Question

You write a call option with X = \(50 and buy a call with X = \)60. The options are on the same stock and have the same expiration date. One of the calls sells for \(3; the other sells for \)9.

a. Draw the payoff graph for this strategy at the option expiration date.

b. Draw the profit graph for this strategy.

c. What is the break-even point for this strategy? Is the investor bullish or bearish on the stock?

Short answer

Answer

a & b. As below

c. $56; bearish.

Step-by-step solution

Drawing a payoff graph with given information “a, b”

Position	ST< 50	50 < ST< 60	ST> 60
Long call (X=60)	0	0	ST- 60
Short call (X=50)	0	-(ST– 50)	-(ST– 50)
Total	0	-(ST– 50)	-10

From the above, it’s clear that the payoff is either zero or negative.

Explanation on “break even” and investor’s bullish/bearish ‘c’

The proceeds = $9 - $3 = $6

Breakeven would happen when the payoff even out the proceeds of $6.

This happens at stock price of ST= $56.

The investor is bearish as he entered into bear spread.