The variance of a portfolio containing n assets:
A)Increases as n increases
B)Decreases as n increases
C)Is constant for any n greater than two
D)Does not change in a predictable way when n increases

Question

Quizplus · Accepted Answer

The variance of a portfolio containing n assets decreases as n increases because the variance of the portfolio is a weighted average of the variances of the individual assets, and the more assets that are added to the portfolio, the more diversified it becomes. Diversification reduces the overall risk of the portfolio, which is captured by the variance, so the variance decreases. However, this effect levels off as the portfolio becomes sufficiently diversified, so the variance is not constant for any n greater than two, as option C suggests. Option A is incorrect because the variance does not necessarily increase as n increases. Option D is incorrect because the variance does change in a predictable way as n increases.

The Variance of a Portfolio Containing N Assets