The Statistical Limit of Arbitrage

Rui Da, Stefan Nagel and Dacheng Xiu

No 33070, NBER Working Papers from National Bureau of Economic Research, Inc

Abstract: We investigate the economic consequences of statistical learning for arbitrage pricing in a high-dimensional setting. Arbitrageurs learn about alphas from historical data. When alphas are weak and rare, estimation errors hinder arbitrageurs—even those employing optimal machine learning techniques—from fully exploiting all true pricing errors. This statistical limit to arbitrage widens the equilibrium bounds of alphas beyond what traditional arbitrage pricing theory predicts, leading to a significant divergence between the feasible Sharpe ratio achievable by arbitrageurs and the unattainable theoretical maximum under perfect knowledge of alphas.

JEL-codes: C55 C58 G11 G14 (search for similar items in EconPapers)
Date: 2024-10
Note: AP
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