Adoption of deep neural networks in fields such as economics or finance has been constrained by the lack of interpretability of model outcomes. This paper proposes a generative neural network architecture -- the parameter encoder neural network (PENN) -- capable of estimating local posterior distributions for the parameters of a regression model. The parameters fully explain predictions in terms of the inputs and permit visualization, interpretation and inference in the presence of complex heterogeneous effects and feature dependencies. The use of Bayesian inference techniques offers an intuitive mechanism to regularize local parameter estimates towards a stable solution, and to reduce noise-fitting in settings of limited data availability. The proposed neural network is particularly well-suited to applications in economics and finance, where parameter inference plays an important role. An application to an asset pricing problem demonstrates how the PENN can be used to explore nonlinear risk dynamics in financial markets, and to compare empirical nonlinear effects to behavior posited by financial theory.

The capital asset pricing model (CAPM) is very widely used and is considered to be a very fundamental concept in investing. It determines the link between the risk and expected return of assets, in particular stocks. According to CAPM, the value of α is expected to be zero and that it is very random and cannot be predicted. The equation seen above is in the form of y mx b and therefore it can be treated as a form of linear regression. The scipy package will be used. It has a function to calculate the linear regression.

This research paper explores the performance of Machine Learning (ML) algorithms and techniques that can be used for financial asset price forecasting. The prediction and forecasting of asset prices and returns remains one of the most challenging and exciting problems for quantitative finance and practitioners alike. The massive increase in data generated and captured in recent years presents an opportunity to leverage Machine Learning algorithms. This study directly compares and contrasts state-of-the-art implementations of modern Machine Learning algorithms on high performance computing (HPC) infrastructures versus the traditional and highly popular Capital Asset Pricing Model (CAPM) on U.S equities data. The implemented Machine Learning models - trained on time series data for an entire stock universe (in addition to exogenous macroeconomic variables) significantly outperform the CAPM on out-of-sample (OOS) test data.