What is the Sharpe Ratio?

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.

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

Sharpe Ratio Formula

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.

As an example, suppose two similar strategies, Strategy A and Strategy B, had the following characteristics over one year. For this period, the average risk-free rate is 0.1%.

Please note: the Sharpe Ratio calculation below has monthly measures as inputs and then annualizes the final result.

Although the strategies perform similarly, 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 would be 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.

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.

Arithmetic vs Geometric Mean: Which to use in Performance Appraisal

Most performance appraisal measures utilize a mean return in its calculation. This can be in the form a geometric mean or a simple arithmetic average. Because both types of means can be used, it raises the question: Which measure should be applied?

When calculating performance, we are accustomed to calculating returns geometrically (i.e., including compounding). Because of this, many investment managers use the geometric mean in appraisal calculations as it is easy to use the reported time-weighted return, rather than separately determining the arithmetic mean. But using geometric mean is not the most appropriate choice when evaluating risk-adjusted appraisal measures.

When calculating performance appraisal measures that compare return to risk, such as Sharpe ratio, the return used in the numerator of the ratio should be the arithmetic mean of the return stream, not the geometric mean. In many cases, the difference between using the arithmetic mean versus geometric mean will be immaterial; however, the greater the volatility in the return stream, the more material the difference will be. Let’s look at a simple example that demonstrates this effect:

Strategies with significant volatility have lower geometric means than arithmetic means (7.5% vs. 8.4% for Portfolio 2 above). This is because the geometric mean penalizes the return stream for risk-taking. In the case of the Sharpe Ratio, the standard deviation (which also accounts for risk-taking) in the denominator will be higher as a result of this higher volatility (1.5% for Portfolio 1 vs. 14.2% for Portfolio 2). In this case, using the geometric mean therefore results in a penalty for risk in both the numerator and denominator of the ratio.

Because risk is already being accounted for in the denominator, there is no need to include it in the numerator; in fact, including it would be double-counting the risk taken. As a result, for measures like Sharpe Ratio, it is more appropriate to use the arithmetic mean than geometric mean.

Although, in many cases, using the geometric return will not have a material effect on the outcome when comparing risk-scaled performance measures, it is technically more accurate to use the arithmetic mean. Its implications are more relevant when evaluating strategies with higher volatility.