Decoding the Sharpe ratio: A measure of risk vs. reward

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Reward requires risk … but how much?

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William F. Sharpe’s main contribution to finance was the capital asset pricing model (CAPM), which says that investment portfolios should be optimized to market risk, which he called beta. His later work built on that framework and was almost as influential.

Sharpe developed what is now known as the Sharpe ratio because he suspected that many portfolio managers were generating their returns by taking high levels of risk, but that their returns weren’t all that great after the amount of risk was factored in.

When the market was going up, customers were happy, but when the market went down, the excess risk resulted in huge losses. Furthermore, managers had an incentive to take on too much risk in good times to post performance records without really benefiting customers.

The formula itself is simple:

Sharpe ratio = (portfolio return – risk-free rate) ÷ portfolio standard deviation

Its implications for the investment industry have been profound. The Sharpe ratio showed investors whether they were being compensated for the risks taken by those managing their money. It changed how investment performance was evaluated and portfolio managers were compensated.

The Sharpe ratio is a straightforward yet powerful tool for assessing the risk-adjusted return of an investment or portfolio. The numerator (portfolio return – risk-free rate) is simply the amount of return that the portfolio manager generated above the risk-free rate, typically represented by Treasury securities. After all, anyone can get the risk-free rate for free through government bonds. There’s no reason for anyone to pay an investment manager to get the risk-free rate.

The denominator is the standard deviation, which is a measure of the portfolio’s volatility. The solution is how much return the portfolio manager generated for the amount of risk taken. The higher the Sharpe ratio, the better the risk-adjusted return.

To use the Sharpe ratio, investors simply find the variables for the period being studied, then calculate the ratio. In general, a good Sharpe ratio is higher than 1, indicating that portfolio returns reflect the amount of risk being taken by the manager.

A ratio lower than 1 indicates that the portfolio’s risks are not optimal and reduce its performance, even if the fund seems to beat the market. Sharpe ratios can even be negative, showing that the risks taken detract from portfolio’s performance.

A low Sharpe ratio could mean the manager is taking unnecessary risks, regardless of the posted performance numbers. You may be happy with a fund that has a low Sharpe ratio when the market is going up, but you won’t be happy when the market turns. Also, you can get a better-than-expected return for the same amount of risk by finding a fund with a higher Sharpe ratio.

Although the primary use of the Sharpe ratio is performance evaluation, it can also help portfolio managers select securities that are expected to enhance the overall portfolio’s risk-adjusted return. By choosing assets with higher Sharpe ratios, a manager may be able to improve a portfolio’s performance.

Although it’s simple and powerful, the Sharpe ratio has some problems. The first is that it relies on historical data, which may not accurately predict future returns or risk. The second is that the Sharpe ratio assumes that returns have a normal distribution, which may not be the case.

The third critique is less technical and more practical. The standard deviation looks at how returns differ from the return the portfolio manager expected to receive. That includes returns that are better than expected as well as returns that are worse than expected. But most investors think of better-than-expected returns as a bonus, not a risk.

Over the years, researchers have developed alternatives to the Sharpe ratio to help fix these problems. One popular alternative is the Sortino ratio, which was developed by Frank Sortino of the Pension Research Institute. Like the Sharpe ratio, it assesses the risk-adjusted performance of an investment or portfolio. The difference is how it measures risk. The Sortino ratio uses the standard deviation of negative returns as its denominator.

The equation is:

Sortino ratio = (portfolio return – risk-free rate) ÷ downside standard deviation

Downside standard deviation is the standard deviation of negative returns, which measures the volatility of returns when they fall below a specified minimum acceptable return. That minimum return is usually zero, but it may be the risk-free rate or another hurdle rate. If you’re using the Sortino ratio or reading research based on it, you need to know what return was used to calculate the downside standard deviation in order to evaluate the results.

The Sharpe ratio is a fundamental tool for investors, analysts, and portfolio managers because it provides an objective, quantitative measure of risk-adjusted returns. By breaking out the effect of risk on performance, it shows how the manager added value to the portfolio.

The Sharpe ratio tells investors whether they received the benefits of the risk that the portfolio manager took on, as some managers take unnecessary and uncompensated risks in their quest to beat the market. The simplicity of the ratio lends itself to refinements such as the Sortino ratio, which looks solely at downside risk instead of total risk.