Portfolio Optimization in the Gold–Energy Nexus under Non-Gaussian Risk: A Mean–Tsallis Entropy Framework

Portfolio Optimization in the Gold–Energy Nexus under Non-Gaussian Risk: A Mean–Tsallis Entropy Framework | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Portfolio Optimization in the Gold–Energy Nexus under Non-Gaussian Risk: A Mean–Tsallis Entropy Framework Nam Anh Quach This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8996190/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Financial return distributions in commodity-linked portfolios are well known to exhibit heavy tails, asymmetry, and regime-dependent risk, rendering variance-based optimization frameworks inadequate. This study proposes a Mean–Tsallis Entropy portfolio optimization framework for the gold–energy nexus, explicitly designed to address non-Gaussian downside risk. The entropic index \(q\) is introduced as a calibration parameter governing the sensitivity of the optimization objective to extreme losses rather than as a direct measure of investor risk aversion. Through extensive Monte Carlo simulations and comparative analysis against the classical mean–variance benchmark, we show that portfolio robustness exhibits a non-monotonic relationship with respect to \(q\) . While increasing \(q\) mechanically amplifies tail-loss penalization, excessive penalization leads to conservative allocations that degrade adaptability and recovery, resulting in inferior realized drawdown and risk-adjusted performance. An interior range of \(q\) balances tail awareness with portfolio flexibility and consistently delivers superior robustness under heavy-tailed market dynamics. These findings demonstrate that entropy-based portfolio optimization should be interpreted as a design and calibration framework, where performance emerges from structural trade-offs rather than from maximal tail penalization. The proposed approach offers a principled and practically implementable alternative for portfolio construction under non-Gaussian risk. Econometrics Applied Mathematics Entropy-based portfolio optimization Tsallis entropy non-Gaussian risk downside risk calibration gold–energy nexus robust portfolio design Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8996190","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":598566195,"identity":"96b4a917-45f4-4f9d-b3f3-6c838847b9ba","order_by":0,"name":"Nam Anh Quach","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9UlEQVRIiWNgGAWjYLACxgYQycP4+E8FkGZmbiBaC7MBzxmQFkbitbBJ8LYhuDiBOfvpxM+FO6wT+9vPHpCQnFcbzd8O1PKjYhtOLZY9uZulZ55JT5xxJi/BwHDb8dwZhxkbGHvO3MapxeBA7gZp3rbDiQ03eAwSErcdy20AamFmbMOj5fzbzb9BWuYDtRw4OOdY7nyCWm7kbgPbsuEGj2FjY0NN7gbCWt5us+ZtSzfeeCbHmJnh2IHcjUAtB/H65Xzu5tu8bday846fMf/NUFOXO+/84YMPflTg1gIFzDDGYTB5gJB6ZC11RCgeBaNgFIyCkQYAJ8Fh8iX1/zgAAAAASUVORK5CYII=","orcid":"https://orcid.org/0009-0000-7962-6695","institution":"Hong Bang International University","correspondingAuthor":true,"prefix":"","firstName":"Nam","middleName":"Anh","lastName":"Quach","suffix":""}],"badges":[],"createdAt":"2026-02-28 14:43:48","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-8996190/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8996190/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104401011,"identity":"2bc75f45-1080-46d0-adbd-851873da8d93","added_by":"auto","created_at":"2026-03-11 12:11:40","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":600440,"visible":true,"origin":"","legend":"","description":"","filename":"PortfolioOptimizationintheGold8threvised.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8996190/v1_covered_1cbe6b90-91be-4eb3-9712-0bfd50840663.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003ePortfolio Optimization in the Gold–Energy Nexus under Non-Gaussian Risk: A Mean–Tsallis Entropy Framework\u003c/strong\u003e\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Entropy-based portfolio optimization, Tsallis entropy, non-Gaussian risk, downside risk calibration, gold–energy nexus, robust portfolio design","lastPublishedDoi":"10.21203/rs.3.rs-8996190/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8996190/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eFinancial return distributions in commodity-linked portfolios are well known to exhibit heavy tails, asymmetry, and regime-dependent risk, rendering variance-based optimization frameworks inadequate. This study proposes a Mean\u0026ndash;Tsallis Entropy portfolio optimization framework for the gold\u0026ndash;energy nexus, explicitly designed to address non-Gaussian downside risk. The entropic index \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(q\\)\u003c/span\u003e\u003c/span\u003e is introduced as a calibration parameter governing the sensitivity of the optimization objective to extreme losses rather than as a direct measure of investor risk aversion.\u003c/p\u003e \u003cp\u003eThrough extensive Monte Carlo simulations and comparative analysis against the classical mean\u0026ndash;variance benchmark, we show that portfolio robustness exhibits a non-monotonic relationship with respect to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(q\\)\u003c/span\u003e\u003c/span\u003e. While increasing \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(q\\)\u003c/span\u003e\u003c/span\u003e mechanically amplifies tail-loss penalization, excessive penalization leads to conservative allocations that degrade adaptability and recovery, resulting in inferior realized drawdown and risk-adjusted performance. An interior range of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(q\\)\u003c/span\u003e\u003c/span\u003e balances tail awareness with portfolio flexibility and consistently delivers superior robustness under heavy-tailed market dynamics.\u003c/p\u003e \u003cp\u003eThese findings demonstrate that entropy-based portfolio optimization should be interpreted as a design and calibration framework, where performance emerges from structural trade-offs rather than from maximal tail penalization. The proposed approach offers a principled and practically implementable alternative for portfolio construction under non-Gaussian risk.\u003c/p\u003e","manuscriptTitle":"Portfolio Optimization in the Gold–Energy Nexus under Non-Gaussian Risk: A Mean–Tsallis Entropy Framework","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-03 11:36:18","doi":"10.21203/rs.3.rs-8996190/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"bd2cceed-7ea5-4675-a506-75c0281f3ee9","owner":[],"postedDate":"March 3rd, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":63700323,"name":"Econometrics"},{"id":63700324,"name":"Applied Mathematics"}],"tags":[],"updatedAt":"2026-03-03T11:36:18+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-03 11:36:18","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8996190","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8996190","identity":"rs-8996190","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}