The statistics of asset allocation -- Univariate statistics -- Multivariate statistics -- Modeling the market -- Classical asset allocation -- Estimating the distribution of the market invariants -- Evaluating allocations -- Optimizing allocations -- Accounting for estimation risk -- Estimating the distribution of the market invariants -- Evaluating allocations -- Optimizing allocations.This encyclopedic, self-contained, detailed exposition spans all the steps of one-period allocation from the basics to the most advanced and recent developments. A variety of multivariate estimation methods are analyzed in depth, including non-parametric, maximum-likelihood under non-normal hypotheses, shrinkage, robust, etc., in addition to very general multivariate Bayesian techniques. Evaluation methods such as stochastic dominance, expected utility, value at risk and coherent measures are thoroughly analyzed in a unified setting and applied in a variety of contexts, including total return and benchmark allocation, prospect theory, etc. Portfolio optimization is presented with emphasis on estimation risk, which is tackled by means of Bayesian, resampling and robust optimization techniques. This work is both a reference for practitioners and a textbook for students. The only prerequisites are linear algebra and multivariate calculus. All the statistical tools, such as copulas, location-dispersion ellipsoids and matrix-variate distribution theory, are introduced from the basics. The same holds for the mathematical machinery, such as computational results from cone programming and heuristic arguments from functional analysis. Comprehension is supported by a large number of practical examples, real trading and asset management case studies, figures, geometrical arguments and MATLAB® applications, which can be freely downloaded from symmys.com.