Question

1. Consider the following options portfolio. You write a January expiration call option on IBM with exercise price 130 and premium of $2.18. You write a January IBM put option with exercise price 125 and premium of $2.44.

1. Graph the payoff of this portfolio at option expiration as a function of IBM’s stock price at that time.
2. What will be the profit/loss on this position if IBM is selling at 128 on the option expiration date? What if IBM is selling at 135?
3. At what two stock prices will you just break even on your investment?
4. 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

a)

b) We have written a call option with Exercise price 130.
Initial Premium Received = $2.18

We have written the put option with exercise price 125.
Initial Premium Received = $2.44

Total Premium Received = $2.18+$2.44 = $4.62

If IBM is selling at 128 on the option expiration data :
Both call option and put option are out of the money and both will lapse.
Payoff = 0
Profit = Total Premium Received = $4.62

If IBM is selling at 135 on the option expiration data :
Since Share price is more than exercise price call option will be exercised and payoff will be S-E
Payoff = 135 – 130 = 5
Since we have written call option payoff will be – 5

Since Share price is more than exercise price put option will lapse and payoff will be 0.

Loss = Payoff – Total Premium Received = 5 - 4.62 = $0.38

c) Maximum profit will be initial premium received which is $4.62
Breakeven price for a written call option will be Exercise Price + Initial Premium Received
                                                                                                =130+4.62 = $134.62
Breakeven price for a written put option will be Exercise Price - Initial Premium Received
                                                                                                =125+4.62 = $120.38

d) Since the investor has shorted call and put options the investor is expecting the share price not to move in either direction and to be constant. This means he is betting against the volatility and is expecting should price to be between 125-130. Since he has written put option on exercise price of 125 he is expecting the share price to be above 125. He has written call option on exercise price of 130 he is expecting the share price to be below 130.