{"title":"The maximum geometric mean criterion: revisiting the Markowitz–Samuelson debate: survey and analysis","authors":"Haim Levy","doi":"10.1007/s10479-024-06250-8","DOIUrl":null,"url":null,"abstract":"<p>By the Almost First-degree Stochastic Dominance (AFSD) rule, corresponding only to <i>economically relevant</i> preferences, for an infinite horizon the <span>\\(theoretical\\)</span> claim of both Markowitz and Samuelson is not intact. However, for the practically more relevant case of the long but finite horizon, with stocks-bonds portfolios, Markowitz <span>\\(empirically\\)</span> is right as we find that the MGM portfolio coincides with the optimal myopic portfolio for all risk aversion parameters <span>\\(\\alpha < 1.7\\)</span>. For <span>\\(\\alpha \\ge 1.7\\)</span> the MGM portfolio dominates by AFSD rule all optimal myopic portfolios, as long as the investment horizon is 12–15 years or longer.</p>","PeriodicalId":8215,"journal":{"name":"Annals of Operations Research","volume":"41 1","pages":""},"PeriodicalIF":4.4000,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Operations Research","FirstCategoryId":"91","ListUrlMain":"https://doi.org/10.1007/s10479-024-06250-8","RegionNum":3,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
引用次数: 0
Abstract
By the Almost First-degree Stochastic Dominance (AFSD) rule, corresponding only to economically relevant preferences, for an infinite horizon the \(theoretical\) claim of both Markowitz and Samuelson is not intact. However, for the practically more relevant case of the long but finite horizon, with stocks-bonds portfolios, Markowitz \(empirically\) is right as we find that the MGM portfolio coincides with the optimal myopic portfolio for all risk aversion parameters \(\alpha < 1.7\). For \(\alpha \ge 1.7\) the MGM portfolio dominates by AFSD rule all optimal myopic portfolios, as long as the investment horizon is 12–15 years or longer.
期刊介绍：
The Annals of Operations Research publishes peer-reviewed original articles dealing with key aspects of operations research, including theory, practice, and computation. The journal publishes full-length research articles, short notes, expositions and surveys, reports on computational studies, and case studies that present new and innovative practical applications.
In addition to regular issues, the journal publishes periodic special volumes that focus on defined fields of operations research, ranging from the highly theoretical to the algorithmic and the applied. These volumes have one or more Guest Editors who are responsible for collecting the papers and overseeing the refereeing process.
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