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expiration.
There are now three instead of two outcomes to distinguish: the lowest-price region, where
ST is below both exercise prices; a middle region, where ST is between the two exercise prices;
Bodie’Kane’Marcus: V. Derivative Markets 14. Options Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




509
14 Options Markets


ST X ST X
TA B L E 14.3
ST X
Payoff to a straddle Payoff of call 0
ST)
Payoff of put (X 0
X ST ST X
Total




F I G U R E 14.10
Payoff
Payoff and profit to a
straddle at expiration
Payoff
Profit
A: Call




ST
C
X
Payoff



X
XP
B: Put Payoff




ST
Profit
P
X
Payoff and profit




Payoff
X

C: Straddle
Profit
XPC
P+C




ST
X

(P + C )




and a high-price region, where ST exceeds both exercise prices. Figure 14.11 illustrates the
payoff and profit to this strategy, which is called a bullish spread because the payoff either in-
creases or is unaffected by stock price increases. Holders of bullish spreads benefit from stock
price increases.
Bodie’Kane’Marcus: V. Derivative Markets 14. Options Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




510 Part FIVE Derivative Markets



ST X1 X1 ST X2 ST X2
TA B L E 14.4
Payoff of first call, exercise price X1 ST X1 ST X1
Payoff to 0
Payoff of second call, exercise price X2 X2)
a bullish 0 0 (ST
spread
ST X1 X2 X1
Total 0




F I G U R E 14.11 Payoff
Payoff
Value of a bullish
Profit
spread position at
expiration

A: Call held
(Call 1)



0 ST
X1 X2
C1
Payoff


C2
0 ST
X1 X2
B: Call
written
(Call 2)


Profit
Payoff




Payoff and profit



C: Bullish
spread


Payoff
X2 X1
Profit

0 ST
X1 X2
C2 C1




One motivation for a bullish spread might be that the investor thinks one option is over-
priced relative to another. For example, an investor who believes an X $50 call is cheap
compared to an X $55 call might establish the spread, even without a strong desire to take
a bullish position in the stock.
Bodie’Kane’Marcus: V. Derivative Markets 14. Options Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




EXCE L Applications www.mhhe.com/bkm


> Straddles and Spreads


Using spreadsheets to analyze combinations of options is very helpful. Once the basic models are
built, it is easy to extend the analysis to different bundles of options. The Excel model “Spreads
and Straddles” shown below can be used to evaluate the profitability of different strategies.
You can learn more about this spreadsheet model by using the interactive version available on
our website at www.mhhe.com/bkm.
A B C D E F G H I J K L
1 Spreads and Straddles
2
3 Stock Prices
4 Beginning Market Price 116.5
5 Ending Market Price 130 X 110 Straddle X 120 Straddle
6 Ending Profit Ending Profit
Buying Options:
7 Stock Price -15.40 Stock Price -24.00
8 Call Options Strike Price Payoff Profit Return % 50 24.60 50 36.00
9 110 22.80 20.00 -2.80 -12.28% 60 14.60 60 26.00
10 120 16.80 10.00 -6.80 -40.48% 70 4.60 70 16.00
11 130 13.60 0.00 -13.60 -100.00% 80 -5.40 80 6.00
12 140 10.30 0.00 -10.30 -100.00% 90 -15.40 90 -4.00
13 100 -25.40 100 -14.00
14 Put Options Strike Price Payoff Profit Return % 110 -35.40 110 -24.00
15 110 12.60 0.00 -12.60 -100.00% 120 -25.40 120 -34.00
16 120 17.20 0.00 -17.20 -100.00% 130 -15.40 130 -24.00
17 130 23.60 0.00 -23.60 -100.00% 140 -5.40 140 -14.00
18 140 30.50 10.00 -20.50 -67.21% 150 4.60 150 -4.00
19 160 14.60 160 6.00
20 Straddle Price Payoff Profit Return % 170 24.60 170 16.00
21 110 35.40 20.00 -15.40 -43.50% 180 34.60 180 26.00
22 120 34.00 10.00 -24.00 -70.59% 190 44.60 190 36.00
23 130 37.20 0.00 -37.20 -100.00% 200 54.60 200 46.00
24 140 40.80 10.00 -30.80 -75.49% 210 64.60 210 56.00
25
26
27
28
Selling Options:
29 Bullish
30 Call Options Strike Price Payoff Profit Return % Ending Spread
31 110 22.80 -20 2.80 12.28% Stock Price 7.50
32 120 16.80 -10 6.80 40.48% 50 -12.5
33 130 13.60 0 13.60 100.00% 60 -12.5
34 140 10.30 0 10.30 100.00% 70 -12.5
35 80 -12.5
36 Put Options Strike Price Payoff Profit Return % 90 -12.5
37 110 12.60 0 12.60 100.00% 100 -12.5
38 120 17.20 0 17.20 100.00% 110 -12.5
39 130 23.60 0 23.60 100.00% 120 -2.5
40 140 30.50 10 40.50 132.79% 130 7.5
41 140 17.5
42 Money Spread Price Payoff Profit 150 17.5
43 Bullish Spread 160 17.5
44 Purchase 110 Call 22.80 20.00 -2.80 170 17.5
45 Sell 140 Call 10.30 0 10.30 180 17.5
46 Combined Profit 20.00 7.50 190 17.5
47 200 17.5
48 210 17.5




Collars
A collar is an options strategy that brackets the value of a portfolio between two bounds. Sup- collar
pose that an investor currently is holding a large position in Microsoft, which is currently sell- An options strategy
ing at $70 per share. A lower bound of $60 can be placed on the value of the portfolio by that brackets the
buying a protective put with exercise price $60. This protection, however, requires that the in- value of a portfolio
between two bounds.
vestor pay the put premium. To raise the money to pay for the put, the investor might write a
call option, say with exercise price $80. The call might sell for roughly the same price as the
put, meaning that the net outlay for the two options positions is approximately zero. Writing
the call limits the portfolio™s upside potential. Even if the stock price moves above $80, the in-
vestor will do no better than $80, because at a higher price the stock will be called away. Thus
511
Bodie’Kane’Marcus: V. Derivative Markets 14. Options Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




512 Part FIVE Derivative Markets


the investor obtains the downside protection represented by the exercise price of the put by
selling her claim to any upside potential beyond the exercise price of the call.


A collar would be appropriate for an investor who has a target wealth goal in mind but is un-
willing to risk losses beyond a certain level. Suppose you are contemplating buying a house
14.5 EXAMPLE for $160,000, for example. You might set this figure as your goal. Your current wealth may
be $140,000, and you are unwilling to risk losing more than $20,000. A collar established by
Collars
(1) purchasing 2,000 shares of stock currently selling at $70 per share, (2) purchasing 2,000
put options (20 option contracts) with exercise price $60, and (3) writing 2,000 calls with ex-
ercise price $80 would give you a good chance to realize the $20,000 capital gain without
risking a loss of more than $20,000.

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