Asset Pricing vs Asset Expected Returning in Factor-Portfolio Models

Standard factor-portfolio models focus on returns and leave prices undetermined. This approach ignores information contained in the time-series of asset prices, relevant for long-term investors and for detecting potential mis-pricing. To address this issue, we provide a new (co-)integrated methodology to factor modeling based on both prices and returns. Given a long-run relationship between the value of buy-and-hold portfolios in test assets and factors, we argue that a term---naturally labeled as Equilibrium Correction Term (ECT)---should be included when regressing returns on factors. We also propose to validate factor models by the existence of such a term. Empirically, we show that the ECT predicts equity returns, both in-sample and out-of-sample.