This paper examines two qualitative rules of thumb, frequently invoked in discussions of bank regulatory policy. The first, that equity holders prefer more risk to less, derives from a result in option pricing theory, that an option's value increases monotonically with the riskiness of the underlying asset. This result is shown to depend on very restrictive assumptions regarding the underlying assets return distribution and the type of option being considered. These restrictive assumptions do not generally obtain in practice. The second rule of thumb is that bondholders' and deposit insurers' interests are aligned. The paper shows that, in fact, their interests can diverge in the sense that bondholders and deposit insurers will not necessarily agree on the relative riskiness of different banks or bank portfolios. The conclusion of this paper is that rules of thumb can be misleading. Furthermore, the concept of risk is shown to be model and agent specific.