High-Order Moments and Cumulants of Multivariate Weibull Asset Returns Distributions : Analytical Theory and Empirical Tests: Ii

Using a family of multivariate Weibull distributions to parameterize the non-Gaussian properties of the distributions of asset returns, we offer exact formulas for the moments and cumulants of the distribution of returns of a portfolio made of an arbitrary composition of these assets. Using combinatorial and hypergeometric functions, we are in particular able to extend previous results to the case where the exponents of the Weibull distributions are different from asset to asset and in the presence of dependence between assets. These moments and cumulants can be used as consistent measures of risks to derive (in a companion paper) generalized optimal risk-return portfolio efficient frontiers