Financial market equilibria with heterogeneous agents: CAPM and market segmentation

Abstract

We consider a single-period nancial market model with normally distributed returns and the presence of heterogeneous agents. Specically, some investors are classical Expected Utility maximizers whereas some others follow Cumulative Prospect Theory. Using well-known functional forms for the preferences, we analytically prove that a Security Market Line Theorem holds. This implies that Capital Asset Pricing Model is a necessary (though not sucient) requirement in equilibria with positive prices. We correct some erroneous results about existence of equilibria with Cumulative Prospect Theory investors which had appeared in the last few years and we give sucient conditions for an equilibrium to exist. To circumvent the complexity arising from the interaction of heterogeneous agents, we propose a segmented-market equilibrium model where segmentation is endogenously determined.

A note on the existence of CAPM equilibria with homogeneous cumulative prospect theory preferences

“…However,R 1 does not converge in any natural sense, and (7) is no more helpful since that equation is based on returns. Similarly to Del Vigna (2011), Proposition 2, we have…”

The Capital Asset Pricing Model

“…Despite relaxing one of the assumptions of the conventional CAPM, the introduction of investor heterogeneity preserves certain elements of asset pricing orthodoxy even as it invites theoretical innovation. The segmentation of a market between traders following divergent theories of welfare maximization-namely, expected utility and cumulative prospect theory [132]-nevertheless preserves the security market line, one of the signatures of the conventional CAPM [133]. By the same token, dividing traders into distinct cohorts of arch-rational "fundamentalists" and technical "trend followers" yields an ambitious evolutionary CAPM "characterized by significantly decaying autocorrelation, and positive correlation between, price volatility and trading volume" [134] (p. 185).…”

Myopic loss aversion, reference point, and money illusion

“…De , Levy and Levy (2004), Del Vigna (2013) studied single-period portfolio selection problems from the standpoint of CPT, assuming the returns of risky assets to follow normal distributions. Barberis and Huang (2008b) considered similar problems, but allowing for an additional risky asset that follows a Bernoulli distribution.…”