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RichardGuan · 2020年03月09日

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:

A.

49 stock index futures contracts and 60 bond futures contracts.

B.

51 stock index futures contracts and 58 bond futures contracts.

C.

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,

Ns=(1.0500.98)($12,000,000$250,000)=51.43N\text{s}=(\frac{1.05-0}{0.98})(\frac{\$12,000,000}{\$250,000})=51.43

NB=(5.206.5)($8,000,000$110,000)=58.18N_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。

这道题是简化了,所以没有给conversion factor,是吗?

1 个答案

xiaowan_品职助教 · 2020年03月10日

嗨,努力学习的PZer你好:


同学你好,因为这道题直接给出了 bond futures contract 的 duration,就不需要再进行换算了哈。如果题目中给出的是某个特定的交割债券标的价格,一般是CTD, 那么就还需要一步CF的处理。


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虽然现在很辛苦,但努力过的感觉真的很好,加油!