Forecasting the equity premium: Do deep neural network models work?

Xianzheng Zhou (1) Hui Zhou (2) Huaigang Long (3)
(1) Guosen Securities, China
(2) Tulane University & California State University, United States
(3) Zhejiang University of Finance and Economics, China


This paper constructs deep neural network (DNN) models for equity-premium forecasting. We compare the forecasting performance of DNN models with that of ordinary least squares (OLS) and historical average (HA) models. The DNN models robustly work best and significantly outperform both OLS and HA models in both in- and out-of-sample tests and asset allocation exercises. Specifically, DNN models generate monthly out-of-sample R2 of 3.42% and an annual utility gain of 2.99% for a mean-variance investor from 2011:1 to 2016:12. Moreover, the forecasting performance of DNN models is enhanced by adding additional 14 variables selected from finance literature.

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Baker, M., & Wurgler, J. (2006). Investor Sentiment and the Cross‐Section of Stock Returns. Journal of Finance, 61(4), 1645-1680.

Bekiros, S., Gupta, R., & Majumdar, A. (2016). Incorporating economic policy uncertainty in US equity premium models: A nonlinear predictability analysis. Finance Research Letters, 18, 291-296.

Bengio, Y. (2009). Learning deep architectures for AI. Foundations and Trends® in Machine Learning, 2(1), 1-127.

Campbell, J. Y., & Thompson, S. B. (2008). Predicting Excess Stock Returns out of Sample: Can Anything Beat the Historical Average? Review of Financial Studies, 21(4), 1509-1531.

Cardarelli, R., Elekdag, S., & Lall, S. (2011). Financial stress and economic contractions. Journal of Financial Stability, 7(2), 78-97.

Clark, T. E., & West, K. D. (2007). Approximately normal tests for equal predictive accuracy in nested models. Journal of Econometrics, 138(1), 291-311.

George, T. J., & Hwang, C. Y. (2004). The 52‐week high and momentum investing. Journal of Finance, 59(5), 2145-2176.

Gu, S., Kelly, B. T., & Xiu, D. (2018). Empirical Asset Pricing via Machine Learning. SSRN working paper.

Gupta, R., Mwamba, J. W. M., & Wohar, M. E. (2018). The role of partisan conflict in forecasting the U.S. equity premium: A nonparametric approach. Finance Research Letters, 25, 131-136.

Kandel, S., & Stambaugh, R. F. (1996). On the predictability of stock returns: an asset‐allocation perspective. Journal of Finance, 51(2), 385-424.

Kingma, D. P., & Ba, J. (2014). Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980.

Nair, V., & Hinton, G. E. (2010). Rectified Linear Units Improve Restricted Boltzmann Machines. In Proceedings of the 27th International Conference on Machine Learning (ICML-10), 807-814.

Neely, C. J., Rapach, D. E., & Tu, J. et al. (2014). Forecasting the Equity Risk Premium: The Role of Technical Indicators. Management Science, 60(7), 1772-1791.

Rapach, D. E., Strauss, J. K., & Zhou, G. (2010). Out-of-Sample Equity Premium Prediction: Combination Forecasts and Links to the Real Economy. Review of Financial Studies, 23(2), 821-862.

Rapach, D., & Zhou, G. (2013). Forecasting stock returns. In Handbook of Economic Forecasting (pp. 328-383). Elsevier B.V.

Srivastava, N., Hinton, G., & Krizhevsky, A. et al. (2014). Dropout: A Simple Way to Prevent Neural Networks from Overfitting. Journal of Machine Learning Research, 15(1), 1929-1958.

Tibshirani, R. (2011). Regression Shrinkage and Selection via the Lasso. Journal of the Royal Statistical Society, 73(3), 267-288.

Tikhonov, A. N., Leonov, A. S., & Yagola, A. G. (2018). Nonlinear ill-posed problems. London: Chapman & Hall. ISBN 0412786605.

Welch, I., & Goyal, A. (2008). A Comprehensive Look at the Empirical Performance of Equity Premium Prediction. Review of Financial Studies, 21(4), 1455-1508.


Xianzheng Zhou
Hui Zhou
Huaigang Long (Primary Contact)
Author Biography

Huaigang Long, Zhejiang University of Finance and Economics

School of Finance, Zhejiang University of Finance and Economics, 18 Xueyuan Street, Hangzhou, Zhejiang 310018, China   The New Type Key Think Tank of Zhejiang Province “China Research Institute of Regulation and Public Policy”, Zhejiang University of Finance and Economics, Hangzhou City, Zhejiang Prov 310018, China
Zhou, X., Zhou, H., & Long, H. (2023). Forecasting the equity premium: Do deep neural network models work?. Modern Finance, 1(1), 1–11.

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