Sharpe vs Sortino: Reconcile the Ratios from Your Returns

Suppose two return series both average 1% per period and both have a Sharpe ratio of about 0.354. Are their downside outcomes alike? Not necessarily. One can contain two small shortfalls and another one larger shortfall. The calculation below identifies exactly which rows create that difference; it does not select a strategy for you.

Prepare simple arithmetic returns for equal periods: daily with daily, monthly with monthly. Enter 1 for 1% and −1 for −1%. A price of 1.10, an account balance of 10,000, a cash deposit and a log return are different data types. If cash flows affect your account values, establish a consistent return series before using this calculator. It cannot infer missing valuations or remove deposits from balances.

• Keep the original observation order, including repeated values and zero returns. Do not remove disappointing periods.
• Use one consistent valuation and cost basis. Record whether fees, financing and other relevant costs are included.
• Enter one return per line without a header, date, percent symbol or thousands separator. Decimal point and decimal comma are accepted.
• Record the observation frequency and sample dates separately. A period label does not convert the data or the benchmark rates.

The lab accepts 2–240 observations within its disclosed numeric limits. Its four-period presets are fictional arithmetic examples, not market histories or evidence that a strategy worked. Open the calculator, or download the compatible input file before preparing your own series. Returns, Rf and MAR accept −100% to +1000%, inclusive, with at most six decimal places. These are arithmetic input limits, not plausible or guaranteed yields. Accepting −100% does not model recovery of exhausted capital or chain account wealth.

Let r_i be a return, N the number of observations, Rf a constant risk-free comparison rate and MAR a constant minimum acceptable return. Rf and MAR are separate inputs in the same percentage units and for the same period as r_i. The lab does not fetch a current yield or convert an annual rate into a monthly one.

For Sharpe, a constant Rf changes the mean excess return but not the standard deviation: subtracting the same constant from every observation preserves its distances from the mean. A varying benchmark series needs a different input model. Sharpe’s original discussion provides the differential-return framework and explains why the measurement period matters.

For Sortino, this guide chooses a discrete empirical lower-partial-moment calculation over the full sample. Every row remains in N; a return at or above MAR contributes zero to the sum of squared shortfalls. We do not use only the number of losing periods, N−1 or the standard deviation of the negative subset. The CFA Institute discussion explains why differing targets and downside conventions can change reported results. Our chosen convention is not the only one used by providers.

Inspect the numerator, denominator, observation count and shortfall count together. A ratio alone conceals the inputs that produced it. The component calculates in decimal-return units; displayed rates use percent, squared deviations use percentage-point squared, and the ratios have no units.

Apply your inputs to see the full calculation and export it. Editing any field hides the old result and its dynamic download until you calculate again. The form keeps its inputs in memory and does not submit them or write persistent storage; that statement concerns this component, not the site’s separate analytics.

Use Rf = 0% and MAR = 0% for four fictional equal periods. Series A is −1%, −1%, +1%, +5%; series B is −3%, +1%, +3%, +3%. Their sums are both 4 percentage points, so both arithmetic means are 1%. The table retains every observation, including rows that contribute zero downside.

The last two columns are in percentage-point squared. Deviations from the mean are [−2, −2, 0, +4] for A and [−4, 0, +2, +2] for B. Both squared-deviation sums equal 24. Dividing by N−1 = 3 gives sample variance 8 percentage-point squared, equivalent to 0.0008 in squared decimal-return units. The sample standard deviation is therefore (√8)% ≈ 2.828427124746% for both.

A’s downside denominator is (√0.5)%; B’s is (√2.25)%. Their identical 1% numerator divided by these different denominators produces the two Sortino values. B has fewer below-target observations but a larger squared shortfall. Counting losses alone would miss that distinction. This reconciles a historical sample; it does not establish which series will be preferable in the future.

Rf answers “excess return above which comparison rate?” MAR answers “shortfall below which target?” They can coincide, but the calculation must not silently force them to match. Both are supplied assumptions here, not a claim that a particular guaranteed yield is available.

Keep series A and set Rf = 0.25%, MAR = 1.5% per period. Its mean and sample SD stay unchanged. The +1% observation now falls 0.5 percentage points below MAR even though its period return is positive. A shortfall is a target miss; it need not be a negative return.

The negative Sortino value is a valid result: the mean is below MAR and the denominator is positive. Changing Rf alone changes Sharpe’s numerator. Changing MAR changes both Sortino’s numerator and which observations contribute to its denominator. Compare calculations only after recording both assumptions.

An undefined result does not become zero or infinity. With no below-target observations, this sample supplies a zero downside denominator; it does not prove that future shortfalls are impossible. A flat sample can still fall below a positive target, so its Sortino denominator can be positive while its Sharpe denominator is zero.

A zero numerator is different. If the denominator is positive, mean = Rf gives Sharpe zero, and mean = MAR gives Sortino zero. Negative numerators are also valid. Do not erase those outcomes or convert them into an automatic pass/fail label.

Very small nonzero denominators can generate large ratios from tiny differences. Check the unrounded rates and sample length before interpreting the display. Two observations permit the arithmetic but provide little information about a distribution. This tool produces a finite-sample summary, not confidence intervals, a tail-loss estimate or a forecast.

Paste A’s four input numbers into A2:A5 as −1, −1, 1, 5. These cells contain percentage-point numbers, not spreadsheet percentage-formatted decimals. Put Rf in H2 and MAR in H3 using the same convention. Use zero for both to reproduce the reference, then change them deliberately.

• H5: =AVERAGE(A2:A5). H6: =STDEV.S(A2:A5). The expected mean is 1 and sample SD is √8.
• B2: =A2-$H$5. C2: =B2^2. Copy both formulas through row 5 to inspect the mean deviations and their squares.
• D2: =MIN(0,A2-$H$3). E2: =D2^2. Copy through row 5; keep zero rows in the range.
• Check =SUM(C2:C5)/(COUNT(A2:A5)-1): it must equal 8 for either A or B.
• H9: =SQRT(SUM(E2:E5)/COUNT(A2:A5)). The expected downside deviation for A is √0.5.
• Sharpe: =IF(H6=0,NA(),(H5-H2)/H6). Sortino: =IF(H9=0,NA(),(H5-H3)/H9). NA() flags an unavailable ratio rather than a numerical score.
• Replace A2:A5 with −3, 1, 3, 3 for B. The mean and sample SD stay the same; downside deviation becomes 1.5.

These are English spreadsheet function names; your application may localize function names and argument separators. Microsoft’s STDEV.S documentation confirms its sample N−1 convention. Make sure all intended cells are numeric: a spreadsheet may ignore text or empty cells rather than reject the entire sample as the lab does.

Do not divide the downside sum by COUNTIF(...,"<0"). That counts negative returns, not all observations, and also ignores a positive return that falls below a positive MAR. Do not substitute STDEV.P for the explicitly chosen sample standard deviation.

Download the reference calculation to check the row ledger and assumptions. The static files and this worked example remain available without JavaScript. The input file contains one return per line; the reference is an explanatory export, not a second input schema.

Before comparing two ratios, align the return frequency, sample dates, cost and valuation basis, Rf, MAR and denominator conventions. A daily ratio and a monthly ratio do not become comparable because both are dimensionless. If one provider uses a different downside definition, reproduce that definition separately instead of relabeling the result from this lab.

This calculator performs no annualization. Multiplying by a square root of periods depends on assumptions about return behavior and the benchmark; serial dependence can invalidate a simple scaling rule. Sharpe discusses these time-dependence limitations. A short, favorable window is also not a complete description of future downside, a limitation emphasized in the CFA discussion.

• Save the exact input series, observation frequency, dates and cost basis.
• Record Rf, MAR, N, the shortfall count and both denominator definitions.
• Keep the unrounded calculation or exported precision alongside rounded presentation values.
• Document unavailable inputs or mismatched conventions before making a comparison; the calculator cannot repair them.

Use the verification protocol as a reusable record. It separates what the supplied rows establish from what remains unknown. It does not certify performance, choose an investment or provide a universal “good” Sharpe or Sortino threshold.

Both ratios here ignore the order of the same observations. They do not show the depth or duration of an equity decline. The Calmar guide addresses a drawdown-based comparison, while the equity-curve guide illustrates how path and sequence matter. Those answer different questions; none replaces checking the underlying returns.

Does Sortino always improve on Sharpe?

No single summary answers every risk question. Here Sharpe describes dispersion around the mean relative to Rf; Sortino focuses on squared shortfalls below MAR. The A/B example shows why those summaries can differ, not why one number should always decide a comparison.

Can I enter trade profits instead of period returns?

Not directly. Currency profits, R multiples, pips and returns from trades of unequal duration do not automatically form an equal-period percentage-return series. First determine the capital, cash-flow, valuation and period basis. The lab does not invent that missing information.

Why use all N rows for downside deviation?

That is the declared empirical lower-partial-moment convention in this guide. Above-target observations contribute zero but remain in the denominator. Dividing only by shortfall rows measures a different quantity and can materially change Sortino; do not compare the two without labeling them.

Does a negative ratio mean the calculation is wrong?

No. With a positive denominator, a mean below Rf gives a negative Sharpe and a mean below MAR gives a negative Sortino. Check the assumptions and data before interpreting the result. The lab does not convert a sign into a trading recommendation.

Does zero observed downside mean the strategy is safe?

No. It means no supplied return fell below the selected MAR. The downside denominator is zero and this Sortino ratio is undefined. A different target, a longer sample or future observations may reveal shortfalls absent from this window.

Can these numbers be annualized or used as live rankings?

The component does neither. It uses the rows you supply, has no market feed and applies no automatic scaling. Any comparison across periods requires its own justified assumptions; a historical ratio does not establish future performance or an appropriate position size.