Sharpe vs. Treynor

To understand these ratios, let us first understand the types of risk of a fund. Total risk of a portfolio is measured by the standard deviation of its returns. The total risk actually consists of systematic risk and unsystematic risk. Systematic risk measures the volatility of a portfolio or a fund with respect to the market and is measured by beta (ß). Systematic risk is that part of the total risk that is general to the economy or the market as a whole and hence cannot be diversified. Specific risk or unsystematic risk is that part of the total risk that is specific to the company or the industry and hence can be diversified.

Sharpe Ratio

Sharpe ratio evaluates the performance of a portfolio based on the total risk of a portfolio. It measures the excess return generated by a portfolio over the risk free rate in relation to the total risk or standard deviation of a portfolio.

Sharpe Ratio= (Rp - Rf)/s

Where, Rp=return on the portfolio, Rf= risk free rate and s= standard deviation of the return of the portfolio

Higher the Sharpe ratio, better is the fund.

Illustration: Consider two funds A and B. Let return of fund A be 30% and that of fund B be 25%. On the outset, it appears that fund A has performed better than Fund B. Let us now incorporate the risk factor and find out the Sharpe ratios for the funds. Let risk of Fund A and Fund B be 11% and 5% respectively. This means that the standard deviation of returns - or the volatility of returns of Fund A is much higher than that of Fund B.

If risk free rate is assumed to be 8%,

Sharpe ratio for fund A= (30-8)/11=2% and

Sharpe ratio for fund B= (25-8)/5=3.4%

Higher the Sharpe Ratio, better is the fund on a risk adjusted return metric. Hence, our primary judgement based solely on returns was erroneous. Fund B provides better risk adjusted returns than Fund A and hence is the preferred investment. Producing healthy returns with low volatility is generally preferred by most investors to high returns...