 (Im)Possible Frontiers: A CommentMoshe Levy () and Richard Roll Critical Finance Review, 2015, vol. 4, issue 1, 139-148 Abstract: A totally positive mean-variance efficient aggregate market portfolio — one with no negative weights — is the key equilibrium feature of the Capital Asset Pricing Model (CAPM). Brennan and Lo (2010) designate an efficient frontier as “impossible†when every efficient portfolio has at least one negative weight. For randomly drawn covariance matrices, they prove that the probability of an impossible frontier approaches 1 as the number of assets grows. Impossible frontiers are also invariably found with empirical sample parameters, regardless of the sampling method. These results might seem like a deadly blow to the CAPM. However, we show here that slight variations in sample parameters, well within estimation error bounds, can lead to frontiers with positive portfolio segments. Parameters producing possible frontiers are somewhat like rational numbers on the real line: they occupy a zero-measure of parameter space, but there is always one close by. Thus, starting from an impossible frontier, slight changes in asset prices, as they converge to an economic equilibrium, deliver a possible frontier, consistent with the CAPM. Keywords: Mean-variance analysis; CAPM; Portfolio optimization; Short selling; Reverse optimization (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:now:jnlcfr:104.00000015 Access Statistics for this article More articles in Critical Finance Review from now publishers |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.