Optimal Portfolio Using Factor Graphical Lasso

TL;DR

This paper introduces the Factor Graphical Lasso (FGL), a novel method that combines graphical models with factor structures to improve high-dimensional portfolio optimization, demonstrating robustness and superior empirical performance.

Contribution

The paper develops FGL, integrating factor models with graphical lasso to better estimate precision matrices in portfolio allocation, especially under heavy-tailed distributions.

Findings

FGL accurately estimates portfolio weights and risk exposure.

FGL outperforms traditional methods in empirical tests.

FGL is robust to heavy-tailed financial data.

Abstract

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.