论文标题
高维度的夏普比分析：因子模型中的基于残留的节点回归
Sharpe Ratio Analysis in High Dimensions: Residual-Based Nodewise Regression in Factor Models
论文作者
论文摘要
当使用拟合因子模型的残差时，我们提供了一种新理论，用于淋巴结回归。当投资组合中有许多资产时，我们将结果应用于对Sharpe比率估计器的一致性的分析。我们允许越来越多的资产以及对投资组合的时间观察。由于由于特质错误的未知性质，我们提供了节点回归，因此我们提供了基于可行的基于可行的基于可行的节点回归，以估计误差的精度矩阵，即使资产的数量P超过了投资组合的时间跨度，也是一致的。在另一个新的发展中，我们还表明，即使有越来越多的因素和p> n，也可以始终如一地估算回报的精确矩阵。我们表明：（1）在p> n中，夏普比率估计量在全球最小变异和均值方差投资组合中是一致的； （2）在P> N中，当投资组合权重总和为1时，最大SharpE比率估计器是一致的； （3）在p << n中，最大样本的夏普比率估计器是一致的。
We provide a new theory for nodewise regression when the residuals from a fitted factor model are used. We apply our results to the analysis of the consistency of Sharpe ratio estimators when there are many assets in a portfolio. We allow for an increasing number of assets as well as time observations of the portfolio. Since the nodewise regression is not feasible due to the unknown nature of idiosyncratic errors, we provide a feasible-residual-based nodewise regression to estimate the precision matrix of errors which is consistent even when number of assets, p, exceeds the time span of the portfolio, n. In another new development, we also show that the precision matrix of returns can be estimated consistently, even with an increasing number of factors and p>n. We show that: (1) with p>n, the Sharpe ratio estimators are consistent in global minimum-variance and mean-variance portfolios; and (2) with p>n, the maximum Sharpe ratio estimator is consistent when the portfolio weights sum to one; and (3) with p<<n, the maximum-out-of-sample Sharpe ratio estimator is consistent.
