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Tail risk

The risk of rare, extreme moves that sit far outside normal daily ranges and can cause losses larger than any model expected.

Risk of ruin against risk per tradeA curve climbing steeply as the share of the account risked on each trade grows, even though every trade carries a small positive edge.CHANCE OF LOSING THE ACCOUNT0%20%40%60%80%05%10%15%20%25%RISK PER TRADE (% OF ACCOUNT)2% → 1.8%5% → 20%10% → 45%20% → 67%assumes a 52% win rate at 1:1, ruin = account goneruin chance = (0.48 ÷ 0.52) ^ (100 ÷ risk %)
Risk of ruin. The chance of losing the whole account, plotted against the share of it staked on each trade, for a method that wins 52% of the time at even money. The edge is the same all along the curve; only the bet size changes.

Markets have fat tails: moves of five or more standard deviations happen far more often than a normal distribution predicts. Crashes, flash crashes, currency depegs, and overnight gaps are tail events.

Tail risk is why leverage limits and portfolio-heat caps matter even when a strategy looks safe. Strategies that sell options or volatility earn steadily and lose everything in the tail.

Example: in January 2015 the Swiss franc rose about 30% against the euro in minutes when the peg was removed. Forex traders with normal-looking stop-loss orders were filled 20% or more below them and several brokers failed.

Related: volatility, leverage, portfolio-heat, gap

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