Drawdown
Losses and gains aren't symmetric. The deeper the decline, the disproportionately larger the needed recovery. That's the strongest mathematical argument for limiting risk.
€100 becomes exactly €50 after a minus-50-percent move. To get back to €100 from that €50, you need a gain of 100 percent. Not 50.
That applies in both directions and gets worse with depth. Minus 20 percent needs plus 25. Minus 50 needs plus 100. Minus 80 needs plus 400. Minus 90 needs plus 900.
This is exactly where leveraged strategies fail. An account that's dropped ninety percent is mathematically beyond saving, even if everything goes right afterward.
The conclusion is uncomfortable, but clear: avoiding big losses pays off more than chasing big gains. That's why maximum drawdown is the most honest metric there is for any strategy.
The needed recovery gain follows from g = 1 / (1 − d) − 1, with d the fractional loss. The expression diverges as d approaches one, which explains the acceleration. The cause, again, is multiplicativity: the recovery gain gets applied to the shrunken base.
Recovery time follows t = ln(1 / (1 − d)) / ln(1 + r), assuming a constant return r. At a 50 percent decline and 7 percent return, that comes to roughly ten years. Historical recovery periods for broad stock markets after severe declines have sat in this range, sometimes considerably longer.
As a risk measure for retail investors, maximum drawdown has one advantage over standard deviation: it describes an actually lived path rather than a distribution's width. Its weakness is path dependence, which means a historical maximum drawdown isn't an upper bound for future ones. It should be read as a floor on expectations, not a ceiling.
Summary
- The needed recovery grows disproportionately with the depth of the loss.
- A 90 percent decline is mathematically almost beyond recovery.
- A historical maximum drawdown is a floor, not a ceiling.
Did you get it?
What gain offsets an 80 percent loss?
400 percent, since 20 has to become 100 again.
Why does the needed recovery grow disproportionately?
Because it's applied to the shrunken base. The expression 1/(1−d) − 1 grows toward infinity.
How should a historical maximum drawdown be read?
As a floor on what's possible in the future, not a ceiling.
Related
- The one-percent ruleStage 2
- The market is crashing right nowThe market is crashing right now
- Calculating position sizeStage 2