Formula, in Risk & Portfolio Construction
Maximum Drawdown Formula
Maximum drawdown is the largest percentage decline from a running peak to a subsequent trough in an equity curve. It is the single worst loss an investor holding from the prior high would have endured, and unlike volatility it measures path risk: the depth of the hole, not the average wiggle.
4 variables. Published May 26, 2026. By AI Fin Hub Research.
Drawdown_t = Equity_t / Peak_t - 1
Peak_t = max over s <= t of Equity_s
MaxDrawdown = min over t of Drawdown_t Variables
Equity_t
Equity at time t
The cumulative account value, NAV, or price level at each point in the series.
Peak_t
Running peak (high-water mark)
The highest equity value observed up to and including time t. Drawdown is always measured against this prior maximum, not the start of the series.
Drawdown_t
Drawdown at time t
Current equity relative to the running peak, minus one, so it is zero at a new high and negative otherwise. It expresses how far below the last peak the account currently sits.
MaxDrawdown
Maximum drawdown
The most negative drawdown across the entire series, the worst single peak-to-trough fall. Reported as a negative percentage or its absolute value.
Step by step
- 1
Walk through the equity series and track the running maximum at each point.
Equity 100, 120, 108, 132, 99 has running peaks 100, 120, 120, 132, 132.
- 2
At each point compute the drawdown as current equity over the running peak minus one.
Drawdowns: 0, 0, 108/120 - 1 = -0.10, 0, 99/132 - 1 = -0.25.
- 3
Take the most negative drawdown in the series.
The minimum of {0, 0, -0.10, 0, -0.25} is -0.25.
- 4
Report it as the maximum drawdown, optionally noting the peak date, trough date, and recovery date.
Maximum drawdown of -25%, peaking at 132 and troughing at 99.
Worked example
Daily equity curve over five points
Equity path
100, 120, 108, 132, 99
Running peaks: 100, 120, 120, 132, 132. Drawdowns at each point: 100/100-1 = 0; 120/120-1 = 0; 108/120-1 = -0.100; 132/132-1 = 0; 99/132-1 = -0.250. The minimum is -0.250.
Maximum drawdown of -25%, occurring from the peak of 132 down to 99. Note the deepest drawdown is measured from the 132 peak even though the 99 trough is below the 100 starting value: drawdown is always relative to the prior high-water mark, which is why a strategy can have a large drawdown while still ending above its start.
Common variations
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Sources
- Drawdown Measure in Portfolio Optimization , Chekhlov, Uryasev, Zabarankin, International Journal of Theoretical and Applied Finance (2005)
- On the Maximum Drawdown of a Brownian Motion , Magdon-Ismail, Atiya, Pratap, Abu-Mostafa, Journal of Applied Probability (2004)
Keep the topic connected
- Formula Calmar Ratio Formula
The Calmar ratio formula: annualized return divided by maximum drawdown over the period. A drawdown-based risk-adjusted return with a worked example.
- Formula Ulcer Index Formula
The Ulcer Index formula: the root mean square of percentage drawdowns from running highs. Measures depth and duration of losses, with an example.
- Formula Sterling Ratio Formula
The Sterling ratio formula: annualized return over average annual drawdown plus a 10% penalty. A stricter drawdown-adjusted return, with an example.
- Learn Drawdown
Drawdown explained: peak-to-trough decline, why max drawdown alone is misleading, and the recovery math that actually matters.