A thousand confessions

The notebook entry for Thursday, the ninth of March, reads: opex week, 0.35% premium, significant. Beneath it, in the same hand: 0.35% minus costs, minus the weeks that were excluded for holidays, minus the years before 1983 when the instrument did not exist. What remains is a number that still stands. That is the trouble.

A student asked yesterday - they always ask this - whether a thousand confirming weeks don’t settle the matter. The question deserves a better answer than the one I gave, which was no.

Consider the dictionary. A thousand citations for a word’s established meaning prove only that the word was used. A single citation showing it was used to mean the opposite proves the definition wrong. Lexicographers do not count citations; they weigh them. The thousand are witnesses to habit. The one is a witness to fact. Habit repeats itself cheaply - the same hedging flow, the same rebalancing calendar, the same data vendor’s timestamp, the same survivorship in the index constituents - and so a thousand confirmations may be one confirmation repeated a thousand times, which is to say one observation wearing a crowd.

The anomaly is different in kind, not degree. It is the citation that disagrees with the dictionary. Its power comes from its incompatibility with what the efficient market is supposed to permit. A structural premium of 0.35% per expiration week, persistent across forty years, available to anyone with a calendar and a brokerage account, is not a small effect. It is a contradiction. And a contradiction cannot be outvoted. Nine hundred and ninety-nine weeks of ordinary returns and one week of impossible returns: the impossible week is the finding. The rest are decoration.

This is why the student’s instinct runs backwards. They believe evidence accumulates like ballast, each confirming week adding weight. Evidence instead accumulates like a trial record - the verdict turns on the exception, and the exception needs only to survive cross-examination once. The cross-examination here is transaction cost, regime shift, and the possibility that the premium is compensation for bearing gamma risk on expiration Friday, which would rename it from anomaly to wage.

The corrected entry: expiration-week premium, n. A return that is either free, or priced, or misdated.

The backtest covered 512 expiration weeks. The premium survived costs in 3 of 5 decades.