Explanation

For an equally weighted portfolio with n assets, the portfolio variance formula is:

$\sigma_p^2 = \frac{1}{n} \bar{\sigma}^2 + \frac{n-1}{n} \bar{\text{Cov}}$

Where:

• $\bar{\sigma}^2$ = average variance of individual assets = 0.04
• $\bar{\text{Cov}}$ = average covariance between assets = 0.01
• n = number of assets = 500

Plugging in the values:

$\sigma_p^2 = \frac{1}{500} \times 0.04 + \frac{500-1}{500} \times 0.01$

$\sigma_p^2 = \frac{0.04}{500} + \frac{499}{500} \times 0.01$

$\sigma_p^2 = 0.00008 + 0.00998$

$\sigma_p^2 = 0.01006$

This is closest to 0.01.

Key Concept: As the number of assets in an equally weighted portfolio increases, the portfolio variance approaches the average covariance between assets. This demonstrates the principle of diversification - idiosyncratic risk (individual asset variance) can be diversified away, leaving only systematic risk (covariance risk).