In this paper systemic risk will be meant as risk of breakdown or a major dysfunction in a financial system. The term is used by some researchers to include the potential insolvency of a major player or a component of the financial system. There are many approaches to measure systemic risk (Hansen 2013), but the main distinction entails financial soundness indicators and advanced systemic risk models. The advanced models are based on the statistical multivariate distributions or on the stochastic processes (Benoit, Colliard, Hurlin i Pérignon 2015). The development of these models is observed after the financial crisis of 2007-2008 and significantly after 2010. In the paper the Conditional Value-at-Risk (CoVaR) proposed by Adrian and Brunnermeier (2011, 2016) will be used to assess systemic risk. Two methods, i.e. the conditional (DCC-GARCH) and unconditional (quantile regression) will be applied for these estimations. As a proxy of a financial system a construction of an index, free from disadvantages as opposed to the stock market index, will be proposed by the author. The empirical analysis for the Polish financial system will contain: a model risk analysis, comparison of results for selected measure of systemic risk and estimation methods, an evaluation of results (back testing and a financial condition assessment of financial institutions).