The Ulcer Index measures the root-mean-square depth of historical percentage drawdowns from prior peaks.
The Ulcer Index (UI) measures the root-mean-square depth of historical percentage drawdowns from prior peaks. Unlike standard deviation, it ignores new highs and penalizes periods spent below a previous peak.
UI reflects drawdown depth and persistence indirectly: every observation below the running peak contributes to the average. It does not separately report the longest drawdown or recovery time.
Let \(V_i\) be the value of an investment or cumulative wealth index at observation \(i\). The running peak is:
Percentage drawdown is:
Drawdowns are zero at a new peak and negative below the peak. The Ulcer Index is:
Because drawdowns are squared, deeper declines receive greater weight.
Assume a cumulative value path:
100, 95, 90, 92, 100
The running peak remains 100, so percentage drawdowns are:
0%, -5%, -10%, -8%, and 0%
Maximum drawdown for the same path is 10%. UI is lower because it averages squared drawdown across all observations rather than reporting only the deepest point.
Consider two paths with the same 10% maximum drawdown:
Path B generally has a higher UI because more observations contribute large squared drawdowns. However, UI does not reveal whether the drawdown lasted five weeks or five years unless the observation frequency and history are also known.
Review maximum drawdown, time to trough, recovery time, and time under water alongside UI.
| Measure | Main input | Main question |
|---|---|---|
| Ulcer Index | Percentage drawdowns from running peaks | How deep and persistent were drawdowns across the selected path? |
| Maximum drawdown | Worst peak-to-trough change | What was the deepest observed decline? |
| Standard Deviation | Dispersion of periodic returns | How variable were returns around their average? |
| Downside deviation | Returns below a target | How dispersed were target shortfalls? |
| VaR | Modeled loss distribution | What loss cutoff applies at a stated horizon and confidence level? |
| Expected shortfall | Modeled loss tail | What was average modeled loss beyond the cutoff? |
UI can distinguish paths that have similar return volatility but different time spent below prior peaks. It cannot estimate losses outside the observed path.
Price-only data treat distributions as losses. For investments that pay dividends or interest, a total-return series is usually more appropriate for performance analysis.
Fees and expenses can deepen or extend drawdowns. Gross and net UI values are not directly comparable.
Daily data can capture declines and recoveries hidden by monthly data. Intraday losses remain absent unless intraday observations are used.
Deposits and withdrawals should not be treated as investment gains or losses. Use a properly constructed unit value or time-weighted cumulative return series where appropriate.
Starting near a market peak can increase measured drawdown; starting after a decline can omit it. Report exact dates and whether the opening value is treated as the initial peak.
Do not calculate UI directly from a list of periodic returns without first constructing the cumulative wealth path.
UI can help compare:
Comparison still requires similar mandates, leverage, liquidity, inception history, and data quality. A strategy that reports monthly modeled values should not be assumed less risky than a daily traded portfolio because its UI is lower.
CFTC and NFA materials provide authoritative drawdown context for specified commodity-pool and trading-advisor disclosures. The Ulcer Index itself is an analytical convention rather than a universally prescribed regulatory measure.
This article provides general financial education. It is not personalized investment, fund-selection, trading, performance, statistical, tax, legal, or risk-management advice.