The maths of digging out of a hole
Imagine your account is worth PKR 1,000,000 and falls 30% to PKR 700,000. It's natural to think a 30% gain gets you back. It doesn't: 30% of PKR 700,000 is only PKR 210,000, leaving you at PKR 910,000. You actually need about 42.9%.
The gap widens fast as losses get bigger:
- −10% needs +11.1%
- −20% needs +25%
- −40% needs +66.7%
- −50% needs +100%
- −75% needs +300%
Small losses are easy to recover from. Big ones can take years — and many accounts never get there. That asymmetry is the whole reason risk management exists.
How losing streaks get you there
Big drawdowns rarely come from one disaster. More often it's a string of ordinary losses, each one a bit too big. The second table in the calculator shows this. Losing 1% a trade, ten losses in a row leave about 90% of the account — annoying, but very recoverable. Losing 10% a trade, the same ten losses leave about 35%, and getting back needs a gain of more than 180%.
Ten losses in a row sounds unlikely, but over a few hundred trades it's quite normal for many strategies. The expectancy & losing-streak calculator shows the odds for your own win rate.
What to take from it
- Protecting capital comes first. Avoiding a 40% drawdown does more for long-term returns than finding the next big winner.
- Don't raise risk to win it back. Trading bigger in a drawdown makes the next loss deeper exactly when the account can least afford it.
- Size every trade on purpose. The position size calculator turns a risk percentage into a share count so no single trade can do serious damage.
Frequently asked questions
Why does recovering from a loss take a bigger gain than the loss?
Because the gain is earned on a smaller amount. Lose 50% of PKR 100,000 and you have PKR 50,000. Getting back to PKR 100,000 means adding another PKR 50,000 — which is 100% of what you have left.
What's the formula?
Gain needed = loss ÷ (1 − loss). For a 30% loss: 0.30 ÷ 0.70 = 42.9%. The calculator does this for any loss you enter.
What is a drawdown?
The fall from an account's highest value to its lowest point before it makes a new high. If your account peaked at PKR 1,000,000 and dropped to PKR 800,000 before recovering, the drawdown was 20%.
Does this apply to a single stock as well as an account?
Yes. A share that falls from PKR 200 to PKR 100 needs to double to get back to PKR 200. The arithmetic is the same — which is worth remembering before averaging down into a falling stock.
How do I keep drawdowns small?
Mostly by risking less per trade and respecting stops. Ten losses in a row at 1% risk leave about 90% of the account; at 10% risk they leave about 35%, which then needs a gain of more than 180% to recover. Position sizing is the main lever you control.
These calculators do arithmetic on the numbers you type in. They're for learning and planning, not investment advice, and they don't tell you what to buy or sell. Nothing you enter leaves your browser. See the terms & risk disclaimer.