O.,,ter 18: Buying Puts in Conjunction with Call Purchases 289
there are some differences, as the following discussion will demonstrate. Suppose the
following prices exist:
XYZ common, 47;
XYZ January 45 put, 2; and
XYZ January 50 call, 2.
In this example, both options are out-of-the-money when purchased. This, again, is
the most normal application of the strangle purchase. If XYZ is still between 45 and
50 at January expiration, both options will expire worthless and the strangle buyer
will lose his entire investment. This investment - $400 in the example - is generally
smaller than that required to buy astraddle on XYZ. If XYZ moves in either direc
tion, rising above 50 or falling below 45, the strangle will have some value at expira
tion. In this example, ifXYZ is above 54 at expiration, the call will be worth more than
4 points (the put will expire worthless) and the buyer will make aprofit. In asimilar
manner, if XYZ is below 41 at expiration, the put will have avalue greater than 4
points and the buyer would make aprofit in that case as well. The potential profits
are quite large if the underlying stock should nwve agreat deal before the options
expire. Table 18-2 and Figure 18-2 depict the potential profits or losses from this
position at January expiration. The maximum loss is possible over amuch wider range
than that of astraddle. The straddle achieves its maximum loss only if the stock is
exactly at the striking price of the options at expiration. However, the strangle has its
maximum loss anywhere between the two strikes at expiration. The actual amount of
the loss is smaller for the strangle, and that is acompensating factor. The potential
profits are large for both strategies.
The example above is one in which both options are out-of-the money. It is also
possible to construct avery similar position by utilizing in-the-money options.
Example: With XYZ at 47 as before, the in-the-money options might have the fol
lowing prices: XYZ January 45 call, 4; and XYZ January 50 put, 4. If one purchased
this in-the-rrwney strangle, he would pay atotal cost of 8 points. However, the value
of this strangle will always be at least 5 points, since the striking price of the put is 5
points higher than that of the call. The reader has seen this sort of position before,
when protective follow-up strategies for straddle buying and for call or put buying
were described. Because the strangle will always be worth at least 5 points, the most
that the in-the-money strangle buyer can lose is 3 points in this example. His poten
tial profits are still unlimited should the underlying stock move alarge distance.
Thus, even though it requires alarger initial investment, the in-the-rrwney strangle
may often be asuperior strategy to the out-of the-rrwney strangle, from abuyer's

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290
TABLE 18-2.
Results at expiration of astrangle purchase.
XYZ Price at
Expiration
25
35
41
43
45
47
50
54
60
70
FIGURE 18-2.
Strangle purchase.
C:
0
~ ·c.
Xw
1ii
(/) $0 (/)
0
..J
6
il= -$400 ea.
Put Call
Profit Profit
+$1,800 -$ 200
+ 800 200
+ 200 200
0 200
200 200
200 200
200 200
200 + 200
200 + 800
200 + 1,800
Stock Price at Expiration
Part Ill: Put Option Strategies
Total
Profit
+$1,600
+ 600
0
200
400
400
400
0
+ 600
+ 1,600
viewpoint. The in-the-money strangle purchase certainly involves less percentage
risk: The buyer can never lose all his investment, since he can always get back 5
points, even in the worst case (when XYZ is behveen 45 and 50 at expiration). His
percentage profits are lower with the in-the-money strangle purchase, since he paid
more for the strangle to begin with. These observations should come as no surprise,

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\O.,ter 18: Buying Puts in Conjunction with Call Purchases 291
since when the outright purchase of acall was discussed, it was shown that the
purchase of an in-the-money call was more conservative than the purchase of an out
of-the-money call, in general. The same was true for the outright purchase of puts,
perhaps even more so, because of the smaller time value of an in-the-money put.
Therefore, the strangle created by the two an in-the-money call and an in-the
money put - should be more conservative than the out-of-the-money strangle.
If the underlying stock moves quickly in either direction, the strangle buyer
may sometimes be able to take action to protect some of his profits. He would do so
in amanner similar to that described for the straddle buyer. For example, if the stock
moved up quickly, he could sell the put that he originally bought and buy the put at
the next higher striking price in its place. If he had started from an out-of-the-money
strangle position, this would then place him in astraddle. The strategist should not
blindly take this sort of follow-up action, however. It may be overly expensive to "roll
up" the put in such amanner, depending on the amount of time that has passed and
the actual option prices involved. Therefore, it is best to analyze each situation on acase-by-case basis to see whether it is logical to take any follow-up action at all.
As afinal point, the out-of-the-money strangles may appear deceptively cheap,
both options selling for fractions of apoint as expiration nears. However, the proba
bility of realizing the maximum loss equal to one'sinitial investment is fairly large
with strangles. This is distinctly different from straddle purchases, whereby the prob
ability of losing the entire investment is small. The aggressive speculator should not
place alarge portion of his funds in out-of-the-money strangle purchases. The per
centage risk is smaller with the in-the-money strangle, being equal to the amount of
time value premium paid for the options initially, but commission costs will be some
what larger. In either case, the underlying stock still needs to move by arelatively
large amount in order for the buyer to profit.

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CH.APTER 19
The Sale of a Put
The buyer of aput stands to profit if the underlying stock drops in price. As might
then be expected, the seller of aput will make money if the underlying stock increas
es in price. The uncovered sale of aput is amore common strategy than the covered
sale of aput, and is therefore described first. It is abullishly-oriented strategy.
THE UNCOVERED PUT SALE
Since the buyer of aput has aright to sell stock at the striking price, the writer of aput 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 amaxi
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 afixed potential profit to the upside - $400 in this example and alarge poten
tial loss to the downside (Table 19-1 and Figure 19-1). This downside loss is limited
only by the fact that astock 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 astriking 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 aput.
$400
C
0
~ ·5.
Xw
'lii
(/l $0 (/l
.3 50
0
~ a.
Stock Price at Expiration
293
Put Sale
Profit
-$1,600
600
0
+ 400
+ 400
+ 400
for atotal 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' sstriking price, plus the put premium, even if the computation above
yields asmaller 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 aprofit, possibly the entire amount of the premium received. If the under
lying stock should be unchanged at expiration - aneutral 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'sstriking
price. So, in either strategy, if the position is established with the stock above the
striking price, there is agreater 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 alarger amount of premium dollars for
the in-the-money put and, if the underlying stock advances far enough, he will thus
make alarge 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, aless 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, amore 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 asmaller 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 adebit and might therefore cause him
to disturb aportion of this portfolio. It should be pointed out that one can, ifhe wish
es, write naked puts in acash 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 asubstantial amount, but it should also be pointed
out that the puts on ahigh-yielding stock will have more value and the naked put
writer will thus be taking in ahigher premium initially. From strictly arate of return
viewpoint, naked put writing is superior to covered call writing. Basically, there is adifferent psychology involved in writing naked puts than that required for covered call
writing. The covered call write is acomfortable strategy for most investors, since it
involves common stock ownership. Writing naked options, however, is amore foreign
concept to the average investor, even if the strategies are equivalent. Therefore, it is
relatively unlikely that the same investor would be aparticipant 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 asmall
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
afairly 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 aput 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 aposition 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 alonger-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 aput writing position in adifferent stock.
EVALUATING A NAKED PUT WRITE
The computation of potential returns from anaked 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 aposition 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 anet premi
um of $1,925.
Once this information has been determined, it is asimple 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 atotal 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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t,r 19: The Sale of a Put
ILE 19-2.
297
lculation of the potential return of uncovered put writing.
50
4
less commissions
Potential maximum profit (premium received)
Striking price
Less premium per put ($1,925/5)
Break-even stock price
Collateral required (allowing for stock to drop to 43):
20% of 43
Plus put premium
Requirement for 5 puts
Less premium received
Net collateral
Potential return:
Premium divided by net collateral
$2,000
75
$1,925
$50.00
3.85
46.15
$ 860
+ 700
$1,560
X 5
$7,800
- 1,925
$5,875
$1,925/$5,875 = 32.8%
There are differences of opinion on how to compute the potential returns from
naked put writing. The method presented above is amore conservative one in that it
takes into consideration alarger collateral requirement than the initial requirement.
Of course, since one is not really investing cash, but is merely using the collateral
value of his present portfolio, it may even be correct to claim that one has no invest
ment at all in such aposition. This may be true, but it would be impossible to com
pare various put writing opportunities without having areturn computation available.
One other important feature of return computations is the return if unchanged.
If the put is initially out-of-the-money, the return if unchanged is the same as the
maximum potential return. However, if the put is initially in-the-money, the compu
tation must take into consideration what the writer would have to pay to buy back the
put when it expires.

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298 Part Ill: Put Option Strategies
Example: XYZ is 48 and the XYZ January 50 put is selling for 5 points. The profit
that could be made if the stock were unchanged at expiration would be only 3 points,
less commissions, since the put would have to be repurchased for 2 points with XYZ
at 48 at expiration. Commissions for the buy-back should be included as well, to
make the computation as accurate as possible.
As was the case with covered call writing, one can create several rankings of
naked put writes. One list might be the highest potential returns. Another list could
be the put writes that provide the rrwst downside protection; that is, the ones that
have the least chance of losing money. Both lists need some screening applied to
them, however. When considering the maximum potential returns, one should take
care to ensure at least some room for downside movement.
Example: If XYZ were at 50, the XYZ January 100 put would be selling at 50 also and
would most assuredly have atremendously large maximum potential return.
However, there is no room for downside movement at all, and one would surely not
write such aput. One simple way of allowing for such cases would be to reject any
put that did not offer at least 5% downside protection. Alternatively, one could also
reject situations in which the return if unchanged is below 5%.
The other list, involving maximum downside protection, also must have some
screens applied to it.
Example: With XYZ at 70, the XYZ January 50 put would be selling for½ at most.
Thus, it is extremely unlikely that one would lose money in this situation; the stock
would have to fall 20 points for aloss to occur. However, there is practically nothing
to be made from this position, and one would most likely not ever write such adeeply
out-of-the-money put.
Aminimum acceptable level of return must accompany the items on this list of
put writes. For example, one might decide that the return would have to be at least
12% on an annualized basis in order for the put write to be on the list of positions
offering the most downside protection. Such arequirement would preclude an
extreme situation like that shown above. Once these screens have been applied, the
lists can then be ranked in anormal manner. The put writes offering the highest
returns would be at the top of the more aggressive list, and those offering the high
est percentage of downside protection would be at the top of the more conservative
list. In the strictest sense, amore advanced technique to incorporate the volatility of
the underlying stock should rightfully be employed. As mentioned previously, that
technique is presented in Chapter 28 on mathematical applications.

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19: The Sale of a Put 299
YING STOCK BELOW ITS MARKET PRICE
addition to viewing naked put writing as astrategy unto itself, as was the case in
previous discussion, some investors who actually want to acquire stock will often
te naked puts as well.
bmple: XYZ is a $60 stock and an investor feels it would be agood buy at 55. He
places an open buy order with alimit of 55. Three months later, XYZ has drifted
down to 57 but no lower. It then turns and rises heavily, but the buy limit was never
reached, and the investor misses out on the advance.
This hypothetical investor could have used anaked put to his advantage.
Suppose that when XYZ was originally at 60, this investor wrote anaked three-month
put for 5 points instead of placing an open buy limit order. Then, if XYZ is anywhere
below 60 at expiration, he will have stock put to him at 60. That is, he will have to buy
stock at 60. However, since he received 5 points for the put sale, his net cost for the
stock is 55. Thus, even ifXYZ is at 57 at expiration and has never been any lower, the
investor can still buy XYZ for anet cost of 55.
Of course, if XYZ rose right away and was above 60 at expiration, the put would
not be assigned and the investor would not own XYZ. However, he would still have
made $500 from selling the put, which is now worthless. The put writer thus assumes
amore active role in his investments by acting rather than waiting. He receives at
least some compensation for his efforts, even though he did not get to buy the stock.
If, instead of rising, XYZ fell considerably, say to 40 by expiration, the investor
would be forced to purchase stock at anet cost of 55, thereby giving himself an
immediate paper loss. He was, however, going to buy stock at 55 in any case, so the
put writer and the investor using abuy limit have the same result in this case. Critics
may point out that any buy order for common stock may be canceled if one'sopinion
changes about purchasing the stock. The put writer, of course, may do the same thing
by closing out his obligation through aclosing purchase of the put.
This technique is useful to many types of investors who are oriented toward
eventually owning the stock. Large portfolio managers as well as individual investors
may find the sale of puts useful for this purpose. It is amethod of attempting to accu
mulate astock position at prices lower than today'smarket price. If the stock rises
and the stock is not bought, the investor will at least have received the put premium
as compensation for his efforts.
SOME CAUTION IS REQUIRED
Despite the seemingly benign nature of naked put writing, it can be ahighly dan
gerous strategy for two reasons: (1) Large losses are possible if the underlying stock

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300 Part Ill: Put Option Strategies
takes anasty fall, and (2) collateral requirements are small, so it is possible to utilize
agreat deal of leverage. It may seem like agood idea to write out-of-the-money puts
on "quality" stocks that you "wouldn'tmind owning." However, any stock is subject
to acrushing decline. In almost any year there are serious declines in one or more of
the largest stocks in America (IBM in 1991, Procter and Gamble in 1999, and Xerox
in 1999, just to name afew). If one happens to be short puts on such stocks - and
worse yet, ifhe happens to have overextended himself because he had the initial mar
gin required to sell agreat deal of puts - then he could actually be wiped out on such
adecline. Therefore, do not leverage your account heavily in the naked put strategy,
regardless of the "quality" of the underlying stock.
THE COVERED PUT SALE
By definition, aput sale is covered only if the investor also owns acorresponding put
with striking price equal to or greater than the strike of the written put. This is aspread. However,formargin purposes, one is covered ifhe sells aput and is also short
the underlying stock. The margin required is strictly that for the short sale of the
stock; there is none required for the short put. This creates aposition with limited
profit potential that is obtained if the underlying stock is anywhere below the strik
ing price of the put at expiration. There is unlimited upside risk, since if the under
lying stock rises, the short sale of stock will accrue losses, while the profit from the
put sale is limited. This is really aposition equivalent to anaked call write, except that
the covered put writer must pay out the dividend on the underlying stock, if one
exists. The naked sale of acall also has an advantage over this strategy in that com
mission costs are considerably smaller. In addition, the time value premium of acall
is generally higher than that of aput, so that the naked call writer is taking in more
time premium. The covered put sale is alittle-used strategy that appears to be infe
rior to naked call writing. As aresult, the strategy is not described more fully.
RATIO PUT WRITING
Aratio put write involves the short sale of the underlying stock plus the sale of 2 puts
for each 100 shares sold short. This strategy has aprofit graph exactly like that of aratio call write, achieving its maximum profit at the striking price of the written
options, and having large potential losses if the underlying stock should move too far
in either direction. The ratio call write is ahighly superior strategy, however, for the
reasons just outlined. The ratio call writer receives dividends while the ratio put

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CHAPTER 20
The Sale of a Straddle
Selling astraddle involves selling both aput and acall 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 astraddle 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 astraddle
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. Acovered 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 acovered call writer'sposition
should be obvious. The covered straddle write is actually acovered write - long 100
shares of XYZ plus short one call - coupled with anaked put write. Since the naked
put write has already been shown to be equivalent to acovered 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 acovered 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 anaked put is equivalent to acovered
call write. Hence, acovered 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 acovered
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 agood
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 acovered 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 acall for 5 points - has abreak
even point of 46. The naked put portion of the position has abreak-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 abreak-even point of 46. Again, this
observation is easily defined by an equation:
Bak . 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 acovered 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 acovered write by buying XYZ at 51 and selling the January 50
call at 5 points, he would have aposition with its maximum potential return anywhere
above 50 and with abreak-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 abreak-even point of 46.
Therefore, he does not have to change his outlook on the underlying stock in order
to become acovered 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 ...Jc5
ea. ~,
,,' ,, ,,
,, ,,
,, ,,
,,
-$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 anaked 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 acovered call write. Whenever one would normally roll his call in acovered 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 alonger maturity.
Some writers might prefer to make aslight 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 aput 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 acash basis can switch to the covered straddle writing strategy without put
ting up additional funds. He merely needs to move his stock to amargin 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 aneutral strategy with limited profit potential and large
risk potential. However, the probability of making aprofit is generally quite large,
and methods can be implemented to reduce the risks of the strategy.
Since one is selling both aput and acall 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 aprofit.
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
Astraddle 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 ashape like aroof. 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 anaked 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 asimple 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 amargin 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 apremium for the straddle write that produces aprofit 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 asomewhat subjective measure
ment, although one could construct asimple straddle writer'sindex that ranked strad
dles based on the following simple formula:
Id Straddle time value premium nex= _______ ..._ ___ _
Stock price x Volatility
Refinements would have to be made to such aranking, such as eliminating cases in
which either the put or the call sells for less than ¼ point ( or even 1 point, if amore
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 amore conservative list of straddl<'
writes. For example, one might want to ignore any straddles that are not worth at
least afixed 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 alist 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 abullish one, losses can
occur rapidly and follow-up action must be taken. Since the time premium of aput
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 abreak-even point. The idea behind doing so is to limit the
losses to asmall amount, because the straddle should be selling for only slightly more
than its original value when the stock has reached abreak-even point. In practice,
there are several flaws in this theory. If the underlying stock arrives at abreak-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 afairly large amount
by repurchasing the straddle. Thus, abreak-even point at expiration is probably aloss
point prior to expiration.
Example: After the straddle is established with the stock at 45, there is asudden 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 abullish situation.
ver, the put might be worth 1 ½points.This is also not unusual, as out-of-the
yputs with alarge 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 amisconception to
ieve that one can always buy the straddle back at the break-even point and hold
losses to mere fractions of apoint 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 aprice 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 asmall 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 afixed stock
price, but rather is triggered by the option price itself. It is therefore adynamic 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 avalid break-even point at expiration. Along time before expiration, this stock
price will not represent much of abreak-even point, as was pointed out in the last
example. Thus, buying back only the in-the-money option at afixed price may often
be asuperior 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 aposition with
little potential profit for what could amount to aconsiderable 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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310 Part Ill: Put Option Strategies
value that is 1 point less than the total straddle value initially taken in. This would
then allow him the chance to make a I-point profit overall, if the other option expired
worthless. In any case, there is always the risk that the stock would suddenly revers('
direction and cause aloss on the remaining option as well. This method of follow-up
action is akin to the ratio writing follow-up strategy of using buy and sell stops on th<'
underlying stock.
Before describing other types of follow-up action that are designed to combat
the problems described above, it might be worthwhile to address the method used in
ratio writing - rolling up or rolling down. In straddle writing, there is often little to
be gained from rolling up or rolling down. This is amuch more viable strategy in ratio
writing; one does not want to be constantly moving in and out of stock positions,
because of the commissions involved. Howeve1~ with straddle writing, once one posi
tion is closed, there is no need to pursue asimilar straddle in that same stock. It may
be more desirable to look elsewhere for anew straddle position.
There are two other very simple forms of follow-up action that one might con
sider using, although neither one is for most strategists. First, one might consider
doing nothing at all, even if the underlying stock moves by agreat deal, figuring that
the advantage lies in the probability that the stock will be back near the striking price
by the time the options expire. This action should be used only by the most diversi
fied and well-heeled investors, for in extreme market periods, almost all stocks may
move in unison, generating tremendous losses for anyone who does not take some
sort of action. Amore aggressive type off allow-up action would be to attempt to "leg
out" of the straddle, by buying in the profitable side and then hoping for astock price
reversal in order to buy back the remaining side. In the example above, when XYZ
ran up to 52, an aggressive trader would buy in the put at 1 ½, taking his profit, and
then hope for the stock to fall back in order to buy the call in cheaper. This is avery
aggressive type of follow-up action, because the stock could easily continue to rise in
price, thereby generating larger losses. This is atrader'ssort of action, not that of adisciplined strategist, and it should be avoided.
In essence, follow-up action should be designed to do two things: First, to limit
the risk in the position, and second, to still allow room for apotential profit to be
made. None of the above types of follow-up action accomplish both of these purpos
es. There is, however, afollow-up strategy that does allow the straddle writer to limit
his losses while still allowing for apotential profit.
Example: After the straddle was originally sold for 7 points when the stock was at 45,
the stock experiences arally and the following prices exist:
XYZ common, 50;
XYZ January 45 call, 7;

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Cl,opter 20: The Sale of a Straddle
XYZ January 45 put, l; and
XYZ January 50 call, 3.
311
The January 50 call price is included because it will be part of the follow-up strategy.
Notice that this straddle has aconsiderable amount of time value premium remain
Ing in it, and thus would be rather expensive to buy back at the current time.
Suppose, however, that the straddle writer does not touch the January 45 straddle
tliat he is short, but instead buys the January 50 call for protection to the upside.
Since this call costs 3 points, he will now have aposition with atotal credit of 4 points.
(The straddle was originally sold for 7 points credit and he is now spending 3 points
for the call at 50.) This action of buying acall at ahigher strike than the striking price
of the straddle has limited the potential loss to the upside, no matter how far the
stock might run up. If XYZ is anywhere above 50 at expiration, the put will expire
worthless and the writer will have to pay 5 points to close the call spread short
January 45, long January 50. This means that his maximum potential loss is 1 point
plus commissions if XYZ is anywhere above 50 at expiration.
In addition to being able to limit the upside loss, this type of follow-up action
still allows room for potential profits. If XYZ is anywhere between 41 and 49 at expi
ration - that is, less than 4 points away from the striking price of 45 - the writer will
he able to buy the straddle back for less than 4 points, thereby making aprofit.
Thus, the straddle writer has both limited his potential losses to the upside and
also allowed room for profit potential should the underlying stock fall back in price
toward the original striking price of 45. Only severe price reversal, with the stock
falling back below 40, would cause alarge loss to be taken. In fact, by the time the
stock could reverse its current strong upward momentum and fall all the way back to
40, asignificant amount of time should have passed, thereby allowing the writer to
purchase the straddle back with only arelatively small amount of time premium left
in it.
This follow-up strategy has an effect on the margin requirement of the position.
When the calls are bought as protection to the upside, the writer has, for margin
purposes, abearish spread in the calls and an uncovered put. The margin for this
position would normally be less than that required for the straddle that is 5 points
in-the-money.
Asecondary move is available in this strategy.
Example: The stock continues to climb over the short term and the out-of-the
money put drops to aprice of less than ½ point. The straddle writer might now
consider buying back the put, thereby leaving himself with abear spread in the
calls. His net credit left in the position, after buying back the put at ½, would be

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312 Part Ill: Put Optian Strategies
3½ points. Thus, if XYZ should reverse direction and be within 3½ points of the
striking price - that is, anywhere below 48½ - at expiration, the position will pro
duce aprofit. In fact, if XYZ should be below 45 at expiration, the entire bear
spread will expire worthless and the strategist will have made a 3½-point profit.
Finally, this repurchase of the put releases the margin requirement for the naked
put, and will generally free up excess funds so that anew straddle position can be
established in another stock while the low-requirement bear spread remains in
place.
In summary, this type of follow-up action is broader in purpose than any of the
simpler buy-back strategies described earlier. It will limit the writer'sloss, but not
prevent him from making aprofit. Moreover, he may be able to release enough mar
gin to be able to establish anew position in another stock by buying in the uncov
ered puts at afractional price. This would prevent him from tying up his money
completely while waiting for the original straddle to reach its expiration date. The
same type of strategy also works in adownward market. If the stock falls after the
straddle is written, one can buy the put at the next lower strike to limit the down
side risk, while still allowing for profit potential if the stock rises back to the striking
price.
EQUIVALENT STOCK POSITION FOLLOW-UP
Since there are so many follow-up strategies that can be used with the short straddle,
the one method that summarizes the situation best is again the equivalent stock posi
tion (ESP). Recall that the ESP of an option position is the multiple of the quantity
times the delta times the shares per option. The quantity is anegative number if it is
referring to ashort position. Using the above scenario, an example of the ESP
method follows:
Example: As before, assume that the straddle was originally sold for 7 points, but the
stock rallied. The following prices and deltas exist:
XYZ common, 50;
XYZ Jan 45 call, 7; delta, .90;
XYZ Jan 45 put, l; delta, - .10; and
XYZ Jan 50 call, 3; delta, .60.
Assume that 8 straddles were sold initially and that each option is for 100 shares of
XYZ. The ESP of these 8 short straddles can then be computed:

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Chapter 20: The Sale of a Straddle
Option
Jan 45 call
Jan 45 put
Total ESP
Position
short 8
short 8
Delta
0.90
-0.10
313
ESP
short 720 (-8 x . 9 x 1 00)
long 80 (-8 x -. 1 x 100)
short 640 shares
Obviously, the position is quite short. Unless the trader were extremely bearish
on XYZ, he should make an adjustment. The simplest adjustment would be to buy
600 shares of XYZ. Another possibility would be to buy back 7 of the short January
45 calls. Such apurchase would add adelta long of 630 shares to the position (7 x .9
x 100). This would leave the position essentially neutral. As pointed out in the previ
ous example, however, the strategist may not want to buy that option. If, instead, he
decided to try to buy the January 50 call to hedge the short straddle, he would have
to buy 10 of those to make the position neutral. He would buy that many because the
delta of that January 50 is 0.60; apurchase of 10 would add adelta long of 600 shares
to the position.
Even though the purchase of 10 is theoretically correct, since one is only short
8 straddles, he would probably buy only 8 January 50 calls as apractical matter.
STARTING OUT WITH THE PROTECTION IN PLACE
In certain cases, the straddle writer may be able to initially establish aposition that
has no risk in one direction: He can buy an out-of-the-money put or call at the same
time the straddle is written. This accomplishes the same purposes as the follow-up
action described in the last few paragraphs, but the protective option will cost less
since it is out-of-the-money when it is purchased. There are, of course, both positive
and negative aspects involved in adding an out-of-the-money long option to the strad
dle write at the outset.
Example: Given the following prices:
XYZ, 45;
XYZ January 45 straddle, 7; and
XYZ January 50 call, 1 ½,
the upside risk will be limited. If one writes the January 45 straddle for 7 points and
buys the January 50 call for 1 ½ points, his overall credit will be 5½ points. He has no
upside risk in this position, for if XYZ should rise and be over 50 at expiration, he will
be able to close the position by buying back the call spread for 5 points. The put will
expire worthless. The out-of-the-money call has eliminated any risk above 50 on the

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312 Part Ill: Put Option Strategies
3½ points. Thus, if XYZ should reverse direction and be within 3½ points of the
striking price - that is, anywhere below 48½ - at expiration, the position will pro
duce aprofit. In fact, if XYZ should be below 45 at expiration, the entire bear
spread will expire worthless and the strategist will have made a 3½-point profit.
Finally, this repurchase of the put releases the margin requirement for the naked
put, and will generally free up excess funds so that anew straddle position can be
established in another stock while the low-requirement bear spread remains in
place.
In summary, this type of follow-up action is broader in purpose than any of the
simpler buy-back strategies described earlier. It will limit the writer'sloss, but not
prevent him from making aprofit. Moreover, he may be able to release enough mar
gin to be able to establish anew position in another stock by buying in the uncov
ered puts at afractional price. This would prevent him from tying up his money
completely while waiting for the original straddle to reach its expiration date. The
same type of strategy also works in adownward market. If the stock falls after the
straddle is written, one can buy the put at the next lower strike to limit the down
side risk, while still allowing for profit potential if the stock rises back to the striking
price.
EQUIVALENT STOCK POSITION FOLLOW-UP
Since there are so many follow-up strategies that can be used with the short straddle,
the one method that summarizes the situation best is again the equivalent stock posi
tion (ESP). Recall that the ESP of an option position is the multiple of the quantity
times the delta times the shares per option. The quantity is anegative number if it is
referring to ashort position. Using the above scenario, an example of the ESP
method follows:
Example: As before, assume that the straddle was originally sold for 7 points, but the
stock rallied. The following prices and deltas exist:
XYZ common, 50;
XYZ Jan 45 call, 7; delta, .90;
XYZ Jan 45 put, l; delta, - .10; and
XYZ Jan 50 call, 3; delta, .60.
Assume that 8 straddles were sold initially and that each option is for 100 shares of
XYZ. The ESP of these 8 short straddles can then be computed:

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Chapter 20: The Sale of a Straddle
Option
Jan 45 call
Jan 45 put
Total ESP
Position
short 8
short 8
Delta
0.90
-0.10
313
ESP
short 720 (-8 x .9 x 100)
long 80 (-8 x -. 1 x 1 00)
short 640 shares
Obviously, the position is quite short. Unless the trader were extremely bearish
on XYZ, he should make an adjustment. The simplest adjustment would be to buy
600 shares of XYZ. Another possibility would be to buy back 7 of the short January
45 calls. Such apurchase would add adelta long of 630 shares to the position (7 x .9
x 100). This would leave the position essentially neutral. As pointed out in the previ
ous example, however, the strategist may not want to buy that option. If, instead, he
decided to try to buy the January 50 call to hedge the short straddle, he would have
to buy 10 of those to make the position neutral. He would buy that many because the
delta of that January 50 is 0.60; apurchase of 10 would add adelta long of 600 shares
to the position.
Even though the purchase of 10 is theoretically correct, since one is only short
8 straddles, he would probably buy only 8 January 50 calls as apractical matter.
STARTING OUT WITH THE PROTECTION IN PLACE
In certain cases, the straddle writer may be able to initially establish aposition that
has no risk in one direction: He can buy an out-of-the-money put or call at the same
time the straddle is written. This accomplishes the same purposes as the follow-up
action described in the last few paragraphs, but the protective option will cost less
since it is out-of-the-money when it is purchased. There are, of course, both positive
and negative aspects involved in adding an out-of-the-money long option to the strad
dle write at the outset.
Example: Given the following prices:
XYZ, 45;
XYZ January 45 straddle, 7; and
XYZ January 50 call, 1 ½,
the upside risk will be limited. If one writes the January 45 straddle for 7 points and
buys the January 50 call for 1 ½ points, his overall credit will be 5½ points. He has no
upside risk in this position, for if XYZ should rise and be over 50 at expiration, he will
be able to close the position by buying back the call spread for 5 points. The put will
expire worthless. The out-of-the-money call has eliminated any risk above 50 on the

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314 Part Ill: Put Option Strategies
position. Another advantage of buying the protection initially is that one is protected
if the stock should experience agap opening or atrading halt. Ifhe already owns the
protection, such stock price movement in the direction of the protection is of little
consequence. However, if he was planning to buy the protection as afollow-up
action, the sudden surge in the stock price may ruin his strategy.
The overall profit potential of this position is smaller than that of the normal
straddle write, since the premium paid for the long call will be lost if the stock is
below 50 at expiration. However, the automatic risk-limiting feature of the long call
may prove to be worth more than the decrease in profit potential. The strategist has
peace of mind in arally and does not have to worry about unlimited losses accruing
to the upside.
Downside protection for astraddle writer can be achieved in asimilar manner
by buying an out-of-the-money put at the outset.
Example: With XYZ at 45, one might write the January 45 straddle for 7 and buy a
January 40 put for Ipoint if he is concerned about the stock dropping in price.
It should now be fairly easy to see that the straddle writer could limit risk in
either direction by initially buying both an out-of-the-money call and an out-of-the
money put at the same time that the straddle is written. The major benefit in doing
this is that risk is limited in either direction. Moreover, the margin requirements are
significantly reduced, since the whole position consists of acall spread and aput
spread. There are no longer any naked options. The detriment of buying protection
on both sides initially is that commission costs increase and the overall profit poten
tial of the straddle write is reduced, perhaps significantly, by the cost of two long
options. Therefore, one must evaluate whether the cost of the protection is too large
in comparison to what is received for the straddle write. This completely protected
strategy can be very attractive when available, and it is described again in Chapter 23,
Spreads Combining Calls and Puts.
In summary, any strategy in which the straddle writer also decides to buy pro
tection presents both advantages and disadvantages. Obviously, the risk-limiting fea
ture of the purchased options is an advantage. However, the seller of options does not
like to purchase pure time value premium as protection at any time. He would gen
erally prefer to buy intrinsic value. The reader will note that, in each of the protec
tive buying strategies discussed above, the purchased option has alarge amount of
time value premium left in it. Therefore, the writer must often try to strike adelicate
balance between trying to limit his risk on one hand and trying to hold down the
expenses of buying long options on the other hand. In the final analysis, however, the
risk must be limited regardless of the cost.

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314 Part Ill: Put Option Strategies
position. Another advantage of buying the protection initially is that one is protected
if the stock should experience agap opening or atrading halt. If he already owns the
protection, such stock price movement in the direction of the protection is of little
consequence. However, if he was planning to buy the protection as afollow-up
action, the sudden surge in the stock price may ruin his strategy.
The overall profit potential of this position is smaller than that of the normal
straddle write, since the premium paid for the long call will be lost if the stock is
below 50 at expiration. However, the automatic risk-limiting feature of the long call
may prove to be worth more than the decrease in profit potential. The strategist has
peace of mind in arally and does not have to worry about unlimited losses accruing
to the upside.
Downside protection for astraddle writer can be achieved in asimilar manner
by buying an out-of-the-money put at the outset.
Example: With XYZ at 45, one might write the January 45 straddle for 7 and buy a
January 40 put for lpoint if he is concerned about the stock dropping in price.
It should now be fairly easy to see that the straddle writer could limit risk in
either direction by initially buying both an out-of-the-money call and an out-of-the
money put at the same time that the straddle is written. The major benefit in doing
this is that risk is limited in either direction. Moreover, the margin requirements are
significantly reduced, since the whole position consists of acall spread and aput
spread. There are no longer any naked options. The detriment of buying protection
on both sides initially is that commission costs increase and the overall profit poten
tial of the straddle write is reduced, perhaps significantly, by the cost of two long
options. Therefore, one must evaluate whether the cost of the protection is too large
in comparison to what is received for the straddle write. This completely protected
strategy can be very attractive when available, and it is described again in Chapter 23,
Spreads Combining Calls and Puts.
In summary, any strategy in which the straddle writer also decides to buy pro
tection presents both advantages and disadvantages. Obviously, the risk-limiting fea
ture of the purchased options is an advantage. However, the seller of options does not
like to purchase pure time value premium as protection at any time. He would gen
erally prefer to buy intrinsic value. The reader will note that, in each of the protec
tive buying strategies discussed above, the purchased option has alarge amount of
time value premium left in it. Therefore, the ·writer must often try to strike adelicate
balance between trying to limit his risk on one hand and trying to hold down the
expenses of buying long options on the other hand. In the final analysis, however, the
risk must be limited regardless of the cost.

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314 Part Ill: Put Option Strategies
position. Another advantage of buying the protection initially is that one is protected
if the stock should expe1ience agap opening or atrading halt. If he already owns the
protection, such stock price movement in the direction of the protection is of little
consequence. However, if he was planning to buy the protection as afollow-up
action, the sudden surge in the stock price may ruin his strategy.
The overall profit potential of this position is smaller than that of the normal
straddle write, since the premium paid for the long call will be lost if the stock is
below 50 at ex-piration. However, the automatic risk-limiting feature of the long call
may prove to be worth more than the decrease in profit potential. The strategist has
peace of mind in arally and does not have to worry about unlimited losses accruing
to the upside.
Downside protection for astraddle writer can be achieved in asimilar manner
by buying an out-of-the-money put at the outset.
Example: With XYZ at 45, one might write the January 45 straddle for 7 and buy a
January 40 put for lpoint if he is concerned about the stock dropping in price.
It should now be fairly easy to see that the straddle writer could limit risk in
either direction by initially buying both an out-of-the-money call and an out-of-the
money put at the same time that the straddle is written. The major benefit in doing
this is that risk is limited in either direction. Moreover, the margin requirements are
significantly reduced, since the whole position consists of acall spread and aput
spread. There are no longer any naked options. The detriment of buying protection
on both sides initially is that commission costs increase and the overall profit poten
tial of the straddle write is reduced, perhaps significantly, by the cost of two long
options. Therefore, one must evaluate whether the cost of the protection is too large
in comparison to what is received for the straddle write. This completely protected
strategy can be very attractive when available, and it is described again in Chapter 23,
Spreads Combining Calls and Puts.
In summary, any strategy in which the straddle writer also decides to buy pro
tection presents both advantages and disadvantages. Obviously, the risk-limiting fea
ture of the purchased options is an advantage. However, the seller of options does not
like to purchase pure time value premium as protection at any time. He would gen
erally prefer to buy intrinsic value. The reader will note that, in each of the protec
tive buying strategies discussed above, the purchased option has alarge amount of
time value premium left in it. Therefore, the writer must often try to strike adelicate
balance between trying to limit his risk on one hand and trying to hold down the
expenses of buying long options on the other hand. In the final analysis, however, the
risk must be limited regardless of the cost.

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Chapter 20: The Sale of a Straddle 315
STRANGLE (COMBINATION) WRITING
Recall that astrangle is any position involving both puts and calls, when there is some
difference in the terms of the options. Commonly, the puts and calls will have the
same expiration date but differing striking prices. Astrangle write is usually estab
lished by selling both an out-of-the-money put and an out-of-the-money call with the
stock approximately centered between the two striking prices. In this way, the naked
option writer can remain neutral on the outlook for the underlying stock, even when
the stock is not near astriking price.
This strategy is quite similar to straddle writing, except that the strangle
writer makes his maximum profit over amuch wider range than the straddle
writer does. In this or any other naked writing strategy, the most money that the
strategist can make is the amount of the premium received. The straddle writer
has only aminute chance of making aprofit of the entire straddle premium, since
the stock would have to be exactly at the striking price at expiration in order for
both the written put and call to expire worthless. The strangle writer will make his
maximum profit potential if the stock is anywhere between the two strikes at expi
ration, because both options will expire worthless in that case. This strategy is
equivalent to the variable ratio write described previously in Chapter 6 on ratio
call writing.
Example: Given the following prices:
XYZ common, 65;
XYZ January 70 call, 4; and
XYZ January 60 put, 3,
astrangle write would be established by selling the January 70 call and the January
60 put. IfXYZ is anywhere between 60 and 70 at January expiration, both options will
expire worthless and the strangle writer will make aprofit of 7 points, the amount of
the original credit taken in. If XYZ is above 70 at expiration, the strategist will have
to pay something to buy back the call. For example, if XYZ is at 77 at expiration, the
January 70 call will have to be bought back for 7 points, thereby creating abreak-even
situation. To the downside, if XYZ were at 53 at expiration, the January 60 put would
have to be bought back for 7 points, thereby defining that as the downside break
even point. Table 20-3 and Figure 20-3 outline the potential results of this strangle
write. The profit range in this example is quite wide, extending from 53 on the down
side to 77 on the upside. With the stock presently at 65, this is arelatively neutral
position.

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316
TABLE 20-3.
Results of acombination write.
Stock Price at Coll
Expiration Profit
40 +$ 400
50 + 400
53 + 400
57 + 400
60 + 400
65 + 400
70 + 400
73 + 100
77 300
80 600
90 - 1,600
FIGURE 20-3.
Sale of acombination.
C:
~ +$700
·5.
X
UJ
rn
en en
0 ....Ici
ea..
$0
Put
Profit
$1,700
700
400
0
+ 300
+ 300
+ 300
+ 300
+ 300
+ 300
+ 300
Stock Price at Expiration
Part Ill: Put Option Strategies
Total
Profit
-$1,300
300
0
+ 400
+ 700
+ 700
+ 700
+ 400
0
300
- 1,300
At first glance, this may seem to be amore conservative strategy than straddle
writing, because the profit range is wider and the stock needs to move agreat deal to
reach the break-even points. In the absence of follow-up action, this is atrue obser
vation. However, if the stock begins to rise quickly or to drop dramatically, the stran
gle writer often has little recourse but to buy back the in-the-money option in order

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Chapter 20: The Sale of a Straddle 317
to limit his losses. This can, as has been shown previously, entail apurchase price
involving excess amounts of time value premium, thereby generating asignificant
loss.
The only other alternative that is available to the strangle writer ( outside of
attempting to trade out of the position) is to convert the position into astraddle if the
stock reaches either break-even point.
Example: IfXYZ rose to 70 or 71 in the previous example, the January 70 put would
be sold. Depending on the amount of collateral available, the January 60 put may or
may not be bought back when the January 70 put is sold. This action of converting
the strangle write into astraddle write will work out well if the stock stabilizes. It
will also lessen the pain if the stock continues to rise. However, if the stock revers
es direction, the January 70 put write will prove to be unprofitable. Technical analy
sis of the underlying stock may prove to be of some help in deciding whether or not
to convert the strangle write into astraddle. If there appears to be arelatively large
chance that the stock could fall back in price, it is probably not worthwhile to roll
the put up.
This example of astrangle write is one in which the writer received alarge
amount of premium for selling the put and the call. Many times, however, an aggres
sive strangle writer is tempted to sell two out-of-the-money options that have only ashort life remaining. These options would generally be sold at fractional prices. This
can be an extremely aggressive strategy at times, for if the underlying stock should
move quickly in either direction through astriking price, there is little the strangle
writer can do. He must buy in the options to limit his loss. Nevertheless, this type of
strangle writing - selling short-term, fractionally priced, out-of-the-money options -
appeals to many writers. This is asimilar philosophy to that of the naked call writer
described in Chapter 5, who writes calls that are nearly restricted, figuring there will
be alarge probability that the option will expire worthless. It also has the same risk:
Alarge price change or gap opening can cause such devastating losses that many
profitable trades are wiped away. Selling fractionally priced combinations is apoor
strategy and should be avoided.
Before leaving the topic of strangle writing, it may be useful to determine how
the margin requirements apply to astrangle write. Recall that the margin require
ment for writing astraddle is 20% of the stock price plus the price of either the put
or the call, whichever is in-the-money. In astrangle write, however, both options may
be out-of-the-money, as in the example above. When this is the case, the straddle
writer is allowed to deduct the smaller out-of-the-money amount from his require
ment. Thus, if XYZ were at 68 and the January 60 put and the January 70 call had
been written, the collateral requirement would be 20% of the stock price, plus the

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318 Part Ill: Put Option Strategies
call premium, less $200 - the lesser out-of-the-money amount. The call is 2 points
out-of-the-money and the put is 8 points out-of-the-money. Actually, the true collat
eral requirement for any write involving both puts and calls - straddle write or stran
gle write - is the greater of the requirement on the put or the call, plus the amount by
which the other option is in-the-nwney. The last phrase, the amount by which the
other option is in-the-money, applies to asituation in which astrangle had been con
structed by selling two in-the-money options. This is aless popular strategy, since the
writer generally receives less time value premium by writing two in-the-money
options. An example of an in-the-money strangle is to sell the January 60 call and the
January 70 put with the stock at 65.
FURTHER COMMENTS ON UNCOVERED STRADDLE
AND STRANGLE WRITING
When ratio writing was discussed, it was noted that it was astrategy with ahigh prob
ability of making alimited profit. Since the straddle write is equivalent to the ratio
write and the strangle write is equivalent to the variable ratio write, the same state
ment applies to these strategies. The practitioner of straddle and strangle writing
must realize, however, that protective follow-up action is mandatory in limiting loss
es in avery volatile market. There are other techniques that the straddle writer can
sometimes use to help reduce his risk.
It has often been mentioned that puts lose their time value premium more
quickly when they become in-the-money options than calls do. One can often con
struct aneutral position by writing an extra put or two. That is, if one sells 5 or 6 puts
and 4 calls 'Ai.th the same terms, he may often have created amore neutral position
than astraddle write. If the stock moves up and the call picks up time premium in abullish market, the extra puts 'Aill help to offset the negative effect of the calls. On
the other hand, if the stock drops, the 5 or 6 puts will not hold as much time premi
um as the 4 calls are losing - again aneutral, standoff position. If the stock begins to
drop too much, the writer can always balance out the position by selling another call
or two. The advantage of writing an extra put or two is that it counterbalances the
straddle writer'smost severe enemy: aquick, extremely bullish rise by the underly
ing stock.
USING THE DELTAS
This analysis, that adding an extra short put creates aneutral position, can be sub
stantiated more rigorously. Recall that aratio writer or ratio spreader can use the

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Chapter 20: The Sale of a Straddle 319
deltas of the options involved in his position to determine aneutral ratio. The strad
dle writer can do the same thing, of course. It was stated that the difference between
acall'sdelta and aput' sdelta is approximately one. Using the same prices as in the
previous straddle writing example, and assuming the call'sdelta to be .60, aneutral
ratio can be determined.
Prices
XYZ common:
XYZ January 45 call:
XYZ January 45 put:
45
4
3
Deltas
.60
-.40 (.60 - 1)
The put has anegative delta, to indicate that the put and the underlying stock are
inversely related. Aneutral ratio is determined by dividing the call'sdelta by the put'sdelta and ignoring the minus sign. The resultant ratio - 1.5:1 (.60/.40) in this case -
is the ratio of puts to sell for each call that is sold. Thus, one should sell 3 puts and
sell 2 calls to establish aneutral position. The reader may wonder if the assumption
that an at-the-money call has adelta of .60 is afair one. It generally is, although very
long-term calls will have higher at-the-money deltas, and very short-term calls will
have deltas near .50. Consequently, a 3:2 ratio is often aneutral one. When neutral
ratios were discussed with respect to ratio writing, it was mentioned that selling 5
calls and buying 300 shares of stock often results in neutral ratio. The reader should
note that astraddle constructed by selling 3 puts and 2 calls is equivalent to the ratio
write in which one sells 5 calls and buys 300 shares of stock.
If astraddle writer is going to use the deltas to determine his neutral ratio, he
should compute each one at the time of his initial investment, of course, rather than
relying on agenerality such as that 3 puts and 2 calls often result in aneutral posi
tion. The deltas can be used as afollow-up action, by adjusting the ratio to remain
neutral after amove by the underlying stock.
AVOID EXCESS TRADING
In any of the straddle and strangle writing strategies described above, too much fol
low-up action can be detrimental because of the commission costs involved. Thus,
although it is important to take protective action, the straddle writer should plan in
advance to make the minimum number of strategic moves to protect himself. That is
why buying protection is often useful; not only does it limit the risk in the direction
that the stock is moving, but it also involves only one additional option commission.
In fact, if it is feasible, buying protection at the outset is often abetter strategy than
protecting as asecondary action.

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320 Part Ill: Put Option Strategies
An extension of this concept of trying to avoid too much follow-up action is that
the strategist should not attempt to anticipate movement in an underlying stock. For
example, if the straddle writer has planned to take defensive action should the stock
reach 50, he should not anticipate by taking action with the stock at 48 or 49. It is
possible that the stock could retreat back down; then the writer would have taken adefensive action that not only cost him commissions, but reduced his profit potential.
Of course, there is alittle trader in everyone, and the temptation to anticipate (or to
wait too long) is always there. Unless there are very strong technical reasons for doing
so, the strategist should resist the temptation to trade, and should operate his strate
gy according to his original plan. The ratio writer may actually have an advantage in
this respect, because he can use buy and sell stops on the underlying stock to remove
the emotion from his follow-up strategy. This technique was described in Chapter 6
on ratio call writing. Unfortunately, no such emotionless technique exists for the
straddle or strangle writer.
USING THE CREDITS
In previous chapters, it was mentioned that the sale of uncovered options does not
require any cash investment on the pait of the strategist. He may use the collateral
value of his present portfolio to finance the sale of naked options. Moreover, once he
sells the uncovered options, he can take the premium dollars that he has brought in
from the sales to buy fixed-income securities, such as Treasury bills. The same state
ments naturally apply to the straddle writing and strangle writing strategies. However,
the strategist should not be overly obsessed with continuing to maintain acredit bal
ance in his positions, nor should he strive to hold onto the Treasury bills at all costs. If
one'sfollow-up actions dictate that he must take adebit to avoid losses or that he
should sell out his Treasury bills to keep acredit, he should by all means do so.

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Synthetic Stock Positions
Created by Puts and Calls
It is possible for astrategist to establish aposition that is essentially the same as astock position, and he can do this using only options. The option position generally
requires asmaller margin investment and may have other residual benefits over sim
ply buying stock or selling stock short. In brief, the strategies are summarized by:
1. Buy call and sell put instead of buying stock.
2. Buy put and sell call instead of selling stock short.
SYNTHETIC LONG STOCK
When one buys acall and sells aput at the same strike, he sets up aposition that is
equivalent to owning the stock. His position is sometimes called "synthetic" long
stock.
Example: To verify that this option position acts much like along stock position
would, suppose that the following prices exist:
XYZ common, 50;
XYZ January 50 call, 5; and
XYZ January 50 put, 4.
If one were bullish on XYZ and wanted to buy stock at 50, he might consider the
alternative strategy of buying the January 50 call and selling (uncovered) the January
321

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322 Part Ill: Put Option Strategies
50 put. By using the option strategy, the investor has nearly the same profit and loss
potential as the stock buyer, as shown in Table 21-1. The two right-hand columns of
the table compare the results of the option strategy with the results that would be
obtained by merely owning the stock at .50.
The table shows that the result of the option strategy is exactly $100 less than
the stock results for any price at expiration. Thus, the "synthetic" long stock and the
actual long stock have nearly the same profit and loss potentials. The reason there is
adifference in the results of the two equivalent positions lies in the fact that the
option strategist had to pay 1 point of time premium in order to set up his position.
This time premium represents the $100 by which the "synthetic" position underper
forms the actual stock position at expiration. Note that, with XYZ at 50, both the put
and the call are completely composed of time value premium initially. The synthetic
position consists of paying out 5 points of time premium for the call and receiving in
4 points of time premium for the put. The net time premium is thus a 1-point pay
out.
The reason one would consider using the synthetic long stock position rather
than the stock position itself is that the synthetic position may require amuch small
er investment than buying the stock would require. The purchase of the stock
requires $5,000 in acash account or $2,500 in amargin account (if the margin rate is
50%). However, the synthetic position requires only a $100 debit plus acollateral
requirement - 20% of the stock price, plus the put premium, minus the difference
between the striking price and the stock price. The balance, invested in short-term
funds, would earn enough money, theoretically, to offset the $100 paid for the syn
thetic position. In this example, the collateral requirement would be 20% of $5,000,
or $1,000, plus the $400 put premium, plus the $100 debit incurred by paying 5 for
the call and only receiving 4 for the put. This is atotal of $1,500 initially. There is no
TABLE 21·1.
Synthetic long stock position.
XYZ Price at January 50 January 50 Total Option Long Stock
Expiration Call Result Put Result Result Result
40 -$500 -$600 -$1, 100 -$1,000
45 - 500 - 100 600 500
50 - 500 + 400 100 0
55 0 + 400 + 400 + 500
60 + 500 + 400 + 900 + 1,000

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Chapter 21: Synthetic Stock Positions Created by Puts and Calls 323
initial difference between the stock price and the striking price. Of course, this col
lateral requirement would increase if the stock fell in price, and would decrease if the
stock rose in price, since there is anaked put. Also notice that buying stock creates a
$5,000 debit in the account, whereas the option strategy'sdebit is $100; the rest is acollateral requirement, not acash requirement.
The effect of this reduction in margin required is that some leverage is obtained
in the position. If XYZ rose to 60, the stock position profit would be $1,000 for areturn of 40% on margin ($1,000/$2,500). With the option strategy, the percentage
return would be higher. The profit would be $900 and the return thus 60%
($900/$1,500). Of course, leverage works to the downside as well, so that the percent
risk is also greater in the option strategy.
The synthetic stock strategy is generally not applied merely as an alternative to
buying stock. Besides possibly having asmaller profit potential, the option strategist
does not collect dividends, whereas the stock owner does. However, the strategist is
able to earn interest on the funds that he did not spend for stock ownership. It is
important for the strategist to understand that along call plus ashort put is equiva
lent to long stock. It thus may be possible for the strategist to substitute the synthet
ic option position in certain option strategies that normally call for the purchase of
stock
SYNTHETIC SHORT SALE
Aposition that is equivalent to the short sale of the underlying stock can be estab
lished by selling acall and simultaneously buying aput. This alternative option strat
egy, in general, offers significant benefits when compared with selling the stock short.
Using the prices above - XYZ at 50, January 50 call at 5, and January 50 put at 4 -
Table 21-2 depicts the potential profits and losses at January expiration.
Both the option position and the short stock position have similar results: large
potential profits if the stock declines and unlimited losses if the underlying stock rises
in price. However, the option strategy does better than the stock position, because
the option strategist is getting the benefit of the time value premium. Again, this is
because the call has more time value premium than the put, which works to the
option strategist'sadvantage in this case, when he is selling the call and buying the
put.
Two important factors make the option strategy preferable to the short sale of
stock: (1) There is no need to borrow stock, and (2) there is no need for an uptick.
When one sells stock short, he must first borrow the stock from someone who owns
it. This procedure is handled by one'sbrokerage firm'sstock loan department. If, for

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324 Part Ill: Put Option Strategies
TABLE 21-2.
Synthetic short sale position.
XYZ Price at January 50 January 50 Total Option Short Stock
Expiration Coll Result Put Result Result Result
40 +$500 +$600 +$1, 100 +$1,000
45 + 500 + 100 + 600 + 500
50 + 500 - 400 + 100 0
55 0 - 400 400 500
60 - 500 - 400 900 - 1,000
some reason, no one who owns the stock wants to loan it out, then ashort sale can
not be executed. In addition, both the NYSE and NASDAQ require that astock
being sold short must be sold on an uptick. That is, the price of the short sale must
be higher than the previous sale. This rule was introduced (for the NYSE) years ago
in order to prevent traders from slamming the market down in a "bear raid."
With the option "synthetic short sale" strategy, however, one does not have to
worry about either of these factors. First, calls can be sold short at will; there is no
need to borrow anything. Also, calls can be sold short (and puts bought) even though
the underlying stock might be trading on aminus tick (adowntick). Many profes
sional traders use the "synthetic short sale" strategy because it allows them to get
equivalently short the stock in avery timely manner. If one wants to short stock, and
if he has not previously arranged to borrow it, then some time is wasted while one'sbroker checks with the stock loan department in order to make sure that the stock
can indeed be borrowed.
There is acaveat, however. If one sells calls on astock that cannot be borrowed,
then he must be sure to avoid assignment. For if one is assigned acall, then he too
will be short the stock. If the stock cannot be borrowed, the broker will buy him in.
Thus, in situations in which the stock might be difficult to borrow, one should use astriking price such that the call is out-of-the-money when sold initially. This will
decrease, but not eliminate, the possibility of early assignment.
Leverage is afactor in this strategy also. The short seller would need $2,500 to
collateralize this position, assuming that the margin rate is 50%. The option strategist
initially only needs 20% of the stock price, plus the call price, less the credit received,
for a $1,400 requirement. Moreover, one of the major disadvantages that was men
tioned with the synthetic long stock position is not adisadvantage in the synthetic
short sale strategy: The option trader does not have to pay out dividends on the
options, but the short seller of stock must.

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