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yuxy · 2024年06月19日

money weighted 的r求解有三次方了，可以直接用计算器按出来吗？还是说得解三次方程？

  1. CFA I
  2. Portfolio

NO.PZ2015121801000135

问题如下：

A fund receives investments at the beginning of each year and generates returns
as shown in the table.


Which return measure over the three-year period is negative?

选项：

A.

Geometric mean return

B.

Time-weighted rate of return

C.

Money-weighted rate of return

解释：

C is correct. The money-weighted rate of return considers both the timing and amounts of investments into the fund. To calculate the money-weighted rate of return, tabulate the annual returns and investment amounts to determine the cash flows

CF0 = –$1,000, CF1 = –$2,850, CF2 = –$40,440, CF3 = +$43,200

Each cash inflow or outflow occurs at the end of each year. Thus, CF0 refers to the cash flow at the end of Year 0 or beginning of Year 1, and CF3 refers to the cash flow at end of Year 3 or beginning of Year 4. Because cash flows are being
discounted to the present—that is, end of Year 0 or beginning of Year 1—the period of discounting CF0 is zero whereas the period of discounting for CF3 is 3 years. Results in a value of r = –2.22%

Note that B is incorrect because the time-weighted rate of return (TWR) of the fund is the same as the geometric mean return of the fund and is thus positive

money weighted 的r求解过程是否就是把cf0+cf1+cf2的pv之和求出来，等于cf3的pv，就可以求解方程了。但这个方程中r有三次方了，可以直接用计算器按出来吗？还是说得解三次方程？

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Kiko_品职助教 · 2024年06月19日

嗨，爱思考的PZer你好：


直接计算器就可以按出来。用金融计算器第二行。按CF，依次输入CF0 = –$1,000, CF1 = –$2,850, CF2 = –$40,440, CF3 = +$43,200、然后按CPT →IRR，得到的答案就是。

关于TWRR和MWRR的计算，24年考纲已经做了删除，这道题目也可以不用看了。稍后会做下架处理。

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