Likelihood-based Dynamic Asset Pricing: Learning Time-varying Risk Premia from Cross-Sectional Models

This paper proposes a new parametric approach to estimate linear factor pricing mod-els with time-varying risk premia. In contrast to recent contributions to the literature,the framework presented abstains from introducing instrument variables to describethe time variation of risk prices. Instead, time-varying risk prices and exposures followa recursive updating scheme constructed to reduce the one-step ahead prediction errorfrom a cross-sectional factor model at the current observation. This agnostic approachis particularly useful in situations where instrument variables are unavailable or of poorquality. Estimation and inference are done by likelihood maximization. A Monte Carlostudy compares the ability of the method to predict risk prices and returns to that ofa regression-based method that uses noisy signals from true risk price predictors. Ina realistic setting, the two approaches keep pace when the signal contains 80 percentcorrect information. An application to a macro-finance model of currency carry tradesillustrates the novel approach.