Ulcer Index: Measuring Depth and Length of Loss

Key Takeaways

• The ulcer index is the square root of the average of squared percentage drawdowns over a window.
• Squaring the drawdowns penalizes deep declines far more heavily than shallow ones.
• Unlike standard deviation, it ignores upside volatility and measures only the pain of losses.
• The Martin ratio divides excess return by the ulcer index to rank risk-adjusted performance.

What It Is

Peter Martin and Byron McCann developed the ulcer index in 1987 and introduced it in their 1989 book The Investor's Guide to Fidelity Funds. The name reflects the idea that drawdowns, not upswings, are what cause investors stress.

The ulcer index measures the depth and duration of percentage drawdowns from prior highs. A portfolio that drops hard and stays down for a long stretch produces a high ulcer index. A portfolio that grinds higher with only shallow, brief dips produces a low one. Because it works off drawdowns rather than raw return swings, it captures the experience of holding a losing position over time.

The Intuition

Standard deviation treats a sharp gain and a sharp loss as equally risky. To an investor, they are nothing alike. A surprise gain does not keep anyone awake at night.

The ulcer index addresses this by measuring only the downside, and specifically the downside relative to a prior peak. It also accounts for time. A drawdown that lingers contributes to the index across every period it persists, so a long, shallow decline can register as meaningfully painful. By squaring each drawdown before averaging, the measure makes a single deep fall count for much more than several minor ones, matching the disproportionate stress that large losses create.

How It Works

The calculation runs over a lookback window, often 14 periods.

1. Percent drawdown(t) = ((Close(t) - Max Close over window) / Max Close over window) * 100
2. Squared average = (sum of percent drawdown squared) / N
3. Ulcer Index = square root of squared average

Where Max Close over window is the highest closing value within the lookback period and N is the number of periods. Each percentage drawdown is squared before averaging, which is the step that penalizes deep drawdowns disproportionately. Taking the square root at the end returns the result to percentage units.

Martin also defined the Ulcer Performance Index, or Martin ratio, which adapts the Sharpe ratio idea to downside risk:

Martin Ratio = (portfolio return - risk-free return) / Ulcer Index

A higher Martin ratio means more excess return earned per unit of drawdown pain.

Worked Example

Consider a simplified five-period series where the highest close so far is 100. The closes are 100, 95, 90, 96, 100, giving percentage drawdowns from the running peak of 0, -5, -10, -4, and 0.

Square each drawdown: 0, 25, 100, 16, 0. Their sum is 141. Divide by 5 periods.

Squared average = 141 / 5 = 28.2
Ulcer Index = sqrt(28.2) = 5.31

The ulcer index of 5.31 sits between the shallow 4 percent dip and the deep 10 percent dip, but closer to the high end because squaring pulled the 10 percent drawdown's weight up. If the portfolio had stayed at 90 for several periods instead of recovering, those extra periods of deep drawdown would push the index considerably higher, showing how duration feeds into the measure.

Common Mistakes

1. Comparing across different window lengths. A 14-period and a 50-period ulcer index are not comparable. Fix the window before ranking strategies.
2. Treating it like standard deviation. The ulcer index ignores upside entirely. A high-return strategy with brief, shallow dips can have a very low ulcer index even with large positive swings.
3. Ignoring the reference peak. The measure is relative to the running maximum. A long sideways grind below an old high keeps the index elevated even with no new losses.
4. Forgetting it is path dependent. The same set of returns in a different order produces a different ulcer index, because drawdowns depend on sequence.
5. Using it without a return measure. The ulcer index alone says nothing about reward. Pair it with return, ideally through the Martin ratio, to judge whether the pain was worth it.

Frequently Asked Questions

What is the ulcer index in simple terms? The ulcer index measures how deep and how long a portfolio's drawdowns are, with deep falls counting much more than shallow ones. A low ulcer index means smooth, shallow dips, while a high one means painful, lasting declines.

How does the ulcer index affect investment decisions? It helps investors compare strategies on the pain of holding through losses rather than total volatility. Through the Martin ratio, it ranks how much excess return a strategy delivers per unit of drawdown stress.

What is a real-world example of the ulcer index? A series with drawdowns of 0, 5, 10, 4, and 0 percent yields squared values averaging 28.2, whose square root is an ulcer index of about 5.31. The deep 10 percent dip dominates because of the squaring.

How can investors use the ulcer index effectively? Fix the lookback window when comparing strategies, and use the Martin ratio so the drawdown pain is weighed against the return earned.

How is the ulcer index different from maximum drawdown? Maximum drawdown reports only the single deepest decline. The ulcer index blends the depth and duration of all drawdowns in the window, so it reflects sustained pain, not one extreme point.

Sources

1. StockCharts ChartSchool. Ulcer Index. https://chartschool.stockcharts.com/table-of-contents/technical-indicators-and-overlays/technical-indicators/ulcer-index
2. Martin, P. & McCann, B. (1989). The Investor's Guide to Fidelity Funds. Reference page by Peter Martin. https://www.tangotools.com/ui/ui.htm
3. CFA Institute. Measuring and Managing Market Risk. https://www.cfainstitute.org/insights/professional-learning/refresher-readings/2026/measuring-managing-market-risk
4. Investopedia. Maximum Drawdown (MDD). https://www.investopedia.com/terms/m/maximum-drawdown-mdd.asp

Disclaimer

This article is educational content only and is not financial advice. Nothing here is a recommendation to buy, sell, or hold any security. Consult a licensed advisor before making investment decisions.