Answer to Question #173286 in Statistics and Probability for Denisse Bisuña

Question

In 2015, the mean return of all common stocks on the Philippine Stock Exchange was 3.5%. The standard deviation of the returns was about 26%. A student of finance forms all possible portfolios that invested equal amounts in 5 of these stocks and records the return for each portfolio. This return is the average of the returns of the 5 stocks chosen. What are the mean and standard deviation of the portfolio returns?

Answer 1

Assume that the population distribution of returns on individual common stocks is Normal. Then

$$mean=\mu_{\bar{x}}=\mu=-3.5\%$$

$$standard\ deviation=\sigma_{\bar{x}}=\dfrac{\sigma}{\sqrt{n}}$$

$$=\dfrac{26}{\sqrt{5}}\%\approx11.6276\%$$