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 Joes 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 Sallys strategy always do better than Joes? Which strategy has greater systematic risk?

(5.3%)