Ulcer Index

Maximum drawdown captures the single worst loss, but it ignores how long an investor spent underwater and how often drawdowns happened. The Ulcer Index, developed by Peter Martin and Byron McCann and published in 1989, measures the stress of holding an investment by combining the depth and duration of all drawdowns. Its name reflects the idea that long, deep losses are what give investors ulcers. A strategy that stays close to its highs scores low; one that spends long periods well below its peak scores high.

The formula#

1. Calculate the percentage drawdown from the running peak for each period.
2. Square each drawdown.
3. Average the squared values over all periods.
4. Take the square root.

Ulcer Index = Square root of (Sum of (Drawdown percent ^ 2) / Number of periods)

Squaring makes deep drawdowns count much more than shallow ones, and every period spent underwater adds to the total, so duration matters.

Comparing two strategies#

Both have the same maximum drawdown, but B's investors spent two years underwater. The Ulcer Index separates them; maximum drawdown alone does not. See Maximum Drawdown.

The Martin ratio (Ulcer Performance Index)#

Martin also proposed a risk adjusted return measure using the Ulcer Index in place of volatility:

Martin ratio = (Annual return - Risk free rate) / Ulcer Index

A strategy returning 10% with a risk free rate of 4% and an Ulcer Index of 3 has a Martin ratio of 2.0. Like the Sharpe ratio, higher is better, but it penalises only drawdowns, not upside volatility. See Sharpe Ratio and Sortino Ratio.

Strengths#

• Captures depth and duration together.
• Ignores upside volatility, which investors do not mind.
• Reflects the investor experience of holding through losses.
• Uses the whole equity path, not one event.

Weaknesses#

• Data frequency matters: daily and monthly data give different values.
• Period length matters: compare only over the same dates.
• Less familiar than Sharpe or maximum drawdown.
• Backward looking: a calm history does not guarantee a calm future.

Ulcer Index as a technical indicator#

Some charting platforms apply the Ulcer Index to price over a rolling window, such as 14 periods, to measure how far price sits below its recent high. Rising values signal growing downside stress in the trend. See ATR (Average True Range) for a different volatility indicator.

Using it in practice#

1. Compare strategies with similar returns to see which offers a smoother experience.
2. Track your own equity curve's Ulcer Index over rolling periods.
3. Use alongside maximum drawdown and Calmar ratio. See Calmar and MAR Ratio.
4. Set expectations: knowing a strategy's typical time underwater helps you stay disciplined. See Emotional Control.

Frequently asked questions#

What is the Ulcer Index?#

A downside risk measure that takes the square root of the average squared drawdown, capturing both how deep and how long losses last.

How is the Ulcer Index different from maximum drawdown?#

Maximum drawdown measures only the single worst fall; the Ulcer Index reflects all drawdowns and the time spent below previous highs.

What is the Martin ratio?#

Excess return divided by the Ulcer Index, a risk adjusted return measure that penalises drawdowns rather than volatility.

Next, learn how returns split into market and skill in Alpha and Beta.