Question

Portfolio standard deviation and diversification: You are asked to give financial advice to a mutual fund manager. The fund has had a history of investing in an equally-weighted portfolio of 50 stocks and is considering cutting down the number of stocks to 10 or 20. You assume that all stocks the fund is considering investing in have the same standard deviation of 40% and that the correlation between each pair of stocks is identical and equal to 0.25.
a. To start your analysis, you calculate the standard deviation of the equally weighted portfolios with 10, 20, and 50 assets.

b. Given your answers to part a. what is the advice that you give the mutual fund manager?

Answer 1

Answer:

a) check attachment below

b) Whenever we have  a portfolio whatsoever, that minimizes the variance of the portfolio is always preferred. Therefore, the portfolio of 50 stock is better than portfolio of 20 stocks which is as well better than the 10 stocks portfolio. The fund manager especially the mutual fund manager should not consider cutting down the number of stocks. If reducing the number of  stock is very urgent then he should probably consider reducing it down to  20 as it is variance is less than that of 10 stocks portfolio.

Explanation: