Stochastic Spanning
开发了检验新证券或放松投资约束是否改善所有风险厌恶投资者投资机会集的方法，基于子抽样和线性规划提出“随机跨度”检验，并应用于历史股市数据，发现市场组合有效但拒绝两基金分离，表明高阶矩风险的重要作用。
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.