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-\topmatter
-
-\title{Estimating Risk Aversion from \cr
- Arrow-Debreu Portfolio Choice}
-
-\runningname{Hal R. Varian}
-\runningtitle{Estimating Risk Aversion}
-
-\thanks{This research was supported in part by the National Science
-Foundation. I would like to thank Richard Green for helpful remarks. I am
-especially grateful to an anonymous referee whose comments significantly
-improved the statements and proofs of the results.}
-
-\author{Hal R. Varian}
-
-\affil{University of Michigan}
-
-\date{October 27, 1984}
-
-\version{\today}
-
-\abstract{This paper derives necessary and sufficient conditions for
-Arrow-Debreu choices of contingent consumption to be compatible with the
-maximization of a state independent expected utility function that exhibits
-increasing or decreasing absolute risk aversion, or increasing or
-decreasing relative risk aversion. The conditions can be used to bound
-different measures of risk aversion based on a single observation of
-Arrow-Debreu portfolio choice.}
-
-\keywords{Revealed preference, expected utility, risk aversion, portfolio
-choice.}
-
-
-\address{Hal R. Varian, Department of Economics, University of Michigan,
-Ann Arbor, MI 48109}
-
-\endtopmatter
-
-\document
-
-\noindent {\scten The expected utility} hypothesis forms the basis for much
-of our understanding of investor behavior under uncertainty. It is
-commonly agreed that a well-behaved expected utility function should be an
-increasing and concave function of wealth, or, equivalently, that its first
-derivative should be positive and its second derivative should be negative.
-It is also widely accepted that the Arrow-Pratt measure of absolute risk
-aversion should be declining with wealth. There is much less agreement
-about the behavior of the Arrow-Pratt measure of {\it relative\/} risk
-aversion, although some investigators have argued that it should increase
-with wealth.
-
-In this note I derive necessary and sufficient conditions for choices of
-contingent consumption across states of nature to satisfy various
-hypotheses about the behavior of these measures of risk aversion. If the
-portfolio choice behavior of the consumer is consistent with the conditions
-I derive, then the conditions can be used to bound the Arrow--Pratt
-measures of absolute and relative risk aversion. The conditions are
-derived using methods of the ``nonparametric approach'' to optimizing
-behavior introduced by Afriat (1967) and extended by Diewert (1973),
-Diewert and Parkan (1978), and Varian (1982), (1983a). Applications of
-these methods to choice under uncertainty include Dybvig and Ross (1982),
-Green and Srivastava (1983), and Varian (1983b).
-
-\section The Maximization Problem
-
-Consider an investor who chooses a pattern of consumption across states of
-nature to solve the following problem:
- $$\max \sum_{s=1}^S \pi_s u(c_s) $$
-
-\Refs
-
-\ref
-\by{Afriat, S.} \yr{1967a} \paper{The Construction of a Utility
-Function from Expenditure Data} \jour{International Economic Review}
-\vol{8} \pages{67--77}
-\endref
-
-\ref
-\by{Afriat, S.} \yr{1967b} \paper{The Construction of Separable
-Utility Functions from Expenditure Data} \paperinfo{mimeo, Purdue}
-\endref
-
-\ref \by{Breeden, D. and R. Litzenberger} \yr{1978} \paper{Prices of
-State-Contingent Claims Implicit in Option Prices} \jour{Journal of
-Business} \pages{621--651}
-\endref
-
-\ref
-\by{Diewert, E.} \yr{1973} \paper{Afriat and Revealed Preference Theory}
-\jour{Review of Economic Studies} \vol{40} \pages{419--426}
-\endref
-
-\ref \by{Diewert, E. and C. Parkan} \yr{1978} \paper{Tests for Consistency
-of Consumer Data and Nonparametric Index Numbers} \paperinfo{Working Paper
-78-27, University of British Columbia}
-\endref
-
-\ref \by{Dybvig, P. and S. Ross} \yr{1982} \paper{Portfolio Efficient Sets}
-\jour{Econometrica} \pages{1525--1546}
-\endref
-
-\ref \by{Green, R. and S. Srivastava} \yr{1983} \paper{Preference
-Restrictions, Asset Returns, and Consumption} \paperinfo{mimeo,
-Carnegie--Mellon University}
-\endref
-
-\ref \by{Varian, H.} \yr{1982} \paper{The Nonparametric Approach to Demand
-Analysis} \jour{Econometrica} \vol{50} \pages{945--973}
-\endref
-
-\ref
-\by{Varian, H.} \yr{1983a} \paper{Nonparametric Tests of Models of
-Consumer Behavior} \jour{Review of Economic Studies} \vol{50}
-\pages{99--110}
-\endref
-
-\ref
-\by{Varian, H.} \yr{1983b} \paper{Nonparametric Tests of Models of
-Investor Behavior} \jour{Journal of Financial and Quantitative Analysis}
-\vol{18} \pages{269--278}
-\endref
- \ No newline at end of file