What is the Sharpe Ratio?

The Sharpe ratio was developed by Nobel laureate William F. Sharpe and is used to help investors understand the return of an investment compared to its risk. The ratio is the average return earned in excess of the risk-free rate per unit of volatility or total risk. Volatility is a measure of the price fluctuations of an asset or portfolio.

The Sharpe ratio is calculated as follows: Subtract the risk-free rate from the return of the portfolio. The risk-free rate could be a U.S. Treasury rate or yield, such as the one-year or two-year Treasury yield. Divide the result by the standard deviation of the portfolio’s excess return. The standard deviation helps to show how much the portfolio's return deviates from the expected return. The standard deviation also sheds light on the portfolio's volatility.

Subtracting the risk-free rate from the mean return allows an investor to better isolate the profits associated with risk-taking activities. The risk-free rate of return is the return of an investment with zero risks, meaning it's the return investors could expect for taking no risk. The yield for a U.S. Treasury bond, for example, could be used as the risk-free rate.

The Sharpe ratio is one of the most widely used methods for calculating risk-adjusted return. Modern Portfolio Theory (MPT) states that adding assets to a diversified portfolio that has low correlations can decrease portfolio risk without sacrificing return.

Adding diversification should increase the Sharpe ratio compared to similar portfolios with a lower level of diversification. For this to be true, investors must also accept the assumption that risk is equal to volatility, which is not unreasonable but may be too narrow to be applied to all investments.

The Sharpe ratio can be used to evaluate a portfolio’s past performance (ex-post) where actual returns are used in the formula. Alternatively, an investor could use expected portfolio performance and the expected risk-free rate to calculate an estimated Sharpe ratio (ex-ante).

The Sharpe ratio can also help explain whether a portfolio's excess returns are due to smart investment decisions or a result of too much risk. Although one portfolio or fund can enjoy higher returns than its peers, it is only a good investment if those higher returns do not come with an excess of additional risk.

The greater a portfolio's Sharpe ratio, the better its risk-adjusted performance. If the analysis results in a negative Sharpe ratio, it either means the risk-free rate is greater than the portfolio’s return, or the portfolio's return is expected to be negative. In either case, a negative Sharpe ratio does not convey any useful meaning.

The Sharpe ratio is often used to compare the change in overall risk-return characteristics when a new asset or asset class is added to a portfolio.

For example, an investor is considering adding a hedge fund allocation to their existing portfolio that is currently split between stocks and bonds and has returned 15 per cent over the last year. The current risk-free rate is 3.5 per cent , and the volatility of the portfolio’s returns was 12 per cent , which makes the Sharpe ratio of 95.8per cent , or (15 per cent - 3.5 per cent ) divided by 12per cent .

The investor believes that adding the hedge fund to the portfolio will lower the expected return to 11 per cent for the coming year, but also expects the portfolio’s volatility to drop to 7 per cent .

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