Intertemporal Asset Allocation when the Underlying Factors are unobservable

The aim of this paper is to develop an optimal long-term bond investment strategy which can be applied to real market situations. This paper employs Merton’s intertemporal framework to accommodate the features of a stochastic interest rate and the time-varying dynamics of bond returns. The long-term investors encounter a partial information problem where they can only observe the market bond prices but not the driving factors of the variability of the interest rate and the bond return dynamics. With the assumption of Gaussian factor dynamics, we are able to develop an analytical solution for the optimal long-term investment strategies under the case of full information. To apply the best theoretical investment strategy to the real market we need to be aware of the existence of measurement errors representing the gap between theoretical and empirical models. We estimate the model based on data for the German securities market and then the estimation results are employed to develop long-term bond investment strategies. Because of the presence of measurement errors, we provide a simulation study to examine the performance of the best theoretical investment strategy. We find that the measurement errors have a great impact on the optimality of the investment strategies and that under certain circumstance the best theoretical investment strategies may not perform so well in a real market situation. In the simulation study, we also investigate the role of information about the variability of the stochastic interest rate and the bond return dynamics. Our results show that this information can indeed be used to advantage in making sensible long-term investment decisions. ∗University of Technology, Sydney, Australia and Bielefeld University, Germany †University of Technology, Sydney, Australia ‡New School, New York and Bielefeld University, Germany