Conditioning the information in portfolio optimization

This paper proposes a theoretical analysis of the impact of a suboptimal information set on the two main components used in asset pricing, namely the physical and neutral probability measures and the pricing kernel they define. The analysis is carried out by means of a portfolio optimization problem for a small and rational investor. Solving for the maximal expected utility of terminal wealth, it proves the existence of an information premium between what is required by the theory, that is a complete information set-thus a fully conditional measure-and what is instead achievable by an econometrician using real data. Searching for the best bounds, it then studies the impact of the premium on the pricing kernel. Finally, exploiting the strong interconnection between the pricing kernel and its densities, the impact of the premium on the risk-neutral measure is analyzed.