Financial Modeling
Schwager Gain-to-Pain Ratio (GPR) & 90/10 Tail Ratio Asymmetry Formula
Evaluate CTA and hedge-fund return asymmetry without upside volatility punishment using Jack Schwager’s Gain-to-Pain Ratio SUM(r) / ABS(SUMIF(r, "<0")) and right-to-left Tail Ratio.
Why Sharpe penalizes explosive winning months while Gain-to-Pain rewards them
Trend-following CTAs and macro managers often post modest losing months punctuated by large positive breakout months—inflating standard deviation and depressing traditional Sharpe ratios! Jack Schwager (*Market Wizards*) popularized the Gain-to-Pain Ratio (GPR) = SUM(all_returns) / ABS(SUM(negative_returns)), measuring net cumulative return per unit of cumulative losing-month pain (note the exact algebraic identity with gross Return Profit Factor: SUM(positive_returns) / ABS(SUM(negative_returns)) = GPR + 1).
Pairing GPR with the 90/10 Tail Ratio = ABS(PERCENTILE(returns, 0.90) / PERCENTILE(returns, 0.10)) verifies whether right-tail winners outweigh left-tail losers (> 1.0 indicates positive tail skew; < 1.0 warns of short-volatility crash risk).
| Asymmetry Metric | Worksheet Formula | 6-Month Sample [4%, -2%, 5%, -3%, 6%, 2%] |
|---|---|---|
| Net Gain SUM(B2:B7) | 0.17 - 0.05 | +0.1200 (+12.00%) |
| Cumulative Pain ABS(SUMIF(B2:B7, "<0")) | |-0.02 - 0.03| | 0.0500 (5.00%) |
| Schwager Gain-to-Pain Ratio (GPR) | 0.12 / 0.05 | 2.4000 (Gross Profit Factor = 3.4000) |
| 90/10 Tail Ratio | ABS(P90 / P10) = 0.055 / 0.025 | 2.2000 (Right-skewed) |
Schwager Gain-to-Pain Ratio (GPR) Formula
Divide net cumulative return SUM(B2:B7) by ABS(SUMIF(B2:B7, "<0")), returning "ZERO_PAIN_MONTHS" when no negative periods exist.
=IF(SUMIF(B2:B7, "<0") = 0, "ZERO_PAIN_MONTHS", ROUND(SUM(B2:B7) / ABS(SUMIF(B2:B7, "<0")), 4))90th-to-10th Percentile Tail Ratio Formula
Divide the 90th percentile return by ABS(10th percentile return) to quantify upper-vs-lower tail magnitude.
=IF(PERCENTILE(B2:B7, 0.1) = 0, "ZERO_LEFT_TAIL", ROUND(PERCENTILE(B2:B7, 0.9) / ABS(PERCENTILE(B2:B7, 0.1)), 4))Try the example
Use the original values or change them to test your understanding.