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Sharpe ratio

The Sharpe ratio is a measure of how well an investment compensates the investor for the risk assumed in making the investment.

Expanded Definition

The Sharpe ratio, which was developed by William Forsyth Sharpe, helps investors put risk into meaningful context. Two different investments may have very different risk profiles, but an investor may be quite comfortable taking on that risk if he or she is going to be adequately compensated for assuming it.

Investing in the stock market, for example, has nearly always been riskier than investing in bonds, but the stock market has historically provided much higher returns as well.

To provide that context, the Sharpe ratio compares the risk and return of a given investment with a baseline, low-risk investment such as Treasury bills. A high Sharpe ratio indicates that the investment is providing returns commensurate with its risk profile, while a low Sharpe ratio suggests that the risk is exceeding the expected reward.

To calculate the Sharpe ratio for a given investment, subtract the low-risk investment's rate of return with the investment's rate of return to define the "excess return", then divide that by the investment's standard deviation (which approximates risk).

For example, stocks have historically returned an average of 10%, while Treasury bills have historically returned 2%. Assuming a standard deviation of 15% (historically typical for an S&P index fund), then, stocks would have a Sharpe ratio of 0.53.

(10% - 2%) / 15% = 0.53

The Sharpe ratio is useful for comparing possible investments, but it has two significant challenges. First, it is necessarily backward-looking. If an investment's behavior changes, the Sharpe ratio won't predict it or account for it. Second, it assumes that risk is the same thing as volatility, which is true only in the short term.

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