NBER

Thomas J. Brennan

School of Law, Northwestern University
East Chicago Avenue
Chicago, IL 60611

E-Mail: EmailAddress: hidden: you can email any NBER-related person as first underscore last at nber dot org
Institutional Affiliation: Northwestern University

NBER Working Papers and Publications

December 2008Impossible Frontiers
with Andrew W. Lo: w14525
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 derive conditions on asset-return means, variances, and covariances that yield impossible frontiers. With the exception of the two-asset case, we show that impossible frontiers are difficult to avoid. Moreover, as the number of assets n grows, we prove that the ...

Published: Thomas J. Brennan & Andrew W. Lo, 2010. "Impossible Frontiers," Management Science, INFORMS, vol. 56(6), pages 905-923, June. citation courtesy of

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