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Katherine · 2023年09月07日

这题

NO.PZ2018070201000063

问题如下:

Eunice, an analyst from an investment company, recently made the following statements:

Statement 1: With the increase in the number of investment assets in the equal weight portfolio, the contribution of the variance of each individual asset to the variance of portfolio increase;

Statement 2: With the increase in the number of investment assets in the equal weight portfolio, the contribution of the variance of each individual asset to the variance of portfolio decrease;

Statement 3: With the increase in the number of investment assets in the equal weight portfolio, the contribution of the variance of each individual asset to the variance of portfolio remains the same.

Which statement is most correct?

选项:

A.

Statement 1.

B.

Statement 2.

C.

Statement 3.

解释:

B is correct.

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

σρ2=σ¯2N+N-1NCOV¯=σ¯2N+N-1Nρσ¯2

根据公式,随着数量的增加也就是可以理解成n增大,用极限的思想看,当N趋近于无限大时,1/N趋近于0,N-1/N趋近于1,也就是整个公式只会受COV的影响,题目给出的条件并不影响COV,为什么不是不变呢,我这个理解有什么问题吗

1 个答案

Kiko_品职助教 · 2023年09月07日

嗨,爱思考的PZer你好:


题目给出的条件不影响cov,但是影响N啊。而且这道题就是考察的随着N不断增大的趋势变化,你说的情况只局限于N趋近于无限大,也不符合题目说的条件啊。statement2就是最符合公式描述的。随着N的增大,variance的贡献慢慢变小。statement3说的,随着N的增大,variance的贡献不不变,这明显是错误的。

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