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<p>Multiple-objective portfolio analysis, involving return maximization and mean absolute deviation minimization with a minimax regret criterion (MMR_MAD), enhances portfolio stability and mitigates input uncertainty. In practice, investors are typically more concerned with potential downside losses than with potential upside gains. Therefore, this study adopts the minimax regret criterion to develop a relative robust method based on the Omega model (MMR_Omega), which accounts for both gain and loss, given a return threshold, to address the over-conservatism present in the worst-case Omega model. Furthermore, a rebalancing mechanism is introduced to enable asset reallocation for out-of-sample comparisons and to improve the static performance of existing models. The proposed model is linear and requires less computational time to reach a global optimal solution compared to a nonlinear model when dealing with a large number of asset allocations. Based on rolling windows of seven and fifteen years applied to two composite stock datasets of the S&amp;P 500 index, the results demonstrate that the proposed MMR_Omega model outperforms both the MMR_MAD model and the S&amp;P 500 index.</p>

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A gain–loss portfolio model with a relative robust method

  • 期刊论文

  • 发表日期：

    2025年12月11日

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  • Jing-Rung Yu,
  • Chen Chang,
  • Wen-Yi Lee,
  • Donald Lien

摘要

Multiple-objective portfolio analysis, involving return maximization and mean absolute deviation minimization with a minimax regret criterion (MMR_MAD), enhances portfolio stability and mitigates input uncertainty. In practice, investors are typically more concerned with potential downside losses than with potential upside gains. Therefore, this study adopts the minimax regret criterion to develop a relative robust method based on the Omega model (MMR_Omega), which accounts for both gain and loss, given a return threshold, to address the over-conservatism present in the worst-case Omega model. Furthermore, a rebalancing mechanism is introduced to enable asset reallocation for out-of-sample comparisons and to improve the static performance of existing models. The proposed model is linear and requires less computational time to reach a global optimal solution compared to a nonlinear model when dealing with a large number of asset allocations. Based on rolling windows of seven and fifteen years applied to two composite stock datasets of the S&P 500 index, the results demonstrate that the proposed MMR_Omega model outperforms both the MMR_MAD model and the S&P 500 index.