This week we introduced two major performance evaluation measures: Sharpe’s and Treynor’s. Which measure are you...

This week we introduced two major performance evaluation measures: Sharpe’s and Treynor’s. Which measure are you most likely to use for your current portfolio (the one you reported holding for your client in Portfolio Report 1)? What benchmark would you choose to compare performance of your portfolio?

The use of the Sharpe’s ratio has been more mainstream. Sortino’s is rarely mentioned in undergrad textbooks; however it is used by practitioners. Sortino’s Ratio is only penalizing for harmful volatility. In your opinion, do you think it would be appropriate to utilize this ratio? Would you use it to evaluate your current portfolio?

Expert Solution

Sharpe Ratio = [E(Ri) - Rf] / SDi

Treynor Ratio = [E(Ri)-Rf] / Betai

Sortino Ratio = [E(Ri) - MAR] / Down side deviation

Where E(Ri) is the expected return on security i , Rf is the Risk free rate, SD is the standard deviation of returns of the security i, MAR is the minimum acceptable return. Down side deviation is also called semi standard deviation.

While SD represents total risk i.e. systematic risk + unsystematic risk, Beta only represents market risk. For a well diversified portfolio, the unsytematic risk is neglibile and therefore Sharpe and Treynor ratios converge. If the portfolio is well diversified one can use the Trenynor Ratio. However, if the portfolio is not diversified one, Sharpe ratio is a better measure of portfolio performance.

The Sortinio Ratio differes from Sharpe ratio in that it considers the semi standard deviation in the denominator instead of the standard deviation used in case of Sharpe ratio. Down side deviation is an asymmetric measure of risk. It only considers outcomes when the return on the security was lower than the expected return. In other words, it considers only negative shocks and not positive surprises.

Using Sortiono ratio will result in increased allocation to stocks which have a distribution of returns that is positively skewed and lower allociation to stocks where the distribution of returns is negatively skewed. The Sortino ratio can therefore be used in practice and can improve the selection of stocks. It would help in eliminating stocks with high probability of big down side surprises.

jeff jeffy answered 2 years ago

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