Question
In: Finance
Consider a portfolio consisting of a long position in one stock and a short position in...
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?
Solutions
Expert Solution
(a)
| Expiry Price | Cashflow | On expiry | Net Cashflow | ||||||
| Stock Buy | Sell 2 Call option | Cashflow Today | Sell Stock | Call Option | Value of Call Option | Value of 2 Option | Cashflow on expiry | ||
| $ 5 | $ (20) | $ 6 | $ (14) | $5 | Lapse | $ - | $ - | $ 5 | $ (9) |
| $ 10 | $ (20) | $ 6 | $ (14) | $10 | Lapse | $ - | $ - | $ 10 | $ (4) |
| $ 11 | $ (20) | $ 6 | $ (14) | $11 | Lapse | $ - | $ - | $ 11 | $ (3) |
| $ 12 | $ (20) | $ 6 | $ (14) | $12 | Lapse | $ - | $ - | $ 12 | $ (2) |
| $ 13 | $ (20) | $ 6 | $ (14) | $13 | Lapse | $ - | $ - | $ 13 | $ (1) |
| $ 14 | $ (20) | $ 6 | $ (14) | $14 | Lapse | $ - | $ - | $ 14 | $ - |
| $ 15 | $ (20) | $ 6 | $ (14) | $15 | Lapse | $ - | $ - | $ 15 | $ 1 |
| $ 16 | $ (20) | $ 6 | $ (14) | $16 | Lapse | $ - | $ - | $ 16 | $ 2 |
| $ 17 | $ (20) | $ 6 | $ (14) | $17 | Lapse | $ - | $ - | $ 17 | $ 3 |
| $ 18 | $ (20) | $ 6 | $ (14) | $18 | Lapse | $ - | $ - | $ 18 | $ 4 |
| $ 19 | $ (20) | $ 6 | $ (14) | $19 | Lapse | $ - | $ - | $ 19 | $ 5 |
| $ 20 | $ (20) | $ 6 | $ (14) | $20 | Indiff. | $ - | $ - | $ 20 | $ 6 |
| $ 21 | $ (20) | $ 6 | $ (14) | $21 | Exercise | $ 1 | $ 2 | $ 19 | $ 5 |
| $ 22 | $ (20) | $ 6 | $ (14) | $22 | Exercise | $ 2 | $ 4 | $ 18 | $ 4 |
| $ 23 | $ (20) | $ 6 | $ (14) | $23 | Exercise | $ 3 | $ 6 | $ 17 | $ 3 |
| $ 24 | $ (20) | $ 6 | $ (14) | $24 | Exercise | $ 4 | $ 8 | $ 16 | $ 2 |
| $ 25 | $ (20) | $ 6 | $ (14) | $25 | Exercise | $ 5 | $ 10 | $ 15 | $ 1 |
| $ 26 | $ (20) | $ 6 | $ (14) | $26 | Exercise | $ 6 | $ 12 | $ 14 | $ - |
| $ 27 | $ (20) | $ 6 | $ (14) | $27 | Exercise | $ 7 | $ 14 | $ 13 | $ (1) |
| $ 28 | $ (20) | $ 6 | $ (14) | $28 | Exercise | $ 8 | $ 16 | $ 12 | $ (2) |
| $ 29 | $ (20) | $ 6 | $ (14) | $29 | Exercise | $ 9 | $ 18 | $ 11 | $ (3) |
| $ 30 | $ (20) | $ 6 | $ (14) | $30 | Exercise | $ 10 | $ 20 | $ 10 | $ (4) |
| $ 35 | $ (20) | $ 6 | $ (14) | $35 | Exercise | $ 15 |
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