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

D. A. Bhat, S. A. Sheikh, M. Khanday

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.

Source: semanticscholar · PDF

Read the AI summary, key takeaways and discussion on WOBR Quant Research.