Optimal Growth Portfolios When Yields are Serially Correlated - Hakansson, Nils H.; Liu, Tien-Ching (The Review of Economics and Statistics, 1970)
PpTO date, the bulk of portfolio theory has evolved on the basis of a single-period model. Those writers who have considered sequential portfolio models, for example Tobin [24] and Mossin [19], have invariably assumed investment yields in the various periods to be stochastically independent. The purpose of this paper is to generalize the capital growth model, apparently originated by Latane [17] and Breiman [6], [7], to the case in which investment returns in one period are not statistically independent of returns in previous periods.' The assumptions employed in the present model are given in section II. Essentially, a distinction between risk due to broad market forces and risk due to individual asset factors, similar to that made by Sharpe [23] and King [16], is made. Furthermore, the no-easymoney condition is assumed to hold and the investor is required to remain solvent with probability 1. The formal model is developed in section III and section IV gives some preliminary results, including conditions for long-run growth and ultimate ruin. In section V, an optimal investment strategy is obtained on the basis of a slightly generalized and weakened version of the innocuous criterion that more is preferred to less in the very long run. The properties of the optimal strategy are discussed in section VI; it is noted that the optimal policy is myopic, that it maximizes the long-run growth rate, and that the optimal mix of assets is independent of wealth. Some concluding comments are given in section VII.