问一道题：NO.PZ2016082404000025

问题如下：

The current value of the S&P 500 index is 1,457, and each S&P futures contract is for delivery of 250 times the index. A long-only equity portfolio with market value of USD 300,100,000 has a beta of 1.1. To reduce the portfolio beta to 0.75, how many S&P futures contracts should you sell?

选项：

  288 contracts

  618 contracts

  906 contracts

  574 contracts

解释：

ANSWER: A

This is as in the previous question, but the hedge is partial (i.e., for a change of 1.10 to 0.75). So,$N\ast=-\beta\frac SF=\frac{-(1.10-0.75)\times300,100,000}{1475\times250}=288.3$ contracts