3. Question 3 [Total: 20 marks]

Assume a futures contract with 8 months to maturity is employed to hedge a well-diversified portfolio over the next 6 months. The contract size of one futures contract is $250 times the index (i.e. the futures on the index). The value of the S&P500 index is currently 1200. The current futures price is $1220. The value of the portfolio that you are hedging is $ 40 million. The Beta of the portfolio is 1.25. The risk-free rate of interest is 1.5 % per year and the dividend yield is 0.5 % per year. In 6 months, the index drops to 900 with the futures price becoming $ 907.

1. What is the number of futures contracts that you need to short?

[5 marks]

2. Calculate the gain or the loss on the futures position after 6 months.

[5 marks]

3. What is the expected value of the portfolio at the end of 6 months?

[5 marks]

4. What is the final value of the portfolio after the hedge has been applied?

[5 marks]