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.
Authors
- Acknowledgements & Disclosure
- We are grateful for comments from Adem Atmaz, Lars Hansen, Ye Luo, Andreas Neuhierl, Markus Pelger, Seth Pruitt, Yao Zeng, and seminar and conference participants at Columbia University, Indiana University, Louisiana State University, Princeton University, ITAM Business School, University of Cincinnati, University of Chicago, Yale School of Management, EPFL, ETH Zurich, Stockholm Business School, University of Gothenburg, University of Liverpool, University of Oxford, City University of Hong Kong, Gregory Chow Seminar Series in Econometrics and Statistics, HKUST, KAIST, Peking University, Shanghai University of Finance and Economics, Southern University of Science and Technology, Tsinghua University, University of Melbourne, Sao Paulo School of Economics, American Finance Association Annual Meetings, NBER Summer Institute, Jacobs Levy Center Frontiers in Quantitative Finance Conference, Stanford Institute for Theoretical Economics, SFS Cavalcade North America, Annual SoFiE Conference, Global AI Finance Research Conference in Singapore, China International Conference in Finance, and Wabash River Finance Conference. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research. Stefan Nagel Stefan Nagel declares that he is a consultant for Northern Trust Asset Management and a member of the board of directors of Dimensional Mutual Funds & ETFs.
- DOI
- https://doi.org/10.3386/w33070
- Pages
- 53
- Published in
- United States of America
Table of Contents
- Introduction 3
- Main Theoretical Results 9
- Factor Model Setup 9
- Feasible Near-Arbitrage Opportunities 11
- Arbitrageurs' Decision Problem and Feasible Sharpe Ratio Bound 15
- Bayes Correction for Selection Bias 19
- Constructing the Optimal Arbitrage Portfolio 23
- Estimating Optimal Infeasible Sharpe Ratio 27
- Alternative Strategies for Arbitrage Portfolios 28
- Cross-Sectional Regression 28
- False Discovery Rate Control 30
- Shrinkage Approaches 31
- Simulation Evidence 33
- Empirical Analysis of US Equities 35
- US Equity Data 37
- Analysis of Individual Equity Returns 38
- Rare and Weak Alphas 39
- Modest Feasible vs. Large Infeasible Sharpe Ratios 40
- Analysis of Portfolio Returns 41
- Portfolio Alphas 42
- Accounting for Publication Effects 44
- Conclusion 47
