Multivariate Symmetry and Asymmetry

Serfling, Robert

doi:10.1002/9781118445112.stat00821

Cited by 13 publications

(12 citation statements)

References 45 publications

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“…so the symmetry assumption made here represents the most direct non-parametric extension of univariate symmetry; see Serfling (2006) for more concepts of multivariate symmetry. The class of distributions encompassed by Assumption 1 is very large and includes elliptically symmetric distributions, which play a very important role in mean-variance analysis because they guarantee full compatibility with expected utility maximization regardless of investor preferences (Berk, 1997;Chamberlain, 1983;Owen and Rabinovitch, 1983).…”

Section: Mlr Frameworkmentioning

confidence: 99%

Multivariate Tests of Mean-Variance Efficiency and Spanning With a Large Number of Assets and Time-Varying Covariances

Gungor

Luger

2016

Journal of Business & Economic Statistics

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We develop a finite-sample procedure to test for mean-variance efficiency and spanning without imposing any parametric assumptions on the distribution of model disturbances. In so doing, we provide an exact distribution-free method to test uniform linear restrictions in multivariate linear regression models. The framework allows for unknown forms of non-normalities, and time-varying conditional variances and covariances among the model disturbances. We derive exact bounds on the null distribution of joint F statistics in order to deal with the presence of nuisance parameters, and we show how to implement the resulting generalized non-parametric bounds tests with Monte Carlo resampling techniques. In sharp contrast to the usual tests that are not computable when the number of test assets is too large, the power of the new test procedure potentially increases along both the time and cross-sectional dimensions. JEL classification: C12, C15, C33, G11, G12 Bank classification: Econometric and statistical methods; Asset pricing; Financial markets RésuméLes auteurs élaborent une procédure permettant de tester, en échantillon fini, si un portefeuille est efficient dans le plan moyenne-variance et si son efficience peut être améliorée par l'addition d'actifs sans qu'il soit nécessaire de fixer par hypothèse la distribution des erreurs du modèle. Leur méthode non paramétrique peut servir à tester de façon exacte des restrictions uniformes linéaires dans le cadre de modèles de régression linéaires multivariés. La procédure autorise des formes inconnues de distribution autres que la loi normale ainsi que la variabilité dans le temps des variances et covariances conditionnelles des erreurs. Les auteurs calculent des bornes exactes pour la distribution conjointe des statistiques de Fisher sous l'hypothèse nulle en présence de paramètres de nuisance. Ils montrent aussi comment mettre en oeuvre, au moyen de techniques de rééchantillonnage à la Monte-Carlo, les tests de bornes non paramétriques généralisés qui en résultent. La puissance de la nouvelle procédure peut s'accroître avec l'allongement de la série temporelle et la hausse du nombre des actifs. Cette propriété tranche avec les tests habituels, qui deviennent inexécutables si le nombre d'actifs est trop élevé. Classification JEL : C12, C15, C33, G11, G12 Classification de la Banque : Méthodes économétriques et statistiques; Évaluation des prix des actifs; Marchés financiers Non-technical summaryMean-variance analysis plays an important role in modern investment theory as it provides a simple and intuitive basis for optimal portfolio allocation. In this framework, the merits of alternative portfolios are compared in terms of their expected return and variance of return. The optimal solution to the portfolio allocation problem implies that the investor holds a mean-variance efficient portfolio; i.e., a portfolio with the lowest variance for a given expected return, or more appropriately, with the highest expected return for a given level of variance. The mean-varia...

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Section: Mlr Frameworkmentioning

confidence: 99%

Multivariate Tests of Mean-Variance Efficiency and Spanning With a Large Number of Assets and Time-Varying Covariances

Gungor

Luger

2016

Journal of Business & Economic Statistics

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“…We thus recall several definitions in probability theory and convex optimization. [225]) Let ξ ∈ R r be a random variable, whose probability density function is f : R r → R. If f(ξ − θ) = f(θ − ξ), then ξ has a distribution that is centrally symmetric about θ ∈ R r . [31]) Let x ∈ R n be the decision variables and A i ∈ R (n i −1)×r , H ∈ R p×r and h, c i ∈ R r , β i ∈ R n i −1 , g ∈ R p , d i ∈ R (∀i ∈ {1, .…”

Section: Probabilistic Approachmentioning

confidence: 99%

The multiplicative weights update algorithm for mixed integer nonlinear programming: theory, applications, and limitations

Mencarelli

2018

4OR-Q J Oper Res

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“…As in the GRS framework, we assume that the disturbance vectors ε t in (1) are independently distributed over time, conditional on F. We do not require the disturbance vectors to be identically distributed, but we do assume that they remain symmetrically distributed See Serfling (2006) for more on multivariate symmetry. The class of distributions encompassed by the diagonal symmetry condition includes elliptically symmetric distributions, which play a very important role in mean-variance analysis because they guarantee full compatibility with expected utility maximization regardless of investor preferences; see Chamberlain (1983), Owen andRabinovitch (1983), andBerk (1997).…”

Section: Statistical Frameworkmentioning

confidence: 99%

Testing Linear Factor Pricing Models With Large Cross Sections: A Distribution-Free Approach

Gungor

Luger

2013

Journal of Business & Economic Statistics

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We develop a finite-sample procedure to test the beta-pricing representation of linear factor pricing models that is applicable even if the number of test assets is greater than the length of the time series. Our distribution-free framework leaves open the possibility of unknown forms of non-normalities, heteroskedasticity, time-varying correlations, and even outliers in the asset returns. The power of the proposed test procedure increases as the time-series lengthens and/or the cross-section becomes larger. This stands in sharp contrast to the usual tests that lose power or may not even be computable if the crosssection is too large. Finally, we revisit the CAPM and the Fama-French three factor model. Our results strongly support the mean-variance efficiency of the market portfolio. JEL classification: C12, C14, C33, G11, G12 Bank classification: Econometric and statistical methods; Financial markets RésuméLes auteurs élaborent une procédure permettant de tester, en échantillon fini, la représentation des coefficients bêta donnés par les modèles linéaires d'évaluation factorielle, et ce, même si le nombre des actifs dépasse celui des valeurs de la série chronologique. Leur cadre autorise des formes inconnues de distribution autres que la loi normale ainsi que la présence d'hétéroscédasticité, de structures de corrélation variables dans le temps, voire de rendements aberrants. La puissance de la procédure s'accroît avec l'allongement de la série chronologique et la hausse du nombre des actifs. Cette propriété tranche avec les limites des tests habituels, qui perdent de leur puissance ou peuvent même devenir inexécutables si le nombre des actifs est trop élevé. Pour finir, les auteurs réexaminent le modèle d'évaluation des actifs financiers et le modèle trifactoriel de Fama et French. Leurs résultats indiquent clairement que le portefeuille de marché se situe sur la frontière efficiente dans le plan moyenne-variance.

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Multivariate Symmetry and Asymmetry

Cited by 13 publications

References 45 publications

Multivariate Tests of Mean-Variance Efficiency and Spanning With a Large Number of Assets and Time-Varying Covariances

Multivariate Tests of Mean-Variance Efficiency and Spanning With a Large Number of Assets and Time-Varying Covariances

The multiplicative weights update algorithm for mixed integer nonlinear programming: theory, applications, and limitations

Testing Linear Factor Pricing Models With Large Cross Sections: A Distribution-Free Approach

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