What Is Loss Recovery Math? Definition and Example
Why a 50% loss needs a 100% gain to get back to even, the full table of losses and required gains, and why it makes drawdown control so valuable.
Key takeaways
- Loss recovery math is the rule that the gain needed to recover a loss is larger than the loss itself: required gain = 1 ÷ (1 − loss) − 1, so a 50% loss needs a 100% gain.
- The gap grows fast: a 20% loss needs 25%, a 40% loss 66.7%, a 75% loss 300%.
- The S&P 500 ETF (SPY) fell 56.5% in the 2007–09 crisis in Exent’s data, which needed a 129.7% gain to recover.
- Limiting deep losses matters for long-run wealth because every recovery starts from a lower base.
Why does a 50% loss need a 100% gain?
Because the gain is earned on a smaller base. $100 that falls 50% becomes $50. To get back to $100, the $50 has to double: a 100% gain. Percentages after a loss are measured from the lower value, so recovery always takes more than the loss.
Loss and required gain table
| Loss | Gain needed to break even | Years to recover at 7% a year (illustrative) |
|---|---|---|
| 10% | 11.1% | 1.6 |
| 20% | 25.0% | 3.3 |
| 30% | 42.9% | 5.3 |
| 40% | 66.7% | 7.6 |
| 50% | 100.0% | 10.2 |
| 60% | 150.0% | 13.5 |
| 75% | 300.0% | 20.5 |
| 90% | 900.0% | 34.0 |
Formula: required gain = 1 ÷ (1 − loss) − 1. The 7% a year return is illustrative, not a forecast.
Example: real crashes
In Exent’s data, SPY fell 56.5% peak to trough in the 2007–09 financial crisis, so it needed a 129.7% gain to recover. In the 2022 bear market, NVIDIA fell 61.8%, which required a 161.9% gain. A portfolio’s max drawdown is the input that decides how long the climb back takes; actual recovery times are in how long crash recoveries take.
Why drawdown control matters
Two portfolios with the same average return can end with different wealth: the one with smaller losses compounds from a higher base. That is volatility drag. It is why drawdown, Sortino and Calmar ratios belong next to returns, and why drawdown tolerance is worth setting before a crash.
Common mistakes
- Thinking a 30% gain after a 30% loss gets you back to even (it leaves you 9% down).
- Averaging percentage returns instead of compounding them.
- Ignoring position size: a 90% loss on a 2% position costs 1.8% of the portfolio; on a 30% position, 27%.
See your portfolio’s drawdowns with Exent
- Upload a screenshot of your holdings, or a CSV, Excel, PDF or Google Sheet; no brokerage login.
- Exent reports drawdown, Sortino and Calmar next to returns, and replays the 2008, 2020 and 2022 crashes.
Frequently asked questions
About 42.9%. The formula is 1 divided by (1 minus the loss), minus 1.
Yes. Losing 25% leaves 75% of the money, and 75 needs to grow by a third, about 33.3%, to get back to 100.
Yes, if reinvested. They add to total return and buy more shares at lower prices, which shortens recovery.
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Educational content, not investment advice. Examples are illustrative; past performance does not guarantee future results.