High-Dimensional Estimation, Basis Assets, and the Adaptive Multi-Factor Model

Abstract

The paper proposes a new algorithm for the high-dimensional financial data -- 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, using high-dimensional methods. The AMF model, along with the GIBS algorithm, is shown to have a significantly better fitting and prediction power than the Fama-French 5-factor model.