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The Statistical Limit of Arbitrage

Author

Listed:
  • Rui Da
  • Stefan Nagel
  • Dacheng Xiu

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.

Suggested Citation

  • Rui Da & Stefan Nagel & Dacheng Xiu, 2024. "The Statistical Limit of Arbitrage," NBER Working Papers 33070, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:33070
    Note: AP
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    More about this item

    JEL classification:

    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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