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?
a) Table showing Payoff nad net profit/loss
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) From price 15$ and 25$ this portfolio will provide a net positive return
d) Maximum amount of profit that can be obtained = $6
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