Learning Objectives:

• Understand overfitting and the need for regularization in finance
• Master the fundamentals of Lasso (L1) and Ridge (L2) regularization
• Implement regularized regression for financial applications
• Optimize model parameters using cross-validation
• Interpret and utilize feature selection from Lasso

Core Resources:

1. Theoretical Foundations

• Original Ridge Regression Paper - Hoerl & Kennard (1970)
• The Lasso Method - Tibshirani (1996)

2. Technical Implementation

• Scikit-learn Linear Models Documentation
• Lasso Implementation Guide
• Ridge Implementation Guide
• Cross-Validation Methods

3. Financial Applications

• Data Sources and Tools:
  • WRDS Platform
    • Analytics Tools
    • Python Integration
  • Glassnode
    • Documentation
    • Implementation Guides
• Research Papers and Repositories:
  • Machine Learning in Asset Pricing - Gu, Kelly, Xiu (2020)
  • Open Asset Pricing

Weekly Assignment

Option 1: Predicting Stock Returns with Regularization

1. Data Preparation
   • Use WRDS to obtain monthly stock returns and firm characteristics
   • Include standard factors: Size, Book-to-Market, Momentum
   • Add accounting ratios: ROE, Leverage, Asset Growth
   • Prepare a panel dataset spanning at least 10 years
2. Model Implementation
   • Implement both Lasso and Ridge for return prediction
   • Use expanding window cross-validation (to respect time series nature)
   • Compare with standard OLS using out-of-sample R²
   • Document the impact of different λ values
3. Analysis
   • Which features survive Lasso's variable selection?
   • How do Ridge coefficients differ from OLS?
   • Does prediction improve in high volatility periods?

Option 2: Research-Based Application

Design your own application of regularization in finance. Some suggestions:

• Risk Factor Selection
  • Start with a large set of potential risk factors
  • Use Lasso to identify the most important ones
  • Compare with Fama-French factors
• Credit Risk Assessment
  • Predict corporate defaults using accounting ratios
  • Compare Lasso/Ridge with traditional models
  • Evaluate prediction accuracy

Implementation Tips: