uld have less than 3 months remaining
and the October call would be the long-term call. At April expiration, if XYZ is below
50, the April call will expire worthless. At that time, the July 50 call could be sold
against the October 50 that is held long, thereby creating another calendar spread
with no additional commission cost on the long side.
The advantage of this type of strategy is that it is possible for the two sales (April
50 and July 50 in this example) to actually bring in more credits than were spent for
the one purchase (October 50). Thus, the spreader might be able to create a position
in which he has a guaranteed profit. That is, if the sum of his transactions is actually
a credit, he cannot lose money in the spread (provided that he does not attempt to
"leg" out of the spread). The disadvantage of using the long-term call in the calendar
spread is that the initial debit is larger, and therefore more dollars are initially at risk.
Chapter 9: Calendar Spreads 199
If the underlying stock moves substantially up or down in the first 3 months, the
spreader could realize a larger dollar loss with the October/ April spread because his
loss will approach the initial debit.
The remaining combination of the expiration series is to initially buy the
longest-term call and sell the intermediate-term call against it. This combination will
generally require the smallest initial debit, but there is not much profit potential in
the spread until the intermediate-term expiration date draws near. Thus, there is a
lot of time for the underlying stock to move some distance away from the initial strik
ing price. For this reason, this is generally an inferior approach to calendar spread
ing.
SUMMARY
Calendar spreading is a low-dollar-cost strategy that is a nonaggressive approach, pro
vided that the spreader does not invest a large percentage of his trading capital in the
strategy, and provided that he does not attempt to "leg" into or out of the spreads.
The neutral calendar spread is one in which the strategist is mainly selling time; he
is attempting to capitalize on the known fact that the near-term call will lose time pre
mium more rapidly than will a longer-term call. A more aggressive approach is the
bullish calendar spread, in which the speculator is essentially trying to reduce the net
cost of a longer-term call by the amount of credits taken in from the sale of a nearer
term call. This bullish strategy requires that the near-term call expire worthless and
then that the underlying stock rise in price. In either strategy, the most common
approach is to sell the nearest-term call and buy the intermediate-term call.
However, it may sometimes prove advantageous to sell the near-term and buy the
longest-term initially, with the intention of letting the near-term expire and then pos
sibly writing against the longer-term call a second time.
. CHAPTER 10
The Butterfly Spread
The recipient of one of the more exotic names given to spread positions, the butter
fly spread is a neutral position that is a combination of both a bull spread and a bear
spread. This spread is for the neutral strategist, one who thinks the underlying stock
will not experience much of a net rise or decline by expiration. It generally requires
only a small investment and has limited risk. Although profits are limited as well, they
are larger than the potential risk. For this reason, the butterfly spread is a viable strat
egy. However, it is costly in terms of commissions. In this chapter, the strategy is
explained using only calls. The strategy can also be implemented using a combination
of puts and calls, or with puts only, as will be demonstrated later.
There are three striking prices involved in a butterfiy spread. Using only calls,
the butterfly spread consists of buying one call at the lowest striking price, selling two
calls at the middle striking price, and buying one call at the highest striking price. The
following example will demonstrate how the butterfly spread works.
Example: A butterfly spread is established by buying a July 50 call for 12, selling 2
July 60 calls for 6 each, and buying a July 70 call for 3. The spread requires a rela
tively low debit of $300 (Table 10-1), although there are four option commissions
involved and these may represent a substantial percentage of the net investment. As
usual, the maximum amount of profit is realized at the striking price of the written
calls. With most types of spreads, this is a useful fact to remember, for it can aid in
quick computation of the potential of the spread. In this example, if the stock were
at the striking price of the written options at expiration (60), the two July 60's that are
short would expire worthless for a $1,200 gain. The long July 70 call would expire
worthless for a $300 loss, and the long July 50 call would be worth 10 points, for a
$200 loss on that call. The sum of the gains and losses would thus be a $700 gain, less
commissions. This is the maximum profit potential of the spread.
200
Chapter 10: The Butterfly Spread
TABLE 10-1.
Butterfly spread example.
Current prices:
XYZ common:
XYZ July 50 call:
XYZ July 60 call:
XYZ July 70 call:
Butterfly spread:
Buy 1 July 50 call
Sell 2 July 60 calls
Buy 1 July 70 call
Net debit
60
12
6
3
$1 ,200 debit
$1,200 credit
$300 debit
$300 (plus commissions)
201
The risk is limited in a butterfly spread, both to the upside and to the downside,
and is equal to the amount of the net debit required to establish the spread. In the
example above, the risk is limited to $300 plus commissions.
Table 10-2 and Figure 10-1 depict the results of this butterfly spread at various
prices at expiration. The profit graph resembles that of a ratio write, except that the
loss is limited on both the upside and the downside. There is a profit range within
which the butterfly spread makes money - 53 to 67 in the example, before commis
sions


le above, the risk is limited to $300 plus commissions.
Table 10-2 and Figure 10-1 depict the results of this butterfly spread at various
prices at expiration. The profit graph resembles that of a ratio write, except that the
loss is limited on both the upside and the downside. There is a profit range within
which the butterfly spread makes money - 53 to 67 in the example, before commis
sions are included. Outside this profit range, losses will occur at expiration, but these
losses are limited to the amount of the original debit plus commissions.
In accordance with more lenient margin requirements passed in 2000, the
investment required for a butterfly spread is equal to the net debit expended, which
is the risk in the spread. When the options expire in the same month and the strik
ing prices are evenly spaced (the spacing is 10 points in this example), the following
formulae can be used to quickly compute the important details of the butterfly
spread:
Net investment= Net debit of the spread
Maximum profit = Distance between strikes - Net debit
Downside break-even= Lowest strike+ Net debit
Upside break-even= Highest strike - Net debit
In the example, the distance between strikes is 10 points, the net debit is 3
points (before commissions), the lowest strike used is 50, and the highest strike is 70.
These formulae would then yield the following results for this example spread.
202 Part II: Call Option Strategies
Net investment= 3 points= $300
Maximum profit =10-3 = $700
Downside break-even= 50 + 3 = 53
FIGURE 10-1.
Butterfly spread.
+$700
Upside break-even = 70 - 3 = 67
$0 ___ .....__ _____ _._ __ --' __ _,_ ____ _
70
0
:E -$300----
J:
Stock Price at Expiration
TABLE 10-2.
Results of butterfly spread at expiration.
XYZ Price at July 50 July 60 July 70
Expiration Profit Profit Profit
40 -$1,200 +$1,200 -$300
50 - 1,200 + 1,200 - 300
53 900 + 1,200 - 300
56 600 + 1,200 - 300
60 200 + 1,200 - 300
64 + 200 + 400 - 300
67 + 500 200 - 300
70 + 800 800 - 300
80 + 1,800 - 2,800 + 700
Total
Profit
-$300
- 300
0
+ 300
+ 700
+ 300
0
- 300
- 300
Chapter 10: The Butterfly Spread 203
Note that all of these answers agree with the results that were previously obtained by
analyzing the example spread in detail.
In this example, the maximum profit potential is $700, the maximum risk is
$300, and the investment required is also $300, commissions excluded. In percent
age terms, this means that the butterfly spread has a loss limited to about 100% of
capital invested and could make profits of nearly 133% in this case. These represent
an attractive risk/reward relationship. This is, however, just an example, and two fac
tors that exist in the actual marketplace may greatly affect these numbers. First, com
missions are large; it is possible that eight commissions might have to be paid to
establish and liquidate the spread. Second, depending on the level of premiums to
be found in the market at any point in time, it may not be possible to establish a
spread for a debit as low as 3 points when the strikes are 10 points apart.
SELECTING THE SPREAD
Ideally, one would want to establish a butterfly spread at as small of a debit as pos
sible in order to limit his risk to a small amount, although that risk is still equal to
100% of the dollars invested in the spread. One would also like to have the stock be
near the middle striking price to begin with, because he will then be in his maximum
profit area if the stock remains relatively unchanged. Unfortunately, it is difficult to
satisfy both conditions simultaneously.
The smallest-debit butterfly spreads are those in which the stock is some dis
tance away from the middle striking price. To see this, note that if the stock were
well above the middle strike and all the options were at parity, the net debit would
be zero. Although no one would attempt to establish a butterfly spread with parity
options because of the risk of early assignment, it may be somewhat useful to try to
obtain a small debit by taking an opinion on the underlying stock. For example, if
the stock is close to the higher striking price, the debit would be small normally, but
the investor would have to be somewhat bearish on the underlying stock in order to
maximize his profit; that is, the stock would have to decline in price from the upper
striking price to the middle striking price for the maximum profit to be realized. An
analogous situation exists when the underlying stock is originally close to the lower
striking price. The investor could establish the spread for a small debit in this case
also, but he would now have to be somewhat bullish on the underlying stock in order
to attempt to realize his maximum profit.
Example: XYZ is at 70. One may be able to establish a low-debit butterfly spread
with the 50's, 60's, and 70's if the following prices exist:
204
XYZ common, 70;
XYZ July 50, 20;
XYZ July 60, 12; and
XYZ July 70, 5.
Part II: Call Option Strategies
The butterfly spread would require a debit of only $100 plus commissions to estab
lish, because the cost of the calls at the higher and lower strike is 25 points, and a 24-
point credit would be obtained by selling two calls at the middle strike. This is indeed
a low-cost butterfly spread, but the stock will have to move down in price for much
of a profit to be realized. The maximum profit of $900 less commissions would be
realized at 60 at expiration. The strategist would have to be bearish on XYZ to want
to establish such a spread.
Without the aid of an example, the reader should be able to determine that if
XYZ were originally at 50, a low-cost butterfly spread could be established by buying
the 50, selling two 60's, and buying a 70. In this case, however, the investor would
have to be bullish on the stock, because he would want it to move up to 60 by expi
ration in order for the maximum profit to be realized.
In general, then, if the butterfl

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ample, the reader should be able to determine that if
XYZ were originally at 50, a low-cost butterfly spread could be established by buying
the 50, selling two 60's, and buying a 70. In this case, however, the investor would
have to be bullish on the stock, because he would want it to move up to 60 by expi
ration in order for the maximum profit to be realized.
In general, then, if the butterfly spread is to be established at an extremely low
debit, the spreader will have to make a decision as to whether he wants to be bullish
or bearish on the underlying stock. Many strategists prefer to remain as neutral as
possible on the underlying stock at all times in any strategy. This philosophy would
lead to slightly higher debits, such as the $300 debit in the example at the beginning
of this chapter, but would theoretically have a better chance of making money
because there would be a profit if the stock remained relatively unchanged, the most
probable occurrence.
In either philosophy, there are other considerations for the butterfly spread.
The best butterfly spreads are generally found on the more expensive and/or more
volatile stocks that have striking prices spaced 10 or 20 points apart. In these situa
tions, the maximum profit is large enough to overcome the weight of the commission
costs involved in the butterfly spread. When one establishes butterfly spreads on
lower-priced stocks whose striking prices are only 5 points apart, he is normally put
ting himself at a disadvantage unless the debit is extremely small. One exception to
this rule is that attractive situations are often found on higher-priced stocks with
striking prices 5 points apart (50, 55, and 60, for example). They do exist from time
to time.
In analyzing butterfly spreads, one commonly works with closing prices. It was
mentioned earlier that using closing prices for analysis can prove somewhat mislead
ing, since the actual execution will have to be done at bid and asked prices, and these
Chapter 10: The Butterfly Spread 205
may differ somewhat from closing prices. Normally, this difference is small, but since
there are three different calls involved in a butterfly spread, the difference could be
substantial. Therefore, it is usually necessary to check the appropriate bid and asked
price for each call before entering the spread, in order to be able to place a reason
able debit on the order. As with other types of spreads, the butterfly spread order can
be placed as one order.
Before moving on to discuss follow-up action, it may be worthwhile to describe
a tactic for stocks with 5 points between striking prices. For example, the butterfly
spreader might work with strikes of 45, 50, and 60. If he sets up the usual type of but
terfly spread, he would end up with a position that has too much risk near 60 and very
little or none at all near 45. If this is what he wants, fine; but if he wants to remain
neutral, the standard type of butterfly spread will have to be modified slightly.
Example: The following prices exist:
XYZ common, 50;
July 45 call, 7;
July 50 call, 5; and
July 60 call, 2.
The normal type of butterfly spread- buying one 45, selling two 50's, and buying one
60 - can actually be done for a credit of 1 point. However, the profitability is no
longer symmetric about the middle striking price. In this example, the investor can
not lose to the downside because, even if the stock collapses and all the calls expire
worthless, he will still make his I-point credit. However, to the upside, there is risk:
If XYZ is anywhere above 60 at expiration, the risk is 4 points. This is no longer a neu
tral position. The fact that the lower strike is only 5 points from the middle strike
while the higher strike is 10 points away has made this a somewhat bearish position.
If the spreader wants to be neutral and still use these striking prices, he will have to
put on two bull spreads and only one bear spread. That is, he should:
Buy 2 July 45's:
Sell 3 July 50's:
Buy 1 July 60:
$1,400 debit
$1,500 credit
$200 debit
This position now has a net debit of $100 but has a better balance of risk at either
end. If XYZ drops and is below 45 at expiration, the spreader will lose his $100 ini
tial debit. But now, if XYZ is at or above 60 at expiration, he will lose $100 in that
range also. Thus, by establishing two bull spreads with a 5-point difference between
206 Part II: Call Option Strategies
strikes versus one bear spread with a IO-point difference between strikes, the risk has
been balanced at both ends. When one uses strike prices that are not evenly spaced
apart, his margin requirement increases substantially. In such a case, one has to mar
gin the individual component spreads separately. Therefore, in this example, he
would have to pay for the two bull spreads ( $200 each, for a total of $400) and then
margin the additional call bear spread ($700: the $1,000 difference in the strikes, less
the $300 credit taken in for that portion of the spread). Hence, in this example, the
margin requirement would be $1,100, even though the risk is only $100. Technically,
of that $1,100 requirement, the spread trader pays out only $100 in cash (the actual
debit of the spread), and the rest of the requirement can be satisfied with excess
equity in his account.
The same analysis obviously applies whenever 5-point striking price intervals
exist. There are numerous combinations that could be worked out for lower-priced
stocks by merely skipping over a striking price ( using the 25's, 30's, and 40's, for exam
ple). Although there are not normally many stocks trading over $100 per share, the
same analysis is applicable using 130's, 140's, and 160's, for example.
FOLLOW-UP ACTION
Since the butterfly spread has limited risk by its construction, there is usually little
that the spreader has to do in the way of follow-up action other than avoiding early
exercise or possibly dosing out the positi


r exam
ple). Although there are not normally many stocks trading over $100 per share, the
same analysis is applicable using 130's, 140's, and 160's, for example.
FOLLOW-UP ACTION
Since the butterfly spread has limited risk by its construction, there is usually little
that the spreader has to do in the way of follow-up action other than avoiding early
exercise or possibly dosing out the position early to take profits or limit losses even
further. The only part of the spread that is subject to assignment is the call at the mid
dle strike. If this call trades at or near parity, in-the-money, the spread should be
closed. This may happen before expiration if the underlying stock is about to go ex
dividend. It should be noted that accepting assignment will not increase the risk of
the spread (because any short calls assigned would still be protected by the remain
ing long calls). However, the margin requirement would change substantially, since
one would now have a synthetic put (long calls, short stock) in place. Plus, there may
be more onerous commissions for trading stock. Therefore, it is usually wise to avoid
assignment in a butterfly spread, or in any spread, for that matter.
If the stock is near the middle strike after a reasonable amount of time has
passed, an unrealized profit will begin to accrue to the spreader. If one feels that the
underlying stock is about to move away from the middle striking price and thereby
jeopardize these profits, it may be advantageous to close the spread to take the avail
able profit. Be certain to include commission costs when determining if an unreal
ized profit exists. As a general rule of thumb, if one is doing 10 spreads at a time, he
Chapter 10: Tire Butterfly Spread 207
can estimate that the commission cost for each option is about 1/s point. That is, if one
has 10 butterfly spreads and the spread is currently at 6 points, he could figure that
he would net about 5½ points after commissions to close the spread. This 1/s estimate
is only valid if the spreader has at least 10 options at each strike involved in a spread.
Normally, one would not close the spread early to limit losses, since these loss
es are limited to the original net debit in any case. However, if the original debit was
large and the stock is beginning to break out above the higher strike or to break down
below the lower strike, the spreader may want to close the spread to limit losses even
further.
It has been repeatedly stated that one should not attempt to ''leg" out of a
spread because of the risk that is incurred if one is wrong. However, there is a
method of legging out of a butterfly spread that is acceptable and may even be pru
dent. Since the spread consists of both a bull spread and a bear spread, it may often
be the case that the stock experiences a relatively substantial move in one direction
or the other during the life of the butterfly spread, and that the bull spread portion
or the bear spread portion could be closed out near their maximum profit potentials.
If this situation arises, the spreader may want to take advantage of it in order to be
able to profit more if the underlying stock reverses direction and comes back into the
profit range.
Exampk: This strategy can be explained by using the initial example from this chap
ter and then assuming that the stock falls from 60 to 45. Recall that this spread was
initially established with a 3-point debit and a maximum profit potential of 7 points.
The profit range was 53 to 67 at July expiration. However, a rather unpleasant situa
tion has occurred: The stock has fallen quickly and is below the profit range. If the
spreader does nothing and keeps the spread on, he will lose 3 points at most if the
stock remains below 50 until July expiration. However, by increasing his risk slightly,
he may be able to improve his position. Notice in Table 10-3 that the bear spread por
tion of the overall spread - short July 60, long July 70 - has very nearly reached its
maximum potential. The bear spread could be bought back for ½ point total (pay 1
point to buy back the July 60 and receive½ point from selling out the July 70). Thus,
the spreader could convert the butterfly spread to a bull spread by spending ½ point.
What would such an action do to his overall position? First, his risk would be
increased by the ½ point spent to close the bear spread. That is, if XYZ continues to
remain below 50 until July expiration, he would now lose 3½ rather than 3 points,
plus commissions in either case. He has, however, potentially helped his chances of
realizing something close to the maximum profit available from the original butterfly
spread.
208 Part II: Call Option Strategies
TABLE 10-3.
Initial spread and current prices.
Initial Spread Current Prices
XYZ common: 60 XYZ common: 45
July 50 call: 12 July 50 call: 2
July 60 call: 6 July 60 call: 1
July 70 call: 3 July 70 call: 1/2
After buying back the bear spread, he is left with the following bull spread:
Long July 50 call _ N t d b·t 3u, . t
h l all e e 1 ,2 pom s S ort Ju y 60 c
He has a bull spread at the total cost paid to date - 3½ points. From the earlier dis
cussion of bull spreads, the reader should know that the break-even point for this
position is 53½ at expiration, and it could make a 6½ point profit if XYZ is anywhere
over 60 at July expiration. Hence, the break-even point for the position was raised
from 53 to 53½ by the expense of the ½ point to buy back the bear spread. However,
if the stock should rally back above 60, the strategist will be making a profit nearly
equal to the original maximum profit that he was aiming for (7 points). Moreover, this
profit is now available anywhere over 60, not just exactly at 60 as it was in the origi
nal position. Although the chances of such a rally cannot be considered great, it does
not cost the spreader much to restructure himself into a position with a much broad
er maximum p


ategist will be making a profit nearly
equal to the original maximum profit that he was aiming for (7 points). Moreover, this
profit is now available anywhere over 60, not just exactly at 60 as it was in the origi
nal position. Although the chances of such a rally cannot be considered great, it does
not cost the spreader much to restructure himself into a position with a much broad
er maximum profit area.
A similar situation is available if the underlying stock moves up in price. In that
case, the bull spread may be able to be removed at nearly its maximum profit poten
tial, thereby leaving a bear spread. Again, suppose that the same initial spread was
established but that XYZ has risen to 75. When the underlying stock advances sub
stantially, the bull spread portion of the butterfly spread may expand to near its max
imum potential. Since the strikes are 10 points apart in this bull spread, the widest it
can grow to is 10 points. At the prices shown in Table 10-4, the bull spread - long
July 50 and short July 60 - has grown to 9½ points. Thus, the bull spread position
could be removed within ½ point of its maximum profit potential and the original
butterfly spread would become a bear spread. Note that the closing of the bull spread
portion generates a 9½ point credit: The July 50 is sold at 25½ and the July 60 is
bought back at 16. The original butterfly spread was established at a 3-point debit, so
the net position is the remaining position:
Chapter 10: The BatterRy Spread 209
Long July 70 call .
Short July 60 call - Net credit 6½ points
This bear spread has a maximum profit potential of 6½ points anywhere below 60 at
July expiration. The maximum risk is 3½ points anywhere above 70 at expiration.
Thus, the original butterfly spread was again converted into a position such that a
stock price reversal to any price below 60 could produce something close to the max
imum profit. Moreover, the risk was only increased by an additional ½ point.
TABLE 10-4.
Initial spread and new current prices.
I nitiol Spread
XYZ common: 60
XYZ July 50 call: 12
July 60 call: 6
July 70 call: 3
SUMMARY
Current Prices
XYZ common:
July 50 call:
July 60 call:
July 70 call:
75
251/2
16
7
The butterfly spread is a viable, low-cost strategy with both limited profit potential
and limited risk. It is actually a combination of a bull spread and a bear spread, and
involves using three striking prices. The risk is limited should the underlying stock
fall below the lowest strike or rise above the highest strike. The maximum profit is
obtained at the middle strike. One can keep his initial debits to a minimum by ini
tially assuming a bullish or bearish posture on the underlying stock. If he would
rather remain neutral, he will normally have to pay a slightly larger debit to establish
the spread, but may have a better chance of making money. If the underlying stock
experiences a large move in one direction or the other prior to expiration, the spread
er may want to close the profitable side of his butterfly spread near its maximum
profit potential in order to be able to capitalize on a stock price reversal, should one
occur.
Ratio Call Spreads
A ratio call spread is a neutral strategy in which one buys a number of calls at a lower
strike and sells more calls at a higher strike. It is somewhat similar to a ratio write in
concept, although the spread has less downside risk and normally requires a smaller
investment than does a ratio write. The ratio spread and ratio write are similar in that
both involve uncovered calls, and both have profit ranges within which a profit can
be made at expiration. Other comparisons are demonstrated throughout the chapter.
Example: The following prices exist:
XYZ common, 44;
XYZ April 40 call, 5; and
XYZ April 45 call, 3.
A 2:1 ratio call spread could be established by buying one April 40 call and simulta
neously selling two April 45's. This spread would be done for a credit of 1 point - the
sale of the two April 45's bringing in 6 points and the purchase of the April 40 cost
ing 5 points. This spread can be entered as one spread order, specifying the net cred
it or debit for the position. In this case, the spread would be entered at a net credit
of 1 point.
Ratio spreads, unlike ratio writes, have a relatively small, limited downside risk.
In fact, if the spread is established at an initial credit, there is no downside risk at all.
In a ratio spread, the profit or loss at expiration is constant below the lower striking
price, because both options would be worthless in that area. In the example above, if
XYZ is below 40 at April expiration, all the options would expire worthless and the
spreader would have made a profit of his initial I-point credit, less commissions. This
I-point gain would occur anywhere below 40 at expiration; it is a constant.
210
Chapter 11: Ratio Call Spreads 211
The maximum profit at expiration for a ratio spread occurs if the stock is exact
ly at the striking price of the written options. This is true for nearly all types of strate
gies involving written options. In the example, if XYZ were at 45 at April expiration,
the April 45 calls would expire worthless for a gain of $600 on the two of them, and
the April 40 call would be worth 5 points, resulting in no gain or loss on that call.
Thus, the total profit would be $600 less commissions.
The greatest risk in a ratio call spread lies to the upside, where the loss may the
oretically be unlimited. The upside break-even point in this example is 51, as shown
in Table 11-1. The table and Figure 11-1 illustrate the statements made in the pre
ceding paragraphs.
In a 2:1 ratio spread, two calls are sold for each one purchased. The maximum
profit amount and the upside break-even point can easily be computed by using the
following formulae:
Points of maximum profit = Initial credit + Difference between strikes or
= Difference between strikes - Initial


in Table 11-1. The table and Figure 11-1 illustrate the statements made in the pre
ceding paragraphs.
In a 2:1 ratio spread, two calls are sold for each one purchased. The maximum
profit amount and the upside break-even point can easily be computed by using the
following formulae:
Points of maximum profit = Initial credit + Difference between strikes or
= Difference between strikes - Initial debit
Upside break-even point= Higher strike price+ Points of maximum profit
In the preceding example, the initial credit was 1 point, so the points of maxi
mum profit = 1 + 5 = 6, or $600. The upside break-even point is then 45 + 6, or 51.
This agrees with the results determined earlier. Note that if the spread is established
at a debit rather than a credit, the debit is subtracted from the striking price differ
ential to determine the points of maximum profit.
Many neutral investors prefer ratio spreads over ratio writes for two reasons:
TABLE 11-1.
Ratio call spread.
XYZ Price of April 40 Coll April 45 Coll Total
Expiration Profits Profits Profits
35 -$ 500 +$ 600 +$100
40 - 500 + 600 + 100
42 - 300 + 600 + 300
45 0 + 600 + 600
48 + 300 0 + 300
51 + 600 - 600 0
55 +1,000 -1,400 - 400
60 + 1,500 -2,400 - 900
212 Part II: Call Option Strategies
FIGURE 11 • 1.
Ratio call spread (2: 1 ).
Stock Price at Expiration
1. The downside risk or gain is predetermined in the ratio spread at expiration, and
therefore the position does not require much monitoring on the downside.
2. The margin investment required for a ratio spread is normally smaller than that
required for a ratio write, since on the long side one is buying a call rather than
buying the common stock itself.
For margin purposes, a ratio spread is really the combination of a bull spread
and a naked call write. There is no margin requirement for a bull spread other than
the net debit to establish the bull spread. The net investment for the ratio spread is
thus equal to the collateral required for the naked calls in the spread plus or minus
the net debit or credit of the spread. In the example above, there is one naked call.
The requirement for the naked call is 20% of the stock price plus the call premium,
less the out-of-the-money amount. So the requirement in the example would be 20%
of 44, or $880, plus the call premium of $300, less the one point that the stock is
below the striking price - a $1,080 requirement for the naked call. Since the spread
was established at a credit of one point, this credit can also be applied against the ini
tial requirement, thereby reducing that requirement to $980. Since there is a naked
call in this spread, there will be a mark to market if the stock moves up. Just as was
recommended for the ratio write, it is recommended that the ratio spreader allow at
least enough collateral to reach the upside break-even point. Since the upside break
even point is 51 in this example, the spreader should allow 20% of 51, or $1,020, plus
Chapter 11: Ratio Call Spreads 213
the 6 points that the call would be worth less the 1-point initial net credit - a total of
$1,520 for this spread ($1,020 + $600 - $100).
DIFFERING PHILOSOPHIES
For many strategies, there is more than one philosophy of how to implement the
strategy. Ratio spreads are no exception, with three philosophies being predominant.
One philosophy holds that ratio spreading is quite similar to ratio writing - that one
should be looking for opportunities to purchase an in-the-money call with little or no
time premium in it so that the ratio spread simulates the profit opportunities from
the ratio write as closely as possible with a smaller investment. The ratio spreads
established under this philosophy may have rather large debits if the purchased call
is substantially in-the-money. Another philosophy of ratio spreading is that spreads
should be established for credits so that there is no chance of losing money on the
downside. Both philosophies have merit and both are described. A third philosophy,
called the "delta spread," is more concerned with neutrality, regardless of the initial
debit or credit. It is also described.
RATIO SPREAD AS RATIO WRITE
There are several spread strategies similar to strategies that involve common stock. In
this case, the ratio spread is similar to the ratio write. Whenever such a similarity
exists, it may be possible for the strategist to buy an in-the-money call with little or no
time premium as a substitute for buying the common stock. This was seen earlier in
the covered call writing strategy, where it was shown that the purchase of in-the
money calls or warrants might be a viable substitute for the purchase of stock. If one
is able to buy an in-the-rrwney call as a substitute for the stock, he will not affect his
profit potential substantially. When comparing a ratio spread to a ratio write, the max
imum profit potential and the profit range are reduced by the time value premium
paid for the long call. If this call is at parity (the time value premium is thus zero), the
ratio spread and the ratio write have exactly the same profit potential. Moreover, the
net investment is reduced and there is less downside risk should the stock fall in price
below the striking price of the purchased call. The spread also involves smaller com
mission costs than does the ratio write, which involves a stock purchase. The ratio
writer does receive stock dividends, if any are paid, whereas the spreader does not.
Example: XYZ is at 50, and an XYZ July 40 call is selling for 11 while an XYZ July 50
call is selling for 5. Table 11-2 compares the important points between the ratio write
and the ratio spread.
214
TABLE 11-2.
Ratio write and ratio spread compared.
Profit range
Maximum profit
Downside risk
Upside risk
Initial investment
Ratio Write:
Buy XYZ of 50 and
Sell 2 July SO's at 5
40 to 60
10 points
40 points
40 points
$3,000
Part II: Call Option Strategies
Ratio


ly 50
call is selling for 5. Table 11-2 compares the important points between the ratio write
and the ratio spread.
214
TABLE 11-2.
Ratio write and ratio spread compared.
Profit range
Maximum profit
Downside risk
Upside risk
Initial investment
Ratio Write:
Buy XYZ of 50 and
Sell 2 July SO's at 5
40 to 60
10 points
40 points
40 points
$3,000
Part II: Call Option Strategies
Ratio Spread:
Buy 1 July 40 of 11 and
Sell 2 July SO's at 5
41 to 59
9 points
1 point
Unlimited
$1,600
In Chapter 6, it was pointed out that ratio writing was one of the better strate
gies from a probability of profit viewpoint. That is, the profit potential conforms well
to the expected movement of the underlying stock. The same statement holds true
for ratio spreads as substitutes for ratio writes. In fact, the ratio spread may often be
a better position than the ratio write itself, when the long call can be purchased with
little or no time value premium in it.
RATIO SPREAD FOR CREDITS
The second philosophy of ratio spreads is to establish them only for credits.
Strategists who follow this philosophy generally want a second criterion fulfilled also:
that the underlying stock be below the striking price of the written calls when the
spread is established. In fact, the farther the stock is below the strike, the more
attractive the spread would be. This type of ratio spread has no downside risk
because, even if the stock collapses, the spreader will still make a profit equal to the
initial credit received. This application of the ratio spread strategy is actually a sub
case of the application discussed above. That is, it may be possible both to buy a long
call for little or no time premium, thereby simulating a ratio write, and also to be able
to set up the position for a credit.
Since the underlying stock is generally below the maximum profit point when
one establishes a ratio spread for a credit, this is actually a mildly bullish position.
The investor would want the stock to move up slightly in order for his maximum prof
it potential to be realized. Of course, the position does have unlimited upside risk, so
it is not an overly bullish strategy.
Chapter 11: Ratio Call Spreads 215
These two philosophies are not mutually exclusive. The strategist who uses ratio
spreads without regard for whether they are debit or credit spreads will generally
have a broader array of spreads to choose from and will also be able to assume a more
neutral posture on the stock. The spreader who insists on generating credits only will
be forced to establish spreads on which his return will be slightly smaller if the under
lying stock remains relatively unchanged. However, he will not have to worry about
downside defensive action, since he has no risk to the downside. The third philoso
phy, the "delta spread," is described after the next section, in which the uses of ratios
other than 2: 1 are described.
ALTERING THE RATIO
Under either of the two philosophies discussed above, the strategist may find that a
3:1 ratio or a 3:2 ratio better suits his purposes than the 2:1 ratio. It is not common
to write in a ratio of greater than 4: 1 because of the large increase in upside risk at
such high ratios. The higher the ratio that is used, the higher will be the credits of
the spread. This means that the profits to the downside will be greater if the stock
collapses. The lower the ratio that is used, the higher the upside break-even point will
be, thereby reducing upside risk.
Example: If the same prices are used as in the initial example in this chapter, it will
be possible to demonstrate these facts using three different ratios (Table 11-3):
XYZ common, 44;
XYZ April 40 call, 5; and
XYZ April 45 call, 3.
TABLE 11-3.
Comparison of three ratios.
Price of spread
(downside risk)
Upside break-even
Downside break-even
Maximum profit
3:2 Ratio:
Buy 2 April 40's
Sell 3 April 45's
1 debit
54
401/2
9
2:1 Ratio: 3:1 Ratio:
By 1 April 40 Buy 1 April 40
Sell 2 April 45's Sell 3 April 45's
1 credit 4 credit
51 49½
None None
6 9
216 Part II: Call Option Strategies
In Chapter 6 on ratio writing, it was seen that it was possible to alter the ratio
to adjust the position to one's outlook for the underlying stock The altering of the
ratio in a ratio spread accomplishes the same objective. In fact, as will be pointed out
later in the chapter, the ratio may be adjusted continuously to achieve what is con
sidered to be a "neutral spread." A similar tactic, using the option's delta, was
described for ratio writes.
The following formulae allow one to determine the maximum profit potential
and upside break~even point for any ratio:
Points of maximum = Net credit+ Number oflong calls x
profit Difference in striking prices or
= Number of long calls X Difference in
striking prices - Net debit
Upside break-even = Points of maximum profit ff h t "ki .
point Number of naked calls + ig er s n ng pnce
These formulae can easily be verified by checking the numbers in Table 11-3.
THE "DELTA SPREAD"
The third philosophy of ratio spreading is a more sophisticated approach that is often
referred to as the delta spread, because the deltas of the options are used to estab
lish and monitor the spread. Recall that the delta of a call option is the amount by
which the option is expected to increase in price if the underlying stock should rise
by one point. Delta spreads are neutral spreads in that one uses the deltas of the two
calls to set up a position that is initially neutral.
Example: The deltas of the two calls that appeared in the previous examples were
.80 and .50 for the April 40 and April 45, respectively. If one were to buy 5 of the
April 40's and simultaneously sell 8 of the April 45's, he would have a delta-neutral
spread. That is, if XYZ moved up by one point, the 5 April 40 calls would appreciate
by .80 point each, for a net gain of 4 points. Similarly, the 8 April


e deltas of the two calls that appeared in the previous examples were
.80 and .50 for the April 40 and April 45, respectively. If one were to buy 5 of the
April 40's and simultaneously sell 8 of the April 45's, he would have a delta-neutral
spread. That is, if XYZ moved up by one point, the 5 April 40 calls would appreciate
by .80 point each, for a net gain of 4 points. Similarly, the 8 April 45 calls that he is
short would each appreciate by .50 point for a net loss of 4 points on the short side.
Thus, the spread is initially neutral - the long side and the short side will offset each
other. The idea of setting up this type of neutral spread is to be able to capture the
time value premium decay in the preponderance of short calls without subjecting the
spread to an inordinate amount of market risk. The actual credit or debit of the
spread is not a determining factor.
Chapter 11: Ratio Call Spreads 217
It is a fairly simple matter to determine the correct ratio to use in the delta
spread: Merely divide the delta of the purchased call by the delta of the written call.
In the example, this implies that the neutral ratio is .80 divided by .50, or 1.6:1.
Obviously, one cannot sell 1.6 calls, so it is common practice to express that ratio as
16:10. Thus, the neutral spread would consist of buying 10 April 40's and selling 16
April 45's. This is the same as an 8:5 ratio. Notice that this calculation does not
include anything about debits or credits involved in the spread. In this example, an
8:5 ratio would involve a small debit of one point (5 April 40's cost 25 points and 8
April 45's bring in 24 points). Generally, reasonably selected delta spreads involve
small debits.
Certain selection criteria can be offered to help the spreader eliminate some of
the myriad possibilities of delta spreads on a day-to-day basis. First, one does not
want the ratio of the spread to be too large. An absolute limit, such as 4:1, can be
placed on all spread candidates. Also, if one eliminates any options selling for less
than ½ point as candidates for the short side of the spread, the higher ratios will be
eliminated. Second, one does not want the ratio to be too small. If the delta-neutral
ratio is less than 1.2:1 (6:5), the spread should probably be rejected. Finally, if one is
concerned with downside risk, he might want to limit the total debit outlay. This
might be done with a simple parameter, such as not paying a debit of more than 1
point per long option. Thus, in a spread involving 10 long calls, the total debit must
be 10 points or less. These screens are easily applied, especially with the aid of a com
puter analysis. One merely uses the deltas to determine the neutral ratio. Then, if it
is too small or too large, or if it requires the outlay of too large a debit, the spread is
rejected from consideration. If not, it is a potential candidate for investment.
FOLLOW-UP ACTION
Depending on the initial credit or debit of the spread, it may not be necessary to take
any downside defensive action at all. If the initial debit was large, the writer may roll
down the written calls as in a ratio write.
Example: An investor has established the ratio write by buying an XYZ July 40 call
and selling two July 60 calls with the stock near 60. He might have done this because
the July 40 was selling at parity. If the underlying stock declines, this spreader could
roll down to the 50's and then to the 45's, in the same manner as he would with a ratio
write. On the other hand, if the spread was initially set up with contiguous striking
prices, the lower strike being just below the higher strike, no rolling-down action
would be necessary.
218 Part II: Call Option Strategies
REDUCING THE RATIO
Upside fallow-up action does not normally consist of rolling up as it does in a ratio
write. Rather, one should usually buy some more long calls to reduce the ratio in the
spread. Eventually, he would want to reduce the spread to 1:1, or a normal bull
spread. An example may help to illustrate this concept.
Example: In the initial example, one April 40 call was bought and two April 45's were
sold, for a net credit of one point. Assume that the spreader is going to buy one more
April 40 as a means of upside defensive action if he has to. When and if he buys this
second long call, his total position will be a normal bull spread - long 2 April 40's and
short 2 April 45's. The liquidating value of this bull spread would be 10 points if XYZ
were above 45 at April expiration, since each of the two bull spreads would widen to
its maximum potential (5 points) with the stock above 45 in April. The ratio spread
er originally brought in a one-point credit for the 2:1 spread. If he were later to pay
11 points to buy the additional long April 40 call, his total outlay would have been 10
points. This would represent a break-even situation at April expiration if XYZ were
above 45 at that time, since it was just shown that the spread could be liquidated for
10 points in that case. So the ratio spreader could wait to take defensive action until
the April call was selling for 11 points. This is a dynamic type of follow-up action, one
that is dependent on the options' price, not the stock price per se.
This outlay of 11 points for the April 40 would leave a break-even situation as
long as the stock did not reverse and fall in price below 45 after the call was bought.
The spreader may decide that he would rather leave some room for upside profit
rather than merely trying to break even if the stock rallies too far. He might thus
decide to buy the additional long call at 9 or 10 points rather than waiting for it to get
to 11. Of course, this might increase the chances of a whipsaw occurring, but it would
leave some room for upside profits if the stock continues to rise.
Where ratios other than 2:1 are involved initially, the same thinking can be
applied. In fact, the purchase of the ad


k rallies too far. He might thus
decide to buy the additional long call at 9 or 10 points rather than waiting for it to get
to 11. Of course, this might increase the chances of a whipsaw occurring, but it would
leave some room for upside profits if the stock continues to rise.
Where ratios other than 2:1 are involved initially, the same thinking can be
applied. In fact, the purchase of the additional long calls might take place in a two
step process.
Example: If the spread was initially long 5 calls and short 10 calls, the spreader
would not necessarily have to wait until the April 40's were selling at 11 and then buy
all 5 needed to make the spread a normal bull spread. He might decide to buy 2 or
3 at a lower price, thereby reducing his ratio somewhat. Then, if the stock rallied
even further, he could buy the needed long calls. By buying a few at a cheaper price,
the spreader gives himself the leeway to wait considerably longer to the upside. In
essence, all 5 additional long calls in this spread would have to be bought at an aver
age price of 11 or lower in order for the spread to break even. However, if the first 2
Chapter 11: Ratio Call Spreads 219
of them are bought for 8 points, the spreader would not have to buy the remaining 3
until they were selling around 13. Thus, he could wait longer to the upside before
reducing the spread ratio to 1:1 (a bull spread). A formula can be applied to deter
mine the price one would have to pay for the additional long calls, to convert the ratio
spread into a bull spread. If the calls are bought, such a bull spread would break even
with the stock above the higher striking price at expiration:
Break-even cost of Number of short calls x Difference in strikes -Total debit to date
long calls - Number of naked calls
In the simple 2: 1 example, the number of short calls was 2, the difference in the
strikes was 5, the total debit was minus one (-1) (since it was actually a 1.:.point cred
it), and the number of naked calls is 1. Thus, the break-even cost of the additional
long call is [2 x 5- (-1)(1)]/l = 11. As another verification of the formula, consider
the 10:5 spread at the same prices. The initial credit of this spread would be 5 points,
and the break-even cost of the five additional long calls is 11 points each. Assume that
the spreader bought two additional April 40's for 8 points each (16 debit). This would
make the total debit to date of the spread equal to 11 points, and reduce the number
of naked calls to 3. The break-even cost of the remaining 3 long calls that would need
to be purchased if the stock continued to rally would be (10 x 5 - 11)/3 = 13. This
agrees with the observation made earlier. This formula can be used before actual fol
low-up action is implemented. For example, in the 10:5 spread, if the April 40's were
. selling for 8, the spreader might ask: "To what would I raise the purchase price of the
remaining long calls if I buy 2 April 40's for 8 right now?" By using the formula, he
could easily see that the answer would be 13.
ADJUSTING WITH THE DELTA
The theoretically-oriented spreader can use the delta-neutral ratio to monitor his
spreads as well as to establish them. If the underlying stock moves up in price too far
or down in price too far, the delta-neutral ratio of the spread will change. The spread
er can then readjust his spread to a neutral status by buying some additional long calls
on an upside movement by the stock, or by selling some additional short calls on a
downward movement by the stock Either action will serve to make the spread delta
neutral again. The public customer who is employing the delta-neutral adjustment
method of follow-up action should be careful not to overadjust, because the com
mission costs would become prohibitive. A more detailed description of the use of
deltas as a means of follow-up action is contained in Chapter 28 on mathematical
applications, under the heading "Facilitation or Institutional Block Positioning." The
general concept, however, is the same as that shown earlier for ratio writing.
220 Part II: Call Option Strategies
Example: Early in this chapter, when selection criteria were described, a neutral
ratio was determined to be 16:10, with XYZ at 44. Suppose, after establishing the
spread, that the common rallied to 4 7. One could use the current deltas to adjust.
This information is summarized in Table 11-4. The current neutral ratio is approxi
mately 14:10. Thus, two of the short April 45's could be bought closing. In practice,
one usually decreases his ratio by adding to the long side. Consequently, one would
buy two April 40's, decreasing his overall ratio to 16:12, which is 1.33 and is close to
the actual neutral ratio of 1.38. The position would therefore be delta-neutral once
more.
An alternative way of looking at this is to use the equivalent stock position
(ESP), which, for any option, is the multiple of the quantity times the delta times the
shares per option. The last three lines of Table 11-4 show the ESP for each call and
for the position as a whole. Initially, the position has an ESP of 0, indicating that it is
perfectly delta-neutral. In the current situation, however, the position is delta short
140 shares. Thus, one could adjust the position to be delta-neutral by buying 140
shares of XYZ. If he wanted to use the options rather than the stock, he could buy
two April 45's, which would add a delta long of 130 ESP (2 x .65 x 100), leaving the
position delta short 10 shares, which is very near neutral. As pointed out in the above
paragraph, the spreader probably should buy the call with the most intrinsic value -
the April 40. Each one of these has an ESP of 90 (1 x .9 x 100). Thus, if one were
bought, the position would be delta short 50 shares; if two were bought, the total
position would be delta long 40 shares. It would be a matter of individual preference
whether the spreader wanted to be long or s


ut in the above
paragraph, the spreader probably should buy the call with the most intrinsic value -
the April 40. Each one of these has an ESP of 90 (1 x .9 x 100). Thus, if one were
bought, the position would be delta short 50 shares; if two were bought, the total
position would be delta long 40 shares. It would be a matter of individual preference
whether the spreader wanted to be long or short the "odd lot" of 40 or 50 shares,
respectively.
TABLE 11-4.
Original and current prices and deltas.
XYZ common
April 40 call
April 45 call
April 40 delta
April 45 delta
Neutral ratio
April 40 ESP
April 45 ESP
Total ESP
Original Situation
44
5
3
.80
.50
16:10 (.80/.50)
800 long (l Ox .8 x 100)
800 shrt ( 16 x .5 x l 00)
0 (neutral)
Current Situation
47
8
5
.90
.65
14:10 (.90/.65 = 1.38)
900 long (10 x .9 x 100)
l ,040 shrt ( 16 x .65 x l 00)
140 shrt
Chapter 11: Ratio Call Spreads 221
The ESP method is merely a confirmation of the other method. Either one
works well. The spreader should become familiar with the ESP method because, in
a position with many different options, it reduces the exposure of the entire position
to a single number.
TAKING PROFITS
In addition to defensive action, the spreader may find that he can close the spread
early to take a profit or to limit losses. If enough time has passed and the underlying
stock is close to the maximum profit point - the higher striking price - the spreader
may want to consider closing the spread and taking his profit. Similarly, if the under
lying stock is somewhere between the two strikes as expiration draws near, the writer
will normally find himself with a profit as the long call retains some intrinsic value
and the short calls are nearly worthless. If at this time one feels that there is little to
gain (a price decline might wipe out the long call value), he should close the spread
and take his profit.
SUMMARY
Ratio spreads can be an attractive strategy, similar in some ways to ratio writing. Both
strategies offer a large probability of making a limited profit. The ratio spread has
limited downside risk, or possibly no downside risk at all. In addition, if the long
call(s) in the spread can be bought with little or no time value premium in them, the
ratio spread becomes a superior strategy to the ratio write. One can adjust the ratio
used to reflect his opinion of the underlying stock or to make a neutral profit range
if desired. The ratio adjustment can be accomplished by using the deltas of the
options. In a broad sense, this is one of the more attractive forms of spreading, since
the strategist is buying mostly intrinsic value and is selling a relatively large amount
of time value.
Cotnbining Calendar
and Ratio Spreads
The previous chapters on spreading introduced the basic types of spreads. The sim
plest forms of bull spreads, bear spreads, or calendar spreads can often be combined
to produce a position with a more attractive potential. The butterfly spread, which is
a combination of a bull spread and a bear spread, is an example of such a combina
tion. The next three chapters are devoted to describing other combinations of
spreads, wherein the strategist not only mixes basic strategies ..:... bull, bear, and calen
dar - but uses varying expiration dates as well. Although they may seem overly com
plicated at first glance, these combinations are often employed by professionals in the
field.
RATIO CALENDAR SPREAD
The ratio cdendar spread is a combination of the techniques used in the calendar
and ratio spreads. Recall that one philosophy of the calendar spread strategy was to
sell the near-term call and buy a longer-term call, with both being out-of-the-money.
This is a bullish calendar spread. If the underlying stock never advances, the spread
er loses the entire amount of the relatively small debit that he paid for the spread.
However, if the stock advances after the near-term call expires worthless, large prof
its are possible. It was stated that this bullish calendar spread philosophy had a small
probability of attaining large profits, and that the few profits could easily exceed the
preponderance of small losses.
The ratio calendar spread is an attempt to raise the probabilities while allowing
for large potential profits. In the ratio calendar spread, one sells a number of near-
222
Chapter 12: Combining Calendar and Ratio Spreads 223
term calls while buyingfewer of the intermediate-term or long-term calls. Since more
calls are being sold than are being bought, naked options are involved. It is often pos
sible to set up a ratio calendar spread for a credit, meaning that if the underlying
stock never rallies above the strike, the strategist will still make money. However,
since naked calls are involved, the collateral requirements for participating in this
strategy may be large.
Example: As in the bullish calendar spreads described in Chapter 9, the prices are:
XYZ common, 45;
XYZ April 50 call, l; and
XYZ July 50 call, l½.
In the bullish calendar spread strategy, one July 50 is bought for each April 50 sold.
This means that the spread is established for a debit of½ point and that the invest
ment is $50 per spread, plus commissions. The strategist using the ratio calendar
/ spread has essentially the same philosophy as the bullish calendar spreader: The
stock will remain below 50 until April expiration and may then rally. The ratio calen
dar spread might be set up as follows:
Buy 1 XYZ July 50 call at l½
Sell 2 XYZ April 50 calls at 1 each
Net
l½ debit
2 credit
½ credit
Although there is no cash involved in setting up the ratio spread since it is done for
a credit, there is a collateral requirement for the naked April 50 call.
If the stock remains below 50 until April expiration, the long call - the July 50
- will be owned free. After that, no matter what happens to the underlying stock, the
spread cannot lose money. In fact, if the u


bit
2 credit
½ credit
Although there is no cash involved in setting up the ratio spread since it is done for
a credit, there is a collateral requirement for the naked April 50 call.
If the stock remains below 50 until April expiration, the long call - the July 50
- will be owned free. After that, no matter what happens to the underlying stock, the
spread cannot lose money. In fact, if the underlying stock advances dramatically after
near-term expiration, large profits will accrue as the July 50 call increases in value. Of
course, this is entirely dependent on the near-term call expiring worthless. If the
underlying stock should rally above 50 before the April calls expire, the ratio calen
dar spread is in danger of losing a large amount of money because of the naked calls,
and defensive action must be taken. Follow-up actions are described later.
The collateral required for the ratio calendar spread is equal to the amount of
collateral required for the naked calls less the credit taken in for the spread. Since
naked calls will be marked to market as the stock moves up, it is always best to allow
enough collateral to get to a defensive action point. In the example above, suppose
that one felt he would definitely be taking defensive action if the stock rallied to 53
224 Part II: Call Option Strategies
before April expiration. He should then figure his collateral requirement as if the
stock were at 53, regardless of what the collateral requirement is at the current time.
This is a prudent tactic whenever naked options are involved, since the strategist will
never be forced into an unwanted close-out before his defensive action point is
reached. The collateral required for this example would then be as follows, assuming
the call is trading at 3½:
20% of 53
Call premium
Less initial credit
Total collateral to set aside
$1,060
+ 350
-___fill
$1,360
The strategist is not really "investing" anything in this strategy, because his require
ment is in the form of collateral, not cash. That is, his current portfolio assets need
not be disturbed to set up this spread, although losses would, of course, create deb
its in the account. Many naked option strategies are similar in this respect, and the
strategist may earn additional money from the collateral value of his portfolio with
out disturbing the portfolio itself. However, he should take care to operate such
strategies in a conservative manner, since any income earned is "free," but losses may
force him to disturb his portfolio. In light of this fact, it is always difficult to compute
returns on investment in a strategy that requires only collateral to operate. One can,
of course, compute the return on the maximum collateral required during the life of
the position. The large investor participating in such a strategy should be satisfied
with any sort of positive return.
Returning to the example above, the strategist would make his $50 credit, less
commissions, if the underlying stock remained below 50 until July expiration. It is not
possible to determine the results to the upside so definitively. If the April 50 calls
expire worthless and then the stock rallies, the potential profits are limited only by
time. The case in which the stock rallies before April expiration is of the most con
cern. If the stock rallies immediately, the spread will undoubtedly show a loss. If the
stock rallies to 50 more slowly, but still before April expiration, it is possible that the
spread will not have changed much. Using the same example, suppose that XYZ ral
lies to 50 with only a few weeks of life remaining in the April 50 calls. Then the April
50 calls might be selling at l ½ while the July 50 call might be selling at 3. The ratio
spread could be closed for even money at that point; the cost of buying back the 2
April 50's would equal the credit received from selling the one July 50. He would thus
make½ point, less commissions, on the entire spread transaction. Finally, at the expi
ration date of the April 50 calls, one can estimate where he would break even.
Suppose one estimated that the July 50 call would be selling for 5½ points if XYZ
were at 53 at April expiration. Since the April 50 calls would be selling for 3 at that
Chapter 12: Combining Calendar and Ratio Spreads 225
time (they would be at parity), there would be a debit of½ point to close the ratio
spread. The two April 50 calls would be bought for 6 points and the July 50 call sold
for 5½ - a ½ debit. The entire spread transaction would thus have broken even, less
commissions, at 53 at April expiration, since the spread was put on for a ½ credit and
was taken off for a ½ debit. The risk to the upside depends clearly, then, on how
quickly the stock rallies above 50 before April expiration.
CHOOSING THE SPREAD
Some of the same criteria used in setting up a bullish calendar spread apply here as
well. Select a stock that is volatile enough to move above the striking price in the
allotted time - after the near-term expires, but before the long call expires. Do not
use calls that are so far out-of-the-money that it would be virtually impossible for the
stock to reach the striking price. Always set up the spread for a credit, commissions
included. This will assure that a profit will be made even if the stock goes nowhere.
However, if the credit has to be generated by using an extremely large ratio - greater
than 3 short calls to every long one - one should probably reject that choice, since
the potential losses in an immediate rally would be large.
The upside break-even point prior to April expiration should be determined
using a pricing model. Such a model, or the output from one, can generally be
obtained from a data service or from some brokerage firms. It is useful to the strate
gist to know exactly how much room he has to the upside if the stock begins to rally.
This will allow him to take defensive action in the form of closing


e.
The upside break-even point prior to April expiration should be determined
using a pricing model. Such a model, or the output from one, can generally be
obtained from a data service or from some brokerage firms. It is useful to the strate
gist to know exactly how much room he has to the upside if the stock begins to rally.
This will allow him to take defensive action in the form of closing out the spread
before his break-even point is reached. Since a pricing model can estimate a call
price for any length of time, the strategist can compute his break-even points at
April expiration, 1 month before April expiration, 6 weeks before, and so on. When
the long option in a spread expires at a different time from the short option, the
break-even point is dynamic. That is, it changes with time. Table 12-1 shows how
this information might be accumulated for the example spread used above. Since
this example spread was established for a ½-point credit with the stock at 45, the
break-even points would be at stock prices where the spread could be removed for
a ½-point debit. Suppose the spread was initiated with 95 days remaining until April
expiration. In each line of the table, the cost for buying 2 April 50's is ½ point more
than the price of the July 50. That is, there would be a ½-point debit involved in
closing the spread at those prices. Notice that the break-even price increases as time
passes. Initially, the spread would show a loss if the stock moved up at all. This is to
be expected, since an immediate move would not allow for any erosion in the time
value premium of the near-term calls. As more and more time passes, time weighs
226 Part II: Call Option Strategies
more heavily on the near-term April calls than on the longer-term July call. Once the
strategist has this information, he might then look at a chart of the underlying stock.
If there is resistance for XYZ below 53, his eventual break-even point at April expi
ration, he could then feel more confident about this spread.
FOLLOW-UP ACTION
The main purpose of defensive action in this strategy is to limit losses if the stock
should rally before April e:xJ)iration. The strategist should be quick to close out the
spread before any serious losses accrue. The long call quite adequately compen
sates for the losses on the short calls up to a certain point, a fact demonstrated in
Table 12-1. However, the stock cannot be allowed to run. A rule of thumb that is
often useful is to close the spread if the stock breaks out above technical resistance
or if it breaks above the eventual break-even point at expiration. In the example
above, the strategist would close the spread if, at any time, XYZ rose above 53
(before April expiration, of course).
If a significant amount of time has passed, the strategist might act even more
quickly in closing the spread. As was shown earlier, if the stock rallies to 50 with only
a few weeks of time remaining, the spread may actually be at a slight profit at that
time. It is often the best course of action to take the small profit, if the stock rises
above the striking price.
TABLE 12-1.
Break-even points changing over time.
Estimated Estimated
Days Remaining until Break-Even Point April 50 July 50
April Expiration (Stock Price) Price Price
90 45 11/2
60 48 Jl/2 21/2
30 51 21/2 4 1/2
0 53 3 51/2
THE PROBABILITIES ARE GOOD
This is a strategy with a rather large probability of profit, provided that the defensive
action described above is adhered to. The spread will make money if the stock never
rallies above the striking price, since the spread is established for a credit. This in
Chapter 12: Combining Calendar and Ratio Spreads 227
itself is a rather high-probability event, because the stock is initially below the strik
ing price. In addition, the spread can make large potential profits if the stock rallies
after the near-term calls expire. Although this is a much less probable event, the prof
its that can accrue add to the expected return of the spread. The only time the spread
loses is when the stock rallies quickly, and the strategist should close out the spread
in that case to limit losses.
Although Table 12-2 is not mathematically definitive, it can be seen that this
strategy has a positive expected return. Small profits occur more frequently than
small losses do, and sometimes large profits can occur. These expected outcomes,
when coupled with the fact that the strategist may utilize collateral such as stocks,
bonds, or government securities to set up these spreads, demonstrate that this is a
viable strategy for the advanced investor.
TABLE 12-2.
Profitability of ratio calendar spreading.
Event
Stock never rallies above
strike
Stock rallies above strike in a
short time
Stock rallies above strike after
near-term call expires
Outcome
Small profit.
Small loss if defensive
action employed
Large potential profit
DELTA-NEUTRAL CALENDAR SPREADS
Probability
Large probability
Small probability
Small probability
The preceding discussion dealt with a specific kind of ratio calendar spread, the out
of-the-money call spread. A more accurate ratio can be constructed using the deltas
of the calls involved, similar to the ratio spreads in Chapter 11. The spread can be
created with either out-of-the-money calls or in-the-money calls. The former has
naked calls, while the latter has extra long calls. Both types of ratio calendars are
described.
In either case, the number of calls to sell for each one purchased is determined
by dividing the delta of the long call by the delta of the short call. This is the same
for any ratio spread, not just calendars.
Example: Suppose XYZ is trading at 45 and one is considering using the July 50 call
and the April 50 call to establish a ratio calendar spread. This is the same situation
228 Part II: Call Option Strategies
that was described earlier in this chapter. Furthermore, assume that the deltas of


the long call by the delta of the short call. This is the same
for any ratio spread, not just calendars.
Example: Suppose XYZ is trading at 45 and one is considering using the July 50 call
and the April 50 call to establish a ratio calendar spread. This is the same situation
228 Part II: Call Option Strategies
that was described earlier in this chapter. Furthermore, assume that the deltas of the
calls in question are .25 for the July and .15 for the April. Given that information, one
can compute the neutral ratio to be 1.667 to 1 (.25/.15). That is, one would sell 1.667
calls for each one he bought; restated, he would sell 5 for each 3 bought.
This out-of-the-money neutral calendar is typical. One normally sells more calls
than he buys to establish a neutral calendar when the calls are out-of-the-money. The
ramifications of this strategy have already been described in this chapter. Follow-up
strategy is slightly different, though, and is described later.
THE IN-THE-MONEY CALENDAR SPREAD
When the calls are in-the-money, the neutral spread has a distinctly different look.
An example will help in describing the situation.
Example: XYZ is trading at 49, and one wants to establish a neutral calendar spread
using the July 45 and April 45 calls. The deltas of these in-the-money calls are .8 for
the April and .7 for the July. Note that for in-the-rrwney calls, a shorter-term call has
a higher delta than a longer-term call.
The neutral ratio for this in-the-money spread would be .875 to 1 (.7/.8). This
means that .875 calls would be sold for each one bought; restated, 7 calls would be
sold and 8 bought. Thus, the spreader is buying more calls than he is selling when
establishing an in-the-money neutral calendar. In some sense, one is establishing
some "regular'' calendar spreads (seven of them, in this example) and simultaneous
ly buying a few extra long calls to go along with them ( one extra long call, in this
example).
This type of position can be quite attractive. First of all, there is no risk to the
upside as there is with the out-of-the-money calendar; the in-the-money calendar
would make money, because there are extra long calls in the position. Thus, if there
were to be a large gap to the upside in XYZ perhaps caused by a takeover attempt
- the in-the-money calendar would make money. If, on the other hand, XYZ stays in
the same area, then the regular calendar spread portion of the strategy will make
money. Even though the extra call would probably lose some time value premium in
that event, the other seven spreads would make a large enough profit to easily com
pensate for the loss on the one long call. The least desirable result would be for XYZ
to drop precipitously. However, in that case, the loss is limited to the amount of the
initial debit of the spread. Even in the case of XYZ dropping, though, follow-up
action can be taken. There are no naked calls to margin with this strategy, making it
attractive to many smaller investors. In the above example, one would need to pay for
the entire debit of the position, but there would be no further requirements.
Chapter 12: Combining Calendar and Ratio Spreads
FOLLOW-UP ACTION
229
If one decides to preserve a neutral strategy with follow-up action in either type of
ratio call calendar, he would merely need to look at the deltas of the calls and keep
the ratio neutral. Doing so might mean that one would switch from one type of cal
endar spread to the other, from the out-of-the-money with naked calls to the in-the
money with extra long calls, or vice versa. For example, if XYZ started at 45, as in the
first example, one would have sold more calls than he bought. If XYZ then rallied
above 50, he would have to move his position into the in-the-money ratio and get
long more calls than he is short.
While such follow-up action is strategically correct maintaining the neutral
ratio - it might not make sense practically, especially if the size of the original spread
were small. If one had originally sold 5 and bought 3, he would be better to adhere
to the follow-up strategy outlined earlier in this chapter. The spread is not large
enough to dictate adjusting via the delta-neutral ratios. If, however, a large trader had
originally sold 500 calls and bought 300, then he has enough profitability in the
spread to make several adjustments along the way.
In a similar manner, the spreader who had established a small in-the-money cal
endar might decide not to bother rationing the spread if the stock dropped below the
strike. He knows his risk is limited to his initial debit, and that would be small for a
small spread. He might not want to introduce naked options into the position if XYZ
declines. However, if the same spread were established by a large trader, it should be
adjusted because of the greater tolerance of the spread to being adjusted, merely
because of its size.
Reverse Spreads
In general, when a strategy has the term "reverse" in its name, the strategy is the
opposite of a more commonly used strategy. The reader should be familiar with this
nomenclature from the earlier discussions comparing ratio writing (buying stock and
selling calls) with reverse hedging (shorting stock and buying calls). If the reverse
strategy is sufficiently well-known, it usually acquires a name of its own. For exam
ple, the bear spread is really the reverse of the bull spread, but the bear spread is a
popular enough strategy in its own right to have acquired a shorter, unique name.
REVERSE CALENDAR SPREAD
The reverse calendar spread is an infrequently used strategy, at least for public cus
tomers trading stock or index options, because of the margin requirements. However,
even then, it does have a place in the arsenal of the option strategist. Meanwhile, pro
fessionals and futures option traders use the strategy with more frequency because
the margin treatment is more favorable for them.
As its name im


erse calendar spread is an infrequently used strategy, at least for public cus
tomers trading stock or index options, because of the margin requirements. However,
even then, it does have a place in the arsenal of the option strategist. Meanwhile, pro
fessionals and futures option traders use the strategy with more frequency because
the margin treatment is more favorable for them.
As its name implies, the reverse calendar spread is a position that is just the
opposite of a "normal" calendar spread. In the reverse calendar spread, one sells a
long-term call option and simultaneously buys a shorter-term call option. The spread
can be constructed with puts as well, as will be shown in a later chapter. Both calls
have the same striking price.
This strategy will make money if one of two things happens: Either (1) the stock
price moves away from the striking price by a great deal, or (2) the inplied volatility
of the options involved in the spread shrinks. For readers familiar with the "normal"
calendar spread strategy, the first way to profit should be obvious, because a "normal"
230
Chapter 13: Reverse Spreads 231
calendar spread makes the most money if the stock is right at the strike price at expi
ration, and it loses money if the stock rises or falls too far.
As with any spread involving options expiring in differing months, it is common
practice to look at the profitability of the position at or before the near-term expira
tion. An example will show how this strategy can profit.
Example: Suppose the current month is April and that XYZ is trading at 80.
Furthermore, suppose that XYZ's options are quite expensive, and one believes the
underlying stock will be volatile. A reverse calendar spread would be a way to profit
from these assumptions. The following prices exist:
XYZ December 80 call: 12
XYZ July 80 call: 7
A reverse calendar spread is established by selling the December 80 call for 12
points, and buying the July 80 call for 7, a net credit of 5 points for the spread.
If, later, XYZ falls dramatically, both call options will be nearly worthless and the
spread could be bought back for a price well below 5. For example, if XYZ were to
fall to 50 in a month or so, the July 80 call would be nearly worthless and the
December 80 call could be bought back for about a point. Thus, the spread would
have shrunk from its initial price of 5 to a price of about 1, a profit of 4 points.
The other way to make money would be for implied volatility to decrease.
Suppose implied volatility dropped after a month had passed. Then the spread might
be worth something like 4 points - an unrealized profit of about 1 point, since it was
sold for a price of 5 initially.
The profit graph in Figure 13-1 shows the profitability of the reverse calendar.
There are two lines on the graph, both of which depict the results at the expiration
of the near-term option (the July 80 call in the above example). The lower line shows
where profits and losses would occur if implied volatility remained unchanged. You
can see that the position could profit if XYZ were to rise above 98 or fall below 70.
In addition, the higher curve on the graph shows where profits would lie if implied
volatility fell prior to expiration of the near-term options. In that case, additional prof
its would accrue, as depicted on the graph.
So there are two ways to make money with this strategy, and it is therefore best
to establish it when implied volatility is high and the underlying has a tendency to be
volatile.
The problem with this spread, for stock and index option traders, is that the call
that is sold is considered to be naked. This is preposterous, of course, since the short
term call is a perfectly valid hedge until it expires. Yet the margin requirements
remain onerous. When they were overhauled recently, this glaring inefficiency was
232 Part II: Call Option Strategies
Figure 13-1 •
Calendar spread sale at near-term expiration.
$400
$300
Implied Volatility
Lower
$200 \
f/)
$100 f/)
0
~
$0 50 60 110 120
a. -$100
-$200
-$300
Implied Volatility
-$400 Remains High
-$500
Underlying Price
allowed to stand because none of the member firms cared about changing it. Still, if
one has excess collateral - perhaps from a large stock portfolio - and is interested in
generating excess income in a hedged manner, then the strategy might be applicable
for him as well. Futures option traders receive more favorable margin requirements,
and it thus might be a more economical strategy for them.
REVERSE RATIO SPREAD (BACKSPREAD)
A more popular reverse strategy is the reverse ratio call spread, which is comrrwnly
known as a backspread. In this type of spread, one would sell a call at one striking
price and then would buy several calls at a higher striking price. This is exactly the
opposite of the ratio spread described in Chapter 11. Some traders refer to any
spread with unlimited profit potential on at least one side as a backspread. Thus, in
most backspreading strategies, the spreader wants the stock to rrwve dramatically. He
does not generally care whether it moves up or down. Recall that in the reverse
hedge strategy (similar to a straddle buy) described in Chapter 4, the strategist had
the potential for large profits if the stock moved either up or down by a great deal.
In the backspread strategy discussed here, large potential profits exist if the stock
moves up dramatically, but there is limited profit potential to the downside.
Example: XYZ is selling for 43 and the July 40 call is at 4, with the July 45 call at l.
A reverse ratio spread would be established as follows: ·
Chapter 13: Reverse Spreads
Buy 2 July 45 calls at 1 each
Sell 1 July 40 call at 4
Net
2 debit
4 credit
2 credit
233
These spreads are generally established for credits. In fact, if the spread cannot
be initiated at a credit, it is usually not attractive. If the underlying stock drops in
pric


is at 4, with the July 45 call at l.
A reverse ratio spread would be established as follows: ·
Chapter 13: Reverse Spreads
Buy 2 July 45 calls at 1 each
Sell 1 July 40 call at 4
Net
2 debit
4 credit
2 credit
233
These spreads are generally established for credits. In fact, if the spread cannot
be initiated at a credit, it is usually not attractive. If the underlying stock drops in
price and is below 40 at July expiration, all the calls will expire worthless and the
strategist will make a profit equal to his initial credit. The maximum downside poten
tial of the reverse ratio spread is equal to the initial credit received. On the other
hand, if the stock rallies substantially, the potential upside profits are unlimited, since
the spreader owns more calls than he is short. Simplistically, the investor is bullish
and is buying out-of the-money calls but is simultaneously hedging himself by selling
another call. He can profit if the stock rises in price, as he thought it would, but he
also profits if the stock collapses and all the calls expire worthless.
This strategy has limited risk. With most spreads, the maximum loss is attained
at expiration at the striking price of the purchased call. This is a true statement for
backspreads.
Example: IfXYZ is at exactly 45 at July expiration, the July 45 calls will expire worth
less for a loss of $200 and the July 40 call will have to be bought back for 5 points, a
$100 loss on that call. The total loss would thus be $300, and this is the most that can
be lost in this example. If the underlying stock should rally dramatically, this strategy
has unlimited profit potential, since there are two long calls for each short one. In
fact, one can always compute the upside break-even point at expiration. That break
even point happens to be 48 in this example. At 48 at July expiration, each July 45
call would be worth 3 points, for a net gain of $400 on the two of them. The July 40
call would be worth 8 with the stock at 48 at expiration, representing a $400 loss on
that call. Thus, the gain and the loss are offsetting and the spread breaks even, except
for commissions, at 48 at expiration. If the stock is higher than 48 at July expiration,
profits will result.
Table 13-1 and Figure 13-2 depict the potential profits and losses from this
example of a reverse ratio spread. Note that the profit graph is exactly like the prof
it graph of a ratio spread that has been rotated around the stock price axis. Refer to
Figure 11-1 for a graph of the ratio spread. There is actually a range outside of which
profits can be made - below 42 or above 48 in this example. The maximum loss
occurs at the striking price of the purchased calls, or 45, at expiration.
There are no naked calls in this strategy, so the investment is relatively small.
The strategy is actually a long call added to a bear spread. In this example, the bear
234 Part II: Call Option Strategies
TABLE 13·1.
Profits and losses for reverse ratio spread.
XYZ Price at Profit on Profit on Total
July Expiration 1 July 40 2 July 45's Profit
35 +$ 400 -$ 200 +$ 200
40 + 400 200 + 200
42 + 200 200 0
45 100 200 300
48 400 + 400 0
55 - 1,100 + 1,800 + 700
70 - 2,600 + 4,800 + 2,200
spread portion is long the July 45 and short the July 40. This requires a $500 collat
eral requirement, because there are 5 points difference in the striking prices. The
credit of $200 received for the entire spread can be applied against the initial
requirement, so that the total requirement would be $300 plus commissions. There
is no increase or decrease in this requirement, since there are no naked calls.
Notice that the concept of a delta-neutral spread can be utilized in this strate
gy, in much the same way that it was used for the ratio call spread. The number of
calls to buy and sell can be computed mathematically by using the deltas of the
options involved.
Example: The neutral ratio is determined by dividing the delta of the July 45 into the
delta of the July 40.
Prices
XYZ common: = 43
XYZ July 40 call: 4
XYZ July 45 call:
Delta
.80
.35
In this case, that would be a ratio of 2.29:1 (.80/.35). That is, if one sold 5 July 40's,
he would buy 11 July 45's (or if he sold 10, he would then buy 23). By beginning with
a neutral ratio, the spreader should be able to make money on a quick move by the
stock in either direction.
The neutral ratio can also help the spreader to avoid being too bearish or too
bullish to begin with. For example, a spreader would not be bullish enough if he
Chapter 13: Reverse Spreads
FIGURE 13-2.
Reverse ratio spread (backspread).
C:
~ +$200
;%
:!::
e
a. -$300
Stock Price at Expiration
235
merely used a 2:1 ratio for convenience, instead of using the 2.3:l ratio. If anything,
one might normally establish the spread with an extra bullish emphasis, since the
largest profits are to the upside. There is little reason for the spreader to have too lit
tle bullishness in this strategy. Thus, if the deltas are correct, the neutral ratio can aid
the spreader in the determination of a more accurate initial ratio.
The strategist must be alert to the possibility of early exercise in this type of
spread, since he has sold a call that is in-the-money. Aside from watching for this pos
sibility, there is little in the way of defensive follow-up action that needs to be imple
mented, since the risk is limited by the nature of the position. He might take profits
by closing the spread if the stock rallies before expiration.
This strategy presents a reasonable method of attempting to capitalize on a
large stock movement with little tie-up of collateral. Generally, the strategist would
seek out volatile stocks for implementation of this strategy, because he would want as
much potential movement as possible by the time the calls expire. In Chapter 14, it
will be shown that this strategy can become more attractive by buying calls with a
longer mat


ble method of attempting to capitalize on a
large stock movement with little tie-up of collateral. Generally, the strategist would
seek out volatile stocks for implementation of this strategy, because he would want as
much potential movement as possible by the time the calls expire. In Chapter 14, it
will be shown that this strategy can become more attractive by buying calls with a
longer maturity than the calls sold.
CH.APTER 14
Diagonalizing a Spread
When one uses both different striking prices and different expiration dates in a
spread, it is a diagonal spread. Generally, the long side of the spread would expire
later than the short side of the spread. Note that this is within the definition of a
spread for margin purposes: The long side must have a maturity equal to or longer
than the maturity of the short side. With the exception of calendar spreads, all the
previous chapters on spreads have described ones in which the expiration dates of the
short call and the long call were the same. However, any of these spreads can be diag
onalized; one can replace the long call in any spread with one expiring at a later date.
In general, diagonalizing a spread in this manner makes it slightly rrwre bear
ish at near-term expiration. This can be seen by observing what would happen if the
stock fell or rose substantially. If the stock falls, the long side of the spread will retain
some value because of its longer maturity. Thus, a diagonal spread will generally do
better to the downside than will a regular spread. If the stock rises substantially, all
calls will come to parity. Thus, there is no advantage in the long-term call; it will be
selling for approximately the same price as the purchased call in a normal spread.
However, since the strategist had to pay more originally for the longer-term call, his
upside profits would not be as great.
A diagonalized position has an advantage in that one can reestablish the posi
tion if the written calls expire worthless in the spread. Thus, the increased cost of
buying a longer-term call initially may prove to be a savings if one can write against
it twice. These tactics are described for various spread strategies.
THE DIAGONAL BULL SPREAD
A vertical call bull spread consists of buying a call at a lower striking price and sell
ing a call at a higher striking price, both with the same expiration date. The diagonal
236
Chapter 14: Diagonalizing a Spread 231
bull spread would be similar except that one would buy a longer-tenn call at the lower
strike and would sell a near-tenn call at the higher strike. The number of calls long
and short would still be the same. By diagonalizing the spread, the position is hedged
somewhat on the downside in case the stock does not advance by near-term expira
tion. Moreover, once the near-term option expires, the spread can often be reestab
lished by selling the call with the next maturity.
Example: The following prices exist:
Strike April Ju~ October Stock Price
XYZ 30 3 4 5 32
XYZ 35 11/2 2 32
A vertical bull spread could be established in any of the expiration series by buying
the call with 30 strike and selling the call with 35 strike. A diagonal bull spread would
consist of buying the July 30 or October 30 and selling the April 35. To compare a
vertical bull spread with a diagonal spread, the following two spreads will be used:
Vertical bull spread: buy the April 30 call, sell the April 35 - 2 debit
Diagonal bull spread: buy the July 30 call, sell the April 35 3 debit
The vertical bull spread has a 3-point potential profit if XYZ is above 35 at April expi
ration. The maximum risk in the normal bull spread is 2 points (the original debit) if
XYZ is anywhere below 30 at April expiration. By diagonalizing the spread, the strate
gist lowers his potential profit slightly at April expiration, but also lowers the proba
bility of losing 2 points in the position. Table 14-1 compares the two types of spreads
at April expiration. The price of the July 30 call is estimated in order to derive the
estimated profits or losses from the diagonal bull spread at that time. If the underly
ing stock drops too far - to 20, for example - both spreads will experience nearly a
total loss at April expiration. However, the diagonal spread will not lose its entire
value if XYZ is much above 24 at expiration, according to Table 14-1. The diagonal
spread actually has a smaller dollar loss than the normal spread between 27 and 32
at expiration, despite the fact that the diagonal spread was more expensive to estab
lish. On a percentage basis, the diagonal spread has an even larger advantage in this
range. If the stock rallies aboye 35 by expiration, the normal spread will provide a
larger profit. There is an interesting characteristic of the diagonal spread that is
shown in Table 14-1. If the stock advances substantially and all the calls come to par
ity, the profit on the diagonal spread is limited to 2 points. However, if the stock is
near 35 at April expiration, the long call will have some time premium in it and the
238 Part II: Call Option Strategies
TABLE 14-1.
Comparison of spreads at expiration.
Vertical Bull
XYZ Price at April 30 April 35 July 30 Spread Diagonal
April Expiration Price Price Price Profit Spread Profit
20 0 0 0 -$200 -$300
24 0 0 1/2 - 200 - 250
27 0 0 1 - 200 - 200
30 0 0 2 - 200 - 100
32 2 0 3 0 0
35 5 0 51/2 + 300 + 250
40 10 5 10 + 300 + 200
45 15 10 15 + 300 + 200
spread will actually widen to more than 5 points. Thus, the maximum area of profit
at April expiration for the diagonal spread is to have the stock near the striking price
of the written call. The figures demonstrate that the diagonal spread gives up a small
portion of potential upside profits to provide a hedge to the downside.
Once the April 35 call expires, the diagonal spread can be closed. However, if
the stock is below 35 at that time, it may be more prudent to then sell the July 35 ca