Losses and recoveries are not symmetrical. If a portfolio falls 20%, a 20% rebound does not take it back to the starting point. That simple fact becomes increasingly important as drawdowns deepen.
The reason is not mysterious finance. It is basic percentage math: after a loss, every future percentage gain is calculated from a smaller capital base.
Required recovery gain = loss ÷ remaining capital. A 10% loss needs about 11.1% to recover, 20% needs 25%, 50% needs 100%, and 80% needs 400%. Preventing very deep drawdowns matters because recovery difficulty accelerates nonlinearly.
Why a 20% Loss Is Not Repaired by a 20% Gain
Start with $100. Lose 20%, and you have $80. If that $80 then gains 20%, it becomes $96. You are still $4 below the starting point because the gain was calculated on a smaller base.
To recover the missing $20 from an $80 balance, you need $20 ÷ $80 = 25%. The deeper the loss, the smaller the remaining base and the larger the percentage gain required to rebuild it.
| Drawdown | Capital remaining | Gain needed to recover |
|---|---|---|
| -10% | $90 from $100 | +11.1% |
| -20% | $80 from $100 | +25.0% |
| -30% | $70 from $100 | +42.9% |
| -50% | $50 from $100 | +100.0% |
| -80% | $20 from $100 | +400.0% |
This Does Not Mean Every Drawdown Is a Disaster
Drawdowns are part of investing and trading. The lesson is not to panic at every decline. A temporary paper loss in an unleveraged, diversified position is very different from a forced liquidation or a strategy that has lost its edge.
The math becomes most useful when setting risk boundaries. If your strategy can routinely suffer a 50% account drawdown, you are asking future performance to double the remaining capital merely to get back to zero. That is a very different recovery challenge from keeping drawdowns around 10% or 15%.
Avoiding catastrophic losses does not guarantee profit. It preserves the capital base from which future returns are earned, which is why loss control compounds in your favor over time.
How to Use Drawdown Math in a Risk Plan
Define an account-level drawdown that would force you to reduce risk, stop trading, or reassess the strategy. Then work backward to position size and single-trade risk. The objective is not a magical universal percentage; it is a boundary your capital and psychology can realistically survive.
Also separate strategy drawdown from a broken thesis. A sound strategy can have losing periods. What matters is whether losses remain within the range you planned for and whether the evidence supporting the strategy still exists.
Frequently Asked Questions
Why does a 50% loss require a 100% gain?
Because half the capital remains. Doubling the remaining 50 brings the account back to the original 100.
Is a 20% drawdown always unacceptable?
No. Acceptability depends on strategy, time horizon, leverage, diversification, and your predefined risk tolerance and capacity.
Can I use this formula for any percentage loss?
Yes. Divide the percentage lost by the percentage of capital remaining after the loss.
