The multiperiod mean-variance (MV) portfolio optimization serves as a vital expansion of Markowitz's static MV portfolio selection framework. Just like its static counterpart, the multiperiod MV portfolio remains susceptible to estimation errors. We propose a reference-regulated multiperiod mean-variance (RRMV) framework that penalizes deviations from a reference policy. Therefore, this new optimization successfully combines the advantages of dynamic strategies and reference portfolios. A key contribution of this paper is the characterization of the out-of-sample Sharpe ratio under high-dimensional asymptotics with estimation errors in both the mean vector and the covariance matrix. We show how the reference penalty and the investment horizon jointly affect the optimized portfolio performance, and how regularization operates differently from the single-period portfolio optimization. Extensive simulation and real data studies demonstrate that the proposed framework improves the stability and out-of-sample Sharpe ratios of multiperiod policies significantly.

翻译：多阶段均值-方差投资组合优化是马科维茨静态均值-方差投资组合选择框架的重要扩展。与其静态对应模型类似，多阶段均值-方差投资组合仍易受估计误差影响。我们提出一种参考约束多阶段均值-方差框架，该框架通过惩罚对参考策略的偏离来实现优化。因此，这一新优化方法成功结合了动态策略与参考投资组合的优势。本文的核心贡献在于刻画了在均值向量与协方差矩阵均存在估计误差的高维渐近情形下样本外夏普比率。我们揭示了参考惩罚项与投资期限如何共同影响优化投资组合的表现，以及正则化机制与单阶段投资组合优化的差异。广泛的模拟与真实数据研究表明，所提框架能显著提升多阶段策略的稳定性与样本外夏普比率。