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 newly‐defined Partitioned Value‐at‐Risk (PVaR) risk measure by using half‐space statistical information. Using simulated data, the PVaR approach always generates better risk‐return tradeoffs in the optimal portfolios when compared to traditional Markowitz mean–variance approach. When using real financial data, our approach also outperforms the Markowitz approach in the risk‐return tradeoff. Given that the PVaR measure is also a robust risk measure, our new approach can be very useful for optimal portfolio allocations when asset return distributions are asymmetrical.