After a 20% loss, why does a 20% gain not break even?
Losses and subsequent gains use different starting balances. A recovery percentage must be calculated from the reduced amount rather than simply reversing the sign of the original loss.
Investment calculator →Identify the new base
After a loss, less capital remains to participate in the next gain. Restoring the same monetary shortfall therefore requires a larger percentage of that smaller balance. Adding a negative percentage and a positive percentage is not the correct way to combine successive investment returns. The sequence involves multiplying growth factors.
Calculate the recovery explicitly
An investment of 10,000 that falls by 20% becomes 8,000. A subsequent 20% gain brings it to 9,600, not 10,000. Restoring the original amount requires an increase of 2,000 from the 8,000 balance, so the required gain is 2,000/8,000 = 25%. The example assumes no contributions, withdrawals, distributions or expenses; adding those cash flows would require a separate reconciliation.
Separate scenarios from performance analysis
A fixed-rate investment projection illustrates an assumed path; it does not recreate the ordering or volatility of market returns. Percentage-change and ROI tools can help check simple historical differences, but intermediate cash flows complicate the interpretation of performance. Increasing a future-return assumption does not guarantee recovery. Nor can the required 25% gain tell you when it will occur. A recovery target and a forecast are different statements.
Try the calculators
- Investment calculator
Project an investment with regular contributions.
- Percentage change
Measure the change between two values.
- Return on investment calculator
Calculate net gain and ROI from cost, final value, income and expenses.