The global financial crisis has highlighted the limitations of risk-sensitive bank capital ratios. To tackle this problem, the Basel III regulatory framework has introduced a minimum leverage ratio, defined as a bank's Tier 1 capital over an exposure measure, which is independent of risk assessment. Using a medium sized DSGE model that features a banking sector, financial frictions and various economic agents with differing degrees of creditworthiness, we seek to answer three questions: 1) How does the leverage ratio behave over the cycle compared with the risk-weighted asset ratio? 2) What are the costs and the benefits of introducing a leverage ratio, in terms of the levels and volatilities of some key macro variables of interest? 3) What can we learn about the interaction of the two regulatory ratios in the long run? The main answers are the following: 1) The leverage ratio acts as a backstop to the risk-sensitive capital requirement: it is a tight constraint during a boom and a soft constraint in a bust; 2) the net benefits of introducing the leverage ratio could be substantial; 3) the steady state value of the regulatory minima for the two ratios strongly depends on the riskiness and the composition of bank lending portfolios.