Question

Suppose that over the same time period two portfolios have the same average return and the same standard deviation of return, but portfolio A has a higher beta than portfolio B. According to the Sharpe measure, the performance of portfolio A __________.

is better than the performance of portfolio B

is the same as the performance of portfolio B

is poorer than the performance of portfolio B

cannot be measured since there is no data on the alpha of the portfolio

Answer 1

is the same as the performance of portfolio B.

The Sharpe ratio is the average return earned in excess of the risk-free rate per unit of volatility or total risk. Mathematically, the formula for same is represented as:

Now, the two portfolios in our question have same average return and same standard deviation. Risk free rate would be same for all asset portfolios. Hence, sharpe's ratio would be same for both portfolios.

Beta is higher for portfolio A, hence it has higher systematic risk associated with it. But, Sharpe's ratio talks about total risk, which is, systematic risk + unsystematic risk.