SRISK methodology recently proposed in the literature is refined and extended. The refinement is to define systemic risk using a formalised stress testing framework including a stress function. Baseline risk and the stress risk are in terms of the ordinary and stressed expectation. Stressed expectation is expectation computed under a hypothetical stress, modelled with the stress function and scenarios. Systemic stress is defined in terms of a stress function and systemic scenarios impacting on a number of firms or financial entities. Stress functions are chosen by the practitioner and typically exaggerate undesirable extreme outcomes. Properties and characterisations of stress and stress related quantities are displayed and explored. Application is made to the study of the stability of Australian banks using daily time series data.