論文

暗号資産の市場の進展に伴い，パフォーマンス評価のための指数の整備が進んでいるが，こうした指数は現状，時価加重型 （CW） のものが中心である．株式の資産クラスでは，過去の実証研究により，最小分散ポートフォリオ（MV） はCW よりもリスク・リターンの効率性で優位である点が指摘されており，これを基に新たな指数の開発が進み，最小分散指数に基づく資産運用は人気のある投資戦略の1 つとして定着している．暗号資産クラスでは，伝統的資産のポートフォリオに暗号資産を追加することでの効果検証に関する研究は多数存在するものの，暗号資産クラスの中でのポートフォリオ構築に関する研究は少なく，MV とCW とを比較した研究は筆者の知る限りまだ存在しない．そこで，本研究では，暗号資産市場において，MVとCW のリスク・リターン特性を比較分析した．MV の構築には，Binance 取引所の130 銘柄の月次リターンデータを使用し，高次元かつサンプル数が限られる状況を考慮して，Oya and Nakatsuma (2022) の改良版ベイズ型グラフィカルLASSOを用いている．2022 年から2024 年まで3 年間の運用実験を実施し，代表的なCWであるS&P Cryptocurrency Broad Digital Market Index （BDM 指数） と比較した．その結果，MV はCW に比べリスクを低減しつつ，より高いリターンを達成しており，リスク・リターンの効率性において優位であることが明らかとなった．この結果は，株式市場におけるMV の優位性を示す先行研究と整合し，暗号資産市場においても類似の傾向が存在する可能性を示している．

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.

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.

Self-esteem is a key topic in psychology and health research. It influences well-being, happiness, and even medicine. However, existing studies on self-esteem have yielded conflicting results, suggesting that a global consensus remains elusive. This study examines how demographic and socioeconomic factors influence self-esteem in Japan. We analyzed panel data sampled from the entire Japanese population, with separate estimates performed for marital status and gender to account for potential differences in the impact of these factors. Using a Bayesian panel logit model with the Markov chain Monte Carlo method and the ancillarity–sufficiency interweaving strategy for efficient estimation, we found similarities and differences compared with studies from other countries. Furthermore, when comparing the overall data with data stratified by marital status and gender, we observed significant differences in how these factors influenced self-esteem, even among the same individuals. These findings underscore the importance of considering such variations when incorporating self-esteem into medical and healthcare contexts.

Alcohol use is closely related to health, emotional state, and social behavior. However, no clear consensus exists on how socioeconomic factors influence drinking habits or how the COVID-19 pandemic affected alcohol use. This study examines these relationships in Japan using panel data from a questionnaire survey (2014–2022), consisting of 10,836 responses provided by 1289 respondents, and logistic regression analysis. The results revealed that males, individuals aged 40–69, cigarette smokers, and those who exercise regularly are more likely to drink alcohol, whereas those working at least 2 days per week, earning higher incomes, and in good health are less likely to drink alcohol. The impact of COVID-19 on drinking behavior varied by region, with significant effects observed in specific regions. Additionally, an identified decline in alcohol use since 2016 highlights rising health awareness and shifting values, particularly among younger generations. These findings underscore the strong association between drinking behavior and socioeconomic attributes and emphasize the need to consider regional differences in policy and cultural influences. Overall, this study provides key insights for future research and public health policies on alcohol use in Japan.