使用因子图Lasso的最优投资组合
Optimal Portfolio Using Factor Graphical Lasso
AI总结：
本文提出Factor Graphical Lasso（FGL）框架，通过将精度矩阵分解为低秩和稀疏成分以解决共同因子驱动下精度矩阵非稀疏问题，实现更优的投资组合配置。
摘要：
图模型是估计高维逆协方差（精度）矩阵的强大工具，已被应用于投资组合配置问题。这些模型所做的假设是精度矩阵的稀疏性。然而，当股票收益由共同因子驱动时，这种假设并不成立。我们解决了这一局限性，并开发了一个框架，即因子图Lasso（FGL），该框架在投资组合配置的背景下，通过将精度矩阵分解为低秩和稀疏成分，将图模型与因子结构相结合。我们的理论结果和模拟表明，FGL能一致地估计投资组合权重和风险暴露，并且FGL对重尾分布具有稳健性，这使得我们的方法适用于金融应用。在针对S&P500成分股的实证应用中，基于FGL的投资组合被证明表现出优于包括等权重和指数投资组合在内的几个突出竞争对手的表现。
英文摘要：
Graphical models are a powerful tool to estimate a high-dimensional inverse covariance (precision) matrix, which has been applied for a portfolio allocation problem. The assumption made by these models is a sparsity of the precision matrix. However, when stock returns are driven by common factors, such assumption does not hold. We address this limitation and develop a framework, Factor Graphical Lasso (FGL), which integrates graphical models with the factor structure in the context of portfolio allocation by decomposing a precision matrix into low-rank and sparse components. Our theoretical results and simulations show that FGL consistently estimates the portfolio weights and risk exposure and also that FGL is robust to heavy-tailed distributions which makes our method suitable for financial applications. FGL-based portfolios are shown to exhibit superior performance over several prominent competitors including equal-weighted and Index portfolios in the empirical application for the S&P500 constituents.
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