Question

Consider the following options portfolio. You write an August expiration call option on IBM
with exercise price $150. You write an August IBM put option with exercise price $145.
a. Graph the payoff of this portfolio at option expiration as a function of IBM’s stock price at
that time.
b. What will be the profit/loss on this position if IBM is selling at $153 on the option expiration
date? What if IBM is selling at $160? Use the data in Figure 20.1 to answer this question.
c. At what two stock prices will you just break even on your investment?
d. What kind of “bet” is this investor making; that is, what must this investor believe about
IBM’s stock price to justify this position?

Answer 1

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Answer:

The question is based on trading strategy in options with the concept of payoff from option as,

For Write August Call option,

Pay off = MAX (strike price - stock price, 0)

For Write Put option,

Pay off = MAX (-strike price + stock price, 0)

Answer a)

Payoff for Write August Call option with X= $ 150, (150 -S)

Payoff for Write August Put option with X= $ 145, (S-145

So, Pay off table for the portfolio as

Position	S<145	145< =S<=150	S>150
Write August Call option with X= $ 150	5	0	0
Write August Put option with X= $ 145	0	0	5
Total Pay off	5	0	5

The maximum profit from the strategy will be $ 5 at any price

PayOff diagram ,

Payoff at S=$153

Payoff for Write August Call option with X= $ 150, (150 -153 =-3

Payoff for Write August Put option with X= $ 145, (153-145) = 8

                                                                             Total pay off = 5

Payoff at S=$160

Payoff for Write August Call option with X= $ 150, (150 -160) =-10

Payoff for Write August Put option with X= $ 145, (160-145) = 15

                                                                             Total pay off = 5

b)

Calculate the profit or loss for IBM, if selling at 128 or 135 on the option expiration date:

The following table shows the profit or loss calculation for IBM:

Following is the diagrammatic representation of the above table:

c)

For breakeven point in the investment, net profit should be zero.

From the payoff graph, S= 145 and S= 150 create a Zero profit situation for the strategy .

So, Answer at S= $ 145 and S= $ 150 .

d)

The investor is betting that IBM stock price have low volatility, and stock price prevail in between of $ 125 to $ 130. This position is similar to “straddle”.