Question

You have a market portfolio and the risk premium for holding it is 5% per year. rf = 5%. There are two new stock issues: A or B. A stock has a standard deviation of 40%, a beta of 0.5, and an expected return of 8.0%. B stock has a standard deviation of 30%, a beta of 1.0, and an expected return of 9.0%. If you can add at most one stock to your portfolio, which one do you choose?

Answer 1

One of the primary measures in portfolio management is Risk adjusted return measure also given by Sharpe ratio.

Sharpe ratio = (Rs - Rf)/ s where Rs is the stock return, Rf is the risk free rate and s is the standard deviation of the stock.

Sharpe ratio for A = (8% - 5%)/40% = 0.075

Sharpe ratio for B = (9%-5%)/30% = 0.133

As Sharpe ratio for B is larger, B will be chosen as the stock to the portfolio.