Tools · Drawdown recovery
A 20% fall needs a 25.0% gain.
A fall and its recovery are not symmetrical: the gain required is always larger than the loss, and it grows faster the deeper the fall goes. Enter a drawdown below to see the gain required to return to the previous peak, and how long that takes at a rate you choose.
Calculator
This page is showing a worked example. The figures below are for a 20% fall with an assumed rate of 8.0% a year. Enable JavaScript to enter your own figures; the formula, reference table and worked example on this page do not need it.
- Fall from peak
- 20%
- 100 becomes 80.0
- Gain required
- 25.0%
- to return to the previous peak
- Time to recover
- 2.9years
- at 8.0% a year
Squares mark the reference points in the table below. The curve is the identity gain = 1 ÷ (1 − loss) − 1; it has no vertical limit, because a fall of 100% cannot be recovered at all.
Reference
The gain required at each depth.
Years are calculated at 8.0% a year, chosen only to make the column comparable. It is an assumption, not an expectation.
| Fall from peak | 100 becomes | Gain required | Years at 8.0% |
|---|---|---|---|
| 10% | 90.0 | 11.1% | 1.4 |
| 20% | 80.0 | 25.0% | 2.9 |
| 30% | 70.0 | 42.9% | 4.6 |
| 40% | 60.0 | 66.7% | 6.6 |
| 50% | 50.0 | 100.0% | 9.0 |
| 60% | 40.0 | 150.0% | 11.9 |
| 70% | 30.0 | 233.3% | 15.6 |
Read across: a 50% fall turns 100 into 50, and 50 must double to become 100 again. The gain required passes the size of the loss at every depth, and the gap widens as the fall deepens.
Method
How it is calculated.
Two identities, both exact. Neither depends on any assumption about markets.
Gain required
gain = 1 ÷ (1 − loss) − 1
A fall of 20% leaves 80.0 of every 100. To get 80.0 back to 100, it has to rise by 100 ÷ 80.0 − 1 = 25.0%. The loss is measured against the starting value; the gain is measured against the smaller value that is left, which is why the two are never equal.
Time to recover
years = ln(1 ÷ (1 − loss)) ÷ ln(1 + r)
At a constant 8.0% a year, recovering the same 20% fall takes 2.9 years. This assumes the rate is steady and compounds annually, that nothing is added or withdrawn, and that no tax or transaction cost applies. Real recoveries are not steady, so treat the figure as a scale, not a schedule.
Limits
What this calculation leaves out.
- Contributions and withdrawals. Money added during a drawdown recovers alongside the rest; money withdrawn during one locks the loss in. Both change the outcome substantially, and neither is modelled here.
- Costs and tax. The rate you enter is treated as the rate actually earned. Costs and tax reduce it, and lengthen the time to recover.
- The path. A steady rate is a convenience, not a description. Two portfolios reaching the same average rate by different paths recover at different times.
- The measurement window. A drawdown measured month-end to month-end understates the fall experienced intra-month. The record on this website is stated on that basis and says so.
This calculator is provided for general information only and is directed to wholesale and professional investors. It is not personal advice: it does not take into account the objectives, financial situation or needs of any person, and it is not an offer, invitation or recommendation to acquire any financial product. Investing involves risk, including the possible loss of capital. Past performance is not a reliable indicator of future performance.
Definitions
Terms on this page.
Each links to the glossary entry, which states the convention the term assumes as well as what it means.
- Drawdown recovery — the gain needed to return to a previous peak.
- Maximum drawdown — the largest fall from a high point to the subsequent low.
- Annualised return — the constant annual rate giving the same outcome.
- Cumulative return — the total change in value, compounded.
Questions
Common questions.
Why is the gain required larger than the loss?
Because the two are measured against different bases. A 20% fall is 20% of the starting value, but the gain that reverses it is measured against what is left — 80 of the original 100. Twenty is a quarter of eighty, so the recovery is 25%, not 20%. The deeper the fall, the smaller the base the recovery is measured against, and the larger the required gain becomes.
What gain is needed to recover a 50% loss?
100%. A 50% fall turns 100 into 50, and 50 has to double to reach 100 again. At an assumed 8% a year, that takes about 9.0 years.
Can a 100% loss be recovered?
No. The formula divides by the fraction remaining, so a 100% fall has no recovery gain: there is nothing left to compound. This is why limiting the depth of a drawdown matters more than the rate earned afterwards.
Does this tell me how long my own portfolio takes to recover?
No. It shows how long a constant rate of your choosing takes to undo a fall of a given size. Real portfolios earn an uneven rate, take in and pay out money, and carry costs and tax. Use the result as a sense of scale, and as general information only.
Is anything I enter sent to KyperX Capital?
No. The calculation runs in your browser. The figures are not transmitted, recorded or stored anywhere, and this website receives none of them.