High Dimensional Estimation, Basis Assets, and Adaptive Multi-Factor Models

The paper proposes a new high-dimensional algorithm, the Groupwise Interpretable Basis Selection (GIBS) algorithm to estimate a new Adaptive Multi-Factor (AMF) asset pricing model, implied by the recently developed Generalized Arbitrage Pricing Theory, which relaxes the convention that the number of risk-factors is small. We first obtain an adaptive collection of basis assets and then simultaneously test which basis assets correspond to which securities. Since the collection of basis assets is quite large and highly correlated, high-dimension methods are used. The AMF model along with the GIBS algorithm is shown to have a significantly better fit than the Fama-French 5-factor model.