Portfolio Optimization in the Gold–Energy Nexus under Non-Gaussian Risk: A Mean–Tsallis Entropy Framework

Financial return distributions in commodity-linked portfolios are well known to exhibit heavy tails, asymmetry, and regime-dependent risk, rendering variance-based optimization frameworks inadequate. This study proposes a Mean–Tsallis Entropy portfolio optimization framework for the gold–energy nexus, explicitly designed to address non-Gaussian downside risk. The entropic index \(q\) is introduced as a calibration parameter governing the sensitivity of the optimization objective to extreme losses rather than as a direct measure of investor risk aversion. Through extensive Monte Carlo simulations and comparative analysis against the classical mean–variance benchmark, we show that portfolio robustness exhibits a non-monotonic relationship with respect to \(q\). While increasing \(q\) mechanically amplifies tail-loss penalization, excessive penalization leads to conservative allocations that degrade adaptability and recovery, resulting in inferior realized drawdown and risk-adjusted performance. An interior range of \(q\) balances tail awareness with portfolio flexibility and consistently delivers superior robustness under heavy-tailed market dynamics. These findings demonstrate that entropy-based portfolio optimization should be interpreted as a design and calibration framework, where performance emerges from structural trade-offs rather than from maximal tail penalization. The proposed approach offers a principled and practically implementable alternative for portfolio construction under non-Gaussian risk.