Sharpe Ratio

The Sharpe ratio compares the return of an investment with its risk. It’s a mathematical expression of the insight that excess returns over a period of time may signify more volatility and risk, rather than investing skill.

Economist William F. Sharpe proposed the Sharpe ratio in 1966 as an outgrowth of his work on the capital asset pricing model (CAPM), calling it the reward-to-variability ratio. Sharpe won the Nobel Prize in economics for his work on CAPM in 1990.

The Sharpe ratio’s numerator is the difference over time between realized, or expected, returns and a benchmark such as the risk-free rate of return or the performance of a particular investment category. Its denominator is the standard deviation of returns over the same period of time, a measure of volatility and risk. The Sharpe ratio divides a portfolio’s excess returns by a measure of its volatility to assess risk-adjusted performance. Excess returns are those above an industry benchmark or the risk-free rate of return. The calculation may be based on historical returns or forecasts. A higher Sharpe ratio is better when comparing similar portfolios. The Sharpe ratio has inherent weaknesses and may be overstated for some investment strategies.

Standard deviation is derived from the variability of returns for a series of time intervals adding up to the total performance sample under consideration. The numerator’s total return differential versus a benchmark (Rp - Rf) is calculated as the average of the return differentials in each of the incremental time periods making up the total. For example, the numerator of a 10-year Sharpe ratio might be the average of 120 monthly return differentials for a fund versus an industry benchmark.

The Sharpe ratio’s denominator in that example will be those monthly returns’ standard deviation, calculated as follows: Take the return variance from the average return in each of the incremental periods, square it, and sum the squares from all of the incremental periods. Divide the sum by the number of incremental time periods. Take a square root of the quotient.

The Sharpe ratio is one of the most widely used methods for measuring risk-adjusted relative returns. It compares a fund’s historical or projected returns relative to an investment benchmark with the historical or expected variability of such returns.

The risk-free rate was initially used in the formula to denote an investor’s hypothetical minimal borrowing costs. More generally, it represents the risk premium of an investment versus a safe asset such as a Treasury bill or bond.

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