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Calmar ratio

Compound annualised return per unit of absolute maximum drawdown over the same interval, strongly conditional on the path and observation window.

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Who this is for — Readers relating annualised growth to the worst observed peak-to-trough fall while keeping the interval, wealth curve and conventions identical.

The Calmar ratio compares annualised return with the absolute magnitude of maximum drawdown over the same period:

Calmar = annualised return / |MDD|

In contemporary use the numerator is often CAGR. The metric belongs to the return-to-drawdown family: it replaces volatility with one path-dependent feature. It does not measure average loss, drawdown frequency or the probability of a future event.

Sources and providers use variants in numerator, sign and window. Cyclepedia therefore does not turn a historically common duration such as 36 months into a rule. Every convention must be stated.

Calmar ratio: return and path loss Annualised return and maximum drawdown must use the same perimeter Calmar ratio: return and path loss Annualised return and maximum drawdown must use the same perimeter Calmar = annualised return / |maximum drawdown| Numerator Annualisation method, gross/netbasis and currency must beexplicit. Denominator Maximum drawdown from the sameseries and observation window. Path dependence Return order and starting pointcan change drawdown. Conventions Windows and definitions vary;no cut-off fits every use. Cyclepedia · educational diagram: state conventions, period and data
The ratio uses two properties of one wealth curve: equivalent growth and its worst observed fall over the same interval.

The numerator

For positive opening value Vᵢ, positive closing value V_f and duration Y in years:

CAGR = (V_f / Vᵢ)^(1/Y) − 1

CAGR is a compound equivalent, not the arithmetic mean of annual returns. With external flows, raw account-balance CAGR confuses contributions and performance. Price/total-return basis, gross/net status, currency and cost must match the curve used for drawdown. Variants subtracting a risk-free rate or using another annual average are not directly comparable with CAGR/MDD.

The denominator

Signed drawdown is:

DDₜ = Wₜ / max_{u≤t}(Wᵤ) − 1

Calmar normally uses positive magnitude |MDD|. If observed MDD is zero, the ratio is undefined. Adding an arbitrary small denominator to publish a finite number creates a new metric.

MDD is one extreme observation. Start date, valuation frequency and window can change both peak and trough; a shorter record has fewer opportunities to contain a severe drawdown.

Example

A hypothetical portfolio grows from 100 to 121 in two years without external flows. CAGR is:

(121/100)^(1/2) − 1 = 10%

Its maximum drawdown over the same interval is −20%, so under the CAGR/absolute- MDD convention:

Calmar = 10% / 20% = 0.50

Analysing only year two could change both numbers. The value 0.50 belongs to no universal band and does not predict the next drawdown.

Comparable calculations

Two ratios need matching start and end dates or, with care, the same length and regime; valuation frequency and calendar; currency and hedging; price/total- return basis; flow treatment; costs, fees and taxes; annualised-return formula; MDD definition and sign; and live, composite or simulated status.

An intraday gross backtest and a monthly net fund series are not comparable: the first observes finer troughs while the second may contain fees and delayed marks.

Calmar, Sharpe and Sortino

Ratio Denominator Main property
Sharpe standard deviation of differential return uses the full periodic distribution
Sortino downside deviation below a target depends on MAR and shortfalls
Calmar maximum drawdown depends on return order and one observed extreme

No ratio dominates every context. Sharpe may penalise upside dispersion; Sortino may have too few shortfalls; Calmar may be driven by one episode. Using several measures exposes useful contradictions but does not create a universal score.

Limitations and reporting

Calmar is window-dependent; ignores the rest of the drawdown distribution and underwater duration; can favour short or smoothed track records; does not correct liquidity, unobserved tails or selection bias; is unstable with a small denominator; is not additive; and does not separate leverage, factors, luck and skill.

Magdon-Ismail and Atiya show that MDD scaling changes with drift and horizon under specific models. No universal transformation can therefore align Calmar across windows.

A complete report includes formula and window, wealth curve, numerator, peak and trough dates, decline and recovery duration, open drawdowns, flows and costs, a like-for-like benchmark, the broader drawdown distribution and its ex-post nature.

Common error — Using five-year CAGR with a three-year MDD. Numerator and denominator must come from the same curve and interval.

Sources

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