{"paper":{"title":"The Mathematics of Heuristic Portfolio Optimization (HPO)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-fin.PM","authors_text":"Miquel Noguer i Alonso","submitted_at":"2026-06-10T19:13:53Z","abstract_excerpt":"Practitioners allocate capital with forecast-light rules such as equal weight, inverse volatility, risk parity, HRP, and return-adjusted HRP (RA-HRP). This paper develops \\emph{Heuristic Portfolio Optimization} (HPO): an information-restricted projection of the Markowitz/tangency solution onto a stable rule class. The implied-return principle, $\\w$ is maximum-Sharpe iff $\\bmu_e\\propto\\bSigma\\w$, gives closed-form optimality sets for leading heuristics and exposes the Schur-complement substitutions behind HRP. For RA-HRP, we introduce fixed-tree cluster-Sharpe recursion, unit-free HRP--RA-HRP i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.12612","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.12612/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}