Ulcer Index¶
The Ulcer Index is the root mean square of percentage drawdowns below a running high, measuring how deep and persistent a past investment path stayed underwater.
Core Idea¶
The Ulcer Index (UI) is the root mean square of each observation's percentage shortfall below the highest value reached earlier in a specified investment-value series. New highs contribute zero; deep losses and long time below a former peak raise UI. It is a historical drawdown-path statistic, not a forecast of future loss.
Cross-Domain Echoes¶
See how this entry connects to another domain.
Scope of Application¶
Peter G. Martin developed UI for comparing mutual-fund paths and explains the exact high-water-mark calculation in his first-party article. He rearranged one 2000–2009 S&P 500 fund monthly return set into three orders: annualized return and return standard deviation stayed the same, while drawdown profiles differed. His separate 1940–1997 buy-and-hold versus momentum-timing backtest reports UI 8.85 versus 5.14. Both are retrospective demonstrations, not evidence of future strategy superiority.
Clarity¶
For hypothetical values 100,90,90,100,110, percent drawdowns below running highs are 0,−10,−10,0,0. UI is sqrt((100+100)/5)≈6.32 percentage points. Repeated time at 90 counts twice; maximum drawdown would record only 10%. This arithmetic is illustrative, not a published market series.
Manages Complexity¶
UI keeps the order of gains and losses through a running peak, unlike return standard deviation. Its one number discards dates, causes and upside dispersion, and it cannot describe risks not realized in the sample. A fair comparison uses the same evaluation period, sampling frequency, dividend and cost conventions.
Abstract Reasoning¶
For positive value V_t, set M_t to the greatest value from the beginning of the analyzed window through t, compute d_t=100(V_t/M_t−1), and return sqrt(mean(d_t²)). Zero observations at new highs stay in the average. A separate sliding local maximum can produce a different metric if it forgets older highs; state the peak-reset and window rule.
Knowledge Transfer¶
The formula transfers to other positive fund, stock or strategy-value paths if measured comparably. Its retrospective root-mean-square calculation presupposes Aggregation of sampled drawdowns, but aggregation alone is not UI. The creator cautions that coarse sampling can miss drawdown-and-recovery episodes. UI measures the long-holder's historical underwater experience; return dispersion, total return, maximum loss and future risk remain distinct questions. The Ulcer Performance Index/Martin ratio divides excess return by UI and is not UI itself.
Relationships to Other Abstractions¶
Current abstraction Ulcer Index Domain-specific
Parents (1) — more general patterns this builds on
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Ulcer Index presupposes Aggregation Prime
UI presupposes aggregation of sampled drawdowns.
Hierarchy path (1) — routes to 1 parentless root
- Ulcer Index → Aggregation → Micro Macro Linkage
Neighborhood in Abstraction Space¶
Ulcer Index sits in a sparse region of the domain-specific corpus (66th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.
Family — Financial Markets & Pricing Anomalies (13 abstractions)
Nearest neighbors
- Sterling Ratio — 0.85
- Divisia Index — 0.84
- Put/Call Ratio — 0.84
- Portfolio Optimization — 0.84
- Basis-Risk Failure — 0.84
Computed from structural-signature embeddings · 2026-10-08