Investments, tenth edition

A: Call

+ B: Put

= C: Straddle

S

T

S

T

Profit

Profit

Payoff

P 

+ C

Payoff

X

X

X 

− P

− C

−P

0

0

X

X 

− P − C

− (P + C)

0

 Table 20.3 

 Value of a straddle 

position at option 

expiration 

S

T

 * X

S

T

 # X

 Payoff of call

0

S

T

 2 X

1 

Payoff of put

X 2 S

T

0

5

  TOTAL

X 2 S

T

S

T

 2 X

 Figure 20.9 

Value of a straddle at expiration  

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  C H A P T E R  

2 0

  Options Markets: Introduction

697

S

T

Payoff

Payoff and Profit

Payoff

X

1

X

2

 

− X

1

C

2

 

− C

1

Profit

S

T

S

T

Payoff

Profit

Payoff

Profit

Payoff

X

2

A: Call Held

(Strike price 

5 X

1

)

B: Call Written

   (Strike price 

5 X

2

)

− C

1

X

1

X

2

X

1

C

2

0

0

C: Bullish

Spread

0

X

2

 Figure 20.10 

Value of a bullish spread position at expiration  

S

T

 " X

1

X

1

 * S

T

 " X

2

S

T

 # X

2

 Payoff of purchased call, exercise price 5 X

1

  0

S

T

 2 X

1

S

T

 2 X

1

1 

Payoff of written call, exercise price 5 X

2

2

0

2

0

2

(S

T

 2 X

2

)

5 

TOTAL

  0

S

T

 2 X

1

X

2

 2 X

1

 Table 20.4 

 Value of a bullish 

spread position at 

expiration 

bod61671_ch20_678-721.indd   697

bod61671_ch20_678-721.indd   697

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698 

P A R T   V I

  Options, Futures, and Other Derivatives

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 $110, the 

investor will do no better than $110, because at a higher price the stock will be called away. 

Thus 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 unwilling to risk losses beyond a certain level. If you are contemplating buying a house 

for $220,000, for example, you might set this figure as your goal. Your current wealth 

may be $200,000, and you are unwilling to risk losing more than $20,000. A collar 

established by (1) purchasing 2,000 shares of stock currently selling at $100 per share, 

(2) purchasing 2,000 put options (20 options contracts) with exercise price $90, and (3) 

writing 2,000 calls with exercise price $110 would give you a good chance to realize the 

$20,000 capital gain without risking a loss of more than $20,000. 

 Example  20.5 

Collars 

 Graph the payoff diagram for the collar described in Example 20.5. 

 CONCEPT CHECK 

20.5 

  We saw in the previous section that a protective put portfolio, comprising a stock position 

and a put option on that position, provides a payoff with a guaranteed minimum value, 

but with unlimited upside potential. This is not the only way to achieve such protection, 

however. A call-plus-bills portfolio also can provide limited downside risk with unlimited 

upside potential. 

 Consider the strategy of buying a call option and, in addition, buying Treasury bills with 

face value equal to the exercise price of the call, and with maturity date equal to the expira-

tion date of the option. For example, if the exercise price of the call option is $100, then 

each option contract (which is written on 100 shares) would require payment of $10,000 

upon exercise. Therefore, you would purchase a T-bill with a maturity value of $10,000. 

More generally, for each option that you hold with exercise price  X,  you would purchase a 

risk-free zero-coupon bond with face value  X.  

 Examine the value of this position at time  T,  when the options expire and the zero-

coupon bond matures: 

    20.4 

The Put-Call Parity Relationship