Carrying the Normal Table

Question

A trading strategy's daily P&L is roughly normal with mean 10k and standard deviation 50k. Roughly how often do you lose more than 90k in a day? And how bad is a 1-in-1000 day?

Accepted Answer

Losing > 90k: that's frac-90 - 1050 = -2 standard deviations. P(Z < -2) approx 2.3% approx textonce every 44 text trading days, about monthly. 1-in-1000 day: z approx -3.1 → P&L approx 10 - 3.1 times 50 approx -145k. The numbers worth knowing cold: 68/95/99.7 inside ±1/2/3σ; one-sided tails 16%, 2.3%, 0.13%; z = 1.645 for 5%, z approx 2.33 for 1%, z approx 3.1 for 0.1%. A year has ~252 trading days, so "a 3σ daily event" should happen about once every 3 years if returns were normal. The mandatory caveat that upgrades your answer: real P&L distributions have fat tails: 3σ+ days arrive far more often than the normal predicts (kurtosis, vol clustering, jumps). The normal table is the right first reflex and the wrong last word; say both halves and you sound like someone who has actually watched a P&L.

Carrying the Normal Table

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