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NeuralBeta: Estimating Beta Using Deep Learning

Yuxin Liu, Jimin Lin, Achintya Gopal

TL;DR

This work has developed a novel method using neural networks called NeuralBeta, capable of handling both synthetic and real-life scenarios and tracking the dynamic behavior of β, and introduces a new output layer inspired by regularized weighted linear regression, which provides transparency into the model’s decision-making process.

Abstract

Traditional approaches to estimating beta in finance often involve rigid assumptions and fail to adequately capture beta dynamics, limiting their effectiveness in use cases like hedging. To address these limitations, we have developed a novel method using neural networks called NeuralBeta, which is capable of handling both univariate and multivariate scenarios and tracking the dynamic behavior of beta. To address the issue of interpretability, we introduce a new output layer inspired by regularized weighted linear regression, which provides transparency into the model's decision-making process. We conducted extensive experiments on both synthetic and market data, demonstrating NeuralBeta's superior performance compared to benchmark methods across various scenarios, especially instances where beta is highly time-varying, e.g., during regime shifts in the market. This model not only represents an advancement in the field of beta estimation, but also shows potential for applications in other financial contexts that assume linear relationships.

NeuralBeta: Estimating Beta Using Deep Learning

TL;DR

This work has developed a novel method using neural networks called NeuralBeta, capable of handling both synthetic and real-life scenarios and tracking the dynamic behavior of β, and introduces a new output layer inspired by regularized weighted linear regression, which provides transparency into the model’s decision-making process.

Abstract

Traditional approaches to estimating beta in finance often involve rigid assumptions and fail to adequately capture beta dynamics, limiting their effectiveness in use cases like hedging. To address these limitations, we have developed a novel method using neural networks called NeuralBeta, which is capable of handling both univariate and multivariate scenarios and tracking the dynamic behavior of beta. To address the issue of interpretability, we introduce a new output layer inspired by regularized weighted linear regression, which provides transparency into the model's decision-making process. We conducted extensive experiments on both synthetic and market data, demonstrating NeuralBeta's superior performance compared to benchmark methods across various scenarios, especially instances where beta is highly time-varying, e.g., during regime shifts in the market. This model not only represents an advancement in the field of beta estimation, but also shows potential for applications in other financial contexts that assume linear relationships.
Paper Structure (21 sections, 17 equations, 9 figures, 1 table)

This paper contains 21 sections, 17 equations, 9 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methodology
  3. Problem Setup
  4. Ordinary Linear Regression
  5. Rolling Regression
  6. NeuralBeta Model Architecture
  7. General Framework
  8. Interpretable Neural Network Architecture
  9. Experiments
  10. Synthetic Data
  11. Constant $\beta$
  12. Stepwise $\beta$
  13. Cyclical $\beta$
  14. Performance Analysis
  15. Comparing RMSE($\hat{y}$) and RMSE($\hat{\beta}$)
  16. ...and 6 more sections

Figures (9)

  • Figure 1: $\beta$ Estimation Framework
  • Figure 2: A diagrammatic representation of NeuralBeta-Interpretable. $l$ refers to the lookback window size and $||$ denotes concatenation. Details are in Section \ref{['sec:interp']}.
  • Figure 3: Estimations of $\beta$. RMSE($\hat{y}$) of each model is shown in parentheses in the legend.
  • Figure 4: Improvements compared with OLS for cyclical $\beta$ across different periods. NeuralBeta achieves best performance when $\beta$ changes at a moderate rate.
  • Figure 5: RMSE($\hat{y}$) and RMSE($\hat{\beta}$) are highly correlated.
  • ...and 4 more figures