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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. The authors call such efficient frontiers "Impossible", and derive conditions on asset-return means, variances, and covariance's that yield impossible frontiers.
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