Breakeven After a Loss
Breakeven after a loss is the percentage gain needed to return to the starting balance, and it is always larger than the loss because the gain is calculated on what remains. Losing 20% requires 25% to get back, and the requirement accelerates rather than rising steadily.
What the loss really costs
Defaults take a 10,000 account down 20%.
The money to make back is the same amount you lost, and the percentage is different only because the base shrank. That is the whole asymmetry, and it is arithmetic rather than psychology.
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How the number is built
One subtraction and one division, and the division is where the surprise lives.
Gain needed = 1 ÷ (1 − loss) − 1
The amount of money never changes. Lose 2,000 from 10,000 and you need to make 2,000 back. What changes is that 2,000 is 20% of the original balance and 25% of what is left.
A worked example
Take the defaults: 10,000 down 20%.
You have 8,000 left and 2,000 to make back.
2,000 ÷ 8,000 = 25%.
So a 20% loss needs a 25% gain, and the extra five points are the cost of having a smaller base to work from.
At 50% the two numbers separate completely. Half the account gone requires doubling what remains, and doubling is a different kind of task from recovering.
The curve accelerates
Walk it in steps of ten and the gap widens every time. 10% needs 11.11%. 20% needs 25%. 30% needs 42.86%. 40% needs 66.67%. 50% needs 100%. 60% needs 150%.
The first ten points add 1.11 points of extra requirement and the sixth ten adds 50. Nothing about the market changed between those rows; only the denominator did.
Under about 10% the two numbers are nearly the same, which is the specific reason a small loss is a different category of event rather than a smaller version of a large one.
Losses compound
Two 20% losses are not a 40% loss. They leave 0.8 × 0.8 = 0.64 of the account, so the requirement is 56.25% rather than the 66.67% a 40% loss would demand — and rather than the 50% intuition suggests.
Three of them leave 51.2% and need 95.31%. Four leave 40.96% and need 144.14%.
Which means a losing streak does its damage faster than an arithmetic reading of the individual losses implies, and on this site’s shared series the average direction run is 2.01 bars with a longest run of 11 across 286 runs.
The argument for cutting
A stop is not a prediction that the position will fall further. It is a decision to stay in the region where an ordinary gain can undo an ordinary mistake, and the calculator makes that concrete: an exit at 8% needs 8.70% back, and an exit at 40% needs 66.67%.
Costs sit on top of that. On this site’s shared series a round trip measures about 2% of the median
bar range of 0.493 — paid when you exit and paid again on whatever trade tries to recover it. The
figures are in research/series-measurements.json.
Position size decides which curve you sit on
The same loss can be either row of the table, depending only on how large the position was. A holding that falls 50% needs 100% back — but if it was 5% of the account, the account fell 2.5% and needs 2.56%.
That is the entire function of a position limit. It does not stop the holding from behaving badly; it decides whether the holding’s bad behaviour lands on the flat part of the account’s curve or the steep part.
Run the two numbers separately and the picture stops being alarming. Ask what the position needs to recover, then ask what the account needs, and act on the second — because the account is the thing with a survival constraint and the position is replaceable.
The original data
Of the 24,971 unique videos in research/search-study-corpus.jsonl, 2 have an instruction-shaped
title about breaking even after a loss, at a median of 41,001 views across 2 channels — and 0% are
calculator-shaped. Drawdown recovery, which is the same arithmetic at portfolio level, appears in 7
at 3,813. The counts come from site/rank_tools2.py, which deduplicates by video id.
Two videos at 41,001 against seven at 3,813 for the identical calculation under a different name. The per-trade framing carries eleven times the audience of the portfolio framing, which is a useful fact about how people actually think about losses.
The answer to the question on that chart is that holding is a decision to buy the position again at the current price. If you would not open it here with fresh money, continuing to hold it is the same choice made passively. The 25% requirement is not an argument for holding or selling on its own — it is the price of the information that the original reason for the trade may have been wrong.
When it fails
The arithmetic is exact and the input often is not. A stop set at 8% does not guarantee an 8% loss: in a thin market or through a gap the fill arrives lower, and the realised loss can be several times the planned one while the account still believes the rule was followed. That is the single most common way a position that was supposed to stay on the flat part of this curve ends up somewhere else.
The second failure is adding to the position to lower the average. That changes the size, not the arithmetic.
A third is measuring against the account rather than the position. A 50% loss on 5% of an account is 2.5% of the account.
A fourth is treating successive losses as additive. They multiply.
A fifth is ignoring costs. They are paid on the exit and on the recovery.
And a sixth is using this to justify never taking a loss. A loss never taken becomes the large one the curve is warning about.
Related
Stop-loss is the tool that keeps losses in the recoverable range. Risk management is where the size of an acceptable loss gets decided. And expectancy is what makes a run of small losses survivable.
This is the piece of arithmetic that finally made me set stops before entering rather than deciding in the moment. In the moment, a 20% loss feels like it needs a 20% gain to fix, and it needs 25. Two of them feel like they need 40, and they need 56.25. The gap between how it feels and what it is grows exactly as the position gets worse.
— Michael Whitman
This page is educational, not financial advice. Test every idea on your own charts before risking money.