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.

► A new Partitioned Value-at-Risk (PVAR) portfolio optimization approach is proposed.
► The PVAR approach considers positive and negative return spaces separately.
► The PVAR approach accommodates ambiguous asymmetric return distributions.
► The PVAR approach performs better when returns are more asymmetrically distributed.
► The PVAR risk measure can be a coherent risk measure under certain conditions.