Chapter 22: Basic Put Spreads 333
above the higher strike. These are the same qualities that were displayed by a call bull
spread (Chapter 7). The name "bull spread" is derived from the fact that this is a bull
ish position: The strategist wants the underlying stock to rise in price.
The risk is limited in this spread. If the underlying stock should decline by expi
ration, the maximum loss will be realized with XYZ anywhere below 50 at that time.
The risk is 5 points in this example. To see this, note that if XYZ were anywhere below
50 at expiration, the differential between the two puts would widen to 10 points,
since that is the difference between their striking prices. Thus, the spreader would
have to pay 10 points to buy the spread back, or to close out the position. Since he
initially took in a 5-point credit, this means his loss is equal to 5 points - the 10-point
cost of closing out less the 5 points he received initially.
The investment required for a bullish put spread is actually a collateral require
ment, since the spread is a credit spread. The amount of collateral required is equal
-1-r.. f-ha rliffa:rannci, hahuaan tho cfr-il;nrr r\rint::u.:- lace th.-:;). not nrorlit ror-A-iuorl fnr thA
\..V l,,J...111._, Ul.J..J..V.lV.l.l.\..,V LIV\..VVVVJ..l '-- J.'L, oJ\..l..l.J.'-l.J.J..o .t'.l.J..\,.,VoJ J.VoJ,J I..J.J.'-' J..1.V\.. \,.,.l.V"-AJ.l.- .LVV'-'..l.Y'-'"'--4 .J..'-.-".I. .__...._.._ .......
spread. In this example, the collateral requirement is $500- the $1,000, or 10-point,
differential in the striking prices less the $500 credit received from the spread. Note
that the maximum possible loss is always equal to the collateral requirement in a bull
ish put spread.
It is not difficult to calculate the break-even point in a bullish spread. ·In this
example, the break-even point before commissions is 55 at expiration. With XYZ at
55 in January, the January 50 put would expire worthless and the January 60 put
would have to be bought back for 5 points. It would be 5 points in-the-money with
XYZ at 55. Thus, the spreader would break even, since he originally received 5 points
credit for the spread and would then pay out 5 points to close the spread. The fol
lowing formulae allow one to quickly compute the details of a bullish put spread:
Maximum potential risk = Initial collateral requirement
= Difference in striking prices - Net credit received
Maximum potential profit= Net credit
Break-even price = Higher striking price - Net credit
CALENDAR SPREAD
In a calendar spread, a near-term option is sold and a longer-term option is bought,
both with the same striking price. This definition applies to either a put or a call cal
endar spread. In Chapter 9, it was shown that there were two philosophies available
for call calendar spreads, either neutral or bullish. Similarly, there are two philoso
phies available for put calendar spreads: neutral or bearish.

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334 Part Ill: Put Option Strategies
In a neutral calendar spread, one sets up the spread with the idea of closing the
spread when the near-term call or put expires. In this type of spread, the maximum
profit will be realized if the stock is exactly at the striking price at expiration. The
spreader is merely attempting to capitalize on the fact that the time value premium
disappears more rapidly from a near-term option than it does from a longer-term one.
Example: XYZ is at 50 and a January 50 put is selling for 2 points while an April 50
put is selling for 3 points. A neutral calendar spread can be established for a 1-point
debit by selling the January 50 put and buying the April 50 put. The investment
required for this position is the amount of the net debit, and it must be paid for in
full. If XYZ is exactly at 50 at January expiration, the January 50 put will expire worth
less and the April 50 put will be worth about 2 points, assuming other factors are the
same. The neutral spreader would then sell the April 50 put for 2 points and take his
profit. The spreader's profit in this case would be one point before commissions,
because he originally paid a 1-point debit to set up the spread and then liquidates the
position by selling the April 50 put for 2 points. Since commission costs can cut into
available profits substantially, spreads should be established in a large enough quan
tity to minimize the percentage cost of commissions. This means that at least 10
spreads should be set up initially.
In any type of calendar spread, the risk is limited to the amount of the net debit.
This maximum loss would be realized if the underlying stock moved substantially far
away from the striking price by the time the near-term option expired. If this hap
pened, both options would trade at nearly the same price and the differential would
shrink to practically nothing, the worst case for the calendar spreader. For example,
if the underlying stock drops substantially, say to 20, both the near-term and the long
term put would trade at nearly 30 points. On the other hand, if the underlying stock
rose substantially, say to 80, both puts would trade at a very low price, say 1/15 or 1/s,
and again the spread would shrink to nearly zero.
Neutral call calendar spreads are generally superior to neutral put calendar
spreads. Since the amount of time value premium is usually greater in a call option
(unless the underlying stock pays a large dividend), the spreader who is interested in
selling time value would be better off utilizing call options.
The second philosophy of calendar spreading is a more aggressive one. With put
options, a bearish strategy can be constructed using a calendar spread. In this case,
one would establish the spread with out-of-the-money puts.
Example: With XYZ at 55, one would sell the January 50 put for 1 point and buy the
April 50 put for 1 ½ points. He would then like the underlying stock to remain above
the striking price until the near-term January put expires. If this happens, he would

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Chapter 22: Basic Put Spreads 335
make the I-point profit from the sale of that put, reducing his net cost for the April
50 put to ½ point. Then, he would become bearish, hoping for the underlying stock
to decline in price substantially before April expiration in order that he might be able
to generate large profits on the April 50 put he holds.
Just as the bullish calendar spread with calls can be a relatively attractive strat
egy, so can the bearish calendar spread with puts. Granted, two criteria have to be
fulfilled in order for the position to work to the optimum: The near-term put must
expire worthless, and then the underlying stock must drop in order to generate prof
its on the long side. Although these conditions may not occur frequently, one prof
itable situation can more than make up for several losing ones. This is true because
the initial debit for a bearish calendar spread is small, ½ point in the example above.
Thus, the losses will be small and the potential profits could be very large if things
work out right.
The aggressive spreader must be careful not to "leg out" of his spread, since he
could generate a large loss by doing so. The object of the strategy is to accept a rather
large number of small losses, with the idea that the infrequent large profits will more
than offset the sum of the losses. If one generates a large loss somewhere along the
way, this may ruin the overall strategy. Also, if the underlying stock should fall to the
striking price before the near-term put expires, the spread will normally have
widened enough to produce a small profit; that profit should be taken by closing the
spread at that time.

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Spreads Cotnbining
Calls and Puts
Certain types of spreads can be constructed that utilize both puts and calls. One of
these strategies has been discussed before: the butterfly spread. However, other
strategies exist that off er potentially large profits to the spreader. These other strate
gies are all variations of calendar spreads and/or straddles that involve both put and
call options.
THE BUTTERFLY SPREAD
This strategy has been described previously, although its usage in Chapter 10 was
restricted to constructing the spread with calls. Recall that the butterfly spread is a
neutral position that has limited risk as well as limited profits. The position involves
three striking prices, utilizing a bull spread between the lower two strikes and a bear
spread between the higher two strikes. The maximum profit is realized at the middle
strike at expiration, and the maximum loss is realized if the stock is above the higher
strike or below the lower strike at expiration.
Since either a bull spread or a bear spread can be constructed with puts or calls,
it should be obvious that a butterfly spread ( consisting of both a bull spread and a
bear spread) can be constructed in a number of ways. In fact, there are four ways in
which the spread can be established. If option prices are fairly balanced - that is, the
arbitrageurs are keeping prices in line - any of the four ways will have the same
potential profits and losses at expiration of the options. However, because of the ways
in which puts and calls behave prior to their expiration, certain advantages or disad-
336

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340 Part Ill: Put Option Strategies
to look at it is this: The sale of the put spread reduces the call price down to a more
moderate level, one that might be in line with its "theoretical value." In other words,
the call would not be considered expensive if it were priced at 7 instead of 10. The sale
of the put spread can be considered a way to reduce the overall cost of the call.
Of course, the sale of the put spread brings some extra risk into the position
because, if the stock were to fall dramatically, the put spread could lose 7 points ( the
width of the strikes in the spread, 10 points, less the initial credit received, 3 points).
This, added to the call's cost of 10 points, means that the entire risk here is 17 points.
In fact, that is the margin required for this spread as well. Thus, the overall spread
still has limited risk, because both the call purchase and the put credit spread are lim
ited-risk strategies. However, the total risk of the two combined is larger than for
either one separately.
Remember that one must be bullish on the underlying in order to employ this
strategy. So, if his analysis is correct, the upside is what he wants to maximize. If he
is wrong on his outlook for the stock, then he needs to employ some sort of stop-loss
measures before the maximum risk of the position is realized.
The resulting position is shown in Figure 23-1, along with two other plots. The
straight line marked "Spread at expiration" shows how the profitability of the call pur
chase combined with a bull spread would look at December expiration. In addition,
there is a plot with straight lines of the purchase of the December 100 call for 10
points. That plot can be compared with the three-way spread to see where extra risk
and reward occur. Note that the three-way spread does better than the outright pur
chase of the December 100 call as long as the stock is higher than 87 at expiration.
Since the stock is initially at 100 and,since one is initially bullish on the stock, one
would have to surmise that the odds of it falling to 87 are fairly small. Thus, the three
way spread outperforms the outright purchase of the call over a large range of stock
prices.
The final plot in Figure 23-1 is that of the three-way spread's profit and losses
halfway to the expiration date. You can see that it looks much like the profitability of
merely owning a call: The curve has the same shape as the call pricing curve shown
in Chapter 1.
Hence, this three-way strategy can often be more attractive and more profitable
than merely owning a call option. Remember, though, that it does increase risk and
require a larger collateral deposit than the outright purchase of the at-the-money call
would. One can experiment with this strategy, too, in that he might consider buying
an out-of-the-money call and selling a put spread that brings in enough credit to com
pletely pay for the call. In that way, he would have no risk as long as the stock
remained above the higher striking price used in the put credit spread.

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Chapter 23: Spreads Combining Calls and Puts
FIGURE 23-1.
Call buy and put credit (bull) spread.
+$2,000
+$1,000
(/J
(/J
0 ..J
0 $0 -e a.
-$1,000
-$2,000
70 80
.... ,, -----,, -=-----'
THE BEARISH SCENARIO
~ Spread at Expiration
Call Buy Only, at Expiration
341
Stock
In a similar manner, one can construct a position to take advantage of a bearish opin
ion on a stock. Again, this would be most useful when the options were overpriced
and one felt that an at-the-money put was too expensive to purchase by itself.
Example: XYZ is trading at 80, and one has a definite bearish opinion on the stock.
However, the December 80 put, which is selling for 8, is expensive according to an
option analysis. Therefore, one might consider selling a call credit spread (out-of-the
money) to help reduce the cost of the put. The entire position would thus be:
Buy 1 December 80 put:
Sell l December 90 call:
Buy 1 December 100 call:
Total cost:
8 debit
4 credit
2 debit
6 debit ($600)
The profitability of this position is shown in Figure 23-2. The straight line on that
graph shows how the position would behave at expiration. The introduction of the
call credit spread has increased the risk to $1,600 if the stock should rally to 100 or
higher by expiration. Note that the risk is limited since both the put purchase and the
call credit spread are limited-risk strategies. The margin required would be this max
imum risk, or $1,600.

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342 Part Ill: Put Option Strategies
FIGURE 23-2.
Put buy and call credit (bear) spread.
+$1,000 Halfway to Expiration
/
Stock
0 60 110
-e a.
-$1,000 At Expiration
-$2,000
The curved line on Figure 23-2 shows how the three-way spread would behave
if one looked at it halfway to its expiration date. In that case, it has a curved appear
ance much like the outright purchase of a put option.
Thus, this strategy could be appealing to bearishly-oriented traders, especially
when the options are expensive. It might have certain advantages over an outright put
purchase in that case, but it does require a larger margin investment and has theo
retically larger risk.
A SIMPLE FOLLOW-UP ACTION
FOR BULL OR BEAR SPREADS
Another way of combining puts and calls in a spread can sometimes be used when
one has a bull or bear spread already in place. Suppose that one owns a call bull
spread and the underlying stock has advanced nicely. In fact, it is above both of the
strikes used in the spread. However, as is often the case, the bull spread may not have
widened out to its maximum profit potential. One can use the puts for two purposes
at this point: (1) to determine whether the call spread is trading at a "reasonable"
value, and (2) to try to lock in some profits. First, let's look at an example of the "rea
sonable value" verification.

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344 Part Ill: Put Option Strategies
it of 9.30. Since the maximum value of the spread is l 0, one is giving away 70 cents,
quite a bit for just such a short time remaining.
However, suppose that one looks at the puts and finds these prices:
Put
January 80 put
January 70 put
Bid Price
0.20
none
Asked Price
0.40
0.10
One could "lock in" his call spread profits by buying the January 80 put for 40 cents.
Ignoring commissions for a moment, if he bought that put and then held it along with
the call spread until expiration, he would unwind the call spread for a 10 credit at
expiration. He paid 40 cents for the put, so his net credit to exit the spread would be
9.60 - considerably better than the 9.30 he could have gotten above for the call
spread alone.
This put strategy has one big advantage: If the underlying stock should sudden
ly collapse and tumble beneath 70 - admittedly, a remote possibility - large profits
could accrue. The purchase of the January 80 put has protected the bull spread's
profits at all prices. But below 70, the put starts to make extra money, and the spread
er could profit handsomely. Such a drop in price would only occur if some material
ly damaging news surfaced regarding X'iZ Company, but it does occasionally happen.
If one utilizes this strategy, he needs to carefully consider his commission costs
and the possibility of early assignment. For a professional trader, these are irrelevant,
and so the professional trader should endeavor to exit bull spreads in this manner
whenever it makes sense. However, if the public customer allows stock to be assigned
at 80 and exercises to buy stock at 70, he will have two stock commissions plus one
put option commission. That should be compared to the cost of two in-the-money
call option commissions to remove the call spread directly. Furthermore, if the pub
lic customer receives an early assignment notice on the short January 80 calls, he may
need to provide day-trade margin as he exercises his January 70 calls the next day.
Without going into as much detail, a bear spread's profits can be locked in via a
similar strategy. Suppose that one owns a January 60 put and has sold a January 50
put to create a bear spread. Later, with the stock at 45, the spreader wants to remove
the spread, but again finds that the markets for the in-the-money puts are so wide
that he cannot realize anywhere near the 10 points that the spread is theoretically
worth. He should then see what the January 50 call is selling for. If it is fractionally
priced, as it most likely will be if expiration is drawing nigh, then it can be purchased
to lock in the profits from the put spread. Again, commission costs should be con
sidered by the public customer before finalizing his strategy.

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Chapter 23: Spreads Combining Calls and Puts 345
THREE USEFUL BUT COMPLEX STRATEGIES
The three strategies presented in this section are all designed to limit risk while
allowing for large potential profits if correct market conditions develop. Each is a
combination strategy - that is, it involves both puts and calls and each is a calendar
strategy, in which near-term options are sold and longer-term options are bought. (A
fourth strategy that is similar in nature to those about to be discussed is presented in
the next chapter.) Although all of these are somewhat complex and are for the most
advanced strategist, they do provide attractive risk/reward opportunities. In addition,
the strategies can be employed by the public customer; they are not designed strict
ly for professionals. All three strategies are described conceptually in this section;
specific selection criteria are presented in the next section.
A TWO-PRONGED ATTACK {THE CALENDAR COMBINATION}
A bullish calendar spread was shown to be a rather attractive strategy. A bullish call
calendar spread is established with out-of-the-money calls for a relatively small debit.
If the near-term call expires worthless and the stock then rises substantially before
the longer-term call expires, the profits could potentially be large. In any case, the
risk is limited to the small debit required to establish the spread. In a similar man
ner, the bearish calendar spread that uses put options can be an attractive strategy
as well. In this strategy, one would set up the spread with out-of-the-money puts. He
would then want the near-term put to expire worthless, followed by a substantial drop
in the stock price in order to profit on the longer-term put.
Since both strategies are attractive by themselves, the combination of the two
should be attractive as well. That is, with a stock midway between two striking prices,
one might set up a bullish out-of-the-money call calendar spread and simultaneously
establish a bearish out-of-the-money put calendar spread. If the stock remains rela
tively stable, both near-term options would expire worthless. Then a substantial stock
price movement in either direction could produce large profits. With this strategy,
the spreader does not care which direction the stock moves after the near options
expire worthless; he only hopes that the stock becomes volatile and moves a large dis
tance in either direction.
Example: Suppose that the following prices exist three months before the January
options expire:
January 70 call: 3
April 70 call: 5
XYZ common: 65
January 60 put: 2
April 60 put: 3

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346 Part Ill: Put Option Strategies
The bullish portion of this combination of calendar spreads would be set up by sell
ing the shorter-term January 70 call for 3 points and simultaneously buying the
longer-term April 70 call for 5 points. This portion of the spread requires a 2-point
debit. The bearish portion of the spread would be constructed using the puts. The
near-term January 60 put would be sold for 2 points, while the longer-term April 60
put would be bought for 3. Thus, the put portion of the spread is a I-point debit.
Overall, then, the combination of the calendar spreads requires a 3-point debit, plus
commissions. This debit is the required investment; no additional collateral is
required. Since there are four options involved, the commission cost will be large.
Again, establishing the spreads in quantity can reduce the percentage cost of com
missions.
Note that all the options involved in this position are initially out-of-the-money.
The stock is below the striking price of the calls and is above the striking price of the
puts. One has sold a near-term put and call combination and purchased a longer-term
combination. For nomenclature purposes, this strategy is called a "calendar combi
nation."
There are a variety of possible outcomes from this position. First, it should be
understood that the risk is limited to the amount of the initial debit, 3 points in this
example. If the underlying stock should rise dramatically or fall dramatically before
the near-term options expire, both the call spread and the put spread will shrink to
nearly nothing. This would be the least desirable result. In actual practice, the spread
would probably have a small positive differential left even after a premature move by
the underlying stock, so that the probability of a loss of the entire debit would be
small.
If the near-term options both expire worthless, a profit will generally exist at
that time.
Example: IfXYZ were still at 65 at January expiration in the prior example, the posi
tion should be profitable at that time. The January call and put would expire worth
less with XYZ at 65, and the April options might be worth a total of 5 points. The
spread could thus be closed for a profit with XYZ at 65 in January, since the April
options could be sold for 5 points and the initial "cost" of the spread was only 3 points.
Although commissions would substantially reduce this 2-point gross profit, there
would still be a good percentage profit on the overall position. If the strategist decides
to take his profit at this time, he would be operating in a conservative manner.
However, the strategist may want to be more aggressive and hold onto the April
combination in hopes that the stock might experience a substantial movement before
those options expire. Should this occur, the potential profits could be quite large.

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348 Part Ill: Put Option Strategies
In summary, this is a reasonable strategy if one operates it over a period of time
long enough to encompass several market cycles. The strategist must be careful not
to place a large portion of his trading capital in the strategy, however, since even
though the losses are limited, they still represent his entire net investment. A varia
tion of this strategy, whereby one sells more options than he buys, is described in the
next chapter.
THE CALENDAR STRADDLE
Another strategy that combines calendar spreads on both put and call options can be
constructed by selling a near-term straddle and simultaneously purchasing a longer
term straddle. Since the time value premium of the near-term straddle will decrease
more rapidly than that of the longer-term straddle, one could make profits on a lim
ited investment. This strategy is somewhat inferior to the one described in the pre
vious section, but it is interesting enough to examine.
Example: Suppose that three months before January expiration, the following prices
exist:
XYZ common: 40
January 40 straddle: 5 April 40 straddle: 7
A calendar spread of the straddles could be established by selling the January 40
straddle and simultaneously buying the April 40 straddle. This would involve a cost
of 2 points, or the debit of the transaction, plus commissions.
The risk is limited to the amount of this debit up until {he time the near-term
straddle expires. That is, even if XYZ moves up in price by a substantial amount or
declines in price by a substantial amount, the worst that can happen is that the dif
ference between the straddle prices shrinks to zero. This could cause one to lose an
amount equal to his original debit, plus commissions. This limit on the risk applies
only until the near-term options expire. If the strategist decides to buy back the near
term straddle and continue to hold the longer-term one, his risk then increases by the
cost of buying back the near-term straddle.
Example: XYZ is at 43 when the January options expire. The January 40 call can now
be bought back for 3 points. The put expires worthless; so the whole straddle was
closed out for 3 points. The April 40 straddle might be selling for 6 points at that
time. If the strategist wants to hold on to the April straddle, in hopes that the stock
might experience a large price swing, he is free to do so after buying back the January

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Chapter 23: Spreads Combining Calls and Puts 349
40 straddle. However, he has now invested a total of 5 points in the position: the orig
inal 2-point debit plus the 3 points that he paid to buy back the January 40 straddle.
Hence, his risk has increased to 5 points. If XYZ were to be at exactly 40 at April expi
ration, he would lose the entire 5 points. While the probability of losing the entire 5
points must be considered small, there is a substantial chance that he might lose
more than 2 points his original debit. Thus, he has increased his risk by buying back
the near-term straddle and continuing to hold the longer-term one.
This is actually a neutral strategy. Recall that when calendar spreads were dis
cussed previously, it was pointed out that one establishes a neutral calendar spread
with the stock near the striking price. This is true for either a call calendar spread or
a put calendar spread. This strategy - a calendar spread with straddles is merely the
combination of a neutral call calendar spread and a neutral put calendar spread.
Moreover, recall that the neutral calendar spreader generally establishes the position
with the intention of closing it out once the near-term option expires. He is mainly
interested in selling time in an attempt to capitalize on the fact that a near-term
option loses time value premium more rapidly than a longer-term option does. The
straddle calendar spread should be treated in the same manner. It is generally best
to close it out at near-term expiration. If the stock is near the striking price at that
time, a profit will generally result. To verify this, refer again to the prices in the pre
ceding paragraph, with XYZ at 43 at January expiration. The January 40 straddle can
be bought back for 3 points and the April 40 straddle can be sold for 6. Thus, the dif
ferential between the two straddles has widened to 3 points. Since the original dif
ferential was 2 points, this represents a profit to the strategist.
The maximum profit would be realized if XYZ were exactly at the striking price
at near-term expiration. In this case, the January 40 straddle could be bought back
for a very small fraction and the April 40 straddle might be worth about 5 points. The
differential would have widened from the original 2 points to nearly 5 points in this
case.
This strategy is inferior to the one described in the previous section (the "calen
dar combination"). In order to have a chance for unlimited profits, the investor must
increase his net debit by the cost of buying back the near-term straddle.
Consequently, this strategy should be used only in cases when the near-term straddle
appears to be extremely overpriced. Furthermore, the position should be closed at
near-term expiration unless the stock is so close to the striking price at that time that
the near-term straddle can be bought back for a fractional price. This fractional buy
back would then give the strategist the opportunity to make large potential profits
with only a small increase in his risk. This situation of being able to buy back the near
term straddle at a fractional price will occur very infrequently, much more infre-

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350 Part Ill: Put Option Strategies
quently than the case in which both the out-of-the-money put and call expire worth
less in the previous strategy. Thus, the "calendar combination" strategy will afford the
spreader more opportunities for large profits, and will also never force him to
increase his risk.
OWNING A ✓,,FREE" COMBINATION (THE ""DIAGONAL
BUTTERFLY SPREAD")
The strategies described in the previous sections are established for debits. This
means that even if the near-term options expire worthless, the strategist still has risk.
The long options he then holds could proceed to expire worthless as well, thereby
leaving him with an overall loss equal to his original debit. There is another strategy
involving both put and call options that gives the strategist the opportunity to own a
"free" combination. That is, the profits from the near-term options could equal or
exceed the entire cost of his long-term options.
This strategy consists of selling a near-term straddle and simultaneously pur
chasing both a longer-term, out-of the-money call and a longer-term, out-of the
money put. This differs from the protected straddle write previously described in that
the long options have a more distant maturity than do the short options.
Example:
XYZ common: 40
April 35 put:
January 40 straddle:
April 45 call:
If one were to sell the short-term January 40 straddle for 7 points and simultaneous
ly purchase the out-of-the-money put and call combination -April 35 put and April
45 call - he would establish a credit spread. The credit for the position is 3 points less
commissions, since 7 points are brought in from the straddle sale and 4 points are
paid for the out-of-the-money combination. Note that the position technically con
sists of a bearish spread in the calls - buy the higher strike and sell the lower strike -
coupled with a bullish spread in the puts - buy the lower strike and sell the higher
strike. The investment required is in the form of collateral since both spreads are
credit spreads, and is equal to the differential in the striking prices, less the net cred
it received. In this example, then, the investment would be 10 points for the striking
price differential (5 points for the calls and 5 points for the puts) less the 3-point
credit received, for a total collateral requirement of $700, plus commissions.

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360
FIGURE 24-1.
Ratio put spread.
+$500
C:
0
~ ·5.
X
w
iil
(/) $0 (/)
0 ....I
0
e a.
Part Ill: Put Option Strategies
Stock Price at Expiration
price, plus the premium, minus the amount by which the option is out-of-the-money,
the actual dollar requirement in this example would be $700 (20% of $5,000, plus the
$200 premium, minus the $500 by which the January 45 put is out-of-the-money). As
with all types of naked writing positions, the strategist should allow enough collater
al for an adverse stock move to occur. This will allow enough room for stock move
ment without forcing early liquidation of the position due to a margin call. If, in this
example, the strategist felt that he might stay with the position until the stock
declined to 39, he should allow $1,380 in collateral (20% of $3,900 plus the $600 in
the-money amount).
The ratio put spread is generally most attractive when the underlying stock is
initially between the two striking prices. That is, if XYZ were somewhere between 45
and 50, one might find the ratio put spread used in the example attractive. If the
stock is initially below the lower striking price, a ratio put spread is not as attractive,
since the stock is already too close to the downside risk point. Alternatively, if the
stock is too far above the striking price of the written calls, one would normally have
to pay a large debit to establish the position. Although one could eliminate the debit
by writing four or five short options to each put bought, large ratios have extraordi
narily large downside risk and are therefore very aggressive.
Follow-up action is rather simple in the ratio put spread. There is very little that
one need do, except for closing the position if the stock breaks below the downside
break-even point. Since put options tend to lose time value premium rather quickly
after they become in-the-money options, there is not normally an opportunity to roll

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Chapter 24: Ratio Spreads Using Puts 361
down. Rather, one should be able to close the position with the puts close to parity if
the stock breaks below the downside break-even point. The spreader may want to buy
in additional long puts, as was described for call spreads in Chapter 11, but this is not
as advantageous in the put spread because of the time value premium shrinkage.
This strategy may prove psychologically pleasing to the less experienced
investor because he will not lose money on an upward move by the underlying stock.
Many of the ratio strategies that involve call options have upside risk, and a large
number of investors do not like to lose money when stocks move up. Thus, although
these investors might be attracted to ratio strategies because of the possibility of col
lecting the profits on the sale of multiple out-of-the-money options, they may often
prefer ratio put spreads to ratio call spreads because of the small upside risk in the
put strategy.
USING DELTAS
The "delta spread" concept can also be used for establishing and adjusting neutral
ratio put spreads. The delta spread was first described in Chapter 11. A neutral put
spread can be constructed by using the deltas of the two put options involved in the
spread. The neutral ratio is determined by dividing the delta of the put at the higher
strike by the delta of the put at the lower strike. Referring to the previous example,
suppose the delta of the January 45 put is -.30 and the delta of the January 50 put is
-.50. Then a neutral ratio would be 1.67 (-.50 divided by -.30). That is, 1.67 puts
would be sold for each put bought. One might thus sell 5 January 45 puts and buy 3
January 50 puts.
This type of spread would not change much in price for small fluctuations in the
underlying stock price. However, as time passes, the preponderance of time value
premium sold via the January 45 puts would begin to tum a profit. As the underlying
stock moves up or down by more than a small distance, the neutral ratio between the
two puts will change. The spreader can adjust his position back into a neutral one by
selling more January 45's or buying more January 50's.
THE RATIO PUT CALENDAR SPREAD
The ratio put calendar spread consists of buying a longer-term put and selling a larg
er quantity of shorter-term puts, all with the same striking price. The position is gen
erally established with out-of-the-money puts that is, the stock is above the striking
price - so that there is a greater probability that the near-term puts will expire worth-

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362 Part Ill: Put Option Strategies
less. Also, the position should be established for a credit, such that the money
brought in from the sale of the near-term puts more than covers the cost of the
longer-term put. If this is done and the near-term puts expire worthless, the strate
gist will then own the longer-term put free, and large profits could result if the stock
subsequently experiences a sizable downward movement.
Example: If XYZ were at 55, and the January 50 put was at 1 ½ with the April 50 at
2, one could establish a ratio put calendar spread by buying the April 50 and selling
two January 50 puts. This is a credit position, because the sale of the two January 50
puts would bring in $300 while the cost of the April 50 put is only $200. If the stock
remains above 50 until January expiration, the January 50 puts will expire worthless
and the April 50 put will be owned for free. In fact, even if the April 50 put should
then expire worthless, the strategist will make a small profit on the overall position in
the amount of his original credit - $100 - less commissions. However, after the
Januarys have expired worthless, if XYZ should drop dramatically to 25 or 20, a very
large profit would accrue on the April 50 put that is still owned.
The risk in the position could be very large if the stock should drop well below
50 before the January puts expire. For example, if XYZ fell to 30 prior to January
expiration, one would have to pay $4,000 to buy back the January 50 puts and would
receive only $2,000 from selling out his long April 50 put. This would represent a
rather large loss. Of course, this type of tragedy can be avoided by taking appropri
ate follow-up action. Nomwlly, one would close the position if the stock fell rrwre than
8 to 10% below the striking price before the near-term puts expire.
As with any type of ratio position, naked options are involved. This increases the
collateral requirement for the position and also means that the strategist should allow
enough collateral in order for the follow-up action point to be reached. In this exam
ple, the initial requirement would be $750 (20% of $5,500, plus the $150 January
premium, less the $500 by which the naked January 50 put is out-of-the-money).
However, if the strategist decides that he will hold the position until XYZ falls to 46,
he should allow $1,320 in collateral (20% of $4,600 plus the $400 in-the-money
amount). Of course, the $100 credit, less commissions, generated by the initial posi
tion can be applied against these collateral requirements.
This strategy is a sensible one for the investor who is willing to accept the risk of
writing a naked put. Since the position should be established with the stock above the
striking price of the put options, there is a reasonable chance that the near-term puts
will expire worthless. This means that some profit will be generated, and that the
profit could be large if the stock should then experience a large downward move
before the longer-term puts expire. One should take care, however, to limit his losses

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394 Part Ill: Put Option Strategies
Downside Protection. The actual downside break-even point might enter into
one's thinking as well. A downside break-even point of 40.3 is available by using the
LEAPS write, and that is a known quantity. No matter how far XYZ might fall, as long
as it can recover to slightly over 40 by expiration two years from now, the investment
will at least break even. A problem arises if XYZ falls to 40 quickly. If that happened,
the LEAPS call would still have a significant amount of time value premium remain
ing on it. Thus, if the investor attempted to sell his stock at that time and buy back
his call, he would have a loss, not a break-even situation.
The short-term write offers downside protection only to a stock price of 46.2.
Of course, repeated writes of 6-month calls over the next 2 years would lower the
break-even point below that level. The problem is that if XYZ declines and one is
forced to keep selling 6-month calls every 6 months, he may be forced to use a lower
striking price, thereby locking in a smaller profit ( or possibly even a loss) if premium
levels shrink. The concepts of rolling down are described in detail in Chapter 2.
A further word about rolling down may be in order here. Recall that rolling
down means buying back the call that is currently written and selling another one
with a lower striking price. Such action always reduces the profitability of the over
all position, although it may be necessary to prevent further downside losses if the
common stock keeps declining. Now that LEAPS are available, the short-term writer
faced with rolling down may look to the LEAPS as a means of bringing in a healthy
premium even though he is rolling down. It is true that a large premium could be
brought into the account. But remember that by doing so, one is committing himself
to sell the stock at a lower price than he had originally intended. This is why the
rolling down reduces the original profit potential. If he rolls down into a LEAPS call,
he is reducing his maximum profit potential for a longer period of time.
Consequently, one should not always roll dm,vn into an option with a longer maturi
ty. Instead, he should carefully analyze whether he wants to be committed for an
even longer time to a position in which the underlying common stock is declining.
To summarize, the large absolute premiums available in LEAPS calls may make
a covered write of those calls seem unusually attractive. However, one should calcu
late the returns available and decide whether a short-term write might not serve his
purpose as well. Even though the large LEAPS premium might reduce the initial
investment to a mere pittance, be aware that this creates a great amount of leverage,
and leverage can be a dangerous thing.
The large amount of downside protection offered by the LEAPS call is real, but
if the stock falls quickly, there would definitely be a loss at the calculated downside
break-even point. Finally, one cannot always roll down into a LEAPS call if trouble
develops, because he will be committing himself for an even longer period of time to
sell his stock at a lower price than he had originally intended.

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Chapter 25: LEAPS 39S
✓,,FREE" COVERED CALL WRITES
In Chapter 2, a strategy of writing expensive LEAPS options was briefly described.
In this section, a more detailed analysis is offered. A certain type of covered call
write, one in which the call is quite expensive, sometimes attracts traders looking for
a "free ride." To a certain extent, this strategy is something of a free ride. As you
might imagine, though, there can be major problems.
The investment required for a covered call write on margin is 50% of the stock
price, less the proceeds received from selling the call. In theory, it is possible for an
option to sell for more than 50% of the stock cost. This is a margin account, a cov
ered write could be established for "free." Let's discuss this in terms of two types of
calls: the in-the-money call write and the out-of-the-money call write.
Out-of-the-Money Covered Call Write. This is the simplest way to approach
the strategy. One may be able to find LEAPS options that are just slightly out-of-the
money, which sell for 50% of the stock price. Understandably, such a stock would be
quite volatile.
Example: GOGO stock is selling for $38 per share. GOGO has listed options, and a
2-year LEAPS call with a striking price of 40 is selling for $19. The requirement for
this covered write would be zero, although some commission costs would be
involved. The debit balance would be 19 points per share, the amount the broker
loans you on margin.
Certain brokerage firms might require some sort of minimum margin deposit, but
technically there is no further requirement for this position. Of course, the leverage
is infinite. Suppose one decided to buy 10,000 shares of GOGO and sell 100 calls,
covered. His risk is $190,000 if the stock falls to zero! That also happens to be the
debit balance in his account. Thus, for a minimal investment, one could lose a for
tune. In addition, if the stock begins to fall, one's broker is going to want maintenance
margin. He probably wouldn't let the stock slip more than a couple of points before
asking for margin. If one owns 10,000 shares and the broker wants two points main
tenance margin, that means the margin call would be $20,000.
The profits wouldn't be as big as they might at first seem. The maximum gross
profit potential is $210,000 if the 10,000 shares are called away at 40. The covered
write makes 21 points on each share - the $40 sale price less the original cost of $19.
However, one will have had to pay interest on the debit balance of $190,000 for two
years. At 10%, say, that's a total of $38,000. There would also be commissions on the
purchase and the sale.

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396 Part Ill: Put Option Strategies
In summary, this is a position with tremendous, even dangerous, leverage.
In-the-Money Covered Call Write. The situation is slightly different if the
option is in-the-money to begin with. The above margin requirements actually don't
quite accurately state the case for a margined covered call write. When a covered call
is written against the stock, there is a catch: Only 50% of the stock price or the strike
price, whichever is less, is available for "release." Thus, one will actually be required
to put up more than 50% of the stock price to begin with.
Example: XYZ is trading at 50, and there is a 2-year LEAPS call with a strike price
of 30, selling for 25 points. One might think that the requirement for a covered call
write would be zero, since the call sells for 50% of the stock price. But that's not the
case with in-the-money covered calls.
Margin requirement:
Buy stock: 50 points
Less option proceeds -25
Less margin release* -15*
Net requirement: 10 points
* 50% of the strike price or 50% of stock price, whichever is less.
This position still has a lot ofleverage: One invests 10 points in hopes of making 5, if
the stock is called away at 30. One also would have to pay interest on the 15-point
debit balance, of course, for the two-year duration of the position. Furthermore,
should the stock fall below the strike price, the broker would begin to require main
tenance margin.
Note that the above "formula" for the net requirement works equally well for
the out-of-the-money covered call write, since 50% of the stock price is always less
than 50% of the strike price in that case.
To summarize this "free ride" strategy: If one should decide to use this strate
gy, he must be extremely aware of the dangers of high leverage. One must not risk
more money than he can afford to lose, regardless of how small the initial investment
might be. Also, he must plan for some method of being able to make the margin pay
ments along the way. Finally, the in-the-money alternative is probably better, because
there is less probability that maintenance margin will be asked for.
SELLING UNCOVERED LEAPS
Uncovered option selling can be a viable strategy, especially if premiums are over
priced. LEAPS options may be sold uncovered with the same margin requirements
as short-term options. Of course, the particular characteristics of the long-term
option may either help or hinder the uncovered writer, depending on his objective.

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Chapter 25: LEAPS 397
Uncovered Put Selling. Naked put selling is addressed first because, as a strat
egy, it is equivalent to covered writing, and covered writing was just discussed. Two
strategies are equivalent if they have the same profit picture at expiration. Naked put
selling and covered call writing are equivalent because they have the profit picture
depicted in Graph I, Appendix D. Both have limited upside profit potential and large
loss exposure to the downside. In general, when two strategies are equivalent, one of
the two has certain advantages over the other.
In this case, naked put selling is normally the more advantageous of the two
because of the way margin requirements are set. One need not actually invest cash
in the sale of a naked put; the margin requirement that is asked for may be satisfied
with collateral. This means the naked put writer may use stocks, bonds, T-bills, or
money market funds as collateral. Moreover, the actual amount of collateral that is
required is less than the cash or margin investment required to buy stock and sell a
call. This means that one could operate his portfolio normally - buying stock, then
selling it and putting the proceeds in a Treasury bill or perhaps buying another stock
- without disturbing his naked put position, as long as he maintained the
collateral requirement.
Consequently, the strategist who is buying stock and selling calls should probably
be selling naked puts instead. This does not apply to covered writers who are writing
against existing stock or who are using the incremental return concept of covered writ
ing, because stock ownership is part of their strategy. However, the strategist who is
looking to take in premium to profit if the underlying stock remains relatively
unchanged or rises, while having a modicum of downside protection ( which is the
definition of both naked put writing and covered writing), should be selling naked
puts. As an example of this, consider the LEAPS covered write discussed previously.
Example: XYZ is selling at 50. The investor is debating between a 500-share covered
write using 2-year LEAPS calls or selling five 2-year LEAPS puts. The January 50
LEAPS call sells for 8½ and has two years of life, while the January 50 LEAPS put
sells for 3½. Further assume that XYZ pays a dividend of $0.25 per quarter.
The net investment required for the covered write is calculated as it was before.
Net Investment Required - Covered Write
Stock cost (500 shares @ 50)
Plus stock commission
Less option premiums received
Plus option commissions
Net cash investment
+
$25,000
300
- 4,250
+ 100
$21,150

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398 Part Ill: Put Option Strategies
The collateral requirement for the naked put write is the same as that for any
naked equity option: 20% of the stock price, plus the option price, less any out-of
the-money amount, with an absolute minimum requirement of 15% of the stock
price.
Collateral Requirement - Naked Put
20% of stock price (.20 x 500 x $50)
Plus option premium
Less out-of-the-money amount
Total collateral requirement
$5,000
1,750
0
$6,750
Note that the actual premium received by the naked put seller is $1,750 less com
missions of $100, for example, or $1,650. This net premium could be used to reduce
the total collateral requirement.
Now one can compare the profitability of the two investments:
Return If Stock Over 50 at Expiration
Stock sale {500 @ 50)
Less stock commission
Plus dividends earned until expiration
Less net investment
Net profit if exercised
Net put premium received
Dividends received
Net profit
Covered Write
$25,000
300
+ 1,000
- 21,150
$ 4,55_0
Naked Put Sole
$1,650
0
$1,650
Now the returns can be compared, if XYZ is over 50 at expiration of the LEAPS:
Return if XYZ over 50
(net profit/net investment)
Naked put sale: 24.4%
Covered write: 21 .5%
The naked put write has a better rate of return, even before the following fact
is considered. The strategist who is using the naked put write does not have to spend
the $6,750 collateral requirement in the form of cash. That money can be kept in a

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Chapter 25: LEAPS 399
Treasury bill and earn interest over the two years that the put write is in place. Even
if the T-bill were earning only 4% per year, that would increase the overall two-year
return for the naked put sale by 8%, to 32.4%. This should make it obvious that naked
put selling is rrwre strategically advantageous than covered call writing.
Even so, one might rightfully wonder if LEAPS put selling is better than selling
shorter-term equity puts. As was the case with covered call writing, the answer
depends on what the investor is trying to accomplish. Short-term puts will not bring
as much premium into the account, so when they expire, one will be forced to find
another suitable put sale to replace it. On the other hand, the LEAPS put sale brings
in a larger premium and one does not have to find a replacement until the longer
term LEAPS put expires. The negative aspect to selling the LEAPS puts is that time
decay won't help much right away and, even if the stock moves higher (which is
ostensibly good for the position), the put won't decline in price by a large amount,
since the delta of the put is relatively small.
One other factor might enter in the decision regarding whether to use short
term puts or LEAPS puts. Some put writers are actually attempting to buy stock
below the market price. That is, they would not mind being assigned on the put they
sell, meaning that they would buy stock at a net cost of the striking price less the pre
mium they received from the sale of the put. If they don't get assigned, they get to
keep a profit equal to the premium they received when they first sold the put.
Generally, a person would only sell puts in this manner on a stock that he had faith
in, so that if he was assigned on the put, he would view that as a buying opportunity
in the underlying stock. This strategy does not lend itself well to LEAPS. Since the
LEAPS puts will carry a significant amount of time premium, there is little (if any)
chance that the put writer will actually be assigned until the life of the put shortens
substantially. This means that it is unlikely that the put writer will become a stock
owner via assignment at any time in the near future. Consequently, if one is attempt
ing to wTite puts in order to eventually buy the common stock when he is assigned,
he would be better served to write shorter-term puts.
UNCOVERED CALL SELLING
There are very few differences between using LEAPS for naked call selling and using
shorter-term calls, except for the ones that have been discussed already with regard
to selling uncovered LEAPS: Time value decay occurs more slowly and, if the stock
rallies and the naked calls have to be covered, the call writer will normally be paying
more time premium than he is used to when he covers the call. Of course, the rea
son that one is engaged in naked call writing might shed some more light on the use
of LEAPS for that purpose.

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400 Part Ill: Put Option Strategies
The overriding reason that most strategists sell naked calls is to collect the time
premium before the stock can rise above the striking price. These strategists gener
ally have an opinion about the stock's direction, believing that it is perhaps trapped
in a trading range or even headed lower over the short term. This strategy does not
lend itself well to using LEAPS, since it would be difficult to project that the stock
would remain below the strike for so long a period of time.
Short LEAPS Instead of Short Stock. Another reason that naked calls are
sold is as a strategy akin to shorting the common stock. In this case, in-the-money
calls are sold. The advantages are threefold:
l. The amount of collateral required to sell the call is less than that required to sell
stock short.
2. One does not have to borrow an option in order to sell it short, although one must
borrow common stock in order to sell it short.
3. An uptick is not required to sell the option, but one is required in order to sell
stock short.
For these reasons, one might opt to sell an in-the-money call instead of shorting
stock.
The profit potentials of the two strategies are different. The short seller of stock
has a very large profit potential if the stock declines substantially, while the seller of
an in-the-money call can collect only the call premium no matter how far the stock
drops. Moreover, the call's price decline will slow as the stock nears the strike.
Another way to express this is to say that the delta of the call shrinks from a number
close to l (which means the call mirrors stock movements closely) to something more
like 0.50 at the strike (which means that the call is only declining half as quickly as
the stock).
Another problem that may occur for the call seller is early assignment, a topic
that is addressed shortly. One should not attempt this strategy if the underlying stock
is not borrowable for ordinary short sales. If the underlying stock is not available for
borrowing, it generally means that extraneous forces are at work; perhaps there is a
tender offer or exchange offer going on, or some form of convertible arbitrage is tak
ing place. In any case, if the underlying stock is not borrowable, one should not be
deluded into thinking that he can sell an in-the-money call instead and have a worry
free position. In these cases, the call will normally have little or no time premium and
may be subject to early assignment. If such assignment does occur, the strategist will
become short the stock and, since it is not borrowable, will have to cover the stock.
At the least, he will cost himself some commissions by this unprofitable strategy; and
at worst, he will have to pay a higher price to buy back the stock as well.

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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 a
stock 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 a long 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 a better 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 a discount 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 a long-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 a tender 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 a better 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 l when this topic
was covered. Rather, it is a more 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 a credit 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 a striking price of 20.
A 50-cent quarterly dividend on a striking 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 a candidate 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 a
credit 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's exercise of the call means that someone is going to be
assigned. If you are a writer 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 a call trading at parity or a discount. Thus, even a LEAPS call with a sub
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 a strategy whereby one attempts
to sell ( overpriced) options in order to produce a range 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 a three-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 a profit 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 a profit 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. A whipsaw occurs when one makes
a follow-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 a whipsaw will occur after any follow-up
action, and the more expensive it will be, since there will be a lot 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 a longer-term option and selling a short
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 a large debit in such a spread and
may have substantial risk if the stock performs adversely. Other risks may be pres
ent as well. As a means of demonstrating these facts, let us consider a simple bull
spread using calls.

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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 a bull spread is the difference in the strikes less the initial debit paid. For this
diagonal spread, that would be $1,000 minus $2,050, a loss! 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 - a standard 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 a very high price, the diagonal spread would actually have a loss (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 a great deal in either direction, the diagonal spread
is the worst of the three. This means that the diagonal spread strategy is a neutral
strategy: One wants the underlying common to remain near the written strike until
the near-term option expires. This is a true statement even if the diagonal spread is
under the guise of a bullish spread, as in the previous example.
Many traders are fond of buying LEAPS and selling an out-of-the-money near
term call as a hedge. Be careful about doing this. If the underlying common rises too
fast and/or interest rates fall and/or volatility decreases, this could be a poor 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's why he chose
bull spreads. If XYZ became a wildly bullish stock and rose from 100 to 180 in three
months, the diagonal spreader would have lost money. He couldn't have 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 a good clue as to
how it is going to perform. Recall that a short-term, in-the-money option acquires a
rather 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 a high delta and long an option with a
smaller 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 a bull 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's
what 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 a diagonal spread could even be considered as a substitute for a cov
ered write in some special cases. It was shown that a LEAPS call can sometimes be
used as a substitute 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 T
bills). Suppose that an investor is a covered 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 a diagonal bull spread. Such a diagonal 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 a covered 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 a cov
ered write as much as he thought it would.
The "bottom line" is that if one pays a debit 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 a loss if
the overall credit he has received is less than the difference in the strikes - a quite
likely event. So, for those who think this strategy is akin to a guaranteed 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 a greater quan
tity of longer-term (LEAPS) at- or out-of-the money calls are bought. (This was
referred to as a diagonal 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't happen, and the stock declines instead, at least the premium captured from
the in-the-money sale will be a gain 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 a significant debit in the spread and
could lose a significant portion of it should the underlying stock fall a great 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 a neutral spread.
Example: XYZ is at 105 and a spreader wants to establish a backspread. Recall that
the quantity of options to use in a neutral 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, a neutral spread would be:
Buy 6 July 110 calls
Sell 4 April l 00 calls
As a second 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 28: Mathematical Applications
TABLE 28-3.
Distance weighting factors.
465
Option
Distonce
from
Stock Price
Distance
Weighting Factor
January 30
January 35
April 35
April 40
TABLE 28-4.
Option's implied volatility.
.091 (3/33)
.061 (2/33)
.061 (2/33)
.212 (7 /33)
.41
.57
.57
.02
Volume Distance Option's Implied
Option Factor Factor Volotility
January 30 .25 .41 .34
January 35 .45 .57 .28
April 35 .275 .57 .30
April40 .025 .02 .38
Implied = .25 x .41 x .34 + .45 x .57 x .28 + .275 x .57 x .30 + .025 x .02 x .38
volatility. .25 x .41 + .45 x .57 + .275 x .57 + .025 x .02
= .298
ual option's implied volatilities. Rather, it is a composite figure that gives the most
weight to the heavily traded, near-the-money options, and very little weight to the
lightly-traded (5 contracts), deeply out-of-the-money April 40 call. This implied
volatility is still a form of standard deviation, and can thus be used whenever a stan
dard deviation volatility is called for.
This method of computing volatility is quite accurate and proves to be sensitive
to changes in the volatility of a stock. For example, as markets become bullish or
bearish (generating large rallies or declines), most stocks will react in a volatile man
ner as well. Option premiums expand rather quickly, and this method of implied
volatility is able to pick up the change quickly. One last bit of fine-tuning needs to be
done before the final volatility of the stock is arrived at. On a day-to-day basis, the
implied volatility for a stock - especially one whose options are not too active may
fluctuate more than the strategist would like. A smoothing effect can be obtained by

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466 Part IV: Additional Considerations
taking a moving average of the last 20 or 30 days' implied volatilities. An alternative
that does not require the saving of many previous days' worth of data is to use a
momentum calculation on the implied volatility. For example, today's final volatility
might be computed by adding 5% of today's implied volatility to 95% of yesterday's
final volatility. This method requires saving only one previous piece of data - yester
day's final volatility - and still preserves a "smoothing" effect.
Once this implied volatility has been computed, it can then be used in the
Black-Scholes model ( or any other model) as the volatility variable. Thus one could
compute the theoretical value of each option according to the Black-Scholes formu
la, utilizing the implied volatility for the stock. Since the implied volatility for the
stock will most likely be somewhat different from the implied volatility of this par
ticular option, there will be a discrepancy between the option's actual closing price
and the theoretical price as computed by the model. This differential represents the
amount by which the option is theoretically overpriced or underpriced, compared to
other options on that same stock.
EXPECTED RETURN
Certain investors will enter positions only when the historical percentages are on
their side. When one enters into a transaction, he normally has a belief as to the pos
sibility of making a profit. For example, when he buys stock he may think that there
is a "good chance" that there will be a rally or that earnings will increase. The investor
may consciously or unconsciously evaluate the probabilities, but invariably, an invest
ment is made based on a positive expectation of profit. Since options have fixed
terms, they lend themselves to a more rigorous computation of expected profit than
the aforementioned intuitive appraisal. This more rigorous approach consists of com
puting the expected return. The expected retum is nothing more than the retum that
the position should yield over a large number of cases.
A simple example may help to explain the concept. The crucial variable in com
puting expected return is to outline what the chances are of the stock being at a cer
tain price at some future time.
Example: XYZ is selling at 33, and an investor is interested in determining where
XYZ will be in 6 months. Assume that there is a 20% chance of XYZ being below 30
in 6 months, and that there is a 40% chance that XYZ will be above 35 in 6 months.
Finally, assume that XYZ has an equal 10% chance of being at 31, 32, 33, or 34 in 6
months. All other prices are ignored for simplification. Table 28-5 summarizes these
assumptions.

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Chapter 28: Mathematical Applications
TABLE 28-5.
Calculation of expected returns.
Price of XYZ in 6 Months
Below 30
31
32
33
34
Above 35
467
Chance of XYZ Being at That Price ·
20%
10%
10%
10%
10%
40%
100%
Since the percentages total 100%, all the outcomes have theoretically been
allowed for. Now suppose a February 30 call is trading at 4 and a February 35 call is
trading at 2 points. A bull spread could be established by buying the February 30 and
selling the February 35. This position would cost 2 points - that is, it is a 2-point
debit. The spreader could make 3 points if XYZ were above 35 at expiration for a
return of 150%, or he could lose 100% if XYZ were below 30 at expiration. The
expected return for this spread can be computed by multiplying the outcome at expi
ration for each price by the probability of being at that price, and then summing the
results. For example, if XYZ is below 30 at expiration, the spreader loses $200. It was
assumed that there is a 20% chance of XYZ being below 30 at expiration, so the
expected loss is 20% times $200, or $40. Table 28-6 shows the computation of the
expected results at all the prices. The total expected profit is $100. This means that
the expected return (profit divided by investment) is 50% ($100/$200). This appears
to be an attractive spread, because the spreader could "expect" to make 50% of his
money, less commissions.
What has really been calculated in this example is merely the return that one
would expect to make in the long run if he invested in the same position many times
throughout history. Saying that a particular position has an expected return of 8 or
9% is no different from saying that common stocks return 8 or 9% in the long run.
Of course, in bull markets stock would do much better, and in bear markets much
worse. In a similar manner, this example bull spread with an expected return of 50%
may do as well as the maximum profit or as poorly as losing 100% in any one case. It
is the total return on many cases that has the expected return of 50%. Mathematical
theory holds that, if one constantly invests in positions with positive expected returns,
he should have a better chance of making rrwney.

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Chapter 28: Mathematical Applications 471
Thus, once the low starting point is chosen and the probability of being below that
price is determined, one can compute the probability of being at prices that are suc
cessively higher merely by iterating with the preceding formula. In reality, one is
using this information to integrate the distribution curve. Any method of approxi
mating the integral that is used in basic calculus, such as the Trapezoidal Rule or
Simpson's Rule, would be applicable here for more accurate results, if they are
desired.
A partial example of an expected return calculation follows.
Example: XYZ is currently at 33 and has an annual volatility of 25%. The previous
bull spread is being established- buy the February 30 and sell the February 35 for a
2-point debit - and these are 6-month options. Table 28-7 gives the necessary com
ponents for computing the expected return. Column (A), the probability of being
below price q, is computed according to the previously given formula, where p = 33
and vt = .177 (t = .25-V ½). The first stock price that needs to be looked at is 30, since
all results for the bull spread are equal below that price - a 100% loss on the spread.
The calculations would be performed for each eighth (or tenth) of a point up through
a price of 35. The expected return is compute<l by multiplying the two right-hand
columns, (B) and (C), and summing the results. Note that column (B) is determined
by subtracting successive numbers in column (A). It would not be particularly
enlightening to carry this example to completion, since the rest of the computations
are similar and there is a large number of them.
In theory, if one had the data and the computer power, he could evaluate a wide
range of strategies every day and come up with the best positions on an expected
return basis. He would probably get a few option buys (puts or calls), some bull
TABLE 28-7.
Calculation of expected returns.
Price at Expiration (A) (B) (()
(q) P (below q) P (of being at q) Profit on Spread
30 .295 .295 -$200
30 1/s .301 .006 - 187.50
30 1/4 .308 .007 - 175
303/s .316 .008 - 162.50

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472 Part IV: Additional Considerations
spreads, some naked writes and ratio calendar spreads, fewer straddles and ratio
writes, and a few covered call writes. This theory would be somewhat difficult to apply
in practice, because of the massive numbers of calculations involved and also because
of the accuracy of closing price data. It was mentioned previously that a computer will
assume that "bad" closing prices are actually attainable. By a "bad" closing price, it is
meant that the option did not trade simultaneously with the stock later in the day, and
that the actual market for the option is somewhat different in price than is reflected
by the closing price for the option. A daily contract volume "screen" will help allevi
ate this problem. For example, one may want to discard any option from his calcula
tions if that option did not trade a predetermined, minimum number of contracts
during the previous day. Data that give closing bids and offers for each option are
more expensive but also more reliable, and would alleviate the problem of "bad"
closing prices. In addition to a volume screen, another way of reducing the calcula
tions required is to limit oneself to strategies in which one has interest, or which one
is reasonably certain will fit in well with his investment objectives. Regardless of the
limitations that one places upon the quantity of computations, some computer power
is necessary to compute expected return. A sophisticated programmable calculator
may be able to provide a real-time calculation, but could never be used to evaluate
the entire option universe and come up with a ranking of the preferable situations
each day. On-line computer systems are also available that can provide these types of
calculations using up-to-the-minute prices. While real-time prices may occasionally
be useful, it is not an absolute necessity to have them.
One other by-product of the expected return calculation is that it could be used
as another model for predicting the theoretical value of an option. All one would have
to do is compute the probabilities of the stock being at each successive price above
the striking price of the option by expiration, and sum them up. The result would be
the theoretical option value. These data are published by some services and general
ly give a different theoretical value than would the Black-Scholes model. The reason
for the difference most readily lies in the inclusion of the risk-free interest rate in the
Black-Scholes model and its omission in the expected return model.
APPLYING THE CALCULATIONS TO STRATEGY DECISIONS
CALL WRITING
One method of ranking covered call writes that was described in Chapter 2 was to
rank all the writes that provided at least a minimal acceptable level of return by their
probability of not losing money. If one were interested in safety, he might decide to
use this approach. Suppose he decided that he would consider any write that provid-

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Chapter 28: Mathematical Applications 413
ed an annualized total return (capital gains, dividends, and commissions) of at least
12%. This would eliminate many potential writes, but would leave him with a fairly
large number of writing candidates each day. He knows the downside break-even
point at expiration in each write. Therefore, the probability of the stock being below
that break-even point at expiration can be computed quickly. His final list would rank
those writes with the least chance of being below the break-even point at expiration
as the best writes. Again, this ranking is based on an expected probability and is, of
course, no guarantee that the stock will not, in reality, fall below the break-even
point. However, over time, a list of this sort should provide the rrwst conservative cov
ered writes.
Example: XYZ is selling for 43 and a 6-month July 40 call is selling for 8 points. After
including dividends and commission costs for a 500-share position, the downside
break-even point at expiration is 36. If the annualized volatility of XYZ is 25%, the
probability of making money at expiration can be computed. The 6-month volatility
is 17.7% (25% times the square root of½ year). The probability of being below 36
can be computed by using the formula given earlier in this section:
The expected probability of XYZ being below 36 in 6 months is 15.8%. Therefore,
this would be an attractive write on a conservative basis, because it has a large prob
ability of making money (nearly 85% chance of not being below the break-even point
at expiration). The return if exercised in this example is approximately 20% annual
ized, so it should be acceptable from a profit potential viewpoint as well. It is a rela
tively easy matter to perform a similar calculation, with the aid of a computer, on all
covered writing candidates.
The ability to measure downside protection in terms of a common denomina
tor - volatility - can be useful in other types of covered call writing analyses. The
writer interested in writing out-of-the-money calls, which generally have higher
profit potential, is still interested in having an idea of what his downside protection
is. He might, for example, decide that he wants to invest in situations in which the
probability of making money is at least 60%. This is not an unusually difficult
requirement to fulfill, and will leave many attractive covered writes with a high prof
it potential to choose from. A downside requirement stated in terms of probability
of success removes the necessity of having to impose arbitrary requirements. Typical

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478 Part IV: Additional Considerations
The listed put' s price can be estimated by using the call pricing model and the
arbitrage formula. Recall that the arbitrageur must include the cost of carrying the
position as well as the dividends to be received.
Theoretical Theoretical Strike Stock Carrying n· 'd d = + - - + IVI en s put call price price price cost
The "theoretical call price" is obtained from the Black-Scholes model. The carrying
cost is the cost of money (interest rate) times the striking price, multiplied by the
time to expiration. Recall that this is the approximation formula for carrying cost (see
Chapter 27 for comments on present value and compounding). Consequently, ifXYZ
were at 41 and a 6-month January 40 call option were valued at 4 points by the
Black-Scholes model, the theoretical put price could be estimated. Assume that the
cost of money interest rate is 10% annually, and that the stock will pay $.50 in divi
dends in 6 months (t = ½ year).
Theoretical put price = 4 + 40 - 41- (.10 x 40 x ½) + .50
=3-2+½
=l½
This means that if the call could be sold for 4 points, the arbitrageur would be will
ing to pay up to 1 ½ points for the put to establish a conversion. The arbitrageur's
price is used as the theoretical listed put price estimate.
PUT BUYING
Put option purchases can be ranked in a manner very similar to that described for call
option buying. Reward opportunities occur when the stock falls in accordance with
its volatility. An upward stock movement represents risk for the put buyer. All of the
11 steps in the previous section on call buying are applicable to put buying. The pric
ing of the put necessary for steps 4 and 8 is done in accordance with the arbitrage
model just presented.
If an underlying stock does not have listed puts trading, the synthetic put can
be considered. While all U.S.-listed stocks have both puts and calls at every strike,
there are still situations with warrants, especially in foreign countries, that are appli
cable to the following discussion. Recall that synthetic puts are created for customers
by some brokerage houses. The brokerage sells the stock short and buys a call. The
customer can purchase the synthetic put for the amount of the risk involved, plus any
dividends to be paid by the underlying stock. The synthetic put pricing formula that
would be used in steps 4 and 8 of the option buying analysis is exactly the same as the
arbitrage model for listed puts, except that the carrying costs are omitted:

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