发表机构
University of Waterloo（滑铁卢大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对分布不确定下的增强指数跟踪问题，提出基于帕累托最优的稳健模型，最小化最坏情况平均损失与下行风险凸组合，实证优于指数及多种稳健模型。
AI 中文摘要
增强指数跟踪（EIT）投资组合选择问题旨在构建一个预期能超越基准指数的投资组合。在实践中，投资者面临资产与指数损失联合分布的不确定性，因为真实分布通常是未知的，只能获得部分信息。此外，投资组合选择需要在追求更高收益的同时，平衡平均损失与下行风险之间的权衡。因此，在EIT投资组合选择中有效建模和管理这些因素，既具有实践意义，也具有研究价值。为应对这些挑战，本文以帕累托最优理论为指导，提出了分布不确定性下的稳健EIT投资组合选择模型。这些模型在约束最坏情况平均收益的条件下，最小化最坏情况平均损失与下行风险的凸组合。本文考虑了两种不确定性集合：一种假设已知平均损失向量和协方差矩阵，另一种是矩未知的更一般集合。对于前者，推导出了闭式解；对于后者，则转化为可处理的凸优化问题。基于真实市场数据的实证结果表明，所提出的模型在样本外累计财富以及夏普比率、索提诺比率和欧米伽比率方面，不仅优于被跟踪的指数，还优于等权重投资组合、稳健均值-方差模型和稳健方差模型。此外，最小化最坏情况平均损失与下行风险凸组合的投资组合，始终优于仅最小化下行风险的投资组合。本文还为有效平衡风险与收益提供了选择最优权重系数的实用指导。
英文摘要
The enhanced index tracking (EIT) portfolio selection problem aims to construct a portfolio that is expected to outperform a benchmark index. In practice, investors face uncertainty in the joint distribution of asset and index losses, as the true distribution is typically unknown and only partial information is available. Moreover, portfolio selection requires balancing the trade-off between mean loss and downside risk while targeting higher returns. Effectively modeling and managing these factors in EIT portfolio selection is therefore of both practical and research interest. To address these challenges, this paper proposes robust EIT portfolio selection models under distributional uncertainty, guided by Pareto-optimality theory. The models minimize a convex combination of worst-case mean loss and downside risk, subject to a constraint on worst-case mean return. Two uncertainty sets are considered: one assuming a known mean loss vector and covariance matrix, and a more general set with unknown moments. Closed-form solutions are derived for the former, while the latter reduces to tractable convex optimization problems. Empirical results based on real market data show that the proposed models outperform not only the tracked index but also the equally weighted portfolio, robust mean-variance models, and robust variance models in terms of out-of-sample cumulative wealth, as well as Sharpe, Sortino, and Omega ratios. Moreover, portfolios that minimize a convex combination of worst-case mean loss and downside risk consistently outperform those that minimize downside risk alone. We also provide practical guidance for selecting optimal weighting coefficients to effectively balance risk and return.
