Maximum drawdown explained

How maximum drawdown is calculated

Let E_t be portfolio equity at the end of session t. First calculate the highest equity observed up to that point:

P[t] = max(E[0], E[1], …, E[t])

The drawdown at session t is the current equity relative to that running peak:

D[t] = E[t] / P[t] − 1

Drawdown is zero at a new high and negative below it. Maximum drawdown is the minimum value in the drawdown series:

MDD = min(D[0], D[1], …, D[T])

Some reports display the magnitude as a positive number. TickRun displays the signed result, so a 20% peak-to-trough loss appears as −20.00%. Neither convention is wrong, but mixing them can reverse comparisons or break formulas. Always check which convention a system uses.

A worked example

Suppose a strategy’s end-of-day equity is 100, 110, 104.50, 88, 96, and 120. The full calculation is:

The maximum drawdown is −20%, from the 110 peak to the 88 trough. The recovery is not complete when equity rises to 96; the original peak remains 110 until session 5 exceeds it.

Loss and recovery percentages are asymmetric. After a 20% fall, equity is 80% of its former value and needs a 25% gain to recover: 1 / (1 − 0.20) − 1 = 0.25. A 50% drawdown requires a 100% gain. This asymmetry is one reason deep losses have an outsized effect on long-term compounding.

Exactly what TickRun measures

TickRun constructs a strategy equity curve by compounding its net daily returns from an initial value of one:

E[t] = E[t−1] × (1 + strategy_return[t])

Its strategy return uses the position held at the end of the previous session and subtracts the modeled transaction cost when position changes:

strategy_return[t] = position[t−1] × asset_return[t] − cost[t]

Maximum drawdown is then calculated by scanning that net equity curve, updating the running peak, and retaining the most negative E[t] / peak − 1 value. This has several consequences:

• Open-position gains and losses are included each day; drawdown is not limited to completed trades.
• Entry and exit costs reduce equity and can deepen the measured drawdown.
• Flat periods preserve equity because TickRun currently assigns no return to cash.
• The Buy & Hold benchmark receives its own independently calculated drawdown.
• The metric uses daily observations. A deeper intraday decline that recovers before the daily close is invisible.

The source prices are adjusted daily closes from the saved server dataset. That is appropriate for a close-to-close research model and makes corporate-action history more coherent, but it is not an intraday risk model. It also means the result inherits the quality and coverage of the selected ticker file.

Drawdown is path-dependent

Total return depends on the beginning and ending equity. Maximum drawdown depends on the order of every observation between them. Two strategies can both finish at 130 from a starting value of 100, yet one may rise steadily while the other climbs to 150, falls to 90, and then recovers. Their total returns match, but their drawdown experiences do not.

Reordering the same set of daily returns can change maximum drawdown dramatically because losses that cluster after a peak create a deeper decline than losses separated by recoveries. This is why volatility and drawdown are related but not interchangeable. Volatility treats upside and downside deviations symmetrically and loses much of their sequence; drawdown focuses on cumulative loss relative to prior wealth.

A drawdown is an episode, not just a percentage

A complete drawdown episode has three landmarks:

1. Peak: the last equity high before the decline.
2. Trough: the lowest equity reached before recovery.
3. Recovery: the first later observation that regains or exceeds the old peak.

The percentage from peak to trough measures depth. Peak-to-trough time measures the decline phase. Peak-to-recovery time measures the investor’s total time under water. A shallow drawdown lasting three years can be harder to hold than a deeper drop that reverses within weeks, yet the headline maximum-drawdown number reports only depth.

If the test ends before recovery, the drawdown is still open. Reporting it as an ordinary completed episode hides important information. A fuller risk report should show the peak date, trough date, recovery date or “not recovered,” and duration alongside depth.

Why the test window changes the answer

Maximum drawdown can only select the worst event present in the sample. Extend a calm five-year test to include a crisis and the number may change sharply even though the strategy rules are identical. Short samples have fewer opportunities to encounter extreme sequences; longer samples mechanically offer more chances for a severe drawdown.

The starting date also matters. If the data begins halfway through an existing market decline, the series creates a new artificial peak at its first observation and misses the loss that occurred before it. If it begins at a market trough, early results can look unusually favorable. Comparing strategies requires the same ticker, dates, and usable warm-up period.

Indicator warm-up adds another wrinkle. A 200-day rule cannot produce a valid rolling statistic on day one. If different strategies begin active measurement on different dates, their drawdowns cover different market paths. A rigorous comparison aligns the evaluated interval after every candidate has enough history.

How to compare drawdowns responsibly

A smaller historical drawdown is not automatically a better strategy. Consider exposure first. A strategy invested only 20% of the time would normally be expected to experience less market drawdown than one invested continuously, but it may also earn less return and leaves cash-return assumptions more important.

Use maximum drawdown with complementary evidence:

• Total and annualized return describe the reward earned over the same interval.
• Exposure shows how often capital was subject to the ticker’s return.
• Drawdown duration distinguishes brief shocks from prolonged stagnation.
• Multiple drawdown episodes reveal whether the worst event was isolated or typical.
• Volatility and downside measures describe fluctuations that never became the single worst drawdown.
• Out-of-sample results test whether a low fitted drawdown survives untouched data.

The Calmar ratio, commonly expressed as annualized return divided by the positive magnitude of maximum drawdown, can put reward and drawdown in one number. TickRun does not currently report Calmar. If calculating it separately, document the annualization window and avoid comparing ratios built from different histories. A tiny denominator can also make the ratio unstable.

The danger of optimizing for drawdown

Choosing the lowest maximum drawdown from thousands of parameter combinations does not make drawdown an objective fact about the winner. It makes drawdown the selection target. With enough trials, some configuration will avoid the sample’s worst dates by chance.

A low in-sample drawdown may be produced by one threshold that exited immediately before one historical crash. Move that threshold slightly, shift the dates, or evaluate another ticker and the advantage may disappear. Examine neighboring parameters, untouched periods, different regimes, trade count, and exposure. The same multiple-testing problem that inflates return can deflate selected drawdown.

TickRun’s optimizer ranks configurations using the chosen metric and fixed saved history; it does not automatically create train/test partitions or correct for repeated trials. Treat its output as candidate generation. Validate the frozen rule separately before interpreting its maximum drawdown as evidence.

What maximum drawdown does not tell you

• It does not estimate the worst possible future loss.
• It does not reveal how likely the historical event was.
• It does not show the second- or third-worst decline.
• It does not measure liquidity, leverage, forced liquidation, or execution capacity.
• It does not capture intraday lows when calculated from daily closes.
• It does not say whether an investor could tolerate the time under water.
• It does not correct selection bias from testing many strategies.

Maximum drawdown is most useful as a precise description of one realized equity path under stated assumptions. Its clarity is a strength as long as that clarity is not mistaken for a forecast.

Drawdown review checklist

• Is the calculation based on compounded portfolio equity rather than summed trade returns?
• Are open positions, costs, dividends, and cash treatment represented consistently?
• Are strategy and benchmark measured over identical dates?
• Is the sign convention clear?
• Are peak, trough, recovery, and duration reported?
• Does the history include varied market regimes?
• Was the strategy selected because it minimized this same in-sample metric?
• Has the drawdown behavior been checked out of sample?

Research reference and further reading

• Magdon-Ismail, Atiya, Pratap, and Abu-Mostafa: On the Maximum Drawdown of a Brownian Motion
• In-sample, out-of-sample, and walk-forward testing
• Overfitting in backtesting
• TickRun user manual