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

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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 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 call
against the July 30 call that is held long. This would establish a normal 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's volatility 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 a normal July bull spread for a net 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 a cheaper cost than he could have originally. This is a specific 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 a normal 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 a normal bull spread if the stock is at a favorable 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 a long call at a substantially reduced cost, possibly even for free.
The easiest w~y to see this would be to consider a diagonal 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. A diagonal bear spread could be
established by selling the April 30 and buying the July 35. This is still a bear spread,
because a call with a lower striking price is being sold while a call at a higher strike
is being purchased. However, since the purchased call has a longer 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 a regular bear
spread. If XYZ should advance by a great 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 a strategist might attempt a diagonal bear spread would not be
for the slight downside advantage that the diagonalizing effect produces. Rather it
would be because he has a chance of owning the July 35 call - the longer-term call -
for a substantially 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 a rally

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240 Part II: Call Option Strategies
by the underlying stock. If such a rally 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 a prof
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 a diagonal spread for a credit, there is always the potential that he could own a call
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, a desirable 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's at 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's will be owned
at a reduced cost. In Chapter 13, when reverse spreads were discussed, the strategy
in which one sells a call with a lower strike and then buys more calls at a higher strike
was termed a reverse ratio spread, or backspread. The strategy just described is
merely the diagonalizing of a backspread. This is a strategy 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 a longer 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 a
rather low-probability event, though, and would still represent a limited 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 a call takes place.
Recall that it was determined that a call loses most of its time value premium in the
last stages of its life. When it is a very long-term option, the rate of decay is small.
Knowing this fact, it makes sense that one would want to sell options with a short life
remaining, so that the maximum benefit of the decay could be obtained.
Correspondingly, the purchase of a longer-term call would mean that the buyer is not
subjecting himself to a substantial loss in time value premium, at least over the first
three months of ownership. A diagonal spread encompasses both of these features -
selling a short-term call to try to obtain the maximum rate of time decay, while buy
ing a longer-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 a vehicle that the astute strategist can use to set up a wide
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 a stock
will not move very far in a short time period.
The investor who is not familiar with options should generally begin with a sim
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.
A great 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 a full understanding of how these things might affect
one's position, one cannot operate an advanced strategy correctly.

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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 a certain strike, say on a particular 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 a put or a call, 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 a call. 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 a put is hopingfor a stock 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 a profit. The holder
of the put could buy stock in the open market and then exercise his put to sell that
stock for a profit 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 a put option to sell stock at the striking price when he could merely go to the
open market and sell the stock for a higher price. Thus, as the price of the underly
ing stock declines, the put becomes more valuable. This is, of course, the opposite of
a call option's price action.
The meaning of in-the-money and out-of-the-money are altered when one is
speaking of put options. A put 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 a put 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 . S k · St "ki · • ) == ut option + toe pnce - n ng 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 a put 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 a call 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 a stock that pays a large 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 a phenom
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 a part 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
* A deeply in-the-money option may actually trade at a discount from intrinsic value in advance of
expiration.
of its options, both puts and calls. Moreover, the marketplace may at any time value
options at a higher 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 a put 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 a great deal of time value premium.
THE EFFECT OF DIVIDENDS ON PUT OPTION PREMIUMS
The dividend of the underlying stock is a negative 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:
.Q
a.
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's
time 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 a higher price for the put and the seller of the put will also demand
a higher 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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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 a put option can anticipate assignment in the same way that the writer
of a call can. When the time value premium of an in-the-money put option disappears,
there is a risk of assignment, regardless of the time remaining until expiration. In
Chapter 1, a form 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 a discount to parity. Similarly, there is a method for these traders to take advantage
of an in-the-money put selling at a discount 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 a net 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 a secondary market that might not otherwise
exist. It allows the public holder of an in-the-money put to sell his option at a price
near its intrinsic value. Without these arbitrageurs, there might not be a reasonable
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 a relatively 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 a net profit of ¼ point. Thus, as the ex-dividend date of a stock 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 a much 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 a position 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 a process
known as a conversion. This term dates back to the over-the-counter option days
when a dealer who owned a put ( or could buy one) was able to satisfy the needs of a
potential call buyer by "converting" the put to a call. 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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258 Part Ill: Put Option Strategies
chase can achieve. If the underlying stock remains relatively unchanged, the short
seller would do better because he does not risk losing his entire investment in a lim
ited amount of time if the underlying stock changes only slightly in price. However,
if the underlying stock should rise dramatically, the short seller can actually lose more
than his initial investment. The short sale of stock has theoretically unlimited risk.
Such is not true of the put option purchase, whereby the risk is limited to the amount
of the initial investment. One other point should be made when comparing the pur
chase of a put and the short sale of stock: The short seller of stock is obligated to pay
the dividends on the stock, but the put option holder has no such obligation. This is
an additional advantage to the holder of the put.
TABLE 16-2.
Results of selling short.
XYZ Price at Put Option
Expiration Short Sale Purchase
20 + $3,000 (+ 120%) +$2,500 (+ 500%)
30 + 2,000 (+ 80%) + 1,500 (+ 300%)
40 + 1,000 (+ 40%) + 500 (+ 100%)
45 + 500(+ 20%) 0( 0%)
48 + 200(+ 80%) 300 (- 60%)
50 0( 0%) 500 (- 100%)
60 - 1,000 (- 40%) 500 (- 100%)
75 - 2,500 (- 100%) 500 (- 100%)
100 - 5,000 (- 200%) 500 (- 100%)
SELECTING WHICH PUT TO BUY
Many of the same types of analyses that the call buyer goes through in deciding which
call to buy can be used by the prospective put buyer as well. First, when approach
ing put buying as a speculative strategy, one should not place more than 15% of his
risk capital in the strategy. Some investors participate in put buying to add some
amount of downside protection to their basically bullishly-oriented common stock
portfolios. More is said in Chapter 17 about buying puts on stocks that one actually
owns.
The out-ofthe-nwney put offers both higher reward potentials and higher risk
potentials than does the in-the-nwney put. If the underlying stock drops substantial-

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G,pter 16: Put Option Buying 259
ly, the percentage returns from having purchased a cheaper, out-of-the-money put
will be greater. However, should the underlying stock decline only moderately in
price, the in-the-rrwney put will often prove to be the better choice. In fact, since a
put option tends to lose its time value premium quickly as it becomes an in-the
money option, there is an even greater advantage to the purchase of the in-the
money put.
Example: XYZ is at 49 and the following prices exist:
XYZ, 49;
XYZ July 45 put, l; and
XYZ July 50 put, 3.
If the underlying stock were to drop to 40 by expiration, the July 45 put would be
worth 5 points, a 400% profit. The July 50 put would be worth 10 points, a 233%
profit over its initial purchase price of 3. Thus, in a substantial downward move, the
out-of-the-money put purchase provides higher reward potential. However, if the
underlying stock drops only moderately, say to t:15, the purchaser of the July 45 put
would lose his entire investment, since the put would be worthless at expiration. The
purchaser of the in-the-money July 50 put would have a 2-point profit with XYZ at
45 at expiration.
The preceding analysis is based on holding the put until expiration. For the
option buyer, this is generally an erroneous form of analysis, because the buyer
generally tends to liquidate his option purchase in advance of expiration. When
considering what happens to the put option in advance of expiration, it is helpful to
remember that an in-the-money put tends to lose its time premium rather quickly.
In the example above, the July 45 put is completely composed of time value pre
mium. If the underlying stock begins to drop below 45, the price of the put will not
increase as rapidly as would the price of a call that is going into-the-money.
Example: If XYZ fell by 5 points to 44, definitely a move in the put buyer's favor, he
may fmd that the July 45 put has increased in value only to 2 or 2½ points. This is
somewhat disappointing because, with call options, one would expect to do signifi
cantly better on a 5-point stock movement in his favor. Thus, when purchasing put
options for speculation, it is generally best to concentrate on in-the-rrwney puts unless
a very substantial decline in the price of the underlying stock is anticipated.
Once the put option is in-the-money, the time value premium will decrease
even in the longer-term series. Since this time premium is small in all series, the put

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260 Part Ill: Put Option Strategies
buyer can often purchase a longer-term option for very little extra money, thus gain
ing more time to work with. Call option buyers are generally forced to avoid the
longer-term series because the extra cost is not worth the risk involved, especially in
a trading situation. However, the put buyer does not necessarily have this disadvan
tage. If he can purchase the longer-term put for nearly the same price as the near
term put, he should do so in case the underlying stock takes longer to drop than he
had originally anticipated it would.
It is not uncommon to see such prices as the following:
XYZ common, 46:
XYZ April 50 put, 4;
XYZ July 50 put, 4½; and
XYZ October 50 put, 5.
None of these three puts have much time value premium in their prices. Thus, the
buyer might be willing to spend the extra 1 point and buy the longest-term put. If the
underlying stock should drop in price immediately, he will profit, but not as much as
if he had bought one of the less expensive puts. However, should the underlying stock
rise in price, he will own the longest-term put and will therefore suffer less of a loss,
percentagewise. If the underlying stock rises in price, some amount of time value
premium will come back into the various puts, and the longest-term put will have the
largest amount of time premium. For example, if the stock rises back to 50, the fol
lowing prices might exist:
XYZ common, 50;
XYZ April 50 put, l;
XYZ July 50 put, 2½; and
XYZ October 50 put, 3½.
The purchase of the longer-term October 50 put would have suffered the least loss,
percentagewise, in this event. Consequently, when one is purchasing an in-the
money put, he may often want to consider buying the longest-term put if the time
value premium is small when compared to the time premium in the nearer-term
puts.
In Chapter 3, the delta of an option was described as the amount by which one
might expect the option will increase or decrease in price if the underlying stock
moves by a fixed amount (generally considered to be one point, for simplicity). Thus,
if XYZ is at 49 and a call option is priced at 3 with a delta of ½, one would expect the
call to sell for 3½ with XYZ at 50 and to sell at 2¼ with XYZ at 48. In reality, the delta

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268
TABLE 16-6.
Summary of rolling-up transactions.
Original trade:
Later:
Net position:
Buy 1 October 45 put for 3
with XYZ at 45
With XYZ at 48, sell 2
October 45's for 11/2 each
and buy l October 50 put for 3
Long 1 October 50 put
Short 1 October 45 put
Part Ill: Put Option Strategies
$300 debit
$300 credit
$300 debit
$300 debit
The effect of creating this spread is that the investor has not increased his risk
at all, but has raised the break-even point for his position. That is, if XYZ merely falls
a small distance, he will be able to get out even. Without the effect of creating the
spread, the put holder would need XYZ to fall back to 42 at expiration in order for
him to break even, since he originally paid 3 points for the October 45 put. His orig
inal risk was $300. IfXYZ continues to rise in price and the puts in the spread expire
worthless, the net loss will still be only $300 plus additional commissions. Admittedly,
the commissions for the spread will increase the loss slightly, but they are small in
comparison to the debit of the position ($300). On the other hand, if the stock should
fall back only slightly, to 47 by expiration, the spread will break even. At expiration,
with XYZ at 47, the in-the-money October 50 put will be worth 3 points and the out
of-the-money October 45 put will expire worthless. Thus, the investor will recover his
$300 cost, except for commissions, with XYZ at 47 at expiration. His break-even point
is raised from 42 to 47, a substantial improvement of his chances for recovery.
The implementation of this spread strategy reduces the profit potential of the
position, however. The maximum potential of the spread is 2 points. If XYZ is any
where below 45 at expiration, the spread will be worth 5 points, since the October 50
put will sell for 5 points more than the October 45 put. The investor has limited his
potential profit to 2 points - the 5-point maximum width of the spread, less the 3
points that he paid to get into the position. He can no longer gain substantially on a
large drop in price by the underlying stock. This is normally of little concern to the
put holder faced with an unrealized loss and the potential for a total loss. He gener
ally would be appreciative of getting out even or of making a small profit. The cre
ation of the spread accomplishes this objective for him.
It should also be pointed out that he does not incur the maximum loss of his
entire debit plus commissions, unless XYZ closes above 50 at expiration. If XYZ is

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O,apter 16: Put Option Buying 269
anywhere below 50, the October 50 will have some value and the investor will be able
to recover something from the position. This is distinctly different from the original
put holding of the October 45, whereby the maximum loss would be incurred unless
the stock were below 45 at expiration. Thus, the introduction of the spread also
reduces the chances of having to realize the maximum loss.
In summary, the put holder faced with an unrealized loss may be able to create
a spread by selling twice the number of puts that he is currently long and simultane
ously buying the put at the next higher strike. This action should be used only if the
spread can be transacted at a small debit or, preferably, at even money (zero debit).
The spread position offers a much better chance of breaking even and also reduces
the possibility of having to realize the maximum loss in the position. However, the
introduction of these loss-limiting measures reduces the maximum potential of the
position if the underlying stock should subsequently decline in price by a significant
amount. Using this spread strategy for puts would require a margin account, just as
calls do.
THE CALENDAR SPREAD STRATEGY
Another strategy is sometimes available to the put holder who has an unrealized loss.
If the put that he is holding has an intermediate-term or long-term expiration date,
he might be able to create a calendar spread by selling the near-term put against the
put that he currently holds.
Example: An investor bought an XYZ October 45 put for 3 points when the stock was
at 45. The stock rises to 48, moving in the wrong direction for the put buyer, and his
put falls in value to 1 ½. He might, at that time, consider selling the near-term July
45 put for 1 point. The ideal situation would be for the July 45 put to expire worth
less, reducing the cost of his long put by 1 point. Then, if the underlying stock
declined below 45, he could profit after July expiration.
The major drawback to this strategy is that little or no profit will be made - in
fact, a loss is quite possible - if the underlying stock falls back to 45 or below before
the near-term July option expires. Puts display different qualities in their time value
premiums than calls do, as has been noted before. With the stock at 45, the differ
ential between the July 45 put and the October 45 put might not widen much at all.
This would mean that the spread has not gained anything, and the spreader has a loss
equal to his commissions plus the initial unrealized loss. In the example above, ifXYZ
dropped quickly back to 45, the July 45 might be worth 1 ½ and the October worth
2½. At this point, the spreader would have a loss on both sides of his spread: He sold
the July 45 put for 1 and it is now 1 ½; he bought the October 45 for 3 and it is now

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270 Part Ill: Put Option Strategies
2½; plus he has spent two commissions to date and would have to spend two more
to liquidate the position.
At this point, the strategist may decide to do nothing and take his chances that
the stock will subsequently rally so that the July 45 put will expire worthless.
However, if the stock continues to decline below 45, the spread will most certainly
become more of a loss as both puts come closer to parity.
This type of spread strategy is not as attractive as the "rolling-up" strategy. In
the "rolling-up" strategy, one is not subjected to a loss if the stock declines after the
spread is established, although he does limit his profits. The fact that the calendar
spread strategy can lead to a loss even if the stock declines makes it a less desirable
alternative.
EQUIVALENT POSITIONS
Before considering other put-oriented strategies, the reader should understand the
definition of an equivalent position. Two strategies, or positions, are equivalent when
they have the same profit potential. They may have different collateral or investment
requirements, but they have similar profit potentials. Many of the call-oriented
strategies that were discussed in Part II of the book have an equivalent put strategy.
One such case has already been described: The "protected short sale," or shorting the
common stock and buying a call, is equivalent to the purchase of a put. That is, both
have a limited risk above the striking price of the option and relatively large profit
potential to the downside. An easy way to tell if two strategies are equivalent is to see
if their profit graphs have the same shape. The put purchase and the "protected short
sale" have profit graphs with exactly the same shape (Figures 16-1 and 4-1, respec
tively). As more put strategies are discussed, it will always be mentioned if the put
strategy is equivalent to a previously described call strategy. This may help to clarify
the put strategies, which understandably may seem complex to the reader who is not
familiar with put options.

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274 Part Ill: Put Option Strategies
At the opposite end of the spectrum, the stock owner might buy an in-the
money put as protection. This would quite severely limit his profit potential, since the
underlying stock would have to rise above the strike and more for him to make a
profit. However, the in-the-money put provides vast quantities of downside protec
tion, limiting his loss to a very small amount.
Example: XYZ is again at 40 and there is an October 45 put selling for 5½. The stock
owner who purchases the October 45 put would have a maximum risk of½ point, for
he could always exercise the put to sell stock at 45, giving him a 5-point gain on the
stock, but he paid 5½ points for the put, thereby giving him an overall maximum loss
of ½ point. He would have difficulty making any profit during the life of the put,
however. XYZ would have to rise by more than 5½ points (the cost of the put) for
him to make any total profit on the position by October expiration.
The deep in-the-money put purchase is overly conservative and is usually not a
good strategy. On the other hand, it is not wise to purchase a put that is too deeply
out-of-the-money as protection. Generally, one should purchase a slightly out-ofthe
money put as protection. This helps to achieve a balance between the positive feature
of protection for the common stock and the negative feature of limiting profits.
The reader may find it interesting to know that he has actually gone through this
analysis, back in Chapter 3. Glance again at the profit graph for this strategy of using
the put purchase to protect a common stock holding (Figure 17-1). It has exactly the
same shape as the profit graph of a simple call purchase. Therefore, the call purchase
and the long put/long stock strategies are equivalent. Again, by equivalent it is meant
that they have similar profit potentials. Obviously, the ownership of a call differs sub
stantially from the ownership of common stock and a put. The stock owner continues
to maintain his position for an indefinite period of time, while the call holder does not.
Also, the stockholder is forced to pay substantially more for his position than is the call
holder, and he also receives dividends whereas the call holder does not. Therefore,
"equivalent" does not mean exactly the same when comparing call-oriented and put
oriented strategies, but rather denotes that they have similar profit potentials.
In Chapter 3, it was determined that the slightly in-the-money call often offers
the best ratio between risk and reward. When the call is slightly in-the-money, the
stock is above the striking price. Similarly, the slightly out-of-the-money put often
offers the best ratio between risk and reward for the common stockholder who is buy
ing the put for protection. Again, the stock is slightly above the striking price. Actually,
since the two positions are equivalent, the same conclusions should be arrived at; that
is why it was stated that the reader has been through this analysis previously.

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G,pter 17: Put Buying in Conjunction with Common Stock Ownership
TAX CONSIDERATIONS
275
Although tax considerations are covered in detail in a later chapter, an important tax
law concerning the purchase of puts against a common stock holding should be men
tioned at this time. If the stock owner is already a long-term holder of the stock at the
time that he buys the put, the put purchase has no effect on his tax status. Similarly,
if the stock buyer buys the stock at the time that he buys the put and identifies the
position as a hedge, there is no effect on the tax status of his stock. However, if one
Is currently a short-tenn holder of the common stock at the time that he buys a put,
he eliminates any accrued holding period on his common stock. Moreover, the hold
ing period for that stock does not begin again until the put is sold.
Example: Assume the long-term holding period is 6 months. That is, a stock owner
must own the stock for 6 months before it can be considered a long-term capital gain.
An investor who bought the stock and held it for 5 months and then purchased a put
would wipe out his entire holding period of 5 months. Suppose he then held the put
and the stock simultaneously for 6 months, liquidating the put at the end of 6 months.
His holding period would start all over again for that common stock. Even though he
has owned the stock for 11 months - 5 months prior to the put purchase and 6
months more while he simultaneously owned the put - his holding period for tax pur
poses is considered to be zero!
This law could have important tax ramifications, and one should consult a tax advisor
if he is in doubt as to the effect that a put purchase might have on the taxability of
his common stock holdings.
PUT BUYING AS PROTECTION FOR THE COVERED CALL WRITER
Since put purchases afford protection to the owner of common stock, some investors
naturally feel that the same protective feature could be used to limit their downside
risk in the covered call writing strategy. Recall that the covered call writing strategy
involves the purchase of stock and the sale of a call option against that stock. The cov
ered write has limited upside profit potential and offers protection to the downside in
the amount of the call premium. The covered writer will make money if the stock falls
a little, remains unchanged, or rises by expiration. The covered writer can actually lose
money only if the stock falls by more than the call premium received. He has poten
tially large downside losses. This strategy is known as a protective collar or, more sim
ply, a "collar." (It is also called a "hedge wrapper," although that is an outdated term.)

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274 Part Ill: Put Option Strategies
At the opposite end of the spectrum, the stock owner might buy an in-the
money put as protection. This would quite severely limit his profit potential, since the
underlying stock would have to rise above the stiike and more for him to make a
profit. However, the in-the-money put provides vast quantities of downside protec
tion, limiting his loss to a very small amount.
Example: XYZ is again at 40 and there is an October 45 put selling for 5½. The stock
owner who purchases the October 45 put would have a maximum risk of½ point, for
he could always exercise the put to sell stock at 45, giving him a 5-point gain on the
stock, but he paid 5½ points for the put, thereby giving him an overall maximum loss
of ½ point. He would have difficulty making any profit during the life of the put,
however. XYZ would have to rise by more than 5½ points (the cost of the put) for
him to make any total profit on the position by October expiration.
The deep in-the-money put purchase is overly conservative and is usually not a
good strategy. On the other hand, it is not wise to purchase a put that is too deeply
out-of-the-money as protection. Generally, one should purchase a slightly out-ofthe
nwney put as protection. This helps to achieve a balance between the positive feature
of protection for the common stock and the negative feature of limiting profits.
The reader may find it interesting to know that he has actually gone through this
analysis, back in Chapter 3. Glance again at the profit graph for this strategy of using
the put purchase to protect a common stock holding (Figure 17-1). It has exactly the
same shape as the profit graph of a simple call purchase. Therefore, the call purchase
and the long put/long stock strategies are equivalent. Again, by equivalent it is meant
that they have similar profit potentials. Obviously, the ovvnership of a call differs sub
stantially from the ownership of common stock and a put. The stock owner continues
to maintain his position for an indefinite period of time, while the call holder does not.
Also, the stockholder is forced to pay substantially more for his position than is the call
holder, and he also receives dividends whereas the call holder does not. Therefore,
"equivalent" does not mean exactly the same when comparing call-oriented and put
oriented strategies, but rather denotes that they have similar profit potentials.
In Chapter 3, it was determined that the slightly in-the-money call often offers
the best ratio between 1isk and reward. When the call is slightly in-the-money, the
stock is above the striking price. Similarly, the slightly out-of-the-money put often
offers the best ratio between risk and reward for the common stockholder who is buy
ing the put for protection. Again, the stock is slightly above the striking price. Actually,
since the two positions are equivalent, the same conclusions should be arrived at; that
is why it was stated that the reader has been through this analysis previously.

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0.,,,,, I 7: Put Buying in Conjundion with Common Stock Ownership
JAX CONSIDERATIONS
275
Although tax considerations are covered in detail in a later chapter, an important tax
law concerning the purchase of puts against a common stock holding should be men
tioned at this time. If the stock owner is already a long-term holder of the stock at the
time that he buys the put, the put purchase has no effect on his tax status. Similarly,
if the stock buyer buys the stock at the time that he buys the put and identifies the
position as a hedge, there is no effect on the tax status of his stock. However, if one
is currently a short-term holder of the comrrwn stock at the time that he buys a put,
he eliminates any accrued holding period on his comrrwn stock. Moreover, the hold
ing period for that stock does not begin again until the put is sold.
Example: Assume the long-term holding period is 6 months. That is, a stock owner
must own the stock for 6 months before it can be considered a long-term capital gain.
An investor who bought the stock and held it for 5 months and then purchased a put
would wipe out his entire holding period of 5 months. Suppose he then held the put
and the stock simultaneously for 6 months, liquidating the put at the end of 6 months.
His holding period would start all over again for that common stock. Even though he
has owned the stock for 11 months - 5 months prior to the put purchase and 6
months more while he simultaneously owned the put - his holding period for tax pur
poses is considered to be zero!
This law could have important tax ramifications, and one should consult a tax advisor
if he is in doubt as to the effect that a put purchase might have on the taxability of
his common stock holdings.
PUT BUYING AS PROTECTION FOR THE COVERED CALL WRITER
Since put purchases afford protection to the owner of common stock, some investors
naturally feel that the same protective feature could be used to limit their downside
risk in the covered call writing strategy. Recall that the covered call writing strategy
involves the purchase of stock and the sale of a call option against that stock. The cov
ered write has limited upside profit potential and offers protection to the downside in
the amount of the call premium. The covered writer will make money if the stock falls
a little, remains unchanged, or rises by expiration. The covered writer can actually lose
money only if the stock falls by more than the call premium received. He has poten
tially large downside losses. This strategy is known as a protective collar or, more sim
ply, a "collar." (It is also called a "hedge wrapper," although that is an outdated term.)

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276 Part Ill: Put Option Strategies
The purchase of an out-of the-money put option can eliminate the risk of large
potential losses for the covered write, although the money spent for the put purchase
will reduce the overall return from the covered write. One must therefore include
the put cost in his initial calculations to determine if it is worthwhile to buy the put.
Example: X'YZ is at 39 and there is an XYZ October 40 call selling for 3 points and an
XYZ October 35 put selling for ½ point. A covered write could be established by buy
ing the common at 39 and selling the October 40 call for 3. This covered write would
have a maximum profit potential of 4 points if XYZ were anywhere above 40 at expi
ration. The write would lose money if XYZ were anywhere below 36, the break-even
point, at October expiration. By also purchasing the October 35 put at the time the
covered write is initiated, the covered writer will limit his profit potential slightly, but
will also greatly reduce his risk potential. If the put purchase is added to the covered
write, the maximum profit potential is reduced to 3½ points at October expiration. The
break-even point moves up to 36½, and the writer will experience some loss if XYZ is
below 36½ at expiration. However, the most that the writer could lose would be 1 ¼
points if XYZ were below 35 at expiration. The purchase of the put option produces
this loss-limiting effect. Table 17-2 and Figure 17-2 depict the profitability of both the
regular covered write and the covered write that is protected by the put purchase.
Commissions should be carefully included in the covered writer's return calcula
tions, as well as the cost of the put. It was demonstrated in Chapter 2 that the covered
writer must include all commissions and margin interest expenses as well as all divi
dends received in order to produce an accurate "total return" picture of the covered
write. Figure 17-2 shows that the break-even point is raised slightly and the overall prof
it potential is reduced by the purchase of the put. However, the maximum risk is quite
small and the writer need never be forced to roll down in a disadvantageous situation.
Recall that the covered writer who does not have the protective put in place is
forced to roll down in order to gain increased downside protection. Rolling down
merely means that he buys back the call that is currently written and writes another
call, with a lower striking price, in its place. This rolling-down action can be helpful
if the stock stabilizes after falling; but if the stock reverses and climbs upward in price
again, the covered writer who rolled down would have limited his gains. In fact, he
may even have "locked in" a loss. The writer who has the protective put need not be
bothered with such things. He never has to roll down, for he has a limited maximum
loss. Therefore, he should never get into a "locked-in" loss situation. This can be a
great advantage, especially from an emotional viewpoint, because the writer is never
forced to make a decision as to the future price of the stock in the middle of the
stock's decline. With the put in place, he can feel free to take no action at all, since
his overall loss is limited. If the stock should rally upward later, he will still be in a
position to make his maximum profit.

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Chapter 17: Put Buying in Conjundion with Common Stock Ownership
TABLE 17·2.
Comparison of regular and protected covered writes.
XYZ Price at Stock October 40 October 35
Expiration Profit Call Profit Put Profit
25 -$1,400 +$300 +$950
30 900 + 300 + 450
35 400 + 300 - 50
36.50 250 + 300 - 50
38 100 + 300 - 50
40 + 100 + 300 - 50
45 + 600 - 200 - 50
50 + 1,100 - 700 - 50
FIGURE 17-2.
Covered call write protected by a put purchase.
C
0
e ·5.
X
LU
co $0 CJ)
CJ)
0 .J
0
~ -$150 a..
,,
},.,,'
;
,,
Regular
Covered ,,'
Write/
36 / , ,
;
,,'
+$400
,----------➔ ,,,' _____ ...,..
, +$350
,,,'
40
Stock Price at Expiration
277
Total
Profit
-$150
- 150
- 150
0
+ 150
+ 350
+ 350
+ 350
The longer-term effects of buying puts in combination with covered writes are
not easily definable, but it would appear that the writer reduces his overall rate of
return slightly by buying the puts. This is because he gives something away if the
stock falls slightly, remains unchanged, or rises in price. He only "gains" something if
the stock falls heavily. Since the odds of a stock falling heavily are small in compari
son to the other events (falling slightly, remaining unchanged, or rising), the writer
will be gaining something in only a small percentage of cases. However, the put buy
ing strategy may still prove useful in that it removes the emotional uncertainty of

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CH.APTER 19
The Sale of a Put
The buyer of a put stands to profit if the underlying stock drops in price. As might
then be expected, the seller of a put will make money if the underlying stock increas
es in price. The uncovered sale of a put is a more common strategy than the covered
sale of a put, and is therefore described first. It is a bullishly-oriented strategy.
THE UNCOVERED PUT SALE
Since the buyer of a put has a right to sell stock at the striking price, the writer of a
put is obligating himself to buy that stock at the striking price. For assuming this obli
gation, he receives the put option premium. If the underlying stock advances and the
put expires worthless, the put writer will not be assigned and he could make a maxi
mum profit equal to the premium received. He has large downside risk, since the
stock could fall substantially, thereby increasing the value of the written put and caus
ing large losses to occur. An example will aid in explaining these general statements
about risk and reward.
Example: XYZ is at 50 and a 6-month put is selling for 4 points. The naked put writer
has a fixed potential profit to the upside - $400 in this example and a large poten
tial loss to the downside (Table 19-1 and Figure 19-1). This downside loss is limited
only by the fact that a stock cannot go below zero.
The collateral requirement for writing naked puts is the same as that for writ
ing naked calls. The requirement is equal to 20% of the current stock price plus the
put premium minus any out-of-the-money amount.
Example: If XYZ is at 50, the collateral requirement for writing a 4-point put with a
striking price of 50 would be $1,000 (20% of 5,000) plus $400 for the put premium
292

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Cl,opter 19: The Sale of a Put
TABLE 19-1.
Results from the sale of an uncovered put.
XYZ Price at Put Price at
Expiration Expiration (Parity)
30 20
40 10
46 4
50 0
60 0
70 0
f IGURE 19-1.
Uncovered sale of a put.
$400
C
0
~ ·5.
X
w
'lii
(/l $0 (/l
.3 50
0
~ a.
Stock Price at Expiration
293
Put Sale
Profit
-$1,600
600
0
+ 400
+ 400
+ 400
for a total of $1,400. If the stock were above the striking price, the striking price dif
forential would be subtracted from the requirement. The minimum requirement is
I 0% of the put' s striking price, plus the put premium, even if the computation above
yields a smaller result.
The uncovered put writing strategy is similar in many ways to the covered call
writing strategy. Note that the profit graphs have the same shape; this means that the
two strategies are equivalent. It may be helpful to the reader to describe the aspects
of naked put writing by comparing them to similar aspects of covered call writing.

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294 Part Ill: Put Option Strategies
In either strategy, one needs to be somewhat bullish, or at least neutral, on the
underlying stock. If the underlying stock moves upward, the uncovered put writer
will make a profit, possibly the entire amount of the premium received. If the under
lying stock should be unchanged at expiration - a neutral situation - the put writer
will profit by the amount of the time value premium received when he initially wrote
the put. This could represent the maximum profit if the put was out-of-the-money
initially, since that would mean that the entire put premium was composed of time
value premium. For an in-the-money put, however, the time value premium would
represent something less than the entire value of the option. These are similar qual
ities to those inherent in covered call writing. If the stock moves up, the covered call
writer can make his maximum profit. However, if the stock is unchanged at expira
tion, he will make his maximum profit only if the stock is above the call's striking
price. So, in either strategy, if the position is established with the stock above the
striking price, there is a greater probability of achieving the maximum profit. This
represents the less aggressive application: writing an out-of-the-money put initially,
which is equivalent to the covered write of an in-the-money call.
The more aggressive application of naked put writing is to write an in-the
money put initially. The writer will receive a larger amount of premium dollars for
the in-the-money put and, if the underlying stock advances far enough, he will thus
make a large profit. By increasing his profit potential in this manner, he assumes
more risk. If the underlying stock should fall, the in-the-money put writer will lose
money more quickly than one who initially wrote an out-of-the-money put. Again,
these facts were demonstrated much earlier with covered call writing. An in-the
money covered call write affords more downside protection but less profit potential
than does an out-of-the-money covered call write.
It is fairly easy to summarize all of this by noting that in either the naked put
writing strategy or the covered call writing strategy, a less aggressive position is estab
lished when the stock is higher than the striking price of the written option. If the
stock is below the striking price initially, a more aggressive position is created.
There are, of course, some basic differences between covered call writing and
naked put writing. First, the naked put write will generally require a smaller invest
ment, since one is only collateralizing 20% of the stock price plus the put premium,
as opposed to 50% for the covered call write on margin. Also, the naked put writer is
not actually investing cash; collateral is used, so he may finance his naked put writing
through the value of his present portfolio, whether it be stocks, bonds, or government
securities. However, any losses would create a debit and might therefore cause him
to disturb a portion of this portfolio. It should be pointed out that one can, ifhe wish
es, write naked puts in a cash account by depositing cash or cash equivalents equal to
the striking price of the put. This is called "cash-based put writing." The covered call

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O.,,ter 19: The Sale of a Put 295
writer receives the dividends on the underlying stock, but the naked put writer does
not. In certain cases, this may be a substantial amount, but it should also be pointed
out that the puts on a high-yielding stock will have more value and the naked put
writer will thus be taking in a higher premium initially. From strictly a rate of return
viewpoint, naked put writing is superior to covered call writing. Basically, there is a
different psychology involved in writing naked puts than that required for covered call
writing. The covered call write is a comfortable strategy for most investors, since it
involves common stock ownership. Writing naked options, however, is a more foreign
concept to the average investor, even if the strategies are equivalent. Therefore, it is
relatively unlikely that the same investor would be a participant in both strategies.
FOLLOW-UP ACTION
The naked put writer would take protective follow-up action if the underlying stock
drops in price. His simplest form of follow-up action is to close the position at a small
loss if the stock drops. Since in-the-money puts tend to lose time value premium rap
idly, he may find that his loss is often quite small if the stock goes against him. In the
example above, XYZ was at 50 with the put at 4. If the stock falls to 45, the writer
may be able to quite easily repurchase the put for 5½ or 6 points, thereby incurring
a fairly small loss.
In the covered call writing strategy, it was recommended that the strategist roll
down wherever possible. One reason for doing so, rather than closing the covered call
position, is that stock commissions are quite large and one cannot generally afford to
be moving in and out of stocks all the time. It is more advantageous to try to preserve
the stock position and roll the calls down. This commission disadvantage does not
exist with naked put writing. When one closes the naked put position, he merely buys
in the put. Therefore, rolling down is not as advantageous for the naked put writer.
For example, in the paragraph above, the put writer buys in the put for 5½ or 6
points. He could roll down by selling a put with striking price 45 at that time.
However, there may be better put writing situations in other stocks, and there should
be no reason for him to continue to preserve a position in XYZ stock
In fact, this same reasoning can be applied to any sort of rolling action for the
naked put writer. It is extremely advantageous for the covered call writer to roll for
ward; that is, to buy back the call when it has little or no time value premium remain
ing in it and sell a longer-term call at the same striking price. By doing so, he takes in
additional premium without having to disturb his stock position at all. However, the
naked put writer has little advantage in rolling forward. He can also take in addition
al premium, but when he closes the initial uncovered put, he should then evaluate

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296 Part Ill: Put Option Strategies
other available put writing positions before deciding to write another put on the sam<'
underlying stock. His commission costs are the same if he remains in XYZ stock or if
he goes on to a put writing position in a different stock.
EVALUATING A NAKED PUT WRITE
The computation of potential returns from a naked put write is not as straightforward
as were the computations for covered call writing. The reason for this is that the col
lateral requirement changes as the stock moves up or down, since any naked option
position is marked to the market. The most conservative approach is to allow enough
collateral in the position in case the underlying stock should fall, thus increasing the
requirement. In this way, the naked put writer would not be forced to prematurely
close a position because he cannot maintain the margin required.
Example: XYZ is at 50 and the October 50 put is selling for 4 points. The initial col
lateral requirement is 20% of 50 plus $400, or $1,400. There is no additional require
ment, since the stock is exactly at the striking price of the put. Furthermore, let us
assume that the writer is going to close the position should the underlying stock fall
to 43. To maintain his put write, he should therefore allow enough margin to collat
eralize the position if the stock were at 43. The requirement at that stock price would
be $1,560 (20% of 43 plus at least 7 points for the in-the-money amount). Thus, the
put writer who is establishing this position should allow $1,560 of collateral value for
each put written. Of course, this collateral requirement can be reduced by the
amount of the proceeds received from the put sale, $400 per put less commissions in
this example. If we assume that the writer sells 5 puts, his gross premium inflow
would be $2,000 and his commission expense would be about $75, for a net premi
um of $1,925.
Once this information has been determined, it is a simple matter to determine
the maximum potential return and also the downside break-even point. To achieve
the maximum potential return, the put would expire worthless with the underlying
stock above the striking price. Therefore, the maximum potential profit is equal to
the net premium received. The return is merely that profit divided by the collateral
used. In the example above, the maximum potential profit is $1,925. The collateral
required is $1,560 per put (allowing for the stock to drop to 43) or $7,800 for 5 puts,
reduced by the $1,925 premium received, for a total requirement of $5,875. The
potential return is then $1,925 divided by $5,875, or 32.8%. Table 19-2 summarizes
these calculations.

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CHAPTER 20
The Sale of a Straddle
Selling a straddle involves selling both a put and a call with the same terms. As with
any type of option sale, the straddle sale may be either covered or uncovered. Both
uses are fairly common. The covered sale of a straddle is very similar to the covered
call writing strategy and would generally appeal to the same type of investor. The
uncovered straddle write is more similar to ratio call writing, and is attractive to the
more aggressive strategist who is interested in selling large amounts of time premi
um in hopes of collecting larger profits if the underlying stock remains fairly stable.
THE COVERED STRADDLE WRITE
In this strategy, one owns the underlying stock and simultaneously writes a straddle
on that stock. This may be particularly appealing to investors who are already
involved in covered call writing. In reality, this position is not totally covered - only
the sale of the call is covered by the ownership of the stock. The sale of the put is
uncovered. However, the name "covered straddle" is generally used for this type of
position in order to distinguish it from the uncovered straddle write.
Example: XYZ is at 51 and an XYZ January 50 call is selling for 5 points while an XYZ
January 50 put is selling for 4 points. A covered straddle write would be established
by buying 100 shares of the underlying stock and simultaneously selling one put and
one call. The similarity between this position and a covered call writer's position
should be obvious. The covered straddle write is actually a covered write - long 100
shares of XYZ plus short one call - coupled with a naked put write. Since the naked
put write has already been shown to be equivalent to a covered call write, this posi
tion is quite similar to a 200-share covered call write. In fact, all the profit and loss
302

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er 20: The Sale of a Straddle 303
aracteristics of a covered call write are the same for the covered straddle write.
There is limited upside profit potential and potentially large downside risk.
Readers will remember that the sale of a naked put is equivalent to a covered
call write. Hence, a covered straddle write can be thought of either as the equivalent
of a 200-share covered call write, or as the sale of two uncovered puts. In fact, there
•• some merit to the strategy of selling two puts instead of establishing a covered
straddle write. Commission costs would be smaller in that case, and so would the ini
tial investment required (although the introduction of leverage is not always a good
tlting).
The maximum profit is attained if XYZ is anywhere above the striking price of
50 at expiration. The amount of maximum profit in this example is $800: the premi
um received from selling the straddle, less the 1-point loss on the stock if it is called
11way at 50. In fact, the maximum profit potential of a covered straddle write is quick
ly computed using the following formula:
Maximum profit = Straddle premium + Striking price - Initial stock price
The break-even point in this example is 46. Note that the covered writing por
tion of this example buying stock at 51 and selling a call for 5 points - has a break
even point of 46. The naked put portion of the position has a break-even point of 46
as well, since the January 50 put was sold for 4 points. Therefore, the combined posi
tion - the covered straddle write - must have a break-even point of 46. Again, this
observation is easily defined by an equation:
B ak . Stock price + Strike price - Straddle premium re -even pnce =
2
Table 20-1 and Figure 20-1 compare the covered straddle write to a 100-share cov
ered call write of the XYZ January 50 at expiration.
The attraction for the covered call writer to become a covered straddle writer is
that he may be able to increase his return without substantially altering the parame
ters of his covered call writing position. Using the prices in Table 20-1, if one had
decided to establish a covered write by buying XYZ at 51 and selling the January 50
call at 5 points, he would have a position with its maximum potential return anywhere
above 50 and with a break-even point of 46. By adding the naked put to his covered
call position, he does not change the price parameters of his position; he still makes
his maximum profit anywhere above 50 and he still has a break-even point of 46.
Therefore, he does not have to change his outlook on the underlying stock in order
to become a covered straddle writer.
The investment is increased by the addition of the naked put, as are the poten
tial dollars of profit if the stock is above 50 and the potential dollars of loss if the stock

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304 Part Ill: Put Option Strategies
TABLE 20-1.
Results at expiration of covered straddle write.
Stock (A) 100-Shore (8) Put
Price Covered Write Write
35
40
46
50
60
FIGURE 20-1.
-$1, 100
600
0
+ 400
+ 400
Covered straddle write.
+$800
§ +$400
e ·5.
~
al
en $0 en 0 ...J
c5
e a. ~,
,,' ,, ,,
,, ,,
,, ,,
,,
-$1, 100
600
0
+ 400
+ 400
100-Share Covered
Call Write
~-----------------►
, 46 50
Stock Price at Expiration
Covered Straddle
Write (A+ 8)
-$2,200
- 1,200
0
+ 800
+ 800
is below 46 at expiration. The covered straddle writer loses money twice as fast on
the downside, since his position is similar to a 200-share covered write. Because the
commissions are smaller for the naked put write than for the covered call write, the
covered call writer who adds a naked put to his position will generally increase his
return somewhat.
Follow-up action can be implemented in much the same way it would be for a
covered call write. Whenever one would normally roll his call in a covered situation,

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t,r 20: The Sale ol a Straddle 305
now rolls the entire straddle - rolling down for protection, rolling up for an
ease in profit potential, and rolling forward when the time value premium of the
die dissipates. Rolling up or down would probably involve debits, unless one
led to a longer maturity.
Some writers might prefer to make a slight adjustment to the covered straddle
ting strategy. Instead of selling the put and call at the same price, they prefer to
ell an out-of-the-money put against the covered call write. That is, if one is buying
XYZ at 50 and selling the call, he might then also sell a put at 45. This would increase
his upside profit potential and would allow for the possibility of both options expir
ing worthless if XYZ were anywhere between 45 and 50 at expiration. Such action
would, of course, increase the potential dollars of risk if XYZ fell below 45 by expira
tion, but the writer could always roll the call down to obtain additional downside pro
tection.
One final point should be made with regard to this strategy. The covered call
writer who is writing on margin and is fully utilizing his borrowing power for call writ
ing will have to add additional collateral in order to write covered straddles. This is
because the put write is uncovered. However, the covered call writer who is operat
ing on a cash basis can switch to the covered straddle writing strategy without put
ting up additional funds. He merely needs to move his stock to a margin account and
use the collateral value of the stock he already owns in order to sell the puts neces
sary to implement the covered straddle writes.
THE UNCOVERED STRADDLE WRITE
In an uncovered straddle write, one sells the straddle without owning the underlying
stock. In broad terms, this is a neutral strategy with limited profit potential and large
risk potential. However, the probability of making a profit is generally quite large,
and methods can be implemented to reduce the risks of the strategy.
Since one is selling both a put and a call in this strategy, he is initially taking in
large amounts of time value premium. If the underlying stock is relatively unchanged
at expiration, the straddle writer will be able to buy the straddle back for its intrinsic
value, which would normally leave him with a profit.
Example: The following prices exist:
XYZ common, 45;
XYZ January 45 call, 4; and
XYZ January 45 put, 3.

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306 Part Ill: Put Option Strategies
A straddle could be sold for 7 points. If the stock were above 38 and below 52 at expi
ration, the straddle writer would profit, since the in-the-money option could ht·
bought back for less than 7 points in that case, while the out-of-the-money option
expires worthless (Table 20-2).
TABLE 20-2.
The naked straddle write.
XYZ Price at Call Put Total
Expiration Profit Profit Profit
30 +$ 400 -$1,200 -$800
35 + 400 700 - 300
38 + 400 400 0
40 + 400 200 + 200
45 + 400 + 300 + 700
50 100 + 300 + 200
52 300 + 300 0
55 600 + 300 - 300
60 - 1,100 + 300 - 800
Notice that Figure 20-2 has a shape like a roof. The maximum potential profit
point is at the striking price at expiration, and large potential losses exist in either
direction if the underlying stock should move too far. The reader may recall that the
ratio call writing strategy - buying 100 shares of the underlying stock and selling two
calls - has the same profit graph. These two strategies, the naked straddle write and
the ratio call write, are equivalent. The two strategies do have some differences, of
course, as do all equivalent strategies; but they are similar in that both are highly
probabilistic strategies that can be somewhat complex. In addition, both have large
potential risks under adverse market conditions or if follow-up strategies are not
applied.
The investment required for a naked straddle is the greater of the requirement
on the call or the put. In general, this means that the margin requirement is equal to
the requirement for the in-the-money option in a simple naked write. This require
ment is 20% of the stock price plus the in-the-money option premium. The straddle
writer should allow enough collateral so that he can take whatever follow-up actions
he deems necessary without having to incur a margin call. If he is intending to close
out the straddle if the stock should reach the upside break-even point - 52 in the
example above - then he should allow enough collateral to finance the position with

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ler 20: The Sale of a Straddle
GURE 20-2.
ked straddle sale.
307
Stock Price at Expiration
the stock at 52. If, however, he is planning to take other action that might involve
staying with the position if the stock goes to 55 or 56, he should allow enough collat
eral to be able to finance that action. If the stock never gets that high, he will have
excess collateral while the position is in place.
SELECTING A STRADDLE WRITE
Ideally, one would like to receive a premium for the straddle write that produces a
profit range that is wide in relation to the volatility of the underlying stock. In the
example above, the profit range is 38 to 52. This may or may not be extraordinarily
wide, depending on the volatility of XYZ. This is a somewhat subjective measure
ment, although one could construct a simple straddle writer's index that ranked strad
dles based on the following simple formula:
I d Straddle time value premium n ex= _______ ..._ ___ _
Stock price x Volatility
Refinements would have to be made to such a ranking, such as eliminating cases in
which either the put or the call sells for less than ¼ point ( or even 1 point, if a more
restrictive requirement is desired) or cases in which the in-the-money time premium
is small. Furthermore, the index would have to be annualized to be able to compare
straddles for different expiration months. More advanced selection criteria, in the

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308 Part Ill: Put Option Strategies
form of an expected return analysis, will be presented in Chapter 28 on mathemati
cal applications.
More screens can be added to produce a more conservative list of straddl<'
writes. For example, one might want to ignore any straddles that are not worth at
least a fixed percentage, say 10%, of the underlying stock price. Also, straddles that
are too short-term, such as ones with less than 30 days of life remaining, might b<'
thrown out as well. The remaining list of straddle writing candidates should be ones
that will provide reasonable returns under favorable conditions, and also should be
readily adaptable to some of the follow-up strategies discussed later. Finally, one
would generally like to have some amount of technical support at or above the lower
break-even price and some technical resistance at or below the upper break-even
point. Thus, once the computer has generated a list of straddles ranked by an index
such as the one listed above, the straddle writer can further pare down the list by
looking at the technical pictures of the underlying stocks.
FOLLOW-UP ACTION
The risks involved in straddle writing can be quite large. When market conditions are
favorable, one can make considerable profits, even with restrictive selection require
ments, and even by allowing considerable extra collateral for adverse stock move
ments. However, in an extremely volatile market, especially a bullish one, losses can
occur rapidly and follow-up action must be taken. Since the time premium of a put
tends to shrink when it goes into-the-money, there is actually slightly less risk to the
downside than there is to the upside. In an extremely bullish market, the time value
premiums of call options will not shrink much at all and might even expand. This may
force the straddle writer to pay excessive amounts of time value premium to buy back
the written straddle, especially if the movement occurs well in advance of expiration.
The simplest form of follow-up action is to buy the straddle back when and if the
underlying stock reaches a break-even point. The idea behind doing so is to limit the
losses to a small amount, because the straddle should be selling for only slightly more
than its original value when the stock has reached a break-even point. In practice,
there are several flaws in this theory. If the underlying stock arrives at a break-even
point well in advance of expiration, the amount of time value premium remaining in
the straddle may be extremely large and the writer will be losing a fairly large amount
by repurchasing the straddle. Thus, a break-even point at expiration is probably a loss
point prior to expiration.
Example: After the straddle is established with the stock at 45, there is a sudden rally
in the stock and it climbs quickly to 52. The call might be selling for 9 points, even

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20: The Sale of a Straddle 309
gh it is 7 points in-the-money. This is not unusual in a bullish situation.
ver, the put might be worth 1 ½points.This is also not unusual, as out-of-the
y puts with a large amount of time remaining tend to hold time value premium
well. Thus, the straddle writer would have to pay 10½ points to buy back this
dle, even though it is at the break-even point, 7 points in-the-money on the call
This example is included merely to demonstrate that it is a misconception to
ieve that one can always buy the straddle back at the break-even point and hold
losses to mere fractions of a point by doing so. This type of buy-back strategy
ks best when there is little time remaining in the straddle. In that case, the
options will indeed be close to parity and the straddle will be able to be bought back
for close to its initial value when the stock reaches the break-even point.
Another follow-up strategy that can be employed, similar to the previous one
but with certain improvements, is to buy back only the in-the-money option when it
reaches a price equal to that of the initial straddle price.
~mple: Again using the same situation, suppose that when XYZ began to climb
heavily, the call was worth 7 points when the stock reached 50. The in-the-money
option the call - is now worth an amount equal to the initial straddle value. It could
then be bought back, leaving the out-of-the-money put naked. As long as the stock
then remained above 45, the put would expire worthless. In practice, the put could
be bought back for a small fraction after enough time had passed or if the underly
Ing stock continued to climb in price.
This type of follow-up action does not depend on taking action at a fixed stock
price, but rather is triggered by the option price itself. It is therefore a dynamic sort
of follow-up action, one in which the same action could be applied at various stock
prices, depending on the amount of time remaining until expiration. One of the prob
lems with closing the straddle at the break-even points is that the break-even point is
C)nly a valid break-even point at expiration. A long time before expiration, this stock
price will not represent much of a break-even point, as was pointed out in the last
example. Thus, buying back only the in-the-money option at a fixed price may often
be a superior strategy. The drawback is that one does not release much collateral by
buying back the in-the-money option, and he is therefore stuck in a position with
little potential profit for what could amount to a considerable length of time. The
collateral released amounts to the in-the-money amount; the writer still needs to
C.'Ollateralize 20% of the stock price.
One could adjust this follow-up method to attempt to retain some profit. For
example, he might decide to buy the in-the-money option when it has reached a

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