Sharpe ratio

Measuring the performance of a portfolio over time by just looking at its profitability is not a good idea. The reason is that different portfolios can have obtained other profits even though they all have the same underlying strategy. A good performance metric thus incorporates the risk component. The most basic performance metric is the Share ratio. Also known as the return-to-variability ratio introduced by Sharpe. This metric indicates the amount of return a portfolio is earning in excess of the risk free rate adjusted for volatility. The higher the portfolio return, the better its performance. The lower its volatility, the better the its performance.

 SR = \dfrac{r_p-r_f}{\sigma_p}

Sharpe ratio and risk free rate choice

The risk free rate stated in the Sharpe ratio is a theoretical concept and doesn’t exist in reality. However, in practice often the 3-month T-Bill or the Libor rate is used as the risk free rate. Retail investors could also opt for using the interest rate of their savings account. Implying that this is their best ‘risk-free’ alternative. Any investment should thus in the long-run beat the return earned on a regular savings account.

Sharpe ratio problems

The Sharpe ratio is a good and simple performance metric. However, it may not be a good metric in case on non-normal returns. The return could for example be skewed, and or have a fat tail. In these cases, the Sharpe ratio metric underestimates the risk component, and therefore is too optimistic. Investors unaware of this issue can thus easily be fooled and surprised when times get though.

Summary

The Sharpe ratio, or return-to-variability ratio, is a risk-adjusted performance measure. It indicates the extra return a certain strategy, manager, or portfolio has earned for every unit of risk taken.

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