Why a 50% Loss Requires a 100% Gain to Recover
Gains and losses are percentages of different amounts, so recovering from a loss always takes a bigger gain. The formula, a full table, how long recovery takes, and what it means for risk limits.
By the AURAX teamPublished 4 min read
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A 50% loss halves the account, and doubling it again takes a 100% gain. The percentage lost is taken from a larger amount than the percentage gained afterwards, so every loss needs a larger gain to undo it — and the gap widens fast. A 10% loss needs 11.1%; a 50% loss needs 100%; a 90% loss needs 900%.
gain needed = loss ÷ (1 − loss)
- loss and gain as fractions: 0.50 ÷ (1 − 0.50) = 1.00 = 100%
- $10,000 − 50% = $5,000; $5,000 + 100% = $10,000
Part of the Drawdown and risk guide.
The recovery table
| Loss | Gain needed to recover | Relative size |
|---|---|---|
| −5% | +5.3% | |
| −10% | +11% | |
| −20% | +25% | |
| −25% | +33% | |
| −30% | +43% | |
| −40% | +67% | |
| −50% | +100% | |
| −60% | +150% | |
| −75% | +300% | |
| −90% | +900% | off scale |
Up to about 20% the difference is small. Past 30% it accelerates, and beyond 50% recovery becomes a different order of problem. The shape is why professional risk management concentrates on the left of this table.
Why it works this way
Percentages are relative to the amount they are applied to. Lose 50% of $10,000 and you lose $5,000. Gain 50% on the $5,000 that is left and you gain only $2,500 — ending at $7,500. The loss was applied to a large balance; the gain to a small one.
How long recovery takes
The gain needed is only half of the problem; the other half is time. At a steady monthly return, the months needed are:
months = ln(1 ÷ (1 − loss)) ÷ ln(1 + monthly return)
- 20% loss at 2% a month: ln(1.25) ÷ ln(1.02) ≈ 11.3 months
- 50% loss at 2% a month: ln(2) ÷ ln(1.02) ≈ 35 months
| Loss | At 1% / month | At 2% / month | At 5% / month |
|---|---|---|---|
| 10% | 10.6 | 5.3 | 2.2 |
| 20% | 22.4 | 11.3 | 4.6 |
| 30% | 35.8 | 18.0 | 7.3 |
| 50% | 69.7 | 35.0 | 14.2 |
Losing streaks and risk per trade
Most deep drawdowns are not one catastrophic trade but a run of ordinary losses. With a fixed fraction of the account risked on each trade, ten losses in a row compound like this:
| Risk per trade | Drawdown after 10 losses | Gain needed to recover |
|---|---|---|
| 1% | 9.6% | 10.6% |
| 2% | 18.3% | 22.4% |
| 5% | 40.1% | 67.0% |
Ten losses in a row is not rare over hundreds of trades, even for a strategy that wins more often than it loses. At 1% per trade the streak is an inconvenience; at 5% it is a drawdown that takes most traders years to climb out of, if they do. Choosing the risk per trade is choosing which row of the recovery table you will eventually visit — see XAUUSD lot size explained for turning a risk percentage into a position size.
What it means for risk
- Cap the drawdown, not just the trade. A per-trade stop limits one loss; an account-level limit caps the sequence.
- Set limits on the left of the table. A 20% maximum drawdown needs a 25% gain to undo; a 50% one needs 100%.
- Be most careful with strategies that lose rarely but heavily. Grids and martingales produce exactly the losses that sit on the right of the table — see grid trading drawdown.
- Do not size up to win it back. Increasing risk after a loss is how a recoverable drawdown becomes a terminal one.
The drawdown recovery calculator computes the gain and time for any loss and monthly return.
Educational content, not financial advice. Trading gold and other leveraged products carries a high level of risk, including the possible loss of some or all of your capital. Automated strategies do not guarantee profit, and past or simulated performance is not indicative of future results. Risk disclosure.