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11 Dec 2019

Index futures are often used to hedge portfolios that are not exactly the index. This is called cross-hedging. Suppose that we have a portfolio that is not the S&P 500, and we wish to shift the portfolio into T-bills. Assume that the portfolio and the S&P 500 are perfectly correlated. Suppose that we own $200 million of stocks with a beta relative to the S&P 500 of 1.2. Assume that the S&P 500 is 1200 with a zero dividend yield and the effective annual rate of 10%.

(a) Find the future price

(b) You believe that the S&P 500 index price will drop in the future and you decide to hedge your portfolio. You need to short some quantity of the S&P 500. How many S&P 500 index futures can you short?

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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.

Suppose you own a well diversified stock portfolio currently woth 10 million. The portfolio has a beta of 0.8. Assume the S&P 500 futures price is 1,200. Describe in detail the futures transaction you would undertake to hedge the value of your portfolio. How many contracts would you buy or sell?

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