Infinite Horizon Capm Equilibrium¤

This paper derives the equilibrium of an in ̄nite-horizon discrete-time CAPM economy in which agents have discounted expected quadratic utility functions. We show that there is an income stream obtainable by trading on the ̄nancial markets which best approximates perfect consumption smoothing (called the least variable income stream or LVI) such that the equilibrium consumption of each agent is some multiple of the LVI and some share of aggregate output. The welfare of agents is a decreasing function of the lack of consumption smoothing achievable, measured by the distance of the LVI from the perpetuity of one unit of income for ever. If in addition the economy has a Markov structure, the LVI, and hence the equilibrium, can be calculated by dynamic programming. When the model is calibrated to US data a striking prediction emerges: the quasi-irrelevance of the bond market. In ̄nitely-lived agents achieve almost all their desired consumption smoothing by applying carryover strategies to equity, the proportion of agents' portfolios in bonds rarely exceeding 3%. JEL Classi ̄cation Numbers: D 52, D 58, D 90, G 10. ¤We are grateful to participants in seminars at U.C. Davis, U.C. Santa Barbara, Stanford University, U.C.L.A., U.C. Santa Cruz, University of Paris, the Summer Meeting of the Econometric Society, University of Montreal, Canada, June 1998, and the Conference of the Society for Economic Dynamics, University of Pennsylvania, June 1998, for stimulating comments; and to Steve LeRoy, Rajiv Mehra and Andy Neumeyer for helpful discussions. An earlier version of this paper circulated as "Equity, Bonds, Growth and In°ation in a Quadratic In ̄nite Horizon Economy".