Quantitative Analysis · Data Science · Machine Learning

# Evaluation Metrics: Sharpe Ratio

The Sharpe Ratio is a measure of the risk-adjusted return of an investment. It was developed by economist William F. Sharpe and is widely used as a trading evaluation metric.  It is calculated as the average return of an investment minus the risk-free rate, divided by the standard deviation of the returns. The risk-free rate is the return on an investment with no risk, such as a Treasury bill, and the standard deviation is a measure of the volatility of the returns.

The higher the Sharpe Ratio, the better the risk-adjusted return of the investment. A Sharpe Ratio of 1.0 is considered good, while a ratio of 2.0 or higher is considered excellent. A ratio below 1.0 indicates that the investment has underperformed a risk-free investment.
The Sharpe Ratio is often used to compare the performance of different investments or trading strategies. It can be especially useful for evaluating the performance of investments with high volatility, since it takes into account the risk of the investment.

Here’s the formula for the Sharpe ratio:

### Sharpe ratio = (portfolio return – risk-free rate of return) / portfolio standard deviation

For example, let’s say a portfolio has a return of 8% and a standard deviation of 4%, and the risk-free rate of return is 2%. The Sharpe ratio would be:

### (8 – 2) / 4 = 1

A Sharpe ratio of 1 indicates that the portfolio is generating a return that is equal to the level of risk it is taking on. A Sharpe ratio greater than 1 indicates that the portfolio is generating a return that is higher than the level of risk it is taking on, while a Sharpe ratio less than 1 indicates that the portfolio is generating a return that is lower than the level of risk it is taking on.

The Sharpe ratio is a commonly used metric for evaluating the risk-adjusted performance of a portfolio and it is a good way to compare the performance of different portfolios on a level playing field. However, it’s important to note that the Sharpe ratio does not account for the skewness or the kurtosis of the return distribution, which are other important aspects of the risk.

Additionally, it is also important to consider the Sharpe ratio in the context of the investor’s risk tolerance. For example, if an investor is willing to take on more risk for the chance of higher returns, a portfolio with a higher Sharpe ratio may be more attractive than one with a lower Sharpe ratio.