Drawdown and recovery: why −20% needs +25%
Measure a decline from peak capital and calculate the gain needed to regain that peak.
A drawdown is a decline from a previous high in the account value you measure. It is not necessarily a loss since opening the account: capital can remain above the initial deposit while sitting below a recent peak.
Identify the value being measured
For 100 → 120 → 90, the drawdown from the peak is (90 / 120 − 1) × 100 = −25%. The change from the initial 100 is −10%. These use different comparison bases.
Maximum drawdown is the deepest such decline within the selected history. Daily closing values can miss a deeper intraday decline. Specify the observation frequency and account for deposits and withdrawals separately.
Why recovery percentages are asymmetric
Losing 20% of 100 leaves 80. Recovering 20 requires 20 / 80 = 25%. For a loss fraction d with 0 ≤ d < 1, the required gain is d / (1 − d). The table expresses losses as positive magnitudes.
A 100% loss leaves zero. No finite percentage return can restore the original amount without new capital. The formula also says nothing about the probability or time required for recovery.
Our own teaching example; all figures are hypothetical.
d / (1 − d); 0.20 / 0.80 = 0.25 = 25%
| Loss from peak | Remaining from 100 | Gain needed to recover |
|---|---|---|
| 10% | 90 | 11.1111% |
| 20% | 80 | 25% |
| 30% | 70 | 42.8571% |
| 50% | 50 | 100% |
| 75% | 25 | 300% |
| 90% | 10 | 900% |
| 100% | 0 | No finite percentage |
Use the calculation in a journal
Record the capital peak, current valuation, date and treatment of cash flows. Do not substitute the price of one position for total portfolio value or add successive percentage losses.
A historical drawdown is not a ceiling on future risk. A useful next step is to record the conditions for checking a scenario in advance: which observations would support it and which would invalidate it.
Capital falls from 150 to 120. Would a 20% rise regain the peak?
No: 120 × 1.2 = 144. Returning to 150 requires 25%.
Sources
Sources checked: 2026-10-20
This material and its translations were prepared with AI assistance. Educational calculations were checked programmatically. Sources explain concepts; examples and files were created for this article.
Related reading
Next step
Continue to the scenario journal and record a checking rule before observing the outcome.
A market-scenario journal: test an idea without hindsight →