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

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