The APT model as reduced-rank regression

Integrating the two steps of an arbitrage pricing theory (APT) model leads to a reduced-rank regression (RRR) model. So the results on RRR can be used to estimate APT models, making estimation very simple. We give a succinct derivation of estimation of RRR, derive the asymptotic variance of RRR estimators for a general case, and discuss how undersized samples (more assets than time periods) can be dealt with.