EconPapers    
Economics at your fingertips  
 

(Im)Possible Frontiers: A Comment

Moshe 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)
JEL-codes: G11 G12 (search for similar items in EconPapers)
Date: 2015
References: Add references at CitEc
Citations: View citations in EconPapers (1) Track citations by RSS feed

Downloads: (external link)
http://dx.doi.org/10.1561/104.00000015 (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

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
Bibliographic data for series maintained by Alet Heezemans ().

 
Page updated 2019-10-10
Handle: RePEc:now:jnlcfr:104.00000015