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子非鱼113 · 2019年12月27日

问一道题：NO.PZ2018070201000066

  1. CFA I
  2. Portfolio

问题如下：

The return projections have been made by Eunice. an analyst from an investment company, for each of the assets with the same probability of occurrence, which two assets are perfectly negatively correlated?

选项：

A.

Asset A and Asset B.

B.

Asset A and Asset C.

C.

Asset B and Asset C.

解释：

C is correct.

Asset B and Asset C have returns that are the same for Outcome 2, but the exact opposite returns for Outcome 1 and Outcome 3; therefore, because they move in opposite directions at the same magnitude, they are perfectly negatively correlated.

We can also use the calculator to measure the correlation. The correlation between asset B and asset C is -1, so perfectly negatively correlated.

看不懂，能解释一下吗

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1 个答案

星星_品职助教 · 2019年12月27日

同学你好，

首先要看明白这个表格，以B，C两个资产为例，第一个结果（outcome 1）就相当于B的结果是20%，C的结果是0%，以此类推。

可以用计算器直接解这类题目。首先2nd 7，然后输入X01=20，Y01=0，X02=10，Y02=10....................以此类推。输入结束后，按2nd 8，一直往下按，可以找到r=-1（前两项是a=20，b=-1）.这个r就是B和C的outcome的相关系数，所以是perfectly negatively correlated。

计算器的逻辑其实就是算出B，C各自的outcome的均值和标准差，然后根据公式求协方差和相关系数。

从理解的角度，可以观察到B和C的outcome2和outcome4是完全一样的，而outcome1相当于B在ooutcome2/4的基础上上涨了10%，C下降了10%。同理适用于outcome3，所以B，C的outcome是一个反方向变化。也就是perfectly negatively correlated。

考试的时候直接这么考我觉得概率不高，要是一旦真出现了，计算器的方法更快捷一些，也不用判断。加油

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