基于二阶随机占优的稀疏生成投资组合与分散化不足
Sparse spanning portfolios and under-diversification with second-order stochastic dominance
AI总结：
本文基于贪婪算法与线性规划提出稀疏二阶随机占优生成估计方法，发现最优稀疏组合投资10个行业板块，扩展至超过45项资产无益，且在危机期缩减至25项资产以降低尾部风险。
摘要：
我们开发并实施了方法，以确定放宽投资组合的稀疏性约束是否能改善风险规避投资者的投资机会集。我们基于贪婪算法和线性规划，提出了一种新的稀疏二阶随机占优生成估计程序。我们证明了无论占优是否成立，都能渐近地最优恢复稀疏解。从大型股票数据集中，我们估计了由可能的分散化不足导致的期望效用损失，并发现将稀疏机会集扩展到超过45项资产并无益处。最优稀疏组合投资于10个行业板块，且与稀疏均值-方差组合相比降低了尾部风险。在滚动窗口基础上，危机时期资产数量缩减至25项资产，而标准因子模型无法解释该稀疏组合的表现。
英文摘要：
We develop and implement methods for determining whether relaxing sparsity constraints on portfolios improves the investment opportunity set for risk-averse investors. We formulate a new estimation procedure for sparse second-order stochastic spanning based on a greedy algorithm and Linear Programming. We show the optimal recovery of the sparse solution asymptotically whether spanning holds or not. From large equity datasets, we estimate the expected utility loss due to possible under-diversification, and find that there is no benefit from expanding a sparse opportunity set beyond 45 assets. The optimal sparse portfolio invests in 10 industry sectors and cuts tail risk when compared to a sparse mean-variance portfolio. On a rolling-window basis, the number of assets shrinks to 25 assets in crisis periods, while standard factor models cannot explain the performance of the sparse portfolios.
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