Ulcer Index: Measuring Both Drawdown Depth and Duration

A strategy recovering from a 20% drawdown within a month and one remaining underwater for nine months both show “MDD 20%.” Holding the account feels very different. The Ulcer Index combines drawdown depth with how long it persists.

What Is the Ulcer Index?

The Ulcer Index, UI, is the root mean square of an equity curve's percentage drawdowns below its previous peak. Peter Martin and Byron McCann developed it in 1987 to compare funds. Its name refers to the discomfort of remaining underwater.

The calculation has three steps.

① Calculate drawdown at each observation: the percentage below the highest value reached so far.
② Square each drawdown.
③ Average those squares and take the square root.

UI = √(Σ(Drawdown %)² ÷ N). Include zero-drawdown observations at new highs in N. Frequent new highs contribute many zeros and lower UI; remaining underwater repeatedly contributes nonzero values and raises it.

Squaring penalizes deeper drawdowns more heavily. A −20% observation contributes four times the penalty of −10%, not twice. This reflects the observation that investor discomfort accelerates rather than scaling evenly with loss.

A Five-Observation Calculation

Use the highest value known at each point, the running maximum. May's 11,200 does not retroactively become March's reference. This matches MDD calculation; getting it wrong distorts the indicator.

Identical MDD, Nearly Double the UI

Consider two strategies with the same maximum drawdown of 20%.

A regains its peak in one month; B leaves the account underwater for nine months. MDD cannot distinguish them, and the Calmar ratio, with MDD in its denominator, has the same limitation. UI is one of the few standard measures that separates this experience.

Duration often causes abandonment more than depth. As described in drawdown psychology, people can find months without recovery harder to bear than one sharp fall.

UPI, or Martin Ratio: Adding Return

UI measures risk alone, with lower values preferable. To combine it with return, use the Ulcer Performance Index, UPI, or Martin ratio.

UPI = (CAGR − Risk-free rate) ÷ Ulcer Index

The Sharpe ratio treats upside and downside volatility as risk; the Sortino ratio considers downside volatility. Both measure fluctuations and do not directly represent drawdown duration. A slow nine-month decline can have low measured volatility and a superficially reasonable Sharpe ratio. UPI penalizes that interval.

The definitions differ: Sharpe measures total volatility, Sortino downside volatility, Calmar the single worst drawdown, and Ulcer the combined depth and duration of drawdowns. They complement rather than replace one another. Adding profit factor fills out the comparison.

Practical Use

Fix the sampling interval. Daily and monthly UI differ. Daily sampling captures smaller fluctuations and tends to increase the value. The original convention is monthly, but whichever you choose, compare the same interval and period. Mixing them is using different rulers.

Apply it to equity, not merely price. UI can analyze an individual asset, but strategy evaluation requires the account curve after fees, slippage, and funding. Ignoring costs makes drawdowns appear shallower.

Do not trust short periods. A bot run for three months has had few chances to encounter a major drawdown. Use at least 12 months, preferably 36. If backtested UI looks good, first investigate whether overfitting artificially reduced drawdowns, and cite values from periods that passed walk-forward validation.

Use relative benchmarks. There is no universal UI threshold. “Below 5 is good” breaks across assets, intervals, and leverage. Use it to rank candidates under comparable conditions. To assess a broader range, shuffle trade order through Monte Carlo simulation and examine the UI distribution.

More leverage also raises UI. Doubling exposure roughly doubles drawdowns and UI. UPI's numerator and denominator rise together, leaving the ratio broadly unchanged. Leverage cannot rescue a low-UPI strategy. Leverage concerns position sizing, not improving the metric.

Limitations

It summarizes the past. UI compresses a historical curve; it does not cap future drawdowns. Live drawdowns commonly exceed backtested ones.

Many zeros lower it. Long periods with little trading can contribute many zero-drawdown observations and make UI artificially low. Account for this when comparing very different trading frequencies.

It is less familiar. Unlike Sharpe, “UI 8.4” may convey little by itself. Common practice reports it alongside MDD and recovery duration. Treat it as a complementary dimension that MDD misses.

Three Key Points

① UI squares each drawdown, averages, then takes the square root, combining depth and duration in one risk measure.
② At the same 20% MDD, one-month and nine-month recoveries can have nearly twofold UI differences, a dimension MDD and Calmar miss.
③ UPI = Excess return ÷ UI combines return and risk. Compare only equal intervals and periods using equity curves after costs.

Notice

Capital, return, and drawdown figures are hypothetical calculation examples, not measured strategy performance or forecasts. All performance metrics summarize historical data and guarantee neither future profit nor a drawdown ceiling. Leveraged trading can lose all principal. Investment decisions and responsibility are yours.