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kevinzhu · 2020年01月13日

问一道题：NO.PZ2015121801000067

  1. CFA I
  2. Portfolio

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).

完全负相关可得出该组合有最低的标准差,计算机是不是也可以算出标准差，为啥我1&2,2&3算出来的标准差是一样的，能否麻烦把1&2, 2&3，1&3的计算器步骤都写出来，然后比较标准差


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2 个答案

🐳Sakura · 2020年01月13日

上图可得2和3的变动完全相反，correlation两两组合中是最小的，那么风险分散度最大，所以组合的方差最小

星星_品职助教 · 2020年01月13日

这个图我有点没看明白，横纵轴分别是什么？

星星_品职助教 · 2020年01月13日

同学你好，

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。这两个可以自己按一下熟练一下。最后解题的思路是通过比较相关系数来比较组合的标准差，相关系数为-1的分散化效果最好，组合标准差最小。

🐳Sakura · 2020年01月13日

老师，我一直用另外一个方法解题，请老师看一下思路对嘛

🐳Sakura · 2020年01月14日

纵轴是收益率，横轴是Outcome的顺序

星星_品职助教 · 2020年01月14日

我觉得例如第一个1和2都是12的情况，outcome 2=12%应该画在横轴“2”的正上方这个部分。但这样就没法形成你想表达的那个直线了

🐳Sakura · 2020年01月14日

老师我没太明白你指的是哪一个点呢？你的意思是如果题目改变数字就没办法画图了是吗？

星星_品职助教 · 2020年01月14日

哦，我看明白了。我觉得这道题这么解是可以的，因为2,3正好是完全相反的关系。但我不确定换了数字还行不行，如果不是恰好是-1，例如是-0.7和-0.5直接对比，可能从图上没法直接看出来

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