We develop a general approach for stress testing correlations of financial asset portfolios. Based on methods from interest rate modelling, the correlation matrix of asset returns is specified in a parametric form, where correlations are represented as a function of risk factors, such as country and industry factors. A sparse factor structure linking assets and risk factors is built using Bayesian variable selection methods. Regular calibration yields a joint distribution of economically meaningful stress scenarios of the factors. As such, the method also lends itself as a reverse stress testing framework: using the Mahalanobis distance or Highest Density Regions (HDR) on the joint risk factor distribution allows to infer worst-case correlation scenarios. We give examples of stress tests on a large portfolio of European and North American stocks. In an outlook, I will present some ideas on how to aggregate existing risk factors giving rise to further risk scenarios.