Some aggregation formulas that are used in the insurance and financial industry implicitly assume that the knowledge of marginal distributions and of some measure of dependence (e.g., the average correlation) leads to an appropriate estimation of the Value-at-Risk (VaR). We challenge this idea by investigating under which conditions the unconstrained VaR bounds (which are the maximum and minimum VaR when only the knowledge on the marginal distributions of the components is assumed) coincide with the VaR bounds when in addition one has information on some measure of dependence (e.g., Pearson correlation, Spearman's rho or Kendall's tau). We show that correlation has typically no effect on the highest possible VaR whereas it impacts the lowest possible VaR. To reduce the VaR upper bound, we show that additional tail information is needed. Additional results for TVaR and Range VaR supplement the study.