Losing Half Requires Doubling; Losing Ninety Requires Tenfold
Published 10/30/2026 · 3 min read · Finance calculators
The asymmetry comes from the base changing. A 50 % fall takes 100 down to 50, and getting from 50 back to 100 is a 100 % gain because the rise is measured against the smaller number. The deeper the hole, the more brutal the arithmetic: 80 % down leaves 20, which must quintuple — a 400 % gain — and 90 % down leaves 10, which must go up tenfold. Even a mild-sounding 20 % fall needs 25 % to undo. Nothing about this is specific to any asset class; it is what percentages do when the denominator moves, and it is the reason avoiding a large loss is worth more than capturing a large gain.
A 20 % fall needs a 25 % rise to undo. A 50 % fall needs 100 %. An 80 % fall needs 400 %, and a 90 % fall needs 900 %.
Up fifty then down fifty is not flat
Gain 50 % and then lose 50 % and you are left with 75 % of what you started with, not 100 %. Reverse the order and the answer is identical, because multiplication does not care about sequence: 1.5 × 0.5 and 0.5 × 1.5 both give 0.75. This is why an average return quoted as a simple mean overstates what an investor actually experienced — twenty days alternating between +10 % and −10 % averages zero and delivers −9.6 %. The compounding penalty grows with volatility, which is the quantitative version of the observation that a bumpy road to the same destination costs more fuel.
What the number is actually for
Not to encourage waiting for a recovery. A position 90 % down needs a tenfold rise from here, and the only useful question is whether the same money would reach that tenfold more easily somewhere else — which it usually would, since the required gain has nothing to do with the asset's prospects and everything to do with what was paid for it. The market does not know your purchase price. Holding on because a specific number would restore a specific loss is the sunk cost argument wearing a percentage sign, and this calculator's honest use is to show how large the required rise has become, not to suggest it is coming.
| Loss | Gain needed | Multiple |
|---|---|---|
| −20 % | +25 % | 1.25× |
| −33.3 % | +50 % | 1.5× |
| −50 % | +100 % | 2× |
| −80 % | +400 % | 5× |
| −90 % | +900 % | 10× |
Worked with our own calculator
Loss recovery calculator
Given
- Loss (%)
- 50
Result
- Gain needed to recover
- 100%
- Price multiple needed
- 2
These figures are produced by the calculator below, not typed in by hand — they are recomputed whenever the tool changes.
Run it on your own figures →Frequently asked questions
- Is a 100 % loss recoverable?
- No, and the formula says so by refusing to answer: dividing by zero has no result, because no percentage gain applied to nothing produces something. That is the practical difference between an asset that has fallen far and one that has gone to zero — the first still has a recovery path, however steep, while the second has left the arithmetic entirely. It is also why leverage changes the character of a position rather than merely its size: a borrowed position can reach zero on a move that an unleveraged one would merely have dented.
- Does buying more on the way down change the arithmetic?
- It lowers the average price paid, which lowers the rise needed to break even on the whole position — and it does so by putting more money at risk in something that has been falling. The two effects are separate and both real: the break-even point genuinely moves closer, and the amount that can be lost genuinely grows. Whether that is sensible depends on why the price fell, which is a judgement the calculator cannot make; what it can do is show the new break-even honestly, using the blended average rather than the original entry price.
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