Sharpe vs Sortino: Correct Denominators and a Worked Example

Sharpe and Sortino use different denominators. A historical Sharpe calculation summarises differential return relative to its overall variability. A specified Sortino calculation uses shortfalls below a target. Neither is universally better for forex, provider evaluation or tail protection; state the data and conventions before comparing them.

Put Both Formulas on the Same Period

For Sharpe, subtract the comparison observation by observation; a varying comparison can change both mean and deviation. For Sortino, shortfalls are min(return−MAR,0). Positive returns below a positive target are included as shortfalls. Sharpe’s explanation and the CFA Institute’s Sortino discussion provide the underlying definitions.

A Fully Specified Upside Example

Use four hypothetical monthly after-cost returns with no external cash flows, zero comparison return and zero MAR. Do not annualise either statistic.

Both series contain one −1% shortfall and three non-shortfalls. Increasing one winning return raises the mean and overall deviation. Sharpe rises in this example, too: a larger positive observation does not automatically lower Sharpe. Sortino rises more here because its shortfall denominator stays unchanged. The higher number does not establish a more skilled trader or guarantee a later loss pattern.

Why a Different Target or Denominator Changes the Answer

Downside deviation here uses all N periods, not just the shortfalls, and does not subtract the mean of the losing observations. One identical losing observation therefore does not make downside deviation zero. The Sortino calculation guide shows the same full return series at two targets.

Sharpe sample deviation divides squared deviations by N−1; a population convention divides by N. Both need explicit labels. A finite observed ratio requires a positive denominator; zero deviation or no shortfalls should not be presented as zero future risk. Negative numerator cases also require more care than a blanket higher-is-better ranking.

Neither Denominator Is Maximum Drawdown

Maximum drawdown depends on the ordered valuation path. Reordering identical return observations leaves both fixed-comparison Sharpe and fixed-target Sortino unchanged while potentially altering drawdown. Neither ratio establishes when an old peak was regained or enforces daily loss limits. Sortino versus Calmar gives the ordered-path example.

A formula can be calculated without assuming normal returns; using mean/deviation alone to describe all investment risk is a separate limitation. Tail losses, changing exposure, cash flows, missing data, serial dependence and selection of the reporting window need additional inspection. Do not replace this with invented provider cutoffs, universal valid sample lengths or guaranteed challenge outcomes.

Compare Compatible Records

1. Use the same dates, currency, return frequency and cost/cash-flow treatment.
2. Disclose each comparison/target series and sample/population/all-N convention.
3. Keep periodic values separate from any annualisation; square-root scaling has assumptions.
4. Keep reported cash P/L distinct from capital-normalised returns and balance distinct from floating equity.
5. Review ordered drawdowns and actual provider terms separately from a historical ratio.

Reconcile MyVeridex’s Displayed Fields

Current reviewed recomputation uses reported closed-trade money P/L grouped by date with closed records. Sharpe uses population deviation; Sortino uses a zero threshold and squared negative P/L divided by all included dates. Both use √252 scaling, a five-date gate and zero fallbacks. These are product conventions, not automatically the sample percentage-return comparison above.

Days without closed trades do not appear in the series, and commission and swap are stored separately, so reconcile costs, deposits, withdrawals and changing capital before comparing ratios. MyVeridex connects MT4 and MT5 accounts directly and also imports supported MetaTrader statements.