風(fēng)險和資產(chǎn)配置

前言

In an asset allocation problem the investor, who can be the trader, or thefund manager, or the private investor, seeks the combination of securitiesthat best suit their needs in an uncertain environment. In order to determinethe optimum allocation, the investor needs to model, estimate, assess andmanage uncertainty.The most popular approach to asset allocation is the mean-variance frame-work pioneered by Markowitz, where the investor aims at maximizing theportfolio's expected return for a given level of variance and a given set of investment constraints. Under a few assumptions it is possible to estimate themarket parameters that feed the model and then solve the ensuing optimization problem.More recently, measures of risk such as the value at risk or the expectedshortfall have found supporters in the financial community. These measuresemphasize the potential downside of an allocation more than its potential benefits. Therefore, they are better suited to handle asset allocation in modern,highly asymmetrical markets.All of the above approaches are highly intuitive. Paradoxically, this can bea drawback, in that one is tempted to rush to conclusions or implementations,without pondering the underlying assumptions.For instance, the term "mean-variance" hints at the identification of theexpected value with its sample counterpart, the mean. Sample estimates makesense only if the quantities to estimate are market invariants, i.e. if they displaythe same statistical behavior independently across different periods. In equitylike securities the returns are approximately market invariants: this is why themean-variance approach is usually set in terms of returns. Consider insteadan investment in a zero-coupon bond that expires, say, in one month. Thetime series of the past monthly returns of this bond is not useful in estimatingthe expected value and the variance after one month, which are known withcertainty: the returns are not market invariants.

內(nèi)容概要

本書是一部全面介紹風(fēng)險與資產(chǎn)分配的統(tǒng)計教材。多變量估計的方法分析深入，包括非正態(tài)假設(shè)下的無參和極大似然估計，壓縮理論、魯棒以及一般的貝葉斯技巧。作者用獨到的眼光講述了資產(chǎn)分配，給出了該學(xué)科的精華。重點突出，包含了MATLAB數(shù)學(xué)工具軟件，對于以數(shù)學(xué)為中心的投資行業(yè)來說該書是一本必選書。目次：資產(chǎn)分配統(tǒng)計學(xué)；經(jīng)典資產(chǎn)分配；估計風(fēng)險的計算；附錄。

作者簡介

作者：(美國)梅烏奇(Meucci，Attilio)

書籍目錄

Preface Audience and style Structure of the work A guided tour by means of a simplistic example Acknowledgments Part I The statistics of asset allocation   1 Univariate statistics     1.1 Building blocks     1.2 Summary statistics     1.3 Taxonomy of distributions     1.T Technical appendix     1.E Exercises   2 Multivariate statistics     2.1 Building blocks     2.2 Factorization of a distribution     2.3 Dependence     2.4 Shape summary statistics     2.5 Dependence summary statistics     2.6 Taxonomy of distributions     2.7 Special classes of distributions     2.T Technical appendix     2.E Exercises   3 Modeling the market     3.1 The quest for invariance     3.2 Projection of the invariants to the investment horizon.     3.3 From invariants to market prices     3.4 Dimension reduction     3.5 Case study: modeling the swap market     3.T Technical appendix     3.E Exercises part II Classical asset allocation   4 Estimating the distribution of the market invariants     4.1 Estimators     4.2 Nonparametric estimators     4.3 Maximum likelihood estimators     4.4 Shrinkage estimators     4.5 Robustness     4.6 Practical tips     4.T Technical appendix     4.E Exercises   5 Evaluating allocations     5.1 Investor's objectives     5.2 Stochastic dominance     5.3 Satisfaction     5.4 Certainty-equivalent (expected utility)     5.5 Quantile (value at risk)     5.6 Coherent indices (expected shortfall)     5.T Technical appendix     5.E Exercises   6 Optimizing allocations part III Accounting for estimation risk   7 Estimating the distribution of the market invariants   8 Evaluating allocations   9 Optimizing allocations Part IV Appendices   A Linear algebra   B Functional Analysis References List of figures Notation Index

章節(jié)摘錄

插圖：The financial markets contain many sources of risk. When dealing with severalsources of risk at a time we cannot treat them separately: the joint structureof multi-dimensionai randomness contains a wealth of information that goesbeyond the juxtaposition of the information contained in each single variable.In this chapter we discuss multivariate statistics. The structure of thischapter reflects that of Chapter 1: to ease the comprehension of the multi-variate case refer to the respective section in that chapter. For more on thissubject see also references such as Mardia, Kent, and Bibby （1979）, Press（1982） and Morrison （2002）.In Section 2.1 we introduce the building blocks of multivariate distributionswhich are direct generalizations of the one-dimensional case. These include thethree equivalent representations of a distribution in terms of the probabilitydensity function, the characteristic function and the cumulative distributionfunction.In Section 2.2 we discuss the factorization of a distribution into its purelyunivariate components, namely the marginal distributions, and its purely jointcomponent, namely the copula. To present copulas we use the leading exampleof vanilla options.In Section 2.3 we introduce the concept of independence among randomvariables and the related concept of conditional distribution.In Section 2.4 we discuss the location summary statistics of a distributionsuch as its expected value and its mode, and the dispersion summary statisticssuch as the covariance matrix and the modal dispersion. We detail the geo- metrical representations of these statistics in terms of the location-dispersionellipsoid, .and their probabilistic interpretations in terms of a multivariateversion of Chebyshev's inequality. We conclude introducing more summarystatistics such as the multivariate moments, which provide a deeper insightinto the shape of a multivariate distribution.

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