NeuralBeta: Estimating Beta Using Deep Learning (2408.01387v2)

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.

• The paper introduces NeuralBeta, a deep learning model that accurately estimates dynamic beta coefficients in financial markets.
• Its interpretable variant uses a weighted least squares approach to maintain transparency and support risk management.
• Extensive experiments on synthetic and market data demonstrate its robustness, particularly during market regime shifts.

Overview of "NeuralBeta: Estimating Beta Using Deep Learning"

The paper "NeuralBeta: Estimating Beta using Deep Learning" addresses the challenges in estimating the beta ($\beta$) coefficient in finance. Traditional methods such as OLS and rolling regression exhibit limitations in capturing the dynamic behavior of $\beta$, particularly during market regime shifts. This paper introduces NeuralBeta, a deep learning-based model that can handle both univariate and multivariate scenarios to offer more precise and adaptive $\beta$ estimation.

Core Contributions

NeuralBeta Framework: The researchers propose NeuralBeta as a deep learning-based beta estimation model that effectively handles the non-linearity and dynamic nature of financial data. The model is designed to learn complex patterns from historical data and predict $\beta$ coefficients accurately.

Interpretable Neural Network: They also introduce NeuralBeta-Interpretable (NBI), an interpretable version that maintains transparency through an output layer inspired by regularized weighted linear regression. This interpretable variant aims to balance the model's performance with the necessity for explainability, crucial for risk management and governance.

Comprehensive Experiments: The paper reports extensive experiments conducted on both synthetic and real market data. The results reveal that NeuralBeta consistently outperforms conventional models, particularly in scenarios where $\beta$ is highly volatile, such as during market regime shifts.

Methodology

Problem Setup

The problem is formulated as a time series prediction task where the goal is to estimate $\beta_t$ in the relationship $y_t = \langle \beta_t, x_t \rangle + \epsilon_t$, where $y_t$ and $x_t$ are the response and explanatory variables, respectively. Traditional approaches such as OLS and rolling regression either assume a static $\beta$ or employ windowing techniques that might misspecify data relevance.

NeuralBeta Model Architecture

NeuralBeta employs a neural network where $\beta$ is a functional form: $\hat{\beta}_{t+1} = f(t, D_{0,t}; \theta)$

The network captures relationships between the input features and the response variable over time, dynamically adjusting $\beta$ to minimize the prediction error.

Interpretable NeuralBeta Architecture

NBI enhances interpretability by outputting weights for each data point in the lookback window, used to calculate a weighted least squares (WLS) estimate: $$\left(\Sigma^{-1} + X_{t-h,t}^T W_{t-h,t} X_{t-h,t}\right)^{-1}(\Sigma^{-1} \bm{\mu} + X_{t-h,t}^T W_{t-h,t} y_{t-h,t})$$ Here, $\bm{\mu}$ and $\Sigma$ are global parameters, and $W_{t-h,t}$ are weights derived from a sequence model.

Experimental Results

NeuralBeta was evaluated on synthetic and market data to validate its capability to adapt to various scenarios:

• Synthetic Data: Three cases were considered: constant $\beta$, stepwise $\beta$, and cyclical $\beta$. NeuralBeta, particularly its interpretable variant, demonstrated superior adaptability and accuracy in estimating $\beta$. For instance, it detected jumps in $\beta$ during regime shifts and tracked cyclical patterns effectively.
• Market Data: Using the CAPM model for S&P 500 components, NeuralBeta significantly outperformed traditional methods in predicting stock returns. NBI's ability to alter weighting based on market conditions (e.g., during the COVID-19 pandemic) showcased its dynamic nature.

Practical and Theoretical Implications

The implications of NeuralBeta span both practical and theoretical realms:

• Practical Implications: NeuralBeta offers a robust tool for more accurate and adaptive $\beta$ estimation, essential for risk management, portfolio optimization, and asset pricing. Its interpretable nature makes it suitable for regulatory compliance and stakeholder transparency.
• Theoretical Implications: The ability to incorporate deep learning models in financial contexts that traditionally rely on linear assumptions opens avenues for research into more complex, non-linear relationships. Future work can extend these methods to other financial metrics like an option's delta in options pricing.

Conclusion

NeuralBeta represents a significant advancement in the field of $\beta$ estimation. By leveraging the power of neural networks and incorporating an interpretable architecture, the model not only enhances prediction accuracy but also maintains transparency—a critical aspect in financial applications. The potential extensions to other financial contexts underscore its versatility and broad applicability.