Downside Risk Optimization Under Asymmetric Laplace Distribution

In this paper, we develop a downside risk portfolio optimization model based on the Asymmetric Laplace (AL) distribution, where downside risk is measured by the Lower Partial Moment (LPM). Under this framework, we explicitly derive the expressions for the first- and second-order LPMs and develop a semi-analytical framework to determine the optimal portfolio weights. Empirical analysis compares the proposed AL distribution-based strategy with the normal-based downside risk minimization and equally weighted portfolio. The results show that the AL distribution-based strategy achieves better downside risk control and improved risk-adjusted performance compared to normal-based benchmarks.