The global financial crisis of 2007 – 2009 revealed the importance of systemic risk: the risk that may destabilize the global economy due to financial contagion. Accurate assessment of systemic risk would not only enable regulators to introduce suitable policies to mitigate the risk, but also allow individual institutions to monitor and mitigate their vulnerability. An effective measurement of systemic risk should be able to capture the co-movements between a financial system (or market) and individual financial institutions. One popular measure of systemic risk is CoVaR. In this talk, a methodology is proposed to compute dynamic forecasts of CoVaR semi-parametrically within the classical framework of multivariate extreme value theory (EVT). According to the definition, CoVaR can be viewed as a high quantile of a conditional distribution where the conditioning event corresponds to large losses of an institution. The idea of our methodology is to relate this conditional distribution to the tail dependence function. We develop an EVT-based framework to estimate CoVaR statically by combining parametric modelling of the tail dependence function to address the issue of data sparsity in the joint tail regions and semi-parametric univariate tail estimation techniques. The performance of the methodology is illustrated via simulation studies and real data examples.