# Sharpe Ratio

The most famous return-versus-risk measurement, the Sharpe ratio represents the added value over the risk-free rate per unit of volatility risk.

## How Is it Useful?

The Sharpe ratio simplifies the options facing the investor by separating investments into one of two choices: the risk-free rate or anything else. Thus, the Sharpe ratio allows investors to compare very different investments by the same criteria. Anything that isn’t the risk-free investment can be compared against any other investment. The Sharpe ratio allows for apples-to-oranges comparisons.

## What Is a Good Number?

Sharpe ratios should be high, with the larger the number the better. This would imply significantoutperformance versus the risk-free rate and/or a low standard deviation. However, there is no set-in-stone breakpoint above which is good and below which is bad. The Sharpe ratio should be compared against an index or an appropriate peer group. Keep in mind that it is possible for Sharpe ratios to be negative. If the investment has negative returns and falls short of the risk-free rate, the Sharpe ratio will be negative.

## What Are the Limitations?

The Sharpe ratio defines risk as standard deviation so it carries the limitations inherent in standard deviation. Standard deviation fails to differentiate between upside deviation and downside deviation. Also, standard deviation does not take into account the timing of returns.

## What Do the Graphs Show Me?

The graphs below illustrate the two halves of the Sharpe ratio. The upper graph shows the numerator, the excess return over the risk-free rate. The blue line is the investment. The red line is the risk-free rate on a rolling, three-year basis. More often than not, the investment’s return exceeds that of the risk-free rate, leading to a positive numerator.

The lower graph shows the risk metric used in the denominator, standard deviation. Standard deviation measures how volatile an investment’s returns have been.

## What Are Typical Values?

Historically speaking, fixed income investments have offered the best return-versus-risk trade-offs, when defined by the Sharpe ratio. International stocks have fared the worst, once volatility is weighed against return. Sharpe ratios were lower in the 2000s compared to the 1980s and 1990s. Featuring two large bear markets, many equity asset classes struggled or even failed to outperform cash during this decade. Some Sharpe ratios were negative in the 2000s.

Math Corner:

First proposed by William Sharpe in his landmark 1966 paper “Mutual Fund Performance,” the original version of the Sharpe ratio was known as the reward-to-variability ratio. Sharpe revised the formula in 1994 to acknowledge that the risk-free rate used as the reference point is variable, not a constant.

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