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

We have Bought stock @20 .

Premium recieved on call option = $3

Total Initial Outflow = 20 - 3*2 = $14

Stock Price (S)	Call Exercised or Lapsed	Payoff from Call option A = -2(S - E)	Payoff from Stock (B )	Total Payoff ( C =A + B)	Initial Outflow ( D )	Profit ( E = D-C)
12	Lapsed	0	12	12	14	-2
14	Lapsed	0	14	14	14	0
16	Lapsed	0	16	16	14	2
18	Lapsed	0	18	18	14	4
20	Lapsed	0	20	20	14	6
22	Exercised	-4	22	18	14	4
24	Exercised	-8	24	16	14	2
26	Exercised	-12	26	14	14	0
28	Exercised	-16	28	12	14	-2

c)

From stock price ranging from 16-24 the portfolio provides a net positive return.

d)

The Mamimum profit that can be obtained is 6 . The same is evident from the graph as well as the payoff table created.