Continuous-Time Fama-MacBeth Regressions

Abstract

We develop an asymptotic framework for conducting inference on continuous-time asset pricing models using high-frequency returns over an increasing time horizon. Our study focuses on the identification and estimation of risk premia associated with continuous component and jumps of various size brackets. We extend the classical Fama-MacBeth regression from the discrete-time setting to a continuous-time factor model, incorporating general dynamics for factors, idiosyncratic components, and factor loadings. Our empirical analysis of U.S. equities, foreign exchange, and commodities underscores the distinct significance of continuous and jump risk premia for the specific factors constructed within each asset class in determining expected returns.

Keywords: Fama-MacBeth, two-pass regression, cross-section of expected returns, arbitrage pricing theory, high frequency data, semimartingales