We use a flexible semi‐parametric estimation approach and a sample of 7,227 U.S., U.K., and Canadian banks for 2009–2015 to provide evidence that banking stability is non‐linearly determined by competition. We show that stability is not monotonic against competition, and may increase and decrease at high competition, has a mixed behaviour at medium competition, and increases at low competition. This non‐monotonic stability behaviour at different competition levels is attributed to the intervention quality, which is found to be an important determinant of the competition–stability relation. It is non‐linearly related to and being revised at different competition levels. As intervention is a policy variable, its level can be adjusted to reduce the competition effects on stability. We illustrate that for the U.S. banking sector, the intervention quality has to hedge these competition effects. Regulators should treat intervention quality as a “hedging instrument” against the destabilizing competition effects.