It is July 16. A company has a portfolio of stocks worth $100 million. The beta

Question

It is July 16. A company has a portfolio of stocks worth $100 million. The beta of the portfolio is 1.2. The company would like to use the CME December futures contract on the S&P 500 to change the beta of the portfolio to 0.5 during the period July 16 to November 16. The index futures price is currently 1,000 and each contract is on $250 times the index.

(a) What position should the company take?

(b) Suppose that the company changes its mind and decides to increase the beta of the portfolio from 1.2 to 1.5. What position in futures contracts should it take?

Explanation / Answer

Ans(a)- When the beta of the company is 1.2 and it want to reduce the beta to 0.5 using the futures, therefore to minimise the risk the company should adopt the position of shorting the contracts and number of contracts to be shrted will be

1.2x100,000,000/1000x250=480 contracts to be shorted.

And to reduce the beta to 0.5 the company will have to take the short position by shorting 200 contracts i.e 0.5 x 100,000,000/1000x250-200 contracts.

Ans(b) The company will have to take the long position if it wants to increase its beta from 1.2 to 1.5

Logics: Futures tracks a diversified stock index. So it is an ideal representation of systematic risk factor. It should have very low unsystematic risk component. Systematic risk sensitivity is nothing but beta. Therefore, taking the long position in index futures contracts will increase the beta and leverage up the position. Shorting the futures reduces the beta.

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