The S&P 500 index is currently priced at 1,400. The dividend yield on the index

Question

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 maker’s 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?

Explanation / Answer

Value of shares = 50000 * 26.93 = 1346500

Value of one lot S&P = 1400*250 = 350000

N = value of shares * beta / Value of S&P 500

= 1346500 * 1.3 / 350000

= 5

Since the original position is long and beta is postive, thus he should short sell 5 contracts of s&P500

N=-5

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