Maximum Drawdown and Recovery Math: Why a 40% Loss Needs a 67% Gain
October 29, 2026
A drawdown is the decline from a previous peak to a later low, expressed as a percentage of the peak. Maximum drawdown is the largest such decline in a period. It captures the pain of an investment's worst stretch in a way that average return and volatility do not.
Suppose a portfolio's value over time is 100, 120, 90, 110, 70, 95. The highest peak before the low is 120, and the lowest point after it is 70. Maximum drawdown = (70 − 120) ÷ 120 = −41.7%.
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After a loss L (as a fraction), the gain needed to get back to the peak is L ÷ (1 − L). For the 41.7% drawdown: 0.417 ÷ 0.583 = 71.4%, which equals 120 ÷ 70 − 1. A 40% loss needs 66.7%; a 30% loss needs 42.9%; a 50% loss needs 100%. The time to recover depends on the growth rate afterward: at 7% a year, going from 70 to 120 takes ln(120 ÷ 70) ÷ ln(1.07) = 0.539 ÷ 0.0677 = 8.0 years. At 4% it takes 13.7 years, and at 10%, 5.7 years.
| Drawdown | Gain needed to recover | Years to recover at 7% | Years at 4% |
|---|---|---|---|
| -10% | 11.1% | 1.6 | 2.7 |
| -20% | 25.0% | 3.3 | 5.7 |
| -30% | 42.9% | 5.3 | 9.1 |
| -40% | 66.7% | 7.5 | 13.0 |
| -50% | 100.0% | 10.2 | 17.7 |
Risk Tolerance and Planning
Historical equity markets have experienced drawdowns of 30% to 55% several times in a century, and recoveries have taken from a couple of years to over a decade. The practical question is how you would behave in a 40% decline: selling at the bottom turns a temporary loss into a permanent one. Match your allocation to the maximum drawdown you can tolerate emotionally and financially. For someone needing to withdraw money soon, such as a retiree, large drawdowns early are particularly damaging because withdrawals take place at depressed prices (sequence-of-returns risk).
Using Drawdown in Analysis
Compare funds by their maximum drawdown and by how long they took to recover (the drawdown duration). The Calmar ratio divides the annual return by the maximum drawdown. Diversification, bonds, and cash reserves reduce drawdowns. Rebalancing during declines buys low. Check the period used: a drawdown over a short window may not include a major crisis.
Caveats
Past drawdowns do not set limits on future ones. Figures here are simplified. This article is educational, not investment advice.
Frequently Asked Questions
What is maximum drawdown?
The largest percentage decline from a peak to a subsequent low.
What gain is needed to recover from a 40% loss?
66.7%.
How long does recovery take?
It depends on the growth rate; about 8 years at 7% for a 41.7% drawdown.
What is sequence-of-returns risk?
The risk that early losses combined with withdrawals harm long-term outcomes.
What is the Calmar ratio?
Annual return divided by maximum drawdown.