Risk Management · Lesson 17 · Beginner
The mathematics of ruin: why comebacks are so hard
You understand why losses are asymmetric, why leverage raises the probability of ruin nonlinearly, and you calculate your risk concretely on an account with 1,000 USDT.
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Why minus 50 percent needs plus 100 percent
The first hard truth of your restart is pure arithmetic, and it is merciless. Losses and gains are not symmetric. If your account falls from 1,000 USDT by 50 percent to 500 USDT, you then need not 50 percent but 100 percent gain to be back at 1,000. You have to double the halved account.
The deeper the drawdown, the more brutal the curve gets. Minus 20 percent needs plus 25 percent. Minus 50 percent needs plus 100 percent. Minus 90 percent needs plus 900 percent. For context: BTC fell about 77 percent in 2022, and that without leverage. With leverage you reach such drawdowns in hours, not months.
Play with the drawdown and see how much gain the recovery really needs.
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The absorbing barrier
There is a line beyond which the recovery mathematics no longer applies at all: zero. Taleb calls this an absorbing barrier. An account driven to zero by liquidation does not come back, no matter how good your average edge was. You are simply out of the game.
His image for it: someone driving through the city at 250 mph on average never arrives, their effective speed is zero because they crash first. A trader who doubles their account five times a week but gets liquidated at some point has an effective return of minus 100 percent. That is why survival comes before performance. No expected gain, however large, justifies a nonzero probability of being wiped out.
Why 10x leverage does not raise the probability of ruin linearly
A common error of thought is that 10x leverage is simply ten times as risky as 1x. That is not true, it is worse. The relationship is nonlinear. A 5 percent move against a 10x position is not a 5 percent loss but a 50 percent loss of your margin. Near liquidation the effect compounds even further, because forced sales and liquidation cascades of other leveraged traders hit exactly when the market is already running against you.
Taleb puts it in a nutshell: with leverage you don't experience the average, you experience the worst path. You can be right about your direction on average and still get liquidated, because a single extreme move kills you first. Whoever is leveraged has written a short option on volatility, whether they know it or not. Lower leverage is the most direct measure to reduce the probability of ruin.
The 2-percent rule at 1,000 USDT
Now the concrete antidote. Elder's 2-percent rule: never risk more than 2 percent of your account equity on any single trade, including slippage and fees. On an account with 1,000 USDT that is 20 USDT maximum risk per trade. Many of the Market Wizards go even lower, Hite and Kovner never above 1 percent, so 10 USDT. For the restart, 1 percent is the clear recommendation.
What matters is Hite's logic: risk only counts relative to capital, never as a constant quantity. 20 USDT risk against a 1,000 USDT account is the same as 1 billion against 20 billion. If your account falls, the absolute risk amount automatically falls with it. If it rises, it rises with it. Only the ratio counts.
The 6-percent monthly rule
The 2-percent rule protects the individual trade, the 6-percent rule protects the month. If your equity falls in a month more than 6 percent below the closing balance of the previous month, you stop trading for the rest of the month. At 1,000 USDT that is 60 USDT. At 2 percent risk per trade that means: after three losses in a row the month is over. That is a forced cooldown, exactly when tilt and revenge trades are most likely.
This is how you calculate your available risk: realized monthly losses plus the capital currently risked in open trades. Paper profits do not count as a buffer, open risk counts in full. When this sum reaches 6 percent, no more new trades.
Position size backward from the stop
The last and most important step: position size follows from account, risk percent and stop distance, never from the leverage. The order is non-negotiable. First you set the stop on the chart, behind a real structure, then you derive the quantity. The formula: quantity equals (account times risk percent) divided by (entry minus stop).
Example at 1,000 USDT, 1 percent risk, so 10 USDT. Entry 100, stop 96, distance 4. 10 divided by 4 gives 2.5 units. If the sensible stop is further away, you trade fewer units, you never squeeze the stop tighter just to buy more. The leverage does not appear in this calculation, it only determines the margin tied up. Don't do this in your head, use the calculator at /positionsgroessen-rechner.
Set account 1,000 USDT, your risk, entry and stop, and read off the position size. The leverage follows from it, it does not determine it.
Interactive exercise: here you learn right on the chart, with feedback on every click. Sign up freeto start it.
Test yourself
Your account falls from 1,000 to 500 USDT. How much gain do you need for a full recovery?
- 100 percent
- 50 percent
- 75 percent
Account 1,000 USDT, 1 percent risk, entry 100, stop 95. How large is the position?
- 2 units
- 10 units
- Depends on the leverage
Why is 10x leverage more dangerous than ten times 1x?
- Because the relationship is nonlinear and you experience the worst path
- It isn't, it is exactly ten times as risky
Sign up free for the answers with an explanation for each option.
The key points at a glance
- Minus 50 percent needs plus 100 percent to recover, losses are not symmetric.
- Ruin is absorbing: an account at zero never recovers, no matter how good your edge is.
- Position size is worked backward from the stop, never from the leverage.
Deep dive
The recovery curve: why deep drawdowns cost months
The asymmetry of losses is not an opinion, it is arithmetic. The gain needed to recover grows nonlinearly and is always larger than the loss.
A deep drawdown costs you twice: the money and the time just to get back. BTC fell around 77 percent in 2022, with no leverage at all. With leverage you reach depths like that in hours.
- Minus 10 percent needs plus 11 percent to get back.
- Minus 25 percent needs plus 33 percent.
- Minus 50 percent needs plus 100 percent.
- Minus 75 percent needs plus 300 percent.
- Minus 90 percent needs plus 900 percent.
The absorbing barrier: zero is the end
At zero the recovery maths no longer applies. Taleb calls it an absorbing barrier: a liquidated account does not come back, no matter how good your edge was. This is exactly what survival before performance means.
Taleb's image: someone driving through the city at 250 mph never arrives on average, because he crashes first. The average does not count if the path kills you before you get there.
Why 10x leverage is disproportionately riskier
The mistake goes: 10x is ten times as risky as 1x. Wrong, it is worse, because the relationship is nonlinear. A 5 percent move against a 10x position eats 50 percent of the margin.
Near liquidation the effect compounds: forced selling and liquidation cascades hit exactly when the market is already running against you. Slippage grows convexly. Cutting leverage is the single most direct measure against ruin.
The antidote on 1,000 USDT: 1 percent, 6 percent, stop first
Hite's logic: risk only counts relative to capital. When the account drops, the absolute risk amount drops with it automatically. Position size follows from the account, the risk percentage and the stop distance, never from the leverage.
- 2 percent rule per trade (Elder): on 1,000 USDT that is 20 USDT. Hite and Kovner never above 1 percent.
- 6 percent rule per month: at 60 USDT of losses you stop until month end.
- Available risk = realised monthly losses plus open risk.
- Units = (account x risk percentage) / (entry minus stop).
- Example: 10 / 4 = 2.5 units. A wider stop means fewer units, never squeeze it tighter.
Sources: Taleb (Antifragile), Elder (The New Trading for a Living), Schwager (Market Wizards), Kahneman (Thinking, Fast and Slow)
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