Verbal humility, behavioral overconfidence, and the cost of ego: a Kelly-optimal consistency test for Form 13F strategy cloning

This paper develops a normative decision framework for a common behavioral tension in delegated investing. Many investors are willing to acknowledge that a benchmark manager is likely superior to their own discretionary stock-picking, yet still retain a personal trading sleeve. Under a long-run log-growth (Kelly) objective, such a choice is not merely a “style preference”: it becomes a testable consistency problem about what the investor is implicitly claiming. The model separates two questions. First, when is delayed replication viable once information staleness and implementation frictions are accounted for? Second, when mixing is feasible, when is an all-in clone uniquely optimal? In a tractable diffusion benchmark with a reduced-form lag penalty, the paper derives (i) a viability boundary for replication, (ii) sufficient conditions—including an explicit correlation threshold—for which any positive weight on an inferior, positively correlated discretionary sleeve strictly reduces expected log growth, and (iii) a closed-form “Cost of Ego” that prices the compounding sacrificed to preserve subjective control. Importantly, holding cash for fractional-Kelly sizing is distinguished from retaining an inferior risky sleeve. An empirical calibration using Form 13F filings is used only to bound the lag-cost channel rather than to claim systematic outperformance. In two low-turnover case studies, the implied annualized log-growth penalty from a one-quarter delay is on the order of 0.4%–1.2%, providing a concrete scale for the “delay fear” objection. The framework yields operational diagnostics—how to compute lag, turnover/continuity proxies, and how to apply the viability and consistency tests—along with transparent scope limits rooted in 13F’s structural blind spots and discrete rebalancing risk. Archived version (DOI): https://doi.org/10.5281/zenodo.18639091 Zenodo record: https://zenodo.org/records/18639091