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庄鑫 · 2022年09月23日

求解

  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).

这道题目都没给出彼此间的Correlation或者Covariance，怎么计算呢？

计算过程请明示。

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已采纳答案

Kiko_品职助教 · 2022年09月26日

嗨，从没放弃的小努力你好：


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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庄鑫 · 2022年09月26日

以A选项资产1 & 资产2为例，计算出二者间的correlation之后，是不是用：根号下W1²E(R1)²W2²E(R2)²那个长长的公式计算expected standard deviation？

庄鑫 · 2022年09月26日

什么样的数据可以直接用计算器算出相关系数？有什么特征吗？

Kiko_品职助教 · 2022年09月28日

嗨，从没放弃的小努力你好：


是的。但是可以不用算，根据ρ大小直接判断。根据公式，ρ越小，σ越小。ρ最小取-1，此时组合的标准差最小。


什么样的数据可以直接用计算器算出相关系数？有什么特征吗？

----就是这道题这样啊，给了不同资产的几个outcome。

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