In this paper, a sensitivity analysis using pair-copula decomposition of multivariate dependency models is performed on estimates of value-at-risk (VaR) and conditional value-at-risk (CVaR). To illustrate the results, we use four financial share portfolios selected to exemplify this purpose. For each share, we calculate filtered log returns using autoregressive moving average-generalized autoregressive conditional heteroscedasticity models and study their dependence. We analyze how selecting pairs of assets to define vines prior to pair-copula decomposition affects the estimated VaR and CVaR. Further, using bootstrap confidence intervals, we compare the results of different risk measures obtained by employing alternative measures of dependence to select the order in which the drawable vine (D-vine) is defined in different portfolios. Moreover, we carry out a simulation study to analyze the finite sample properties of the different criteria for selecting the pair-copula decomposition associated with the D-vine. We find some differences between the results obtained for VaR and CVaR.