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Normal distribution

The symmetric bell-shaped distribution assumed by most textbook finance. Market returns resemble it in the middle and not at all in the tails.

Under a normal distribution, a move of five standard deviations should happen about once every 3.5 million observations, or roughly once in 14,000 years of trading days. Equity indices have produced several such days in the last century alone.

The assumption is still used because it makes maths tractable: variance adds, sums stay normal, and option pricing has a closed form. Treat it as a first approximation with a known failure mode rather than a description of reality.

For anything that depends on the tail, position sizing through a crash, risk-of-ruin, or stop placement in a gap-prone name, replace the assumption with resampled history or an explicitly fat-tailed model.

Related: fat-tails, kurtosis, skewness, tail-risk

See it drawn

Original diagrams for the ideas on this page. Illustrative, not real market data.

How a position size is worked outAccount size, risk per trade and stop distance feed into one box giving the number of shares.ACCOUNT SIZE$25,000your capitalRISK PER TRADE1%of the accountSTOP DISTANCE$0.50entry to stopPOSITION SIZE500 sharesrisk budget: $25,000 × 1% = $250position size: $250 ÷ $0.50 = 500 shares
Working out a position size. Three numbers decide how big a trade is: the account, the share of it put at risk, and the distance from entry to stop. One percent of $25,000 is a $250 budget, and a $0.50 stop divides into that 500 times.

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