Portfolio Optimization for Commodity ETFs Under Heavy-Tailed Returns

This paper examined whether portfolio-objective choice or forecasting complexity was more consequential in heavy-tailed commodity ETF allocation. Using daily Bloomberg data for 30 U.S.-listed commodity ETFs from 12 December 2018 to 16 December 2024, we compared historical and dynamic mean–variance and conditional value-at-risk (CVaR) portfolios under long-only and long–short constraints. The dynamic framework combined ARMA–GARCH marginals, Student-t innovations, and copula dependence. Minimum-variance and minimum-CVaR portfolios generally produced higher Sharpe, Calmar, and STARR ratios than tangent portfolios across the baseline and robustness analyses. Dynamic estimation produced higher Sharpe, Calmar, and STARR0.95 point estimates for C99 and the tangent portfolios, but none of the historical–dynamic differences remained significant after max-t adjustment. Hill estimates indicated heavy downside tails, while VaR and Expected Shortfall backtests showed no calibration rejections for the minimum-risk portfolios and revealed 95% VaR failures for dynamic tangent portfolios. The long-only minimum-variance and 95% minimum-CVaR portfolios recorded higher Sharpe, Calmar, and STARR0.95 ratios than the 60/40 SPY–AGG benchmark, whereas the benchmark had a smaller maximum drawdown and lower VaR and Expected Shortfall. Overall, portfolio-objective choice was more consistently associated with realized performance than additional forecasting complexity.