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Understanding The Virtue of Complexity

Author

Listed:
  • 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)

Abstract

Recent papers have challenged certain aspects of the "virtue of complexity" described by Kelly et al. (2024b) (KMZ) and related work. These challenges ultimately have little bearing on the theoretical arguments or empirical findings of KMZ. They do, however, provide a valuable opportunity to better understand the nuanced behavior of complex models. In addition to responding to recent challenges, 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.

Suggested Citation

  • Bryan T. Kelly & Semyon Malamud, 2025. "Understanding The Virtue of Complexity," Swiss Finance Institute Research Paper Series 25-96, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp2596
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    JEL classification:

    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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