A Two-Parameter Model of Dispersion Aversion
The idea of representing choice under uncertainty as a trade-off between mean returns and some measure of risk or uncertainty is fundamental to the analysis of investment decisions. In this paper, we show that preferences can be characterized in this way, even in the absence of ob jective probabilities. We develop a model of uncertainty averse preferences that is based on a mean and a measure of the dispersion of the state-wise utility of an act. The dispersion measure exhibits positive linear homogeneity, sub-additivity, translation invariance and complementary symmetry. Since preferences are only weakly separable in terms of these two summary statistics, the uncertainty premium need not be constant. We show that the standard results originally derived in the context of mean-variance analysis and expected utility theory apply in this more generally setting. In particular, we generalize the concept of decreasing absolute risk aversion and show that the usual comparative static results from EU theory remain valid. Further we derive two-fund separation and asset pricing results analogous to those that hold for the standard CAPM.
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- Thomas J. Sargent & LarsPeter Hansen, 2001. "Robust Control and Model Uncertainty," American Economic Review, American Economic Association, vol. 91(2), pages 60-66, May.
- Marciano Siniscalchi, 2009.
"Vector Expected Utility and Attitudes Toward Variation,"
Econometric Society, vol. 77(3), pages 801-855, 05.
- Marciano Siniscalchi, 2007. "Vector Expected Utility and Attitudes toward Variation," Discussion Papers 1455, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Mark J. Machina, 2009. "Risk, Ambiguity, and the Rank-Dependence Axioms," American Economic Review, American Economic Association, vol. 99(1), pages 385-92, March.
- John Y. Campbell, 2002.
"Consumption-Based Asset Pricing,"
Harvard Institute of Economic Research Working Papers
1974, Harvard - Institute of Economic Research.
- Machina,Mark & Schmeidler,David, 1991.
"A more robust definition of subjective probability,"
Discussion Paper Serie A
365, University of Bonn, Germany.
- Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-80, July.
- Mark J. Machina & David Schmeidler, 1990. "A More Robust Definition of Subjective Probability," Discussion Paper Serie A 306, University of Bonn, Germany.
- Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006.
"Dynamic Variational Preferences,"
Carlo Alberto Notebooks
1, Collegio Carlo Alberto.
- Ross, Stephen A, 1978. "A Simple Approach to the Valuation of Risky Streams," The Journal of Business, University of Chicago Press, vol. 51(3), pages 453-75, July.
- Itzhak Gilboa & David Schmeidler, 1989.
"Maxmin Expected Utility with Non-Unique Prior,"
- French, Kenneth R & Poterba, James M, 1991.
"Investor Diversification and International Equity Markets,"
American Economic Review,
American Economic Association, vol. 81(2), pages 222-26, May.
- Kenneth R. French & James M. Poterba, 1991. "Investor Diversification and International Equity Markets," NBER Working Papers 3609, National Bureau of Economic Research, Inc.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- Simon Grant & Ben Polak, 2011.
"Mean-Dispersion Preferences and Constant Absolute Uncertainty Aversion,"
Cowles Foundation Discussion Papers
1805, Cowles Foundation for Research in Economics, Yale University.
- Grant, Simon & Polak, Ben, 2013. "Mean-dispersion preferences and constant absolute uncertainty aversion," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1361-1398.
- Hansen, Lars Peter & Singleton, Kenneth J, 1982. "Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 50(5), pages 1269-86, September.
- Chew, Soo Hong & Sagi, Jacob S., 2008. "Small worlds: Modeling attitudes toward sources of uncertainty," Journal of Economic Theory, Elsevier, vol. 139(1), pages 1-24, March.
- William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, 09.
- Sandmo, Agnar, 1971. "On the Theory of the Competitive Firm under Price Uncertainty," American Economic Review, American Economic Association, vol. 61(1), pages 65-73, March.
- Epstein, Larry G, 1985. "Decreasing Risk Aversion and Mean-Variance Analysis," Econometrica, Econometric Society, vol. 53(4), pages 945-61, July.
- Ormiston, Michael B & Schlee, Edward E, 2001. "Mean-Variance Preferences and Investor Behaviour," Economic Journal, Royal Economic Society, vol. 111(474), pages 849-61, October.
- Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
- Meyer, Jack, 1987. "Two-moment Decision Models and Expected Utility Maximization," American Economic Review, American Economic Association, vol. 77(3), pages 421-30, June.
- Ormiston, Michael B & Quiggin, John, 1993. "Two-Parameter Decision Models and Rank-Dependent Expected Utility," Journal of Risk and Uncertainty, Springer, vol. 7(3), pages 273-82, December.
- Laetitia Placido & Aurélien Baillon & Olivier L'Haridon, 2011.
"Ambiguity models and the Machina paradoxes,"
Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers)
- Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
- Quiggin, John & Chambers, R.G.Robert G., 2004. "Invariant risk attitudes," Journal of Economic Theory, Elsevier, vol. 117(1), pages 96-118, July.
- R. Rockafellar & Stan Uryasev & Michael Zabarankin, 2006. "Generalized deviations in risk analysis," Finance and Stochastics, Springer, vol. 10(1), pages 51-74, 01.
- Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
- Ergin, Haluk & Gul, Faruk, 2009. "A theory of subjective compound lotteries," Journal of Economic Theory, Elsevier, vol. 144(3), pages 899-929, May.
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