Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2607.09505

Objective and subjective entropy measures of portfolio suboptimality

Ati S Sharma
View original source ↗Read source document ↗Export metadata ↓

Abstract

The cost of holding a suboptimal portfolio instead of the Kelly-optimal one admits two exact relative-entropy representations. Under the true measure, the expected log-wealth shortfall equals the KL divergence from the true measure to the measure under which the suboptimal portfolio would be optimal. Under that measure, the suboptimal portfolio appears to outperform the Kelly portfolio, and the apparent outperformance equals the reverse KL divergence.

Explore related subjects

q-fin.PMq-fin.MF

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Ati S Sharma. 2026-07-10. Objective and subjective entropy measures of portfolio suboptimality. https://arxiv.org/abs/2607.09505

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Financially Guided Deep Portfolio Optimization

Portfolio optimization in real-world financial markets is notoriously difficult due to non-stationarity, noisy data, and high transaction costs. Standard predict-then-optimize methods first forecast returns and then solve for weights, compounding prediction errors and often failing under regime shifts. We propose an end-to-end framework that directly optimizes differentiable surrogates of key financial metrics (Sharpe ratio, Omega ratio, Conditional Value-at-Risk, and risk parity), allowing neural networks to learn portfolio weights via backpropagation. Our expanding-window walk-forward procedure, applied to 50 S&P 500 stocks from 2007 to 2023, incorporates realistic bid-ask spread costs and rebalances quarterly. On the challenging out-of-sample test period (2022-2023), the best model, an AttentionLSTM with the Omega-CVaR-RiskParity loss, achieves an annualized Sharpe of 0.29 and a total compounded return of +7.86%, while the S&P 500 delivers -4.52% total compounded return and an annualized Sharpe of -0.02. This outperforms the S&P 500 by 12.38 percentage points, while keeping tail risk (CVaR) nearly unchanged. The framework outperforms the equal-weight portfolio, S&P 500, and traditional methods (MVP, HRP, NCO, ERC), demonstrating that embedding financial objectives directly into model training yields robust, economically meaningful outperformance even in adverse market conditions.

q-fin.PM↗
arXiv2026

The geometry of higher order modern portfolio theory

In this article, we study the generalized modern portfolio theory, with utility functions admitting higher-order cumulants. We establish that under certain genericity conditions, the utility function has a constant number of complex critical points. We study the discriminant locus of complex critical points with multiplicity. Finally, we switch our attention to the generalization of the feasible portfolio set (variety), determine its dimension, and give a formula for its degree.

q-fin.PM↗
arXiv2026

Special Markowitz: Thermodynamic Formalism for the Joint Regularisation of Returns and Covariance

Special Markowitz (SM) regularises returns and covariance jointly, relative to a reference state (mu_ref, Sigma_ref). Each eigendirection of the whitened relative operator carries a signed spectral potential Phi_k, with persistence factor psi_k = exp(-Phi_k) > 0. Positive potentials attenuate empirical deviations from the reference geometry, zero potential preserves them, and negative potentials amplify them. The persistence factor psi_k governs both the return signal and the covariance deviation: the regularised deviation from the reference is psi_k times the empirical deviation. The logarithmic potential coordinate is characterised by a multiplicative composition law on the multiplicative group of positive real numbers; the Stein loss is characterised as the unique free-energy density (within a natural class) compatible with the resulting coupling. The SM pressure functional is additive across modes the defining property of Special Markowitz.

q-fin.PM↗