Equilibrium Risk Premia for Risk Seekers
31 Pages Posted: 3 Feb 2005
Date Written: February 2006
Several landmark papers (Friedman and Savage 1948, Markowitz 1952, Kahneman and Tversky 1979, Tversky and Kahneman 1992) have suggested that utility functions of individual investors have convex regions corresponding to risk seeking behavior. At the same time, the degree of individual risk aversion required to explain aggregate equity returns must be high (the "equity premium puzzle" of Mehra and Prescott 1985). Can both be true? Can high aggregate risk premium be consistent with individual investors exhibiting risk seeking behavior? We study aggregation properties in an economy where all agents are risk seeking. Under perfect competition when all agents are homogeneous, we prove that although individual agents have concave indifference curves (corresponding to risk seeking), the aggregate economy has a convex(linear) indifference curve that corresponds to risk aversion. When agents are heterogeneous in their initial endowment, aggregating risk seeking individual agents under perfect competition leads to an aggregate indifference curve that is strictly convex indicating that the economy demands a risk premium. We prove that the converse is also true. For an economy that in the aggregate exhibits risk aversion we can construct an economy of all risk seeking agents that in the aggregate produces the given indifference curve.
Keywords: Risk Aversion, Risk-Seeking, Investor Sentiment, Risk Premium
JEL Classification: G10, D11, D80
Suggested Citation: Suggested Citation