Optimal portfolio policies under time-dependent returns

Abstract

This paper investigates analytically and numerically intertemporal equilibrium portfolio policies under time dependent returns. The analysis is performed using a new method for obtaining approximate closed form solutions to the optimal portfolio-consumption problem that does not require the imposition of constraints on the conditional moments of consumption and that allows for autoregressive conditional heteroskedasticity in stock returns. The analytical and numerical results show that the elasticity of intertemporal substitution is irrelevant for the determination of the portfolio policy when returns are persistent and follow GARCH processes. In addition, results show that small departures from the i.i.d. assumption produce an important variability in the portfolio holdings that contrasts with the static CAPM constant portfolio policies. However, a conditional version of the static CAPM with the inclusion of a Jensen inequality correction is able to explain the overwhelming majority of the mean and almost all the variability of portfolio