Lab notebook · chapter 5 of 7 · page 2 of 2

Small caps and turnover continued

Low turnover: the cost problem is solved, the signal problem replaces it

Full surface in results/turnover_sweep_2026-09-09.txt. 12 configurations per universe (lookback 60/120/250 × hold 21/63/126/252), costs applied through costs.sensitivity() rather than by re-running, position-age rule disabled so it cannot force closes inside a 252-session hold.

Costs stop mattering. Turnover falls from 22–30x to 0.6–3.6x. In small caps the spread drag collapses from 43 points at the weekly baseline to under 2 at an annual hold. The 14.27bps toll that killed the fast version is no longer the binding constraint.

But the surface is a random field. Excess over equal-weight ranges from −228 to +225 points with a standard deviation of ~129, and the largest swing from a single parameter step is 302 points (large cap, hold 126, lookback 120→250). A real effect produces a gradient. This does not.

Main effects are the only honest read, and they are weak:

large small
lookback 60d −18.8 −159.3
lookback 120d −45.2 −42.2
lookback 250d +109.8 +0.8
hold 21d +151.4 −16.2
hold 252d −97.8 −97.7

Long formation with a short hold — the canonical 12-1 momentum specification — is the only direction that shows up in both universes, and it is a prior from the literature rather than a post-hoc pick, which is the one thing that makes it worth noting at all.

The standout cell is what selection looks like. look=250/hold=21 in large caps returned +225% over equal-weight, or +4.82%/yr. But it was chosen from 12 cells whose mean is +15.2 and whose sd is 129 — under a pure-noise null the expected maximum of 12 draws sits ~210 points above the mean. The observed 225 is almost exactly what noise produces when you sort it. And at 9.2 years, even an information ratio of 0.5 only reaches t=1.52.

Slowing down fixed the cost problem and revealed that there was never enough statistical power to see the signal underneath it.

Pre-registered test of the standout cell

look=250 / hold=21, single configuration, no sweep. Year-by-year excess over equal-weight:

large cap small cap
years positive 5 / 9 4 / 9
mean excess +5.5%/yr +3.9%/yr
t 1.07 1.32

The large-cap +225% comes almost entirely from three years — 2020 (+26.3%), 2024 (+19.9%), 2026 (+24.9%). Six of nine years are flat or negative. That is the shape of a few lucky stretches, not an edge.

Both t-statistics are what a sweep's best cell looks like when you test it honestly. Confirmed noise.