Portfolio Efficiency and Discount Factor Bounds with Conditioning Information: A Unified Approach

Abstract

In this paper, we develop a unified framework for the study of mean-variance efficiency and discount factor bounds in the presence of conditioning information. We extend the Hilbert space framework of Hansen and Richard (1987) to obtain new characterizations of the efficient portfolio frontier and variance bounds on discount factors, as functions of the conditioning information. We introduce a covariance-orthogonal representation of the asset return space, which allows us to derive several new results, and provide a portfolio-based interpretation of existing results. Our analysis is inspired by, and extends the recent work of Ferson and Siegel (2001,2002), and Bekaert and Liu (2001). Our results have several important applications in empirical asset pricing, such as the construction of portfolio-based tests of asset pricing models, conditional measures of portfolio performance, and tests of return predictability.

JEL Classification: G11, G12