© 2005

Risk and Asset Allocation

  • The only book that truly discusses in a self-contained and general way all the practical and theoretical aspects of one-period asset allocation, i.e. market Modeling, invariants estimation, portfolia evaluation, and portfolio optimization in the presence of estimation risk

  • The choice of the subjects is "bottom-up", the approach is "top-down"

  • Software based, many of the exercises simulate in Matlab the solution to practical problems and can be downloaded from the book's web-site


Part of the Springer Finance book series (FINANCE)

Table of contents

  1. Front Matter
    Pages I-XXVI
  2. The statistics of asset allocation

    1. Front Matter
      Pages 1-1
    2. Attilio Meucci
      Pages 3-31
    3. Attilio Meucci
      Pages 33-99
    4. Attilio Meucci
      Pages 101-166
  3. Classical asset allocation

    1. Front Matter
      Pages 167-167
    2. Attilio Meucci
      Pages 237-300
    3. Attilio Meucci
      Pages 301-359
  4. Accounting for estimation risk

    1. Front Matter
      Pages 361-361
    2. Attilio Meucci
      Pages 389-416
    3. Attilio Meucci
      Pages 417-461
  5. Back Matter
    Pages 463-532

About this book


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


Asset Allocation Asset Management MATLAB Matrix Multivariate statistics Portfolio Portfolio Optimization Random variable Resampling linear algebra optimization

Authors and affiliations

  1. 1.Lehman Brothers, Inc.New YorkUSA

About the authors

Attilio Meucci holds a BA summa cum laude in Physics and a PhD in Mathematics from the University of Milan, an MA in Economics from Bocconi University in Milan, and is CFA chartholder.

Attilio Meucci is a vice president at Lehman Brothers, Inc., New York, in the fixed-income research division. Previously, the author was a trader at Relative Value International, a hedge fund in Greenwich, CT that trades in equities and fixed-income securities worldwide. Previously, he was a consultant in the Milan office of Bain & Co., where he designed tools of personal financial planning, credit-and market-risk management, portfolio insurance, tactical and strategic asset allocation.

Attilio Meucci is the author of several publications in mathematics and finance and has taught graduate courses on Asset Allocation and Risk Management worldwide.

Bibliographic information

Industry Sectors
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From the reviews:

This exciting new book takes a fresh look at asset allocation and offers up a masterly account of this important subject. The quantitative emphasis and included MATLAB software make it a must-read for the mathematically oriented investment professional.

Peter Carr, Head of Quantitative Research, Bloomberg LP, Director of Masters in Mathematical Finance program, NYU

Meucci’s Risk and Asset Allocation is one of those rare books that takes a completely fresh look at a well-studied problem, optimal financial portfolio allocation based on statistically estimated models of risk and expected return. Designed for graduate students or quantitatively oriented asset managers, Meucci provides a sophisticated and integrated treatment, from investment theory, to optimization methods, to statistical analysis of multi-variate return data, through computational implementation of the results. This is rigorous and relevant!

Darrel Duffie, Professor of Graduate Business School, Stanford University

A wonderful book! Mathematically rigorous and yet practical, heavily illustrated with graphs and worked examples, Attilio Meucci has written a comprehensive treatment of asset allocation starting from statistical concepts, covering investment primitives, and leading to portfolio optimization in a Bayesian context with parameter uncertainty.

Bob Litterman, Head of Quantitative Resources, Goldman Sachs Asset Management

This book takes the reader on a journey through portfolio management starting with the basics and reaching some fascinating terrain. Attilio Meucci shows a real talent for explaining the most difficult of subjects in a very clear manner.

Paul Wilmott,

"This book presents a detailed and well-explained introduction to one-period asset allocation techniques … . the book gives an impressive and comprehensive introduction to static one-period asset allocation. It explains most of the concepts intuitively and with a minimal mathematical machinery. … For practitioners, the book serves as a theoretical basis of their actual work. For students of finance and economics it gives a self-contained overview of the main quantitative concepts in the subject." (Ludger Overbeck, SIAM Review, Vol. 48 (3), 2006)

"This book delves into the classical mathematics of portfolio optimization with a few nods to more recent developments in risk measurement such as value-at-risk and copulas. … For anyone with an interest in the mathematics of portfolio optimization, the book is certainly worth a look. … The author covers a wealth of statistical and optimization techniques that are worth reading about." (, May, 2006)

"The book offers a wide exposition of the main approaches to asset allocation, starting from the classical models up to the recent developments in portfolio management. … By virtue of the sequential structure of the subjects and the simple but efficacious mathematical treatment, the monograph is useful for graduate students and quantitatively-oriented practitioners too. … The book is complemented by online resources, consisting of software applications performed by MATLAB … ." (Emilia Di Lorenzo, Zentralblatt MATH, Vol. 1102 (4), 2007)