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 abroader array of spreads to choose from and will also be able to assume amore
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 aratio 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

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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'soutlook for the underlying stock The altering of the
ratio in aratio 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." Asimilar tactic, using the option'sdelta, 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 xprofit Difference in striking prices or
= Number of long calls X Difference in
striking prices - Net debit
Upside break-even = Points of maximum profit ff ht "ki .
point Number of naked calls + ig er snng 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 amore 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 acall 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 aposition 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'sand simultaneously sell 8 of the April 45's, he would have adelta-neutral
spread. That is, if XYZ moved up by one point, the 5 April 40 calls would appreciate
by .80 point each, for anet gain of 4 points. Similarly, the 8 April 45 calls that he is
short would each appreciate by .50 point for anet 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 adetermining factor.

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Chapter 11: Ratio Call Spreads 217
It is afairly 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'sand 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 asmall debit of one point (5 April 40'scost 25 points and 8
April 45'sbring 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 aday-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 asimple parameter, such as not paying adebit of more than 1
point per long option. Thus, in aspread involving 10 long calls, the total debit must
be 10 points or less. These screens are easily applied, especially with the aid of acom
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 adebit, the spread is
rejected from consideration. If not, it is apotential 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 aratio 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'sand then to the 45's, in the same manner as he would with aratio
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.

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218 Part II: Call Option Strategies
REDUCING THE RATIO
Upside fallow-up action does not normally consist of rolling up as it does in aratio
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 anormal 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'swere
sold, for anet credit of one point. Assume that the spreader is going to buy one more
April 40 as ameans of upside defensive action if he has to. When and if he buys this
second long call, his total position will be anormal bull spread - long 2 April 40'sand
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 aone-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 abreak-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 adynamic 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 abreak-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 awhipsaw 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 atwo
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'swere selling at 11 and then buy
all 5 needed to make the spread anormal bull spread. He might decide to buy 2 or
3 at alower price, thereby reducing his ratio somewhat. Then, if the stock rallied
even further, he could buy the needed long calls. By buying afew at acheaper 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

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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 (abull spread). Aformula can be applied to deter
mine the price one would have to pay for the additional long calls, to convert the ratio
spread into abull spread. If the calls are bought, such abull 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'sfor 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'swere
. selling for 8, the spreader might ask: "To what would Iraise the purchase price of the
remaining long calls if Ibuy 2 April 40'sfor 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 aneutral status by buying some additional long calls
on an upside movement by the stock, or by selling some additional short calls on adownward 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. Amore detailed description of the use of
deltas as ameans 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.

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220 Part II: Call Option Strategies
Example: Early in this chapter, when selection criteria were described, aneutral
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'scould 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 awhole. 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 adelta 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 amatter 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 xl 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 xl 00)
140 shrt

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Chapter 11: Ratio Call Spreads 221
The ESP method is merely aconfirmation of the other method. Either one
works well. The spreader should become familiar with the ESP method because, in
aposition with many different options, it reduces the exposure of the entire position
to asingle number.
TAKING PROFITS
In addition to defensive action, the spreader may find that he can close the spread
early to take aprofit 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 aprofit 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 (aprice 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 alarge probability of making alimited 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 asuperior strategy to the ratio write. One can adjust the ratio
used to reflect his opinion of the underlying stock or to make aneutral profit range
if desired. The ratio adjustment can be accomplished by using the deltas of the
options. In abroad sense, this is one of the more attractive forms of spreading, since
the strategist is buying mostly intrinsic value and is selling arelatively large amount
of time value.

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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 aposition with amore attractive potential. The butterfly spread, which is
acombination of abull spread and abear spread, is an example of such acombina
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 acombination 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 alonger-term call, with both being out-of-the-money.
This is abullish 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 asmall
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 anumber of near-
222

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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 aratio calendar spread for acredit, 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 adebit 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
acredit, there is acollateral 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 alarge 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 adefensive action point. In the example above, suppose
that one felt he would definitely be taking defensive action if the stock rallied to 53

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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 aprudent 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 aconservative 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 astrategy 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 astrategy 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 aloss. 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 afew 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'swould 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

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Chapter 12: Combining Calendar and Ratio Spreads 225
time (they would be at parity), there would be adebit 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 abullish calendar spread apply here as
well. Select astock 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 acredit, commissions
included. This will assure that aprofit 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 apricing model. Such amodel, or the output from one, can generally be
obtained from adata 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 apricing model can estimate acall
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 aspread expires at adifferent 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'sis 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 aloss 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

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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 achart 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 acertain point, afact demonstrated in
Table 12-1. However, the stock cannot be allowed to run. Arule 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 asignificant 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
afew weeks of time remaining, the spread may actually be at aslight 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 astrategy with arather 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 acredit. This in

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Chapter 12: Combining Calendar and Ratio Spreads 227
itself is arather 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 amuch 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 apositive 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 aviable strategy for the advanced investor.
TABLE 12-2.
Profitability of ratio calendar spreading.
Event
Stock never rallies above
strike
Stock rallies above strike in ashort 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 aspecific kind of ratio calendar spread, the out
of-the-money call spread. Amore 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 aratio calendar spread. This is the same situation

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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 aneutral 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 adistinctly different look.
An example will help in describing the situation.
Example: XYZ is trading at 49, and one wants to establish aneutral 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, ashorter-term call has
ahigher delta than alonger-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 afew 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 alarge gap to the upside in XYZ perhaps caused by atakeover 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 alarge 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.

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Chapter 12: Combining Calendar and Ratio Spreads
FOLLOW-UP ACTION
229
If one decides to preserve aneutral 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, alarge 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 asimilar manner, the spreader who had established asmall 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 asmall spread. He might not want to introduce naked options into the position if XYZ
declines. However, if the same spread were established by alarge trader, it should be
adjusted because of the greater tolerance of the spread to being adjusted, merely
because of its size.

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Reverse Spreads
In general, when astrategy has the term "reverse" in its name, the strategy is the
opposite of amore 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 aname of its own. For exam
ple, the bear spread is really the reverse of the bull spread, but the bear spread is apopular enough strategy in its own right to have acquired ashorter, 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 aplace 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 aposition that is just the
opposite of a "normal" calendar spread. In the reverse calendar spread, one sells along-term call option and simultaneously buys ashorter-term call option. The spread
can be constructed with puts as well, as will be shown in alater 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 agreat 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

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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'soptions are quite expensive, and one believes the
underlying stock will be volatile. Areverse calendar spread would be away to profit
from these assumptions. The following prices exist:
XYZ December 80 call: 12
XYZ July 80 call: 7
Areverse calendar spread is established by selling the December 80 call for 12
points, and buying the July 80 call for 7, anet 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 aprice well below 5. For example, if XYZ were to
fall to 50 in amonth or so, the July 80 call would be nearly worthless and the
December 80 call could be bought back for about apoint. Thus, the spread would
have shrunk from its initial price of 5 to aprice of about 1, aprofit of 4 points.
The other way to make money would be for implied volatility to decrease.
Suppose implied volatility dropped after amonth had passed. Then the spread might
be worth something like 4 points - an unrealized profit of about 1 point, since it was
sold for aprice 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 atendency 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 aperfectly valid hedge until it expires. Yet the margin requirements
remain onerous. When they were overhauled recently, this glaring inefficiency was

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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 alarge stock portfolio - and is interested in
generating excess income in ahedged manner, then the strategy might be applicable
for him as well. Futures option traders receive more favorable margin requirements,
and it thus might be amore economical strategy for them.
REVERSE RATIO SPREAD (BACKSPREAD)
Amore popular reverse strategy is the reverse ratio call spread, which is comrrwnly
known as abackspread. In this type of spread, one would sell acall at one striking
price and then would buy several calls at ahigher 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 abackspread. 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 astraddle buy) described in Chapter 4, the strategist had
the potential for large profits if the stock moved either up or down by agreat 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.
Areverse ratio spread would be established as follows: ·

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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 acredit, 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 aprofit 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 atrue statement for
backspreads.
Example: IfXYZ is at exactly 45 at July expiration, the July 45 calls will expire worth
less for aloss 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 anet 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 areverse ratio spread. Note that the profit graph is exactly like the prof
it graph of aratio spread that has been rotated around the stock price axis. Refer to
Figure 11-1 for agraph of the ratio spread. There is actually arange 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 along call added to abear spread. In this example, the bear

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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 adelta-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 aratio 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
aneutral ratio, the spreader should be able to make money on aquick 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, aspreader would not be bullish enough if he

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Chapter 13: Reverse Spreads
FIGURE 13-2.
Reverse ratio spread (backspread).
C:
~ +$200
;%
:!::
ea. -$300
Stock Price at Expiration
235
merely used a 2:1 ratio for convenience, instead of using the 2.3:lratio. 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 amore accurate initial ratio.
The strategist must be alert to the possibility of early exercise in this type of
spread, since he has sold acall 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 areasonable method of attempting to capitalize on alarge 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 alonger maturity than the calls sold.

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CH.APTER 14
Diagonalizing a Spread
When one uses both different striking prices and different expiration dates in aspread, it is adiagonal 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 aspread for margin purposes: The long side must have amaturity 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 alater date.
In general, diagonalizing aspread 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, adiagonal spread will generally do
better to the downside than will aregular 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 anormal spread.
However, since the strategist had to pay more originally for the longer-term call, his
upside profits would not be as great.
Adiagonalized 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 alonger-term call initially may prove to be asavings if one can write against
it twice. These tactics are described for various spread strategies.
THE DIAGONAL BULL SPREAD
Avertical call bull spread consists of buying acall at alower striking price and sell
ing acall at ahigher striking price, both with the same expiration date. The diagonal
236

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Chapter 14: Diagonalizing a Spread 231
bull spread would be similar except that one would buy alonger-tenn call at the lower
strike and would sell anear-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
Avertical 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. Adiagonal bull spread would
consist of buying the July 30 or October 30 and selling the April 35. To compare avertical bull spread with adiagonal 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 atotal 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 asmaller 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 apercentage 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 alarger 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

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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 asmall
portion of potential upside profits to provide ahedge 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 call
against the July 30 call that is held long. This would establish anormal bull spread for
the 3 months remaining until July expiration. Note that ifXYZ were still at 32 at April
expiration, the July 35 call might be sold for 1 point if the stock'svolatility was about
the same. This should be true, since the April 35 call was worth 1 point with the stock
at 32 three months before expiration. Consequently, the strategist who had pursued
this course of action would end up with anormal July bull spread for anet debit of 2
points: He originally paid 4 for the July 30 call, but then sold the April 35 for 1 point
and subsequently sold the July 35 for 1 point. By looking at the table of prices for the
first example in this chapter, the reader can see that it would have cost 2½ points to
set up the normal July bull spread originally. Thus, by diagonalizing and having the
near-term call expire worthless, the strategist is able to acquire the normal July bull
spread at acheaper cost than he could have originally. This is aspecific example of
how the diagonalizing effect can prove beneficial if the writer is able to write against
the same long call two times, or three times if he originally purchased the longest
term call. In this example, if XYZ were anywhere between 30 and 35 at April expira
tion, the spread would be converted to anormal July bull spread. If the stock were
above 35, the spread should be closed to take the profit. Below 30, the July 30 call
would probably be closed or left outright long.

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Chapter 14: Diagonalizing a Spread 239
In summary, the diagonal bull spread may often be an improvement over the
normal bull spread. The diagonal spread is an improvement when the stock remains
relatively unchanged or falls, up until the near-term written call expires. At that time,
the spread can be converted to anormal bull spread if the stock is at afavorable price.
Of course, if at any time the underlying stock rises above the higher striking price at
an expiration date, the diagonal spread will be profitable.
OWNING A CALL FOR "FREE"
Diagonalization can be used in other spread strategies to accomplish much the same
purposes already described; but in addition, it may also be possible for the spreader
to wind up owning along call at asubstantially reduced cost, possibly even for free.
The easiest w~yto see this would be to consider adiagonal bear spread.
Example: XYZ is at 32 and the near-term April 30 call is selling for 3 points while the
longer-term July 35 call is selling for 1 ½ points. Adiagonal bear spread could be
established by selling the April 30 and buying the July 35. This is still abear spread,
because acall with alower striking price is being sold while acall at ahigher strike
is being purchased. However, since the purchased call has alonger maturity date
than the written call, the spread is diagonalized.
This diagonal bear spread will make money ifXYZ falls in price before the near
term April call expires. For example, ifXYZ is at 29 at expiration, the written call will
expire worthless and the July 35 will still have some value, perhaps ½. Thus, the prof
it would be 3 points on the April 30, less a 1-point loss on the July 35, for an overall
profit of 2 points. The risk in the position lies to the upside, just as in aregular bear
spread. If XYZ should advance by agreat deal, both options would be at parity and
the spread would have widened to 5 points. Since the initial credit was 1 ½ points, the
loss would be 5 minus 1 ½, or 3½ points in that case. As in all diagonal spreads, the
spread will do slightly better to the downside because the long call will hold some
value, but it will do slightly worse to the upside if the underlying stock advances sub
stantially.
The reason that astrategist might attempt adiagonal bear spread would not be
for the slight downside advantage that the diagonalizing effect produces. Rather it
would be because he has achance of owning the July 35 call - the longer-term call -
for asubstantially reduced cost. In the example, the cost of the July 35 call was 1 ½
points and the premium received from the sale of the April 30 call was 3 points. If
the spreader can make 1 ½ points from the sale of the April 30 call, he will have com
pletely covered the cost of his July option. He can then sit back and hope for arally

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240 Part II: Call Option Strategies
by the underlying stock. If such arally occurred, he could make unlimited profits on
the long side. If it did not, he loses nothing.
Example: Assume that the same spread was established as in the last example. Then,
if XYZ is at or below 31 ½ at April expiration, the April 30 call can be purchased for
1 ½ points or less. Since the call was originally sold for 3, this would represent aprof
it of at least 1 ½ points on the April 30 call. This profit on the near-term option cov
ers the entire cost of the July 35. Consequently, the strategist owns the July 35 for
free. If XYZ never rallies above 35, he would make nothing from the overall trade.
However, if XYZ were to rally above 35 after April expiration (but before July expi
ration, of course), he could make potentially large profits. Thus, when one establish
es adiagonal spread for acredit, there is always the potential that he could own acall
for free. That is, the profits from the sale of the near-term call could equal or exceed
the original cost of the long call. This is, of course, adesirable position to be in, for if
the underlying stock should rally substantially after profits are realized on the short
side, large profits could accrue.
DIAGONAL BACKSPREADS
In an analogous strategy, one might buy more than one longer-term call against the
short-term call that is sold. Using the foregoing prices, one might sell the April 30 for
3 points and buy 2 July 35'sat 1 ½ points each. This would be an even money spread.
. The credits equal the debits when the position is established. If the April 30 call
expires worthless, which would happen if the stock was below 30 in April, the spread
er would own 2 July 35 calls for free. Even if the April 30 does not expire totally
worthless, but if some profit can be made on the sale of it, the July 35'swill be owned
at areduced cost. In Chapter 13, when reverse spreads were discussed, the strategy
in which one sells acall with alower strike and then buys more calls at ahigher strike
was termed areverse ratio spread, or backspread. The strategy just described is
merely the diagonalizing of abackspread. This is astrategy that is favored by some
professionals, because the short call reduces the risk of owning the longer-term calls
if the underlying stock declines. Moreover, if the underlying stock advances, the pre
ponderance of long calls with alonger maturity will certainly outdistance the losses
on the written call. The worst situation that could result would be for the underlying
stock to rise very slightly by near-term expiration. If this happened, it might be pos
sible to lose money on both sides of the spread. This would have to be considered arather low-probability event, though, and would still represent alimited loss, so it
does not substantially offset the positive aspects of the strategy.

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0.,ter 14: Diagonalizing a Spread 241
Any type of spread may be diagonalized. There are some who prefer to diago
nalize even butterfly spreads, figuring that the extra time to maturity in the purchased
calls will be of benefit. Overall, the benefits of diagonalizing can be generalized by
recalling the way in which the decay of the time value premium of acall takes place.
Recall that it was determined that acall loses most of its time value premium in the
last stages of its life. When it is avery long-term option, the rate of decay is small.
Knowing this fact, it makes sense that one would want to sell options with ashort life
remaining, so that the maximum benefit of the decay could be obtained.
Correspondingly, the purchase of alonger-term call would mean that the buyer is not
subjecting himself to asubstantial loss in time value premium, at least over the first
three months of ownership. Adiagonal spread encompasses both of these features -
selling ashort-term call to try to obtain the maximum rate of time decay, while buy
ing alonger-term call to try to lessen the effect of time decay on the long side.
CALL OPTION SUMMARY
This concludes the description of strategies that utilize only call options. The call
option has been seen to be avehicle that the astute strategist can use to set up awide
variety of positions. He can be bullish or bearish, aggressive or conservative. In addi
tion, he can attempt to be neutral, trying to capitalize on the probability that astock
will not move very far in ashort time period.
The investor who is not familiar with options should generally begin with asim
ple strategy, such as covered call writing or outright call purchases. The simplest
types of spreads are the bull spread, the bear spread, and the calendar spread. The
more sophisticated investor might consider using ratios in his call strategies - ratio
writing against stock or ratio spreading using only calls.
Once the strategist feels that he understands the risk and reward relationships
between longer-term and short-term calls, between in-the-money and out-of-the
money calls, and between long calls and short calls, he could then consider utilizing
the most advanced types of strategies. This might include reverse ratio spreads, diag
onal spreads, and more advanced types of ratios, such as the ratio calendar spread.
Agreat deal of information, some of it rather technical in detail, has been pre
sented in preceding chapters. The best pattern for an investor to follow would be to
attempt only strategies that he fully comprehends. This does not mean that he mere
ly understands the profitability aspects (especially the risk) of the strategy. One must
also be able to readily understand the potential effects of early assignments, large div
idend payments, striking price adjustments, and the like, if he is going to operate
advanced strategies. Without afull understanding of how these things might affect
one'sposition, one cannot operate an advanced strategy correctly.

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INTRODUCTION
Aput option gives the holder the right to sell the underlying security at the striking
price at any time until the expiration date of the option. Listed put options are
slightly newer than listed call options, having been introduced on June 3, 1977. The
introduction of listed puts has provided amuch wider range of strategies for both
conservative and aggressive investors. The call option is least effective in strategies
in which downward price movement by the underlying stock is concerned. The put
option is auseful tool in that case.
All stocks with listed call options have listed put options as well. The use of puts
or the combination of puts and calls can provide more versatility to the strategist.
When listed put options exist, it is no longer necessary to implement strategies
involving long calls and short stock. Listed put options can be used more efficiently
in such situations. There are many similarities between call strategies and put
strategies. For example, put spread strategies and call spread strategies employ sim
ilar tactics, although there are technical differences, of course. In certain strategies,
the tactics for puts may appear largely to be arepetition of those used for calls, but
they are nevertheless spelled out in detail here. The strategies that involve the use
of both puts and calls together - straddles and combinations - have techniques of
their own, but even in these cases the reader will recognize certain similarities to
strategies previously discussed. Thus, the introduction of put options not only
widens the realm of potential strategies, but also makes more efficient some of the
strategies previously described.
244

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CH.APTER 15
Put Option Basics
Much of the same terminology that is applied to call options also pertains to put
options. Underlying security, striking price, and expiration date are all terms that
have the same meaning for puts as they do for calls. The expiration dates of listed put
options agree with the expiration dates of the calls on the same underlying stock. In
addition, puts and calls have the same striking prices. This means that if there are
options at acertain strike, say on aparticular underlying stock that has both listed
puts and calls, both calls at 50 and puts at 50 will be trading, regardless of the price
of the underlying stock. Note that it is no longer sufficient to describe an option as
an "XYZ July 50." It must also be stated whether the option is aput or acall, for an
XYZ July 50 call and an XYZ July 50 put are two different securities.
In many respects, the put option and its associated strategies will be very near
ly the opposite of corresponding call-oriented strategies. However, it is not correct to
say that the put is exactly the opposite of acall. In this introductory section on puts,
the characteristics of puts are described in an attempt to show how they are similar
to calls and how they are not.
PUT STRATEGIES
In the simplest terms, the outright buyer of aput is hoping for astock price decline
in order for his put to become more valuable. If the stock were to decline well below
the striking price of the put option, the put holder could make aprofit. The holder
of the put could buy stock in the open market and then exercise his put to sell that
stock for aprofit at the striking price, which is higher.
Example: If XYZ stock is at 40, an XYZ July 50 put would be worth at least 10 points,
for the put grants the holder the right to sell XYZ at 50 - 10 points above its current
245

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CHAPTER 15
Put Option Basics
Much of the same terminology that is applied to call options also pertains to put
options. Underlying security, striking price, and expiration date are all terms that
have the same meaning for puts as they do for calls. The expiration dates of listed put
options agree with the expiration dates of the calls on the same underlying stock. In
addition, puts and calls have the same striking prices. This means that if there are
options at acertain strike, say on aparticular underlying stock that has both listed
puts and calls, both calls at 50 and puts at 50 will be trading, regardless of the price
of the underlying stock. Note that it is no longer sufficient to describe an option as
an "XYZ July 50." It must also be stated whether the option is aput or acall, for an
XYZ July 50 call and an XYZ July 50 put are two different securities.
In many respects, the put option and its associated strategies will be very near
ly the opposite of corresponding call-oriented strategies. However, it is not correct to
say that the put is exactly the opposite of acall. In this introductory section on puts,
the characteristics of puts are described in an attempt to show how they are similar
to calls and how they are not.
PUT STRATEGIES
In the simplest terms, the outright buyer of aput is hopingfor astock price decline
in order for his put to become more valuable. If the stock were to decline well below
the striking price of the put option, the put holder could make aprofit. The holder
of the put could buy stock in the open market and then exercise his put to sell that
stock for aprofit at the striking price, which is higher.
Example: If XYZ stock is at 40, an XYZ July 50 put would be worth at least 10 points,
for the put grants the holder the right to sell XYZ at 50 10 points above its current
245

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246 Part Ill: Put Option Strategies
price. On the other hand, if the stock price were above the striking price of the put
option at expiration, the put would be worthless. No one would logically want to exer
cise aput option to sell stock at the striking price when he could merely go to the
open market and sell the stock for ahigher price. Thus, as the price of the underly
ing stock declines, the put becomes more valuable. This is, of course, the opposite of
acall option'sprice action.
The meaning of in-the-money and out-of-the-money are altered when one is
speaking of put options. Aput is considered to be in-the-money when the underlying
stock is below the striking price of the put option; it is out-of the-money when the
stock is above the striking price. This, again, is the opposite of the call option. IfXYZ
is at 45, the XYZ July 50 put is in-the-money and the XYZ July 50 call is out-of-the
money. However, ifXYZ were at 55, the July 50 put would be out-of-the-money while
the July 50 call would be in-the-money. The broad definition of an in-the-money
option as "an option that has intrinsic value" would cover the situation for both puts
and calls. Note that aput option has intrinsic value when the underlying stock is
below the striking price of the put. That is, the put has some "real" value when the
stock is below the striking price.
The intrinsic value of an in-the-money put is merely the difference between
the striking price and the stock price. Since the put is an option (to sell), it will gen
erally sell for more than its intrinsic value when there is time remaining until the
expiration date. This excess value over its intrinsic value is referred to as the time
value premium, just as is the case with calls.
Example: XYZ is at 47 and the XYZ July 50 put is selling for 5, the intrinsic value is
3 points (50- 47), so the time value premium must be 2 points. The time value pre
mium of an in-the-money put option can always be quickly computed by the follow
ing formula:
Time value premium p . Sk · St "ki · • ) == ut option + toe pnce - nng pnce (m-the-money put
This is not the same formula that was applied to in-the-money call options, although
it is always true that the time value premium of an option is the excess value over
intrinsic value.
Time value premium Call ti S ·ki · St k · . all == op on + tn ng pnce - oc pnce (m-the-money c )
If the put is out-of-the-money, the entire premium of the put is composed of time
value premium, for the intrinsic value of an out-of-the-money option is always zero.

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O.,,ter 15: Put Option Basks 247
The time value premium of aput is largest when the stock is at the striking price of
the put. As the option becomes deeply in-the-money or deeply out-of-the-money, the
time value premium will shrink substantially. These statements on the magnitude of
the time value premium are true for both puts and calls. Table 15-1 will help to illus
trate the relationship of stock price and option price for both puts and calls. The
reader may want to refer to Table 1-1, which described the time value premium rela
tionship for calls. Table 15-1 describes the prices of an XYZ July 50 call option and
an XYZ July 50 put option.
Table 15-1 demonstrates several basic facts. As the stock drops, the actual price
of acall option decreases while the value of the put option increases. Conversely, as
the stock rises, the call option increases in value and the put option decreases in
value. Both the put and the call have their maximum time value premium when the
stock is exactly at the striking price. However, the call will generally sell for rrwre than
the put when the stock is at the strike. Notice in Table 15-1 that, with XYZ at 50, the
call is worth 5 points while the put is worth only 4 points. This is true in general,
except in the case of astock that pays alarge dividend. This phenomenon has to do
with the cost of carrying stock. More will be said about this effect later. Table 15-1
also describes an effect of put options that normally holds true: An in-the-rrwney put
( stock is below strike) loses time value premium rrwre quickly than an in-the-rrwney
call does. Notice that with XYZ at 43 in Table 15-1, the put is 7 points in-the-money
and has lost all its time value premium. But when the call is 7 points in-the-money,
XYZ at 57, the call still has 2 points of time value premium. Again, this is aphenom
enon that could be affected by the dividend payout of the underlying stock, but is
true in general.
PRICING PUT OPTIONS
The same factors that determine the price of the call option also determine the price
of the put option: price of the underlying stock, striking price of the option, time
remaining until expiration, volatility of the underlying stock, dividend rate of the
underlying stock, and the current risk-free interest rate (Treasury bill rate, for exam
ple). Market dynamics - supply, demand, and investor psychology - play apart as
well.
Without going into as much detail as was shown in Chapter 1, the pricing curve
of the put option can be developed. Certain facts remain true for the put option as
they did for the call option. The rate of decay of the put option is not linear; that is,
the time value premium will decay more rapidly in the weeks immediately preced
ing expiration. The more volatile the underlying stock, the higher will be the price

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248 Part Ill: Put Option Strategies
TABLE 15-1.
Call and put options compared.
XYZ XYZ Coll Coll XYZ Put Put
Stock July 50 Intrinsic Time Value July 50 Intrinsic Time Value
Price Coll Price Value Premium Put Price Value Premium
40 1/2 0 1/2 93/4 10 -1/4*
43 1 0 1 7 7 0
45 2 0 2 6 5
47 3 0 3 5 3 2
50 5 0 5 4 0 4
53 7 3 4 3 0 3
55 8 5 3 2 0 2
57 9 7 2 0
60 101/2 10 1/2 1/2 0 l/2
70 193/4 20 -1/4 * 1/4 0 1/4
* Adeeply in-the-money option may actually trade at adiscount from intrinsic value in advance of
expiration.
of its options, both puts and calls. Moreover, the marketplace may at any time value
options at ahigher or lower volatility than the underlying stock actually exhibits.
This is called implied volatility, as distinguished from actual volatility. Also, the put
option is usually worth at least its intrinsic value at any time, and should be worth
exactly its intrinsic value on the day that it expires. Figure 15-1 shows where one
might expect the XYZ July 50 put to sell, for any stock price, if there are 6 months
remaining until expiration. Compare this with the similar pricing curve for the call
option (Figure 15-2). Note that the intrinsic value line for the put option faces in
the opposite direction from the intrinsic value line for call options; that is, it gains
value as the stock falls below the striking price. This put option pricing curve
demonstrates the effect mentioned earlier, that aput option loses time value pre
mium more quickly when it is in-the-money, and also shows that an out-of-the
money put holds agreat deal of time value premium.
THE EFFECT OF DIVIDENDS ON PUT OPTION PREMIUMS
The dividend of the underlying stock is anegative factor on the price of its call
options. The opposite is true for puts. The larger the dividend, the nwre valuable the
puts will be. This is true because, as the stock goes ex-dividend, it will be reduced in

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Cl,opter 15: Put Option Basics
FIGURE 1 5-1.
Put option price curve.
~
it
C:
.Qa.
0
FIGURE 1 5-2.
Call option price curve.
~
ct
C:
0
11
10
9
8
7
6
a 5
Striking
Price (50)
Greatest
Value for
Time Value
Stock Price
0 4 ----------------------
3
2
1
0
40 45
represents the option'stime value premium. ________ L ________ _
50\ 55 60 Stock Price Intrinsic value
remains at zero
until striking price
is passed.
249
price by the amount of the dividend. That is, the stock will decrease in price and
therefore the put will become more valuable. Consequently, the buyer of the put will
be willing to pay ahigher price for the put and the seller of the put will also demand
ahigher price. As with listed calls, listed puts are not adjusted for the payment of cash
dividends on the underlying stock. However, the price of the option itself will reflect
the dividend payments on the stock.

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250 Part Ill: Put Option Strategies
Example: XYZ is selling for $25 per share and will pay $1 in dividends over the next
6 months. Then a 6-month put option with strike 25 should automatically be worth
at least $1, regardless of any other factor concerning the underlying stock. During the
next 6 months, the stock will be reduced in price by the amount of its dividends- $1
- and if everything else remained the same, the stock would then be at 24. With the
stock at 24, the put would be 1 point in-the-money and would thus be worth at least
its intrinsic value of 1 point. Thus, in advance, this large dividend payout of the
underlying stock will help to increase the price of the put options on this stock.
On the day before astock goes ex-dividend, the time value premium of an in
the-money put should be at least as large as the impending cash dividend payment.
That is, if XYZ is 40 and is about to pay a $.50 dividend, an XYZ January 50 put should
sell for at least l 0½. This is true because the stock will be reduced in price by the
amount of its dividend on the day of the ex-dividend.
EXERCISE AND ASSIGNMENT
When the holder of aput option exercises his option, he sells stock at the striking
price. He may exercise this right at any time during the life of the put option. When
this happens, the writer of aput option with the same terms is assigned an obligation
to buy stock at the striking price. It is important to notice the difference between
puts and calls in this case. The call holder exercises to buy stock and the call writer is
obligated to sell stock. The reverse is true for the put holder and writer.
The methods of assignment via the OCC and the brokerage firm are the same
for puts and calls; any fair method of random or first-in/first-out assignment is
allowed. Stock commissions are charged on both the purchase and sale of the stock
via the assignment and exercise.
When the holder of aput option exercises his right to sell stock, he may be sell
ing stock that he currently holds in his portfolio. Second, he may simultaneously go
into the open market and buy stock for sale via the put exercise. Finally, he may want
to sell the stock in his short stock account; that is, he may short the underlying stock
by exercising his put option. He would have to be able to borrow stock and supply
the margin collateral for ashort sale of stock if he chose this third course of action.
The writer of the put option also has several choices in how he wants to handle
the stock purchase that he is required to make. The put writer who is assigned must
receive stock. (The call writer who is assigned delivers stock.) The put writer may cur
rently be short the underlying stock, in which case he will merely use the receipt of
stock from the assignment to cover his short sale. He may also decide to immediate-

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0.,ter 15: Put Option Basics 251
ly sell stock in the open market to offset the purchase that he is forced to make via
the put assignment. Finally, he may decide to retain the stock that is delivered to him;
he merely keeps the stock in his portfolio. He would, of course, have to pay for ( or
margin) the stock if he decides to keep it.
The mechanics as to how the put holder wants to deliver the stock and how the
put writer wants to receive the stock are relatively simple. Each one merely notifies
his brokerage firm of the way in which he wants to operate and, provided that he can
meet the margin requirements, the exercise or assignment will be made in the
desired manner.
ANTICIPATING ASSIGNMENT
The writer of aput option can anticipate assignment in the same way that the writer
of acall can. When the time value premium of an in-the-money put option disappears,
there is arisk of assignment, regardless of the time remaining until expiration. In
Chapter 1, aform of arbitrage was described in which market-makers or firm traders,
who pay little or no commissions, can take advantage of an in-the-money call selling
at adiscount to parity. Similarly, there is amethod for these traders to take advantage
of an in-the-money put selling at adiscount to parity.
Example: XYZ is at 40 and an XYZ July 50 put is selling for 9¾ a ¼ discount from
parity. That is, the option is selling for ¼ point below its intrinsic value. The arbi
trageur could take advantage of this situation through the following actions:
1. Buy the July put at 9¾.
2. Buy XYZ common stock at 40.
3. Exercise the put to sell XYZ at 50.
The arbitrageur makes 10 points on the stock portion of the transaction, buying the
common at 40 and selling it at 50 via exercise of his put. He paid 9¾ for the put
option and he loses this entire amount upon exercise. However, his overall profit is
thus ¼ point, the amount of the original discount from parity. Since his commission
costs are minimal, he can actually make anet profit on this transaction.
As was the case with deeply in-the-money calls, this type of arbitrage with
deeply in-the-money puts provides asecondary market that might not otherwise
exist. It allows the public holder of an in-the-money put to sell his option at aprice
near its intrinsic value. Without these arbitrageurs, there might not be areasonable
secondary market in which public put holders could liquidate.

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252 Part Ill: Put Option Strategies
Dividend payment dates may also have an effect on the frequency of assign
ment. For call options, the writer might expect to receive an assignment on the day
the stock goes ex-dividend. The holder of the call is able to collect the dividend by
so exercising. Things are slightly different for the writer of puts. He might expect
to receive an assignment on the day after the ex-dividend date of the underlying
stock. Since the writer of the put is obligated to buy stock, it is unlikely that any
one would put the stock to him until after the dividend has been paid. In any case,
the writer of the put can use arelatively simple gauge to anticipate assignment near
the ex-dividend date. If the time value premium of an in-the-money put is less than
the amount of the dividend to be paid, the writer may often anticipate that he will
be assigned immediately after the ex-dividend of the stock. An example will show
why this is true.
Example: XYZ is at 45 and it will pay a $.50 dividend. Furthermore, the XYZ July 50
put is selling at 5¼. Note that the time value premium of the July 50 put is ¼ point
- less than the amount of the dividend, which is ½ point. An arbitrageur could take
the following actions:
1. Buy XYZ at 45.
2. Buy the July 50 put at 5¼.
3. Collect the ½-point dividend (he must hold the stock until the ex-date to collect
the dividend).
4. Exercise his put to sell XYZ at 50 ( writer would receive assignment on the day
after the ex-date).
The arbitrageur makes 5 points on the stock trades, buying XYZ at 45 and selling it
at 50 via exercise of the put. He also collects the ½-point dividend, making his total
intake equal to 5½ points. He loses the 5¼ points that he paid for the put but still
has anet profit of ¼ point. Thus, as the ex-dividend date of astock approaches, the
time value premium of all in-the-money puts on that stock will tend to equal or exceed
the amount of the dividend payment.
This is quite different from the call option. It was shown in Chapter 1 that the
call writer only needs to observe whether the call was trading at or below parity,
regardless of the amount of the dividend, as the ex-dividend date approaches. The
put writer must determine if the time value premium of the put exceeds the amount
of the dividend to be paid. If it does, there is amuch smaller chance of assignment
because of the dividend. In any case, the put writer can anticipate the assignment if
he carefully monitors his position.

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O.,ter 15: Put Option Basics
POSITION LIMITS
253
Recall that the position limit rule states that one cannot have aposition of more than
the limit of options on the same side of the market in the same underlying security.
The limit varies depending on the trading activity and volatility of the underlying stock
and is set by the exchange on which the options are traded. The actual limits are
13,500, 22,500, 31,500, 60,000, or 75,000 contracts, depending on these factors. One
cannot have more than 75,000 option contracts on the bullish side of the market - long
calls and/or short puts - nor can he have more than 75,000 contracts on the bearish
side of the market - short calls and/or long puts. He may, however, have 75,000 con
tracts on each side of the market; he could simultaneously be long 75,000 calls and
long 75,000 puts.
For the following examples, assume that one is concerned with an underlying
stock whose position limit is 75,000 contracts.
Long 75,000 calls, long 75,000 puts - no violation; 75,000 contracts bullish (long
calls) and 75,000 contracts bearish (long puts).
Long 38,000 calls, short 37,000 puts - no violation; total of 75,000 contracts bullish.
Long 38,000 calls, short 38,000 puts - violation; total of 76,000 contracts bullish.
Money managers should be aware that these position limits apply to all "related"
accounts, so that someone managing several accounts must total all the accounts'
positions when considering the position limit rule.
CONVERSION
Many of the relationships between call prices and put prices relate to aprocess
known as aconversion. This term dates back to the over-the-counter option days
when adealer who owned aput ( or could buy one) was able to satisfy the needs of apotential call buyer by "converting" the put to acall. This terminology is somewhat
confusing, and the actual position that the dealer would take is little more than an
arbitrage position. In the listed market, arbitrageurs and firm traders can set up the
same position that the converter did.
The actual details of the conversion process, which must include the carrying
cost of owning stock and the inclusion of all dividends to be paid by the stock during
the time the position is held, are described later. However, it is important for the put
option trader to understand what the arbitrageur is attempting to do in order for him
to fully understand the relationship between put and call prices in the listed option
market.

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254 Part Ill: Put Option Strategies
Aconversion position has no risk. The arbitrageur will do three things:
1. Buy 100 shares of the underlying stock.
2. Buy 1 put option at acertain striking price.
3. Sell lcall option at the same striking price.
The arbitrageur has no risk in this position. If the underlying stock drops, he can
always exercise his long put to sell the stock at ahigher price. If the underlying stock
rises, his long stock offsets the loss on his short call. Of course, the prices that the
arbitrageur pays for the individual securities determine whether or not aconversion
will be profitable. At times, apublic customer may look at prices in the newspaper
and see that he could establish aposition similar to the foregoing one for aprofit,
even after commissions. However, unless prices are out of line, the public customer
would not normally be able to make abetter return than he could by putting his
money into abank or a Treasury bill, because of the commission costs he would pay.
Without needing to understand, at this time, exactly what prices would make an
attractive conversion, it is possible to see that it would not always be possible for the
arbitrageur to do aconversion. The mere action of many arbitrageurs doing the same
conversion would force the prices into line. The stock price would rise because arbi
trageurs are buying the stock, as would the put price; and the call price would drop
because of the preponderance of sellers.
When this happens, another arbitrage, known as areversal ( or reverse conver
sion), is possible. In this case, the arbitrageur does the opposite: He shorts the under
lying stock, sells 1 put, and buys 1 call. Again, this is aposition with no risk. If the
stock rises, he can always exercise his call to buy stock at alower price and cover his
short sale. If the stock falls, his short stock will offset any losses on his short put.
The point of introducing this information, which is relatively complicated, at
this place in the text is to demonstrate that there is arelationship between put and
call prices, when both have the same striking price and expiration date. They are not
independent of one another. If the put becomes "cheap" with respect to the call, arbi
trageurs will move in to do conversions and force the prices back in line. On the other
hand, if the put becomes expensive with relationship to the call, arbitrageurs will do
reversals until the prices move back into line.
Because of the way in which the carrying cost of the stock and the dividend rate
of the stock are involved in doing these conversions or reversals, two facts come to
light regarding the relationship of put prices and call prices. Both of these facts have
to do with the carrying costs incurred during the conversion. First, aput option will
generally sell for less than acall option when the underlying stock is exactly at the
striking price, unless the stock pays alarge dividend. In the older over-the-counter

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