This paper studies capital adequacy rules based on Value-at-Risk (VaR), leverage ratios, and stress testing. VaR is the basis of Basel II, and all three approaches are proposed in Basel III. This paper makes three contributions to the literature. First, we prove that these three rules provide an incentive to increase the probability of catastrophic financial institution failure. Collectively, these rules provide an incentive to increase (not decrease) systemic risk. Second, we argue that an unintended consequence of the Basel II VaR capital adequacy rules was the 2007 credit crisis. Third, we argue that to reduce systemic risk, a new capital adequacy rule is needed. One that is based on a risk measure related to the conditional expected loss given insolvency.