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考拉女士 · 2022年04月04日

5,20,38.46是哪里来的?

NO.PZ2015122802000051

问题如下:

An analyst gathers the following data for an equally-weighted index:

The return on the index over the period is:

选项:

A.

4.2%.

B.

6.8%.

C.

7.1%.

解释:

C is correct.

With an equal-weighted index, the same amount is invested in each security. Assuming $1,000 is invested in each of the three stocks, the index value is $3,000 at the beginning of the period and the following number of shares is purchased for each stock:

Security A: 50 shares

Security B: 20 shares

Security C: 38.46 shares.

Using the prices at the beginning of the period for each security, the index value at the end of the period is

$3,213.8: ($22 × 50) + ($48 × 20) + ($30 × 38.46). The price return is $3,213.8/$3,000 1 = 7.1%.

考点:等权重指数计算收益率

等权重有两种思路来计算,一种方式也是李老师上课讲的(直接计算收益率之和除以3)。还有一种就是这道题的思路,它是从等权重最本源的含义出发的:假设每只股票买相同的金额,因此每只股票在指数中的权重是相等的。两种方法的结果是一致的。但解析做法没有咱们上课讲的直接计算收益率之和除以3简便。

简单说一下,假设每只股票没相同的金额1000, 因此期初三只股票价值=1000*3=3000(这只是题目假设,可以是任意金额,10,100,1000任何数字都可以),那么期初A股票可以买1000/20=50只,B可以买20只,C可以买38.46只股票。到了期末由于三只股票价格发生变化,A价值=50*22=1100,B价值=20*48=960, C价值=38.46*30=1153.8,所以期末三只股票的价值=1100+960+1153.8=3213.8

因此该股指的收益率就等于期末价值除以期初价值减1= $3213.8/$3,000 – 1 =7.1%.

如题,5,20,38.46是哪里来的?

1 个答案

王园圆_品职助教 · 2022年04月04日

嗨,努力学习的PZer你好:


同学你好,因为是等权重方式构建的index,所以意思就是指数里的每个股票在构建的一开始买相同的金额。解析中假设了每支股票在期初都买1000元:“ Assuming $1,000 is invested in each of the three stocks, the index value is $3,000 at the beginning of the period and the following number of shares is purchased for each stock”,那就可以计算出期初每支股票期初买了多少股

A股票期初价格20,所以期初买的股份数=1000/20 = 50

B股票期初价格50,所以期初买的股份数 = 1000/50 =20

C股票期初价格26,所以期初买的股份数 = 1000/26 = 38.46



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