Ulcer Index

The Ulcer Index, introduced by Peter Martin in 1987, is a single-number risk metric that captures both the depth and the duration of drawdowns. Maximum Drawdown captures only the worst single instance; the Ulcer Index integrates how long the portfolio stayed under water. A strategy with two −10% drawdowns each lasting six months is "less ulcerous" than one with a single −12% drawdown that took three years to recover.

Formula

DD_t = ( V_t − M_t ) / M_t        ( ≤ 0 )
UI = sqrt( mean( DD_t² ) ) × 100

where V_t is portfolio value, M_t is the running peak, and the mean is taken over the measurement window. Squaring the drawdowns penalises larger declines disproportionately; taking the root keeps the answer in percentage units.

Reading the number

• ·UI < 2 — gently drawing strategies (well-diversified bond + equity).
• ·UI 2-6 — typical equity-heavy multi-asset portfolios.
• ·UI > 10 — concentrated equity or single-name positions.

The Ulcer Performance Index (UPI) divides excess return by UI — the same idea as Sharpe but with drawdown discomfort instead of volatility in the denominator. Useful when comparing strategies whose distributions are not symmetric.

How MEDGE Capital uses the Ulcer Index

Min Ulcer is one of the 12 optimization objectives. Reports surface UI next to Max DD and the Pain Index so you can distinguish strategies that are "deep but quick" (low UI, high MaxDD) from "shallow but long" (high UI, low MaxDD).