Original research across decision intelligence, machine learning, economic modeling, and quantitative finance. Rigorous analysis written to be genuinely understood.
We extend the Brennan-Lo evolutionary framework to continuous-time asset allocation by shifting the unit of selection from investors to individual dollars. The growth-optimal strategy is randomization: a Kelly-Merton deterministic core plus a stochastic term governed by the investor's belief alignment with true market randomness. Misaligned beliefs destroy three times what aligned beliefs create — and the spread around Kelly is always positive for any finite horizon.
Standard GBM imposes strong assumptions on drift and volatility that empirical asset returns routinely violate. We develop a generalized framework that relaxes these constraints while preserving analytical tractability, with applications to derivative pricing and risk modeling.
Building on Nature Abhors an Undiversified Bet, we decompose portfolio returns into three components — Table Stakes (β), Skill (α), and Luck (ω) — and show that Skill is precisely an investor's ability to predict the non-systematic component of risky-asset price changes. The framework clarifies what genuine alpha generation requires and where apparent outperformance is merely a draw from the randomization term.
Conventional target-date glidepaths reduce equity exposure monotonically as retirement approaches. We examine conditions under which a downward-sloping allocation path is suboptimal, and derive alternative structures that better match liability profiles under stochastic returns.
Log returns are analytically convenient but economically misleading as a basis for portfolio decisions. The core problem is one of units: optimization in log-return space tells the investor how to allocate capital across the log-return process, but investors allocate by purchasing shares of securities with cash — quantities denominated in gross returns. We trace the practical consequences of this mismatch for the well-known growth-optimal allocation rule, and derive a closed-form mapping from optimal log-return allocations to the gross-return allocations an investor can actually implement. This note reconciles the textbook log-return formulation with the gross-return allocations practitioners trade.
Investing — as distinct from speculation — means holding a portfolio whose positive drift is expected to dominate its volatility over the relevant horizon. The Sharpe-One (S1) strategy operationalizes this by constructing each annual savings cohort as an independent sub-portfolio with an equity allocation set so that cumulative drift equals cumulative volatility over its remaining horizon, yielding a sub-portfolio Sharpe ratio of one. The result is a horizon-aware glidepath in which every portfolio dollar carries exposure appropriate to the time it actually has to work.
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