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

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 (2020) 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. We also compare them with portfolios based on random matrix theory filtering and Ledoit-Wolf shrinkage estimation which were used by Torri et al. (2019). In this comparison, the proposed approach produces more stable results than the non-Bayesian approach and the other comparative approaches in terms of Sharpe ratio, portfolio composition and turnover even if $n$ is much smaller than $p$.