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jay1180 · 2022年12月29日

这题没看懂题干和答案。。。。

  1. CFA I
  2. Portfolio

NO.PZ2015121801000067

问题如下：

An analyst has made the following return projections for each of three possible outcomes with an equal likelihood of occurrence:

If the analyst constructs two-asset portfolios that are equally-weighted, which pair of assets has the lowest expected standard deviation?

选项：

A.

Asset 1 and Asset 2.

B.

Asset 1 and Asset 3.

C.

Asset 2 and Asset 3.

解释：

C  is correct.

An equally weighted portfolio of Asset 2 and Asset 3 will have the lowest portfolio standard deviation, because for each outcome, the portfolio has the same expected return (they are perfectly negatively correlated).

辛苦老师讲一下。。。谢谢

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1 个答案

pzqa27 · 2022年12月29日

嗨，爱思考的PZer你好：


题目说如果把表格里的资产22组合，问哪两个资产组合后的标准差最小，这个是考察2个资产之间分散化程度的，所以我们用协方差来考量，选一个协方差最小的即可，当然了，协方差不好直接算，可以算相关系数，选一个相关系数最小的也一样

这个题于其说是考组合，不如说是考数量，不过都能做，主要考察的是算2个随机变量之间的相关系数。推荐使用计算器计算，带公式手算太麻烦。请严格按照下面步骤按计算器

以A选项资产1、资产2的收益率相关性系数计算为例，打开金融计算器：[2nd][7]进入data模式，依次输入X01=12，Y01=12；X02=0，Y02=6；X03=6，Y03=0，然后[2nd][8]进入STAT模式，一直按下箭头，直到屏幕出现r=，算出来是0.5。说明两组数据的相关性系数=0.5。同理，可以计算出资产1、资产3收益率的相关性系数为-0.5，资产2、3的相关性系数为-1。

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