Many investors make the mistake of simply focusing on return. But risk is a key element of portfolio performance, and in many cases, it doesn't make sense to take on extra risk for a minimal amount of potential reward. The Sharpe ratio, which was named after Nobel Prize winner William F. Sharpe, gives you the ability to assess risk based on the volatility of your portfolio's returns and on how your average return on investment compares to risk-free returns on assets like short-term Treasury bills. By comparing your Sharpe ratio to the corresponding figures for investing benchmarks, you can get a sense of whether you're getting properly rewarded for the risk you're taking.

How the Sharpe ratio works

Fortunately, it doesn't take a Nobel laureate to understand the basic math behind the Sharpe ratio. The ratio equals the difference between the portfolio's return and the risk-free return, divided by the statistical standard deviation of the portfolio's excess return.

That might sound like a mouthful, but in practical terms, it translates to the following observations:

  • The greater your return over the risk-free return, the higher your Sharpe ratio will be.
  • The smoother your returns are over time, the higher your Sharpe ratio will be.
Stock charts and metrics.

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For example, consider a couple of basic comparisons. As a starting point, say that the risk-free annual return recently has been 2% and you have a stock portfolio that has averaged 8% annual returns over the past five years. From year to year, the returns have all been within a couple percentage points of the 8% mark.

In the first comparison, you're going up against another investor's portfolio. That investor has only managed to average 7% annually, but the year-to-year returns have all been similarly scattered within just a couple percentage points of the 7% figure. In that case, volatility will be the same, but the excess return in your portfolio -- 8% less 2%, or 6% -- is higher than the other investor's 5% excess return. Therefore, your Sharpe ratio is higher. That's pretty easy to understand, because your return was higher.

The second comparison is a little more subtle. Say that the other investor matches your 8% average annual return. However, from year to year, the moves in the portfolio are much more abrupt, with huge gains in some years followed by outright losses in others. In that case, the excess return is the same, but the volatility of your portfolio is less. Dividing the same excess return by a smaller volatility leads to a higher Sharpe ratio. That reflects the fact that even though both portfolios earned the same return, your portfolio did so with less inherent risk.

Where the Sharpe ratio gets complicated

In situations like the ones above, it's clear that one portfolio is better than another. But in other cases, reasonable people can differ about whether the Sharpe ratio accurately measures risk in a way that matches with investors' risk tolerance.

For instance, say that one portfolio offers twice the excess return of another portfolio but with three times the volatility. According to the Sharpe ratio, this riskier portfolio doesn't have enough excess return to justify the added volatility. However, if you're a long-term investor with a time horizon that extends several decades into the future, the year-to-year volatility of your portfolio is essentially meaningless. In that case, you'd be willing to endure more of a roller-coaster ride along the way, as long as you got to a better end result. By contrast, if you have a short time horizon, then your tolerance for volatility could be smaller than average. That might lead you to forgo higher-return investment options, even if the Sharpe ratio suggested they were smarter than the lower-return options, because you value the stability of the portfolio more than the Sharpe ratio's math does.

Finally, bear in mind that when you use backward-looking performance and volatility figures, the Sharpe ratio assumes that future results will be in line with the past. That's a dangerous assumption to make, and it's one that often gets investors into trouble.

The Sharpe ratio can give you a good starting point on whether your investment style gives you returns that justify the risk you take. It's not a perfect measure, but once you get used to its results, you can take your own particular risk tolerance into account and use the Sharpe ratio more effectively for your own personal portfolio decisions.