# Existence of Equilibrium in CAPM

By Lars Tyge Nielsen

Journal of Economic Theory 52 (1990), 223-231

### Abstract

In the mean-variance capital asset pricing model (CAPM), nonmonotonicity of preferences may lead to satiation, and short-selling as well as satiation may lead to non-existence of equilibrium. This paper identifies several sets of sufficient conditions for equilibrium to exist. The nature of the central conditions is to impose bounds on the investors’ degree of risk aversion, as measured by the marginal rate of substitution between mean and standard deviation of return. These bounds do not need to hold globally but only in a relevant range of portfolios or combinations of mean and standard deviation.

Journal of Economic Litterature Classification Numbers: 021, 026, 521.