Sharpe Ratio Calculator
Calculate annualized Sharpe and Sortino ratios from periodic summary statistics. Compare total volatility with downside volatility and test a target risk-adjusted ratio.
Risk-adjusted return results
| Measure | Periodic | Annualized |
|---|
Sharpe ratio formula
The Sharpe ratio divides return above a risk-free rate by total return volatility. With periodic inputs and N periods per year:
Annualized Sharpe ratio = (average return − risk-free rate) ÷ standard deviation × √N
The percentages in the numerator and denominator must use the same period. The ratio has no currency unit.
Sortino ratio formula
The Sortino ratio replaces total volatility with downside deviation and compares return with a minimum acceptable return (MAR):
Annualized Sortino ratio = (average return − MAR) ÷ downside deviation × √N
Downside-deviation conventions vary. Use a value calculated from the same return series, period and MAR as the other inputs.
Verified examples
| Periodic inputs | Result |
|---|---|
| Monthly: return 1%, risk-free 0.25%, standard deviation 4%, MAR 0.5%, downside deviation 3% | Sharpe 0.6495; Sortino 0.5774; annualized arithmetic return 12%; annualized volatility 13.8564% |
| Daily: return 0.05%, risk-free 0.01%, standard deviation 1%, MAR 0%, downside deviation 0.7% | Sharpe 0.6350; Sortino 1.1339; annualized arithmetic return 12.60% |
| Monthly: return −0.5%, risk-free 0.2%, standard deviation 5%, MAR 0%, downside deviation 4% | Sharpe −0.4850; Sortino −0.4330 |
How to interpret the results
A positive ratio means average return exceeded the selected benchmark; a negative ratio means it did not. A higher ratio indicates more excess return per unit of the risk measure entered, but it does not guarantee better future performance. Sharpe penalizes upside and downside variation equally; Sortino isolates downside variation according to the entered definition.
Do not compare ratios built from different frequencies, date ranges, risk-free rates, MAR values, data-cleaning rules or standard-deviation conventions.
Limits and assumptions
- Average return, risk-free rate and MAR may range from −100% through 1,000% per selected period, with up to six decimal places.
- Standard deviation and downside deviation must be greater than zero and no more than 1,000%, with up to six decimal places.
- The target ratio may range from −100 through 100, with up to six decimal places.
- Annualized arithmetic return is periodic mean × periods per year; annualized volatility is periodic deviation × √periods.
- Square-root annualization assumes comparable independent periods and stable volatility. Serial correlation, changing volatility and non-normal returns can make it misleading.
- The calculator does not derive returns from prices, choose a risk-free proxy, estimate downside deviation, account for fees or taxes, or predict performance.
- Results are educational estimates, not investment advice.
For annual inputs choose “Annual — 1 period/year.” For monthly, weekly or daily inputs, convert every rate and deviation to that same period before calculating.
Frequently asked questions
Can I compare Sharpe and Sortino directly?
They use different denominators, so their magnitudes are not interchangeable. Compare each ratio with results calculated under the same convention.
Should I use a sample or population standard deviation?
Either may be used if it matches your source and is disclosed consistently. A sample estimate is common when historical observations represent a sample of future uncertainty.
Why is the required target return arithmetic?
The calculator rearranges the ratio formula and multiplies the periodic mean by the number of periods. It does not convert that arithmetic mean into a compounded geometric return.
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