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Working Paper
Understanding The Virtue of Complexity
July 10, 2025
We respond to recent academic challenges to aspects of the “virtue of complexity” described in our prior research. We provide detailed discussions of how complex models learn in small samples, the roles of “nominal” and “effective” complexity, the unique effects of implicit regularization, and the importance of limits to learning. We then present new empirical and theoretical analyses that expand on KMZ. Finally, we introduce and demonstrate the virtue of ensemble complexity.
Working Paper
APT or “AIPT”? The Surprising Dominance of Large Factor Models
October 1, 2024
The authors introduce artificial intelligence pricing theory (AIPT), which conjectures that returns are driven by a large number of factors.
Journal Article
The Virtue of Complexity in Return Prediction
March 1, 2024
Contrary to conventional wisdom, we theoretically prove that simple models severely understate return predictability compared to “complex” models in which the number of parameters exceeds the number of observations. We empirically document the virtue of complexity in U.S. equity market return prediction. Our findings establish the rationale for modeling expected returns through machine learning.
Working Paper
Machine Learning and the Implementable Efficient Frontier
August 18, 2022
We propose that investment strategies should be evaluated based on their net-of-trading-cost return for each level of risk, which we term the "implementable efficient frontier." While numerous studies use machine learning return forecasts to generate portfolios, their agnosticism toward trading costs leads to excessive reliance on fleeting small-scale characteristics, resulting in poor net returns. We develop a framework that produces a superior frontier by integrating trading-cost-aware portfolio optimization with machine learning