# Understanding the Sharpe Ratio

It is very important for any investor to know how well their portfolio is performing. This is doubly true for quantitative traders testing multiple strategies; after all, you wouldn’t want to put your money in an underperforming strategy. While there are multiple ways one could asses the performance of a portfolio, the Sharpe ratio remains one of the most popular among institutional investors especially.

The **Sharpe Ratio** is a measure for calculating risk-adjusted return developed by Nobel laureate William F. Sharpe. It is the ratio of average return earned in the excess of risk free rate per unit of standard deviation or risk. It tells you the return an asset gives you per unit of risk taken to invest in that asset. The greater the Sharpe ratio the better. Sharpe Ratios above 1.00 are considered good, as this would suggest that the portfolio is offering excess returns relative to its volatility. Sharpe Ratios below 1.00 are considered bad, as this would suggest that the portfolio is offering supbar returns relative to the risk being taken, meaning the risk-free rate is greater than the portfolio’s return, or the portfolio's return is negative.

To calculate the Sharpe ratio one must subtract their risk-free return rate from their portfolio’s return rate. The risk free return rate is the return of an investment with zero risk. The yield for a U.S. Treasury bond, for example, could be used as the risk-free rate. It is also common to use the average return rate of the S&P 500 when evaluating investments. While not risk free, it does provide a good baseline. One can ask themselves if investing in portfolio X gives a better return than investing in the S&P 500 for the relative risk.

The Sharpe ratio can be used to evaluate a portfolio’s past performance when backtesting a quantitative strategy. An investor could also use expected future portfolio performance to calculate an estimated Sharpe ratio.

## Limitations of the Sharpe Ratio

The Sharpe ratio uses the standard deviation of returns in the denominator as its proxy of total portfolio risk, which assumes that returns are normally distributed. Not only are returns in the financial markets skewed away from the average, the standard deviation assumes that price movements in either direction are equally risky which isn’t the case here.

Another inherent risk to blindly trusting the Sharpe Ratio is that it can be relatively easily manipulated by simply lengthening the measurement interval. This will result in a lower estimate of volatility. For example, the standard deviation of daily returns is generally higher than that of weekly returns which is, in turn, higher than that of monthly returns.

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