2013issue C0563
Constructing the Sharpe ratio as return over variability
The Sharpe ratio subtracts a risk-free interest rate from expected return and divides that difference by the standard deviation of returns, comparing return with variability rather than with the risk of losing the original capital.
- The Sharpe ratio is built from three inputs: expected return, a risk-free interest rate, and the standard deviation of returns.
- Construction subtracts the risk-free interest rate from expected return and divides the difference by the standard deviation of returns.
- The method compares return with variability of returns rather than with the risk of losing the original capital.
- Standard deviation describes how a distribution varies around its mean, so a larger value on a profit-and-loss series means more widely varying results.
How the score is assembled
The Sharpe ratio is constructed by subtracting a risk-free interest rate from expected return and dividing that difference by the standard deviation of returns.
The construction uses three inputs: expected return, a risk-free interest rate, and the standard deviation of returns.
The three inputs
Expected return is the return input placed in the numerator of the Sharpe construction before the risk-free interest rate is removed.
The risk-free interest rate is the interest-rate input subtracted from expected return so the remaining figure can be scaled by variability.
The standard deviation of returns is the denominator that measures how widely returns spread around their mean and converts the remaining figure into a return-per-unit-of-variability score.
What standard deviation measures
Standard deviation describes how a given distribution varies around its mean observation.
Standard deviation can be obtained as the square root of the expected value of the squared difference between a random variable and its mean.
Applied to a profit-and-loss series, a larger standard deviation indicates more widely varying results and a smaller one indicates more stable results.
One described use of standard deviation measures fluctuation in a stock's monthly return over the preceding year.
Variability rather than loss of capital
The method compares return with variability of returns rather than with the risk of losing the original capital.
All readings on this track · 12 readings
- 1986Auditing stochastic crossovers with moving-average baselines
- 1994Evaluating system changes with chi-square, Sharpe, and leverage
- 1995Evaluating mechanical switch rules with a stop-loss order and Sharpe ratio
- 1995Intermediate-term allocation with drawdown filters
- 1996Evaluating a multi-market book without picking winners
- 1996Regime-aware allocation beyond a single equity trend
- 1997Evaluating managed futures as portfolio diversifiers
- 2008Audit an out-of-the-money covered-call overlay against a Sharpe control
- 2013Constructing the Sharpe ratio as return over variability
- 2014Expected value and bet size are separate controls
- 2015Constructing a Sharpe-style score from profit and loss variability
- 2019Continuous futures series and long-horizon allocation evaluation