Assume that you manage a $3 million portfolio that pays no dividends,has a beta of 1.45 and an alpha of 1.5% per month.Also,assume that the risk-free rate is 0.025% (per month)and the S&P 500 is at 1220.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 the portfolio, we need to take a short position in S&P 500 futures because we expect the market to fall.

To calculate the number of futures contracts, we use the following formula:

Number of futures contracts = (Portfolio value x Beta) / (Futures price x contract multiplier)

Portfolio value = $3 million
Beta = 1.45
Futures price = S&P 500 value = 1220
Contract multiplier = $250

Plugging in the values, we get:

Number of futures contracts = ($3,000,000 x 1.45) / (1220 x $250) = 14.41

Since we cannot trade fraction of a contract, we round it up to the nearest integer, which gives us 14 contracts.

Therefore, the best choice is to sell 14 S&P 500 futures contracts (choice B) to hedge the portfolio.

Assume That You Manage a $3 Million Portfolio That Pays