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绝世小笼包 · 2020年03月03日

问一道题:NO.PZ2018113001000005 [ CFA III ]

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 value of futures 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=(βTβSβS)(Sf)=(1.20.90.95)($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

题目中不严谨的地方能改吗?value of future不就是一份合约赚的钱吗?何老师课上也强调了,t=0时刻,value of future=0,t=T时刻,future的value就是这份future的净profit呀!
1 个答案

xiaowan_品职助教 · 2020年03月03日

嗨,从没放弃的小努力你好:


同学你好,这里 $262,000是期货合约在期末的价格,这里用value是不严谨的,我们会去更正,抱歉。


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


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