Question

**QUESTION 4**

**A.** Assume that you are a provider of portfolio
insurance and that you are establishing a 3-year program. The
portfolio you manage is currently worth £120 and you aim to provide
a minimum return of 0%. The equity portfolio has a standard
deviation of 30% per year and the risk-free rate is 2% per year.
For simplicity, the portfolio pays no dividends.

**4.1** To hedge, how much money should be placed
in the risk-free assets? How much in equity? (Hint: Use
Black-Scholes for the value of the option needed and the delta for
asset allocation)

**(8%)**

**4.2** If the value of the stock portfolio falls
by 2% on the first day of trading,

what should the manager do?

**(5%)**

**4.3** The example above (4.1-4.2) is called
dynamic hedging. What is it and why is it difficult to maintain a
perfectly hedged portfolio using options? Explain briefly.

**(5%)**

**B.** Joe White has just purchased a stock index
fund, currently selling at £1,200 per share. To avoid downside
risk, Joe also purchased an at-the-money European put option on the
fund for £60, with exercise price £1,200 and 3- month time to
expiration. Sally Black is Joe’s financial advisor and she says
that Joe spends a lot of money on the put. She notes that 3-month
puts with strike prices of £1,170 cost only £45 and advises that
Joe use the cheaper put.

**4.4**

**4.5**

Draw the profit diagrams for both stock-plus-put strategies at expiration. What are the break-even points for each strategy?

**(10%)**

Does Sally’s strategy always do better than Joe’s? Which strategy has greater systematic risk?

**(5.3%)**

Answer #1

B. ANSWER 4.4

STOCK PRICE AT EXPIRATION |
STRIKE PRICE |
Long StockProfit/(Loss) at Expiration |
Long 100 Put Profit/(Loss) at Expiration |
Protective Put Profit/(Loss) at
Expiration |

1280 | 1200 | 80 | -60 | 20 |

1260 | 1200 | 60 | -60 | 0 |

1240 | 1200 | 40 | -60 | -20 |

1220 | 1200 | 20 | -60 | -40 |

1200 | 1200 | 0 | -60 | -60 |

1180 | 1200 | -20 | -40 | -60 |

1160 | 1200 | -40 | -20 | -60 |

1140 | 1200 | -60 | 0 | -60 |

1120 | 1200 | -80 | 20 | -60 |

1100 | 1200 | -100 | 40 | -60 |

BREAK EVEN POINT FOR THIS OPTION:- 1200+60= 1280 STOCK PLUS PUT STRATEGIES

STOCK PRICE AT EXPIRATION |
STRIKE PRICE |
Long StockProfit/(Loss) at Expiration |
Long 100 Put Profit/(Loss) at Expiration |
Protective Put Profit/(Loss) at
Expiration |

1280 | 1170 | 80 | -45 | +35 |

1260 | 1170 | 60 | -45 | +15 |

1240 | 1170 | 40 | -45 | -5 |

1220 | 1170 | 20 | -45 | -25 |

1200 | 1170 | 0 | -45 | -45 |

1180 | 1170 | -20 | -45 | -65 |

1160 | 1170 | -40 | -35 | -75 |

1140 | 1170 | -60 | -15 | -75 |

1120 | 1170 | -80 | +5 | -75 |

1100 | 1170 | -100 | +25 | -75 |

BREAK EVEN POINT FOR THIS OPTION :- 1200+45= 1245

ANSWER 4.5 SALLY BLACK STRATEGY IS BETTER THAN JOE'S STRATEGY BECAUSE AS PER BREAK EVEN POINT IS AT 1245 IN SALLY'S STRATEGY .

Joe Finance has just purchased a stock-index fund, currently
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lot of money on the put. She notes that three-month puts with
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