Question: 3. Question 3 [Total: 20 marks] A fund manager uses a futures contract with 8 months to maturity to hedge a well- diversified portfolio over

3. Question 3 [Total: 20 marks] A fund manager uses a futures contract with 8 months to maturity to hedge a well- diversified portfolio over the next 7 months. Contract size of one futures contract is $250 times the index (i.e., the futures on the index). The value of the S&P500 index is currently 1205. The current futures price is 1230. The value of the portfolio that you are hedging is$ 30 millions. The Beta of the portfolio is 1.5. The risk-free rate of interest is 1 % per year and the dividend yield is 0.5 % per year. In 7 months, the index drops to 917, with the futures price dropping to 925. a) What is the number of futures contracts that you need to short? [5 marks] b) Calculate the gain or the loss on the futures position after 7 months. [5 marks] c) What is the expected value of the portfolio at the end of 7 months? [5 marks] d) What is the final value of the portfolio after the hedge has been applied? [5 marks]

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