An equal-weighted portfolio consists of 100 securities. The average return of the securities is 0.01, the average variance of the securities is 0.08, and the average covariance between any pair of securities is 0.02. What is the return standard deviation of the portfolio?
Question
An equal-weighted portfolio consists of 100 securities. The average return of the securities is 0.01, the average variance of the securities is 0.08, and the average covariance between any pair of securities is 0.02. What is the return standard deviation of the portfolio?
Solution
To calculate the standard deviation of the portfolio, we need to use the formula for the standard deviation of an equally weighted portfolio:
Standard Deviation = sqrt[(1/N)*Variance + [(N-1)/N]*Covariance]
where N is the number of securities, Variance is the average variance of the securities, and Covariance is the average covariance between any pair of securities.
Given that N=100, Variance=0.08, and Covariance=0.02, we can substitute these values into the formula:
Standard Deviation = sqrt[(1/100)*0.08 + [(100-1)/100]*0.02] Standard Deviation = sqrt[0.0008 + 0.0198] Standard Deviation = sqrt[0.0206]
Therefore, the standard deviation of the portfolio is sqrt[0.0206] = 0.1435 or 14.35% when expressed as a percentage.
So, the correct answer is 14.35%.
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