{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,23]],"date-time":"2026-10-23T13:39:12Z","timestamp":1792762752073,"version":"4.5.0"},"posted":{"date-parts":[[2026]]},"group-title":"SSRN","reference-count":0,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.uspto.gov\/ip-policy\/copyright-policy\/copyright-basics"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>Mean-variance portfolio optimization measures risk through the covariance matrix of asset returns, but it does not directly penalize concentration. This paper examines two related specifications. Replacing the covariance matrix with an identity matrix yields mean-concentration optimization, in which the quadratic objective is the sum of squared portfolio weights. Adding that identity-matrix term to the original variance objective yields a three-criterion framework involving expected return, covariance risk, and concentration. At each target return, the investor minimizes portfolio variance plus \u03b7 times concentration. The paper derives analytical solutions, characterizes the efficient set, and establishes that increasing \u03b7 weakly reduces concentration and weakly increases variance at a common return target. A supplied in-sample illustration covering 41 international blue-chip stocks in Swiss francs shows how the additional penalty broadens portfolio allocations over substantial portions of the solution path while moving portfolios away from the conventional mean-variance frontier. The paper connects this trade-off to portfolio norm constraints and diagonal regularization.<\/jats:p>","DOI":"10.2139\/ssrn.7657060","type":"posted-content","created":{"date-parts":[[2026,10,23]],"date-time":"2026-10-23T12:58:37Z","timestamp":1792760317000},"source":"Crossref","is-referenced-by-count":0,"title":["Portfolio Selection with Covariance and Concentration Risk"],"prefix":"10.2139","author":[{"given":"Andreas","family":"Steiner","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","container-title":[],"original-title":[],"deposited":{"date-parts":[[2026,10,23]],"date-time":"2026-10-23T12:58:37Z","timestamp":1792760317000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ssrn.com\/abstract=7657060"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"references-count":0,"URL":"https:\/\/doi.org\/10.2139\/ssrn.7657060","relation":{},"subject":[],"published":{"date-parts":[[2026]]},"subtype":"preprint"}}