How much gain do you need to recover from a loss?

Divide the loss by what is left. In percent, gain needed = drawdown / (100 - drawdown). A 20% loss needs a 25% gain, a 50% loss needs 100%, and a 90% loss needs 900%.

How long does it take to recover from a 40% drawdown?

It depends entirely on future returns, which are not known. As an illustration, at a steady 6% a year with no further losses it would take about 8.8 years to get back to the old high.

Drawdown math and recovery

Drawdown recovery math explained: the gain needed after any loss, how long recovery takes at a steady return, and why big swings drag on compounding.

Part of the Statistics for Investors and Traders track on Agenticks. About 10 minutes, written for a intermediate reader.

Read first: Compounding and why time horizon matters, Volatility and standard deviation.

Last reviewed 2026-11-08.

Risk notice. Backtested and hypothetical results are simulated: no trades were placed, the rules were applied to past data with the benefit of hindsight, and they may not reflect liquidity, slippage or every cost. Past results, real or simulated, do not predict future results.

Key takeaways

A drawdown is a fall from a previous high, measured as a percentage of that high.
The gain needed to recover is drawdown / (100 - drawdown): 25% after a 20% fall and 100% after a 50% fall.
Years to recover at a steady return are ln(1 / (1 - drawdown)) / ln(1 + return), about 8.8 years for a 40% fall at 6% a year.
Gaining 50% and then losing 50% leaves you 25% behind, so large swings drag on compounded returns.
The deepest drawdown you should expect keeps growing the longer a strategy runs.

A drawdown is a fall from a previous high, measured as a percentage of that high. If an account peaks at $10,000 and drops to $8,000, it is in a 20% drawdown until it climbs back above $10,000. The drawdown lesson in the backtesting track covers how to read drawdowns on an equity curve. This lesson is about the arithmetic underneath, and one fact in particular: losses and gains are not symmetric.

The climb back starts from a smaller base

A 50% fall takes $10,000 to $5,000. Getting back needs $5,000 of gain, but measured on the $5,000 that is left, that is a 100% gain. The fall and the climb cover the same dollars; the climb just starts from a smaller number, so it needs a bigger percentage.

The gain needed to recover from a drawdown is: drawdown / (100 - drawdown), shown as a percent. Try it on a 20% fall: 20 / 80 = 0.25, so a 25% gain is needed. The gap between the fall and the recovery is small for small falls and explodes for big ones. One detail trips people up: a drawdown is measured from the highest point reached, not from where you started. An account that grows from $10,000 to $13,000 and then slips to $10,400 is still up 4% overall, but it is in a 20% drawdown, because $2,600 / $13,000 = 20%. To reach a new high it needs $2,600 / $10,400 = 25%, exactly what the formula gives for a 20% fall.

Worked example: what each fall needs to recover

Gain needed = drawdown / (100 - drawdown). Pure arithmetic, with no market assumptions.

10% fall (10 / 90)	11.11% gain
20% fall (20 / 80)	25% gain
30% fall (30 / 70)	42.86% gain
40% fall (40 / 60)	66.67% gain
50% fall (50 / 50)	100% gain
75% fall (75 / 25)	300% gain
90% fall (90 / 10)	900% gain
The pattern	each extra 10 points of drawdown costs more recovery than the last

The gain is half the story. The other half is how long it takes. If an account earns a steady return each year, the years needed are ln(1 / (1 - drawdown)) / ln(1 + annual return), where ln is the natural logarithm on any calculator. The idea is simple even if the buttons are not: work out how many times the balance must multiply, then how many years of growth produce that multiple.

Worked example: a 40% drawdown at an assumed 6% a year

A $10,000 account falls 40%, then earns a steady 6% a year with no further losses.

Start	$10,000
After a 40% fall ($10,000 x 0.60)	$6,000
Gain needed to get back ($4,000 / $6,000)	66.67%
Growth multiple needed (1 / 0.60)	1.6667
Years at 6% a year (ln(1.6667) / ln(1.06) = 0.51083 / 0.05827)	8.77
Time back to $10,000	about 8.8 years, before any new losses

The 6% is an assumption for illustration, not a forecast. Real returns are uneven and can be negative.

Drawdown recovery calculator

Enter the size of a fall and an assumed steady annual return. The default of 6% a year is an illustrative assumption, not what markets return, and past returns do not guarantee future ones.

The same asymmetry hides inside ordinary swings. Gain 50% and then lose 50%, and $10,000 becomes $15,000 and then $7,500: a 25% loss, even though the two percentages seem to cancel. Gain 10% and then lose 10% and you end at $9,900. Swap the order and the result is identical, because 1.5 x 0.5 = 0.75 whichever comes first. The bigger the swings, the bigger the leak. That is one reason two strategies with the same average yearly return can end at very different places: the more volatile one keeps rebuilding from a lower base after each loss. The volatility lesson measures the swings, and the compounding lesson shows the same multiplication working in your favour.

Drawdowns in trading usually arrive as a run of losses, and the size of each loss decides how deep the hole gets. Losses compound downward the same way gains compound upward: each loss is a share of a smaller balance than the last. Risk 2% of the account on each trade and lose ten in a row, and the balance is 0.98 multiplied by itself ten times, about 0.8171 of where it started. That is an 18.29% drawdown, needing a 22.39% gain to repair. Risk 5% a trade and the same ten losses leave 0.95 to the tenth power, about 0.5987: a 40.13% drawdown that needs a 67.02% gain. Ten losses in a row sounds extreme, but the probability lesson showed how streaks pile up: at a 50% win rate, the chance of at least one run of ten losses somewhere in 200 independent trades is about 9%. The streak is the same in both cases. Only the risk per trade changed the size of the hole.

An account falls 25%. What gain does it need to get back to its old high? 33.33% 25 / (100 - 25) = 25 / 75 = 33.33%.

Drawdowns also deepen with time. Mathematicians who studied the maximum drawdown of a randomly moving price found that the deepest drawdown you should expect keeps growing the longer you watch. A positive average return slows that growth but does not stop it. In plain terms, a strategy's worst drawdown so far is not its worst drawdown ever. A backtest over three years has had less time to find a bad stretch than one over twenty, and a Monte Carlo reshuffle of the same trades usually finds worse paths than the one history happened to take. Funded trading accounts with hard drawdown limits make this arithmetic very concrete, as the prop firm drawdown lesson explains.

Small losses are cheap to repair, big ones are not

Recovering from 10% takes 11.11%. Recovering from 50% takes 100%. That curve is the arithmetic case for deciding in advance how deep a drawdown can go before the position size or the strategy itself is reviewed.

You know the math of a drawdown

You can now work out the gain and the time needed to recover from any fall, explain why swings leak value, and say why the worst drawdown so far is not the worst ever.

Check your understanding

An account drops from $20,000 to $15,000. What gain does it need to get back to $20,000?: 33.33%. It needs $5,000 on a $15,000 base: 5,000 / 15,000 = 33.33%. The formula gives the same: 25 / 75.
Why does a 50% loss need a 100% gain to recover?: The gain is measured on the smaller balance left after the loss. $10,000 falls to $5,000. Getting back needs $5,000 more, which is 100% of $5,000.
A portfolio gains 20% one year and loses 20% the next. Where does it end up?: 4% below where it started. 1.20 x 0.80 = 0.96, a 4% loss overall.
A three-year backtest shows a worst drawdown of 12%. What is the most honest reading?: The worst drawdown in the future could well be deeper, because deeper drawdowns become more likely the longer a strategy runs. The expected maximum drawdown keeps growing with time, even when the average return is positive.

Common questions

How much gain do you need to recover from a loss?: Divide the loss by what is left. In percent, gain needed = drawdown / (100 - drawdown). A 20% loss needs a 25% gain, a 50% loss needs 100%, and a 90% loss needs 900%.
How long does it take to recover from a 40% drawdown?: It depends entirely on future returns, which are not known. As an illustration, at a steady 6% a year with no further losses it would take about 8.8 years to get back to the old high.

Terms defined in this lesson

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Agenticks Learn is general education. It is not financial, investment, tax or legal advice, it does not take your situation into account, and nothing on it is a recommendation to buy, sell or hold any security or to open any account. Examples use illustrative numbers. Investing involves risk, including losing money you put in, and past performance does not predict future results. Tax rules and limits change; the official sources linked in each lesson are the final word.