Levy and Roll (Review of Financial Studies, 2010) have recently revived the debate related to the market portfolio's efficiency suggesting that it may be mean-variance efficient after all. This paper develops an alternative test of portfolio mean-variance efficiency based on the realistic assumption that all assets are risky. The test is based on the vertical distance of a portfolio from the efficient frontier. Monte Carlo simulations show that our test outperforms the previous mean-variance efficiency tests for large samples since it produces smaller size distortions for comparable power. Our empirical application to the US equity market highlights that the market portfolio is not mean-variance efficient, and so invalidates the zerobeta CAPM.