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 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 shortselling across frontier portfolios grows linearly with n, and even when shortsales 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.
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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number
14525.
Length: Date of creation: Dec 2008 Date of revision: Handle: RePEc:nbr:nberwo:14525
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Find related papers by JEL classification: G1 - Financial Economics - - General Financial Markets G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions G12 - Financial Economics - - General Financial Markets - - - Asset Pricing G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies G23 - Financial Economics - - Financial Institutions and Services - - - Pension Funds; Other Private Financial Institutions G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Capital and Ownership Structure
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