Formula, in Backtesting & Validation
Gain-to-Pain Ratio Formula
The gain-to-pain ratio is the sum of all period returns divided by the absolute value of the sum of the negative-period returns. Popularized by Jack Schwager, it measures total return earned per unit of downside pain endured. It is intuitive, hard to game, and unlike the Sharpe ratio it does not penalize upside volatility at all.
3 variables. Published May 26, 2026. By AI Fin Hub Research.
GPR = ( sum of all R_i ) / | sum of R_i where R_i < 0 | Variables
sum of all R_i
Sum of returns
The total of every periodic return, positive and negative. Over monthly data it is the simple sum (not compounded), which keeps the measure additive and transparent.
R_i < 0
Losing-period returns
Only the negative periodic returns. Their absolute sum is the denominator, the total pain. Winning periods do not add to the denominator, so upside dispersion is never penalized.
GPR
Gain-to-pain ratio
Total return per unit of total loss. Schwager treats a monthly GPR above 1.0 as good and above 1.5 as very good; values scale with frequency, so monthly and daily GPRs are not directly comparable.
Step by step
- 1
List the periodic returns over the sample.
Twelve monthly returns for the year.
- 2
Sum all returns for the numerator.
The twelve monthly returns sum to +18%.
- 3
Sum only the negative returns and take the absolute value for the denominator.
The losing months sum to -10%, so the absolute sum of losses is 10%.
- 4
Divide total return by the absolute sum of losses.
18% / 10% = 1.8.
Worked example
One year of monthly returns for a discretionary macro fund
Sum of all monthly returns
+18%
Sum of negative months
-10%
Numerator = sum of all returns = +18% = 0.18. Denominator = absolute sum of losing months = |-10%| = 0.10. GPR = 0.18 / 0.10 = 1.8.
Gain-to-pain ratio of 1.8. The fund earned 1.8 units of total return for every unit of cumulative monthly loss, which Schwager would rate as very good for a monthly series. Because the denominator counts only realized losing months, the measure rewards keeping losses small and frequent winners, and is far more robust to a single outlier return than the Sharpe ratio.
Common variations
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Sources
- Hedge Fund Market Wizards , Jack D. Schwager, Wiley (2012)
- Market Sense and Nonsense , Jack D. Schwager, Wiley (2012)
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