Risk Aversion and the Value of Information

Abstract

Risk Aversion and the Value of Information ABSTRACT A local property is shown to govern the relationship between the expected value of and a risk aversion index. This property will be applied to study a simple portfolio model and to discuss earlier results of Freixas and R. Kihlstrom. Introduction In a context of uncertainty, people usually gather before making decision. Indeed, increasing knowledge before acting is one way to avoid the risks associated with decisions under uncertainty. As a matter of fact, information-gathering activities are close substitutes for insurance contracts as protection against certain types of risks. One important concern is the relationship between information-seeking behavior and attitudes towards risk. Is there a clearcut relation between demand and risk aversion? It seems, a priori, that more risk-averse decision makers should be willing to gather more before acting, than less risk-averse agents, especially in situations where insurance opportunities fail to cover all types of risks. Thus, demand should decrease with risk-aversion. But this proposition is not always correct. Freixas and Kihlstrom (1984) showed that under specific assumptions the opposite relationship may hold. The demand for may decrease with risk aversion. They gave the following intuitive argument for their result. Ex ante, when the of to be demanded has to be planned for, the decision-maker ignores the message he or she is going to observe. Thus ex ante, gathering is a risky activity that risk averse agents are less willing to bear, even if ex post it corresponds to a reduction in risk. This intuitive argument can be explicitly modelled by adopting an alternative setting for the problem. The approach adopted differs from the seminal work of Kihlstrom (1974a, 1974b) about demand. The present analysis is based on the expected value of (EVI) or asking price earlier defined by La Valle (1968). The EVI measures the decision maker's willingness to pay for information. With this definition the difficulty of defining a controversial continuous variable representing the amount of information can be avoided. The author shows that for the class of constant absolute risk averse (CARA) utility functions considered by Freixas and Kihlstrom, the EVI increases (decreases) with risk aversion if and only if the expected risk associated with the decision maker's optimal course of action decreases (increases) with information. This result may be relevant for explaining economic activities such as investment in search processes, buying insurance or speculating. For example, the result presented here tends to sustain Hirshleifer's (1975) analysis of speculation and hedging as information-seeking behaviors. Hedgers are those who invest more in gathering only if they expect a decrease in the risk they are facing, while speculators are willing to buy more if they anticipate higher variability of their payoffs. This is indeed reconcilable with being more or less risk-averse, respectively. The study begins with some basic definitions in order to set out the problem, then shows that the above result is locally true, i.e. holds for small risks. Next a simple portfolio choice model is developed, expanding this result from more general types of risks, provided the further assumption of normally distributed random variables is made. Definitions and Assumptions Consider a decision maker with initial wealth w,(w [is greater than or equal to] o), whose preferences for random payoffs are representable by a strictly increasing and twice differentiable utility function u(.), defined on the real line R. Let D be the decision maker's choice set, and S a finite set of states of the world over which he has prior probability beliefs. …