Drawdown depends on the observed path

A loss measured from a previous high

For a positive wealth path, define the running peak as the highest value observed up to each time, including initial wealth. The drawdown at that time is current wealth divided by the running peak, minus one. This signed quantity is zero at a high and negative below it. Maximum drawdown can be reported either as the most negative signed value or as its positive loss magnitude; PerformanceAnalytics explicitly documents this sign choice. Maximum drawdown is not the worst single-period return. Several modest losses after a peak can combine into a deeper drawdown than any one of them considered alone.

Ordering matters even when compound return agrees

Multiplication of the same positive gross returns gives the same terminal wealth regardless of their order. The intermediate running peaks do not share that invariance. Reordering a return vector can therefore preserve its arithmetic mean, standard deviation and cumulative return while changing maximum drawdown. This makes drawdown a path statistic rather than a summary of the unordered distribution of returns. Including initial wealth is important: otherwise a loss in the first period may disappear from the peak comparison. The starting point also limits the history considered; an analysis beginning after an earlier peak does not measure the complete pre-existing drawdown.

Two paths and one terminal balance

The original synthetic hypothetical starts at 100. Path A applies decimal returns of 0.10, -0.10, -0.10 and 0.10, producing wealth of 110, 99, 89.10 and 98.01. Its peak-to-trough loss magnitude is 0.19. Path B reorders the same returns as -0.10, 0.10, -0.10 and 0.10, producing 90, 99, 89.10 and 98.01. Its running peak remains the initial 100, so maximum loss magnitude is 0.109. Both paths finish with cumulative return of -0.0199. The table compares those paths and a coarser observation schedule; none represents an actual asset or investment history.

Sampling can omit both the peak and trough

Observing path A only at times 0, 2 and 4 gives 100, 99 and 98.01. On that subset, maximum drawdown magnitude is just 0.0199 because the higher interim peak and lower interim trough are absent. For the same positive wealth path and nested observation sets with the same starting point, adding observations cannot reduce the measured maximum drawdown: the earlier ordered peak-trough comparisons remain available. This is an algebraic sampling property, not a prediction of unseen losses. Daily closes similarly cannot reveal intraday extremes. Comparisons across data frequencies can therefore change meaning even when endpoint values agree exactly.

Depth and duration describe different burdens

Drawdown depth records distance below a peak; duration records elapsed time associated with the decline and recovery. The time from peak to trough differs from the time spent underwater until the old peak is regained. PerformanceAnalytics' drawdown documentation treats location and length as separate outputs. An unrecovered drawdown at the end of a dataset is right-censored: its eventual recovery time is unknown, not zero. Counting observations and counting calendar time also differ when dates are irregular. Equal-valued peaks can create ties, making the choice of first or latest peak relevant to duration even when the loss magnitude is unchanged.

The wealth series must represent the intended claim

A contribution can raise raw account value above an earlier peak without recovering an investment loss. A withdrawal can reduce balance without creating one. Performance drawdown therefore differs from drawdown of unadjusted cash balances; a flow-adjusted wealth index and a balance series answer different questions. Income, costs and valuation conventions also affect the path. A smooth appraisal series can hide interim variation that a more frequently marked series reveals. Positive wealth is part of the percentage-drawdown interpretation used here. Negative equity, liquidation and recapitalization require an explicitly different accounting framework rather than silent continuation of a conventional return chain.

An observed maximum is not a future bound

Historical maximum drawdown is the most severe observed episode under a particular window and sampling rule. It is not a quantile of future loss, an expected shortfall estimate or a guarantee that future losses will be smaller. Extending a fixed path's observation horizon cannot remove its earlier maximum, but rolling the starting point can exclude that episode. There is no general square-root annualization for maximum drawdown. A basic return-to-drawdown calculation does not estimate recovery probabilities or confidence intervals. The synthetic comparison establishes the importance of path order and sampling while leaving any assessment of future drawdown risk explicitly unresolved.

Primary references

These sources support methods and conventions. The example values are original constructions, not observations extracted from these documents.

• PerformanceAnalytics documentation: maxDrawdown and sign conventions
• PerformanceAnalytics documentation: Drawdowns and findDrawdowns

Related investigations