A single-period model and some empirical evidences for optimal asset allocation with value-at-risk constraints

In this paper, we consider the optimal asset allocation problems under VaR constraints. It is shown that the separation property holds to a certain extent. The optimal allocation of funds in risky assets is dependent on the distribution of the returns of risky assets and the VaR level, but independent of the acceptable loss ratio; the amount to be borrowed or lent at the risk free rate depends on the acceptable loss ratio. A general asset allocation model under VaR constraints is derived. As an application of our model, we address the optimal asset allocation between two categories of assets—bonds and stocks. Interesting empirical results are obtained for the US, Australia and the UK. The empirical results show that the mechanism of asset allocation under VaR constraints is fundamentally different from the classical mean-variance approach. The empirical results appear to support our model and demonstrate the potential usefulness of our approach.