Drawdown and the Arithmetic of Recovery
Losses and the gains needed to recover them are not symmetric, and the asymmetry gets rapidly worse. This single table is the argument for every risk control there is.
MadStockAlerts Research · Updated August 28, 2026
What to take away
- A 50 percent loss requires a 100 percent gain to recover.
- The asymmetry accelerates: beyond about 30 percent it becomes severe.
- Maximum drawdown is the standard measure of how bad it got.
- The psychological cost of a deep drawdown compounds the arithmetic one.
- Time to recover matters as much as depth.
MAD Academy Training Video · 0:46
The Maths That Punishes Big Losses
Recovery is not symmetric with loss, and the asymmetry gets brutal fast — which is the entire argument for cutting losses early.
This lesson is part of a Stock Alerts + Tools plan.
The table
| Loss | Gain required to recover |
|---|---|
| 10% | 11% |
| 20% | 25% |
| 30% | 43% |
| 50% | 100% |
| 70% | 233% |
| 90% | 900% |
gain required = loss / (1 - loss)
Scroll the chart sideways to see all of it.
The first few rows look manageable and the curve then turns sharply. This is the entire justification for cutting losses while they are small: not that small losses feel better, but that they remain arithmetically recoverable in a way that large ones do not.
Measuring it
Drawdown is measured from a peak to the subsequent trough, in percent. Maximum drawdown is the worst such decline over a period, and it is reported alongside return precisely because return alone says nothing about the path taken to get there.
Two strategies returning ten percent a year, one with a maximum drawdown of eight percent and the other of forty, are entirely different propositions. The second requires a tolerance the first does not, and tolerance is not evenly distributed.
Time as well as depth
The other half of a drawdown is how long it lasts. Recovery time is measured from the peak to the point where that peak is exceeded again, and for broad equity indices that has historically run to years rather than months after a severe decline.
Depth is what tests the arithmetic; duration is what tests the person. A forty percent decline that recovers in nine months and one that takes six years are the same number and completely different experiences.
The behavioural compounding
A deep drawdown does not only reduce capital. It reliably changes behaviour: sizing shrinks, opportunities are declined, and methods are abandoned near the point of maximum pain, which is frequently the worst possible moment to abandon them.
The arithmetic and the psychology work in the same direction, which is why sizing rules that look excessively cautious in a good year are the ones that leave somebody still trading in a bad one.
Why the recovery is not symmetric
A fifty percent decline requires a hundred percent gain to recover, and the asymmetry is not a quirk of the arithmetic but its central feature. The loss is taken on the original capital and the recovery has to be earned on what remains, which is a smaller base. Every percentage point of decline therefore costs slightly more than a point of gain to undo, and the gap widens the further down the scale it goes.
gain required = 1 / (1 - drawdown) - 1
- drawdown is expressed as a decimal, so a 30 percent fall is 0.30
- the result is the gain on the reduced capital needed to return to the starting value
The practical reading is that shallow drawdowns are recoverable in the ordinary course and deep ones are a different kind of problem. A twenty percent decline needs twenty-five percent, which is roughly a good year. An eighty percent decline needs four hundred percent, which is not a year of anything.
This is the arithmetic behind the widespread emphasis on limiting the size of any single loss. It is not that large losses feel worse, though they do. It is that the recovery required grows faster than the loss, so the cost of a decline is superlinear in its depth.
Depth, duration and the underwater curve
A drawdown has two dimensions and the published figure usually reports one. Depth is how far below the previous high the account fell. Duration is how long it stayed below it, and duration is what determines whether a method is actually held through.
| Profile | Depth | Time underwater | What it demands |
|---|---|---|---|
| Sharp and brief | Deep | Weeks | Nerve, once |
| Shallow and long | Modest | Years | Patience, continuously |
| Deep and long | Deep | Years | More than most processes survive |
| Repeated and shallow | Modest, often | Rolling | Tolerance for being wrong routinely |
The second row is the one that is underrated. A method that never falls more than fifteen percent and takes three years to make a new high is far harder to hold than the number suggests, because every month of it is a month of doing the work and seeing no progress. Most abandonments happen there rather than at the bottom of a sharp decline.
The underwater curve, which plots how far below the previous high an account has been at every point, shows both dimensions at once. It is a less flattering chart than an equity curve and a more informative one, because the equity curve makes a long flat stretch look like calm rather than like a drawdown.