Ulcer Index¶
The Ulcer Index is a downside-risk metric developed by Peter Martin in 1987 that measures both the depth and duration of drawdowns from prior highs. Unlike standard deviation, it ignores upside volatility entirely and squares each percentage decline, so deep or prolonged losses dominate the score. It answers the question investors actually feel: how bad was the ride down, and how long did it last?
HOW IT WORKS¶
For each period in a lookback window, the Ulcer Index computes the percentage drawdown from the running maximum price, squares each value, averages them, and takes the square root:
UI = √( Σ Rᵢ² / n )
where Rᵢ = 100 × (Priceᵢ − MaxPrice) / MaxPrice.
Squaring makes depth nonlinear — a 20% drawdown contributes four times as much as a 10% drawdown — and every additional day spent below the peak compounds the score through duration. The companion metric, the Ulcer Performance Index (Martin Ratio), divides excess return by the Ulcer Index and serves the same role as the Sharpe Ratio but penalizes only harmful volatility.
IN TAPEBOARD¶
Tapeboard displays the rolling Ulcer Index on any instrument or strategy equity curve, alongside the Martin Ratio for return-per-unit-of-ulcer ranking. Traders use it to:
- Compare strategies with similar Sharpe Ratios — the lower UI identifies the path that is more capital-efficient and easier to size up.
- Screen positions by ranking holdings on Martin Ratio rather than raw return, filtering out strategies whose apparent volatility is mostly downside grind.
- Set de-risking alerts that trigger when a portfolio's rolling UI breaches a defined threshold, catching slow deterioration that daily volatility metrics miss.