Robust reverse engineering of cross-sectional returns and improved portfolio allocation performance using the CAPM

Following Levy and Roll [2010], we posit that the market portfolio is the efficient tangent Markowitz portfolio, i.e., it is mean-variance efficient. We then reverse engineer the expected returns and variance terms with constraints imposed by empirical data on a hierarchy of asset baskets. This extends the results of Levy and Roll [2010] and shows that only minor adjustments of the input parameters are needed, well within the statistical uncertainties. Applying the Levy-Roll procedure to the 25 Fama-French portfolios sorted by sizes and book-to-market values, we check the consistency of the Levy-Roll approach by investigating how the adjusted stock returns of specific stocks are modified when varying the basket of stocks they belong to. We test the dynamical performance of the Levy-Roll procedure over the period from January 1992 to December 2009 and find that the corresponding dynamical portfolio allocation performs significantly better than standard benchmarks. CAPM, Mean-Variance Portfolio Optimization, Constrained Optimization, Fama-French, Value-Size Portfolios, Dynamical Allocation, Expected Returns