Question

(a) Suppose that you enter into a long six-month forward contract on ABC stock at a forward price of $50. What is the payoff of your long forward position in six months for ABC stock prices of $40, $45, $50, $55, and $60?

(b) Suppose that you buy a six-month call option on ABC stock with a strike price of $50. What is the payoff in six months for ABC stock prices of $40, $45, $50, $55, and $60?

(c) Comparing the payoffs of parts (a) and (b), which contract should be more expensive, the long call or the long forward? why?

Answer 1

a) Long forward position means to buy the underlying asset at a specified future date for a specified price.

Forward price = $50

ABC stock price	Pay off (Price at expiration – Forward price)
$40	-$10
$45	-$5
$50	0
$55	$5
$60	$10

b) Buyer of a call option is the right (not obligation) to buy stock at expiration for the strike price.

Strike price = $50

ABC stock price	Pay off MAX (stock price - strike price, 0)
$40	0
$45	0
$50	0
$55	$5
$60	$10

c)

The long forward is more expensive than long call as long forward is an obligation to buy the underlying asset on expiration whereas long call is option to buy the underlying asset on expiration.

In case the price of s underlying asset on expiration is lower than the contracted price, we have to buy the underlying asset at contracted price if we enter into long forward and therefore we incur loss. Whereas, in long call we will not exercise the call option as it is right not obligation hence no loss.