Return models and dynamic asset allocation strategies

This thesis studies the design of optimal investment strategies. A strategy is considered optimal when it minimizes the variance of terminal portfolio wealth for a given level of expected terminal portfolio wealth, or equivalently, maximizes an investor's utility. We study this issue in two particular situations: when asset returns follow a continuous-time path-independent process, and when they follow a discrete-time path-dependent process. Continuous-time path-independent return models are popular but controversial in the literature. We formulate the criteria for portfolio rules to be considered as optimal in this framework. We construct a portfolio consisting of a risky and a risk-free asset where the return on the risky asset follows a Gaussian diffusion process with non-constant drift and diffusion. Portfolio rules satisfying the specified criteria are shown to be compatible with the objective of utility maximization. Discrete-time path-dependent return models are more realistic, given the fact that almost all historical return data are measured in discrete time and exhibit serial correlation. Hence, we develop a novel methodology to assess the market efficiency and predictability of Australian index returns on equities, debts and cash, which we show are path-dependent empirically. We propose a one-step Multivariate Semi-parametric Maximum Likelihood Estimation (one-step MSMLE) technique to estimate a Vector-autoregressive Multivariate Generalized Autoregressive Conditional Heteroskedasticity (VAR-MGARCH) model of Australian asset returns. The estimation is done using a "rolling historical window" approach so as to highlight and capture path-dependency in asset returns as well as allow for parameter changes. Serial correlation is found in both the return and the volatility levels of the Australian assets that we consider. Having shown this, we then extend a class of reactive portfolio controls to the case when returns follow a VAR-MGARCH process. The portfolio controls are formulated by solving the Lagrangian which minimizes the variance in next period wealth for a given targeted next period wealth. We quantitatively demonstrate that this class of reactive portfolio controls are efficient, even under the existence of market impacts.