研究者詳細 - 大屋　栄

大屋　栄（オオヤ　サカエ）

Oya Sakae

写真a

所属（所属キャンパス）: 経済学部（三田）

職名: 助教（有期）

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

Oya S.

Asia-Pacific Financial Markets （Asia-Pacific Financial Markets） 29 （ 3 ） 507 - 526 2022年09月

ISSN 13872834

　概要を見る

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 (Japanese J Stat Data Sci, 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. We also compare them with portfolios based on random matrix theory filtering and Ledoit-Wolf shrinkage estimation which were used by Torri et al. (Comput Manage Sci 16:375–400, 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.
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A positive-definiteness-assured block Gibbs sampler for Bayesian graphical models with shrinkage priors

Oya S., Nakatsuma T.

Japanese Journal of Statistics and Data Science （Japanese Journal of Statistics and Data Science） 5 （ 1 ） 149 - 164 2022年07月

　概要を見る

Although the block Gibbs sampler for the Bayesian graphical LASSO proposed by Wang (2012) has been widely applied and extended to various shrinkage priors in recent years, it has a less noticeable but possibly severe disadvantage that the positive definiteness of a precision matrix in the Gaussian graphical model is not guaranteed in each cycle of the Gibbs sampler. Specifically, if the dimension of the precision matrix exceeds the sample size, the positive definiteness of the precision matrix will be barely satisfied and the Gibbs sampler will almost surely fail. In this paper, we propose modifying the original block Gibbs sampler so that the precision matrix never fails to be positive definite by sampling it exactly from the domain of the positive definiteness. As we have shown in the Monte Carlo experiments, this modification not only stabilizes the sampling procedure but also significantly improves the performance of the parameter estimation and graphical structure learning. We also apply our proposed algorithm to a graphical model of the monthly return data in which the number of stocks exceeds the sample period, demonstrating its stability and scalability.
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