling the stock short, writing
aput, and buying acall. The options have the same terms. See also Conversion
Arbitrage.
Reverse Hedge: astrategy in which one sells the underlying stock short and buys
calls on more shares than he has sold short. This is also called asynthetic straddle
and is an outmoded strategy for stocks that have listed puts trading. See also Ratio
Write, Straddle.
Reverse Strategy: ageneral name that is given to strategies that are the opposite of
better-known strategies. For example, aratio spread consists of buying calls at alower strike and selling more calls at ahigher strike. Areverse ratio spread, also
known as abackspread, consists of selling the calls at the lower strike and buying
more calls at the higher strike. The results are obviously directly opposite to each
other. See also Reverse Hedge Ratio Write, Reverse Hedge.
Rho: the measure of how much an option changes in price for an incremental mov<'
(generally l % ) in short-term interest rates; more significant for longer-term or i11-
the-money options.
Risk Arbitrage: aform of arbitrage that has some risk associated with it. Commonly
refers to potential takeover situations in which the arbitrageur buys the stock of
the company about to be taken over and sells the stock of the company that is
effecting the takeover. See also Dividend Arbitrage.
Roll: afollow-up action in which the strategist closes options currently in the posi
tion and opens other options with different terms, on the same underlying stock.
See also Roll Down, Roll Forward, and Roll Up.
Roll Down: close out options at one strike and simultaneously open other options al
alower strike.

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Glossary 979
Roll Forward: close out options at anear-term expiration date and open options at
alonger-term expiration date.
Roll Up: close out options at alower strike and open options at ahigher strike.
Rotation: atrading procedure on the open exchanges whereby bids and offers, but
not necessarily trades, are made sequentially for each series of options on an
underlying stock or index.
Secondary M~ket: any market in which securities can be readily bought and sold
after their initial issuance. The national listed option exchanges provided, for the
first time, asecondary market in stock options.
Serial Option: afutures option for which there is no corresponding futures contract
expiring in the same month. The underlying futures contract is the next futures
contract out in time. Example: There is no March gold futures contract, but there
is an April gold futures contract, so March gold options, which are serial options,
are options on April gold futures.
Series: all op,tion contracts on the same underlying stock having the same striking
price, expiration date, and unit of trading.
Skew: See Volatility Skew.
Specialist: an exchange member whose function it is both to make markets-buy
and sell for his own account in the absence of public orders-and to keep the book
of public orders. Most stock exchanges and some option exchanges utilize the spe
cialist system of trading
Spread Order: an order to simultaneously transact two or more option trades.
Typically, one option would be bought while another would simultaneously be
sold. Spread orders may be limit orders, not held orders, or orders with discretion.
They cannot be stop orders, however. The spread order may be either adebit or acredit.
Spread Strategy: any option position having both long options and short options of
the same type on the same underlying security.
Standard Deviation: ameasure of the volatility of astock. It is astatistical quanti
ty measuring the magnitude of the daily price changes of that stock. See also,
Volatility.
Stop Order: an order, placed away from the current market, that becomes amarket
order if the security trades at the price specified on the stop order. Buy stop orders
are placed above the market, while sell stop orders are placed below.

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980 Glossary
Stop-Limit Order: similar to astop order, the stop-limit order becomes alimit
order, rather than amarket order, when the security trades at the price specified
on the stop. See also Stop Order.
Straddle: the purchase or sale of an equal number of puts and calls having the same
terms.
Strangle: acombination involving aput and acall at different strikes with the same
expiration date.
Strategy: with respect to option investments, apreconceived, logical plan of position
selection and follow-up action.
Striking Price: see Exercise Price.
Striking Price Interval: the distance between striking prices on aparticular under
lying security. For stocks, the interval is normally 2.5 points for lower-priced stocks
and 5 points for higher-priced stocks. For indices, the interval is either 5 or 10
points. For futures, the interval is often as low as one or two points.
Structured Product: acombination of securities and possibly options into asingle
security that behaves like stock and trades on alisted stock exchange. Structured
products are created by many of the largest financial institutions (banks and bro
kerage firms). Many of the more popular ones are known by their acronyms, cre
ated by the institutions that issued them: MITTS, TARGETS, BRIDGES, LINKS,
DINKS, ELKS, and PERCS. See also PERCS.
Subindex: see Narrow-Based.
Suitable: describing astrategy or trading philosophy in which the investor is operat
ing in accordance with his financial means and investment objectives.
Support: aterm in technical analysis indicating aprice area lower than the current
price of the stock, where demand is thought to exist. Thus, astock would stop
declining when it reached asupport area. See also Resistance.
Synthetic Put: astrategy constructed by shorting the underlying instrument and
buying acall. The resulting position has the same profit and loss characteristics as
along put option.
Synthetic Stock: an option strategy that is equivalent to the underlying stock. Along
call and ashort put is synthetic long stock. Along put and ashort call is synthetic
short stock.
Technical Analysis: the method of predicting future stock price movements based
on observation of historical stock price movements.

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Glossary 981
Terms: the collective name denoting the expiration date, striking price, and under
lying stock of an option contract.
Theoretical Value: the price of an option, or aspread, as computed by amathe
matical model.
Theta: the measure of how much an option'sprice decays for each day of time that
passes.
Time Spread: see Calendar Spread.
Time Value Premium: the amount by which an option'stotal premium exceeds its
intrinsic value.
Total Return Concept: acovered call writing strategy in which one views the
potential profit of the strategy as the sum of capital gains, dividends, and option
premium.income, rather than viewing each one of the three separately.
Tracking Error: the amount of difference between the performance of aspecific
portfolio of stocks and abroad-based index with which they are being compared.
See Market Basket.
Trader: aspeculative investor or professional who makes frequent purchases and
sales.
Trading Limit: the exchange-imposed maximum daily price change that afutures
contract or futures option contract can undergo.
Treasury BilVOption Strategy: amethod of investment in which one places
approximately 90% of his funds in risk-free, interest-bearing assets such as
Treasury bills, and buys options with the remainder of his assets.
Type: the designation to distinguish between aput or call option.
Uncovered Option: awritten option is considered to be uncovered if the investor
does not have acorresponding position in the underlying security. See also
Covered.
Underlying Security: the security that one has the right to buy or sell via the terms
of alisted option contract.
Undervalued: describing asecurity that is trading at alower price than it logically
should. Usually determined by the use of amathematical model. See also Fair
Value, Overvalued.
Variable Ratio Write: an option strategy in which the investor owns 100 shares of
the underlying security and writes two call options against it, each option having adifferent striking price.

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982 Glossary
Vega: the measure of how much an option'sprice changes for an incremental
change-usually one percentage point-in volatility.
Vertical Spread: any option spread strategy in which the options have different
striking prices but the same expiration dates.
Volatility: ameasure of the amount by which an underlying security is expected to
fluctuate in agiven period of time. Generally measured by the annual standard
deviation of the daily price changes in the security, volatility is not equal to the beta
of the stock. Also called historical volatility, statistical volatility, or actual volatility.
See also Implied Volatility.
Volatility Skew: the term used to describe aphenomenon in which individual
options on asingle underlying instrument have different implied volatilities. I 11
general, not only are the individual options' implied volatilities different, but they
form apattern. If the lower striking prices have the lowest implied volatilities, and
then implied volatility progresses higher as one moves up through the striking
prices, that is called aforward or positive skew. Areverse or negative skew works
in the opposite way: The higher strikes have the lowest implied volatilities.
Warrant: along-term, nonstandardized security that is much like an option.
Warrants on stocks allow one to buy (usually one share of) the common at a ("(•rtain price until acertain date. Index warrants are generally warrants on the pri<·<·
of foreign indices. Warrants have also been listed on other things such as cross-('mrency spreads and the future price of abarrel of oil.
Write: to sell an option. The investor who sells is called the writer.

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984
Assignment of options, 7, 16-22
anticipating, 18-22
automatic, 18-19
call options, 7
of cash-based options, 501
commissions, 17-18
margin requirements, 16-17
put options, 7
Backspreads, 232-235 (see also Reverse spreads)
diagonal, 240-241
effect on of implied volatility changes, 781-782
and LEAPS, 407-408
Bear spreads using call options, 186-190
call bear spread, 186-188
as credit spread, 186
follow-up action, 190
assignment of short call, impending, 190
selecting, 189-190
an aggressive position usually, 189
summary, 190
Bear spread, put, 329-332 (see also Put spreads, basic)
Beta, 533-539
Black, Fisher, 459
Black-Scholes model, 456-466, 538, 610, 611, 635, 640,
644-645,646,647-648,651,677,678, 731,734,
758, 767-768, 798,902 (see also Mathematical
applications)
Black model, 647-648, 651, 677
characteristics, 459-461
dividends paid by common stock not included, 459
formula, 456-457
hedge ratio, 457
historical volatility, lognormal, computing, 461-466
lognormal distribution of stock prices, 460
vega, 750
volatility, computation of, 460-466
weighting factor, 459-460, 463-465
Block positioning, 455, 482-485 (see also Mathematical
applications)
Board broker system, 22
Box spread, 338, 439-44,3, 643-644
risks, 443
"Box" stock, 432
Broad-based indices, 500
Brownian motion, 806
Bull spread, structured product as, 608-612
valuing, 610-612
Bull spreads, 110-111, 113-116, 117, 172-185
aggressiveness, degrees of, 175-176
call bull spread, 172-173
effect on of implied volatility changes, 767-775
follow-up action, 178-180
credit spread, 179
"legging" out of spread, 180
and outright purchase, comparison of, 179
and LEAPS, 403-404
ranking, 176-178
diagonal bull spread, 177
summary, 185
uses, other, 180-184
Index
break-even price on common stock, lowering, 182,
183
simple form of spreading, 180, 185
as "substitute" for covered writing, 182-184
vertical, 172
when options are expensive, 177
Bull spread, put, 332-333 (see also Put spreads, basic)
Bullish calendar spread, 196-198 (see also Calendar
spread)
Butterfly spread, 200-209, 336-338 (see also Put
spreads, basic)
combination of bull and bear spreads, 200, 209
commissions costly, 200, 203
example, 201
follow-up action, 206-209
assignment, 206
"legging out," 207
neutral position, 200
results of at expiration, 201-203
selecting, 203-206
striking prices, three, 200-203
summary, 209
Calendar combination of calls and puts, 345-348
Calendar spread, 116-117, 191-199
as antivolatility strategy, 194
bullish, 196-198, 199
follow-up action, 197-198
definition, 191
expiration series, using all three, 198-199
horizontal spread, 191
in volatility trading, 825-826
and LEAPS, 408-409
mathematical calculations of volatility, applying lo.
478-480
neutral, 192-194, 199
follow-up action, 194-196
volatility, effect of, 194
summary, 199
time spread another name, 191
volatility changes, effect of on, 778-780
with futures options, 704-709 (see also Futtm'soptions and strategies)

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