{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T22:41:08Z","timestamp":1761864068042,"version":"3.37.3"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2020,1,25]],"date-time":"2020-01-25T00:00:00Z","timestamp":1579910400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,1,25]],"date-time":"2020-01-25T00:00:00Z","timestamp":1579910400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Helmut-Schmidt-Universit\u00e4t Universit\u00e4t der Bundeswehr Hamburg"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math Meth Oper Res"],"published-print":{"date-parts":[[2020,8]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The best constant re-balanced portfolio represents the standard estimator for the log-optimal portfolio. It is shown that a quadratic approximation of log-returns works very well on a daily basis and a mean-variance estimator is proposed as an alternative to the best constant re-balanced portfolio. It can easily be computed and the numerical algorithm is very fast even if the number of dimensions is high. Some small-sample and the basic large-sample properties of the estimators are derived. The asymptotic results can be used for constructing hypothesis tests and for computing confidence regions. For this purpose, one should apply a finite-sample correction, which substantially improves the large-sample approximation. However, it is shown that the impact of estimation errors concerning the expected asset returns is serious. The given results confirm a general rule, which has become folklore during the last decades, namely that portfolio optimization typically fails on estimating expected asset returns.\n<\/jats:p>","DOI":"10.1007\/s00186-020-00701-1","type":"journal-article","created":{"date-parts":[[2020,1,25]],"date-time":"2020-01-25T07:04:31Z","timestamp":1579935871000},"page":"1-32","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Statistical properties of estimators for the log-optimal portfolio"],"prefix":"10.1007","volume":"92","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7507-730X","authenticated-orcid":false,"given":"Gabriel","family":"Frahm","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,1,25]]},"reference":[{"key":"701_CR1","doi-asserted-by":"publisher","first-page":"876","DOI":"10.1214\/aop\/1176991793","volume":"16","author":"P Algoet","year":"1988","unstructured":"Algoet P, Cover T (1988) Asymptotic optimality and asymptotic equipartition properties of log-optimum investment. 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