Portfolio Optimization Under Heavy Tails and Asymmetric Volatility: Evidence from Taiwan-Exposed ETFs

Taiwan’s central role in global semiconductor manufacturing exposes Taiwan-related ETFs to technology concentration, geopolitical uncertainty, and supply-chain disruptions, resulting in return distributions characterized by heavy tails, volatility clustering, and asymmetric responses to negative shocks. This study analyzed thirty U.S.-listed ETFs with Taiwan exposure from February 2015 to February 2025 using tail-risk diagnostics, asymmetric volatility modeling, and portfolio optimization under mean–variance and conditional value-at-risk (CVaR) criteria. Hill tail-index estimates documented heavy-tailed behavior across the ETF universe. Although the ETFs exhibited broadly similar asymptotic tail-decay behavior, semiconductor-focused ETFs produced substantially larger VaR and CVaR estimates than diversified benchmarks, indicating that cross-sectional differences in extreme downside risk were driven primarily by differences in return scale rather than tail-index estimates. GJR–GARCH estimates revealed persistent and asymmetric volatility. The apparent long memory in squared returns may therefore largely reflect conditional heteroskedasticity rather than genuine fractional integration, as GJR–GARCH filtering substantially reduced the evidence of long-range dependence. This result was robust across bandwidth choices for EWT, although some bandwidth sensitivity remained for EWP. CVaR optimization produced substantially more concentrated allocations than mean–variance optimization, with the CVaR tangent portfolio allocating a large weight to SMH; this concentration was most pronounced during the post-COVID, AI-driven semiconductor boom and should be interpreted as a feature of this sample period rather than a persistent structural property of semiconductor ETFs. Portfolio rankings depended on the performance measure: the Sharpe ratio and STARR measure favored the equally weighted portfolio, whereas the Rachev ratio favored CVaR-based portfolios. Overall, the results suggested that variance-based frameworks alone provided an incomplete characterization of risk in technology-concentrated investment environments and that variance-based and tail-sensitive performance measures could favor different portfolios over the same sample period.