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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

German

Die klassische Ausführungsphase ist das gesamte Objektplan-Beta-Objekt, das lineare Einfluss, diffusive Preise und einen exogenen Horizont annehmen. Wir untersuchen die Ausführung unter konkavem Power-Law-Effekt und Hurst-Skala-Preisschwankungen und machen zwei Beiträge. Erstens wählen wir den Ausführungshorizont, indem wir das Sharpe-Verhältnis der realisierten Kosten von P&L maximieren. Die Preisbewegungen während des Ausführungsfensters sind Teil dieses P&L, so dass die Ausführung unter einem strukturellen Priorum langsam die Auswirkungs-Persistenz-Lücke reduziert, und weil der Einfluss konkaviert ist, kann es auch die Kosten pro Aktie senken. (ii) Die Notwendigkeit kommt nur von Alpha realis

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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