Entropy-regularized portfolio optimization and financial network entropy: diversification and concentration in a multi-asset ETF portfolio

Dilawar Ahmad Bhat; Sajad Ahmad Sheikh; Manzoor Ahmad Khanday

doi:10.46481/jnsps.2027.3778

Authors

Dilawar Ahmad Bhat dilawar.bhat@ssbf.edu.in Symbiosis School of Banking and Finance, Symbiosis International (Deemed) University, Pune, India
Sajad Ahmad Sheikh Department of Mathematics, University of Kashmir (South Campus), Anantnag, India
Manzoor Ahmad Khanday Department of Statistics, Lovely Professional University, Punjab, India

Keywords:

Portfolio diversification, Shannon entropy, Minimum spanning tree, Financial networks, Exchange-traded funds

Abstract

This study examines whether Shannon entropy regularization can mitigate the concentration associated with classical minimum-variance portfolio optimization while preserving risk-adjusted performance. Using a twelve-ETF global multi-asset universe covering equities, fixed income, precious metals, and real estate, we compare an equal-weight (EW) benchmark, a long-only fully invested minimum-variance (MV) portfolio, and an entropy-regularized minimum-variance (ERMV) portfolio. All portfolio aggregation, wealth compounding, and performance ratios use simple returns, with the risk-free rate expressed on the same basis. The MV optimizer allocates 61.87% to intermediate U.S. Treasury bonds (IEF) and 38.13% to high-yield corporate bonds (HYG), with effectively zero weight on the remaining assets. At λ = 0.01, the ERMV solution is close to equal weighting, with all twelve weights between 0.0828 and 0.0841. A sensitivity analysis over λ ∈ [10⁻⁵, 1] shows a systematic transition from concentration toward the maximum-entropy equal-weight allocation. Full-sample Sharpe ratios under a 4.5% annual risk-free rate are 0.2979 (EW) and 0.2966 (ERMV), and a circular block-bootstrap test indicates no statistically distinguishable difference. A rolling out-of-sample evaluation yields the same qualitative pattern. Correlation-based minimum spanning tree (MST) analysis reveals a core--periphery structure, while rolling spectral entropy identifies the March 2020 COVID-19 sell-off as the period of most concentrated cross-asset dependence. The findings position entropy regularization primarily as a concentration-control mechanism rather than a universal source of superior investment performance.

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