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 lowrank 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 equalweighted and Index portfolios in the empirical application for the S&P500 constituents.​

Keywords: High-dimensionality, Portfolio optimization, Graphical Lasso, Approximate Factor Model, Sharpe Ratio, Elliptical distributions

JEL Classifications: C13, C55, C58, G11, G17​