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Managing a large-scale portfolio with many assets is one of the mostchallenging tasks in the field of finance. It is partly because estimation ofeither covariance or precision matrix of asset returns tends to be unstable oreven infeasible when the number of assets $p$ exceeds the number ofobservations $n$. For this reason, most of the previous studies on portfoliomanagement 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 graphicalLASSO for estimating the precision matrix of asset returns in a large-scaleportfolio. Unlike the previous studies on graphical LASSO in the literature,our approach utilizes a Bayesian estimation method for the precision matrixproposed by Oya and Nakatsuma (2022) so that the positive definiteness of theprecision matrix should be always guaranteed. As an empirical application, weconstruct the global minimum variance portfolio of $p = 100$ for various valuesof n with the proposed approach as well as the non-Bayesian graphical LASSOapproach, and compare their out-of-sample performance with the equal weightportfolio as the benchmark. In this comparison, the proposed approach producesmore stable results than the non-Bayesian approach in terms of Sharpe ratio,portfolio composition and turnover. Furthermore, the proposed approach succeedsin estimating the precision matrix even if $n$ is much smaller than $p$ and thenon-Bayesian approach fails to do so.

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