Drawdown Recovery Math: Why -50% Needs +100%

Lose 50% of your account and you need a 100% gain - not 50% - just to get back to where you started. The asymmetry exists because gains after a loss are earned on a smaller base. This one piece of arithmetic explains more about professional risk management than any indicator ever will, and it's the quiet reason serious systematic traders are obsessive about capping drawdown.

The formula

If you lose a fraction d of your account, the gain required to recover is:

Required gain = d / (1 − d)

Illustrative example: start with £10,000 and lose 50%, leaving £5,000. To return to £10,000, the £5,000 must double - a 100% gain. The formula agrees: 0.5 / (1 − 0.5) = 1.0, i.e. 100%.

The recovery table

• −10% → needs +11.1%
• −20% → needs +25%
• −30% → needs +42.9%
• −40% → needs +66.7%
• −50% → needs +100%
• −60% → needs +150%
• −70% → needs +233%
• −80% → needs +400%
• −90% → needs +900%

Notice the shape: shallow drawdowns cost roughly what they look like, then the curve turns viciously nonlinear. The difference between a 10% and a 20% drawdown is modest; the difference between 50% and 70% is a different life. Risk management is not about avoiding losses - it's about staying on the flat part of this curve.

Why this drives everything else

1. It's why small per-trade risk wins. Under the 1% rule, even ten consecutive losses - painful but survivable - leaves you needing roughly +10.5% to recover. At 5% risk per trade, the same streak digs a hole needing about +67%. Same strategy, same streak, wildly different mountain - all set by position sizing.
2. It's the engine behind risk of ruin. Deep drawdowns don't just hurt - they compound the difficulty of every subsequent recovery, which is why risk of ruin rises so sharply with position size.
3. It's why oversizing “because the edge is good” backfires. The Kelly criterion literature reaches the same conclusion from the other direction: growth is maximised by sizes far smaller than intuition suggests, because the recovery asymmetry punishes volatility.

Common mistakes

• Thinking in symmetric percentages. “I'm down 30%, I just need a good month” - no, you need +42.9%, sustained, without digging deeper.
• Doubling risk to recover faster. Increasing size in a drawdown raises the chance of deepening it, moving you rightwards on the curve exactly when the curve is steepest.
• Judging EAs on returns while ignoring drawdown. Two systems with equal returns and different maximum drawdowns are not equal - one lives on the survivable part of the curve.
• Forgetting the time dimension. Recovery isn't just a percentage; it's months or years of compounding at realistic rates. Deep holes cost time you never get back.

Designing for the flat part of the curve

The practical conclusion: cap the hole, and the recovery maths stays friendly. This is baked into how Nebula builds systems - hard risk caps are enforced in the EA itself, not left as a suggestion, and strategies are validated on unseen data so drawdown estimates aren't just curve-fit optimism. No tool can promise shallow drawdowns; the point is to make the deep ones structurally hard to reach.

Trading carries a high level of risk. Nothing here is financial advice; past performance does not predict future results.