Can you put return per unit of pain into one number?
Sharpe divides return by volatility. If drawdown is the risk you actually feel, the obvious move is to divide return by that instead. Two measures do it, and their weaknesses are as instructive as their strengths.
Calmar ratio: return per unit of worst case
Calmar ratio = annualised return ÷ |maximum drawdown|
Conventionally computed over three years, though longer windows are common.
Worked example. A portfolio compounded at 12% a year over the window and suffered a maximum drawdown of 30%.
12 ÷ 30 = 0.40
Read it as: 0.4 points of annual return for each point of worst-case decline. Higher means the return was produced with a shallower worst episode — over that window, with that one episode.
The flaw sitting in plain sight
The denominator is a single observation: the worst thing that happened once. Every other data point in the history is discarded. Consequences follow immediately.
- Extend the window by one year and, if that year contained a crash, the ratio can halve. Nothing about the strategy changed.
- A strategy that has simply not yet met its bad environment shows a superb Calmar. The absence of a disaster in the sample is not evidence of resilience.
- Two portfolios with the same maximum drawdown, one of which spent six years recovering and one six months, score identically.
Ulcer index: depth and duration together
The ulcer index fixes the last of those by using the whole drawdown series rather than its minimum:
Ulcer index = √( mean of the squared drawdown percentages )
Because it squares and then averages every period's drawdown, both deeper and longer declines raise it.
Worked example. Five periods with drawdowns of 0%, −5%, −10%, −5%, 0%:
- Squares: 0, 25, 100, 25, 0 → sum 150
- Mean: 150 ÷ 5 = 30
- Ulcer index = √30 = 5.48%
Divide excess return by it and you get the Martin ratio — the same shape as everything else in this course: something earned over something endured.
Using them honestly
These ratios rest on fewer effective observations than Sharpe does, so they are noisier, and the noise runs in a flattering direction for young track records. Report the window alongside the number, always. And as with every measure here: a favourable ratio describes a period that has already been survived. It does not identify a good investment, does not forecast the next decline, and is not a reason to buy anything.
Try it now
- One fund, one chart, below. On the 5Y range, Measure the total move to get a CAGR and the largest peak-to-trough fall to get the maximum drawdown. Divide for a Calmar ratio.
- Now press MAX and do exactly the same two measurements again over twenty years. Note how far apart the two Calmar figures are. Nothing about the fund changed between step 1 and step 2; only the window did, and that spread is window sensitivity, quantified.
- Calmar uses one day out of twenty years — the worst one. Sketch the drawdown series across the long window instead and compute the ulcer index from it. Which window looks better under Calmar, and does the ulcer index agree? When they disagree, it is usually because one long shallow decline hurts more than one short deep one.