Meucci Risk and Asset Allocation

2005
ISBN: 978-3-540-27904-4
Verlag: Springer
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 532 Seiten, eBook

Reihe: Springer Finance Textbooks

This encyclopedic, detailed exposition spans all the steps of one-period allocation from the foundations to the most advanced developments.Multivariate estimation methods are analyzed in depth, including non-parametric, maximum-likelihood under non-normal hypotheses, shrinkage, robust, and very general Bayesian techniques. Evaluation methods such as stochastic dominance, expected utility, value at risk and coherent measures are thoroughly discussed in a unified setting and applied in a variety of contexts, including prospect theory, total return and benchmark allocation.Portfolio optimization is presented with emphasis on estimation risk, which is tackled by means of Bayesian, resampling and robust optimization techniques.All the statistical and mathematical tools, such as copulas, location-dispersion ellipsoids, matrix-variate distributions, cone programming, are introduced from the basics. Comprehension is supported by a large number of figures and examples, as well as real trading and asset management case studies.
At symmys.com the reader will find freely downloadable complementary materials: the Exercise Book; a set of thoroughly documented MATLAB
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applications; and the Technical Appendices with all the proofs. More materials and complete reviews can also be found at symmys.com.

Zielgruppe

Graduate

Autoren/Hrsg.

Meucci, Attilio

Inhaltsverzeichnis

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.

Leseproben

5 Evaluating allocations (p.237)

An allocation is a portfolio of securities in a given market. In this chapter we discuss how to evaluate an allocation for a given investment horizon, i.e. a linear combination of the prices of the securities at the investment horizon.

In Section 5.1 we introduce the investor’s objectives. An objective is a feature of a given allocation on which the investor focuses his attention. For instance an objective is represented by .nal wealth at the horizon, or net gains, or wealth relative to some benchmark. The objective is a random variable that depends on the allocation. Although it is not possible to compute analytically the distribution of the objective in general markets, we present some approximate techniques that yield satisfactory results in most applications.

In Section 5.2 we tackle the problem of evaluating allocations, or more precisely the distribution of the objective relative to a given allocation. We do this by introducing the concept of stochastic dominance, a criterion that allows us to evaluate the distribution of the objective as a whole: when facing two allocations, i.e. the distributions of two di erent objectives, the investor will choose the one that is more advantageous in a global sense. Nevertheless, stochastic dominance presents a few drawbacks, most notably the fact that two generic allocations might not necessarily be comparable. In other words, the investor might not be able to rank allocations and thus make a decision regarding his investment. In the remainder of the chapter we discuss three broad classes of indices of satisfaction that have become popular among academics and practitioners.

As a consequence, in Section 5.3 we take a di erent approach. We summarize all the properties of a distribution in a single number: an index of satisfaction. If the index of satisfaction is properly de.ned the investor can in all circumstances choose the allocation that best suits him. Therefore we analyze a set of criteria that a proper satisfaction index should or could satisfy, such as estimability, consistency with stochastic dominance, constancy, homogeneity, translation invariance, additivity, concavity, risk aversion.

In the remainder of the chapter we discuss three broad classes of indices of satisfaction that have become popular among academics and practitioners.

In Section 5.4 we present the .rst of such indices of satisfaction: the certainty-equivalent. Based on the intuitive concept of expected utility, this has been historically the benchmark criterion to assess allocations. After introducing the de.nition of the certainty-equivalent and discussing its general properties, we show how to build utility functions that cover a wide range of situations, including the non-standard setting of prospect theory. Then we tackle some computational issues. Indeed, the computation of the certaintyequivalent involves integrations and functional inversions, which are in general impossible to perform. Therefore we present some approximate results, such as the Arrow-Pratt expansion. Finally, we perform a second-order sensitivity analysis to determine the curvature of the certainty-equivalent. The curvature is directly linked to the investor’s attitude toward diversi.cation and it is fundamental in view of computing numerical solutions to allocation problems.

Über Autor(innen)

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.