Financial
Required recovery rate: percentage gain needed to break even after a loss
Calculate the asymmetric percentage gain required to recover from a portfolio drawdown or sales drop using LossPct / (1 - LossPct).
Why a 20% drawdown requires a 25% gain to break even
Percentage losses and gains apply to different bases. Losing 20% on a 10,000 portfolio leaves 8,000. Gaining 20% on 8,000 recovers only 1,600 (9,600)—still 400 below break-even.
To climb back from (1 - LossPct) to 1.00, the remaining balance must grow by LossPct / (1 - LossPct): 0.20 / 0.80 = 25%, and a 50% drawdown requires a 100% gain.
| Drawdown Loss % | Remaining Base | Required Gain Formula | Break-Even Gain % |
|---|---|---|---|
| 10% (0.10) | 90% | 0.10 / 0.90 | 11.11% |
| 20% (0.20) | 80% | 0.20 / 0.80 | 25.00% |
| 50% (0.50) | 50% | 0.50 / 0.50 | 100.00% |
Break-even recovery percentage formula
Guard LossPct >= 1 (100% total loss) because a zero remaining balance can never compound back.
=IF(OR(B2<0, B2>1), "Invalid loss", IF(B2=1, "Unrecoverable", ROUND(B2 / (1 - B2), 4)))Verify dollar recovery back to starting balance
Multiplying remaining value A2 * (1 - B2) by (1 + RecoveryRate) restores A2.
=(A2 * (1 - B2)) * (1 + B2 / (1 - B2))Inputs and interpretation
Assume a positive starting amount, no deposits/withdrawals, and loss entered as a fraction from 0 through 1. At 100% loss no finite percentage gain on the zero balance restores it; new funding is a different scenario. The recovery check requires loss below 1 and uses an unrounded ratio. Fees, taxes and changing cash flows are omitted.
Try the example
Use the original values or change them to test your understanding.