ABSTRACTSome equilibrium prices in CAPM may be negative because of nonmonotonicity of preferences. We identify several sets of sufficient conditions for prices to be positive. The central conditions impose bounds on the investors' risk aversion. These bounds do not need to hold globally but only in a relevant range of portfolios or combinations of mean and standard deviation. The relevant range is specified on the basis of exogenous parameters and variables, and it must contain any endogenously determined equilibrium. The bounds on risk aversion ensure that the preferences for assets are sufficiently well‐behaved within the relevant range.