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Why a 50% loss needs a 100% gain

If your account falls 50%, you need to double what is left to get back to even. The math is simple, and it is the strongest argument for controlling drawdowns.

  • 5 min read
  • By a.b
  • Updated October 2026

The asymmetry

Start with $10,000 and lose 50%. You have $5,000. To get back to $10,000 you must earn $5,000, which is a 100% gain on the $5,000 that remains. A gain of 50% would only take you to $7,500.

The formula

gain needed = drawdown ÷ (1 − drawdown)Drawdown is a fraction. 50% is 0.5, so the gain needed is 0.5 ÷ 0.5 = 1, or 100%.

Gain needed at different drawdowns

DrawdownGain needed to recover
10%+11.1%
20%+25.0%
30%+42.9%
40%+66.7%
50%+100.0%
60%+150.0%
70%+233.3%
80%+400.0%
90%+900.0%

The curve bends upward. A 10% loss needs 11.1%, but each extra point of drawdown costs more to repair than the one before. Past 50% the required gain is more than 100%, and at 90% it is 900%.

How long does recovery take?

Time to recover = ln(1 ÷ (1 − drawdown)) ÷ ln(1 + monthly return). At a steady 2% a month, a 20% drawdown takes 11 months, a 30% drawdown takes 18 months, and a 50% drawdown takes 35 months. At 5% a month those become 5, 7 and 14 months. Few traders sustain 5% a month, so real recoveries take longer.

Equal losses and gains do not cancel

Lose 30% then gain 30%: 0.7 × 1.3 = 0.91. You are still down 9%. This is why a strategy that makes and loses the same percentage in turn slowly shrinks, a drag sometimes called volatility decay.

What to do with this

Keep reading

a.b

Written by a.b. I have published trading indicators on TradingView since 2015. These guides are for education only. Message me on TradingView chat with questions or topics you want covered.

Last updated October 2026. For education only. Not financial advice.