The paper introduces the Adaptive Multi-Factor (AMF) model, derived from the generalized Arbitrage Pricing Theory (APT), which relaxes the assumption of a small number of risk-factors. To estimate this model, the authors propose the Groupwise Interpretable Basis Selection (GIBS) algorithm, a hybrid high-dimensional method that first uses minimax prototype clustering to group correlated basis assets (e.g., ETFs) and select representative prototypes, then applies LASSO regression with the 1se rule to identify sparse, stock-specific basis assets. This approach addresses the challenges of high-dimensionality (p > n) and multicollinearity, yielding interpretable and tradeable basis assets.

Empirically, using weekly returns over three-year windows, the AMF model is tested against the Fama-French 5-factor (FF5) model on a large cross-section of stocks. The results show that the AMF model has fewer significant intercepts (alphas), suggesting consistency with no-arbitrage, and significantly higher in-sample and out-of-sample R² values (58% improvement in prediction). The GIBS algorithm selects 186 basis assets, with each stock linked to only 3.4 on average, confirming sparsity. Additionally, 78% of these basis assets earn significant risk premiums, identifying them as risk-factors. The paper also demonstrates that positive alpha strategies do not yield arbitrage, supporting the model's validity. Comparisons with alternative methods (e.g., Elastic Net, standard LASSO) show GIBS's superior performance in prediction and interpretability.