Final answer:
The variance of an equally weighted portfolio is a combination of the average variance of the individual stocks and their average covariance, adjusted for the diversifying effect of holding a portfolio. As the number of portfolio stocks increases, the overall risk typically decreases, demonstrating the value of diversification.
Step-by-step explanation:
The formula for the variance of an equally weighted portfolio (Var(Rp)) is given by:
Var(Rp) = (1/n) × Average Variance of the Individual Stocks + (1 - 1/n) × Average Covariance between the Stocks
In this formula, n represents the number of stocks in the portfolio, and the portfolio weights are 1/n for each stock since it is equally weighted. The first term, Average Variance of the Individual Stocks, measures the average risk of the stocks if they were held in isolation. The second term, Average Covariance between the Stocks, measures the degree to which the stocks in the portfolio move together. The factor of (1 - 1/n) adjusts the average covariance between the stock pairs for the diversifying effect of holding a portfolio of n stocks.
The benefits of portfolio diversification can be observed as n increases, where the overall portfolio risk (variance) decreases, assuming the stocks are not perfectly correlated. This formula underscores the importance of diversification in risk management for investment portfolios.