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ditto · 2024年11月11日

公式里面也有协方差，为什么C不对

  1. CFA I
  2. Portfolio

NO.PZ2018070201000064

问题如下：

Eunice, an analyst from an investment company, recently made the following statements about an equally-weighted portfolio consisting of a large number of assets：

Statement 1: Average variance of the individual assets contributes the most to the volatility of the portfolio.

Statement 2: Standard deviation of the individual assets contributes the most to the volatility of the portfolio.

Statement 3: Average covariance between all pairs of assets contributes the most to the volatility of the portfolio.

Which statement is most correct?

选项：

A.

Statement 1.

B.

Statement 2.

C.

Statement 3.

解释：

C is correct.

As the number of assets in the same weighting portfolio increases, the co-movement between assets also increases. As the number of assets contained in the equally weighted portfolio increases, the contribution of each individual asset's variance to portfolio volatility decreases.The following equation for the variance of an equally weighted portfolio illustrates these points:

σ p 2 = σ -2 N + N−1 N COV ¯ = σ -2 N + N−1 N ρ ¯ σ ¯ 2

A是公式的定义理解了，

对于C ，加号后面的部分里面有协方差呀， 为什么C不对

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已采纳答案

Kiko_品职助教 · 2024年11月12日

嗨，爱思考的PZer你好：


这道题答案是选C啊。C是对的。

这道题首先要记忆一个结论，就是当资产数量很多的时候，协方差对于整个组合的方差的影响要大于单个资产的方差。答案就是C。

这个结论可以从答案解析里那个公式得到，这个公式其实有几个前提假设，首先各个资产的方差都相同，其次各个资产两两之间协方差都相同，最后就是equally weighted。可以从公式中观察到组合方差是单个资产方差和协方差之间的加权平均，但协方差的权重（当N很大时）要远大于方差的权重，事实上只要N＞2，协方差的权重就会更大，也就是对组合方差影响的更多。这个公式的推导过程的意义不大，建议直接从加权平均的角度进行记忆。

所以单个资产的方差虽然也会影响组合方差，但是影响程度没有协方差那么大。

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