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威廉王Wei Wang · 2023年06月02日

计算分式是否正确？

  1. CFA I
  2. Equity

NO.PZ2018062002000044

问题如下：

Ahern, an analyst from an investment company, recently gathered the following information for an equal-weighted index comprised of assets A, B, and C:

What is the total return of this index?

选项：

A.

2.7%.

B.

3.79%.

C.

9.69%.

解释：

C is correct.

The total return of the index is calculated based on the price change of the underlying securities plus the total amount of received income or total amount of the weighted total returns of each security. The total return of A is 31.25 percent; the total return of B is -8.18 percent; and the total return of C is 6 percent:

A:10−8+0.58=31.25%\frac{10-8+0.5}8=31.25\%

B:19−22+1.222=−8.18%\frac{19-22+1.2}{22}=-8.18\%

C:25−25+1.525=6%\frac{25-25+1.5}{25}=6\%

An equal-weighted index applies the same weight (is13\frac13 ) to each security’s return; therefore, the total return =<span>31.25%+(−8.18%)+6%3=9.69%\frac{31.25\%+(-8.18\%)+6\%}3=9.69\%.

考点：Methods of index construction

这道题让我们计算的是等权重构建方法下的指数的total return，所以我们首先要区分price return和total return，计算total return需要包括期间的收益即股息。第二，这里是等权重的构建方法，等权重相当于每只股票买了相同的金额，那么我们就先计算每种股票的收益率再除以股票种类。

既然每个成分股权重相等，假设每成分股持有一股，计算分式不应该是（（10-8+0.5）+（19-22+1.2）+（25-25+0.5））/(10+19+25）？

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1 个答案

王园圆_品职助教 · 2023年06月02日

不对，同学，等权重不是每个股票买一股，而是每个股票都只买一块钱——所以实际每个股票能够买到的股数是不同的

请看以下讲义截图蓝色框部分，就是一般等权重的指数就是用以下这个公式计算的。

你的计算，其实是以价格为权重的计算方式

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3.79%. 9.69%. The totreturn of the inx is calculatebaseon the prichange of the unrlying securities plus the totamount of receiveincome or totamount of the weightetotreturns of easecurity. The totreturn of A is 31.25 percent; the totreturn of B is -8.18 percent; anthe totreturn of C is 6 percent: 10−8+0.58=31.25%\frac{10-8+0.5}8=31.25\%810−8+0.5​=31.25% 19−22+1.222=−8.18%\frac{19-22+1.2}{22}=-8.18\%2219−22+1.2​=−8.18% 25−25+1.525=6%\frac{25-25+1.5}{25}=6\%2525−25+1.5​=6% equal-weighteinx applies the same weight (is 13\frac1331​ ) to easecurity’s return; therefore, the totreturn = 31.25%+(−8.18%)+6%3=9.69%\frac{31.25\%+(-8.18\%)+6\%}3=9.69\%331.25%+(−8.18%)+6%​=9.69%.请问为什么equweighting inx 不考虑分红呢？

2020-10-16 00:39 1 · 回答

老师，看这道题题干和其他题库中求Equweight inx中的return题干毫无区别，但是这道题在求每个股票return时都是算上分红的，其他几道都是不算分红的。请问equweight 是不是不需要计算分红？equweight inx中是否有区分计算中是否加分红的办法。

2020-06-13 12:43 1 · 回答

3.79%. 9.69%. The totreturn of the inx is calculatebaseon the prichange of the unrlying securities plus the totamount of receiveincome or totamount of the weightetotreturns of easecurity. The totreturn of A is 31.25 percent; the totreturn of B is -8.18 percent; anthe totreturn of C is 6 percent: 10−8+0.58=31.25%\frac{10-8+0.5}8=31.25\%810−8+0.5​=31.25% 19−22+1.222=−8.18%\frac{19-22+1.2}{22}=-8.18\%2219−22+1.2​=−8.18% 25−25+1.525=6%\frac{25-25+1.5}{25}=6\%2525−25+1.5​=6% equal-weighteinx applies the same weight (is 13\frac1331​ ) to easecurity’s return; therefore, the totreturn = 31.25%+(−8.18%)+6%3=9.69%\frac{31.25\%+(-8.18\%)+6\%}3=9.69\%331.25%+(−8.18%)+6%​=9.69%.这一章节完全听得一头雾水，根据题干都不知道应该用哪个公式。有没有指数对应公式列表啊？

2020-06-12 00:02 1 · 回答