  We introduce a faithful representation of the heavy tail multivariate
distribution of asset returns, as parsimonous as the Gaussian framework. Using
calculation techniques of functional integration and Feynman diagrams borrowed
from particle physics, we characterize precisely, through its cumulants of high
order, the distribution of wealth variations of a portfolio composed of an
arbitrary mixture of assets. The portfolio which minimizes the variance, i.e.
the relatively small risks, often increases larger risks as measured by higher
normalized cumulants and by the Value-at-risk.
