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The S&P 500 Index is currently at 1,600. You manage a $12 million indexed equity portfolio. The S&P 500 futures contract has a multiplier of $250.

a;. If you are temporarily bearish on the stock market, how many contracts should you sell to fully eliminate your exposure over the next six months? Number of contracts 30

b. If T-bills pay 1.5% per six months and the semiannual dividend yield is 1.4%, what is the parity value of the futures price? (Round your answer to 2 decimal places. Do not round intermediate calculations.) Parity value ?

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Nestor Rutherford
Nestor RutherfordLv2
28 Sep 2019

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You hold a well diversified portfolio of stocks valued at $10 million whose beta is equal to 1.5. You intend to use S&P 500 futures to decrease the effective beta of your portfolio down to 0.5. The multiplier for S&P 500 contracts is $250 and the index is currently at 2,399 (futures price). Will you buy or sell futures contracts? How many contracts (report fractional contracts)? Assuming S&P 500 drops by 10% by the expiration date, please find (a) the new value of your stocks, (b) profit/loss on the futures position, (b) the new value of your overall hedged portfolio, and (c) the holding period return on your overall hedged portfolio.

A fund manager has a portfolio worth $50 million with a beta of 0.95. The manager is concerned

about the performance of the market over the next 2 months and plans to use 3-month futures

contracts on the S&P 500 to hedge the risk. The current level of the index is 2,300, one contract is on

250 times the index, the risk-free rate is 5% per annum, and the dividend yield on the index is 2%

per annum.

a) Calculate the theoretical futures price of a 3-month S&P 500 futures price.

b) How many futures contracts should the manager buy or sell to hedge the exposure to the

market over the next 2 months?

c) Calculate the value of the hedged position (stock and futures) if the index in 2 months is 2000.

A fund manager has a portfolio worth $100 million with a beta of 1.5.  The manager is concerned about the performance of the market over the next two months and plans to use three-month futures contracts on the S&P 500 to hedge the risk.  The current level of the index is 2250, one contract is on 250 times the index, the risk free rate is 2%, and the        dividend yield on the index is 1.7% per year. (Assume all the rates are continuously compounded.)

 

  1. What is the theoretical futures price for the three-month futures contract?

 

  1. What position should the fund manger takes to eliminate all exposure to the market over the next two months?
  2. c) Calculate the effect of your strategy on the fund manager’s returns if the level of the market in two months is 2,000, 2,200, 2,500, 2,800, and 3,000.

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