Statistical inference for systemic risk-driven portfolio selection

Abstract

Portfolio selection in modern finance involves constructing optimal asset allocation strategies that balance risk and return. However, traditional portfolio selection faces new challenges due to systemic events, as exemplified by the financial crisis and the COVID-19 pandemic. In response, we introduce a nonparametric systemic risk-driven portfolio selection approach that models market and portfolio losses using kernel density estimation. In the event of market underperformance, we aim to minimize the conditional expected shortfall (CoES) of portfolio losses while targeting a specific return. We observe that directly estimating CoES using nonparametric kernel methods does not produce a convex objective function with respect to portfolio weights. To address this, we propose an augmentation of the objective function to ensure convexity, guaranteeing a unique solution for optimal portfolio weights regardless of the sample size. Through simulations, we demonstrate our proposed approach’s consistency and out-of-sample performance compared to benchmark portfolio criteria and CoES-based parametric models. Applying this method to a real dataset showcases its superior risk–return performance relative to existing approaches.