[Verse 1] Markets dance in measured steps, statistics say they're tame Bell curves promise gentle slopes, predictions all the same But crashes thunder from the void when models fall apart Black swans crash the party with their mathematical art [Chorus] Fat tails hiding in the shadows, extreme events break through Normal curves can't see the dangers lurking in the blue Tail risk strikes when least expected, blowing up your plan Fat tails hiding in the shadows, more than models span [Verse 2] Standard deviation whispers lies about the edge Three sigma moves should barely come, that's what the books allege But markets spike and crater down beyond the normal range Kurtosis tells a different tale of probability's strange [Chorus] Fat tails hiding in the shadows, extreme events break through Normal curves can't see the dangers lurking in the blue Tail risk strikes when least expected, blowing up your plan Fat tails hiding in the shadows, more than models span [Bridge] Leptokurtic distributions paint a darker scene Platykurtic spreads things thin, mesokurtic in between But when the tails grow thick and wide, disasters multiply What should happen once per century hits before your eyes [Verse 3] Value at Risk calculations crumble at the seams Expected shortfall measures what reality redeems Portfolio managers learn the hard way statistics bend When fat-tailed beasts come prowling at the market's bitter end [Chorus] Fat tails hiding in the shadows, extreme events break through Normal curves can't see the dangers lurking in the blue Tail risk strikes when least expected, blowing up your plan Fat tails hiding in the shadows, more than models span [Outro] So remember when you're building models for the street Fat tails make extreme events far more likely than they seem
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