DP6566 Duality in Mean-Variance Frontiers with Conditioning Information

Author(s): Francisco PeƱaranda, Enrique Sentana
Publication Date: November 2007
Keyword(s): Asset Pricing, Dynamic Portfolio Strategies, Representing portfolios, Stochastic Discount Factors
JEL(s): G11, G12
Programme Areas: Financial Economics
Link to this Page: cepr.org/active/publications/discussion_papers/dp.php?dpno=6566

Portfolio and stochastic discount factor (SDF) frontiers are usually regarded as dual objects, and researchers sometimes use one to answer questions about the other. However, the introduction of conditioning information and active portfolio strategies alters this relationship. For instance, the unconditional portfolio frontier in Hansen and Richard (1987) is not dual to the unconditional SDF frontier in Gallant, Hansen and Tauchen (1990). We characterise the dual objects to those frontiers, and relate them to the frontiers generated with managed portfolios, which are commonly used in empirical work. We also study the implications of a safe asset and other special cases.