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Impossible frontiers / Thomas J. Brennan in Management science, Vol. 56 N° 6 (Juin 2010) 

Public ISBD [article]  in Management science > Vol. 56 N° 6 (Juin 2010) . - pp. 905-923 Titre : Impossible frontiers Type de document : texte imprimé Auteurs : Thomas J. Brennan, Auteur ; Andrew W. Lo, Auteur Année de publication : 2010 Article en page(s) : pp. 905-923 Note générale : Management Langues : Anglais (eng) Mots-clés : Short  selling  Long/short  Portfolio  optimization  Mean-variance  analysis  CAPM Index. décimale : 658 Organisation des entreprises. Techniques du commerce Résumé : A key result of the capital asset pricing model (CAPM) is that the market portfolio—the portfolio of all assets in which each asset's weight is proportional to its total market capitalization—lies on the mean-variance-efficient frontier, the set of portfolios having mean-variance characteristics that cannot be improved upon. Therefore, the CAPM cannot be consistent with efficient frontiers for which every frontier portfolio has at least one negative weight or short position. We call such efficient frontiers “impossible,” and show that impossible frontiers are difficult to avoid. In particular, as the number of assets, n, grows, we prove that the probability that a generically chosen frontier is impossible tends to one at a geometric rate. In fact, for one natural class of distributions, nearly one-eighth of all assets on a frontier is expected to have negative weights for every portfolio on the frontier. We also show that the expected minimum amount of short selling across frontier portfolios grows linearly with n, and even when short sales are constrained to some finite level, an impossible frontier remains impossible. Using daily and monthly U.S. stock returns, we document the impossibility of efficient frontiers in the data. DEWEY : 658 ISSN : 0025-1909 En ligne : http://mansci.journal.informs.org/content/56/6.toc [article] Impossible frontiers [texte imprimé] / Thomas J. Brennan, Auteur ; Andrew W. Lo, Auteur . - 2010 . - pp. 905-923. Management Langues : Anglais (eng) in Management science > Vol. 56 N° 6 (Juin 2010) . - pp. 905-923 Mots-clés : Short  selling  Long/short  Portfolio  optimization  Mean-variance  analysis  CAPM Index. décimale : 658 Organisation des entreprises. Techniques du commerce Résumé : A key result of the capital asset pricing model (CAPM) is that the market portfolio—the portfolio of all assets in which each asset's weight is proportional to its total market capitalization—lies on the mean-variance-efficient frontier, the set of portfolios having mean-variance characteristics that cannot be improved upon. Therefore, the CAPM cannot be consistent with efficient frontiers for which every frontier portfolio has at least one negative weight or short position. We call such efficient frontiers “impossible,” and show that impossible frontiers are difficult to avoid. In particular, as the number of assets, n, grows, we prove that the probability that a generically chosen frontier is impossible tends to one at a geometric rate. In fact, for one natural class of distributions, nearly one-eighth of all assets on a frontier is expected to have negative weights for every portfolio on the frontier. We also show that the expected minimum amount of short selling across frontier portfolios grows linearly with n, and even when short sales are constrained to some finite level, an impossible frontier remains impossible. Using daily and monthly U.S. stock returns, we document the impossibility of efficient frontiers in the data. DEWEY : 658 ISSN : 0025-1909 En ligne : http://mansci.journal.informs.org/content/56/6.toc