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From Alpha to Execution: Trading Horizons, Regimes, and Schedules under Concave Impact and Hurst Scaling

Dnyanesh Kulkarni, Revant Nayar · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.23749 · cited by 0 works (OpenAlex) · open-access PDF

Spanish

El esquema de ejecución clásico de Hurst es el esquema plano de WAP que asume el impacto lineal, los precios difusivos y un horizonte exógeno. Estudiamos la ejecución bajo el impacto de la ley de poder concave y las fluctuaciones del precio escalado de Hurst, y hacemos dos contribuciones. En primer lugar, elegimos el horizonte de ejecución maximizando la relación Sharpe del coste realizado por el comercio. Los movimientos de precio durante la ventana de ejecución son parte de ese P&A$, por lo que ejecutar más lentamente reduce su diferencia de impacto, y porque el impacto es concave también puede reducir el coste por acción. (ii) la urgencia solo proviene de la alfa realizada mientras se está trabajando. El problema se rige por los signos de dos cantidades: (i)

Machine translation (Meta M2M100); the English original follows.

Abstract

Classical execution models assume linear impact, diffusive prices, and an exogenous horizon. We study execution under concave power-law impact and Hurst-scaled price fluctuations, and make two contributions. First, we choose the execution horizon by maximizing the Sharpe ratio of the trade's realized P&L. Price moves during the execution window are part of that P&L, so executing more slowly reduces its variance, and because impact is concave it can also lower cost per share. Urgency comes only from alpha realized while the order is being worked. The problem is governed by the signs of two quantities: (i) the duration elasticity of impact $a$, which under a structural prior equals the impact-persistence gap $β- H$ and can take either sign; and (ii) the net urgency $ν$, the rate of alpha realization net of exposure relief. When $ν$ keeps its sign over the window, an interior optimum exists, to leading order in $T/t_f$, only when both are positive; otherwise the order should be worked at the fastest or slowest admissible pace. In the interior regime the first-order condition involves no impact coefficient, order size or volume, and the objective is flat: for a large-cap example, the window within 1% of maximal Sharpe spans more than an order of magnitude. Second, given the window, we derive the schedule shape by convex programming under an envelope cost. For any increasing per-share cost of delay $w(t)$, the KKT solution is $ϕ\propto (λ- w(t))_+^{1/β}$. For a Hurst-scaled envelope $w \propto t^H$, the normalized schedule depends only on $(β, H)$, has a closed form via the incomplete beta function, is front-loaded, and tapers smoothly to zero, saving 10-17% of envelope cost relative to a constant-rate (TWAP) schedule of equal duration. Whether it uses the whole window depends on a single dimensionless robustness level, for which we give a calibration.

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Topics: Regular polygon, Mathematical optimization, Mathematics, Scaling, Scheduling (production processes), Schedule

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