Document Type : Research Article

Author

Department of Statistics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran

10.22054/jmmf.2025.85583.1178

Abstract

‎Accurate forecasting of asset returns is essential for informed investment decisions and effective portfolio management‎. ‎This paper explores a hybrid model that combines the Capital Asset Pricing Model (CAPM) with Neural Network Autoregressive (NNAR) models to enhance return predictions‎. ‎While CAPM traditionally estimates expected returns based on market behavior‎, ‎it has limitations due to its linear assumptions‎. ‎In contrast‎, ‎NNAR models excel at capturing complex‎, ‎nonlinear relationships in financial time series data‎. ‎Our study integrates NNAR forecasts of market returns into the CAPM framework‎, ‎hypothesizing that this combined approach will yield superior accuracy‎, ‎particularly in volatile market conditions‎. ‎Through empirical analysis‎, ‎we demonstrate that our hybrid model outperforms traditional CAPM predictions‎, ‎highlighting the potential of machine learning techniques in asset valuation‎. ‎The findings provide valuable insights for future research and practical applications in financial forecasting‎.

Keywords

[1] Black, F., Capital market equilibrium with restricted borrowing, J. Business 45 (1972), 444–
455.
[2] Chen, J. M., The capital asset pricing model, Encyclopedia 1 (2021), 915–933.
[3] Dhamija, A. K. and Bhalla, V. K., Financial time series forecasting: comparison of neural
networks and arch models, Internat. Res. J. Finance Econom. 49 (2010), 185–202.
[4] Fama, E. F. and MacBeth, J. D., Risk, return, and equilibrium: Empirical tests, J. Political
Econ. 81 (1973), 607–636.
[5] Gumparthi, S., Prasad, D. V. V., Rentachintala, B., Krishna, A. T., and Ajwad, A. M., Nnar
as a reliable tool for predicting volume-weighted average price behaviour, Internat. J. Central
Banking 20 (2024), 578–589.
[6] Gumparthi, S. et al., Predicting stock behaviour using var and nnar models: A comparative
analysis, Internat. J. Central Banking 20 (2024), 590–616.
[7] Hyndman, R., Forecasting: principles and practice, OTexts, 2018.
[8] Lintner, J., The valuation of risk assets and the selection of risky investments in stock
portfolios and capital budgets, In Stochastic optimization models in finance, Elsevier, 1975,
pp. 131–155.
[9] Perold, A. F., The capital asset pricing model, J. Econ. Perspect. 18 (2004), 3–24.
[10] Shadbolt, J., Neural networks and the financial markets: predicting, combining and portfolio
optimisation, Springer, 2012.
[11] Sharpe, W. F., Capital asset prices: A theory of market equilibrium under conditions of risk,
J. Finance 19 (1964), 425–442.
[12] Tang, Z., De Almeida, C., and Fishwick, P. A., Time series forecasting using neural networks
vs. box-jenkins methodology, Simulation 57 (1991), 303–310.
[13] Taskaya-Temizel, T. and Casey, M. C., A comparative study of autoregressive neural network
hybrids, Neural Networks 18 (2005), 781–789.
[14] Zhang, G., Patuwo, B. E., and Hu, M. Y., Forecasting with artificial neural networks:: The
state of the art, Internat. J. Forecasting 14 (1998), 35–62.
[15] Zhang, G. P., Time series forecasting using a hybrid arima and neural network model, Neurocomputing 50 (2003), 159–175.