Risk & Money Management · Beginner · 5 min
Drawdown maths: why -50% needs +100%
You can calculate the gain needed to recover from any drawdown and explain why deep drawdowns are so hard to repair.
−50%, then +50%
Imagine your account falls by 50%. Then it gains 50%. Are you back where you started?
Most people's first instinct says yes. The answer is no, and not even close. This lesson explains the simple arithmetic behind it, which is one of the most important reasons why risk management focuses on keeping losses small.
Gains must outrun losses
A drawdown, as introduced in the crypto chapter, is the fall from a previous peak to a later low, in percent. After a drawdown, the money left is smaller than before. To get back to the peak, that smaller amount has to grow by more than the percentage that was lost.
The gain needed after a loss of L% is:
Gain needed = L ÷ (100 − L), as a percentage.
- −10% leaves 90. Getting back to 100 needs +10 ÷ 90 = +11.1%.
- −25% leaves 75. It needs +33.3%.
- −50% leaves 50. It needs +100%: the money has to double.
- −75% leaves 25. It needs +300%: the money has to quadruple.
The relationship is not linear. Small losses need gains only slightly larger than the loss. Deep losses need gains that are many times larger, and those are much harder and slower to achieve.
That is why traders track the maximum drawdown: the largest peak-to-trough fall over a period. It tells you how deep the worst hole was, and so how hard the climb out of it would have been. It is also a better measure of how painful a strategy was to follow than its average return.
Time matters too. A portfolio that falls 50% and then grows 10% a year needs a little over seven years just to get back to where it was, before it makes any new gains.
Half needs double
A fictional account holds 10,000.
- A bad period cuts it by 50% to 5,000.
- The next period is good: +50%. The account rises to 7,500.
- It is still 25% below the start. To reach 10,000, the 7,500 needs another +33.3%.
Now compare a trader who limits each loss so that the worst drawdown stays at 15%. From 8,500, the climb back needs +17.6%, which a working strategy can reach in a reasonable time. Both traders may have similar skills. One of them is in a much deeper hole.
The same arithmetic explains why small, controlled losses matter so much. A trader who never lets the account fall more than 15% always needs less than 18% to recover. A trader who allows 50% needs 100%, and may need years to get there.
Common mistakes
- Adding and subtracting percentages. −50% and +50% do not cancel out.
- Planning to win it back with bigger risk. That usually makes the hole deeper.
- Judging a strategy by average return only. Check the maximum drawdown too.
- Ignoring time. Deep drawdowns can take years to recover.
- Treating a deep drawdown as normal. A strategy that regularly falls 40% may be too risky to follow at all.
The takeaway
After a loss, the rest must grow by more than the loss to get back. Deep losses need far larger gains, so keep each loss small.
Check yourself
Quick quiz
4 questions. Instant feedback, nothing is saved.
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1Tap the loss that needs a doubling of what is left to recover.
Tap the chart.
After −50%, half is left. Getting back to the start means doubling that half: +100%.
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2An account falls from 20,000 to 15,000. What gain is needed to get back to 20,000?
The loss is 25%. The gain needed is 5,000 ÷ 15,000 = 33.3%.
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3What is the formula for the gain needed after a loss of L%?
For L = 50: 50 ÷ 50 = 1, so +100%. For L = 20: 20 ÷ 80 = 0.25, so +25%.
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4An account goes 10,000 → 12,000 → 9,000 → 11,000. What was the maximum drawdown?
The maximum drawdown is the largest fall from a peak to a later low: from 12,000 to 9,000 is −25%.
of 4 correct.