Ulcer index: measuring drawdown severity over time
The ulcer index measures the severity of a portfolio's drawdowns by combining both their depth and their duration. A brief but sharp drawdown and a prolonged shallow decline of the same average depth will produce different ulcer index values—the prolonged one scores higher because it sustains discomfort across more periods. This makes the ulcer index a more complete picture of downside experience than maximum drawdown alone, which only records the single worst peak-to-trough decline without regard for how long it lasted.
What the ulcer index measures
At each point in time, the drawdown is calculated as the percentage decline from the portfolio's most recent peak. These drawdown values are squared—which magnifies deep drawdowns relative to shallow ones—and then averaged across the full period. The ulcer index is the square root of this average, expressed in percentage terms. Squaring the drawdowns serves two purposes: it ensures the metric is always positive, and it penalises deep drawdowns more severely than shallow ones, which aligns with how investors actually experience losses.
The ulcer index is sometimes called a drawdown-weighted volatility measure. It captures not just how far the portfolio fell, but how persistently it remained below its previous high. A portfolio that recovers quickly from drawdowns—even if those drawdowns are deep—will have a lower ulcer index than a portfolio that takes a long time to recover from even moderate declines.
The formula
Formula
UI = √( (1/n) × Σ DD(t)² )
Where:
DD(t) = drawdown at time t, expressed as a percentage (negative decimal)
n = number of periods
The sum runs over all periods in the measurement window
How to interpret the ulcer index
A lower ulcer index is better—it indicates fewer and shallower drawdowns, or faster recovery. A ulcer index of 5% means that, on average across the measurement period, the portfolio was 5% below its previous peak on a root-mean-squared basis. A ulcer index of 15% indicates a much more painful holding experience.
The Martin ratio—analogous to the Calmar ratio but using the ulcer index as the denominator rather than maximum drawdown—divides the portfolio's annualised excess return by its ulcer index. This produces a return-per-unit-of-sustained-drawdown figure that rewards portfolios that recover quickly from losses, not just portfolios that avoid large single drawdowns.
Rolling ulcer index
The scalar ulcer index summarises the full period. The rolling ulcer index applies the same calculation over a sliding window, showing how the portfolio's drawdown character evolves over time. Periods of market stress—such as the 2020 COVID drawdown or the 2022 rate shock—will appear as spikes in the rolling ulcer index. A portfolio that shows elevated rolling ulcer index values consistently, rather than only during broad market crises, may have structural issues with its recovery dynamics. Rolling analysis reveals regime-dependent variation in the metric over time.
Limitations
The ulcer index is price-based: it tracks the percentage decline from the most recent price peak. It does not distinguish between a drawdown caused by a genuine adverse move and one caused by temporary illiquidity or data artefacts. For assets with infrequent price data, the calculated drawdowns can be understated because intervening lows are not observed.
Like maximum drawdown, the ulcer index is backward-looking. A low historical ulcer index does not bound future drawdown severity. Comparing the ulcer index across portfolios is only meaningful when using the same measurement period and return frequency; a portfolio with a 10-year history will almost certainly have a higher ulcer index than one measured over only two years, simply because it has had more time to experience adverse periods.
Ulcer index in pfolio
The ulcer index is not currently displayed in pfolio Insights. Related drawdown metrics—drawdown depth, maximum drawdown, and time underwater—are visible in the drawdown section of Insights and provide related context on the severity and duration of losses.
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