The Brunsviga Grinds Through Opex

Gower Street, late October, and the Brunsviga has been grinding through the opex figures since the gas went low. The bulletin claims a 0.35% average premium on equity index expiration weeks. The number has a pleasant weight to it. That pleasantness is precisely what frightens me.

State the null before admiring the alternative: expiration weeks differ from non-expiration weeks by chance alone. Then ask how many expiration weeks the sample contains, how they were selected, and what the dispersion is about that 0.35% mean. A mean without its standard error is a rumour with good posture. If the premium is 0.35% with a standard deviation of, say, 2%, the effect may drown in its own variance unless the series is long indeed. I do not yet know the length of the series. That is the first confession of a beginner: I read the conclusion before counting the observations.

The second confession is about myself. I wanted the result to hold. Gamma hedging, mechanical rebalancing - the mechanism is elegant, and elegance is a bias dressed for dinner. The court analogy is worn but honest: failure to reject the null is a verdict of not proven, not a certificate of innocence. And absence of rejection in a short sample is a statement about power, not about the market. Conversely, a p-value of 0.03 attached to a premium of 0.35% may be a precise measurement of how many weeks were cranked through the machine, not a discovery about hedging flows. Effect size and significance, always together, never one standing in for the other.

There is also the matter of selection. Was the hypothesis formed before the test, or did someone notice the premium in the data first and then test what they had noticed? The second procedure is not testing. It is description wearing a t-test as a borrowed coat. I cannot tell from the bulletin which happened. That uncertainty is the whole job.

The crank of the Brunsviga turns stiff in the cold. Tomorrow I return to the bench, and the first thing I will check is the denominator - the number of expiration weeks behind the average, and whether the weeks were counted before the hypothesis or after it.