Portfolio Selection with Time-Varying Value-at-Risk

We propose a portfolio-selection model that maximizes expected returns subject to a time-varying 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 an 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 a risky portfolio. An empirical application illustrates in an out-of-sample context which models are preferred from a statistical and economic point of view.