Consider the following option portfolio: You write a January 2012 expiration cal
ID: 2645873 • Letter: C
Question
Consider the following option portfolio: You write a January 2012 expiration call option on IBM with exercise price $168, and the price of the call option is $8.93. You also write a January expiration IBM put option with exercise price $163, 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 $161 on the option expiration date? $
b. What will be the profit/loss on this position if IBM is selling at $172 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: $
Explanation / Answer
a. IBM is selling at $ 161
Position of call option:-
The exercise price is $ 168 whereas IBM is trading at $ 161 which is lesser than the exercise price.
Hence the buyer of the call option will not exercise the call. Instead he will buy the security from the open market.
Hence, net profit to the call option writer is the Call permium of $ 8.93
Position of put option:
The exercise price is $ 163 whereas IBM is trading at $ 161 which is lesser than the exercise price.
Hence the buyer of the put option will exercise the put option and sell the security to the writer.
If the writer had purchased the security in the open market, he would have got at $ 161, whereas he is buying the same at $ 163.
Hence, loss on exercise of put option is $ (163-161) = $ 2
The put premium earned is $ 10.93.
Hence, net profit is $ (10.93-2) = 8.93
Thus, the total profit earned is $ (8.93 + 8.93) = $ 17.86
b. IBM is selling at $ 172
Position of call option:-
The exercise price is $ 168 whereas IBM is trading at $ 172 which is higher than the exercise price.
Hence the buyer of the call option will exercise the call and will buy the security from the writer.
If the writer had sold the security in the open market he would have got $ 172, whereas under the call option he will get only $ 168
Loss on sale of security is $ (171-168) = $ 3
Call premium earned is $ 8.93
Hence, net profit to the call option writer is $ (8.93 - 3) = $ 5.93
Position of put option:
The exercise price is $ 163 whereas IBM is trading at $ 172 which is lesser than the exercise price.
Hence the buyer of the put option will not exercise the put option. Instead he will sell the security in the open market at a higher rate.
Hence, net profit is the put premium earned of $ 10.93
Thus, the total profit earned is $ (5.93 + 10.93) = $ 16.86
c. Breakeven point of call and put option
For the put option
The break even price in case of the put option should be such that, it will square off the put premium earned.
In this case, the put premium earned is $ 10.93 and exercise price is $ 163
The put option will be exercised by the buyer only when the security is selling at a rate lower than the exercise price.
Hence, if the price of the security is lower than $ 163 by $ 10.93, then the buyer of the put will exercise the option
and sell the security to the writer at $ 163, which will lead to a loss of $ 10.93
This will lead to a breakeven situation.
Therefore, break-even stock price in case of put option is $ (163 - 10.93) = $ 152.07
For call option
The break even price in case of call option should be such that it will square off the call premium earned.
In this case, call premium earned is $ 8.93 and exercise price is $ 168
The call option will be exercised only when the security is selling at a higher rate than the exercise price.
Hence, if the price of the security is higher than $ 168 by $ 8.93, then the buyer of the call will exercise the option
and buy the security from the writer at $ 168 which will lead to a loss of $ 8.93
This will lead to a breakeven situation.
Therefore, break-even stock price in case of put option is $ (168 - 8.93) = $ 159.07
Call option Writing a call option means selling a call option. The writer gets the call premium (call price) upfront for writing the call option On the exercise date, if the buyer of the call option decides to exercise the option, then the writer has to sell the instrument compulsorily. Put option Writing a put option means selling a put option. The writer gets the put premium (put price) upfront for writing the put option On the exercise date, if the buyer of the put option decides to exercise the option, then the writer has to buy the instrument compulsorily.