Understanding the Sharpe Ratio

History has shown that it's nearly impossible to predict the ups and downs an investment will experience in the future. But by looking at historical swings, and comparing them to historical returns, the Sharpe Ratio may offer meaningful information about the balance between risk and reward.

Good investment decisions are based on a prudent assessment of risk. Investors who are uncertain about risks in their investment programs may be taking on additional risk.¹ Financial professionals have long known about this danger, and many of them have dedicated their careers to developing tools that help investors analyze risk. One well-known specialist is William Sharpe,² whose work has produced, among other achievements, a risk measurement that bears his name: The Sharpe Ratio. The ratio measures the relationship between an investment's historical return and its volatility, describing how much excess return an investment has generated per unit of risk.

Interpreting the results

In general, the higher the value of your fund's Sharpe Ratio, the better chance the fund could have at delivering excess returns potential over the long term while attempting to control volatility. When comparing investments that have positive excess returns, a Sharpe Ratio greater than 1 is good, greater than 2 is very good, and greater than 3 is excellent. (But note that when comparing investments that have negative excess returns, the results can be counterintuitive. For example, if two funds have identical negative returns, the fund with the most volatility will have a higher Sharpe Ratio.)

Sharpe Ratio: pros and cons

Pro: The ratio is calculated the exact same way regardless of type of investment, making it easy to use when comparing different types of funds. The Sharpe Ratio is always calculated in absolute terms — not relative to a market index — and it thereby treats each investment exactly the same. This makes it a natural comparative tool.

Con: If you're only looking at one investment, the ratio isn't very meaningful. For instance, if you know that the Sharpe Ratio for a particular fund is 1.2, that doesn't tell you very much by itself. But if you know the ratio for five funds, it will reveal which funds have delivered the highest returns for the amount of volatility experienced.

One tool among many

The Sharpe Ratio isn't the only tool for measuring the trade-off between risk and potential reward. But it may provide an additional layer of information to help you determine if an investment is in line with your risk preference.

Sharpe Ratio: the math

The ratio's calculation is not complex, but it does involve some reasonably advanced math along the way.

Here is the formula, assuming that we are analyzing a mutual fund's performance over a 24-month period:

What each variable stands for:

• x is the mutual fund being analyzed
• rx is the the fund's average rate of return for a given time period (since our time period in this example is 24 months, the percentage returns for each month are added up and divided by 24)
• Rf is the "risk-free" return — the return available without taking any risk — traditionally defined as the return on the 90-day Treasury bill.
• StdDev is the standard deviation of the fund's historical returns for the 24-month period (this measure looks at monthly returns and determines how much they stray from the average return during the period). Standard deviation is defined as a statistical measurement of dispersion around an average or mean.

¹ For a look at the perils of disregarding risk, and how such indifference contributed to the stock-market turmoil of 2008, see Joe Nocera's article, "Risk Mismanagement," in the January 4, 2009 issue of The New York Times Magazine.

² Professor Sharpe teaches at Stanford University and is among the three economists who received the 1990 Nobel Memorial Prize in Economic Sciences for their work on what is now called Modern Portfolio Theory, a commonly accepted framework for classifying and estimating risk. His home page is at http://www.stanford.edu/~wfsharpe.

Investing involves risk, including the possible loss of principal.

Views expressed and the information contained in this publication are current as of April 2009, and should not be considered a recommendation to buy, hold, or sell any security, and should not be relied on as research or investment advice.

Article is for informational purposes only and not meant to predict actual results. Information should not be construed as financial advice.

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