Answer to Question #304271 in Statistics and Probability for stephensean

Question

In 2015, the mean return of all common stocks on the Philippine Stock Exchange was 0.45. The standard deviation of the returns was about 6.2. A student of finance forms all possible portfolios that invested equal amounts in 4 of these stocks and records the return for each portfolio. This return is the average of the returns of the 4 stocks chosen. What is the variance of the portfolio returns?

Answer 1

Let X be a random variable representing the average return of the 4 stocks, Y - representing return of 1 stock, then $V(Y)={\frac {V(X)} 4}={\frac {6.2^2} 4}={\frac {38.44} 4}=9.61$