Question

Consider an investor in April holds 20,000 shares of a company, each share worth$100. The investorbelieves the stock will outperform the market in the next three months, but worries the market may godown. The beta of the company is 1.1. Suppose the futures price for the August contract on the S&P 500index is 900, and each contract corresponds to 250 times the index. What should be the strategy of theinvestor? Suppose that the investor closes out the position in July, when the stock price of the companyis$90, and the futures price of the S&P 500 index is 750. Calculate the gain or lose of the investor.

Answer 1

The number of contracts on which short position should be taken is calculated as follows:

Beta × Current portfolio value / Current stock value underlying one futures contract = 1.1 × 20,000 × $100 / 900 × 250 = 9.78 i.e. 10.

The gain of the investor is calculated as follows:

The stock price of the company declines to $90 in July leading to a loss of 20,000 × (100 - 90) = $200,000 to the investor.

The futures price of the S&P 500 index also declines to 750 in July leading to a gain of 10 × 250 × (900 - 750) = $375,000 to the investor on the futures contracts.

Therefore, the net gain to the investor on closing out the position in July = $375,000 - $200,000 = $175,000.