Sharpe vs Sortino Ratio: Calculate and Compare Them

Two ratios answer different questions

A trading report can show a smooth balance curve while hiding open losses, or a high average return created by one unusually successful month. A risk-adjusted ratio helps summarize a return series, but its value depends on what went into that series. Start with account equity, consistently timed observations and a clear treatment of deposits and withdrawals. A list of winning trades is not a substitute for complete account returns.

Sharpe includes variability on both sides of the average. Sortino focuses on returns below a specified target. That difference can matter for a strategy with occasional large gains, yet it does not make one ratio universally superior. A trader with strict daily loss limits may also need information about intraday losses that neither monthly statistic contains.

The definitions follow William Sharpe’s explanation of differential returns and the Sortino calculation paper hosted by CME Group. The example and reporting workflow below are our own educational illustration.

Set up the calculation before comparing numbers

For Sharpe, calculate each period’s account return minus the return of the chosen benchmark. Divide the arithmetic mean of those differential returns by their standard deviation. If a risk-free proxy is the benchmark, record which proxy and how its return was aligned to the observation dates. Subtracting an annual rate directly from every monthly return would mix units.

For the Sortino convention used here, subtract a per-period target from every return. Keep negative shortfalls, replace nonnegative differences with zero, square those values, average over all observations and take the square root. Divide the mean return minus the target by this downside deviation. Using only the number of negative observations in the denominator produces a different statistic, so label that convention if your software uses it.

Decision	Record in the report	Why it matters
Return frequency	Daily, weekly or monthly	Ratios change when observations change
Benchmark and target	Per-period values and source	Zero and a positive hurdle answer different questions
Cost treatment	Commissions, funding and fees	Gross and net series are not comparable
Standard deviation	Sample or population	Small samples are particularly sensitive
Cash flows	How external flows are removed	A deposit is not trading performance

A worked four-period example

Consider hypothetical monthly returns of +2%, −1%, +3% and 0%. Use a zero benchmark and a zero target solely to keep the arithmetic visible. The average monthly return is 1%. Deviations from that mean are +1, −2, +2 and −1 percentage points. Their squared sum is 10 squared percentage points. Using sample standard deviation gives the square root of 10 divided by 3, or approximately 1.826%.

The unannualized monthly Sharpe ratio is therefore 1 divided by 1.826, approximately 0.548. For Sortino, the shortfalls are 0%, −1%, 0% and 0%. The squared shortfalls average to 0.25 squared percentage points across four observations. Downside deviation is 0.5%, making the unannualized monthly Sortino ratio 2.0.

These two numbers describe exactly the same four returns. The larger Sortino number does not mean the account became safer when we changed the formula. It means the denominator measures something different. Four observations are also far too little evidence for a confident assessment of a trading process; this small series exists to make the calculation reproducible.

Compounding gives another useful check: 1.02 × 0.99 × 1.03 × 1.00 = 1.040094, a total gain of about 4.0094%. That is a separate measure from either ratio. Retain it in the report so a dimensionless statistic does not obscure the actual path of money.

Now change only the benchmark to a hypothetical constant 0.1% each month. Mean excess return becomes 0.9%, while the standard deviation remains approximately 1.826% because subtracting the same constant leaves deviations unchanged. Sharpe becomes about 0.493. A varying monthly benchmark needs a fresh standard deviation of the complete differential-return series. Subtracting the benchmark’s average from the numerator while keeping the account-only denominator would generally calculate a different statistic. Keep both dated series to make that distinction auditable.

Why the downside target changes the answer

Now require 1% per month in the same illustrative series. The mean return equals the target, so the Sortino numerator becomes zero. Shortfalls are 0, −2, 0 and −1 percentage points. Their squared average is 1.25, giving downside deviation of about 1.118%. Sortino becomes zero. The account did not change; the requirement did.

This is why a manager using a zero hurdle should not be ranked directly against another using a higher hurdle. Record the target before looking at the results. Choosing whichever hurdle flatters an account turns measurement into presentation. A target is an analytical choice, not a promised return or a recommended personal objective.

If no observation falls below the target, downside deviation is zero. Do not display a finite ratio invented by replacing that denominator with a tiny positive number. Mark the statistic undefined under the selected formula and report the number of observations. A short period without losses does not demonstrate an absence of downside risk.

Annualization needs an explanation

Many reports multiply an unannualized monthly Sharpe ratio by the square root of 12. This familiar scaling depends on assumptions about how returns aggregate and their dependence through time. It is not a device that creates twelve months of evidence from four observations. Overlapping positions, stale prices and repeated exposure to the same market event can make the assumptions poor.

Show the unannualized value and observation frequency alongside any annualized figure. If two platforms disagree, first compare their calendars, benchmark series, cash-flow adjustments and sample versus population conventions. Investigating a small numerical difference is usually more productive than declaring one platform wrong because its headline ratio is lower.

Use a comparison sheet that reveals missing information

A useful account comparison has one row for the evaluation period, another for the number of return observations and another for the treatment of floating positions. Then include net return, worst peak-to-trough equity decline, the two ratios and exposure. The purpose is to let a reader recreate the comparison, including unfavorable months.

For example, suppose Account A reports only closed-trade balance and Account B reports daily marked equity. A has a higher Sharpe ratio, but an open losing position was excluded throughout the period. The first task is to rebuild A on the same equity basis. Ranking the published numbers before that reconciliation would reward a reporting difference.

Also inspect how much of the result came from the largest gain. Recalculate with that observation clearly identified, without silently deleting it from the official history. A sensitivity view can reveal concentration while preserving the actual result. Keep both outputs and explain the exercise rather than replacing the original with a preferred story.

What these ratios do not answer

Neither ratio tells you whether an exit would have filled during a gap, whether leverage was permitted, or whether several accounts shared the same risk. They do not establish operational reliability, withdrawal availability or suitability for a particular person. A serial-correlation check, a drawdown recovery calculation and a review of return asymmetry and tail behavior answer additional questions.

Copied accounts can have different returns even with the same trade direction. Contract size, rounding, commissions, currency conversion and fills all affect the series. Compare each follower with its own complete equity history. Multiplying a master’s ratio by an account-size ratio has no sound interpretation.

A repeatable monthly review

1. Freeze the reporting window and export the complete equity and cash-flow history.
2. Reconcile missing observations, duplicated records and valuation times.
3. Calculate both ratios with written conventions and retain the underlying return series.
4. Compare drawdown, concentration and execution differences alongside the ratios.
5. Record questions for further testing without treating a historical statistic as an instruction to increase size.

TradeCopier’s activity logs can help investigate copying events, while account statements remain necessary for a complete performance calculation. Use the trading journal workflow to retain the decisions behind each review. A transparent, reproducible calculation is more useful than an impressive number whose inputs cannot be recovered.