Conformal Kelly: Conformal Prediction Intervals as the Scale in Fractional Kelly Position Sizing

Abstract

Conformal prediction has traditionally been used to quantify prediction uncertainty. We put that uncertainty to a second use, combining a 75% conformal interval with fractional Kelly to size portfolio positions: as the range widens we shrink the position, and as it narrows we grow it. On a six-year development window (2016-2021), with trading costs and strict leverage caps, this compounds at 28.5% annualised net log growth with a Sharpe ratio of 1.34 and a 27.7% maximum drawdown, versus 15.9% for holding the S&P 500 and 21-22% for passive portfolios at the same leverage. Our main development-window finding runs against the literature's advice for conformal prediction on time series. Every tweak that adapts the interval faster to market conditions costs 0.7 to 5.3 points of annual growth; the winner is the simplest method: slow, unweighted, per-asset rolling quantiles. When an interval sizes a position rather than describing one forecast, width stability beats local sharpness. It also beats the textbook standard deviation by 2.1 points at matched leverage. We also implement a risk control: when the intervals miss on the downside far more than their historical rate, we cut leverage. On the development window this cut maximum drawdown from 27.7% to 20.3% while raising the Sharpe ratio, beating all 40 placebo timings (rank-based p = 1/41). These numbers came from an autonomous LLM-agent search over 200 configurations, so we sealed all data from 2022 onward and pre-registered configurations, benchmarks, and interpretation rules before one evaluation. Calibration held (0.745 coverage against 0.750, weakest through 2022); growth did not: the two configurations earned 8.5% and 7.0% per year, below the passive benchmarks, and a pre-registered hindsight benchmark beat them on raw growth while taking a 46% drawdown. All outcomes are reported as pre-registered.