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添晴 · 2023年10月23日

完全没懂

  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).

请问老师这是在考察哪个知识点呀？能系统解答一下吗？

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Kiko_品职助教 · 2023年10月23日

嗨，从没放弃的小努力你好：


这道题考察2个随机变量之间的相关系数计算。

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。

直接利用计算器求两组资产之间的相关系数。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，首先清除历史记录【2nd】【CLR WORK】

依次输入两组数据：X01=12【↓】Y01=12【↓】X02=0【↓】Y02=6【↓】X03=6【↓】Y03=0【↓】；

[2nd][8]进入STAT模式，一直按向下的箭头，直到出现r，r=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&资产3收益率的相关性系数为-1。

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