Risk-value models

Abstract In this paper we propose a risk-value model for evaluating decisions under risk. In this model preference for a gamble is determined by its riskiness and its value or worth. In a simple form of the risk-value model, risk is measured by variance and value by expected returns. We discuss several other empirically more attractive forms of the risk-value model. We show that the risk-value model provides a framework for unifying the streams of research on risk judgments and on modeling choices. We explore the consistency of the risk-value model with both expected utility and non-expected utility preferences. Specifically, we show that if we define risk and value in appropriate ways, the rank order produced by the risk-value model will be consistent with a suitably chosen expected utility or non-expected utility model. We briefly discuss application of the risk-value model to the theory of finance and to social risk analysis.

[1]  M. Machina.  "Expected Utility" Analysis without the Independence Axiom , 1982 .

[2]  Clyde H. Coombs,et al.  Tests of a portfolio theory of risk preference , 1970 .

[3]  P. Slovic.  Perception of risk. , 1987, Science.

[4]  C. Starr.  Social benefit versus technological risk. , 1969, Science.

[5]  Richard J. Zeckhauser,et al.  Where Now for Saving Lives , 1976 .

[6]  Ronald A. Howard,et al.  Life and Death Decision Analysis. , 1979 .

[7]  Elke U. Weber,et al.  Combine and conquer: A joint application of conjoint and functional approaches to the problem of risk measurement , 1984 .

[8]  M. Allais.  Le comportement de l'homme rationnel devant le risque : critique des postulats et axiomes de l'ecole americaine , 1953 .

[9]  R. Schwing,et al.  Societal Risk Assessment , 1980 .

[10]  Elke U. Weber,et al.  An axiomatic theory of conjoint expected risk , 1986 .

[11]  Rakesh K. Sarin,et al.  Some extensions of Luce's measures of risk , 1987 .

[12]  P. Slovic,et al.  FACTS AND FEARS: UNDERSTANDING PERCEIVED RISK.: P/3 , 1980 .

[13]  R. Duncan Luce,et al.  Several possible measures of risk , 1980 .

[14]  Ramesh K. S. Rao,et al.  Mean Lower Partial Moment Valuation and Lognormally Distributed Returns , 1988 .

[15]  Peter C. Fishburn,et al.  Behavioral Models of Risk Taking in Business Decisions: A Survey and Evaluation , 1977 .

[16]  L. J. Savage,et al.  The Foundations of Statistics , 1955 .

[17]  Paul E. Lehner,et al.  Conjoint Design and Analysis of the Bilinear Model: An Application to Judgments of Risk , 1984 .

[18]  R. Howard.  On Making Life and Death Decisions , 1980 .

[19]  P. Fishburn.  Mean-Risk Analysis with Risk Associated with Below-Target Returns , 1977 .

[20]  Clyde H. Coombs,et al.  A test of ve-theories of risk and the effect of the central limit theorem , 1971 .

[21]  William P. Bottom,et al.  An Empirical Evaluation of the Transitivity, Monotonicity, Accounting, and Conjoint Axioms for Perceived Risk , 1990 .

[22]  Lola L. Lopes.  Risk and Distributional Inequality. , 1984 .

[23]  W. Sharpe.  CAPITAL ASSET PRICES: A THEORY OF MARKET EQUILIBRIUM UNDER CONDITIONS OF RISK* , 1964 .

[24]  J. Mossin.  EQUILIBRIUM IN A CAPITAL ASSET MARKET , 1966 .

[25]  M. Rothschild,et al.  Increasing risk: I. A definition , 1970 .

[26]  Alexander Pollatsek,et al.  A theory of risk , 1970 .

[27]  B. Stone.  A GENERAL CLASS OF THREE-PARAMETER RISK MEASURES , 1973 .

[28]  Clyde H. Coombs,et al.  Polynomial psychophysics of risk , 1970 .

[29]  M. Allais,et al.  The So-Called Allais Paradox and Rational Decisions under Uncertainty , 1979 .

[30]  Peter C. Fishburn,et al.  Foundations of Risk Measurement. I. Risk As Probable Loss , 1984 .

[31]  J. Pratt.  RISK AVERSION IN THE SMALL AND IN THE LARGE11This research was supported by the National Science Foundation (grant NSF-G24035). Reproduction in whole or in part is permitted for any purpose of the United States Government. , 1964 .

[32]  R. Litzenberger,et al.  SKEWNESS PREFERENCE AND THE VALUATION OF RISK ASSETS , 1976 .

[33]  Paul E. Lehner,et al.  Evaluation of two alternative models for a theory of risk: I. Are moments of distributions useful in assessing risk? , 1981 .

[34]  A. Tversky,et al.  Prospect Theory : An Analysis of Decision under Risk Author ( s ) : , 2007 .

[35]  Paul Slovic,et al.  The relative influence of probabilities and payoffs upon perceived risk of a gamble , 1967 .

[36]  Ramesh K. S. Rao,et al.  Asset Pricing in a Generalized Mean-Lower Partial Moment Framework: Theory and Evidence , 1989, Journal of Financial and Quantitative Analysis.

[37]  J. Lintner.  THE VALUATION OF RISK ASSETS AND THE SELECTION OF RISKY INVESTMENTS IN STOCK PORTFOLIOS AND CAPITAL BUDGETS , 1965 .

[38]  Peter C. Fishburn,et al.  Foundations of risk measurement. II. Effects of gains on risk , 1982 .

[39]  Mark J. Machina,et al.  A Stronger Characterization of Declining Risk Aversion , 1982 .

[40]  T. Copeland,et al.  Financial Theory and Corporate Policy. , 1980 .

[41]  R. Duncan Luce,et al.  Correction to ‘several possible measures of risk’ , 1981 .

[42]  Ole Hagen,et al.  Towards a Positive Theory of Preferences under Risk , 1979 .

[43]  G. Shafer,et al.  Expected Utility Hypotheses and the Allais Paradox. , 1982 .

[44]  A. Tversky,et al.  Prospect theory: analysis of decision under risk , 1979 .

[45]  Kenneth R. MacCrimmon,et al.  Taking Risks, the Management of Uncertainty , 1987 .

[46]  Colin Camerer,et al.  Recent developments in modelling preferences under risk , 1987 .

[47]  Howard Raiffa,et al.  Decision analysis: introductory lectures on choices under uncertainty. 1968. , 1969, M.D.Computing.

[48]  L. Robin Keller,et al.  Empirical investigation of some properties of the perceived riskiness of gambles , 1986 .

[49]  Jaap Van Brakel,et al.  Foundations of measurement , 1983 .

[50]  S. Ross.  SOME STRONGER MEASURES OF RISK AVERSION IN THE SMALL AND THE LARGE WITH APPLICATIONS , 1981 .

[51]  H. Levy.  Stochastic dominance and expected utility: survey and analysis , 1992 .

[52]  Martin Weber.  Risikoentscheidungskalküle in der Finanzierungstheorie , 1990 .

[53]  Clyde H. Coombs,et al.  Additivity of risk in portfolios , 1971 .

[54]  John W. Payne,et al.  Relation of perceived risk to preferences among gambles. , 1975 .