An NSGA-III-HOP Algorithm for Solving the Cardinality-Constrained Multi-Period PO Problem Using Wavelet CVaR

This paper studies the construction of multi-period, cardinality-constrained portfolios that prioritize early downside protection while meeting a prescribed terminal-return target under realistic market frictions. We employ Wavelet Conditional Value-at-Risk (WCVaR), which applies a wavelet decomposition to portfolio return paths to estimate tail risk at multiple horizons. We then propose NSGA-III-HOP, an augmented Non-dominated Sorting Genetic Algorithm III that imposes a Hierarchical Objectives Preference: minimize month-by-month WCVaR before optimizing terminal wealth. The model incorporates transaction fees, dividend timing, matched-volume limits, and cardinality constraints. Using 249 continuously traded Vietnamese equities (2009–2023), NSGA-III-HOP delivers material reductions in early-month WCVaR relative to NSGA-III, C-TAEA, SMS-EMOA, U-NSGA-III, and R-NSGA-III; paired Wilcoxon signed-rank tests indicate statistical significance at the 5% level in most months. On the summary metric of minimum mean WCVaR across 12-month investments, NSGA-III-HOP attains the best performance while maintaining terminal wealth above a bank-deposit benchmark. For financial engineering, the framework provides a general mechanism to encode temporal risk priorities within evolutionary multi-objective optimization and to assess risk at user-selected horizons. For investors and portfolio managers — particularly in retail-dominated markets — it offers a practical approach to protecting capital early in the investment trajectory while continuing to pursue end-of-horizon gains.