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Leptokurtic
Finance Is Geometry, and It All Comes Back to Jensen’s Inequality
Logarithms, Kelly, ergodicity, and tail risk meet at the same geometry: wealth compounds multiplicatively, the logarithm is concave, and Jensen's inequality measures the cost of variability.
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Leptokurtic
The Tail Hedge Debate: Spitznagel Is Right, AQR Is Answering the Wrong Question
We tested Spitznagel's tail hedging strategy and AQR's critique with 17 years of real SPY options data. In the allocation-reducing framing AQR uses, selling SPY to fund puts, deep OTM puts lose at every budget. In the externally funded overlay Spitznagel actually proposes (100% SPY + put budget on top), the strategy shows a positive raw gap versus plain SPY only when the OTM band is set by strike (not delta), held for longer than the article first published, and tested across rolling windows that include a crash. The edge is regime-conditional: it pays in 6 of 13 rolling 5-year windows (every window that contains a ≥25% SPY drawdown) and drags by 2-3pp/yr in windows that don't.