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Maximum drawdown

The largest observed loss from a prior peak to a later trough in a wealth curve, conditional on the path, window and valuation frequency.

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This reference cites the Cyclepedia entry. The documents it draws on are listed in the entry’s sources.

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Who this is for — Readers measuring the worst historical loss along a wealth path and distinguishing depth, decline duration and time to recovery.

Maximum drawdown (MDD) is the largest observed fall from a prior peak to a later trough within a defined interval. It is path-dependent: two series with the same mean return and volatility can have different drawdowns because their returns occur in a different order.

MDD may be reported as a negative loss or as a positive magnitude. The sign convention must be stated. It is neither an automatic forecast of future loss nor an operating threshold; it is the worst episode in the series under its prices, flows, costs and valuation frequency.

Anatomy of a drawdown Positive curve, external flows neutralised: depth and duration are separate measures Anatomy of a drawdown Positive curve, external flows neutralised: depth and duration are separate measures Dₜ = 1 − Vₜ / Mₜ ≥ 0 ; |MDD| = maxₜ Dₜ ; 0.20 = 20% previous peaktroughpeak recovereddepthduration Running maximum Mₜ Maximum observed within the window upto t, including the current value. Depth Dₜ is a nonnegative fraction of thepeak. Historical depth does not capfuture losses. Duration From the peak before the decline to thefirst return to that level or above. Cyclepedia · educational diagram: state conventions, period and data
Depth and duration are separate measures. Here recovery is the first return to the prior peak or above; equality suffices.

Formula on a wealth curve

On a positive wealth curve Wₜ, set 0 as the window start and define its running maximum:

Mₜ = max(W₀, W₁, …, Wₜ)
DDₜ = Wₜ / Mₜ − 1
MDD = minₜ DDₜ

Here DDₜ is a signed fraction: −0.28 = −28%. The positive magnitude is |MDD|, the maximum of Dₜ = −DDₜ used in Drawdown. With periodic returns adjusted for external flows, use Wₜ = W₀ × ∏ᵢ₌₁ᵗ(1+rᵢ), with W₀ > 0. Adding returns generally gives a different curve.

This ordinary interpretation assumes positive values. Zero means complete loss against a positive peak; negative balances need separate treatment, and a zero peak makes the ratio undefined. A decline starting before the window loses its earlier peak under this formula; any inherited starting peak must be disclosed.

Peak, trough, duration and recovery

Here underwater time runs from the last observation at the peak before the decline to the first value observed at or above that peak.

A drawdown episode should identify peak date and value; subsequent trough; percentage or monetary depth; time from peak to trough; total time below the peak; recovery date, if any; and any episode still open at the end.

“Drawdown duration” can mean peak-to-recovery time or the declining phase alone. Those are not identical, so the report must define the term. A brief, deep loss and a shallower multi-year loss create different liquidity, behavioural and liability problems.

Returns, flows and valuations

Contributions and withdrawals are not returns. To isolate manager performance, a unitised index neutralises these flows by geometrically linking time-weighted returns. If an account falls from 100 to 80 solely because 20 is withdrawn, its balance falls 20%, but performance return and drawdown are zero. A money-weighted return summarises the effect of flow amounts and timing on investor experience; that single rate supplies no path from which to compute MDD. Personal balance and performance index answer different questions.

Material choices include dividend and coupon treatment; transaction, management and performance fees; base currency and FX hedges; intraday, daily or monthly values; estimated, stale or illiquid marks; and margin calls, liquidations or negative balances. Monthly data can miss an intramonth trough, while smoothed valuations can suppress both drawdown and volatility.

Dependence on the window

The magnitude |MDD| cannot decrease when observations are appended while the starting date, previous values and conventions stay fixed; signed MDD cannot increase. This does not apply to a rolling window that drops old observations. Three- and twenty-year records expose the measure to different samples; align windows for comparison. Changing the start can change the relevant peak and trough.

The Brownian result concerns absolute declines of the process, distinct from percentage drawdown on a positive wealth curve.

Magdon-Ismail, Atiya, Pratap and Abu-Mostafa analyse maximum drawdown under a Brownian-motion model and show its expected behaviour depends on horizon, drift and volatility. This model-specific result explains window dependence; it does not justify multiplying a backtest MDD by a universal factor.

There is no general rule that a live drawdown will be 1.5 or 2 times its historical value. An uncertainty range needs explicit models, assumptions and stress tests.

Example

A hypothetical wealth curve moves from 100 to 125, falls to 90 and later rises to 130. The peak before the trough is 125:

DD = 90 / 125 − 1 = −28%

Recovering from 90 to 125 requires 125/90 − 1 ≈ 38.89%, not 28%, because the base is smaller. Reaching 125 already suffices; 130 is the first recovery observed in the sampled example. A contribution before that recovery would need to be separated from performance.

Generally, with drawdown magnitude x as a fraction, recovery requires x/(1−x) for 0 ≤ x < 1, without new contributions. After a 100% loss, no finite percentage return on zero remaining capital restores the peak. This does not predict recovery time or probability.

Appropriate use

MDD can describe the worst sample experience, compare scenarios on aligned windows, test whether liquidity and mandate can survive a path, support a Calmar ratio, and reveal extended underwater periods in a backtest. It does not measure average loss, drawdown frequency, tail outcomes beyond the sample or recurrence probability.

Full drawdown distribution, duration, scenarios, volatility, Expected Shortfall and liquidity provide context that one extreme observation cannot.

Common error — Treating historical MDD as the greatest possible loss. It is the worst observation in the available series; a new path can be deeper or longer.

Sources

Sources accessed 8 September 2026; the public introductions and summaries of the CFA refresher readings were checked. Examples, conventions and formula checks are Cyclepedia teaching calculations.

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