{"title":"下行风险汇总和投资组合选择","authors":"Conrad Spanaus, Jan Wenzelburger","doi":"10.1016/j.jmateco.2025.103138","DOIUrl":null,"url":null,"abstract":"<div><div>This article refines Markowitz’s classical portfolio theory by replacing standard deviation with a below-target deviation measure referred to as <em>downside risk</em>, in which only returns below the safe return of the market contribute to the quantification of risk. Downside risk is economically intuitive but neither a general deviation nor a coherent risk measure. We establish the existence and uniqueness of downside-efficient portfolios that aggregate the downside risks of finitely many assets. The tractability of downside-efficient portfolios allows for a risk analysis that parallels the classical mean–variance analysis. We show that all central tenets carry over if standard deviation is substituted with downside risk. A numerical example illustrates when downside-efficient portfolios outperform mean–variance efficient portfolios.</div></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":"119 ","pages":"Article 103138"},"PeriodicalIF":0.7000,"publicationDate":"2025-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Aggregation of downside risk and portfolio selection\",\"authors\":\"Conrad Spanaus, Jan Wenzelburger\",\"doi\":\"10.1016/j.jmateco.2025.103138\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>This article refines Markowitz’s classical portfolio theory by replacing standard deviation with a below-target deviation measure referred to as <em>downside risk</em>, in which only returns below the safe return of the market contribute to the quantification of risk. Downside risk is economically intuitive but neither a general deviation nor a coherent risk measure. We establish the existence and uniqueness of downside-efficient portfolios that aggregate the downside risks of finitely many assets. The tractability of downside-efficient portfolios allows for a risk analysis that parallels the classical mean–variance analysis. We show that all central tenets carry over if standard deviation is substituted with downside risk. A numerical example illustrates when downside-efficient portfolios outperform mean–variance efficient portfolios.</div></div>\",\"PeriodicalId\":50145,\"journal\":{\"name\":\"Journal of Mathematical Economics\",\"volume\":\"119 \",\"pages\":\"Article 103138\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2025-06-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Economics\",\"FirstCategoryId\":\"96\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0304406825000552\",\"RegionNum\":4,\"RegionCategory\":\"经济学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ECONOMICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Economics","FirstCategoryId":"96","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0304406825000552","RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ECONOMICS","Score":null,"Total":0}
Aggregation of downside risk and portfolio selection
This article refines Markowitz’s classical portfolio theory by replacing standard deviation with a below-target deviation measure referred to as downside risk, in which only returns below the safe return of the market contribute to the quantification of risk. Downside risk is economically intuitive but neither a general deviation nor a coherent risk measure. We establish the existence and uniqueness of downside-efficient portfolios that aggregate the downside risks of finitely many assets. The tractability of downside-efficient portfolios allows for a risk analysis that parallels the classical mean–variance analysis. We show that all central tenets carry over if standard deviation is substituted with downside risk. A numerical example illustrates when downside-efficient portfolios outperform mean–variance efficient portfolios.
期刊介绍:
The primary objective of the Journal is to provide a forum for work in economic theory which expresses economic ideas using formal mathematical reasoning. For work to add to this primary objective, it is not sufficient that the mathematical reasoning be new and correct. The work must have real economic content. The economic ideas must be interesting and important. These ideas may pertain to any field of economics or any school of economic thought.