Fisher Separation and Project Valuation in Partially Complete Markets

This paper presents an extension of the Fisher Separation Theorem applicable in multiperiod, "partially complete" markets where some, but not all, risks may be hedged by trading securities. Given necessary and sufficient conditions on preferences, an investor contemplating investments in productive opportunities (or projects) and financial securities can decompose this problem into production and portfolio-consumption problems that may be solved sequentially. In the production problem, the investor evaluates alternative production plans using a dynamic programming-like procedure that integrates contingent-claims techniques and the recursive utility approach developed by Kreps and Porteus, using market prices to value market risks and the investor's beliefs and preferences to value private risks. In the portfolioconsumption problem, the investor can ignore the project details and choose a trading strategy to maximize his expected utility of consumption, given an initial wealth reflecting the maximal project value. The valuation procedure can be used to generate bounds on project values when the preference assumptions are not exactly satisfied and can be used with aggregate investor beliefs and preferences in the case of multiple investors sharing a project. DRAFT: August 8, 1996 *I am grateful for helpful conversations with Pete Kyle, Kevin McCardle, Bob Nau, and Bob Winkler during the preparation of this paper. This work was supported in part by National Science Foundation grand SBR95-11364.