Tail Risk

Fatter Tails Than the Model Assumes

Much of standard portfolio and options math — value-at-risk, the Sharpe ratio, the pricing assumptions behind Black-Scholes — assumes returns are roughly normally distributed, clustered tightly around a mean with extreme moves becoming exponentially rarer the further they sit from it. Actual market returns do not obey that assumption. Large moves — crashes, sudden gap-downs, abrupt repricings — occur far more often, and run far larger, than a normal curve would predict, a property researchers describe as fat tails. A risk model built on the normal-curve assumption will systematically understate both the odds and the size of the worst outcomes precisely in the region where it matters most to a portfolio's survival.

Negative Skew vs Convexity

Strategies differ sharply in how they sit relative to the tail, and the difference is the whole risk story. A negative-skew strategy — the classic case is selling uncovered options premium — collects small, steady gains most of the time and remains exposed to an occasional large loss: win small, often, lose big, once. A convex strategy runs the opposite shape — it risks small, steady costs for the chance of a large gain if a tail move actually occurs, the profile of a long option position or a standing tail hedge. Neither shape is inherently superior to the other; they carry opposite risk profiles, opposite emotional experiences month to month, and are usually sized very differently as a direct result of that asymmetry.

Sizing Around the Tail

Because tail risk by definition shows up rarely in any short backtest, position sizing that looks entirely reasonable against realized volatility can still be badly wrong for the tail event that simply hasn't happened yet inside the sample being used. Closelook's read on this, laid out in the negative-skew trap strategy note, is that a premium seller should be sized off the one bad month the strategy will eventually produce, not off the many good months that came before it — the win-rate on a short-tail strategy is the least informative number in the entire approach, precisely because it is designed by construction to look flattering right up until the month it doesn't.