# What is the Sharpe Ratio?

Sean P. Gilligan, CFA, CPA, CIPM

March 10, 2020

The Sharpe Ratio is calculated as the strategy’s mean return minus the mean risk-free rate divided by the standard deviation of the strategy. The Sharpe Ratio measures the excess return for taking on additional risk.

As one of the most popular performance appraisals measures, the Sharpe Ratio is used to compare and rank managers with similar strategies.

### Annualized Sharpe Ratio

When calculating the Sharpe Ratio using monthly data, the Sharpe Ratio is annualized by multiplying the entire result by the square root of 12.

### What is a Good Sharpe Ratio?

The Sharpe Ratio is a ranking device so a portfolio’s Sharpe Ratio should be compared to the Sharpe Ratio of other portfolios rather than evaluated independently.

Since the Sharpe Ratio measures excess return per unit of risk, investors prefer a higher Sharpe Ratio when comparing similarly managed portfolios.

### Example Sharpe Ratio Calculation

Suppose two similar strategies, Strategy A and Strategy B, had the following characteristics over one year. For this period, the average monthly risk-free rate is 0.10%.

Please note that the Sharpe Ratio calculated in this example is based on monthly data and, therefore, must be annualized to get the final result. The full calculation is as follows:

Although the strategies have the same average monthly return over the one-year period, the Sharpe Ratios differ significantly due to their differences in volatility (i.e., standard deviation). Because Strategy B has a much higher Sharpe Ratio, it is preferred over Strategy A to an investor deciding between the two.

### Sharpe Ratio Interpretation

The Sharpe Ratio is intended to be used for strategies with normal return distributions; it should not be used for a strategy that treats upside and downside volatility differently. The Sharpe Ratio treats both types of volatility the same. For example, if a manager is looking for high reward investments then upside volatility can be a good thing, but the Sharpe Ratio penalizes the strategy for any type of volatility. For return streams with non-normal distributions, such as hedge funds, the Sortino Ratio may be more appropriate.

### Why is the Sharpe Ratio Important?

The Sharpe Ratio is important when assessing portfolio performance because it adjusts for risk. Comparing returns without accounting for risk does not provide a complete picture of the strategy.

The Sharpe Ratio is commonly used in investment strategy marketing materials because it is the most widely known and understood measure of risk-adjusted performance.

#### Sharpe Ratio Calculation: Using Arithmetic Mean or Geometric Mean

Because the Sharpe Ratio compares return to risk (through Standard Deviation), Arithmetic Mean should be used to calculate the strategy return and risk-free rate’s average values. Geometric Mean penalizes the return stream for taking on more risk. However, since the Sharpe Ratio already accounts for risk in the denominator, using Geometric Mean in the numerator would account for risk twice. For more information on the use of arithmetic vs. geometric mean when calculating performance appraisal measures, please check out Arithmetic vs Geometric Mean: Which to use in Performance Appraisal.