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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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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 Peak, trough and recovery describe the depth and duration of the path Anatomy of a drawdown Peak, trough and recovery describe the depth and duration of the path Positive magnitude: Dₜ = 1 − Vₜ / maxᵤ≤ₜ(Vᵤ) ; |MDD| = maxₜ(Dₜ) previous peaktroughpeak recovereddepthduration High-water mark The prior maximum updates only whenportfolio value exceeds it. Depth Percentage loss depends on the series,currency and treatment of cash flows. Duration Time from peak to recovery: informationdistinct from depth. Cyclepedia · educational diagram: state conventions, period and data
Depth and duration are different coordinates. Recovery ends only when wealth regains the prior peak under the chosen convention.

Formula on a wealth curve

With wealth Wₜ and running maximum:

Mₜ = max(W₀, W₁, …, Wₜ)

signed percentage drawdown and maximum drawdown are:

DDₜ = Wₜ / Mₜ − 1
MDD = minₜ DDₜ

The positive magnitude is |MDD|. With periodic returns and no unaccounted flows, the curve is Wₜ = W₀ × ∏(1+rₜ). An arithmetic cumulative sum can produce a different path.

Peak, trough, duration and recovery

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

The wealth curve must be coherent. Contributions and withdrawals are not return. Evaluating a manager may call for time-weighted returns; describing an investor's wealth experience may call for money-weighted analysis. Manager drawdown and personal-wealth drawdown can therefore 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 positive MDD magnitude can only stay the same or increase as the same sample is extended, because more severe episodes may be added. Comparing three years of one strategy with twenty years of another without aligning windows favours the shorter record. The starting date can also change the relevant peak and trough.

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. The later value of 130 closes the episode. A contribution before that recovery would need to be separated from performance.

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.

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