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Disentangling Risk Aversion and Intertemporal Substitution Through a Reference Level

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  • 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.

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Bibliographic Info

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

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Date of creation: 01 Apr 2003
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Handle: RePEc:cir:cirwor:2003s-12

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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;

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Citations

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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. Grammig, Joachim & Schrimpf, Andreas, 2009. "Asset ppricing with a reference level of consumption: New evidence from the cross-section of stock returns," CFR Working Papers 07-05, University of Cologne, Centre for Financial Research (CFR).
  4. 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.
  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. 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.
  8. 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.
  9. 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.

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