Description
Convert annual effective rate through expm1(log1p(rate)/periods); subtract from period return and divide by period volatility, then multiply by sqrt(periods) for annualized Sharpe.
A simple return is a change relative to an initial value, while a gross return is a wealth multiplier and a log return uses a logarithm of that multiplier. Dividend, split, fee and currency conventions change what is included.
Convert annual effective rate through expm1(log1p(rate)/periods); subtract from period return and divide by period volatility, then multiply by sqrt(periods) for annualized Sharpe.
When to use this tool
Use Sharpe Risk Free Frequency Consistency Term when you need a stated return-basis conversion or contribution.
How to use the tool and how it works
- Enter periodReturn, riskFreeAnnual, periodsPerYear, periodVolatility. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read periodRiskFree, periodSharpe, annualizedSharpe. Use the output convention below.
Require annual risk-free return above -1, positive periods/year and period volatility. Convert annual effective rate through expm1(log1p(rate)/periods); subtract from period return and divide by period volatility, then multiply by sqrt(periods) for annualized Sharpe.1
The square-root time scaling assumes summed period excess returns with zero serial correlation. Supplied period returns and volatility must have compatible definitions.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| periodReturn | Return fraction for one modeled period; use mean return when interpreting an estimated Sharpe ratio. | Required. Finite number. |
| riskFreeAnnual | Annual effective risk-free return fraction greater than -1. | Required. Finite number; strictly above -1. |
| periodsPerYear | Periods Per Year | Required. Finite number; strictly above 0. |
| periodVolatility | Positive return standard deviation on that same period and fractional scale. | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| periodRiskFree | Period Risk Free | Required. Finite number. |
| periodSharpe | Period Sharpe | Required. Finite number. |
| annualizedSharpe | Annualized Sharpe | Required. Finite number. |
{
"input": {
"periodReturn": 0.02,
"riskFreeAnnual": 0,
"periodsPerYear": 12,
"periodVolatility": 0.04
},
"output": {
"periodRiskFree": 0,
"periodSharpe": 0.5,
"annualizedSharpe": 1.7320508075688772
}
}Limitations and assumptions
- Returns and volatility use fractions on the same period basis. Square-root annualization assumes appropriate uncorrelated period returns and is not a performance guarantee or complete statistical estimate.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Reconstruct the full investment cashflow and adjustment history for performance analysis. Align horizons, quote direction and numeric return scales, and include relevant fees and taxes explicitly.
References
-
Calculation and input contract: financial-economics/sharpe-risk-free-frequency-consistency-term — tool.io
-
The Sharpe Ratio — William F. Sharpe
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