Value at Risk (VaR) and Average Value at Risk (AVaR) are among the most widely-used risk measures by market participants to assess the risk of individual financial firms and institutions. Despite their popularity, both measures fail to account for spillover effects between firms. To address this limitation, the CoVaR (Conditional Value at Risk) measure was introduced, which defines the VaR of a financial system conditional on the state of another institution. The traditional approach to estimating CoVaR involves a regression model combined with a quantile method to estimate the model’s parameters. This paper proposes a composite quantile regression method to enhance the accuracy of CoVaR estimation. We apply this methodology to several U.S. companies across various sectors, including finance, consumer goods, energy, industry, and technology. An analysis of the out-of-sample forecast accuracy using two popular backtesting criteria demonstrates that the composite quantile method provides more accurate CoVaR estimates than the standard quantile method. All computation codes are freely available in both R and MATLAB.