Chapter 25: LEAPS 401
LEAPS calls may help to alleviate this problem. Since they are such long-term
calls, they are likely to have some time value premium in them. In-the-money calls that
have time value premium are not normally assigned. As an alternative to shorting astock that is not borrowable, one might try to sell an in-the-money LEAPS call, but
only if it has time value premium remaining. Just because the call has along time
remaining until expiration does not mean that it must have time value premium, as will
be seen in the following discussion. Finally, if one does sell the LEAPS call, he must
realize that if the stock drops, the LEAPS call will not follow it completely. As the stock
nears the strike, the amount of time value premium will build up to an even greater
level in the LEAPS. Still, the naked call seller would make some profit in that case, and
it presents abetter alternative than not being able to sell the stock short at all.
Early Assignment. An American-style option is one that can be exercised at any
time during its life. All listed equity options, LEAPS included, are of this variety.
Thus, any in-the-money option that has been sold may become subject to early
assignment. The clue to whether early assignment is imminent is whether there is
time value premium in the option. If the option has no time value premium - in other
words, it is trading at parity or at adiscount then assignment may be close at hand.
The option writer who does not want to be assigned would want to cover the option
when it no longer carries time premium.
LEAPS may be subject to early assignment as well. It is possible, albeit far less
likely, that along-term option would lose all of its time value premium and therefore
be subject to early assignment. This would certainly happen if the underlying stock
were being taken over and atender off er were coming to fruition. However, it may
also occur because of an impending dividend payment, or more specifically, because
the stock is about to go ex-dividend. Recall that the call owner, LEAPS calls includ
ed, is not entitled to any dividends paid by the underlying stock. So if the call owner
wants the dividend, he exercises his call on the day before the stock goes ex-dividend.
This makes him an owner of the common stock just in the nick of time to get the div
idend.
What economic factors motivate him to exercise the call? If there is any time
value premium at all in the call, the call holder would be better off selling the call in
the open market and then purchasing the stock in the open market as well. In this
manner, he would still get the dividend, but he would get abetter price for his call
when he sold it. If, however, there is no time value premium in the call, he does not
have to bother with two transactions in the open market; he merely exercises his call
in order to buy stock.
All well and good, but what makes the call sell at parity before expiration? It has
to do with the arbitrage that is available for any call option. In this case, the arbitrage

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402 Part Ill: Put Option Strategies
is not the simple discount arbitrage that was discussed in Chapter lwhen this topic
was covered. Rather, it is amore complicated form that is discussed in greater detail
in Chapter 28. Suffice it to say that if the dividend is larger than the interest that can
be earned from acredit balance equal to the striking price, then the time value pre
mium will disappear from the call.
Example: XYZ is a $30 stock and about to go ex-dividend 50 cents. The prevailing
short-term interest rate is 5% and there are LEAPS with astriking price of 20.
A 50-cent quarterly dividend on astriking price of 20 is an annual dividend rate
(on the strike) of 10%. Since short-term rates are much lower than that, arbitrageurs
economically cannot pay out 10% for dividends and earn 5% for their credit balances.
In this situation, the LEAPS call would lose its time value premium and would
be acandidate for early exercise when the stock goes ex-dividend.
In actual practice, the situation is more complicated than this, because the price
of the puts comes into play; but this example shows the general reasoning that the
arbitrageur must go through.
Certain arbitrageurs construct positions that allow them to earn interest on acredit balance equal to the striking price of the call. This position involves being short
the underlying stock and being long the call. Thus, when the stock goes ex-dividend,
the arbitrageur will owe the dividend. If, however, the amount of the dividend is
more than he vvill earn in interest from his credit balance, he will merely exercise his
call to cover his short stock. This action will prevent him from having to pay out the
dividend.
The arbitrageur'sexercise of the call means that someone is going to be
assigned. If you are awriter of the call, it could be you. It is not important to under
stand the arbitrage completely; its effect will be reflected in the marketplace in the
form of acall trading at parity or adiscount. Thus, even a LEAPS call with asub
stantial anwunt of time rernaining may be assigned if it is trading at parity.
STRADDLE SELLING
Straddle selling is equivalent to ratio writing and is astrategy whereby one attempts
to sell ( overpriced) options in order to produce arange of stock prices within which
the option seller can profit. The strategy often involves follow-up action as the stock
moves around, and the strategist feels that he must adjust his position in order to pre
vent large losses. LEAPS puts and calls might be used for this strategy. However,
their long-term nature is often not conducive to the aims of straddle selling.
First, consider the effect of time decay. One might normally sell athree-month
straddle. If the stock "behaves" and is relatively unchanged after two months have

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Chapter 25: LEAPS 403
passed, the straddle seller could reasonably expect to have aprofit of about 40% of
the original straddle price. However, if one had sold a 2-year LEAPS straddle, and
the stock were relatively unchanged after two months, he would only have aprofit of
about 7% of the original sale price. This should not be surprising in light of what has
been demonstrated about the decaying of long-term options. It should make the
straddle seller somewhat leery of using LEAPS, however, unless he truly thinks the
options are overpriced.
Second, consider follow-up action. Recall that in Chapter 20, it was shown that
the bane of the straddle seller was the whipsaw. Awhipsaw occurs when one makes
afollow-up protective action on one side (for instance, he does something bullish
because the underlying stock is rising and the short calls are losing money), only to
have the stock reverse and come crashing back down. Obviously, the more time left
until expiration, the more likely it is that awhipsaw will occur after any follow-up
action, and the more expensive it will be, since there will be alot of time value pre
mium left in the options that are being repurchased. This makes LEAPS straddle
selling less than attractive.
LEAPS straddles may look expensive because of their large absolute price, and
therefore may appear to be attractive straddle sale candidates. However, the price is
often justified, and the seller of LEAPS straddles will be fighting sudden stock move
ments without getting much benefit from the passage of time. The best time to sell
LEAPS straddles is when short-term rates are high and volatilities are high as well
(i.e., the options are overpriced). At least, in those cases, the seller will derive some
real benefit if rates or volatilities should drop.
SPREADS USING LEAPS
Any of the spread strategies previously discussed can be implemented with LEAPS
as well, if one desires. The margin requirements are the same for LEAPS spreads as
they are for ordinary equity option spreads. One general category of spread lends
itself well to using LEAPS: that of buying alonger-term option and selling ashort
term one. Calendar spreads, as well as diagonal spreads, fall into that category.
The combinations are myriad, but the reasoning is the same. One wants to own
the option that is not so subject to time decay, while simultaneously selling the
option that is quite subject to time decay. Of course, since LEAPS are long-term and
therefore expensive, one is generally taking on alarge debit in such aspread and
may have substantial risk if the stock performs adversely. Other risks may be pres
ent as well. As ameans of demonstrating these facts, let us consider asimple bull
spread using calls.

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404 Part Ill: Put Option Strategies
Example: The following prices exist in the month of January:
XYZ: 105
April 100 call: 10 1/2
April 110 call: 5 1/2
January (2-year) 100 call: 26
January (2-year) 110 call: 21 1/2
An investor is considering abull spread in XYZ and is unsure about whether to use
the short-term calls, the LEAPS calls, or amixture. These are his choices:
Short-term bull spread:
Diagonal bull spread:
LEAPS bull spread:
Buy April 100@ 101/2
Sell April 110@ 51/2
Net Debit: $500
Buy January LEAPS 100 @ 26
Sell April 110@ 51/2
Net Debit: $2,050
Buy January LEAPS 1 00 @ 26
Sell January LEAPS 110@ 21 1/2
Net Debit: $450
Notice that the debit paid for the LEAPS spread is slightly less than that of the short
term bull spread. This means that they have approximately the same profit potential
at their respective expiration dates. However, the strategist is more concerned with
how these compare directly with each other. The obvious point in time to make this
comparison is when the short-term options expire.
Figure 25-7 shows the profitability of these three positions at April expiration.
It was assumed that all of the following were the same in April as they had been in
January: volatility, short-term rates, and dividend payout.
Note that the short-term bull spread has the familiar profit graph from Chapter
7, making its maximum profit over 110 and taking its maximum loss below 100. (See
Table 25-4.)
The LEAPS spread doesn'tgenerate much of either aprofit or aloss in only
three months' time. Even if XYZ rises to 120, the LEAPS bull spread will have only
a $150 profit. Conversely, if XYZ falls to 80, the spread loses only about $200. This
price action is very typical for long-term bull spreads when both options have asig
nificant amount of time premium remaining in them.

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Chapter 25: LEAPS
FIGURE 25-7.
Bull spread comparison at April expiration.
Stock Price
405
The diagonal spread is different, however. Typically, the maximum profit poten
tial of abull spread is the difference in the strikes less the initial debit paid. For this
diagonal spread, that would be $1,000 minus $2,050, aloss! Obviously, this simple
formula is not applicable to diagonal spreads, because the purchased option still has
time value premium when the written option expires. The profit graph shows that
indeed the diagonal spread is the most bullish of the three. It makes its best profit at
the strike of the written option - astandard procedure for any spread - and that prof
it is greater than either of the other two spreads at April expiration ( under the sig-
TABLE 25-4.
Bull spread comparison at April expiration.
Stock Price Short-Term Diagonal LEAPS
80 -500 -1, 100 -200
90 -500 - 600 -150
100 -500 50 - 25
110 500 750 50
120 500 550 150
140 500 150 250
160 500 50 350
180 500 - 350 450

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406 Part Ill: Put Option Strategies
nificant assumption that volatility and interest rates are unchanged). If XYZ trades
higher than llO, the diagonal spread will lose some of its profit; in fact, if XYZ were
to trade at avery high price, the diagonal spread would actually have aloss (see Table
25-4). Whenever the purchased LEAPS call loses its time value premium, the diag
onal spread will not perform as well.
If the common stock drops in price, the diagonal spread has the greatest risk in
dollar terms but not in percentage terms, because it has the largest initial debit. If
XYZ falls to 80 in three months, the spread will lose about $1,100, just over half the
initial $2,050 debit. Obviously, the short-term spread would have lost 100% of its ini
tial debit, which is only $500, at that same point in time.
The diagonal spread presents an opportunity to earn more money if the under
lying common is near the strike of the written option when the written option expires.
However, if the common moves agreat deal in either direction, the diagonal spread
is the worst of the three. This means that the diagonal spread strategy is aneutral
strategy: One wants the underlying common to remain near the written strike until
the near-term option expires. This is atrue statement even if the diagonal spread is
under the guise of abullish spread, as in the previous example.
Many traders are fond of buying LEAPS and selling an out-of-the-money near
term call as ahedge. Be careful about doing this. If the underlying common rises too
fast and/or interest rates fall and/or volatility decreases, this could be apoor strategy.
There is really nothing quite as psychologically damaging as being right about the
stock, but being in the wrong option strategy and therefore losing money. Consider
the above examples. Ostensibly, the spreader was bullish on XYZ; that'swhy he chose
bull spreads. If XYZ became awildly bullish stock and rose from 100 to 180 in three
months, the diagonal spreader would have lost money. He couldn'thave been happy
- no one would be. This is something to keep in mind when diagonalizing a LEAPS
spread.
The deltas of the options involved in the spread will give one agood clue as to
how it is going to perform. Recall that ashort-term, in-the-money option acquires arather high delta, especially as expiration draws nigh. However, an in-the-money
LEAPS call will not have an extremely high delta, because of the vast amount of time
remaining. Thus, one is short an option with ahigh delta and long an option with asmaller delta. These deltas indicate that one is going to lose money if the underlying
stock rises in price. Consider the following situation:
XYZ Stock, 120:
Call
Long 1 January LEAPS 100 call:
Short 1 April 110 call:
Position Delta
0.70
-0.90

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Chapter 25: LEAPS 401
At this point, if XYZ rises in price by 1 point, the spread can be expected to lose 20
cents, since the delta of the short option is 0.20 greater than the delta of the long
option.
This phenomenon has ramifications for the diagonal spreader of LEAPS. If the
two strike prices of the spread are too close together, it may actually be possible to
construct abull spread that loses money on the upside. That would be very difficult
for most traders to accept. In the above example, as depicted in Table 25-4, that'swhat happens. One way around this is to widen the strike prices out so that there is
at least some profit potential, even if the stock rises dramatically. That may be diffi
cult to do and still be able to sell the short-term option for any meaningful amount
of premium.
Note that adiagonal spread could even be considered as asubstitute for acov
ered write in some special cases. It was shown that a LEAPS call can sometimes be
used as asubstitute for the common stock, with the investor placing the difference
between the cost of the LEAPS call and the cost of the stock in the bank (or in Tbills). Suppose that an investor is acovered writer, buying stock and selling relative
ly short-term calls against it. If that investor were to make a LEAPS call substitution
for his stock, he would then have adiagonal bull spread. Such adiagonal spread
would probably have less risk than the one described above, since the investor pre
sumably chose the LEAPS substitution because it was "cheap." Still, the potential
pitfalls of the diagonal bull spread would apply to this situation as well. Thus, if one
is acovered writer, this does not necessarily mean that he can substitute LEAPS calls
for the long stock without taking care. The resulting position may not resemble acov
ered write as much as he thought it would.
The "bottom line" is that if one pays adebit greater than the difference in the
strike prices, he may eventually lose money if the stock rises far enough to virtually
eliminate the time value premium of both options. This comes into play also if one
rolls his options down if the underlying stock declines. Eventually, by doing so, he
may invert the strikes - i.e., the striking price of the written option is lower than the
striking price of the option that is owned. In that case, he will have locked in aloss if
the overall credit he has received is less than the difference in the strikes - aquite
likely event. So, for those who think this strategy is akin to aguaranteed profit, think
again. It most certainly is not.
Backspreads. LEAPS may be applied to other popular forms of diagonal spreads,
such as the one in which in-the-money, near-term options are sold, and agreater quan
tity of longer-term (LEAPS) at- or out-of-the money calls are bought. (This was
referred to as adiagonal backspread in Chapter 14.) This is an excellent strategy, and

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408 Part Ill: Put Option Strategies
a LEAPS may be used as the long option in the spread. Recall that the object of the
spread is for the stock to be volatile, particularly to the upside if calls are used. If that
doesn'thappen, and the stock declines instead, at least the premium captured from
the in-the-money sale will be again to offset against the loss suffered on the longer
term calls that were purchased. The strategy can be established with puts as well, in
which case the spreader would want the underlying stock to fall dramatically while the
spread was in place.
Without going into as much detail as in the examples above, the diagonal back
spreader should realize that he is going to have asignificant debit in the spread and
could lose asignificant portion of it should the underlying stock fall agreat deal in
price. To the upside, his LEAPS calls will retain some time value premium and will
move quite closely with the underlying common stock. Thus, he does not have to buy
as many LEAPS as he might think in order to have aneutral spread.
Example: XYZ is at 105 and aspreader wants to establish abackspread. Recall that
the quantity of options to use in aneutral strategy is determined by dividing the
deltas of the two options. Assume the following prices and deltas exist:
Option
April 100 call
July 110 call
January (2-year) LEAPS 100 call
XYZ: 105 in January
Price
8
5
15
Delta
0.75
0.50
0.60
Two backspreads are available with these options. In the first, one would sell the
April 100 calls and buy the July llO calls. He would be selling 3-month calls and buy
ing 6-month calls. The neutral ratio is 0.75/0.50 or 3 to 2; that is, 3 calls are to be
bought for every 2 sold. Thus, aneutral spread would be:
Buy 6 July 110 calls
Sell 4 April l 00 calls
As asecond alternative, he might use the LEAPS as the long side of the spread; he
would still sell the April 100 calls as the short side of the spread. In this case, his neu
tral ratio would be 0.75/0.60, or 5 to 4. The resulting neutral spread would be:
Buy 5 January LEAPS 110 calls
Sell 4 April 100 calls

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Chapter 25: LEAPS 409
Thus, aneutral backspread involving LEAPS requires buyingfewer calls than aneu
tral backspread involving a 6-rnonth option on the long side. This is because the delta
of the LEAPS call is larger. The significant point here is that, because of the time
value retention of the LEAPS call, even when the stock moves higher, it is not nec
essary to buy as many. If one does not use the deltas, but merely figures that 3 to 2
is agood ratio for any diagonal backspread, then he will be overly bullish if he uses
LEAPS. That could cost him if the underlying stock declines.
Calendar Spreads. LEAPS may also be used in calendar spreads - spreads in
which the striking price of the longer-term option purchased and the shorter-term
option sold are the same. The calendar spread is aneutral strategy, wherein the
spreader wants the underlying stock to be as close as possible to the striking price
when the near-term option expires. Acalendar spread has risk if the stock moves too
far away from the striking price (see Chapters 9 and 22). Purchasing a LEAPS call
increases that risk in terms of dollars, not percentage, because of the larger debit that
one must spend for the spread.
Simplistically, calendar spreads are established with equal quantities of options
bought and sold. This is often not aneutral strategy in the true sense. As was shown
in Chapter 9 on call calendar spreads, one may want to use the deltas of the two
options to establish atruly neutral calendar spread, particularly if the stock is not ini
tially right at the striking price. Out-of-the-money, one would sell more calls than he
is buying. Conversely, in-the-money, one would buy more calls than he is selling.
Both strategies statistically have merit and are attractive. When using LEAPS deltas
to construct the neutral spread, one need generally buy fewer calls than he might
think, because of the higher delta of a LEAPS call. This is the same phenomenon
described in the previous example of adiagonal backspread.
SUMMARY
LEAPS are nothing more than long-term options. They are usable in awide variety
of strategies in the same way that any option would be. Their margin and investment
requirements are similar to those of the more familiar equity options. Both LEAPS
puts and calls are traded, and there is asecondary market for them as well.
There are certain differences between the prices of LEAPS and those of short
er-term options, but the greatest is the relatively large effect that interest rates and
dividends have on the price of LEAPS, because LEAPS are long-term options.
Increases in interest rates will cause LEAPS to increase in price, while increases in
dividend payout will cause LEAPS calls to decrease in price and LEAPS puts to

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410 Part Ill: Put Option Strategies
increase in price. As usual, volatility has amajor effect on the price of an option, and
LEAPS are no exception. Even small changes in the volatility of the underlying com
mon stock can cause large price differences in atwo-year option. The rate of decay
due to time is much smaller for LEAPS, since they are long-term options. Finally, the
deltas of LEAPS calls are larger than those of short-term calls; conversely, the deltas
of LEAPS puts are smaller.
Several common strategies lend themselves well to the usage of LEAPS. A
LEAPS may be used as astock substitute if the cash not invested in the stock is
instead deposited in a CD or T-bill. LEAPS puts can be bought as protection for
common stock. Speculative option buyers will appreciate the low rate of time decay
of LEAPS. LEAPS calls can be written against common stock, thereby creating acovered write, although the sale of naked LEAPS puts is probably abetter strategy
in most cases. Spread strategies with LEAPS may be viable as well, but the spreader
should carefully consider the ramifications of buying along-term option and selling
ashorter-term one against it. If the underlying stock moves agreat distance quickly,
the spread strategy may not perform as expected.
Overall, LEAPS are not very different from the shorter-term options to which
traders and investors have become accustomed. Once these investors become famil
iar with the way these long-term options are affected by the various factors that
determine the price of an option, they will consider the use of LEAPS as an integral
part of astrategic arsenal.

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Buying Options
and Treasury Bills
Numerous strategies have been described, ranging from the simple to the complex.
Each one has advantages, but there are disadvantages as well. In fact, some of them
may be too complex for the average investor to seriously consider implementing. The
reader may feel that there should be an easier answer. Isn'tthere astrategy that
might not require such alarge investment or so much time spent in monitoring the
position, but would still have achance of returning areasonable profit? In fact, there
is astrategy that has not yet been described, astrategy considered by some experts
in the field of mathematical analysis to be the best of them all. Simply stated, the
strategy consists of putting 90% of one'smoney in risk-free investments (such as
short-term Treasury bills) and buying options with the remaining 10% of one'sfunds.
It has previously been pointed out that some of the more attractive strategies
are those that involve small levels of risk with the potential for large profits. Usually,
these types of strategies inherently have arather large frequency of small losses, and
asmall probability of realizing large gains. Their advantage lies in the fact that one or
two large profits can conceivably more than make up for numerous small losses. This
Treasury bill/option strategy is another strategy of this type.
HOW THE TREASURY BILL/OPTION STRATEGY OPERATES
Although there are certain details involved in operating this strategy, it is basically asimple one to approach. First, the most that one can lose is 10%, less the interest
earned on the fixed-income portion of his portfolio (the remaining 90% of his assets),
during the life of the purchased options. It is asimple matter to space out one'scom-
413

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414 Part IV: Additional Considerations
mitments to option purchases so that his overall risk in aone-year period can be kept
down to nearly 10%.
Example: An investor might decide to put 2½% of his money into three-month
option purchases. Thus, in any one year, he would be 1isking 10%. At the same time
he would be earning perhaps 6% from the overall interest generated on the fixed
income securities that make up the remaining 90% of his assets. This would keep his
overall risk down to approximately 4.6% per year.
There are better ways to monitor this risk, and they are described shortly. The
potential profits from this strategy are limited only by time. Since one is owning
options - say call options - he could profit handsomely from alarge upward move in
the stock market. As with any strategy in which one has limited risk and the poten
tial of large profits, asmall number of large profits could offset alarge number of
small losses. In actual practice, of course, his profits will never be overwhelming,
since only approximately 10% of the money is committed to option purchases.
In total, this strategy has greatly reduced 1isk with the potential of making
above-average profits. Since the 10% of the money that is invested in options gives
great leverage, it might be possible for that portion to double or triple in ashort time
under favorable market conditions. This strategy is something like owning aconvert
ible bond. Aconvertible bond, since it is convertible into the common stock, moves
up and down in price with the price of the underlying stock. However, if the stock
should fall agreat deal, the bond will not follow it all the way down, because eventu
ally its yield will provide a "floor" for the price.
Astrategy that is not used very often is called the "synthetic convertible bond."
One buys adebenture and acall option on the same stock. If the stock rises in price,
the call does too, and so the combination of the debenture and the call acts much like
aconvertible bond would to the upside. If, on the other hand, the stock falls, the call
will expire worthless; but the investor will retain most of his investment, because he
will still have the debenture plus any interest that the bond has paid.
The strategy of placing 90% of one'smoney into risk-free, interest-bearing cer
tificates and buying options with the remainder is superior to the convertible bond
or the "synthetic convertible bond," since there is no risk of price fluctuation in the
largest portion of the investment.
The Treasury bill/option strategy is fairly easy to operate, although one does
have to do some work every time new options are purchased. Also, periodic adjust
ments need to be made to keep the level of risk approximately the same at all times.
As for which options to buy, the reader may recall that specifications were outlined
in Chapters 3 and 16 on how to select the best option purchases. These criteria can
be summarized briefly as follows:

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Chapter 26: Buying Options and Treasury Bills 415
1. Assume that each underlying stock can advance or decline in accordance with its
volatility over afixed time period (30, 60, or 90 days).
2. Estimate the call prices after the advance, or put prices after the decline.
3. Rank all potential purchases by the highest reward opportunity.
The user of this strategy need only be interested in those option purchases that
provide the highest reward opportunity under this ranking method. In the previous
chapters on option buying, it was mentioned that one might want to look at the
risk/reward ratios of his potential option purchases in order to have amore conser
vative list. However, that is not necessary in the Treasury bill/option strategy, since
the overall risk has already been limited. Aranking of option purchases via the fore
going criteria will generally give alist of at- or slightly out-of-the-money options.
These are not necessarily "underpriced" options; although if an option is truly under
priced, it will have abetter chance of ranking higher on the selection list than one
that is "overpriced."
Alist of potential option purchases that is constructed with criteria similar to
those outlined above is available from many data services and brokerage firms. The
strategist who is willing to select his option purchases in this manner will find that he
does not have to spend agreat deal of time on the selection process. The reader
should note that this type of option purchase ranking completely ignores the outlook
for the underlying stock. If one would rather make his purchases based on an outlook
for the underlying stock - preferably atechnical outlook - he will be forced to spend
more time on his selection process. Although this may be appealing to some
investors, it will probably yield worse results in the long run than the previously
described unbiased approach to option purchases, unless the strategist is extremely
adept at stock selection.
KEEPING THE RISK LEVEL EQUAL
The second function that the strategist has to perform in this Treasury bill/option
strategy is to keep his risk level approximately equal at all times.
Example: An investor starts the strategy with $90,000 in Treasury bills (T-bills) and
$10,000 in option purchases. After some time has passed, the option purchases may
have worked out well and perhaps he now has $90,000 in T-bills plus $30,000 worth
of options, plus interest from the T-bills. Obviously, he no longer has 90% of his
money in fixed-income securities and 10% in option purchases. The ratio is now 75%
in T-bills and 25% in option purchases. This is too risky aratio, and the strategist
must consequently sell some of his options and buy T-bills with the proceeds. Since
his total assets are $120,000 currently, he must sell out $18,000 of options to bring his

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416 Part IV: Additional Considerations
option investment down from the current $30,000 figure to $12,000, or 10% of his
total assets. If one fails to adhere to this readjustment of his funds after profits are
made, he may eventually lose those profits. Since options can lose agreat percentage
of their worth in ashort time pe1iod, the investor is always running the risk that the
option portion of his investment may be nearly wiped out. If he has kept all his prof
its in the option portion of his strategy, he is constantly risking nearly all of his accu
mulated profits, and that is not wise.
One must also adjust his ratio of T-bills to options after losses occur.
Example: In the first year, the strategist loses all of the $10,000 he originally placed
in options. This would leave him with total assets of $90,000 plus interest (possibly
$6,000 of interest might be earned). He could readjust to a 90:10 ratio by selling out
some of the T-bills and using the proceeds to buy options. If one follows this strate
gy, he will be risking 10% of his funds each year. Thus, aseries of loss years could
depreciate the initial assets, although the net losses in one year would be smaller than
10% because of the interest earned on the T-bills. It is recommended that the strate
gist pursue this method of readjusting his ratios in both up and down markets in
order to constantly provide himself with essentially similar risk/reward opportunities
at all times.
The individual can blend the option selection process and the adjustment of the
T-bill/option ratio to fit his individual portfolio. The larger portfolio can be diversi
fied into options \vith differing holding periods, and the ratio adjustments can be
made quite frequently, perhaps once amonth. The smaller investor should concen
trate on somewhat longer holding periods for his options, and would adjust the ratio
less often. Some examples might help to illustrate the way in which both the large
and small strategist might operate. It should be noted that this T-bill/option strategy
is quite adaptable to fairly small sums of money, as long as the 10% that is going to
be put into option purchases allows one to be able to participate in areasonable man
ner. Atactic for the extremely small investor is also described below.
ANNUALIZED RISK
Before getting into portfolio size, let us describe the concept of annualized risk.
One might want to purchase options with the intent of holding some of them for 30
days, some for 90 days, and some for 180 days. Recall that he does not want his
option purchases to represent more than 10% annual risk at any time. In actual
practice, if one purchases an option that has 90 days of life, but he is planning to
hold the option only 30 days, he will most likely not lose 100% of his investment in

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Chapter 26: Buying Options and Treasury Bills 417
the 30-day period. However, for purposes of computing annualized risk easily, the
assumption that will be made is that the risk during any holding period is 100%,
regardless of the length of time remaining in the life of the option. Thus, a 30-day
option purchase represents an annualized risk of 1,200% (100% risk every 30 days
times twelve 30-day periods in one year). Ninety-day purchases have 400% annual
ized risk, and 180-day purchases have 200% annualized risk. There is amultitude
of ways to combine purchases in these three holding periods so that the overall risk
is 10% annualized.
Example: An investor could put 2½% of his total money into 90-day purchases four
times ayear. That is, 2½% of his total assets are being subjected to a 400% annual
ized risk; 400% times 2½% equals 10% annualized risk on the total assets. Of course,
the remainder of the assets would be placed in risk-free, income-bearing securities.
Another of the many combinations might be to place 1 % of the total assets in 90-day
purchases and also place 3% of the total assets in 180-day purchases. Thus, 1 % of
one'stotal money would be subjected to a 400% annual risk and 3% would be sub
jected to a 200% annual risk (.01 times 400 plus .03 times 200 equals 10% annualized
risk on the entire assets). If one prefers aformula, annualized risk can be computed
as:
Aal. d • k • r 1. Percent of total 360 nnu 1ze ns on entire portro 10 = dxassets investe Holding period
If one is able to diversify into several holding periods, the annualized risk is merely
the sum of the risks for each holding period.
With this information in mind, the strategist can utilize option purchases of 1
month, 3 months, and 6 months, preferably each generated by aseparate computer
analysis similar to the one described earlier. He will know how much of his total
assets he can place into purchases of each holding period, because he will know his
annualized risk.
Example: Suppose that avery large investor, or pool of investors, has $1 million com
mitted to this T-bill/option strategy. Further, suppose ½ of 1 % of the money is to be
committed to 30-day option purchases with the idea of reinvesting every 30 days.
Similarly, ½ of 1 % is to be placed in 90-day purchases and 1 % in 180-day purchases.
The annualized risk is 10%:
Total annualized risk = ½% x 360 + ½% x 360 + 1 % x 360
30 90 180
= .06 + .02 + .02 = 10%

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418 Part IV: Additional Considerations
With asset.sof $1 million, this means that $.5,000 would be committed to 30-day pur
chases; $.5,000 to 90-day purchases; and $10,000 to 180-day purchases. This money
would be reinvested in similar quantities at the end of each holding period.
RISK ADJUSTMENT
The subject of adjusting the ratio to constantly reflect 10% risk must be addressed at
the end of each holding period. Although it is correct for the investor to keep his per
centage commitments constant, he must not be deluded into automatically reinvest
ing the same amount of dollars each time.
Example: At the end of 30 days, the value of the entire portfolio, including potential
option profits and losses, and interest earned, was down to $990,000. Then only ½ of
1 % of that amount should be invested in the next 30-day purchase ($4,9.50).
By operating in this manner - first computing the annualized risk and balanc
ing it through predetermined percentage commitments to holding periods of various
lengths; and second, readjusting the actual dollar commitment at the end of each
holding period - the overall risk/reward ratios v,ill be kept close to the levels
described in the earlier, simple desciiption of this strategy. This may require arela
tively large amount of work on the part of the strategist, but large portfolios usually
do require work.
The smaller investor does not have the luxury of such complete diversification,
but he also does not have to adjust his total position as often.
Example: An investor decided to commit $.50,000 to this strategy. Since there is a
1,200% annualized risk in 30-day purchases, it does not make much sense to even
consider purchases that are so short-term for assets of this size. Rather, he might
decide to commit 1 % of his assets to a 90-day purchase and 3% to a 180-day pur
chase. In dollar amounts, this would be $.500 in a 90-day option and $1,.500 in 180-
day options. Admittedly, this does not leave much room for diversification, but to risk
more in the short-term purchases would expose the investor to too much risk. In
actual practice, this investor would probably just invest .5% of his assets in 180-day
purchases, also a 10% annualized risk. This would mean that he could operate with
only one option buyer'sanalysis (the 180-day one) and could place $2,.500 into selec
tions from that list.
His adjustments of the assets committed to option purchases could not be done
as frequently as the large investor, because of the commissions involved. He certain
ly would have to adjust every 180 days, but might prefer to do so more frequently -
perhaps every 90 days - to be able to space his 180-day commitments over different

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Chapter 26: Buying Options and Treasury Bills 419
option expiration cycles. It should also be pointed out that T-bills can be bought and
sold only in amounts of at least $10,000 and in increments of $5,000 thereafter. That
is, one could buy or sell $10,000 or $15,000 or $20,000 or $25,000, and so on, but
could not buy or sell $5,000 or $8,000 or $23,000 in T-bills. This is of little concern
to the investor with $1 million, since it takes only afraction of apercentage of his
assets to be able to round up to the next $5,000 increment for a T-bill sale or pur
chase. However, the medium-sized investor with a $50,000 portfolio might run into
problems. While short-term T-bills do represent the best risk-free investment, the
medium-sized investor might want to utilize one of the no-load, money market funds
for at least part of his income-bearing assets. Such funds have only slightly more risk
than T-bills and offer the ability to deposit and withdraw in any amount.
The truly small investor might be feeling somewhat left out. Could it be possi
ble to operate this strategy with avery small amount of money, such as $5,000? Yes
it could, but there are several disadvantages.
Example: It would be extremely difficult to keep the risk level down to 10% annual
ly with only $5,000. For example, 5% of the money invested every 180 days is only
$250 in each investment period. Since the option selection process that is described
will tend to select at- or slightly out-of-the-money calls, many of these will cost more
than 2½ points for one option. The small investor might decide to raise his risk level
slightly, although the risk level should never exceed 20% annually, no matter how
small the actual dollar investment. To exceed this risk level would be to completely
defeat the purpose of the fixed-income/option purchase strategy. Obviously, this
small investor cannot buy T-bills, for his total investable assets are below the mini
mum $10,000 purchase level. He might consider utilizing one of the money market
funds. Clearly, an investor of this small magnitude is operating at adouble disadvan
tage: His small dollar commitment to option purchases may preclude him from buy
ing some of the more attractive items; and his fixed-income portion will be earning asmaller percentage interest rate than that of the larger investor who is in T-bills or
some other form of relatively risk-free, income-bearing security. Consequently, the
small investor should carefully consider his financial capability and willingness to
adhere strictly to the criteria of this strategy before actually committing his dollars.
It may appear to the reader that the actual dollars being placed at risk in each
option purchase are quite small in these examples. In fact, they are rather small, but
they have been shown to represent 10% annualized risk. An assumption was made in
these examples that the risk in each option purchase was 100% for the holding peri
od. This is afairly restrictive assumption and, if it were lessened, would allow for alarger dollar commitment in each holding period. It is difficult and dangerous, how-

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420 Part IV: Additional Considerations
ever, to assume that the risk in holding acall option is less than 100% in aholding
period as short as 30 days. The strategist may feel that he is disciplined enough to sell
out when losses occur and thereby hold the risk to less than 100%. Alternatively,
mathematical analysis will generally show that the expected loss in afixed time peri
od is less than 100%. One can also mitigate the probability oflosing all of his money
in an option purchase by buying in-the-money options. While they are more expen
sive, of course, they do have alarger probability of having some residual worth even
if the underlying stock doesn'trise to the trader'sexpectations. Adhering to any of
these criteria can lead one to become too aggressive and therefore be too heavily
committed to option purchases. It is far safer to stick to the simpler, more restrictive
assumption that one is risking all his money, even over afairly short holding period,
when he buys an option.
AVOIDING EXCESSIVE RISK
One final word of caution must be inserted. The investor should not attempt to
become 'Janey" with the income-bearing portion of his assets. T-bills may appear to
be too "tame" to some investors, and they consider using GNMA's (Government
National Mortgage Association certificates), corporate bonds, convertible bonds, or
municipal bonds for the fixed-income portion. Although the latter securities may
yield aslightly higher return than do T-bills, they may also prove to be less liquid and
they quite clearly involve more risk than ashort-term T-bill does. Moreover, some
investors might even consider placing the balance of their funds in other places, such
as high-yield stock or covered call writing. While high-yield stock purchases and cov
ered call writing are conservative investments, as most investments go, they would
have to be considered very speculative in comparison to the purchase of a 90-day Thill. In this strategy, the profit potential is represented by the option purchases. The
yield on short-term T-bills will quite adequately offset the risks. One should take
great care not to attempt to generate much higher yields on the fixed-income portion
of his investment, for he may find that he has assumed risk with the portion of his
money that was not intended to have any risk at all.
Afair amount of rigorous mathematical work has been done on the evaluation
of this strategy. The theoretical papers are quite favorable. Scholars have generally
considered only the purchase of call options as the risk portion of the strategy.
Obviously, the strategist is quite free to purchase put options without harming the
overall intent of the strategy. When only call options are purchased, both static and
down markets harm the performance. If some puts are included in the option pur
chases, only static markets could produce the worst results.

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Chapter 26: Buying Options and Treasury Bills 421
There are trade-offs involved as well. If, after purchasing the options, the mar
ket experiences asubstantial rally, that portion of the option purchase money that is
devoted to put option purchases will be lost. Thus, the combination of both put and
call purchases would do better in adown market than astrategy of buying only calls,
but would do worse in an up market. In abroad sense, it makes sense to include some
put purchases if one has the funds to diversify, since the frequency of market rallies
is smaller than the combined frequency of market rallies and declines. The investor
who owns both puts and calls will be able to profit from substantial moves in either
direction, because the profitable options will be able to overcome the limited losses
on the unprofitable ones.
SUMMARY
In summary, the T-bill/option strategy is attractive from several viewpoints. Its true
advantage lies in the fact that it has predefined risk and does not have alimit on
potential profits. Some theorists claim it is the best strategy available, if the options
are "underpriced" when they are purchased. The strategy is also relatively simple to
operate. It is not necessary to have amargin account or to compute collateral require
ments for uncovered options; the strategy can be operated completely from acash
account. There are no spreads involved, nor is it necessary to worry about details such
as early assignment (because there are no short options in this strategy).
The investor who is going to employ this strategy, however, must not be delud
ed into thinking that it is so simple that it does not take any work at all. The concepts
and application of annualized risk management are very important to the strategy. So
are the mechanics of option buying - particularly adisciplined, rational approach to
the selection of which calls and/or puts to buy. Consequently, this strategy is suitable
only for the investor who has both the time and the discipline to operate it correctly.

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Arbitrage
Arbitrage in the securities market often connotes that one is buying something in
one marketplace and selling it in another marketplace, for asmall profit with little
or no risk. For example, one might buy XYZ at 55 in New York and sell it at 55¼ in
Chicago. Arbitrage, especially option arbitrage, involves afar wider range of tactics
than this simple example. Many of the option arbitrage tactics involve buying one
side of an equivalent position and simultaneously selling the other side. Since there
is alarge number of equivalent strategies, many of which have been pointed out in
earlier chapters, afull-time option arbitrageur is able to construct arather large
number of positions, most of which have little or no risk. The public customer can
not generally operate arbitrage-like strategies because of the commission costs
involved. Arbitrageurs are firm traders or floor traders who are trading through aseat on the appropriate securities exchange, and therefore have only minimal trans
action costs.
The public customer can benefit from understanding arbitrage techniques, even
ifhe does not personally employ them. The arbitrageurs perform auseful function in
the option marketplace, often making markets where amarket might not otherwise
exist (deeply in-the-money options, for example). This chapter is directed at the
strategist who is actually going to be participating in arbitrage. This should not be
confusing to the public customer, for he will better understand the arbitrage strate
gies if he temporarily places himself in the arbitrageur'sshoes.
It is virtually impossible to perform pure arbitrage on dually listed options; that
is, to buy an option on the CBOE and sell it on the American exchange in New York
for aprofit. Such discrepancies occur so infrequently and in such small size that an
option arbitrageur could never hope to be fully employed in this type of simple arbi
trage. Rather, the more complex forms of arbitrage described here are the ones on
which he would normally concentrate.
422

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Chapter 27: Arbitrage 423
BASIC PUT AND CALL ARBITRAGE ("DISCOUNTING")
The basic call and the basic put arbitrages are two of the simpler forms of option arbi
trage. In these situations, the arbitrageur attempts to buy the option at adiscount
while simultaneously taking an opposite position in the underlying stock. He can then
exercise his option immediately and make aprofit equal to the amount of the discount.
The basic call arbitrage is described first. This was also outlined in Chapter 1,
under the section on anticipating exercise.
Example: XYZ is trading at 58 and the XYZ July 50 call is trading at 7¾. The call is
actually at adiscount from parity of ¼ point. Discount options generally either are
quite deeply in-the-money or have only ashort time remaining until expiration, or
both. The call arbitrage would be constructed by:
1. buying the call at 7¾;
2. selling the stock at 58;
3. exercising the call to buy the stock at 50.
The arbitrageur would make 8 points of profit from the stock, having sold it at 58 and
bought it back at 50 via the option exercise. He loses the 7¾ points that he paid for
the call option, but this still leaves him with an overall profit of¼ point. Since he is
amember of the exchange, or is trading the seat of an exchange member, the arbi
trageur pays only asmall charge to transact the trades.
In reality, the stock is not sold short per se, even though it is sold before it is
bought. Rather, the position is designated, at the time of its inception, as an "irrevo
cable exercise." The arbitrageur is promising to exercise the call. As aresult, no
uptick is required to sell the stock.
The main goal in the call arbitrage is to be able to buy the call at adiscount from
the price at which the stock is sold. The differential is the profit potential of the arbi
trage. The basic put arbitrage is quite similar to the call arbitrage. Again, the arbi
trageur is looking to buy the put option at adiscount from parity. The put arbitrage
is completed with astock purchase and option exercise.
Example: XYZ is at 58 and the XYZ July 70 put is at 11 ¾. With the put at ¼ discount
from parity, the arbitrageur might take the following action:
1. Buy put at 11 ¾.
2. Buy stock at 58.
3. Exercise put to sell stock at 70.

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424 Part IV: Additional Considerations
The stock transaction is a 12-point profit, since the stock was bought at 58 and is sold
at 70 via the put exercise. The cost of the put - 11 ¾ points - is lost, but the arbi
trageur still makes ¼-point profit. Again, this profit is equal to the arrwunt of the dis
count in the option when the position was established. Generally, the arbitrageur
would exercise his put option immediately, because he would not want to tie up his
capital to carry the long stock. An exception to this would be if the stock were about
to go ex-dividend. Dividend arbitrage is discussed in the next section.
The basic call and put arbitrages may exist at any time, although they will be
more frequent when there is an abundance of deeply in-the-money options or when
there is avery short time remaining until expiration. After market rallies, the call
arbitrage may be easier to establish; after market declines, the put arbitrage will be
easier to find. As an expiration date draws near, an option that is even slightly in-the
money on the last day or two of trading could be acandidate for discount arbitrage.
The reason that this is true is that public buying interest in the option will normally
wane. The only public buyers would be those who are short and want to cover. Many
covered writers will elect to let the stock be called away, so that will reduce even fur
ther the buying potential of the public. This leaves it to the arbitrageurs to supply the
buying interest.
The arbitrageur obviously wants to establish these positions in as large asize as
possible, since there is no risk in the position if it is established at adiscount. Usually,
there will be alarger market for the stock than there will be for the options, so the
arbitrageur spends more of his time on the option position. However, there may be
occasions when the option markets are larger than the corresponding stock quotes.
When this happens, the arbitrageur has an alternative available to him: He might sell
an in-the-money option at parity rather than take astock position.
Example: XYZ is at 58 and the XYZ July 50 call is at 7¾. These are the same figures
as in the previous example. Furthermore, suppose that the trader is able to buy more
options at 7¾ than he is able to sell stock at 58. If there were another in-the-money
call that could be sold at parity, it could be used in place of the stock sale. For exam
ple, if the XYZ July 40 call could be sold at 18 (parity), the arbitrage could still be
established. Ifhe is assigned on the July 40 that he is short, he will then be short stock
at anet price of 58 - the striking price of 40, plus the 18 points that were brought in
from the sale of the July 40 call. Thus, the sale of the in-the-money call at parity is
equivalent to shorting the stock for the arbitrage purpose.
In asimilar manner, an in-the-money put can be used in the basic put arbitrage.
Example: With XYZ at 58 and the July 70 put at 11¾, the arbitrage could be estab
lished. However, if the trader is having trouble buying enough stock at 58, he might

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Chapter 27: Arbitrage 425
be able to use another in-the-money put. Suppose the XYZ July 80 put could be sold
at 22. This would be the same as buying the stock at 58, because if the put were
assigned, the arbitrageur would be forced to buy stock at 80 - the striking price - but
his net cost would be 80 minus the 22 points he received from the sale of the put, for
anet cost of 58. Again, the arbitrageur is able to use the sale of adeeply in-the-money
option as asubstitute for the stock trade.
The examples above assumed that the arbitrageur sold adeeper in-the-money
option at parity. In actual practice, if an in-the-money option is at adiscount, an even
deeper in-the-money option will generally be at adiscount as well. The arbitrageur
would normally try to sell, at parity, an option that was less deeply in-the-money than
the one he is discounting.
In abroader sense, this technique is applicable to any arbitrage that involves astock trade as part of the arbitrage, except when the dividend in the stock itself is
important. Thus, if the arbitrageur is having trouble buying or selling stock as part of
his arbitrage, he can always check whether there is an in-the-money option that could
be sold to produce aposition equivalent to the stock position.
DIVIDEND ARBITRAGE
Dividend arbitrage is actually quite similar to the basic put arbitrage. The trader can
lock in profits by buying both the stock and the put, then waiting to collect the divi
dend on the underlying stock before exercising his put. In theory, on the day before
astock goes ex-dividend, all puts should have atime value premium at least as large
as the dividend amount. This is true even for deeply in-the-money puts.
Example: XYZ closes at 45 and is going to go ex-dividend by $1 tomorrow. Then aput with striking price of 50 should sell for at least 6 points ( the in-the-money amount
plus the amount of the dividend), because the stock will go ex-dividend and is expect
ed to open at 44, six points in-the-money.
If, however, the put' stime value premium should be less than the amount of the
dividend, the arbitrageur can take ariskless position. Suppose the XYZ July 50 put is
selling for 5¾, with the stock at 45 and about to go ex-dividend by $1. The arbi
trageur can take the following steps:
1. Buy the put at 5¼.
2. Buy the stock at 45.
3. Hold the put and stock until the stock goes ex-dividend (1 point in this case).
4. Exercise the put to sell the stock at 50.

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426 Part IV: Additional Considerations
The trader makes 5 points from the stock trade, buying it at 45 and selling it at 50 via
the put exercise, and also collects the I-point dividend, for atotal inflow of 6 points.
Since he loses the 5¾ points he paid for the put, his net profit is ¼ point.
Far in advance of the ex-dividend date, adeeply in-the-money put may trade
very close to parity. Thus, it would seem that the arbitrageur could "load up" on these
types of positions and merely sit back and wait for the stock to go ex-dividend. There
is aflaw in this line of thinking, however, because the arbitrageur has acarrying cost
for the rrwney that he must tie up in the long stock. This carrying cost fluctuates with
short-term interest rates.
Example: If the current rate of carrying charges were 6% annually, this would be
equivalent to 1 % every 2 months. If the arbitrageur were to establish this example
position 2 months prior to expiration, he would have acarrying cost of .5075 point.
(His total outlay is 50¾ points, 45 for the stock and 5¾ for the options, and he would
pay 1 % to carry that stock and option for the two months until the ex-dividend date.)
This is more than ½ point in costs - clearly more than the ¼-point potential profit.
Consequently, the arbitrageur must be aware of his carrying costs if he attempts to
establish adividend arbitrage well in advance of the ex-dividend date. Of course, if
the ex-dividend date is only ashort time away, the carrying cost has little effect, and
the arbitrageur can gauge the profitability of his position mostly by the amount of the
dividend and the time value premium in the put option.
The arbitrageur should note that this strategy of buying the put and buying the
stock to pick up the dividend might have aresidual, rather profitable side effect. If
the underlying stock should rally up to or above the striking price of the put, there
could be rather large profits in this position. Although it is not likely that such arally
could occur, it would be an added benefit if it did. Even arather small rally might
cause the put to pick up some time premium, allowing the arbitrageur to trade out
his position for aprofit larger than he could have made by the arbitrage discount.
This form of arbitrage occasionally lends itself to alimited form of risk arbi
trage. Risk arbitrage is astrategy that is designed to lock in aprofit if acertain event
occurs. If that event does not occur, there could be aloss (usually quite limited);
hence, the position has risk. This risk element differentiates arisk arbitrage from astandard, no-risk arbitrage. Risk arbitrage is described more fully in alater section,
but the following example concerning aspecial dividend is one form of risk arbitrage.
Example: XYZ has been known to declare extra, or special, dividends with afair
amount of regularity. There are several stocks that do so - Eastman Kodak and
General Motors, for example. In this case, assume that ahypothetical stock, XYZ, has

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Chapter 27: Arbitrage 427
generally declared aspecial dividend in the fourth quarter of each year, but that its
normal quarterly rate is $1.00 per share. Suppose the special dividend in the fourth
quarter has ranged from an extra $1.00 to $3.00 over the past five years. If the arbi
trageur were willing to speculate on the size of the upcoming dividend, he might be
able to make anice profit. Even if he overestimates the size of the special dividend,
he has alimited loss. Suppose XYZ is trading at 55 about two weeks before the com
pany is going to announce the dividend for the fourth quarter. There is no guarantee
that there will, in fact, be aspecial dividend, but assume that XYZ is having arela
tively good year profitwise, and that some special dividend seems forthcoming.
Furthermore, suppose the January 60 put is trading at 7½. This put has 2½ points of
time value premium. If the arbitrageur buys XYZ at 55 and also buys the January 60
put at 7½, he is setting up arisk arbitrage. He will profit regardless of how far the
stock falls or how much time value premium the put loses, if the special dividend is
larger than $1.50. Aspecial dividend of $1.50 plus the regular dividend of $1.00
would add up to $2.50, or 2½ points, thus covering his risk in the position. Note that
$1.50 is in the low end of the $1.00 to $3.00 recent historical range for the special
dividends, so the arbitrageur might be tempted to speculate alittle by establishing
this dividend risk arbitrage. Even if the company unexpectedly decided to declare no
special dividend at all, it would most likely still pay out the $1.00 regular dividend.
Thus, the most that the arbitrageur would lose would be 1 ½ points (his 2½-point ini
tial time value premium cost, less the 1-point dividend). In actual practice, the stock
would probably not change in price by agreat deal over the next two weeks (it is ahigh-yield stock), and therefore the January 60 put would probably have some time
value premium left in it after the stock goes ex-dividend. Thus, the practical risk is
even less than 1 ½ points.
While these types of dividend risk arbitrage are not frequently available, the
arbitrageur who is willing to do some homework and also take some risk may find that
he is able to put on aposition with asmall risk and aprofitability quite abit larger
than the normal discount dividend arbitrage.
There is really not adirect form of dividend arbitrage involving call options. If
arelatively high-yield stock is about to go ex-dividend, holders of the calls will
attempt to sell. They do so because the stock will drop in price, thereby generally
forcing the call to drop in price as well, because of the dividend. However, the hold
er of acall does not receive cash dividends and therefore is not willing to hold the
call if the stock is going to drop by arelatively large amount (perhaps ¾ point or
more). The effect of these call holders attempting to sell their calls may often pro
duce adiscount option, and therefore abasic call arbitrage may be possible. The arbi
trageur should be careful, however, if he is attempting to arbitrage astock that is

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428 Part IV: Additional Considerations
going ex-dividend on the following day. Since he must sell the stock to set up the arbi
trage, he cannot afford to wind up the day being short any stock, for he will then have
to pay out the dividend the following day (the ex-dividend date). Furthermore, his
records must be accurate, so that he exercises all his long options on the day before
the ex-dividend date. If the arbitrageur is careless and is still short some stock on the
ex-date, he may find that the dividend he has to pay out wipes out alarge portion of
the discount profits he has established.
CONVERSIONS AND REVERSALS
In the introductory material on puts, it was shown that put and call prices are relat
ed through aprocess known as conversion. This is an arbitrage process whereby atrader may sometimes be able to lock in aprofit at absolutely no risk. Aconversion
consists of buying the underlying stock, and also buying aput option and selling acall option such that both options have the same terms. This position will have alocked-in profit if the total cost of the position is less than the striking price of the
options.
Example: The following prices exist:
XYZ common, 55;
XYZ January 50 call, 6½; and
XYZ January 50 put, 1.
The total cost of this conversion is 49½ - 55 for the stock, plus 1 for the put, less 6½
for the call. Since 49½ is less than the striking price of 50, there is alocked-in profit
on this position. To see that such aprofit exists, suppose the stock is somewhere
above 50 at expiration. It makes no difference how far above 50 the stock might be;
the result will be the same. With the stock above 50, the call will be assigned and the
stock will be sold at aprice of 50. The put will expire worthless. Thus, the profit is½
point, since the initial cost of the position was 49½ and it can eventually be liquidat
ed for aprice of 50 at expiration. Asimilar result occurs if XYZ is below 50 at expi
ration. In this case, the trader would exercise his put to sell his stock at 50, and the
call would expire worthless. Again, the position is liquidated for aprice of 50 and,
since it only cost 49½ to establish, the same ½-point profit can be made. No matter
where the stock is at expiration, this position has alocked-in-profit of½ point.
This example is rather simplistic because it does not include two very important
factors: the possible dividend paid by the stock and the cost of carrying the position

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Chapter 27: Arbitrage 429
until expiration. The inclusion of these factors complicates things somewhat, and its
discussion is deferred momentarily while the companion strategy, the reversal, is
explained.
Areversal (or reverse conversion, as it is sometimes called) is exactly the oppo
site of aconversion. In areversal, the trader sells stock short, sells aput, and buys acall. Again, the put and call have the same terms. Areversal will be profitable if the
initial credit ( sale price) is greater than the striking price of the options.
Example: Adifferent set of prices will be used to describe areversal:
XYZ common, 55;
XYZ January 60 call, 2; and
XYZ January 60 put, 7½.
The total credit of the reversal is 60½ - 55 from the stock sale, plus 7½ from the put
sale, less the 2-point cost of the call. Since 60½ is greater than the striking price of
the options, 60, there is alocked-in profit equal to the differential of½ point. To ver
ify this, first assume that XYZ is anywhere below 60 at January expiration. The put
will be assigned - stock is bought at 60 - and the call will expire worthless. Thus, the
reversal position is liquidated for acost of 60. A ½-point profit results since the orig
inal sale value ( credit) of the position was 60½. On the other hand, if XYZ were above
60 at expiration, the trader would exercise his call, thus buying stock at 60, and the
put would expire worthless. Again, he would liquidate the position at acost of 60 and
would make a ½-point profit.
Dividends and carrying costs are important in reversals, too; these factors are
addressed here. The conversion involves buying stock, and the trader will thus
receive any dividends paid by the stock during the life of the arbitrage. However, the
converter also has to pay out arather large sum of money to set up his arbitrage, and
must therefore deduct the cost of carrying the position from his potential profits. In
the example above, the conversion position cost 49½ points to establish. If the trad
er'scost of money were 6% annually, he would thus lose .06/12 x 49½, or .2475 point
per month for each month that he holds the position. This is nearly ¼ of apoint per
month. Recall that the potential profit in the example is ½ point, so that if one held
the position for more than two months, his carrying costs would wipe out his profit.
It is extremely important that the arbitrageur compute his carrying costs accurately
prior to establishing any conversion arbitrage.
If one prefers formulae, the profit potentials of aconversion or areversal can
be stated as:

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430 l'art IV: Additional Considerations
Conversion profit = Striking price + Call price - Stock price - Put price +
Dividends to be received - Carrying cost of position
Reversal profit = Stock + Put - Strike - Call + Carrying cost - Dividends
Note that during any one trading day, the only items in the formulae that can change
are the prices of the securities involved. The other items, dividends and carrying cost,
are fixed for the day. Thus, one could have asmall computer program prepared that
listed the fixed charges on aparticular stock for all the strikes on that stock.
Example: It is assumed that XYZ stock is going to pay a ½-point dividend during the
life of the position, and that the position will have to be held for three months at acarrying cost of 6% per year. If the arbitrageur were interested in aconversion with
astriking price of 50, his fixed cost would be:
Conversion fixed cost = Carrying rate x Time held x Striking price -
Dividend to be received
= .06 X 3/12 X 50 - ½
= .75- ½ = .25, or¼ point
The arbitrageur would know that if the profit potential, computed in the simplistic
manner using only the prices of the securities involved, was greater than ¼ point, he
could establish the conversion for an eventual profit, including all costs. Of course,
the carrying costs would be different if the striking price were 40 or 60, so acom
puter printout of all the possible striking prices on each stock would be useful in
order for the trader to be able to refer quickly to atable of his fixed costs each day.
MORE ON CARRYING COSTS
The computation of carrying costs can be made more involved than the simple
method used above. Simplistically, the carrying cost is computed by multiplying the
debit of the position by the interest rate charged and the time that the position will
be held. That is, it could be formulated as:
Carrying cost = Strike xrxtwhere ris the interest rate and tis the time that the position will be held. Relating
this formula for the carrying cost to the conversion profit formula given above, one
would get:
Conversion profit = Call - Stock - Put + Dividend + Strike - Carrying cost
= Call - Stock - Put + Dividend + Strike ( 1 - rt)

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Chapter 27: Arbitrage 431
In an actuarial sense, the carrying cost could be expressed in aslightly more complex
manner. The simple formula (strike xrxt) ignores two things: the compounding
effect of interest rates and the "present value" concept ( the present value of afuture
amount). The absolutely correct formula to include both present value and the com
pounding effect would necessitate replacing the factor strike (1- rt) in the profit for
mula by the factor
Strike
(1 + r)f
Is this effect large? No, not when rand tare small, as they would be for most option
calculations. The interest rate per month would normally be less than 1 %, and the
time would be less than 9 months. Thus, it is generally acceptable, and is the com
mon practice among many arbitrageurs, to use the simple formula for carrying costs.
In fact, this is often amatter of convenience for the arbitrageur if he is computing
the carrying costs on ahand calculator that does not perform exponentiation.
However, in periods of high interest rates when longer-term options are being ana
lyzed, the arbitrageur who is using the simple formula should double-check his cal
culations with the correct formula to assure that his error is not too large.
For purposes of simplicity, the remaining examples use the simple formula for
carrying-cost computations. The reader should remember, however, that it is only aconvenient approximation that works best when the interest rate and the holding
period are small. This discussion of the compounding effect of interest rates also rais
es another interesting point: Any investor using margin should, in theory, calculate
his potential interest charge using the compounding formula. However, as amatter
of practicality, extremely few investors do. An example of this compounding effect on
acovered call write is presented in Chapter 2.
BACK TO CONVERSIONS AND REVERSALS
Profit calculation similar to the conversion profit formula is necessary for the rever
sal arbitrage. Since the reversal necessitates sho1ting stock, the trader must pay out
any dividends on the stock during the time in which the position is held. However,
he is now bringing in acredit when the position is established, and this money can
be put to work to earn interest. In areversal, then, the dividend is acost and the
interest earned is aprofit.

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Chapter 27: Arbitrage 433
available in the marketplace at anet profit of ½ point, or 50 cents. Such areversal
may not be equally attractive to all arbitrageurs. Those who have "box" stock may be
willing to do the reversal for 50 cents; those who have to pay 1 % to borrow stock may
want 0.55 for the reversal; and those who pay 2% to borrow stock may need 0.65 for
the reversal. Thus, arbitrageurs who do conversions and reversals are in competition
with each other not only in the marketplace, but in the stock loan arena as well.
Reversals are generally easier positions for the arbitrageur to locate than are
conversions. This is because the fixed cost of the conversion has arather burdensome
effect. Only if the stock pays arather large dividend that outweighs the carrying cost
could the fixed portion of the conversion formula ever be aprofit as opposed to acost. In practice, the interest rate paid to carry stock is probably higher than the
interest earned from being short stock, but any reasonable computer program should
be able to handle two different interest rates.
The novice trader may find the term "conversion" somewhat illogical. In the
over-the-counter option markets, the dealers create aposition similar to the one
shown here as aresult of actually converting aput to acall.
Example: When someone owns aconventional put on XYZ with astriking price of
60 and the stock falls to 50, there is often little chance of being able to sell the put
profitably in the secondary market. The over-the-counter option dealer might offer
to convert the put into acall. To do this, he would buy the put from the holder, then
buy the stock itself, and then offer acall at the original striking price of 60 to the
holder of the put. Thus, the dealer would be long the stock, long the put, and short
the call - aconversion. The customer would then own acall on XYZ with astriking
price of 60, due to expire on the same date that the put was destined to. The put
that the customer owned has been converted into acall. To effect this conversion,
the dealer pays out to the customer the difference between the current stock price,
50, and the striking price, 60. Thus, the customer receives $1,000 for this conver
sion. Also, the dealer would charge the customer for costs to carry the stock, so that
the dealer had no risk. If the stock rallied back above 60, the customer could make
more money, because he owns the call. The dealer has no risk, as he has an arbitrage
position to begin with. In asimilar manner, the dealer can effect areverse conver
sion - converting acall to aput - but will charge the dividends to the customer for
doing so.
RISKS IN CONVERSIONS AND REVERSALS
Conversions and reversals are generally considered to be riskless arbitrage. That is,
the profit in the arbitrage is fixed from the start and the subsequent movement of the

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434 Part IV: Additional Considerations
underlying stock makes no difference in the eventual outcome. This is generally atrue statement. However, there are some risks, and they are great enough that one
can actually lose money in conversions and reversals if he does not take care. The
risks are fourfold in reversal arbitrage: An extra dividend is declared, the interest rate
falls while the reversal is in place, an early assignment is received, or the stock is
exactly at the striking price at expiration. Converters have similar risks: adividend
cut, an increase in the interest rate, early assignment, or the stock closing at the strike
at expiration.
These risks are first explored from the viewpoint of the reversal trader. If the
company declares an extra dividend, it is highly likely that the reversal will become
unprofitable. This is so because most extra dividends are rather large - more than the
profit of areversal. There is little the arbitrageur can do to avoid being caught by the
declaration of atruly extra dividend. However, some companies have atrack record
of declaring extras with annual regularity. The arbitrageur should be aware of which
companies these are and of the timing of these extra dividends. Aclue sometimes
exists in the marketplace. If the reversal appears overly profitable when the arbi
trageur is first examining it (before he actually establishes it), he should be somewhat
skeptical. Perhaps there is areason why the reversal looks so tempting. An extra div
idend that is being factored into the opinion of the marketplace may be the answer.
The second risk is that of variation in interest rates while the reversal is in
progress. Obviously, rates can change over the life of areversal, normally 3 to 6
months. There are two ways to compensate for this. The simplest way is to leave
some room for rates to move. For example, if rates are currently at 12% annually, one
might allow for amovement of 2 to 3% in rates, depending on the length of time the
reversal is expected to be in place. In order to allow for a 2% move, the arbitrageur
would calculate his initial profit based on arate of 10%, 2% less than the currently
prevailing 12%. He would not establish any reversal that did not at least break even
with a 10% rate. The rate at which areversal breaks even is often called the "effec
tive rate" - 10% in this case. Obviously, if rates average higher than 10% during the
life of the reversal, it will make money. Normally, when one has an entire portfolio of
reversals in place, he should know the effective rate of each set of reversals expiring
at the same time. Thus, he would have an effective rate for his 2-month reversals, his
3-month ones, and so forth.
Allowing this room for rates to move does not necessarily mean that there will
not be an adverse affect if rates do indeed fall. For example, rates could fall farther
than the room allowed. Thus, afurther measure is necessary in order to completely
protect against adrop in rates: One should invest his credit balances generated by the
reversals in interest-bearing paper that expires at approximately the same time the
reversals do, and that bears interest at arate that locks in aprofit for the reversal

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Chapter 27: Arbitrage 435
account. For example, suppose that an arbitrageur has $5 million in 3-month rever
sals at an effective rate of 10%. If he can buy $5 million worth of 3-month Certificates
of Deposit with arate of 11 ½%, then he would lock in aprofit of 1 ½% on his $5 mil
lion. This method of using paper to hedge rate fluctuations is not practiced by all
arbitrageurs; some think it is not worth it. They believe that by leaving the credit bal
ances to fluctuate at prevailing rates, they can make more if rates go up, and that will
cushion the effect when rates decline.
The third risk of reversal arbitrage is reception of an early assignment on the
short puts. This forces the arbitrageur to buy stock and incur adebit. Thus, the posi
tion does not earn as much interest as was originally assumed. If the assignment is
received early enough in the life of the reversal (recall that in-the-money puts can
be assigned very far in advance of expiration), the reversal could actually incur an
overall loss. Such early assignments normally occur during bearish markets. The only
advantage of this early assignment is that one is left with unhedged long calls; these
calls are well out-of-the-money and normally quite low-priced (¼ or less). If the
market should reverse and turn bullish before the expiration of the calls, the arbi
trageur may make money on them. There is no way to hedge completely against amarket decline, but it does help if the arbitrageur tries to establish reversals with the
call in-the-money and the put out-of-the-money. That, plus demanding abetter
overall return for reversals near the strike, should help cushion the effects of the
bear market.
The final risk is the most common one, that of the stock closing exactly at the
strike at expiration. This presents the arbitrageur with adecision to make regarding
exercise of his long calls. Since the stock is exactly at the strike, he is not sure whether
he will be assigned on his short puts at expiration. The outcome is that he may end
up with an unhedged stock position on Monday morning after expiration. If the stock
should open on agap, he could have asubstantial loss that wipes out the profits of
many reversals. This risk of stock closing at the strike may seem minute, but it is not.
In the absence of any real buying or selling in the stock on expiration day, the process
of discounting will force astock that is near the strike virtually right onto the strike.
Once it is near the strike, this risk materializes.
There are two basic scenarios that could occur to produce this unhedged stock
position. First, suppose one decides that he will not get put and he exercises his calls.
However, he was wrong and he does get put. He has bought double the amount of
stock - once via call exercise and again via put assignment. Thus, he will be long on
Monday morning. The other scenario produces the opposite effect. Suppose one
decides that he will get put and he decides not to exercise his calls. If he is wrong in
this case, he does not buy any stock - he didn'texercise nor did he get put.
Consequently, he will be short stock on Monday morning.

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436 Part IV: Additional Considerations
If one is truly undecided about whether he will be assigned on his short puts,
he might look at several clues. First, has any late news come out on Friday evening
that might affect the market'sopening or the stock'sopening on Monday morning? If
so, that should be factored into the decision regarding exercising the calls. Another
clue arises from the price at which the stock was trading during the Friday expiration
day, prior to the close. If the stock was below the strike for most of the day before
closing at the strike, then there is agreater chance that the puts will be assigned. This
is so because other arbitrageurs (discounters) have probably bought puts and bought
stock during the day and will exercise to clean out their positions.
If there is still doubt, it may be wisest to exercise only half of the calls, hoping
for apartial assignment on the puts (always apossibility). This halfway measure will
normally result in some sort of unhedged stock position on Monday morning, but it
will be smaller than the maximum exposure by at least half.
Another approach that the arbitrageur can take if the stock is near the strike of
the reversal during the late trading of the options' life - during the last few days - is
to roll the reversal to alater expiration or, failing that, to roll to another strike in the
same expiration. First, let us consider rolling to another expiration. The arbitrageur
knows the dollar price that equals his effective rate for a 3-month reversal. If the cur
rent options can be closed out and new options opened at the next expiration for at
least the effective rate, then the reversal should be rolled. This is not alikely event,
mostly due to the fact that the spread between the bid and asked prices on four sep
arate options makes it difficult to attain the desired price. Note: This entire four-way
order can be entered as aspread order; it is not necessary to attempt to "leg" the
spread.
The second action - rolling to another strike in the same expiration month -
may be more available. Suppose that one has the July 45 reversal in place (long July
45 call and short July 45 put). If the underlying stock is near 45, he might place an
order to the exchange floor as athree-way spread: Sell the July 45 call (closing), buy
the July 45 put (closing), and sell the July 40 call ( opening) for anet credit of 5 points.
This action costs the arbitrageur nothing except asmall transaction charge, since he
is receiving a 5-point credit for moving the strike by 5 points. Once this is accom
plished, he will have moved the strike approximately 5 points away and will thus have
avoided the problem of the stock closing at the strike.
Overall, these four risks are significant, and reversal arbitrageurs should take
care that they do not fall prey to them. The careless arbitrageur uses effective rates
too close to current market rates, establishes reversals with puts in-the-money, and
routinely accepts the risk of acquiring an unhedged stock position on the morning
after expiration. He will probably sustain alarge loss at some time. Since many rever
sal arbitrageurs work with small capital and/or have convinced their backers that it is

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Chapter 27: Arbitrage 437
ariskless strategy, such aloss may have the effect of putting them out of business.
That is an unnecessary risk to take. There are countermeasures, as described above,
that can reduce the effects of the four risks.
Let us consider the risks for conversion traders more briefly. The risk of stock
closing near the strike is just as bad for the conversion as it is for the reversal. The
same techniques for handling those risks apply equally well to conversions as to
reversals. The other risks are similar to reversal risks, but there are slight nuances.
The conversion arbitrage suffers if there is adividend cut. There is little the
arbitrageur can do to predict this except to be aware of the fundamentals of the com
pany before entering into the conversion. Alternatively, he might avoid conversions
in which the dividend makes up amajor part of the profit of the arbitrage.
Another risk occurs if there is an early assignment on the calls before the ex-div
idend date and the dividend is not received. Moreover, an early assignment leaves the
arbitrageur with long puts, albeit fractional ones since they are surely deeply out-of
the-money. Again, the policy of establishing conversions in which the dividend is not
amajor factor would help to ease the consequences of early assignment.
The final risk is that interest rates increase during the time the conversion is in
place. This makes the carrying costs larger than anticipated and might cause aloss.
The best way to hedge this initially is to allow amargin for error. Thus, if the pre
vailing interest rate is 12%, one might only establish reversals that would break even
if rates rose to 14%. If rates do not rise that far on average, aprofit will result. The
arbitrageur can attempt to hedge this risk by shorting interest-bearing paper that
matures at approximately the same time as the conversions. For example, if one has
$5 million worth of 3-month conversions established at an effective rate of 14% and
he shorts 3-month paper at 12½%, he locks in aprofit of 1 ½%. This is not common
practice for conversion arbitrageurs, but it does hedge the effect of rising interest
rates.
SUMMARY OF CONVERSION ARBITRAGE
The practice of conversion and reversal arbitrage in the listed option markets helps
to keep put and call prices in line. If arbitrageurs are active in aparticular option, the
prices of the put and call will relate to the stock price in line with the formulae given
earlier. Note that this is also avalid reason why puts tend to sell at alower price than
calls do. The cost of money is the determining factor in the difference between put
and call prices. In essence, the "cost" (although it may sometimes be acredit) is sub
tracted from the theoretical put price. Refer again to the formula given above for the
profit potential of aconversion. Assume that things are in perfect alignment. Then
the formula would read:

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438 Part IV: Additional Considerations
Put price = Striking price + Call price - Stock price - Fixed cost
Furthermore, if the stock is at the striking price, the formula reduces to:
Put price = Call price - Fixed cost
So, whenever the fixed cost, which is equal to the carrying charge less the dividends,
is greater than zero (and it usually is), the put will sell for less than the call if astock
is at the striking price. Only in the case of alarge-dividend-paying stock, when the
fixed cost becomes negative (that is, it is not acost, but acredit), does the reverse
hold true. This is supportive evidence for statements made earlier that at-the-money
calls sell for more than at-the-money puts, all other things being equal. The reader
can see quite clearly that it has nothing to do with supply and demand for the puts
and calls, afallacy that is sometimes proffered. This same sort of analysis can be used
to prove the broader statement that calls have agreater time value premium than
puts do, except in the case of alarge-dividend-paying stock.
One final word of advice should be offered to the public customer. He may
sometimes be able to find conversions or reversals, by using the simplistic formula,
that appear to have profit potentials that exceed commission costs. Such positions do
exist from time to time, but the rate of return to the public customer will almost
assuredly be less than the short-term cost of money. If it were not, arbitrageurs would
be onto the position very quickly. The public option trader may not actually be think
ing in terms of comparing the profit potential of aposition with what he could get by
placing the money into abank, but he must do so to convince himself that he cannot
feasibly attempt conversion or reversal arbitrages.
THE "INTEREST PLAY"
In the preceding discussion of reversal arbitrage, it is apparent that asubstantial por
tion of the arbitrageur'sprofits may be due to the interest earned on the credit of the
position. Another type of position is used by many arbitrageurs to take advantage of
this interest earned. The arbitrageur sells the underlying stock short and simultane
ously buys an in-the-money call that is trading slightly over parity. The actual amount
over parity that the arbitrageur can afford to pay for the call is determined by the
interest that he will earn from his short sale and the dividend payout before expira
tion. He does not use aput in this type of position. In fact, this "interest play" strat
egy is merely areversal arbitrage without the short put. This slight variation has aresidual benefit for the arbitrageur: If the underlying stock should drop dramatically
in price, he could make large profits because he is short the underlying stock. In any
case, he will make his interest credit less the amount of time value premium paid for
the call less any dividends lost.

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