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S-shaped utility, subprime crash and the black swan

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  • de Farias Neto, Joao Jose

Abstract

I propose an S-shaped utility function of consumption which, combined with an heterogeneous agents and external habit setting, fits well the first order moments of the American financial and macroeconomic time series relevant for the equity premium puzzle in the second half of XX century. The average relative risk aversion of the agents remains in the 0-3 range. A "black swan"-kind phenomenon makes two of the 50 years considered (the two oil shocks) responsible for half the average of the stochastic discount factor, thus bringing the annual subjective discount factor to a very low level, around 0.5, which solves the risk-free puzzle. The shape of the relative risk aversion function of consumption suggests an explanation for the 2008 suprime crash akin to the breaking of waves on a beach in a lifecycle overlapping generations model.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 12122.

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Date of creation: 12 Dec 2008
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Handle: RePEc:pra:mprapa:12122

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Keywords: financial puzzles; subprime crash; black swan; S-shaped utility;

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  1. Harry Markowitz, 1952. "The Utility of Wealth," Journal of Political Economy, University of Chicago Press, vol. 60, pages 151.
  2. Cochrane, John H. & Campbell, John, 1999. "By Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior," Scholarly Articles 3119444, Harvard University Department of Economics.
  3. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
  4. Björn Hagströmer & Richard G. Anderson & Jane M. Binner & Thomas Elger & Birger Nilsson, 2007. "Mean-variance vs. full-scale optimization: broad evidence for the U.K," Working Papers 2007-016, Federal Reserve Bank of St. Louis.
  5. Jonathan A. Parker & Christian Julliard, 2005. "Consumption Risk and the Cross Section of Expected Returns," Journal of Political Economy, University of Chicago Press, vol. 113(1), pages 185-222, February.
  6. Friedman, Daniel, 1989. "The S-Shaped Value Function as a Constrained Optimum," American Economic Review, American Economic Association, vol. 79(5), pages 1243-48, December.
  7. Andrew B. Abel, 2006. "Equity Premia with Benchmark Levels of Consumption: Closed-Form Results," NBER Working Papers 12290, National Bureau of Economic Research, Inc.
  8. Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
  9. Cysne, Rubens Penha, 2005. "Equity-Premium Puzzle: Evidence From Brazilian Data," Economics Working Papers (Ensaios Economicos da EPGE) 586, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  10. Sergiy Gerasymchuk, 2008. "Asset return and wealth dynamics with reference dependent preferences and heterogeneous beliefs," Working Papers 160, Department of Applied Mathematics, Università Ca' Foscari Venezia.
  11. Neilson, William S, 2002. " Comparative Risk Sensitivity with Reference-Dependent Preferences," Journal of Risk and Uncertainty, Springer, vol. 24(2), pages 131-42, March.
  12. Benartzi, Shlomo & Thaler, Richard H, 1995. "Myopic Loss Aversion and the Equity Premium Puzzle," The Quarterly Journal of Economics, MIT Press, vol. 110(1), pages 73-92, February.
  13. Sergiy Gerasymchuk, 2007. "Mean-Variance Portfolio Selection with Reference Dependent Preferences," Working Papers 150, Department of Applied Mathematics, Università Ca' Foscari Venezia.
  14. Milton Friedman & L. J. Savage, 1948. "The Utility Analysis of Choices Involving Risk," Journal of Political Economy, University of Chicago Press, vol. 56, pages 279.
  15. Nick Netzer, 2008. "Evolution of Time Preferences and Attitudes Towards Risk," TWI Research Paper Series 29, Thurgauer Wirtschaftsinstitut, Universität Konstanz.
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