This study reinvestigates the theoretical relationship between competition in banking and banks' exposure to risk of failure. There is a large existing literature that concludes that when banks are confronted with increased competition, they rationally choose more risky portfolios. We briefly review this literature and argue that it has had a significant influence on regulators and central bankers, causing them to take a less favorable view of competition and encouraging anti-competitive consolidation as a response to banking instability. We then show that existing theoretical analyses of this topic are fragile, since they do not detect two fundamental risk-incentive mechanisms that operate in exactly the opposite direction, causing banks to aquire more risk per portfolios as their markets become more concentrated. We argue that these mechanisms should be essential ingredients of models of bank competition.