If a $1,000 investment loses 50%, the account has $500 left. This is where many people misread the math. It is tempting to think that a 50% gain would recover a 50% loss.
But that is not how the money works. A 50% gain on $500 is $250. The account becomes $750, not $1,000.
If $1,000 falls by 50% to $500, the remaining money must gain 100% to return to the original $1,000.
| Loss | Remaining amount | Gain needed to recover |
|---|---|---|
| -10% | $900 | +11.11% |
| -30% | $700 | +42.86% |
| -50% | $500 | +100.00% |
| -70% | $300 | +233.33% |
| -90% | $100 | +900.00% |
A 10% loss needs an 11.11% gain to recover. That feels close to the original loss, so it does not look surprising.
A 30% loss already feels different. When $1,000 falls to $700, the account needs about a 42.86% gain to return to $1,000. It does not need 30%. It needs more.
A 50% loss makes the point very clear. The account has $500 left. To get back to $1,000, that remaining money must double. A double is a 100% gain.
Why are loss and recovery not symmetrical?
The loss is calculated from the original money. A 50% loss on $1,000 removes $500.
The recovery gain is calculated from the remaining money. If only $500 is left, the account needs to earn another $500 to recover. That is 100% of the remaining money.
This is why drawdowns become harder to recover as they get deeper. After a loss, the base amount is smaller. The same percentage gain is applied to less money.
This calculation is not meant to scare investors. It is meant to make risk visible. A deep loss does not only reduce the account. It also makes the required recovery return much larger.
A 70% loss needs a 233.33% gain to recover. A 90% loss needs a 900% gain. At that point, the issue is no longer just “the account is down.” The recovery path has become much steeper.
That is why loss recovery math is risk math. It shows why protecting capital matters before a drawdown becomes too deep.