The solution to a multi-period portfolio problem can differ substantially from the solution to a static or single-period portfolio problem, as demonstrated originally by Samuelson (1969) and Merton (1969,1971,1973). This paper offers an explicit solution to a basic multi-period dynamic portfolio problem when the return dynamics are described by a multivariate time-series model and the investor is concerned with maximizing the expected utility of wealth at a given horizon. The modeling framework encompasses return generating models where some of the basic state variables are unobserved, and where the investor is faced with a filtering problem as part of the overall dynamic asset allocation problem. Our solution makes it possible to address, e.g., the portfolio implications of an estimated VAR-model that involves return-predictability for investors with different risk aversion and time horizons in a simple and consistent manner. Furthermore, when some of the state-variables are unobserved, we establish a close link between how unobserved state-variables can be handled consistently in the econometric estimation of the model as well as in a subsequent analysis of optimal asset allocation choice by using a Kalman filtering approach. This is explored in a realistic model calibration.

The multivariate discrete-time modeling of return dynamics is basically similar to the multivariate VAR-setting used by Campbell, Chan and Viceira (2003), but extended to the situation where some of the state-variables may not be directly observed by the investor. The general version of our return generating model is based on a state-space representation which consists of a transition equation and a measurement equation. The transition equation describes the return dynamics, and this is exactly the Campbell et al. (2003) multivariate VAR-model. The measurement equation describes what is being observed (and what is not).