Optimal Portfolio and Consumption Decisions in a Stochastic Environment with Precommitment

In this paper we solve the stochastic portfolios-consumption control problem under the assumption that individuals follow precommitment strategies over finite intervals of time. This precommitment approach is an alternative to Merton's (1969) continuous-time stochastic dynamic control problem which assumes instantaneous feedback and costless revisions of choices all along the time path. Our solution to the problem is contrasted with that of Merton and several other contributions to the subject. We show that under precommitment individuals will tend to hold portfolios that are a function of their expected risk and return parameters, but are independent of their wealth levels and risk preferences. We also show that the intertemporal consumption growth path would be a relatively smooth function of the risk-free rate of return, time preference, and the coefficient of relative risk aversion, and independent of the portfolio's risk parameters. The latter would influence only the initial consumption level. We derive a number of empirical implications of our analysis for both portfolio holding and consumption patterns.