Question

Consider a portfolio consisting of a long position in one stock and a short position in two call options. Both the current stock price (S0) and the exercise price (K) of call options are $20. The call option costs $3.

a) Construct a table showing the payoffs and net profits for all possible price ranges.

b) Draw a diagram showing the variation of an investor’s net profit with the terminal stock price

c) For what price range does this portfolio provide a net positive return?

d) What is the maximum amount of profit that can be obtained?

Answer 1

a) Table showing Payoff

Price as at expiry	Profit/Loss on holding Share @ $20	Loss on two shorted call option Strike price = 20$	Payoff	Premium Received	Net Profit/loss
10	-10		-10	6	-4
11	-9		-9	6	-3
12	-8		-8	6	-2
13	-7		-7	6	-1
14	-6		-6	6	0
15	-5		-5	6	1
16	-4		-4	6	2
17	-3		-3	6	3
18	-2		-2	6	4
19	-1		-1	6	5
20	0	0	0	6	6
21	1	-2	-1	6	5
22	2	-4	-2	6	4
23	3	-6	-3	6	3
24	4	-8	-4	6	2
25	5	-10	-5	6	1
26	6	-12	-6	6	0
27	7	-14	-7	6	-1
28	8	-16	-8	6	-2
29	9	-18	-9	6	-3
30	10	-20	-10	6	-4

b) Diagram

C) portfolio will provide a net positive return in price range of $15 to $25

D) maximum amount of profit that can be obtained = $6