Why a 50% Loss Needs a 100% Gain: TheMath of Recovery

Imagine your portfolio drops 50%. Your instinct says a 50% rebound will bring you back. It will not. This
is one of the most important ideas in investing, and crypto's wild swings make it even more relevant.
The simple example
You hold $1,000. It falls 50% and is now worth $500. To get back to $1,000 you need to gain $500, and
$500 is 100% of your current $500. A 50% loss requires a 100% gain to recover.
The recovery formula
Gain needed = Loss / (1 - Loss), with loss written as a decimal. For a 20% loss: 0.20 / 0.80 = 0.25, so
you need a 25% gain.
Loss Gain needed to break even
10% 11.1%
20% 25%
30% 42.9%
50% 100%
75% 300%
90% 900%
Notice how the curve bends. Small losses are easy to recover. Deep losses need huge rallies, and in a
bear market there is no guarantee those rallies come, or come soon.
What this means for you
• Protecting capital matters more than chasing gains. Avoiding one 50% drawdown is worth more
than catching one 50% pump.
• Use stop-losses or position limits. Decide your maximum acceptable loss before you buy.
• Do not average down blindly. Adding to a falling position can deepen the hole if the original thesis
was wrong.
• Think in terms of what you need to recover, not what you hope the market does.
Next time you are down on a position, run the recovery number. If the gain you need looks unrealistic in
your timeframe, that is useful information for your next decision.
Try it yourself: Trades Checker (tradeschecker.com) is a free, browser-based crypto profit calculator.
Enter your buy price, sell price, amount and fees to see your real profit instantly.