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.

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