Optimal Portfolio Using Factor Graphical Lasso

Abstract Graphical models are a powerful tool to estimate high-dimensional inverse covariance (precision) matrix, which has been applied for portfolio allocation problem. The assumption made by these is sparsity of the precision matrix. However, when stock returns driven common factors, such does not hold. We address this limitation and develop framework, Factor Lasso (FGL), integrates graphical with factor structure in context decomposing matrix into low-rank sparse components. Our theoretical results simulations show that FGL consistently estimates weights risk exposure also robust heavy-tailed distributions makes our method suitable financial applications. FGL-based portfolios shown exhibit superior performance over several prominent competitors including equal-weighted index empirical application S&P500 constituents.