Maximum Drawdown

Maximum drawdown (MDD) is the largest percentage fall from a peak in account value to a subsequent low, before a new peak is reached. It answers a simple, painful question: what is the worst loss someone would have suffered if they had started at the worst possible moment? Many traders find maximum drawdown more meaningful than volatility, because drawdowns are what cause investors to redeem, traders to abandon systems and leveraged accounts to be liquidated.

The calculation#

Drawdown at time t = (Value at t - Highest value up to t) / Highest value up to t
Maximum drawdown = The most negative drawdown over the period

In pandas: drawdown = equity / equity.cummax() - 1 and max_dd = drawdown.min(). See NumPy and Pandas for Traders.

The recovery problem#

Gain needed = 1 / (1 - Drawdown) - 1

Losses compound against you: the deeper the hole, the disproportionately harder the climb. This is the mathematical case for strict risk management. See Risk of Ruin and Position Sizing.

Drawdown duration#

Depth is only half the story. Drawdown duration is the time from a peak to the recovery of that peak. A strategy that falls 15% and recovers in two months feels very different from one that falls 15% and takes three years to recover. Track:

The Ulcer Index combines depth and duration into one figure.

Historical examples#

Even broad, diversified markets can lose more than half their value. See The 1929 Crash, The 2008 Financial Crisis and The Dot-Com Bubble.

Using maximum drawdown#

1. Set risk limits based on drawdowns you can tolerate. See Risk, Position, Loss and Drawdown Limits.
2. Size positions so that a drawdown worse than the backtest's worst is survivable.
3. Expect worse live: a backtest's maximum drawdown is one sample; the future's worst can be deeper.
4. Use Monte Carlo reshuffling of returns to estimate a range of possible drawdowns. See Monte Carlo Simulation.
5. Compare strategies with return to drawdown ratios. See Calmar and MAR Ratio.

Limitations#

• One event: it describes the single worst episode, not typical drawdowns.
• Path dependent: the same returns in a different order give a different maximum drawdown.
• Grows with time: longer records usually show deeper drawdowns.
• Data frequency: daily data shows deeper intraday falls than monthly data hides.

Frequently asked questions#

What is maximum drawdown?#

The largest percentage decline from a peak in account or portfolio value to a later low, before a new peak is reached.

How much gain is needed to recover from a drawdown?#

One divided by (one minus the drawdown), minus one; a 50% drawdown requires a 100% gain to recover.

What is an acceptable maximum drawdown?#

It depends on the investor and strategy, but many traders aim to keep drawdowns below 20% to 25% through position sizing and risk limits.

Next, learn a measure that includes how long losses last in Ulcer Index.