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弓 · 2023年02月13日

为什么分子不用equity的增量?

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

既然是计算return,当然分子用期间变化量,分母用初始值。


请问,既然分子的future部分用了变化量,为啥equity部分不用(6'250'000-6'000'000)?

1 个答案
已采纳答案

Lucky_品职助教 · 2023年02月13日

嗨,爱思考的PZer你好:


这个公式是从 βT×S=βS×S + βf × F×Nf 变形过来的,我们用future调equity的beta,equity的量是不变的。$6,250,000是One months later之后的数据了,不是在调整过程中的数据

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

wj2692875531 · 2023年09月02日

老师你的解释我还是没懂 能详细解释一下吗 因为我在算return的时候也用了期末减期初我是这么算的: V0= 6000,000 V1 = 6250,000 + 8*(262000-250000) = 6,346,000 R = (6,346,000 - 6000,000)/6000,000 然后如果像你说的equity 的量不变 (这点我在其他地方也看到过)那为什么你算v1 的时候要把它变成6,250,000呢?如果equiy不变 那么所有的profit or loss 都是futures value改变带来的吧

wj2692875531 · 2023年09月03日

老师不好意思我看错了 公式后面有减掉1。 请忽略我这个问题

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