Advanced Search
MyIDEAS: Login

Disentangling Risk Aversion and Intertemporal Substitution Through a Reference Level

Contents:

Author Info

  • René Garcia
  • Éric Renault

    ()

  • Andrei Semenov

Abstract

In the standard consumption capital asset pricing model (CCAPM), the curvature of the investor's utility function captures two aspects of preferences: as the concavity of the function increases so does his aversion to risk as well as his desire to smooth consumption intertemporally. This restriction is not theoretically justified nor empirically supported. To disentangle the two concepts, Epstein and Zin (1989) and Weil (1989) have proposed a recursive utility framework. However, the ensuing risk aversion measure (1-α) should not be considered as a simple Arrow-Pratt index of relative risk aversion that could be interpreted independently of the level of the elasticity σ. The lack of disentangling comes from the fact that the recursive utility model introduces risk aversion through the definition of a certainty equivalent of future utility that mixes attitudes towards risk and intertemporal substitution. We show that the higher σ is (while remaining smaller than one to be realistic), the more (1-α) underestimates the genuine level of risk aversion since a higher σ facilitates intertemporal diversification and thus substantially lowers the level of risk that is significantly borne. We suggest that the requested disentangling may alternatively be obtained by introducing an exogenous reference level which, in a recursive way, assesses the expected future consumption. Therefore, risk aversion is now defined with respect to the unpredictable discrepancy between actual consumption and this reference level (a quantity independent of the attitude towards risk). In this new framework, preferences are represented by a generalized von Neumann-Morgenstern utility specification whereby satisfaction is derived from consumption relative to an external reference level as well as from this reference level itself. Dans le modèle standard d'évaluation des actifs financiers fondé sur la consommation (CCAPM), la courbure de la fonction d'utilité de l'investisseur associe deux aspects des préférences: l'aversion pour le risque et le désir de lisser la consommation intertemporellement augmentent proportionnellement avec la concavité de la fonction. Cette association n'est ni justifiée théoriquement ni vérifiée empiriquement. Pour séparer les deux concepts, Epstein et Zin (1989) et Weil (1989) ont proposé un cadre fondé sur l'utilité récursive. Toutefois, la mesure d'aversion pour le risque (1-α) qui en résulte ne doit pas être considérée comme un simple indice d'Arrow-Pratt d'aversion relative pour le risque qui pourrait s'interpréter indépendamment du niveau de l'élasticité σ. Cette absence de séparation vient du fait que le modèle d'utilité récursive introduit l'aversion pour le risque en définissant un équivalent certain de l'utilité future qui mélange les attitudes à l'égard du risque et de la substitution intertemporelle. Nous montrons que plus σ est élevée (tout en restant inférieure à un pour rester réaliste), plus (1-α) sous-estime le niveau véritable de l'aversion pour le risque car un σ élevé facilite la diversification intertemporelle et donc réduit subtantiellement le niveau de risque effectivement supporté. Nous proposons de réaliser la séparation désirée en introduisant un niveau de référence exogène qui, de manière récursive, évalue la consommation future attendue. Par conséquent, l'aversion pour le risque se définit à présent par rapport à l'écart imprévisible entre la consommation effective et ce niveau de référence (une quantité indépendante de l'attitude à l'égard du risque). Dans ce nouveau cadre, les préférences sont représentées par une spécification généralisée de l'utilité von Neumann-Morgenstern selon laquelle la satisfaction résulte à la fois de la consommation relativement à un niveau de référence externe et du niveau de référence proprement dit.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://www.cirano.qc.ca/pdf/publication/2003s-12.pdf
Download Restriction: no

Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 2003s-12.

as in new window
Length:
Date of creation: 01 Apr 2003
Date of revision:
Handle: RePEc:cir:cirwor:2003s-12

Contact details of provider:
Postal: 2020 rue University, 25e étage, Montréal, Quéc, H3A 2A5
Phone: (514) 985-4000
Fax: (514) 985-4039
Email:
Web page: http://www.cirano.qc.ca/
More information through EDIRC

Related research

Keywords: Risk aversion; Intertemporal substitution; Recursive utility; Reference Level; Disentangling preferences; aversion pour le risque; substitution intertemporelle; utilité récursive; niveau de référence; séparation des préférences;

Other versions of this item:

This paper has been announced in the following NEP Reports:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Botond Koszegi & Matthew Rabin, 2005. "A Model of Reference-Dependent Preferences," Levine's Bibliography 784828000000000341, UCLA Department of Economics.
  2. R. Mehra & E. Prescott, 2010. "The equity premium: a puzzle," Levine's Working Paper Archive 1401, David K. Levine.
  3. Kreps, David M. & Porteus, Evan L., 1979. "Temporal von neumann-morgenstern and induced preferences," Journal of Economic Theory, Elsevier, vol. 20(1), pages 81-109, February.
  4. Campbell, John, 1993. "Intertemporal Asset Pricing Without Consumption Data," Scholarly Articles 3221491, Harvard University Department of Economics.
  5. Robert E. Lucas Jr. & Nancy L. Stokey, 1982. "Optimal Growth with Many Consumers," Discussion Papers 518, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Startz, Richard, 1989. "The Stochastic Behavior of Durable and Nondurable Consumption," The Review of Economics and Statistics, MIT Press, vol. 71(2), pages 356-63, May.
  7. Epstein, Larry G & Zin, Stanley E, 1991. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 263-86, April.
  8. Martin Lettau & Sydney Ludvigson, 1999. "Resurrecting the (C)CAPM: a cross-sectional test when risk premia are time-varying," Staff Reports 93, Federal Reserve Bank of New York.
  9. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
  10. A. Abel, 2010. "Asset prices under habit formation and catching up with the Jones," Levine's Working Paper Archive 1395, David K. Levine.
  11. Epstein, Larry G & Zin, Stanley E, 1989. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework," Econometrica, Econometric Society, vol. 57(4), pages 937-69, July.
  12. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-94, March.
  13. Alvarez, Fernando & Jermann, Urban J., 2000. "Using Asset Prices to Measure the Cost of Business Cycles," Working Papers 00-1, University of Pennsylvania, Wharton School, Weiss Center.
  14. Hansen, Lars Peter & Singleton, Kenneth J, 1983. "Stochastic Consumption, Risk Aversion, and the Temporal Behavior of Asset Returns," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 249-65, April.
  15. Christopher D. Carroll & Jody Overland & David N. Weil, 1995. "Saving and growth with habit formation," Finance and Economics Discussion Series 95-42, Board of Governors of the Federal Reserve System (U.S.).
  16. Weil, Philippe, 1989. "The equity premium puzzle and the risk-free rate puzzle," Journal of Monetary Economics, Elsevier, vol. 24(3), pages 401-421, November.
  17. Duffie, Darrel & Lions, Pierre-Louis, 1992. "PDE solutions of stochastic differential utility," Journal of Mathematical Economics, Elsevier, vol. 21(6), pages 577-606.
  18. G. Constantinides, 1990. "Habit formation: a resolution of the equity premium puzzle," Levine's Working Paper Archive 1397, David K. Levine.
  19. Eichenbaum, Martin S & Hansen, Lars Peter & Singleton, Kenneth J, 1988. "A Time Series Analysis of Representative Agent Models of Consumption and Leisure Choice under Uncertainty," The Quarterly Journal of Economics, MIT Press, vol. 103(1), pages 51-78, February.
  20. Weil, Philippe, 1990. "Nonexpected Utility in Macroeconomics," The Quarterly Journal of Economics, MIT Press, vol. 105(1), pages 29-42, February.
  21. Ravi Bansal & Amir Yaron, 2004. "Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles," Journal of Finance, American Finance Association, vol. 59(4), pages 1481-1509, 08.
  22. 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.
  23. Campbell, John Y. & Viceira, Luis M., 2002. "Strategic Asset Allocation: Portfolio Choice for Long-Term Investors," OUP Catalogue, Oxford University Press, number 9780198296942.
  24. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-36.
  25. Smith, William T, 2001. "How Does the Spirit of Capitalism Affect Stock Market Prices?," Review of Financial Studies, Society for Financial Studies, vol. 14(4), pages 1215-32.
  26. Gurdip S. Bakshi & Zhiwu Chen, 1996. "The Spirit of Capitalism and Stock-Market Prices," CEMA Working Papers 511, China Economics and Management Academy, Central University of Finance and Economics.
  27. Alberto Giovannini & Philippe Weil, 1989. "Risk Aversion and Intertemporal Substitution in the Capital Asset Pricing Model," NBER Working Papers 2824, National Bureau of Economic Research, Inc.
  28. Sundaresan, Suresh M, 1989. "Intertemporally Dependent Preferences and the Volatility of Consumption and Wealth," Review of Financial Studies, Society for Financial Studies, vol. 2(1), pages 73-89.
  29. Nicholas Barberis & Ming Huang & Tano Santos, 2001. "Prospect Theory And Asset Prices," The Quarterly Journal of Economics, MIT Press, vol. 116(1), pages 1-53, February.
  30. repec:fth:harver:1421 is not listed on IDEAS
  31. Aschauer, David Alan, 1985. "Fiscal Policy and Aggregate Demand," American Economic Review, American Economic Association, vol. 75(1), pages 117-27, March.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Lars Peter Hansen, 2012. "Risk Pricing over Alternative Investment Horizons," Working Papers 2012-008, Becker Friedman Institute for Research In Economics.
  2. Monfort, A. & Pegoraro, F., 2012. "Asset Pricing with Second-Order Esscher Transforms," Working papers 397, Banque de France.
  3. Andrei Semenov, 2003. "An Empirical Assessment of a Consumption CAPM with a Reference Level under Incomplete Consumption Insurance," Working Papers 2003_5, York University, Department of Economics.
  4. Schrimpf, Andreas & Grammig, Joachim G., 2007. "Asset Pricing with a Reference Level of Consumption: New Evidence from the Cross-Section of Stock Returns," ZEW Discussion Papers 06-032 [rev.], ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
  5. Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2007. "Econometric Asset Pricing Modelling," Working Papers 2007-18, Centre de Recherche en Economie et Statistique.
  6. Echevarría, Cruz A., 2012. "Income tax progressivity, physical capital, aggregate uncertainty and long-run growth in an OLG economy," Journal of Macroeconomics, Elsevier, vol. 34(4), pages 955-974.
  7. Basu, Parantap & Semenov, Andrei & Wada, Kenji, 2011. "Uninsurable risk and financial market puzzles," Journal of International Money and Finance, Elsevier, vol. 30(6), pages 1055-1089, October.
  8. Badescu, Alex & Elliott, Robert J. & Siu, Tak Kuen, 2009. "Esscher transforms and consumption-based models," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 337-347, December.
  9. Roche, Hervé, 2011. "Asset prices in an exchange economy when agents have heterogeneous homothetic recursive preferences and no risk free bond is available," Journal of Economic Dynamics and Control, Elsevier, vol. 35(1), pages 80-96, January.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:cir:cirwor:2003s-12. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Webmaster).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.