What are the Ulcer Index and the Ulcer Performance Index?
Maximum Drawdown tells you how bad the single worst moment was. It says nothing about whether a strategy spent one month underwater or eleven years. The Ulcer Index closes that gap.
Ulcer Index
The Ulcer Index measures the depth and the duration of every drawdown across a period, not just the deepest one.
It is computed by walking the equity curve month by month, recording how far below the previous high-water mark each month sits, squaring that figure, and taking the square root of the average across all months. Months at a new high contribute zero. Months deep underwater contribute a great deal, because squaring them punishes depth disproportionately.
The name is literal. It is meant to approximate how much stress holding the strategy would have caused. Lower is better, and unlike most statistics on this site there is no theoretical maximum, only comparisons between strategies over the same window.
Two things follow from the construction:
- Time underwater is penalized directly. A strategy that drops 20% and recovers in four months scores far better than one that drops 20% and takes six years to get back, even though their Max DD figures are identical.
- A strategy that spends most of its life at new highs scores very well, because most months contribute nothing at all.
Ulcer Performance Index (UPI)
UPI turns the Ulcer Index into a risk-adjusted return measure:
UPI = (CAGR - risk-free rate) / Ulcer Index
The numerator is what the strategy earned above cash. The denominator is how much discomfort it caused getting there. Higher is better.
The structure is the same idea as the Sharpe ratio, with one substitution that matters. Sharpe divides excess return by standard deviation, which treats upside volatility as risk. UPI divides by drawdown pain, which counts only the downside and counts prolonged recoveries as worse than quick ones. For a strategy designed around limiting drawdowns rather than limiting volatility, UPI is usually the more informative of the two.
Why UPI is our headline risk-adjusted number
Standard deviation punishes a strategy for a strong upside month exactly as hard as for a weak one. Nobody experiences those two months the same way. Drawdown-based measures line up much more closely with what actually causes an investor to abandon a strategy, which is the failure mode that destroys more returns than any market decline does.
An important caveat: UPI is not leverage-invariant
It is sometimes assumed that a risk-adjusted ratio like UPI stays roughly constant when you scale a position up or down, so that a 3x version of an asset would show similar UPI to the unlevered version. Our own measurement says otherwise, decisively.
Measured against daily data for an unlevered S&P 500 fund and its 2x and 3x counterparts, buy-and-hold UPI at 3x falls to roughly 27% of the unlevered figure. The Ulcer Index does not scale linearly with leverage; across seven leveraged asset-class families it scales at approximately the leverage factor raised to the power 1.3, and that exponent was stable across sub-periods.
The practical consequence: do not compare the UPI of a leveraged strategy against an unleveraged one and conclude the leverage was free. Leverage degrades UPI structurally, before any question of skill or timing enters. A leveraged strategy that holds its UPI near its unleveraged parent's has done something genuinely difficult, and the comparison to make is against the same strategy at the same leverage, not across leverage levels.
How to read these numbers
- Both are window-scoped. Change the date range and both change, because both are computed over the months you have selected.
- Both respond to the toggles. Inflation Adjusted, Trading Friction, and Taxable Account all change the return stream underneath.
- Neither has a natural scale. An Ulcer Index of 4 means nothing in isolation. It means something next to another strategy's 9 over the same period.
- UPI depends on the risk-free rate, which changes what the number means across eras. Cash yielding 8% in the 1980s sets a much higher bar than cash yielding almost nothing in the 2010s.
What they do not tell you
Neither statistic knows anything about why a strategy drew down, whether the conditions that caused it are likely to repeat, or what a drawdown outside the historical record might look like. A strategy with an excellent Ulcer Index has been comfortable to hold across the period tested. That is a real and useful thing to know, and it is not a forecast.