Ulcer index
The ulcer index is the root mean square of the percentage drawdowns of a series from its running peak. Unlike maximum drawdown, it grows with both the depth and the duration of declines, so a curve that stays below its high for a long time scores worse than one that dips and recovers quickly.
Senzoukria · Glossary · Updated September 2026
At a glance
- Formula
- √[(1/N) × Σ Dᵢ²], Dᵢ = 100 × (Vᵢ − running max) ÷ running max
- Origin
- Peter Martin, 1987
- Reading
- 0 = never below a prior peak; lower is better
- Derived ratio
- Martin ratio (ulcer performance index) = excess return ÷ ulcer index
What it measures
At every observation, compute how far the series sits below its highest prior value, in percent. Square each of those drawdowns, average them over all observations, and take the square root. Observations at a new high contribute zero. Because the drawdowns are squared, deep declines weigh more than shallow ones, and because every observation under water contributes, a long stay below the peak raises the index even when the depth does not change.
Peter Martin proposed the measure in 1987 to capture the discomfort of holding an investment through a decline. Dividing an excess return by the ulcer index gives the Martin ratio, also called the ulcer performance index, a return-to-pain measure in the same spirit as the Sharpe ratio.
Same maximum drawdown, different ulcer
Both curves share the same worst point, so their maximum drawdown is identical. The second one spends three observations at −10% instead of one, and its ulcer index is about 55% higher. That is the information the index adds to a drawdown table.
| Curve | Values | Drawdowns (%) | Ulcer index |
|---|---|---|---|
| Quick recovery | 100, 110, 99, 104.5, 110, 121 | 0, 0, −10, −5, 0, 0 | √(125 ÷ 6) ≈ 4.56 |
| Long stay under water | 100, 110, 99, 99, 99, 110 | 0, 0, −10, −10, −10, 0 | √(300 ÷ 6) ≈ 7.07 |
In Senzoukria
The Performance panel reports Ulcer index in its Risk section with the hint that it penalizes a trough that lasts, not only its depth, and that lower is better. The computation runs on the cumulative P&L of closed trades, one observation per trade, and counts a relative drawdown only once the running peak is above zero. Two consequences follow from that design. Duration is counted in trades, not in days, so a slow stretch with few trades weighs less than a busy one. And because the curve starts at zero profit rather than at an account balance, a dip after a small first profit is a large percentage of that profit; compare ulcer values between runs of the same kind rather than with fund statistics computed on account equity.
Common mistakes
- Comparing an ulcer index computed on daily account equity with one computed per trade on cumulative profit.
- Reading a low value on a short sample as proof of smooth performance.
- Using it alone: it says nothing about how much was earned, which is why the Martin ratio pairs it with a return.
Related
In the same section
- Calmar ratio
- Trend day
- Unfinished auction
- Trapped traders
- Unrealized drawdown
- Transaction costs
- Unusual options activity
- Trailing stop
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Frequently asked questions
- Is the ulcer index the same as the average drawdown?
- No. It is a root mean square, not a plain average, so deep drawdowns count disproportionately. A series with many small dips and one deep one has a higher ulcer index than its average drawdown suggests.
- Why is my ulcer index large on a short replay session?
- In the desktop the percentages are relative to the peak of cumulative profit, which starts at zero. After a small first gain, an ordinary losing trade can be a large fraction of that gain. The figure is correct for its definition but should be compared only with runs measured the same way.