  Generally, in the financial literature, the notion of quadratic VaR is
implicitly confused with the Delta-Gamma VaR, because more authors dealt with
portfolios that contains derivatives instruments.
  In this paper, we postpone to estimate the Value-at-Risk of a quadratic
portfolio of securities (i.e equities) without the Delta and Gamma greeks, when
the joint log-returns changes with multivariate elliptic distribution. We have
reduced the estimation of the quadratic VaR of such portfolio to a resolution
of one dimensional integral equation. To illustrate our method, we give special
attention to the mixture of normal and mixture of t-student distribution. For
given VaR, when joint Risk Factors changes with elliptic distribution, we show
how to estimate an Expected Shortfall .
