2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/98975Generally, 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 .Computational Engineering, Finance, and ScienceClassical Analysis and ODEsG.1.9; G.1.10; G.1.2; G.1.1; J.1; J.2; J.4text