In this guide
A 20% exampleWhy 50% is the memorable caseApproaching 100% drawdownWhere the formula is usefulA 20% example
Start with 100. A 20% decline leaves 80. Returning from 80 to 100 requires a gain of 20 on a base of 80, which is 25%. The same absolute change therefore produces different percentages depending on the base.
Why 50% is the memorable case
A 50% drawdown takes 100 to 50. To recover from 50 to 100 requires a 50-point gain on a base of 50, or 100%. This illustrates the nonlinear shape of the recovery formula.
Approaching 100% drawdown
As drawdown approaches 100%, required recovery rises rapidly. At exactly 100%, the remaining value is zero and percentage recovery to the original value is undefined because it would require division by zero.
Where the formula is useful
The math applies to any percentage decline in a positive quantity, not just trading. It can be used to understand account drawdowns, business metrics, portfolio values or any similar percentage-change problem.