A Bayesian Graphical Approach for Large-Scale Portfolio Management with Fewer Historical Data

TL;DR

This paper introduces a Bayesian graphical LASSO method for large-scale portfolio management that effectively estimates asset return precision matrices even with limited data, outperforming non-Bayesian methods in stability and performance.

Contribution

It proposes a novel Bayesian framework for precision matrix estimation in large portfolios, ensuring positive definiteness and robustness with fewer observations.

Findings

The Bayesian approach yields more stable portfolios in terms of Sharpe ratio.

It successfully estimates precision matrices when n is much smaller than p.

The method outperforms non-Bayesian graphical LASSO in empirical tests.

Abstract

Managing a large-scale portfolio with many assets is one of the most challenging tasks in the field of finance. It is partly because estimation of either covariance or precision matrix of asset returns tends to be unstable or even infeasible when the number of assets $p$ exceeds the number of observations $n$. For this reason, most of the previous studies on portfolio management have focused on the case of$ p < n$. To deal with the case of $p > n$, we propose to use a new Bayesian framework based on adaptive graphical LASSO for estimating the precision matrix of asset returns in a large-scale portfolio. Unlike the previous studies on graphical LASSO in the literature, our approach utilizes a Bayesian estimation method for the precision matrix proposed by Oya and Nakatsuma (2022) so that the positive definiteness of the precision matrix should be always guaranteed. As an empirical application, we construct the global minimum variance portfolio of $p = 100$ for various values of n with the proposed approach as well as the non-Bayesian graphical LASSO approach, and compare their out-of-sample performance with the equal weight portfolio as the benchmark. In this comparison, the proposed approach produces more stable results than the non-Bayesian approach in terms of Sharpe ratio, portfolio composition and turnover. Furthermore, the proposed approach succeeds in estimating the precision matrix even if $n$ is much smaller than $p$ and the non-Bayesian approach fails to do so.