𝐶 𝑂 𝑉 ¯ = 𝜌 𝜎 ¯ 2

问题如下：

As the number of assets in an equally-weighted portfolio increases, the contribution of each individual asset’s variance to the volatility of the portfolio:

选项：

A.

increases.

B.

decreases.

C.

remains the same.

解释：

B is correct.

The contribution of each individual asset’s variance (or standard deviation) to the portfolio’s volatility decreases as the number of assets in the equally weighted portfolio increases. The contribution of the co-movement measures between the assets increases (i.e., covariance and correlation) as the number of assets in the equally weighted portfolio increases. The following equation for the variance of an equally weighted portfolio illustrates these points:

${\sigma }_{\rho }^2=\frac{{\overline{\sigma }}^2}{N}+\frac{N-1}{N}\overline{COV}=\frac{{\overline{\sigma }}^2}{N}+\frac{N-1}{N}{\overline{\rho \sigma }}^2$