Why does a 50% loss need a 100% gain?

Because the gain is measured against the smaller balance. Half of an account is a smaller number than half of the original, so getting back to the start means doubling what is left.

Does it account for position size changing during the drawdown?

No. The recovery path uses one step size throughout. Risking a percentage of a shrinking balance changes both the path and the count, which is the difference the risk-of-ruin calculator's fixed-versus-compound switch shows.

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Edge & Analytics

Drawdown recovery calculator

“After a fall of this size, what gain gets me back to where I started — and how many winning trades is that?”

A loss and its recovery are not symmetrical, and the asymmetry grows fast. This calculator states the required gain exactly, converts it into a count of winning trades at a step size you choose, and shows the whole curve so the non-linearity is visible rather than described.

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Free to use, nothing to sign up for, and nothing you type here is sent anywhere — the arithmetic runs in your browser.

What it computes

required gain = (1 / (1 - d) - 1) x 100
trades needed = ln(1 / (1 - d)) / ln(1 + w),  rounded up
streak odds   = win rate ^ streak

What you type in

Field	What it means	Example
Drawdown %	The fall from the peak.	20
Gain per winning trade %	The step size for the recovery path.	5
Win rate %	Used for the streak-probability read.	50

Reading the result

The required gain, which is arithmetic rather than an estimate.
The number of winning trades that gain takes at the step size supplied.
The odds of stringing that many consecutive winners at the win rate supplied.
The curve, where the asymmetry becomes obvious: 20% back needs 25%, 50% needs 100%, and a drawdown approaching 100% needs an infinite gain.

Worked example

A 20% drawdown, 5% gain per winning trade, 50% win rate.

Required gain to break even: 25%
Winning trades needed: 4.57, so 5
Odds of five consecutive winners at a 50% win rate: 3.1%
For contrast, a 50% drawdown requires a 100% gain

What trips people up

The required gain is arithmetic, not an estimate.
The recovery path assumes each winning trade compounds on the reduced balance, which is why the trade count is not simply drawdown divided by gain.
The streak probability assumes independent trades at a fixed win rate.

Questions

Why does a 50% loss need a 100% gain?: Because the gain is measured against the smaller balance. Half of an account is a smaller number than half of the original, so getting back to the start means doubling what is left.
Does it account for position size changing during the drawdown?: No. The recovery path uses one step size throughout. Risking a percentage of a shrinking balance changes both the path and the count, which is the difference the risk-of-ruin calculator's fixed-versus-compound switch shows.

Related calculators

Risk of ruin calculatorWith this edge and this position size, what are the odds of losing a given share of the account before the edge has a chance to show up?Compound growth calculatorIf an account grows at some rate per period, where does it end up — and what does the same account look like once returns arrive unevenly?Trade sample statistics calculatorHere are my actual results — what do they say about win rate, expectancy, streaks and the worst stretch?Portfolio heat calculatorIf every open position hit its stop at the same time, how much of the account would that cost?

These are the same calculators built into Ledger of Alpha, where they read your own trade history instead of numbers you re-type. See the full product

Keep the record these numbers come from

A free account logs the trades you size here, so the win rate and averages you type into these calculators come from your own history rather than a guess.

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