The S&P 500 index is currently priced at 1,400. The dividend yield on the index is zero. The current risk free rate is 5%. Answer

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The S&P 500 index is currently priced at 1,400. The dividend yield on the index is zero. The current risk free rate is 5%.

Answer required for (c) only

(a) What is the no-arbitrage forward price for delivery in 6 months?

(b) You are a market maker. Demonstrate how you would hedge your position resulting from offering a customer (i) a short index forward position with expiration in 6 months, and (ii) a equivalent long index forward position. (Hint: Show the market makers cash flows today and at expiration).

(c) You are an investor holding 50,000 of a certain stock. The market price is $26.93 per share. You want to hedge your position in this stock against movements in the market over the next month and decide to use the S&P 500 futures contract. One such futures contract is for $250 times the index. You run a regression of past returns on your particular stock against concurrent past return on the S&P 500 index, and you find a regression coefficient of 1.3. What strategy should you follow? When will such a strategy be profitable?