Question

Suppose the price of Apple’s common shares is $180/share. The call option contract
(involves 100 shares) on Apple, with a strike price of $195/share is $10/contract. With the
$180 you have, you are looking at two choices:
A: Buy one share of Apple’s common stock
B: Buy 18 call option contracts
(1) What are the rates of return on A and B if the share price has dropped to $170/share?
(2) What are the rates of return on A and B if the share price has increased to $200/share?

Answer 1

1) If price dropped to $170/per share

A) Buy one share of apple's common stock

Here buy price = $180 per share

Price dropped to $170 per share, hence there will be loss of 10$ ($180 - $170)

Thus rate of return = -10/180

=-5.56%

B) Buy 18 call option contracts

Call option gives it's holder right to buy underlying at specified price in future. Thus in order to exercise call option, market price at expiry should be more than strike price

Here strike price is $195 and market price as at expiry is 170$, and hence call option will not be exercised

Premium paid = no of contract x price per contract

=18 x 10

=180$

Thus net profit = profit on exercise of call option - premium paid

=0-180

=-180$

Thus rate of return = -180/180

=-100%

2) If price increased to $200/per share

A) Buy one share of apple's common stock

Here buy price = $180 per share

Price increased to $200/per share, hence there will be profit of 20$ ($200 - $180)

Thus rate of return = 20/180

=11.11%

B) Buy 18 call option contracts

Call option gives it's holder right to buy underlying at specified price in future. Thus in order to exercise call option, market price at expiry should be more than strike price

Here strike price is $195 and market price as at expiry is 200$, and hence call option will be exercised

Thus profit on exercise of call option = (market price as at expiry - strike price) x No of contracts x share per contract

=(200-195) x 18 x 100

=5 x 18 x 100

=9000$

Premium paid = no of contract x price per contract

=18 x 10

=180$

Thus net profit = profit on exercise of call option - premium paid

=9000-180

=8820$

Thus rate of return = 8820/180

=4900%