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花卷喵 · 2023年09月04日

整个头寸的收益=$6,346,000/$6,000,000-1=0.0577

  1. CFA III
  2. Derivative

NO.PZ2018113001000005

问题如下：

The equity portfolio has a market value of $6,000,000, The pension fund plans to use a futures contract priced at $250,000 in order to increase the beta from 0.9 to 1.2 for the period of one month. The futures contract has a beta of 0.95. One months later, the return of equity market is 5%, the market value of equity portfolio is $6,250,000, the price of futures contract is $262,000.

The effective beta of the equity portion of the fund is closest to:

选项：

A.

1.15.

B.

1.20

C.

1.05

解释：

A is correct.

考点：计算effective beta

解析：

将beta从0.9调整为1.2需要的合约数量为：

Nf=(βT−βSβS)(Sf)=(1.2−0.90.95)($6,000,000$250,000)=7.58N_f=(\frac{\beta_T-\beta_S}{\beta_S})(\frac Sf)=(\frac{1.2-0.9}{0.95})(\frac{\$6,000,000}{\$250,000})=7.58

因此，需要买入8份期货合约。

一个月之后：

期货合约所带来的利润=8×（262,000-250,000）=$96,000

股票组合的市场价值变为6,250,000，加上期货合约的收益可以得到整个头寸的价值=$6,250,000+$96,000=$6,346,000，

整个头寸的收益=$6,346,000/$6,000,000-1=0.0577

又因为市场的收益率为5%，而组合的收益率为5.77%，所以组合的有效贝塔为：

0.0577/0.05=1.154

这里算整个头寸收益的时候，为什么不在分母加上买期货的成本？

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已采纳答案

pzqa31 · 2023年09月04日

嗨，从没放弃的小努力你好：


因为期货期初的成本是0

----------------------------------------------
努力的时光都是限量版，加油！

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