Regulatory stress-testing is an important tool for ensuring banking system health in many countries around the world. Current methodologies ensure banks are well capitalized against the scenarios in the test, but it is unclear how resilient banks will be to other plausible scenarios. This paper proposes a new methodology for choosing scenarios that uses a measure of systemic risk with Correlation Pursuit variable selection, and Sliced Inverse Regression factor analysis, to select variables and create factors based on their ability to explain variation in the systemic risk measure. The main result is under appropriate regularity conditions, when the banking system is well capitalized against stress-scenarios based on movements in the factors, then an approximation of systemic risk is low, i.e. the banking system will be well capitalized against the other plausible scenarios that could affect it with high probability. The paper also shows there are circumstances when several scenarios may be required to achieve systemic risk objectives. The methodology should be useful for regulatory stress-testing of banks. Although not done in this paper, the methodology can potentially be adapted for stress-testing of other financial firms including insurance companies and central counterparties.