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chris2.0🔱 · 2022年06月20日

可以这么想么

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=(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

这道题可以这么想么。不考虑远期市场多少份,分别计算现货市场收益增加5%。远期市场,收益率为(262000-25000)除以250000,算出来的收益率不一样

1 个答案

Hertz_品职助教 · 2022年06月21日

嗨,从没放弃的小努力你好:


同学你好

同学的问题:

这道题可以这么想么。不考虑远期市场多少份,分别计算现货市场收益增加5%。远期市场,收益率为(262000-25000)除以250000,算出来的收益率不一样

回答:

1.     首先题目中使用的是期货合约哈不是远期合约。然后同学的意思是不考虑期货合约的份数,计算单份合约的收益率这样。

2.     不可以的。

本题考察的是计算effective β,公式为effective β=组合的收益率/市场的收益率。

现在题目已经告诉了市场的收益率是5%了,这个是不需要计算的;所以我们只需要计算组合的收益即可。

计算组合的收益需要知道期初和期末的价值分别是多少,而这个组合中既包括了期货合约又包括了原来的股票头寸,所以二者缺一不可的哈,而且期货合约的份数也不能忽略掉的,因为8份合约都在组合中呀。

----------------------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!

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