Methodology & Framework

• Core Optimization Problem: The strategy minimizes tracking error relative to the benchmark while controlling exposure to targeted risk factors via a factor tilt penalty:
  • Tracking Error: quantifies active risk and deviations from the benchmark: $TE = (w - w_b)^T\Sigma(w - w_b)$
  • Tilt Penalty: penalizes deviations from target factor exposures: $\text{Penalty} = \lambda_{\text{tilt}}\sum(B^T w - \text{tilt target})^2$
• Operational Constraints:
  • Fully invested portfolio: $\sum w_i = 1$
  • Long-short portfolio flexibility: $-1 \le w_i \le 1$

Data Collection & Processing

• Data Sourcing: stock price and market capitalization data extracted dynamically via a custom `market_data` module using Yahoo Finance.
• Scope: Focuses on the top 10 largest companies across five major sectors: Technology, Healthcare, Consumer, Finance, and Energy, covering a historical timeline from January 2020 to February 2025.
• Multicollinerity & Dimensionality Reduction:
  • Traditional asset-pricing models often face collinearity challenges (e.g., infinite VIF values between traditional Quality and Volatility metrics).
  • This pipeline implements a Tucker Factor Model utilizing Singular Value Decomposition (SVD) to extract independent principal components, successfully preserving 86.52% of the dataset's variance while ensuring regression model stability.
  • A Variance Inflation Factor (VIF) filter is applied; any factor with a VIF exceeding 10 is automatically removed to eliminate redundant data (e.g., handling sector anomalies like Tucker_Factor_1 in Tech or ind_mom in the Consumer sector).

Factor Signals & Performance Drivers
The pipeline evaluates cross-sectional asset returns using two distinct categories of signals:

1. Tucker Factors: macro-level dimensional drivers mapping structural stock behavior.
2. Short-Term Trading Indicators: independent signals capturing alpha from market inefficiencies:
   • Industry Relative Reversal (STR_i): measures 21-day cumulative returns relative to industry averages.
   • Industry Momentum (IND_MOM_i): tracks trailing trends among industry peers.
   • Seasonality (SEA_SAME_i): identifies recurring directional calendar-month patterns over a 10-year rolling window.