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均值方差投资组合优化中的允许使用信息集

文章 arXiv papers · 作者: Alejandro Rodriguez Dominguez
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总结

本文将均值方差投资组合选择所用的信息纳入优化问题。作者认为，如果纳入决策时尚不可得的变量，或将共同变动误认为特质风险，标准投资组合分析就可能产生偏差。作者根据预先设定的可得性、无套利、统计分离约束，以及涉及干预的主张所需的指定制度间不变性，定义允许使用的信息类别。作者不使用风险收益结果来选择信息类别，然后在其中求解经典投资组合问题。

理论结果涉及存在性、重编码不变性及可采信息的价值；研究还指出，依据决策损失选择信息的做法何时可能纳入前视数据。文中报告一个估计量符合二阶后悔标准。在包含 127 个候选驱动因素的市场数据中，这一条件对个股可以达到；对预先分散化的投资组合扩大搜索范围后，结果几乎没有变化。在无法实现精确分离时，最低方差投资组合可在降低换手率的同时达到与收缩法相当的效果，但仍有部分风险无法解释。这些发现依赖于所述的可采性假设，并不能证明因果识别总是值得其搜索成本。

核心观点

  • 信息可得性和统计分离被视为投资组合选择的约束条件。
  • 可采纳性排序在不依赖风险收益结果的情况下选择信息类别。
  • 因果主张要求在明确指定的制度间保持不变性，而识别过程需要承担搜索成本。
  • 实证条件在个股和预先分散化的投资组合中表现不同。
  • 无法实现精确分离时，最低方差投资组合可以降低换手率，但仍留有未解释的风险。

标签

投资组合构建风险管理股票统计学
全文
# 2610.00147


# Admissible Portfolio Optimization: Information Constraints, Conditional Efficient Frontiers, and the Price of Causal Identification









Mean--variance portfolio choice takes the conditioning information as given and optimizes over weights, so two errors about that information pass into the portfolio unseen: using variables unavailable at the decision time and treating common variation as idiosyncratic. We make the conditioning information a decision variable subject to hard admissibility constraints declared in advance: availability, a no-arbitrage-preserving enlargement of the decision filtration, statistical separation and, for interventional claims, invariance across declared regimes. A lexicographic admissibility order in which no risk--return quantity enters selects an optimal information class, and the classical problem is solved inside it. We prove existence, invariance under recodings, and a value-of-admissible-information theorem whose failure conditions show that selection by decision loss admits look-ahead information whenever present; the two-stage solution and the joint envelope are the minimal elements of two orders on one set. Under exact separation the diversifiable part of risk is a property of the admissible class and is interventionally stable only under interventional admissibility; requiring causal identification carries an explicit oracle price traded against search complexity. The estimator is consistent with second-order regret. On market data with 127 candidate drivers the condition is attainable on individual equities, where enlarging the search reduces the defect at a measurable rate, and not on pre-diversified portfolios, where it is nearly invariant to the search because the residual dependence is the common factor itself. Where it fails, the covariance still yields minimum-variance portfolios that match shrinkage at markedly lower turnover while discarding a measurable part of their risk, which an exact decomposition attributes to the residual share, breadth and average residual correlation.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。