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Chinazdk · 2023年12月02日

关于标准差

  1. CFA I
  2. Portfolio

NO.PZ2015121801000068

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 provides the least amount of risk reduction?

选项：

A.

Asset 1 and Asset 2.

B.

Asset 1 and Asset 3.

C.

Asset 2 and Asset 3.

解释：

A  is correct.

An equally weighted portfolio of Asset 1 and Asset 2 has the highest level of volatility of the three pairs. All three pairs have the same expected return; however, the portfolio of Asset 1 and Asset 2 provides the least amount of risk reduction.

每项资产的标准差怎么计算?值是多少?

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Kiko_品职助教 · 2023年12月05日

嗨，努力学习的PZer你好：


每项资产的标准差公式

但是这道题并不需要求每项资产的。是看两两之间组合的标准差。

σp2 = w12σ12+w22σ22+2w1w2σ1σ2ρ1,2

根据这个公式可以看出，我们是要找到哪两对资产收益率的相关性系数是最大的。两两资产之间的相关系数越大，那么分散化效果越差，于是RISK REDUNTION也就越小。

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努力的时光都是限量版，加油！

Chinazdk · 2023年12月15日

还是不太理解 怎么判断Asset 1和 2相关系数呢?

Kiko_品职助教 · 2023年12月18日

嗨，努力学习的PZer你好：


算1和2的相关系数，用计算器就可以算出来。


以1、2资产的相关性计算为例，使用计算器：

[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=0.5。


然后用同样的方法求出1和3，2和3的相关系数，分别是-0.5和-1,所以1,2的相关系数最大，所以分散化减少RISK的效果最差。


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加油吧，让我们一起遇见更好的自己！

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