Methodology · Tool · Last updated 2026-05-08
How Sharpe vs Sortino Calculator works
Formulas behind the four ratios reported by the Sharpe vs Sortino Calculator.
Formulas
excess_t = r_t − rf_daily (rf_daily = rf_annual / 252)
mean = (1/n) · Σ excess_t
σ = √( (1/(n−1)) · Σ (excess_t − mean)² )
σ_d = √( (1/n) · Σ_{t : r_t < rf_daily} (r_t − rf_daily)² )
Sharpe = (mean / σ) · √252
Sortino = (mean / σ_d) · √252
Calmar = mean_ann / max_drawdown
Omega(τ) = Σ max(r − τ, 0) / Σ max(τ − r, 0)Conventions
- Annualization factor 252 (US trading days). For monthly inputs use 12; for weekly use 52. Tool currently assumes daily.
- Downside deviation uses the full-N divisor (Bacon 2008 §11), not the count of below-target observations.
- Max drawdown is computed from the equity curve formed by cumulating (1 + r_t).
When Sortino exceeds Sharpe materially
If σ_d < σ, Sortino > Sharpe — i.e. the strategy's volatility is dominated by upside moves, not losses. Sortino rewards that asymmetry. The tool's "opinion" line surfaces this when the gap exceeds 40%.
References
- Sharpe, W. F. (1966). "Mutual fund performance." Journal of Business 39(1), part 2: 119–138. DOI: 10.1086/294846.
- Sortino, F. A., Price, L. N. (1994). "Performance measurement in a downside risk framework." Journal of Investing 3(3): 59–64. DOI: 10.3905/joi.3.3.59.
- Young, T. W. (1991). "Calmar ratio: A smoother tool." Futures Magazine, October.
- Keating, C., Shadwick, W. F. (2002). "A universal performance measure." Journal of Performance Measurement 6(3): 59–84.
- Bacon, C. R. (2008). Practical Portfolio Performance Measurement and Attribution, 2nd ed., Wiley. ISBN: 978-0-470-05928-9.
Limitations
- Ratios assume i.i.d. returns. Serial correlation deflates the SE on every estimate.
- Calmar uses realised max drawdown — heavily path-dependent on a single sample.
- Omega's threshold τ is set to the daily risk-free rate; conventions vary.