标题： 一种稳健统计方法在最小方差投资组合优化中的应用 显示英文标题

标题： A Robust Statistics Approach to Minimum Variance Portfolio Optimization

摘要： 我们研究在最小风险准则下的投资组合设计。 优化投资组合的表现依赖于投资组合资产收益协方差矩阵估计的准确性。 对于大型投资组合，可用的市场收益数量通常与资产数量处于同一量级，因此样本协方差矩阵作为协方差估计器表现不佳。 此外，金融市场价格数据中常常包含异常值，如果不正确处理，可能会进一步破坏协方差估计。 我们通过研究基于泰勒鲁棒M估计器和Ledoit-Wolf收缩估计器的混合协方差矩阵估计器的性能来解决这些缺点，同时假设样本具有重尾分布。 利用随机矩阵理论的最新结果，我们开发了一个（缩放版本的）实现投资组合风险的一致估计器，该估计器通过在线优化收缩强度来最小化。 我们的投资组合优化方法通过模拟显示，在合成和真实市场价格数据中均优于现有方法。 显示英文摘要

摘要： We study the design of portfolios under a minimum risk criterion. The performance of the optimized portfolio relies on the accuracy of the estimated covariance matrix of the portfolio asset returns. For large portfolios, the number of available market returns is often of similar order to the number of assets, so that the sample covariance matrix performs poorly as a covariance estimator. Additionally, financial market data often contain outliers which, if not correctly handled, may further corrupt the covariance estimation. We address these shortcomings by studying the performance of a hybrid covariance matrix estimator based on Tyler's robust M-estimator and on Ledoit-Wolf's shrinkage estimator while assuming samples with heavy-tailed distribution. Employing recent results from random matrix theory, we develop a consistent estimator of (a scaled version of) the realized portfolio risk, which is minimized by optimizing online the shrinkage intensity. Our portfolio optimization method is shown via simulations to outperform existing methods both for synthetic and real market data.