  Using a family of modified Weibull distributions, encompassing both
sub-exponentials and super-exponentials, to parameterize the marginal
distributions of asset returns and their natural multivariate generalizations,
we give exact formulas for the tails and for the moments and cumulants of the
distribution of returns of a portfolio make of arbitrary compositions 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. We treat in details the problem of risk minimization
using two different measures of risks (cumulants and value-at-risk) for a
portfolio made of two assets and compare the theoretical predictions with
direct empirical data. While good agreement is found, the remaining discrepancy
between theory and data stems from the deviations from the Weibull
parameterization for small returns. Our extended formulas enable us to
determine analytically the conditions under which it is possible to ``have your
cake and eat it too'', i.e., to construct a portfolio with both larger return
and smaller ``large risks''.
