The Interpretation-Prediction Trade-off and The Layered Integration Framework — A Three-Stage Evolution and Methodological Reconstruction of Asset Pricing Models
Main Article Content
Keywords
asset pricing, interpretation-predicted trade-off, layered integration framework, random discount factor, machine learning
Abstract
The evolution of the asset pricing model has undergone a third paradigm transformation from the traditional linear factor period to the machine learning period, and then to the deep integration of the two. Based on the literature review, this article systematically sorts out this evolutionary vein and puts forward the "three-stage evolution model" as a historical framework for understanding the changes in asset pricing theory. On this basis, the "interpretation-prediction trade-off curve" is constructed as an analysis tool to describe the three types of models in "economic interpretation" and "prediction accuracy" with dimensional positioning differences; then, the "layered integration framework" is proposed as a methodological path to meet the weighing challenges, and the stochastic discount factor theory, machine learning methods and interpretability tools are organically integrated to form an operable empirical research system. The theoretical contribution of this article is: first, the system puts forward the evolutionary logic of asset pricing research, revealing the intrinsic motives of the transformation from "interpretation-oriented” to “interpretation-prediction coordination”; second, deepen the understanding of “interpretation-prediction trade-off” from the perspective of model uncertainty and causal inference; third, build a five-layer integrated framework and provide methodological guidance for the systematic construction of the fusion model. This article provides a clear theoretical basis and methodological path for subsequent empirical research, and promotes the evolution of asset pricing research in a more interpretable and predictive direction.
References
- [1]Roll, R. (1977). A critique of the asset pricing theory’s tests Part I: On past and potential testability of the theory. Journal of Financial Economics, 4(2), 129–176. https://doi.org/10.1016/0304-405x(77)90009-5
- [2]Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), 3–56. https://doi.org/10.1016/0304-405x(93)90023-5
- [3]Carhart, M. M. (1997). On persistence in mutual fund performance. The Journal of Finance, 52(1), 57–82. https://doi.org/10.1111/j.1540-6261.1997.tb03808.x
- [4]Ang, A., Hodrick, R. J., Xing, Y., & Zhang, X. (2006). The Cross‐Section of volatility and expected returns. The Journal of Finance, 61(1), 259–299. https://doi.org/10.1111/j.1540-6261.2006.00836.x
- [5]Cochrane, J. H. (2011b). Presidential address: Discount rates. The Journal of Finance, 66(4), 1047–1108. https://doi.org/10.1111/j.1540-6261.2011.01671.x
- [6]Harvey, C. R., Liu, Y., & Zhu, H. (2015). . . . and the Cross-Section of expected returns. Review of Financial Studies, 29(1), 5–68. https://doi.org/10.1093/rfs/hhv059
- [7]Fama, E. F., & French, K. R. (2019). Comparing Cross-Section and Time-Series factor models. Review of Financial Studies, 33(5), 1891–1926. https://doi.org/10.1093/rfs/hhz089
- [8]Gu, S., Kelly, B., & Xiu, D. (2020). Empirical asset pricing via machine learning. Review of Financial Studies, 33(5), 2223–2273. https://doi.org/10.1093/rfs/hhaa009
- [9]Bianchi, D., Büchner, M., & Tamoni, A. (2020). Bond Risk Premiums with Machine Learning. Review of Financial Studies, 34(2), 1046–1089. https://doi.org/10.1093/rfs/hhaa062
- [10]Belkin, M., Hsu, D., Ma, S., & Mandal, S. (2019). Reconciling modern machine-learning practice and the classical bias–variance trade-off. Proceedings of the National Academy of Sciences, 116(32), 15849–15854. https://doi.org/10.1073/pnas.1903070116
- [11]Kelly, B., Malamud, S., & Zhou, K. (2023). The virtue of complexity in return prediction. The Journal of Finance, 79(1), 459–503. https://doi.org/10.1111/jofi.13298
- [12]Coqueret, G., & Guida, T. (2020). Machine learning for factor investing: R version. Chapman and Hall/CRC. https://doi.org/10.1201/9781003034858
- [13]Cochrane, J. H. (2005). Asset pricing (Rev. ed.). Princeton University Press.
- [14]Shi, C. (2025). From Econometrics to Machine Learning: Transforming Empirical asset pricing. Journal of Economic Surveys, 40(1), 528–548. https://doi.org/10.1111/joes.70002
- [15]Chen, L., Pelger, M., & Zhu, J. (2023). Deep learning in asset pricing. Management Science, 70(2), 714–750. https://doi.org/10.1287/mnsc.2023.4695
- [16]Kelly, B. T., Pruitt, S., & Su, Y. (2019). Characteristics are covariances: A unified model of risk and return. Journal of Financial Economics, 134(3), 501–524. https://doi.org/10.1016/j.jfineco.2019.05.001
- [17]Gu, S., Kelly, B., & Xiu, D. (2021). Autoencoder asset pricing models. Journal of Econometrics, 222(1), 429–450. https://doi.org/10.1016/j.jeconom.2020.07.009
- [18]Lettau, M., & Pelger, M. (2020). Estimating latent asset-pricing factors. Journal of Econometrics, 218(1), 1–31. https://doi.org/10.1016/j.jeconom.2020.01.006
- [19]Giannone, D., Lenza, M., & Primiceri, G. E. (2021). Economic predictions with big data: the illusion of sparsity. Econometrica, 89(5), 2409–2437. https://doi.org/10.3982/ecta17842
- [20]Bryzgalova, S., Huang, J., & Julliard, C. (2022). Bayesian solutions for the Factor Zoo: We just ran two quadrillion models. The Journal of Finance, 78(1), 487–557. https://doi.org/10.1111/jofi.13197
- [21]Lopez de Prado, M., & Zoonekynd, V. (2024). Correcting the factor mirage: A research protocol for causal factor investing. SSRN.
- [22]Hünermund, P., & Bareinboim, E. (2025). Causal inference and data fusion in econometrics. Econometrics Journal, 28(1), 41–82. https://doi.org/10.1093/ectj/utad008
- [23]Kozak, S., Nagel, S., & Santosh, S. (2020). Shrinking the cross-section. Journal of Financial Economics, 135(2), 271–292. https://doi.org/10.1016/j.jfineco.2019.06.008
- [24]Bryzgalova, S., Pelger, M., & Zhu, J. (Forthcoming). Forest through the trees: Building cross-sections of stock returns. Journal of Finance.
- [25]Lundberg, S. M., & Lee, S.-I. (2017). A unified approach to interpreting model predictions. Advances in Neural Information Processing Systems, 30, 4765–4774. https://doi.org/10.48550/arXiv.1705.07874
- [26]Ribeiro, M. T., Singh, S., & Guestrin, C. (2016). “Why should I trust you?”: Explaining the predictions of any classifier. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (pp. 1135–1144). Association for Computing Machinery. https://arxiv.org/abs/1606.05386
- [27]Coqueret, G., & Guida, T. (2020). Machine learning for factor investing: R version. Chapman and Hall/CRC. https://doi.org/10.1201/9781003034858
- [28]Gu, S., Kelly, B., & Xiu, D. (2020). Empirical asset pricing via machine learning. The Review of Financial Studies, 33(5), 2223–2273. https://doi.org/10.1093/rfs/hhaa009
- [29]Büchner, M., & Kelly, B. (2022). A factor model for option returns. Journal of Financial Economics, 143(3), 1140–1161. https://doi.org/10.1016/j.jfineco.2021.12.007
- [30]Giglio, S., & Xiu, D. (2021). Asset pricing with omitted factors. Journal of Political Economy, 129(7), 1945–1990. https://doi.org/10.1086/714090
- [31]Avramov, D., Cheng, S., & Metzker, L. (2023). Machine learning vs. economic restrictions: Evidence from stock return predictability. Management Science, 69(5), 2587–2619. https://doi.org/10.1287/mnsc.2022.4449
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