The relationship between risk and return is an essential concept in finance, which argues that riskier investments should compensate investors with higher returns and safer investments should not experience exorbitant price fluctuations.

When comparing the performance of two securities, funds or portfolios, investors must consider risk-adjusted returns to see if they are being adequately compensated for the risk they are assuming. The goal is to achieve the largest return per unit of risk.

William Sharpe devised the Sharpe ratio in 1966 to measure this risk/return relationship, and it has been one of the most-used investment ratios ever since. Here, we discuss how to calculate and interpret the Sharpe ratio.

How Does the Sharpe Ratio Work?

The Sharpe ratio gives you a single number to judge the return of an investment to the variability of those returns. Sharpe’s thought process when creating it was that an investor needed to look at both the expected return and the risk. By doing so, an investor can compare one investment against an alternative.

To fully understand how the Sharpe ratio works, you’ll want to break down each component.

Average Return

The Sharpe ratio was originally developed as a forecasting tool, but it can also be used to calculate a historical risk-adjusted return. Expected average returns are used to calculate the forward-looking ratio, whereas actual returns are used in the historical ratio.

The expected return is also known as the required rate of return because it represents the minimum return investors require to compensate them for the added risk, which includes both the riskiness of the investment and the time value of money.

Risk-Free Rate

The risk-free rate (Rf) is the return investors require to compensate for the time value of money alone. Typically, investors use the return on U.S. Treasury bills for the risk-free rate because it is reasonable to assume the U.S. government will not default on its debt obligations, and thus investors need only be compensated for the time their capital is tied up in the security.

The Sharpe ratio requires that Rf represents the average return of the risk-free rate over the time period under evaluation. When analyzing a three-year period, investors must average the rate of return on T-bills over the same three-year period.

Traditionally, the shortest-dated bill is used since it is the least volatile. However, some argue that the risk-free security should match the duration of the investment. Since equities theoretically have an infinite duration, one could argue that the longest-dated bill should be used.

Standard Deviation

The standard deviation of a security measures how far returns deviate on average from its mean (or average) return. Standard deviation is a common indicator used to measure the volatility, and thus the riskiness, of an investment. For instance, an investment that deviates only 3% from its mean on average is judged as less risky than an investment with a 20% average deviation.

How to Calculate the Sharpe Ratio

You can use the three main components to calculate the Sharpe ratio.

The Sharpe ratio formula is as follows:

Sharpe Ratio = (Average rate of return – Risk free rate of return) ÷ Standard deviation

The Sharpe ratio formula subtracts the risk-free rate of return from the average rate of return of the investment you are evaluating. Once you calculate that, you take this number and divide it by the standard deviation of the security’s average rate of return.

How to Analyze a Company Using the Sharpe Ratio

When computing the Sharpe ratio, investors must first make sure they have an abundance of consistent and comparable data points. The more data points we use, the more likely distribution is normal and thus the more accurate our results will be. Although we use monthly data here, shorter intervals can be used but are more volatile and may require a longer time period to compensate for the added volatility.

Basing the standard deviation on an entire population of returns may be preferable when comparing historical performance, whereas sampling may be preferable when forecasting. We then apply the three main components to the formula to get the Sharpe ratio.

When analyzing the Sharpe ratio, the higher the value, the more excess return investors can expect to receive for the extra volatility they are exposed to by holding a riskier asset. Similarly, a risk-free asset or a portfolio with no excess return would have a Sharpe ratio of zero.

Although choosing the investment with the highest Sharpe ratio is logical, diversification and risk aversion should be considered first.

Investing Using the Sharpe Ratio

The Sharpe ratio is used to determine if an investment’s expected return is high enough to justify its risk. A driving factor behind the Sharpe ratio’s popularity is its ability to make comparisons between investments possible. In addition, the ratio has the advantage of being introduced at a time when alternative measures of assessing risk-adjusted returns were not widely available.

Of course, you’ll want to make sure you are using other financial metrics to determine if the investment is right for your portfolio. Having the right resources, strategies and tools is important to complete your due diligence before investing in a specific security. Learn how utilizing the A+ Investor robust suite of screening tools and financial metrics can help you become a well-informed investor.

Additional Resources About the Sharpe Ratio

Want to learn more about the Sharpe ratio or risk-adjusted returns? Check out some additional resources and articles to better understand how you can use this ratio to invest with confidence:

• Online Exclusive: Understanding Risk-Adjusted Returns via the Sharpe Ratio
• Measuring Risk-Adjusted Performance With the Treynor Ratio
• The Sortino Ratio
• The Pains and Gains of Investing

This article was originally published in Computerized Investing, Fourth Quarter 2012 .