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.

中文翻译：

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使用因子图形套索的最佳投资组合

图模型是估计高维逆协方差（精度）矩阵的强大工具，已应用于投资组合分配问题。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素驱动时，这种假设就不成立了。我们解决了这一限制并开发了一个框架，即因子图形套索 (FGL)，该框架通过将精度矩阵分解为低秩和稀疏分量，将图形模型与投资组合分配背景下的因子结构相结合。我们的理论结果和模拟表明，FGL 始终如一地估计投资组合权重和风险敞口，而且 FGL 对重尾分布具有鲁棒性，这使得我们的方法适用于金融应用。