Assume that you manage a $2 million portfolio that pays no dividends and has a beta of 1.3 and an alpha of 2% per month.Also, assume that the risk-free rate is 0.05% (per month) and the S&P 500 is at 1,500.If you expect the market to fall within the next 30 days, you can hedge your portfolio by ______ S&P 500 futures contracts (the futures contract has a multiplier of $250).

Question

Quizplus · Accepted Answer

To hedge a portfolio against a fall in the market, we must take a short position in the futures contract. The formula to calculate the number of futures contracts needed for hedging is:

Number of contracts = (Portfolio Value x Beta) / (Index Futures Price x Contract Size)

Portfolio Value = $2 million
Beta = 1.3
Index Futures Price = 1,500 (given)
Contract Size = $250 (given)

Number of contracts = (2,000,000 x 1.3) / (1,500 x 250)
Number of contracts = 6.96 or approximately 7

Thus, we need to sell 7 S&P 500 futures contracts to hedge our portfolio against a fall in the market. Option B is the correct choice.

Assume That You Manage a $2 Million Portfolio That Pays