问一道题：NO.PZ2018113001000007

问题如下：

A manager determines that the current level of excess cash is $20 million. She decides to purchase futures contracts to replicate the return on target stock and bond. Her target is：

60% is allocated to stock at average beta of 1.05 and 40% is allocated to bond at average duration of 5.2.

The price of an appropriate stock index futures contract is $250,000 and the beta is 0.98. The price of an appropriate bond futures contract is $110,000 and duration is 6.5. The manager should buy:

选项：

49 stock index futures contracts and 60 bond futures contracts.

51 stock index futures contracts and 58 bond futures contracts.

50 stock index futures contracts and 59 bond futures contracts.

解释：

B is correct.

解析：

从题目可知有$12million投资于股票，$8miilion投资于债券。因为现在为现金头寸，所以beta=0, duration=0。又目标Beta=1.05，目标duration=5.2，

$N\text{s}=(\frac{1.05-0}{0.98})(\frac{\$12,000,000}{\$250,000})=51.43$

$N_B=(\frac{5.2-0}{6.5})(\frac{\$8,000,000}{\$110,000})=58.18$

所以应该买入51份股指期货合约，58份债券期货合约。