Question

Consider the following option portfolio: You write a January 2012 expiration call option on IBM with exercise price $172, and the price of the call option is $8.93. You also write a January expiration IBM put option with exercise price $167, the price of the put option is $10.85.

Instructions: for parts a, b, and c, enter your answer as a decimal rounded to the nearest cent.

a. What will be the profit/loss on this position if IBM is selling at $159 on the option expiration date? $  

b. What will be the profit/loss on this position if IBM is selling at $180 on the option expiration date? $  

c. At what two stock prices will you just break even on your investment (i.e., zero net profit)?

    For the put, this requires that: $  

    For the call this requires that: $  

d. What kind of “bet” is this investor making; that is, what must this investor believe about IBM’s stock price in order to justify the position?

• betting that the IBM stock price will go up.

• betting that the IBM stock price will go down.

• betting that the IBM stock price will have low volatility.

• betting that the IBM stock price will have high volatility.

Answer 1

a) Writing a call option means shorting a call option and writing a put option means shorting a put option.

Initial inflow from writing call option = $8.93

Initial inflow from writing put option = $10.85

Total Initial Inflow = 10.85+8.93 = $19.78

If share price is $159 on the option expiration date :

Since call option has an exercise price of $172 it will expire.

Payoff = 0

Since put option has an exercise price of $167 it will be exercised.

Payoff = Exercise Price - Stock Price

= 167-159

= $8

Total Profit = Initial Inflow - Payoff from put option

= 19.78-8 = $11.78

b) If share price is $180 on the option expiration date :

Since call option has an exercise price of $172 it will be exercised.

Payoff = Share price - Exercise price

= 180 - 172

= $8

Since put option has an exercise price of $167 it will lapse.

Payoff = 0

Total Profit = Initial Inflow - Payoff from call option

= 19.78-8 = $11.78

c) Breakeven for put option = Exercise Price - Initial Inflow from Put option

= 167 - 10.85

= 156.15

Below this share price we will incur a loss as put will be exercised.

Breakeven for call option = Exercise Price + Initial Inflow from Call option

= 172 + 8.93

= 180.93

Above this share price we will incur a loss as call will be exercised.

d) Option C is correct.

The investor is betting that the IBM stock price will have low volatility. This is evident from the fact that investor is writing put option so he is expecting share price not to fall below $167. Also he is writing call option so he is expecting share price not to rise above $172. He is betting that the share price will be between $167-$172.

Hence he is betting that the stock price will have low volatility.