Exergy-dissipation portfolio optimization: A backtest analysis

Exergy-dissipation portfolio optimization (EDPO) is a physics-inspired alternative to mean-variance allocation that treats portfolio formation as a nonequilibrium optimization problem. Rather than maximizing an estimated mean return subject to a variance penalty, EDPO maximizes an exergy rate $X_a(\mathbf{w})$, interpreted as a risk-sensitive certainty equivalent of log-growth, while penalizing an entropy production rate (EPR) $\mathcal{D}(\mathbf{w})$ that quantifies time-irreversibility in the portfolio return process. We propose a tractable long-only implementation with stabilizers including weight caps, Kullback–Leibler (KL), and turnover regularization along with a dissipation-budget thermostat: a primal–dual control law that updates $\lambda$ to keep the in-sample dissipation ${\mathcal{D}}_{\mathrm{I}\mathrm{S}}$ close to a target budget ${\sigma }_{\mathrm{b}\mathrm{u}\mathrm{d}}$ without explicit regime labels. The accompanying theory establishes (i) a variational identity $X_a={\mathbb{E}}_Q[g]+a^{-1}{D}_{\mathrm{K}\mathrm{L}}(Q\Vert P)$, linking exergy to a tilted expected log-growth and an information term, and (ii) a constrained efficient frontier in the $(X_a,\mathcal{D})$ plane, with a convex candidate-set dual used as an internal consistency diagnostic. An ablation study confirms that combining exergy and dissipation improves risk-adjusted performance relative to either term in isolation. Empirically, a rolling backtest over 2015–2025 on four exchange-traded fund (ETF) universes shows that EDPO is competitive with standard benchmarks. In the diversified ETF7 universe, EDPO attains the highest Sharpe ratio (0.955) with moderate quarterly turnover (0.251), while remains comparable in more correlated universes. These model-based thermodynamic diagnostics are economically interpretable: stress episodes coincide with elevated $\mathcal{D}$, and the thermostat raises $\lambda$ when dissipation pressure increases. Finally, $\mathcal{D}$ contains incremental predictive content for realized volatility in three of the four universes, as measured by mean squared error (MSE) ratios below one, although the associated forecast-gain tests remain exploratory once serial dependence and multiple comparisons are taken into account. A compact empirical-evidence package further shows that the conclusions are most sensitive to the coarse-graining level $K$, moderately sensitive to the lookback length $L$, and least sensitive to the smoothing parameter $\alpha$. The strategy remains viable under plausible transaction costs.