{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T18:12:56Z","timestamp":1778868776705,"version":"3.51.4"},"reference-count":55,"publisher":"Public Library of Science (PLoS)","issue":"5","license":[{"start":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T00:00:00Z","timestamp":1778803200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS One"],"abstract":"\n Portfolio diversification is a central theme in modern investment theory. We revisit the classic return\u2013risk trade-off and propose an alternative objective\n \n \n \n \n \n \n Q<\/mml:mi>\n \u03bb<\/mml:mi>\n <\/mml:msub>\n (<\/mml:mo>\n w<\/mml:mi>\n )<\/mml:mo>\n =<\/mml:mo>\n \n \u03bc<\/mml:mi>\n \u22a4<\/mml:mo>\n <\/mml:msup>\n w<\/mml:mi>\n +<\/mml:mo>\n \u03bb<\/mml:mi>\n (<\/mml:mo>\n \n w<\/mml:mi>\n \u22a4<\/mml:mo>\n <\/mml:msup>\n \u03a3<\/mml:mo>\n w<\/mml:mi>\n \n )<\/mml:mo>\n \n \u2212<\/mml:mo>\n 1<\/mml:mn>\n \/<\/mml:mo>\n 2<\/mml:mn>\n <\/mml:mrow>\n <\/mml:msup>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n that balances higher expected returns with a direct penalty on portfolio volatility via the inverse standard deviation. This objective belongs to the axiomatic class of mean\u2013variance preferences (as formalised by [1] for additively separable forms) and admits tractable solutions, including a closed-form characterisation in the two-asset case. In rolling out-of-sample backtests on standard Fama\u2013French equity portfolios with realistic trading costs and long-only constraints,\n \n \n \n \n \n \n Q<\/mml:mi>\n \u03bb<\/mml:mi>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n delivers statistically significantly lower realised volatility (paired t-test\n p<\/jats:italic>\n \u2009<\u20090.01) and shallower maximum drawdowns than the Sharpe-maximising benchmark, while maintaining average performance comparable to Markowitz, equal-weight, and risk-parity strategies. These advantages persist across major stress episodes (GFC, COVID-19, 2022 rate shock) and are robust over a wide range of the trade-off parameter\n \n \n \n \n \n \u03bb<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n . The results position\n \n \n \n \n \n \n Q<\/mml:mi>\n \u03bb<\/mml:mi>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n as a pragmatic alternative for investors who value smoother wealth paths and robust downside protection.\n <\/jats:p>","DOI":"10.1371\/journal.pone.0348577","type":"journal-article","created":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T17:37:51Z","timestamp":1778866671000},"page":"e0348577","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["An alternative strategy for balancing profit maximization and risk reduction"],"prefix":"10.1371","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7663-2675","authenticated-orcid":true,"given":"Youssef","family":"El Khatib","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Farangiz","family":"Mukhamedova","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2026,5,15]]},"reference":[{"key":"pone.0348577.ref001","doi-asserted-by":"crossref","first-page":"536","DOI":"10.1016\/j.jet.2015.10.001","article-title":"Mean-variance utility","volume":"160","author":"Y Nakamura","year":"2015","journal-title":"Journal of Economic Theory"},{"issue":"1","key":"pone.0348577.ref002","first-page":"77","article-title":"Portfolio Selection","volume":"7","author":"H Markowitz","year":"1952","journal-title":"The Journal of Finance"},{"key":"pone.0348577.ref003","doi-asserted-by":"crossref","first-page":"102836","DOI":"10.1016\/j.irfa.2023.102836","article-title":"A bibliometric review of portfolio diversification literature","volume":"90","author":"M Migliavacca","year":"2023","journal-title":"International Review of Financial Analysis"},{"key":"pone.0348577.ref004","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1016\/j.irfa.2018.03.004","article-title":"Portfolio diversification with virtual currency: Evidence from bitcoin","volume":"63","author":"K Guesmi","year":"2019","journal-title":"International Review of Financial Analysis"},{"issue":"3","key":"pone.0348577.ref005","first-page":"835","article-title":"Diversification, Integration and Emerging Market Closed-End Funds","volume":"51","author":"G Bekaert","year":"1996","journal-title":"The Journal of Finance"},{"key":"pone.0348577.ref006","doi-asserted-by":"crossref","first-page":"101248","DOI":"10.1016\/j.ribaf.2020.101248","article-title":"Are cryptocurrencies a safe haven for equity markets? 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