You manage a $15 million hedge fund portfolio with beta = 1.2 and alpha = 2% per

Question

You manage a $15 million hedge fund portfolio with beta = 1.2 and alpha = 2% per quarter. Assume the risk-free rate is 2% per quarter and the current value of the S&P 500 Index is 1,200. You want to exploit the positive alpha, but you are afraid that the stock market may fall and you want to hedge your portfolio by selling 3-month S&P 500 future contracts. The S&P contract multiplier is $250.

How much is the portfolio expected to be worth 3 months from now?

a. $15,000,000

b. $15,450,000

c. $15,600,000

d. $16,000,000

Explanation / Answer

To calculate the value of the portfolio after 3 months, we need to determine the expected return per quarter. The formula for calculating quarterly expected return is:

Quarterly Expected Return = Risk Free Rate + Alpha

The formula for calculating expected value of the portfolio after 3 months can be derived as follows:

Value of the Portfolio = Value of the Hedge Fund Portflio*(1+Quarterly Expected Return)

_____________

Solution:

Quarterly Expected Return = 2% + 2% = 4%

Expected Value of the Portfolio (after 3 months) = 15,000,000*(1+4%) = $15,600,000 (which is Option C)

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