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 .