Portfolio value-at-risk optimization for asymmetrically distributed asset returns

We propose a new approach to portfolio optimization by separating asset return distributions into positive and negative half-spaces. The approach minimizes a so-called Partitioned Value-atRisk (PVaR) measure by using half-space statistical information. Using simulated and real data, the PVaR approach generates better risk-return tradeoffs in the optimal portfolios when compared to Markowitz mean-variance optimization approach. The difference between the two approaches increases in the degree of asymmetry in the underlying asset distributions. Since the PVaR measure is an asymmetric robust risk measure, our new approach can be very useful for portfolio allocations when asset return distributions are skewed and/or abnormal.