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Calculator · Behavior & discipline
How large a gain makes up a loss?
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The calculator shows the gain a portfolio needs to return to its value before a fall and, at a return you assume, how many years that takes. The arithmetic is the same in every country and currency, and no historical market data is used.
Set the decline you accept in your investment policy and see it in context when markets drop.
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A fall and the gain that undoes it are not the same size. If a portfolio of 100,000 falls 30%, it is worth 70,000. To get back to 100,000, the 70,000 has to grow by 30,000, which is 42.9% of the smaller amount. The deeper the fall, the wider the gap between the two percentages: a 50% fall needs a 100% gain to return to where it started.
The calculator answers that question for the fall you enter. If you also enter the return you assume afterwards, it shows how many years the recovery takes at that rate, and if you enter the portfolio value, it shows the amounts.
The gain needed follows from the value that remains after the fall:
Gain needed = loss ÷ (1 − loss) Example: 30% ÷ (1 − 30%) = 0.30 ÷ 0.70 ≈ 42.9%
With an assumed annual return, the calculator finds the number of years in which compounding at that rate covers the gain needed:
Years = ln(1 ÷ (1 − loss)) ÷ ln(1 + return) Example: ln(1 ÷ 0.70) ÷ ln(1.07) ≈ 0.3567 ÷ 0.0677 ≈ 5.3 years
The years appear only for a return above zero. At zero or below, a portfolio left to itself does not recover in this model, so the calculator shows no figure rather than an endless one.
If you enter the portfolio value before the fall, the result also shows the value after it and the amount that has to be regained. A value of 100,000 and a 30% fall leave 70,000, and 30,000 has to be regained. The percentages do not depend on the amount, and the arithmetic is the same in every currency.
The calculator lists the gain needed for six common falls. The years column below applies an assumed 7% a year to each of them; it is arithmetic on that assumption, not an estimate of how any market has recovered or will recover.
| Fall | Gain needed | Years at an assumed 7% a year |
|---|---|---|
| 10% | 11.1% | 1.6 |
| 20% | 25.0% | 3.3 |
| 30% | 42.9% | 5.3 |
| 40% | 66.7% | 7.5 |
| 50% | 100.0% | 10.2 |
| 60% | 150.0% | 13.5 |
The relationship is not linear. A small fall needs only a little more than its own size: 10% needs 11.1%. Beyond about a third, the gain needed rises steeply, and after a 60% fall the remaining value has to grow by one and a half times itself. That curve is the reason the size of a possible fall is worth knowing before it happens rather than after.
The recovery time assumes a constant return from the day after the fall. Real recoveries do not follow a smooth path: gains arrive unevenly, a recovery can take much less or much more time, and a further fall can come first. The calculator uses no historical crash or recovery data, and the years it shows describe your assumption, not the behavior of any market.
Contributions and withdrawals are not included. New money added during a recovery lifts the total value sooner, while the holdings owned before the fall still need the full gain to return to their old value. Withdrawals during a fall work the other way: they shrink the base that has to recover, and the gain needed on what remains becomes larger.
Costs, tax and inflation are not deducted. A recovery to the old nominal value can still leave purchasing power below where it started, because prices have moved on in the meantime.
The figure is a description of arithmetic, and its most practical use is often before a fall rather than during one. A decline in value becomes a realized loss when the holding is sold. Whatever replaces the sold holding then has to earn the full gain needed on its own, from a lower base. The patterns that push investors to sell in a falling market are described in Panic selling: what truly helps in a crash and Loss aversion and mental accounting: the costliest thinking errors.
Some investors write down in advance the fall their portfolio is meant to carry, for example in an investment policy statement, so that a decline is measured against a limit set in calm conditions instead of against the latest headline. How such a document is structured is explained in Investment Policy Statement for private investors: your mandate.
The calculator shows the gain and, at a return you assume, the time that a fall requires. It is not a forecast of how long any market will take to recover, and not a recommendation to hold, buy or sell. Entering a lower and a higher return shows how much the recovery time depends on that one assumption.
Gain needed = loss ÷ (1 − loss). A 30% fall needs a 42.9% gain, and a 50% fall needs a 100% gain. The gain needed is always larger than the loss, because it applies to the smaller value that remains.
With a return you assume: years = ln(1 ÷ (1 − loss)) ÷ ln(1 + return). After a 30% fall, at 7% a year, that is about 5.3 years. At a return of zero or below, the calculator shows no figure.
No. It uses no historical price, crash or recovery data. The time to recover is arithmetic on the constant return you assume, not an estimate of how any market has recovered or will recover.
Contributions are not part of the model. New money lifts the total value sooner, but the holdings owned before the fall still need the full gain to return to their old value. Withdrawals work the other way and raise the gain needed on what remains.
When the holding is sold. Whatever replaces it then has to earn the full gain needed on its own, from the lower base. Some investors therefore set down in advance, for example in an investment policy statement, the fall their portfolio is meant to carry.
Why selling in a panic usually locks losses in, and what the evidence describes as a calm counterweight.
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Amounts are in the currency you choose. Unfinished entries retain their original number notation when the language changes.
Optional. At 0 the amounts are left out.
Optional. At 0 the time is left out.
After a fall of 30%
Gain needed to get back
+42.9%The gain starts from the lower value, so it is always larger than the fall.
At a steady 7% a year. Real returns vary from year to year.
Common falls
| Fall (%) | Gain needed (%) |
|---|---|
| 10 | 11.1 |
| 20 | 25.0 |
| 30 | 42.9 |
| 40 | 66.7 |
| 50 | 100.0 |
| 60 | 150.0 |
Arithmetic only: the same in every country and currency, with no tax and no market history.