Stochastic Spanning

This study develops and implements methods for determining whether introducing new securities or relaxing investment constraints improves the investment opportunity set for all risk averse investors. We develop a test procedure for “stochastic spanning” for two nested portfolio sets based on subsampling and linear programming. The test is statistically consistent and asymptotically exact for a class of weakly dependent processes. A Monte Carlo simulation experiment shows good statistical size and power properties in finite samples of realistic dimensions. In an application to standard datasets of historical stock market returns, we accept market portfolio efficiency but reject two-fund separation, which suggests an important role for higher-order moment risk in portfolio theory and asset pricing. Supplementary materials for this article are available online.

本研究开发并实施了相关方法，用于判断引入新证券或放宽投资约束是否能提升所有风险厌恶型投资者的投资机会集。我们基于子抽样与线性规划方法，针对两类嵌套投资组合集构建了“随机张成（stochastic spanning）”检验程序。该检验针对一类弱相依过程具备统计一致性与渐近精确性。蒙特卡洛模拟实验表明，在符合现实维度的有限样本中，该检验具备良好的统计显著性水平与检验功效特性。在对历史股票市场收益率标准数据集的应用分析中，我们接受市场投资组合效率假说，但拒绝两基金分离定理，这表明高阶矩风险在投资组合理论与资产定价中扮演着重要角色。本文的补充材料可在线获取。