Individual Vs. Aggregate Preferences: The Case of a Small Fish in a Big Pond
Management Science 59 (2) 2013
41 Pages Posted: 28 Feb 2008 Last revised: 23 Apr 2017
Date Written: January 31, 2008
Risk preferences of individual investors can be very different from the aggregate economy's preference for risk. To demonstrate this, we investigate aggregate properties of an economy where all investors have convex utility functions corresponding to risk seeking behavior and we investigate the popular Friedman-Savage S-shaped utility function. We prove that an economy consisting of risk seeking agents can lead to an aggregate economy that is risk averse. We prove that the converse is also true. For an aggregate economy that exhibits risk aversion we can construct an economy of all risk seeking agents that in the aggregate produces the given risk averse indifference curve. That is, an economy demanding a risk premium can be formed from individuals who do not demand such compensation. This is the first paper to study aggregation of Friedman-Savage utility. When individuals have an S-shaped utility function that is risk averse over low consumption levels, risk seeking over mid-levels of consumption and risk averse over high levels of consumption, the risk seeking region vanishes in the aggregate. The aggregate economy is solely risk averse. These findings present an important challenge to the use of unusual utility functions in describing aggregate data since the unusual characteristics of the utility function can vanish in the aggregate.
Keywords: Risk aversion, risk seeking, investor sentiment, risk premium
JEL Classification: G10, D11, D80
Suggested Citation: Suggested Citation