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diff --git a/Master/texmf-dist/doc/plain/vertex/test.tex b/Master/texmf-dist/doc/plain/vertex/test.tex new file mode 100644 index 00000000000..f7e8514047e --- /dev/null +++ b/Master/texmf-dist/doc/plain/vertex/test.tex @@ -0,0 +1,122 @@ +\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 +
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