Portfolio Optimization for Commodity ETFs under Heavy-Tailed Returns

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Highly relevant for quantitative portfolio managers and risk managers working with commodity ETFs. The paper provides actionable insights on: (1) CVaR-based optimization outperforming mean-variance tangency in heavy-tailed commodity markets, (2) the fragility of return-seeking tangent portfolios under estimation error, (3) the importance of turnover control and transaction-cost awareness in dynamic rebalancing, (4) explicit tail-risk diagnostics (Hill index) as a necessary complement to standard performance ratios, and (5) sector heterogeneity in commodity ETF risk profiles. The dynamic ARMA-GARCH-copula framework is directly applicable to systematic commodity allocation strategies.

The methodology involves multiple interconnected components: rolling-window mean-variance and CVaR optimization, ARMA-GARCH marginal model estimation, Student-t copula fitting, Monte Carlo scenario generation, Hill tail-index estimation, and transaction-cost-adjusted performance evaluation. Each component is well-established in the literature, but integrating them into a coherent pipeline requires significant statistical and programming expertise. The optimization constraints (turnover limits, short-sale bounds) add practical complexity. Bloomberg data access and the need for careful parameter calibration (window size, CVaR confidence levels, turnover thresholds) further increase implementation difficulty.

The methodology is described in detail with explicit formulas for optimization, turnover constraints, and Hill estimation. Data source (Bloomberg Professional Services) is specified with access date. However, Bloomberg data requires a paid subscription, and no code or supplementary scripts are provided. The 30 ETF tickers are listed in Appendix A. The rolling-window parameters (504 days), turnover constraint (C_TO = 1/(30*252)), and short-sale limit (w_s = 1/30) are fully specified. Reproducibility is moderate due to proprietary data access requirements.