Limits To (Machine) Learning

Zhimin Chen, Bryan T. Kelly and Semyon Malamud
Additional contact information
Zhimin Chen: Nanyang Business School, Nanyang Technological University
Bryan T. Kelly: Yale SOM; AQR Capital Management, LLC; National Bureau of Economic Research (NBER)
Semyon Malamud: Ecole Polytechnique Federale de Lausanne; Centre for Economic Policy Research (CEPR); Swiss Finance Institute

No 25-106, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

Abstract: Machine learning (ML) methods are highly flexible, but their ability to approximate the true data-generating process is fundamentally constrained by finite samples. We characterize a universal lower bound, the Limits-to-Learning Gap (LLG), quantifying the unavoidable discrepancy between a model's empirical fit and the population benchmark. Recovering the true population R 2 , therefore, requires correcting observed predictive performance by this bound. Using a broad set of variables, including excess returns, yields, credit spreads, and valuation ratios, we find that the implied LLGs are large. This indicates that standard ML approaches can substantially understate true predictability in financial data. We also derive LLG-based refinements to the classic Hansen and Jagannathan (1991) bounds, analyze implications for parameter learning in general-equilibrium settings, and show that the LLG provides a natural mechanism for generating excess volatility.

Keywords: machine learning; asset pricing; predictability; big data; limits to learning; excess volatility; stochastic discount factor; kernel methods (search for similar items in EconPapers)
JEL-codes: C13 C32 C55 C58 G12 G17 (search for similar items in EconPapers)
Pages: 104 pages
Date: 2025-12
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Persistent link: https://EconPapers.repec.org/RePEc:chf:rpseri:rp25106

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