BFS 2002

Poster Presentation

This paper considers the effect of nonnormality on the unconditional inference of the market model when the joint distribution of asset returns and a given portfolio return is elliptically distributed. Based on the conditional covariance matrix formula by Chu (1973) in the class of elliptical distributions, we evaluate the asymptotic covariance matrix of the maximum likelihood estimator derived under the joint normality when the joint distribution is in fact in the class of elliptical distributions as well as in the class of scale mixtures of multivariate normal distributions. The effect of nonnormality on the asymptotic covariance matrix of the maximum likelihood estimator is shown in terms of the weighting function of the representation of the underlying probability density function as an integral of a set of multivariate normal probability density functions. The properties of marginal and conditional distributions in the class of elliptical distributions are made use of to derive the results.