Ulcer Index — Return

RMS of the drawdown % series on the Return curve — penalizes both depth and duration of drawdowns.

Computed from: Equity curve
Scope: Single report
Range: ≥ 0
Direction: Lower is better

Basis

Computed on the low-to-low Return Series (money-weighted) — measured day-worst-point to day-worst-point, not close-to-close.

The Ulcer Index measures how deep and how long an account stayed underwater — below its previous high point — rolled into one number. It's the root-mean-square of the drawdown series: RMS is a kind of average that squares every value before averaging, so a −10% drawdown becomes 100 while a −2% becomes just 4, and the big drops dominate. (See the worked example below.)

Key takeaways

What it is — the RMS (root-mean-square) of the whole drawdown series, in percent. Not one event — the entire underwater history.
Read it as — sustained drawdown pain. Lower is better; a small number means the curve rarely strayed far below its high-water mark (the highest equity the account has reached so far).
Why it matters — the drawdown that makes people quit usually isn't the deepest, it's the longest. A −25% drop that recovers in two weeks is easier to hold than a −15% slide that grinds on for eight months. Max drawdown ranks the −25% as "worse"; the Ulcer Index — which weighs depth and duration — ranks the eight-month grind as worse, and it's right about which one breaks your resolve.
In EquityTruth — computed on the Return and TWR (time-weighted return) curves, as the RMS of each curve's drawdown-from-peak series.

How it's calculated

Ulcer Index = √( mean( drawdown%² ) )

drawdown%(t): how far below the running high-water mark the curve sits at time t, as a percentage (≥ 0)
mean( · ): arithmetic mean of the squared drawdowns over every point in the record
√: square root — returns the result to percentage units

In this product: It is the root-mean-square of the drawdown series, in percent: square each drawdown, average them across the whole record, take the square root. Because every value is squared before averaging, deep drawdowns dominate. EquityTruth emits it on the Return (gain) and TWR curves.

On the Return curve the drawdown is money-weighted — deposits and withdrawals move the denominator. The Ulcer Index here reflects the sustained pain you personally experienced.

What it tells you

These are general bands. Leveraged retail forex runs hotter — an Ulcer of 8–12 that looks severe on a fund's scale can be ordinary on a 1:100 account. Read the band relative to leverage and next to max drawdown, not in absolute terms.

Value	Reading	Notes
< 2	Very smooth	Rarely far below its peak; quick recoveries.
2 – 5	Mild	Normal underwater stretches for an active strategy.
5 – 10	Notable	Meaningful time spent in meaningful drawdown.
> 10	Severe	Deep, prolonged drawdowns dominate the record.

The Ulcer Index is always at most the max drawdown — it's the RMS of the whole drawdown series, not the single worst point, and an average can never exceed its largest value. So it lands well below max drawdown (usually single digits), and if you ever see Ulcer > max drawdown, something is wrong.

Same max drawdown (−20%), very different Ulcer Index. The blue curve dips once and recovers in a day; the teal curve spends the whole record underwater. Max drawdown can't tell them apart — the Ulcer Index can.

Worked example

Suppose a curve sits at drawdowns of 0%, −5%, −10%, −5%, 0% over five points. Squaring gives 0, 25, 100, 25, 0; the mean is 30; the square root is ≈ 5.5. The single −10% point contributes 100 of the 150 total — two-thirds of the weight from one of five points. That squaring is exactly why a deep dip costs more Ulcer than several shallow ones — the property max drawdown's single-number view throws away.

Ulcer and the Martin ratio

The Ulcer Index's real value to an allocator is as a drawdown denominator. The Calmar ratio divides return by max drawdown — but max drawdown is one event, set by a single worst stretch, and it lurches when you add or drop a month of data. The Martin ratio (also called the Ulcer Performance Index, UPI) divides the same return by the Ulcer Index instead — a return-per-pain score, like Sharpe but using sustained drawdown instead of volatility. Because Ulcer is measured over the whole record rather than one point, it's far more stable across samples, so the Martin ratio is a steadier, less luck-dependent measure of return per unit of pain than Calmar. Pros who track Ulcer mostly track it for this.

Pitfalls

Pitfalls & caveats

Needs the whole series. It averages over every point in the record, so a short history under-samples drawdowns and can read deceptively low — it simply hasn't lived through enough.
Penalizes an unfinished drawdown. Fast recovery does lower Ulcer (it shortens the underwater stretch) — but an account still stuck below its peak at the end of the record carries a high reading that won't fall until equity climbs back. Read it next to time under water.
A percentage measure, not a ratio. It's drawdown-only — it ignores returns entirely. Pair it with a return figure (or use the Martin ratio) before judging a strategy as good or bad.
Mode matters. Return-curve and TWR Ulcer diverge when there are deposits or withdrawals — compare like with like.

Ulcer Index vs Max Drawdown vs Pain Index

The three drawdown lenses ask different questions of the same underwater history. Max drawdown is the single worst peak-to-valley fall — one event, one number. The Pain Index is the mean (average) depth below the peak across the record. The Ulcer Index is the RMS depth — the same series as the Pain Index, but squared before averaging, so it weights the deep drawdowns more heavily. So Pain flags accounts that are chronically, mildly underwater; Ulcer flags accounts with occasional deep holes; max drawdown flags the single worst hole.

As pure operators on one drawdown series in one unit, they fall in a fixed order: average ≤ RMS ≤ max, i.e. Pain ≤ Ulcer ≤ Max Drawdown. (Mind the units, though: in EquityTruth the Ulcer Index and max drawdown are percentages on the Return curve, while the Pain Index is in dollars on the P&L curve — so the live dashboard figures aren't directly comparable, even if the math orders them.) A brief crash and a permanent shallow drift can share a max drawdown yet have very different Ulcer values — that spread is itself the signal.

Max drawdown — the single worst peak-to-valley fall.
Pain index — the mean (rather than RMS) drawdown depth.
Time under water — how long equity stayed below its high-water mark.

Compare withMaximum Drawdown Pain Index