When Marginal Coverage Transfers and the Economics Do Not: A Pre-Registered Study of Conformal Interval Widths as Position-Sizing Scales

We size portfolio positions from conformal prediction intervals, reading the interval half-width as the scale in a capped fractional-Kelly rule (Conformal Kelly), and evaluate the rule under a pre-registered protocol. The development record is an autonomous LLM-agent search over roughly 200 configurations on a single six-year window (2016-2021) of eight US-listed ETFs. All later data was sealed before the search, and two final configurations, nine comparison books and the mapping from outcomes to conclusions were registered before unsealing. On the sealed 2022-2024 window, realized coverage was 0.745 against a 0.750 target, but the two configurations' annualised net log growth was 8.5% and 7.0% (28.5% and 25.8% in development), below an unlevered equal-weight book (9.5%), the leveraged passive books (15.6-16.8%) and a registered hindsight four-equity book (10.8%, at a 46% drawdown); both ranked last of eleven entries on Sharpe and Calmar. A post-hoc split, outside the registered protocol, shows the passing coverage averaging 0.592 in 2022 and 0.842 afterwards, with the entire loss in the under-covered year. The split does not show that under-coverage caused the loss: the leverage cap bound on every 2022 trading day, so narrow intervals could not enlarge the book, and a long-equity book in an equity bear market is the simpler account. But the registered acceptance test passed a sixteen-point conditional failure, which motivates, without establishing, conditional coverage as an endpoint for rules that read interval width as a scale. On the development window, a slow per-asset conformal quantile out-grew every locally adaptive alternative tested, but only under a binding leverage cap, and block-bootstrap intervals include zero for 11 of the 13 contrasts we could re-derive.