The Martin ratio, also called the Ulcer Performance Index (UPI), divides an investment's excess return by its Ulcer Index: the root mean square of its drawdowns. It evaluates reward relative to the depth and persistence of losses from earlier peaks. A strategy can finish profitably yet score poorly after spending much of its history underwater.
Peter Martin and Byron McCann introduced the underlying measure in The Investor's Guide to Fidelity Funds. Their performance tables use compound annual returns; Martin's first-party explanation identifies UPI and Martin ratio as names for excess return divided by UI.
Fix the return and observation conventions first
For this article, use a positive, cash-flow-adjusted total-return wealth index , measured at equally spaced dates, with reinvested distributions and costs already reflected. Include the initial mark in the observations and initialise the running peak there:
The signed drawdown is zero at each new peak. With wealth observations, including that initial mark,
Every observation receives weight , including zeros. This is a root mean square about zero, not a standard deviation about the mean drawdown; there is no correction and no restriction to underwater observations. Deeper drawdowns contribute more through squaring; a drawdown that persists contributes on more dates.
For a history spanning years, this article uses compound annual growth rate, , and an annual effective risk-free comparator, :
The numerator is the difference of annual rates, not cumulative excess wealth and not an arithmetic average of period returns. Other reporting conventions can use a different return summary; disclose it before comparing ratios. UI measures the observed path over the full window. Do not multiply it by a square-root-of-time factor to “annualise” it.
Use decimals throughout, or percentage figures throughout: an annual excess return of 4% divided by UI of 5% is , equivalently . Mixing 4 with 0.05 creates a hundredfold error. The annual numerator convention must accompany the reported ratio.
Four marks are three years
Consider a fictional investment with no external cash flows, observed at its start and three successive year-ends:
| Time | Wealth index | Running peak | Signed drawdown |
|---|---|---|---|
| Year 0 | 100 | 100 | 0% |
| Year 1 | 110 | 110 | 0% |
| Year 2 | 99 | 110 | −10% |
| Year 3 | 121 | 121 | 0% |
There are four UI observations but only three one-year return intervals. With a fictional annual risk-free comparator of 2%,
The result is about 0.912 units of annual excess return per unit of RMS drawdown under these conventions. It is neither a probability nor evidence of statistical significance.
Original fictional calculation. Solid blue joins observed wealth marks; the dashed line joins running peaks. Annual sampling is used only to make the arithmetic visible; the chart makes no claim about unobserved intrayear losses.
Excluding the initial zero from the UI average would instead give . That is a different observation convention, not a rounding difference. A report must state whether the starting mark is included.
Similar names, different denominators
The PerformanceAnalytics documentation distinguishes the Pain ratio, whose denominator is the mean absolute drawdown over all observations. For this path it is , rather than UI of 5%. Calling excess return divided by UI a Pain ratio confuses two measures.
| Measure | Risk denominator | What this path contributes |
|---|---|---|
| Martin ratio | Root mean square drawdown | 5% |
| Pain ratio | Mean absolute drawdown | 2.5% |
| Calmar ratio | Magnitude of maximum drawdown | 10% |
Calmar conventionally uses annualised return, often without subtracting a risk-free rate; compare numerator definitions as well as denominators. Martin and Pain retain information across the underwater observations, whereas Calmar's denominator keeps only the worst depth. None summarises every aspect of investment risk.
What to audit before trusting a comparison
Dates and peaks matter. Reordering the same simple returns preserves terminal compounded wealth but can change drawdowns and hence the Martin ratio. Starting a new measurement window also resets the peak unless an earlier high-water mark is explicitly carried in. A window that begins during an existing loss can therefore hide that prior loss.
Sampling can hide losses. Year-end observations may miss a fall and recovery within the year. More frequent observations change both the peaks detected and the weights assigned to underwater states; UI is not exactly invariant to frequency. Equally weighting irregular dates overweights densely sampled stretches. Choose a common grid or explicitly define time weights. Martin's original guidance warns against coarse observations for precisely this reason.
A short record can flatter the denominator. The three-year toy example has only one observed drawdown. It cannot establish a stable risk estimate, capture missing market regimes or justify a universal “good” ratio threshold. Compare the same dates, valuation frequency, cost basis and cash comparator. Illiquid or stale marks can conceal losses between observations. Martin's caveats emphasise long histories and consistent reinvestment and cost treatment.
Zero is a boundary, not a perfect score. When all observed marks are new highs, and the ratio is undefined. Report that state rather than silently replacing it with infinity or zero. A very small UI makes the ratio unstable. If excess return is negative and UI is positive, report the negative result; a less negative ratio obtained by increasing the denominator does not represent a desirable reduction in risk.
For the surrounding evaluation process, Backtest Evaluation connects cash-flow-adjusted returns, drawdown, costs and research uncertainty. The linked page is a public preview; the full lesson requires membership.
Sources
- Peter G. Martin and Byron B. McCann, The Investor's Guide to Fidelity Funds, Chapter 6, printed pp. 77–80 and 84–86. Originally published in 1989; the author-hosted PDF is a later printing. These sections establish RMS retracement, UI Performance and the compound-annual-return convention.
- Peter G. Martin, Ulcer Index: An Alternative Approach to the Measurement of Investment Risk & Risk-Adjusted Performance, “How is Ulcer Index Calculated?”, “Measuring Investment Performance” and “Caveat Emptor.”
- PerformanceAnalytics, PainRatio documentation, “Details”; CalmarRatio documentation, “Description” and “Details.” Used to distinguish neighbouring measures, not as a claim that software conventions are universal.