Abstract
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.
Highlights
Decision making under uncertainty is an important problem in financial economics
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
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— a fully conditional measure—and what is instead achievable by an econometrician using real data
Summary
Decision making under uncertainty is an important problem in financial economics. The role of probability is to provide the tools to try to evaluate, as much accurately as possible, which are the possible future scenarios that an investor can face. Aside from the portfolio optimization problem, the contribution of this paper to the literature has a broader impact It is the scarcity and not the abundance of information the norm for an investors that deals with daily risky decisions using real data. While the above are just a fraction of the huge literature that deals with the estimation of the real-world measure and the relative pricing kernel, it is well known in literature that the estimation of a complete, conditional, real-world filtration set is econometrically a non trivial problem It requires an econometrically advanced model in its estimation, and (and probably more importantly) the availability of particular data. The connection with the risk-neutral measure and its impacts on the risk neutral pricing closes the paper
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