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Olivia.W🌸 · 2024年01月28日

TWR等于几何平均？但是我看讲义的公式TWR不用开方，几何平均要开方呀

  1. CFA I
  2. Quantitative

NO.PZ2022123001000150

问题如下：

A fund receives investments at the beginning of each year and generates returns for three years as follows:

Exhibit 1: Investments and Returns for Three Years

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 = –USD1,000, CF1 = –USD2,850, CF2 = –USD40,440, CF3 = +USD43,200.

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

Solving for IRR results in a value of IRR = −2.22 percent.

Note that A and B are 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 positive:

RT W = [(1.15) (1.14) (0.96)]1/3 − 1 = 7.97% .

TWR等于几何平均？但是我看讲义的公式TWR不用开方，几何平均要开方呀

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1 个答案

品职助教_七七 · 2024年01月29日

嗨，爱思考的PZer你好：


收益率是年化的。如果给出的条件是季度收益率，那么四个季度的1+return相乘后正好就是一年，用不着开方（或者说开的就是1次方）。这就是TWR有时候不用开方的情况，如果是普通计算几何平均遇到这种情况，也同样不用开方。

但如果投资时间超过了一年，此时就要做年化。这是讲义中几何平均公式需要开方的缘故。如果算TWR的时候发现投资时间超过了一年，同样也要做开方年化处理。

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