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

2026-07-17

AI Summary

This study addresses the challenges of modeling risks in Taiwan-exposed ETFs listed in the U.S.—notably heavy-tailed distributions, volatility clustering, and asymmetric responses to negative shocks—stemming from their concentration in technology stocks and exposure to geopolitical and supply chain disruptions. Integrating tail risk diagnostics via Hill estimation, asymmetric volatility modeling through GJR-GARCH, and portfolio optimization under both mean–variance and Conditional Value-at-Risk (CVaR) frameworks, the analysis of 30 ETFs reveals that differences in extreme downside risk arise primarily from scale parameters rather than tail indices. CVaR-based optimization yields substantially more concentrated allocations, and optimal portfolios vary markedly across performance metrics such as the Sharpe, STARR, and Rachev ratios. Empirical results indicate semiconductor ETFs exhibit significantly higher risk than diversified benchmarks, with the CVaR-efficient portfolio heavily overweighting SMH during the AI expansion phase, underscoring the limitations of traditional variance-based approaches in capturing risks of technology-intensive assets.

Abstract

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 paper analyzes 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 document heavy-tailed behavior across the ETF universe. Although the ETFs exhibit broadly similar asymptotic tail-decay behavior, semiconductor-focused ETFs produce substantially larger VaR and CVaR estimates than diversified benchmarks, indicating that cross-sectional differences in extreme downside risk are driven primarily by differences in return scale rather than tail-index estimates. GJR-GARCH estimates reveal persistent, asymmetric volatility, and the apparent long memory in squared returns is largely attributable to conditional heteroskedasticity rather than genuine fractional integration. CVaR optimization produces substantially more concentrated allocations than mean--variance optimization, with the CVaR tangent portfolio allocating a large weight to SMH during the post-COVID AI-driven expansion. Portfolio rankings depend on the performance measure: the Sharpe ratio and STARR measure favor the equally weighted portfolio, whereas the Rachev ratio favors CVaR-based portfolios. Overall, the results suggest that variance-based frameworks alone provide an incomplete characterization of risk in technology-concentrated investment environments and that variance-based and tail-sensitive performance measures may favor different portfolios over the same sample period.

Problem

• Portfolio Optimization
• Heavy Tails
• Asymmetric Volatility
• Tail Risk
• CVaR

Innovation

• heavy tails
• asymmetric volatility
• CVaR optimization
• tail-risk diagnostics
• GJR-GARCH