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问题如下：

Suppose we have a well-diversified $100 million equity portfolio. The portfolio beta relative to the S&P 500 is 1.2. The current value of the 3-month S&P 500 Index is 1,000. The multiplier is 250. If we want to adjust the portfolio beta to 0.8, how many S&P 500 contracts we need?

选项：

A.

long 160 contracts.

B.

short 160 contracts.

C.

long 1,600 contracts.

D.

short 1,600 contracts.

解释：

B is correct.

考点：Hedging With Stock Index Futures

解析：

$\left(0.8-1.2\right)\frac{100,000,000}{1,000\times250}=-0.4\times400=-160$

where beta = 1.2, target beta = 0.8, A = 250 x 1,000, P = $100 million