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# Hedging portfolio using futures

Chapter 3: AD 3: A fund manager has a portfolio worth \$100 million with a beta of 1.15. 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 index level is 950 and one futures contract is on 250 times the index (i.e., the index multiplier is 250). The risk-free rate is 4.5% per annum and the dividend yield on the index is 3.4% per annum. The current three-month futures price is 952.62.

Q1: What position should the fund manager take to hedge exposure to the market over the next two months?

Q2: Calculate the effect of your strategy on the fund manager's returns if the index in two months is 700, 800, 900, 1,000 and 1,100. Assume that the one-month futures price is 0.25% higher than the index level at this time (note, that means when the index is 900 two months from now, the one-month futures price will be 1.0025*900 = 902.25).

To answer part Q2, follow closely the example on pages 62 and 63. A good idea is to write out each step for the index level of 900 in Word and calculate the value of each step with a calculator. Then convert to logic in Excel, and do the remaining index levels in Excel. You should notice that although the original portfolio value varies considerably when the index changes from 900 to 1000 to 1100, etc., the hedged portfolio (portfolio plus futures position) does not change in value very much. The point of the hedge is to reduce risk as measured by (hedged) portfolio variance!

Adapted from Fundamentals of Futures and Options Markets, 6th ed., John C. Hull.

#### Solution Preview

AD 3: A fund manager has a portfolio worth \$100 million with a beta of 1.15. 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 index level is 950 and one futures contract is on 250 times the index (i.e., the index multiplier is 250). The risk-free rate is 4.5% per annum and the dividend yield on the index is 3.4% per annum. The current three-month futures price is 952.62.

Data:

risk free rate =rf= 4.50%
dividend yield= 3.40%
beta= 1.15
current index level= 950
Value of portfolio= \$100,000,000
index multiplier= 250
K=current 3 months futures price= 952.62

Q1: What position should the fund manager take to hedge exposure to the market over the next two months?

Since the fund manager is long on the portfolio, short futures contract.
If we have a short position in futures contract, when the futures price decreases there is a gain on the futures contract and when the futures price increases there is a loss on the futures contract

If the index and therefore the portfolio rises, there is a profit on the portfolio and loss on the futures contract.
If the index and therefore the portfolio falls, there is a loss on the portfolio and profit on ...

#### Solution Summary

The questions on hedging a portfolio using futures contracts on S&P 500, and the effects of using the futures on the fund manager's returns when the index moves to different values have been analyzed.

\$2.19