A coin spendable and round
The ledger for the opex study closed at 4:40 this afternoon, the figure coming out of the regression as 0.3472 percent. The bulletin prints 0.35. Two characters dropped, and with them the whole character of the thing. A premium of 0.3472 is a claim with a decimal’s worth of shame in it; a premium of 0.35 is a coin, spendable, round, trustworthy in the way that nothing measured ever is.
Rounding, n. The ceremony by which an uncertainty is dressed for company. The number does not change; the reader does.
I built the backtest myself, which is the only reason I know what the third decimal did. The sample runs January 1997 through last December, 336 expiration weeks, and the standard error on the mean is 0.11. The t-statistic is 3.16. That survives. What does not survive is the comfortable habit of quoting the result to two decimals, because at two decimals the estimate and its own error occupy different neighborhoods. The error bar reaches up to 0.57 and down to 0.13. Neither end rounds to 0.35. The point estimate is the only resident of its own confidence interval that got a haircut.
The surprise was not in the data. The surprise was in watching myself prefer the rounded figure while writing the summary, the hand moving toward it the way a hand moves toward the official form rather than the annotated draft. The bulletin is the official document. The regression output is the corrected etymology - the word before the dictionary got to it, still carrying its dirt and its second syllable. 0.3472 is the word before the dictionary got to it.
Gamma hedging, market maker rebalancing, mechanical flows - all plausible machinery, none of it tested today. What was tested today: the mean, its error, and my appetite for the tidier of the two numbers. The tidier number won in the bulletin. It should not have.
Tomorrow morning, before anything else is run, I amend the bulletin: the premium is 0.35 percent, standard error 0.11, and the third decimal - 0.3472 - restored to the text where any reader can see what was rounded and what was earned. That is a decision, made tonight, at this desk, with the output still on the screen.