An ex ante scenario
This calculator is an ex ante scenario. Its three inputs are user-supplied assumptions for one future period: expected investment return, the same-period fixed risk-free return, and predicted standard deviation of excess return.
Expected excess return is expected investment return minus the same-period risk-free return. The ex ante Sharpe ratio divides that expected excess return by the predicted standard deviation of the differential return.
Because the benchmark in this scenario is a fixed riskless return for the period, subtracting it does not change the standard deviation. This equivalence does not extend to a variable benchmark.
Example
With a 12% expected investment return, a 4% same-period risk-free return, and 15% predicted excess-return volatility, expected excess return is 8% and the ex ante Sharpe ratio is 8 / 15 = 0.53 after rounding.
The result states expected differential return per unit of predicted differential-return risk for the entered period.
Conventions and limits
Use one horizon and one convention for all three inputs. Do not mix expected inputs with realized historical inputs. This calculator does not derive a mean or standard deviation from a return series and does not annualize the result.
Comparisons require the same period, expected-return construction, benchmark convention, standard-deviation method, and annualization treatment.
The ratio is period-dependent, omits correlation and distribution information beyond mean and standard deviation, and is not a buy, sell, or allocation instruction.
Standard deviation must be at least 0.0001%. This input floor is a calculator validation boundary, not a financial threshold.
Source
- William F. Sharpe, The Sharpe Ratio, The Journal of Portfolio Management, Fall 1994, volume 21, issue 1, pages 49–58 — “The Ratio > The Ex Ante Sharpe Ratio,” equations (1)–(2); “Scale Independence,” opening paragraph; “Related Measures,” first paragraph; “Time Dependence,” opening sentence; “Correlations,” first paragraph.