Suppose you develop a mutual fund that includes 78 stocks, all with equal weights in the fund's portfolio.The average standard deviation of the stocks is 44%, and the average pair-wise correlation among the stocks is 0.30.What is your estimate of the standard deviation of the fund's portfolio?

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Quizplus · Accepted Answer

The standard deviation of a portfolio ($\sigma_p$) can be estimated using the formula: $\sigma_p = \sqrt{\frac{1}{N} + \frac{(N-1)}{N} \times \rho} \times \sigma$, where $N$ is the number of assets in the portfolio, $\rho$ is the average pairwise correlation among the assets, and $\sigma$ is the average standard deviation of the assets. Plugging in the given values ($N = 78$, $\rho = 0.30$, $\sigma = 44\%$), we get $\sigma_p \approx 24.5\%$.

Suppose You Develop a Mutual Fund That Includes 78 Stocks