Ulcer Index

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Peter Martin's measure of how much it actually hurt to hold this portfolio.

Quick Answer

What is Ulcer Index?

Ulcer Index is Peter Martin's drawdown-based volatility measure: the root-mean-square of percentage drawdowns from running maximums over a window. Unlike maximum drawdown (which captures only the worst), Ulcer Index captures the duration and severity of all drawdowns. The name reflects its purpose: how much stomach lining did this portfolio cost you?

UI = sqrt((1/n) · Σ DDᵢ²)

Formula

UI = sqrt((1/n) · Σi=1..n DDi2)
DDi = drawdown at time i (negative value or zero) · n = number of observations in the window · square brings positive sign, average smooths

At every point in time, you record how far below the running peak you are. Square those values, average them, take the square root. The result captures both how deep drawdowns went and how long the portfolio spent in them.

Intuition — what is this number telling you?

Max drawdown measures the worst moment. Ulcer Index measures the entire experience. A portfolio that hit one −30% drawdown and recovered quickly has a similar max DD to one that spent years bouncing between −5% and −20%. The first has lower Ulcer Index; the second is psychologically much harder.

Ulcer Index is the denominator of the Martin Ratio — the cleanest single-number drawdown-aware risk-adjusted return measure.

Worked example

Step-by-step

Drawdowns over 12 months: 0%, 0%, −3%, −8%, −12%, −10%, −7%, −5%, −2%, 0%, 0%, −4%.

Squared: 0, 0, 9, 64, 144, 100, 49, 25, 4, 0, 0, 16. Sum = 411. Mean = 34.25. sqrt = 5.85%.

That is your Ulcer Index. The S&P 500's long-run Ulcer Index over rolling 5-year windows averages around 4–6%; during 2007–2009 it spiked above 20%.

What's a good Ulcer Index value?

Lower is better. Asset-class guidelines:

AssetTypical Ulcer Index
Cash / T-bills~0%
60/40 balanced3–6%
S&P 500 (long-run)4–7%
S&P 500 through GFC20%+
Concentrated equity10–25%
Crypto majors30–50%

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Related metrics

Martin Ratio  ·  Maximum Drawdown  ·  Drawdown  ·  Pain Index

Frequently asked questions about Ulcer Index

How is Ulcer Index different from standard deviation?

Standard deviation measures variance around the mean. Ulcer Index measures only downward deviations from running peaks — the actually-painful kind.

What is the Pain Index?

Same concept but uses absolute drawdown rather than squared. Linear penalty for depth instead of quadratic. See Pain Index.

Why is it called "Ulcer Index"?

Peter Martin coined the name in 1987 because the metric captures the actual stress experienced by investors — proportional to the literal physical toll on your body.

Does Foliolytic compute Ulcer Index?

Yes — alongside Max DD, CDaR, and Pain Index in the drawdown section.

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