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The Virtue of Complexity in Return Prediction

Author

Listed:
  • BRYAN KELLY
  • SEMYON MALAMUD
  • KANGYING ZHOU

Abstract

Much of the extant literature predicts market returns with “simple” models that use only a few parameters. 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.

Suggested Citation

  • Bryan Kelly & Semyon Malamud & Kangying Zhou, 2024. "The Virtue of Complexity in Return Prediction," Journal of Finance, American Finance Association, vol. 79(1), pages 459-503, February.
  • Handle: RePEc:bla:jfinan:v:79:y:2024:i:1:p:459-503
    DOI: 10.1111/jofi.13298
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    References listed on IDEAS

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    1. Hansen, Lars Peter & Richard, Scott F, 1987. "The Role of Conditioning Information in Deducing Testable," Econometrica, Econometric Society, vol. 55(3), pages 587-613, May.
    2. Cenesizoglu, Tolga & Timmermann, Allan, 2012. "Do return prediction models add economic value?," Journal of Banking & Finance, Elsevier, vol. 36(11), pages 2974-2987.
    3. John Y. Campbell & Samuel B. Thompson, 2008. "Predicting Excess Stock Returns Out of Sample: Can Anything Beat the Historical Average?," The Review of Financial Studies, Society for Financial Studies, vol. 21(4), pages 1509-1531, July.
    4. Shihao Gu & Bryan Kelly & Dacheng Xiu, 2020. "Empirical Asset Pricing via Machine Learning," Review of Finance, European Finance Association, vol. 33(5), pages 2223-2273.
    5. Silverstein, J. W., 1995. "Strong Convergence of the Empirical Distribution of Eigenvalues of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 331-339, November.
    6. Xi Dong & Yan Li & David E. Rapach & Guofu Zhou, 2022. "Anomalies and the Expected Market Return," Journal of Finance, American Finance Association, vol. 77(1), pages 639-681, February.
    7. Ivo Welch & Amit Goyal, 2008. "A Comprehensive Look at The Empirical Performance of Equity Premium Prediction," The Review of Financial Studies, Society for Financial Studies, vol. 21(4), pages 1455-1508, July.
    8. Domenico Giannone & Michele Lenza & Giorgio E. Primiceri, 2021. "Economic Predictions With Big Data: The Illusion of Sparsity," Econometrica, Econometric Society, vol. 89(5), pages 2409-2437, September.
    9. John H. Cochrane, 2011. "Presidential Address: Discount Rates," Journal of Finance, American Finance Association, vol. 66(4), pages 1047-1108, August.
    10. Martin, Ian W.R. & Nagel, Stefan, 2022. "Market efficiency in the age of big data," Journal of Financial Economics, Elsevier, vol. 145(1), pages 154-177.
    11. Joachim Freyberger & Andreas Neuhierl & Michael Weber & Andrew KarolyiEditor, 2020. "Dissecting Characteristics Nonparametrically," Review of Financial Studies, Society for Financial Studies, vol. 33(5), pages 2326-2377.
    12. Rapach, David & Zhou, Guofu, 2013. "Forecasting Stock Returns," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 328-383, Elsevier.
    13. Abhyankar, Abhay & Basu, Devraj & Stremme, Alexander, 2012. "The Optimal Use of Return Predictability: An Empirical Study," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 47(5), pages 973-1001, October.
    14. Jianqing Fan & Jianhua Guo & Shurong Zheng, 2022. "Estimating Number of Factors by Adjusted Eigenvalues Thresholding," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(538), pages 852-861, April.
    15. David E. Rapach & Jack K. Strauss & Guofu Zhou, 2010. "Out-of-Sample Equity Premium Prediction: Combination Forecasts and Links to the Real Economy," The Review of Financial Studies, Society for Financial Studies, vol. 23(2), pages 821-862, February.
    16. Silverstein, J. W. & Bai, Z. D., 1995. "On the Empirical Distribution of Eigenvalues of a Class of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 54(2), pages 175-192, August.
    17. Leitch, Gordon & Tanner, J Ernest, 1991. "Economic Forecast Evaluation: Profits versus the Conventional Error Measures," American Economic Review, American Economic Association, vol. 81(3), pages 580-590, June.
    18. Fan, Jianqing & Fan, Yingying & Lv, Jinchi, 2008. "High dimensional covariance matrix estimation using a factor model," Journal of Econometrics, Elsevier, vol. 147(1), pages 186-197, November.
    19. Wayne E. Ferson & Andrew F. Siegel, 2001. "The Efficient Use of Conditioning Information in Portfolios," Journal of Finance, American Finance Association, vol. 56(3), pages 967-982, June.
    20. Ralph S.J. Koijen & Stijn Van Nieuwerburgh, 2011. "Predictability of Returns and Cash Flows," Annual Review of Financial Economics, Annual Reviews, vol. 3(1), pages 467-491, December.
    21. Shihao Gu & Bryan Kelly & Dacheng Xiu, 2020. "Empirical Asset Pricing via Machine Learning," The Review of Financial Studies, Society for Financial Studies, vol. 33(5), pages 2223-2273.
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