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11 Dec 2019

A well-diversified stock portfolio has $40m value, and a beta 1.22 relative to S&P 500 index. The portfolio manager anticipates a bearish horizon. Instead of liquidating, he or she sells N contracts of S&P 500 stock index futures. Suppose one futures contract = $500 futures price in points or notional value. Suppose the S&P 500 futures price is now 1500 points. Suppose the rate of change of the S&P 500 index is the same as the rate of change of the futures index. What is N if the manager wants to hedge perfectly?

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13 Dec 2019
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Related questions

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.

5. In early April, an insurance company portfolio manager has a stock portfolio of $200 million with a portfolio beta of 1.15. The portfolio manager plans on selling the stocks in the portfolio in June to be able to pay out funds to policyholders for annuities, and is worried about a fall in the stock market. In April, the CME Group S&P 500 Futures contract index is 2340.40 for a June futures contract ($250 multiplier for the contract).

a.What type of futures position should be taken to hedge against the stock market going down and how many future contracts are needed for this hedge?

[Hint: # contracts = [Amount Hedged / Futures Index Price x Multiplier] x Beta Portfolio

Type of Position _____________

Explain why ________________________________________

# of Contracts_____________

b. Suppose in June the stock market (S&P500 index) falls by 10% and the S&P500 futures index falls by 10% as well, what is the portfolio manager’s opportunity loss (gain) on his portfolio, and his futures gain (loss) and the net hedging result?

Spot Gain or Loss ____________ Futures Gain or Loss ___________

Net Hedging Result _____________

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.

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