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<p>This paper introduces the <i>Maximum Entropy Portfolio</i> (MEP), an entropy-based optimization framework designed to enhance diversification, robustness, and practical applicability in fixed-income portfolio construction. Building on the mean–variance optimization (MVO) model, the framework relies on the concept of <i>Quasi-Efficient Portfolios</i> (QEPs), derived by maximizing an entropy measure—either Shannon or Rao’s quadratic entropy—subject to tolerance bands expressed in terms of investor utility and modified duration. These portfolios remain close to the efficient frontier, retaining similar characteristics and performance. Methods for determining such maximum deviations are also proposed. A multi-run optimization spanning all levels of constraint tightness generates the <i>QEP solutions surface</i>, which is mapped into <i>diversification isocurves</i>, representing feasible trade-offs between maximum entropy, utility, and duration. On this surface, non-dominated portfolios are identified and optimal allocations are selected through a Pareto front-based process. Empirical validation using a comprehensive dataset of USD-denominated US Treasuries and Public Sector Entities (PSE) bonds (30 years), and EUR-denominated German sovereign and BBB-rated corporate bonds (20 years) provides evidence that the MEP framework consistently improves the trade-off between diversification and risk-adjusted returns compared to traditional models, while effectively integrating key fixed-income asset characteristics into the allocation process. In-sample results based on Stationary Block Bootstrapping, complemented by out-of-sample rolling-window backtests, further confirm the statistical robustness of these findings across varying investment horizons and market conditions.</p>

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Enhancing diversification in fixed-income portfolios: an entropy-based optimization framework

  • 期刊论文

  • 发表日期：

    2025年10月15日

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  • Mario Bajo Traver

摘要

This paper introduces the Maximum Entropy Portfolio (MEP), an entropy-based optimization framework designed to enhance diversification, robustness, and practical applicability in fixed-income portfolio construction. Building on the mean–variance optimization (MVO) model, the framework relies on the concept of Quasi-Efficient Portfolios (QEPs), derived by maximizing an entropy measure—either Shannon or Rao’s quadratic entropy—subject to tolerance bands expressed in terms of investor utility and modified duration. These portfolios remain close to the efficient frontier, retaining similar characteristics and performance. Methods for determining such maximum deviations are also proposed. A multi-run optimization spanning all levels of constraint tightness generates the QEP solutions surface, which is mapped into diversification isocurves, representing feasible trade-offs between maximum entropy, utility, and duration. On this surface, non-dominated portfolios are identified and optimal allocations are selected through a Pareto front-based process. Empirical validation using a comprehensive dataset of USD-denominated US Treasuries and Public Sector Entities (PSE) bonds (30 years), and EUR-denominated German sovereign and BBB-rated corporate bonds (20 years) provides evidence that the MEP framework consistently improves the trade-off between diversification and risk-adjusted returns compared to traditional models, while effectively integrating key fixed-income asset characteristics into the allocation process. In-sample results based on Stationary Block Bootstrapping, complemented by out-of-sample rolling-window backtests, further confirm the statistical robustness of these findings across varying investment horizons and market conditions.