rolling-regression

This project implements rolling regression analysis using the Fama-French Three-Factor Model and industry portfolio returns to analyze time-varying relationships in financial data. The analysis is performed using Python, leveraging libraries such as pandas, statsmodels, matplotlib, and seaborn.

Rolling Regression Analysis with Fama-French Factors

A comprehensive implementation of rolling regression analysis using the Fama-French three-factor model and industry portfolio returns. This project demonstrates how to model time-varying relationships in financial data, analyze risk factor exposures, and apply rolling regression techniques for dynamic portfolio management.

Project Overview

This repository contains a complete analysis pipeline for:

• Rolling CAPM - Dynamic estimation of market betas
• Fama-French Three-Factor Model - Time-varying exposure to market, size, and value factors
• Industry Portfolio Analysis - Comparative risk analysis across 10 industry sectors
• Structural Break Detection - Identifying significant changes in market relationships
• Dynamic Hedging Strategies - Implementing rolling beta-based portfolio hedging

Features

• Data Acquisition: Automated download of Fama-French factors and industry portfolios
• Rolling Regression: Implementation using statsmodels.RollingOLS
• Visualization: Comprehensive plots for parameter trajectories, confidence intervals, and distributions
• Multi-Factor Analysis: Extending beyond CAPM to include size and value factors
• Comparative Analysis: Cross-industry beta comparison and correlation analysis
• Sensitivity Analysis: Window size impact on parameter estimates
• Practical Applications: Dynamic hedging strategy implementation

Repository Structure

rolling_regression/ ├── rolling_regression.ipynb # Main analysis notebook ├── requirements.txt # Python dependencies ├── README.md # Project documentation ├── LICENSE # MIT License └── .gitignore # Version control settings

Installation & Setup

Prerequisites

• Python 3.8+
• pip package manager

Installation

1. Clone the repository:

git clone https://github.com/esosetrov/rolling_regression
cd rolling_regression

2. Install required packages:

pip install -r requirements.txt

Install dependencies

pip install matplotlib numpy pandas pandas_datareader seaborn statsmodels

Dependencies

Key packages include:

• pandas & numpy - Data manipulation
• statsmodels - Rolling regression implementation
• matplotlib & seaborn - Visualization
• pandas-datareader - Financial data acquisition

Data Sources

The analysis uses publicly available data from Kenneth French's Data Library:

• Fama-French Three Factors: Market excess return (Mkt-RF), Size factor (SMB), Value factor (HML)
• 10 Industry Portfolios: Monthly returns for 10 industry sectors (1926-2025)
• Frequency: Monthly data
• Time Period: July 1926 - October 2025

Key Analyses

1. Rolling CAPM Analysis

• Dynamic beta estimation for technology sector
• Confidence interval analysis
• Parameter stability assessment

2. Fama-French Three-Factor Model

• Time-varying exposure to market, size, and value factors
• Factor significance analysis
• Model explanatory power (R-squared)

3. Industry Comparison

• Cross-sectional beta analysis across 10 industries
• Risk ranking and classification
• Diversification potential assessment

4. Structural Break Detection

• Z-score based breakpoint identification
• Analysis of changing market regimes

5. Dynamic Hedging Strategy

• Rolling beta-based hedge ratio calculation
• Performance comparison: hedged vs. unhedged portfolios
• Trading signal generation

Key Findings

Technology Sector Insights:

• Average Beta: 1.21 (consistently above market)
• Beta Volatility: 0.21 (significant time variation)
• Factor Exposures:
  • Market: 1.14 (significant positive)
  • Size: 0.10 (moderate positive)
  • Value: -0.47 (significant negative - growth characteristics)

Model Performance:

• CAPM R²: 50.1% - 96.6%
• 3-Factor R²: 61.8% - 97.0%
• Improvement: +5.6% average explanatory power

Industry Risk Rankings:

1. Highest Beta: HiTec (1.21), Durbl (1.20), Other (1.11)
2. Lowest Beta: Utils (0.64), Telcm (0.69), NoDur (0.78)

Practical Applications

1. Dynamic Risk Management: Time-varying beta estimation for portfolio hedging
2. Factor Timing: Identifying periods of factor significance
3. Portfolio Construction: Industry selection based on rolling risk characteristics
4. Market Regime Detection: Structural break identification for strategy adjustment

Usage Examples

Basic Rolling Regression

from src.rolling_regression import perform_rolling_regression

# Load data
factors, industries = load_famafrench_data()

# Perform rolling CAPM for technology sector
results = perform_rolling_regression(
    returns=industries['HiTec'],
    factors=factors[['Mkt-RF']],
    window=60
)

Industry Comparison

from src.analysis import compare_industry_betas

# Compare beta distributions across industries
beta_comparison = compare_industry_betas(
    industries=industries,
    factors=factors,
    window=60
)

Configuration

Key parameters can be adjusted in the configuration:

• window_size: Rolling window length (default: 60 months)
• confidence_level: For parameter intervals (default: 95%)
• selected_industries: Subset for analysis (default: ['HiTec', 'Hlth', 'Utils', 'NoDur'])

Future Extensions

Potential enhancements include:

1. Additional Factors: Momentum, quality, low volatility factors
2. Non-linear Models: Quantile regression for tail risk
3. Machine Learning: Advanced regime detection algorithms
4. International Data: Cross-market comparison
5. High-Frequency Analysis: Daily or weekly rolling regressions

Contributing

Contributions are welcome! Please feel free to submit a Pull Request.

License

This project is licensed under the MIT License - see the LICENSE file for details.

References

1. Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds.
2. French, K. R. Data Library. https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
3. Statsmodels Documentation: RollingOLS

Acknowledgments

• Kenneth French for maintaining the Fama-French data library
• The statsmodels development team for the RollingOLS implementation
• All contributors to the open-source data science ecosystem

Note: This notebook is designed for educational and research purposes. Real-world applications may require additional considerations and validation. This notebook is not financial advice. Always conduct your own due diligence before making investment decisions.