Dynamic optimal portfolio selection in a VaR framework

We propose a dynamic portfolio selection model that maximizes expected returns subject to a Value-at-Risk constraint. The model allows for time varying skewness and kurtosis of portfolio distributions estimating the model parameters by weighted maximum likelihood in a increasing window setup. We determine the best daily investment recommendations in terms of percentage to borrow or lend and the optimal weights of the assets in the risky portfolio. Two empirical applications illustrate in an out-of-sample context which models are preferred from a statistical and economic point of view. We find that the APARCH(1,1) model outperforms the GARCH(1,1) model. A sensitivity analysis with respect to the distributional innovation hypothesis shows that in general the skewed-t is preferred to the normal and Student-t.