Transparency is a feature. This page explains what these drawdown measures and ratios describe and why we compute them — in plain terms. The precise formulas and numeric conventions are documented in our internal methodology; the summary here is deliberate, not an omission.
These metrics extend md (maximum drawdown and the Ulcer index). They all read from the same underlying idea: at every point in time, how far below its previous high-water mark is the investment? That gap — always zero or negative, since a peak cannot be below itself — is the drawdown, and the whole family of measures below summarizes that series of gaps in different ways.
The pain index is the average depth of drawdown over the whole history — a single number capturing how deep, on average, the investment sat below its prior peak. It is always zero or positive; a bigger value means more sustained time spent underwater.
Conditional Drawdown at Risk (CDaR) is the drawdown analogue of conditional value-at-risk: rather than describing typical pain, it focuses on the worst of it. It averages together the deepest drawdowns — the tail of the very worst episodes — at a chosen confidence level. The stricter the confidence level, the fewer, deeper episodes it looks at, until at the extreme it simply reports the single worst drawdown ever seen (the maximum drawdown).
These ratios ask a common question: how much return did the investment earn for each unit of drawdown pain it inflicted? They all share the same numerator — an annualized measure of return earned above the risk-free rate — and differ only in how they summarize the drawdown pain in the denominator. Higher is better in every case: more reward per unit of downside suffering.
All of these are built on exactly the same high-water-mark path as our core drawdown page, so the pieces line up cleanly: the Martin ratio's downside measure is consistent with the Ulcer index, and CDaR at a strict confidence level agrees with the reported maximum drawdown.
The Sterling ratio is intentionally not offered. Its standard definitions depend on a calendar convention — grouping drawdowns by year and adding a fixed adjustment — rather than being a clean function of the return series itself. For a single, unambiguous drawdown-based reward measure we maintain the Calmar ratio (annualized return relative to the maximum drawdown) instead.
