Stock Market Mean Reversion and the Optimal Equity Allocation of a Long-Lived Investor

This paper solves numerically the intertemporal consumption and portfolio choice problem of an infinitely-lived investor with Epstein-Zin-Weil utility who faces a time-varying equity premium. We find that the optimal portfolio allocation to stocks is almost linear and the optimal log consumption-wealth ratio is almost quadratic in the equity premium except at the upper extreme of the state space, where both optimal rules flatten out. With the exception of this flattening, the solutions are very close to the approximate analytical solutions proposed by Campbell and Viceira (1999). We also consider a constrained version of the problem in which the investor faces borrowing and short-sales constraints. These constraints bind when the equity premium moves away from its mean in either direction, and are particularly severe for risk-tolerant investors. The optimal constrained portfolio rules are similar but not identical to the optimal unconstrained rules with the constraints imposed. The portfolio constraints also affect the optimal consumption policy, reducing the average consumption-wealth ratio whenever the investor's elasticity of intertemporal substitution is below one, and reducing the variability of the optimal consumption-wealth ratio.