The S&P 500 Index price is $925.28 and its annualized dividend yield is 1.40%.LIBOR is 4.2%.How many futures contracts will you need to hedge a $25 million portfolio with a beta of 0.9 for one year?
A) 105
B) 120
C) 80
D) 95

Question

Quizplus · Accepted Answer

To hedge a portfolio using futures contracts, you first calculate the hedge ratio, which is the product of the portfolio's beta and the ratio of the portfolio value to the product of the index level and the multiplier (usually $250 for S&P 500 futures). The formula for the number of contracts needed is: $N = \frac{(Portfolio\ Value \times Beta)}{(Index\ Price \times Multiplier)}$. Given a portfolio value of $25 million, a beta of 0.9, an S&P 500 index price of $925.28, and assuming the standard multiplier of $250, the calculation is $N = \frac{($25,000,000 \times 0.9)}{($925.28 \times 250)}$. This calculation does not directly incorporate the dividend yield or LIBOR rate, as these factors would influence the decision to hedge but not the calculation of the number of contracts needed for a beta hedge. The correct calculation leads to approximately 95 contracts.

The S&P 500 Index Price Is $925