What Is Ulcer Index?
The Ulcer Index (UI) is a downside-risk measure that quantifies the depth and persistence of percentage drawdowns from earlier highs. Peter Martin developed it in 1987; he and Byron McCann first described it in their 1989 book The Investor’s Guide to Fidelity Funds. Its name reflects the investor discomfort associated with a deep or prolonged loss.
Unlike standard deviation, which treats gains and losses symmetrically, UI only increases when the measured value is below a previous high. It is the root mean square of percentage drawdowns: squaring gives deep drawdowns more weight, and a drawdown that persists over several observations contributes at each observation. A lower UI therefore indicates a less severe history of drawdown over the chosen sample. UI is useful when upside volatility is not considered a risk, such as in evaluating a long-only investment or a capital-preservation strategy.
UI is complementary to the Calmar ratio and maximum drawdown. Those measures are driven by one worst peak-to-trough episode, whereas UI incorporates every drawdown observation in its measurement window. This does not make UI immune to short or unrepresentative histories: the look-back period, sampling frequency, and whether the sample includes stressed markets can all materially affect it.
Formula
D_i = 100 × (P_i / max(P_{i-N+1}, ..., P_i) - 1)
UI_N = sqrt((D_{i-N+1}² + ... + D_i²) / N)
Here P_i is the price or portfolio value at observation i, D_i is
its percentage drawdown, and N is the look-back length. This is the common
rolling-indicator implementation: each drawdown is measured against the
highest value in its own preceding N-period window, then the most recent
N squared drawdowns are averaged. A portfolio-analysis implementation may
instead use the running high from the start of a fixed evaluation period;
reports should state which convention, frequency, and look-back were used.
For an investment comparison, use the same dates and total-return series for
every asset, including distributions, fees, costs, and slippage where
applicable.
Pros
Captures both depth and persistence of drawdowns in a single number
Uses all drawdown observations rather than only the worst episode
Penalises large drawdowns more heavily than small ones
Focuses on downside only, unlike standard deviation
Cons
Sensitive to the look-back, sampling frequency, and price or total-return series chosen
Has no universal “good” threshold; values are comparable only when calculated consistently
Does not directly estimate loss probabilities or tail risk
Literature and references:
See also