optimal hedging strategy

On June 15, 2009 an investor owns a stock portfolio made of 10,000 Gamma shares, and needs to hedge her portfolio against systematic risk over the next 5 months. To

do so, she can use futures contracts on the stock index SP1, with expiry 15 December 2009. The value of one futures contract on the index is equal to 25 euros per index

point. On June 15, 2009 the stock portfolio has a beta of 1.1 with respect to the stock index SP1.

a) Discuss the optimal hedging strategy that the investor can design on June 15,

knowing that price of Gamma shares is 75 euro, and the futures price of the 6- month SP1 index contract is equal to 1250 index points.

On August 15, 2009, the rating of company Gamma is downgraded from A to BBB-. As a result, the stock price of Gamma on the market punges to 63 euros and the beta of the stock portfolio with respect to the SP1 index increases to 1.8. On that date, the stock index futures price for December 2009 expiry is equal to 1257 index points.

b) Calculate the beta of the overall position of the investor on August 15, 2009.

c) Following the downgrade of Gamma, explain whether and how the investor

should change her hedging strategy.

On November 15, 2009, the investor closes the hedging position on futures and sells her stock portfolio. On that date, Gamma shares trade at 59 euros on the market, while the futures contract on SP1 with December expiry trades at 1252 index points.

d) Detail the cash flows of profits and losses on the stock portfolio and on the

hedge. What can you conclude on the effectiveness on your hedging strategy? e) Explain what basis risk is in the context of hedging with stock index futures, and which are its components.