  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.
