Risk Management · Lesson 11 · Advanced
Tail Risk and the Lucretius Fallacy
You don't calibrate your position size to the known worst case, because the biggest event is still to come.
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The Lucretius Fallacy
The fool believes the tallest mountain he has ever seen is the tallest one possible. Yet every worst case, when it hit, exceeded the record of its time.
Crypto is Extremistan in its purest form: 50 percent daily moves, the FTX insolvency, the Terra/Luna depeg that wiped out around 60 billion USD. Backtests systematically underestimate tail risk.
The Lucretius fallacy: the next shock is bigger than the known one.
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Test yourself
The biggest crypto crash I have ever seen is a reasonable ceiling for my risk.
- Myth
- Fact
You cannot calculate the exact tail risk, but you can gauge your own fragility.
- Myth
- Fact
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The key points at a glance
- The probabilities of rare events are not calculable, but fragility is.
- Every worst case, when it happened, exceeded the worst case known until then.
- No expected gain justifies a probability of ruin above zero.
Deep dive
Why backtests underestimate tail risk
A backtest only shows what has already happened. The worst future move is by definition not in your history, so every historical maximum drawdown underestimates the true tail risk.
This is the Lucretius error: the fool thinks the highest mountain he has ever seen is the highest possible one. Crypto is Extremistan: 50 percent daily moves, the FTX bankruptcy, the Terra/Luna depeg with about 60 billion USD in value destroyed.
Fragility is measurable, risk is not
Small probabilities react extremely sensitively to assumption errors. At 3 sigma the probability rises by 60 percent if you revise the standard deviation up by just 5 percent. Fat tails simply means: not computable.
What is measurable is your own fragility. The guiding question on every position is not will the trade work, but: what happens if there is a 30 to 50 percent move against me within minutes? That answer you can compute, the probability you cannot.
Position sizing without a known worst case
If the worst case is unknown, you size only by a rule that survives even the unknown case. Fukushima principle: no gain justifies a ruin probability that is different from zero.
- Compute stop and leverage against a crash much larger than the historical one.
- Take the worst daily move ever seen and double it.
- If your account does not survive that, the position is too big.
- Manage the exposure, not the forecast.
Sources: Taleb, Kahneman, Burniske, Ammous
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