$1,000 that falls 3% becomes $970. A 3% gain from there brings it to $999.10, so full recovery needs about +3.0928%.
A stock falling 3% and then gaining 3% can look like a round trip. The percentages are the same, so it is easy to think the money should return to the starting point.
But the second 3% is calculated from a smaller amount. If $1,000 falls by 3%, it becomes $970. A 3% gain on $970 adds $29.10, bringing the money to $999.10.
Here is the same recovery calculation across several loss rates.
| Loss | Money left from $1,000 | Gain needed to recover |
|---|---|---|
| -1% | $990 | +1.0101% |
| -2% | $980 | +2.0408% |
| -3% | $970 | +3.0928% |
| -5% | $950 | +5.2632% |
| -10% | $900 | +11.1111% |
The return is measured from the new base
The key is the base amount. The 3% loss is measured against the original $1,000. After that loss, the account is no longer $1,000. It is $970.
The next 3% gain is measured against $970, not the original $1,000. That is why it adds $29.10 instead of $30. The gap is only $0.90 in this example, but the same logic becomes much more visible when losses get larger.
This is why a loss and a gain with the same percentage do not cancel each other out exactly. The larger the loss, the larger the gain needed to recover the original principal.
This calculation is not investment advice and does not predict what any stock will do next. It ignores fees, taxes, spreads, intraday volatility, and execution prices. It is simply a way to see how a daily loss and recovery return change the money.