Optimal Portfolio Using Factor Graphical Lasso

Tae Hwy Lee and Ekaterina Seregina ()
Additional contact information
Ekaterina Seregina: University of California Riverside

No 202025, Working Papers from University of California at Riverside, Department of Economics

Abstract: Graphical models are a powerful tool to estimate a high-dimensional inverse covariance (precision) matrix, which has been applied for portfolio allocation problem. The assumption made by these models is a sparsity of the precision matrix. However, when the stock returns are driven by the common factors, this assumption does not hold. Our paper develops a framework for estimating a high-dimensional precision matrix which combines the benefits of exploring the factor structure of the stock returns and the sparsity of the precision matrix of the factor-adjusted returns. The proposed algorithm is called Factor Graphical Lasso (FGL). We study a high-dimensional portfolio allocation problem when the asset returns admit the approximate factor model. In high dimensions, when the number of assets is large relative to the sample size, the sample covariance matrix of the excess returns is subject to the large estimation uncertainty, which leads to unstable solutions for portfolio weights. To resolve this issue, we consider the decomposition of low-rank and sparse components. This strategy allows us to consistently estimate the optimal portfolio in high dimensions, even when the covariance matrix is ill-behaved. We establish consistency of the portfolio weights in a high-dimensional setting without assuming sparsity on the covariance or precision matrix of stock returns. Our theoretical results and simulations demonstrate that FGL is robust to heavy-tailed distributions, which makes our method suitable for financial applications. The empirical application uses daily and monthly data for the constituents of the S&P500 to demonstrate superior performance of FGL compared to the equal-weighted portfolio, index and some prominent precision and covariance-based estimators.

Keywords: High-dimensionality; Portfolio optimization; Graphical Lasso; Approximate Factor Model; Sharpe Ratio; Elliptical Distributions (search for similar items in EconPapers)
JEL-codes: C13 C55 C58 G11 G17 (search for similar items in EconPapers)
Pages: 48 Pages
Date: 2020-09
New Economics Papers: this item is included in nep-ecm, nep-ore and nep-rmg
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
https://economics.ucr.edu/repec/ucr/wpaper/202025.pdf First version, 2020 (application/pdf)

Related works:
Journal Article: Optimal Portfolio Using Factor Graphical Lasso* (2024)
Working Paper: Optimal Portfolio Using Factor Graphical Lasso (2023)
Working Paper: Optimal Portfolio Using Factor Graphical Lasso (2023)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ucr:wpaper:202025

Access Statistics for this paper

More papers in Working Papers from University of California at Riverside, Department of Economics Contact information at EDIRC.
Bibliographic data for series maintained by Kelvin Mac ().