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vee · 2022年12月20日

不懂考点

NO.PZ2022081802000024

问题如下:

Question

Investor A and Investor B invest in a fund for two years:


Given the information in the table, which of the following is least likely to be an explanation for the difference between the two money-weighted rates of return?

选项:

A.Investor A increased the investment in the fund at the end of year 1 whereas investor B did not make any additions or withdrawals. B.Investor B decreased the investment in the fund at the end of year 1 whereas investor A did not make any additions or withdrawals. C.The investors invested different amounts at inception and afterward did not make any additions or withdrawals.

解释:

Solution

C is correct. The money-weighted rate of return (MWR) is sensitive to the additions and withdrawals of funds in a portfolio over the course of an investment. If, at inception, investors A and B invest amounts of different size in the same fund but then neither add nor withdraw any cash for two years, they will obtain exactly the same MWR. In contrast, if investor A increases the investment in the fund at the end of year 1 and investor B does not make any additions or withdrawals, then Investor A will have a lower MWR than investor B because in year 2 the fund underperformed with respect to year 1. By the same token, if investor B decreases the investment at the end of year 1 and investor A does not make any additions or withdrawals, then investor B will have a higher MWR than investor A because she decreased the investment before an underperforming year.

A is incorrect. If investor A increases the investment in the fund at the end of year 1 and investor B does not make any additions or withdrawals, then the former will have a lower MWR than the latter because in year 2 the fund underperformed with respect to year 1.

B is incorrect. If investor B decreases the investment at the end of year 1 and investor A does not make any additions or withdrawals, then the former will have a higher MWR than the latter because she decreased the investment before an underperforming year.

不懂考点,能解释一下吗

1 个答案

pzqa27 · 2022年12月20日

嗨,努力学习的PZer你好:



这个题给了1个资产,第一年是正收益,第二年负收益,然后给了2个人,这俩人的MWRR不一样,然后问我们哪个选项不能解释这个事请,这个题是选C的,因为C说了,这俩人期初投资不一样,期间没有从账户里取钱或者加钱。这个是不能解释MWRR不一样的。可以从2个角度判断

第一个角度是公式法,如果同学基本功比较扎实的话,可以知道,MWRR的计算方法的本质就是令NPV=0,由于C说了期间不存钱也不取钱,所以,期间的CF都是0,但是最后一期的CF是跟期初投资有关的,而且可以说是线性关系,当期初投资多的时候,最后一期收的也多,期初投资少的时候,最后一起收到的也少,所以倒解出的MWRR不受影响。

当然上面这个方法对基本功有要求,并且需要一些数学功力,我个人是不推荐的,只是为了说明C是可以从数学的角度证明的,这个题如果是我个人来做的话,我会带点数字验证一下。

比如假设第一年回报率5%,第二年回报率-3%,A这个人期初投资10元, B这个人期初投资30元,符合C的描述,然后我们算一下,请严格按照下列步骤按计算器

A:

CF0=-10, CO1=0, F01=1, CO2=0, FO2=1, CO3=10*(1+5%)*(1-3%)=10.185,然后IRR=算出来是0.6129

B

CF0=-30, CO1=0, F01=1, CO2=0, FO2=1, CO3=30*(1+5%)*(1-3%)=30.555,然后发现IRR依旧是0.61290

可以发现IRR是相同的,并不能解释A和B的MWRR不同,所以C不对,选C

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

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