IDEAS home Printed from https://ideas.repec.org/p/hit/piedp2/323.html
   My bibliography  Save this paper

Representative Consumer's Risk Aversion and Efficient Risk-Sharing Rules

Author

Listed:
  • Hara, Chiaki
  • Huang, James
  • Kuzmics, Christoph

Abstract

We study the representative consumer's risk attitude and efficient risk-sharing rules in a singleperiod, single-good economy in which consumers have homogeneous probabilistic beliefs but heterogeneous risk attitudes. We prove that if all consumers have convex absolute risk tolerance, so must the representative consumer. We also identify a relationship between the curvature of an individual consumer's individual risk sharing rule and his absolute cautiousness, the first derivative of absolute risk-tolerance. Furthermore, we discuss some consequences of these results and refinements of these results for the class of HARA utility functions.

Suggested Citation

  • Hara, Chiaki & Huang, James & Kuzmics, Christoph, 2007. "Representative Consumer's Risk Aversion and Efficient Risk-Sharing Rules," Discussion Paper 323, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University.
  • Handle: RePEc:hit:piedp2:323
    Note: November 6, 2006
    as

    Download full text from publisher

    File URL: http://hermes-ir.lib.hit-u.ac.jp/rs/bitstream/10086/14542/1/pie_dp323.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
    2. Robert B. Barsky & Miles S. Kimball & F. Thomas Juster & Matthew D. Shapiro, 1995. "Preference Parameters and Behavioral Heterogeneity: An Experimental Approach in the Health and Retirement Survey," NBER Working Papers 5213, National Bureau of Economic Research, Inc.
    3. Yeung Lewis Chan & Leonid Kogan, 2002. "Catching Up with the Joneses: Heterogeneous Preferences and the Dynamics of Asset Prices," Journal of Political Economy, University of Chicago Press, vol. 110(6), pages 1255-1285, December.
    4. Olivier J. Blanchard, 1993. "Movements in the Equity Premium," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 24(2), pages 75-138.
    5. Brennan, M.J. & Solanki, R., 1981. "Optimal Portfolio Insurance," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 16(03), pages 279-300, September.
    6. Christian Gollier, 2001. "Wealth Inequality and Asset Pricing," Review of Economic Studies, Oxford University Press, vol. 68(1), pages 181-203.
    7. Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51.
    8. James Huang, 2003. "Impact of Divergent Consumer Confidence on Option Prices," Review of Derivatives Research, Springer, vol. 6(3), pages 165-177, October.
    9. Leland, Hayne E, 1980. " Who Should Buy Portfolio Insurance?," Journal of Finance, American Finance Association, vol. 35(2), pages 581-594, May.
    10. Gollier, Christian & Zeckhauser, Richard J, 2002. "Horizon Length and Portfolio Risk," Journal of Risk and Uncertainty, Springer, vol. 24(3), pages 195-212, May.
    11. John Y. Campbell & John H. Cochrane, 1994. "By force of habit: a consumption-based explanation of aggregate stock market behavior," Working Papers 94-17, Federal Reserve Bank of Philadelphia.
    12. Guiso, Luigi & Jappelli, Tullio & Terlizzese, Daniele, 1996. "Income Risk, Borrowing Constraints, and Portfolio Choice," American Economic Review, American Economic Association, vol. 86(1), pages 158-172, March.
    13. Robert B. Barsky & F. Thomas Juster & Miles S. Kimball & Matthew D. Shapiro, 1997. "Preference Parameters and Behavioral Heterogeneity: An Experimental Approach in the Health and Retirement Study," The Quarterly Journal of Economics, Oxford University Press, vol. 112(2), pages 537-579.
    14. Hara, Chiaki & Huang, James & Kuzmics, Christoph, 2007. "Representative consumer's risk aversion and efficient risk-sharing rules," Journal of Economic Theory, Elsevier, vol. 137(1), pages 652-672, November.
    15. John Y. Campbell & John Cochrane, 1999. "Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior," Journal of Political Economy, University of Chicago Press, vol. 107(2), pages 205-251, April.
    16. Chiaki Hara, 2006. "Heterogeneous Risk Attitudes In A Continuous-Time Model," The Japanese Economic Review, Japanese Economic Association, vol. 57(3), pages 377-405.
    17. Laurent Calvet & Jean-Michel Grandmont & Isabelle Lemaire, 2001. "Aggregation of Heterogenous Beliefs and Asset Pricing in Complete Financial Markets," Working Papers 2001-01, Center for Research in Economics and Statistics.
    18. Kurosaki, Takashi, 2001. "Consumption Smoothing and the Structure of Risk and Time Preferences:Theory and Evidence from Village India," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 42(2), pages 103-117, December.
    19. Dumas, Bernard, 1989. "Two-Person Dynamic Equilibrium in the Capital Market," Review of Financial Studies, Society for Financial Studies, vol. 2(2), pages 157-188.
    20. Magill, Michael & Shafer, Wayne, 1991. "Incomplete markets," Handbook of Mathematical Economics,in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 30, pages 1523-1614 Elsevier.
    21. Benninga, Simon & Mayshar, Joram, 2000. "Heterogeneity and option pricing," Research Report 00E08, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    22. Ravi Jagannathan & Ellen R. McGrattan & Anna Scherbina, 2000. "The declining U.S. equity premium," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Fall, pages 3-19.
    23. repec:dgr:rugsom:00e08 is not listed on IDEAS
    24. LeRoy,Stephen F. & Werner,Jan, 2014. "Principles of Financial Economics," Cambridge Books, Cambridge University Press, number 9781107024120, February.
    25. Guenter Franke & Richard C. Stapleton & Marti G. Subrahmanyam, 1999. "When are Options Overpriced? The Black-Scholes Model and Alternative Characterisations of the Pricing Kernel," Finance 9904004, EconWPA.
    26. Guntar Franke & Richard C. Stapleton & Marti G. Subrahmanyam, 1999. "When are Options Overpriced? The Black-Scholes Model and Alternative Characterizations of the Pricing Kernel," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-003, New York University, Leonard N. Stern School of Business-.
    27. Jiang, Wang, 1996. "The term structure of interest rates in a pure exchange economy with heterogeneous investors," Journal of Financial Economics, Elsevier, vol. 41(1), pages 75-110, May.
    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


    Cited by:

    1. Sylvia Sarantopoulou-Chiourea & George Skiadopoulos, 2015. "A New Predictor of Real Economic Activity: The S&P 500 Option Implied Risk Aversion," Working Papers 741, Queen Mary University of London, School of Economics and Finance.
    2. Laurent E. Calvet & Paolo Sodini, 2014. "Twin Picks: Disentangling the Determinants of Risk-Taking in Household Portfolios," Journal of Finance, American Finance Association, vol. 69(2), pages 867-906, April.
    3. Elyès Jouini & Clotilde Napp & Diego Nocetti, 2013. "Collective risk aversion," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 411-437, February.
    4. Hara, Chiaki & Huang, James & Kuzmics, Christoph, 2007. "Representative consumer's risk aversion and efficient risk-sharing rules," Journal of Economic Theory, Elsevier, vol. 137(1), pages 652-672, November.
    5. Bjarne Astrup Jensen & Jørgen Aase Nielsen, 2016. "How suboptimal are linear sharing rules?," Annals of Finance, Springer, vol. 12(2), pages 221-243, May.
    6. Campos, Rodolfo G., 2013. "Risk-sharing and crises. Global games of regime change with endogenous wealth," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1624-1658.
    7. Ghiglino, Christian & Venditti, Alain, 2011. "Wealth distribution and output fluctuations," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2478-2509.
    8. Dean T. Jamison & Julian Jamison, 2010. "Characterizing the amount and speed of discounting procedures," Working Papers 10-14, Federal Reserve Bank of Boston.
    9. Chiaki Hara & James Huang & Christoph Kuzmics, 2006. "Efficient Risk-Sharing Rules with Heterogeneous Risk Attitudes and Background Risks," KIER Working Papers 621, Kyoto University, Institute of Economic Research.
    10. Beißner, Patrick, 2016. "Radner Equilibria under Ambiguous Volatility," Center for Mathematical Economics Working Papers 493, Center for Mathematical Economics, Bielefeld University.
    11. Marc Fleurbaey & Stéphane Zuber, 2017. "Fair Utilitarianism," Documents de travail du Centre d'Economie de la Sorbonne 17005r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Jul 2017.
    12. Hennessy, David A. & Lapan, Harvey E., 2006. "On the nature of certainty equivalent functionals," Journal of Mathematical Economics, Elsevier, vol. 43(1), pages 1-10, December.
    13. Christian Gollier & Richard Zeckhauser, 2003. "Collective Investment Decision Making with Heterogeneous Time Preferences," CESifo Working Paper Series 915, CESifo Group Munich.
    14. Jamison Dean T. & Jamison Julian, 2011. "Characterizing the Amount and Speed of Discounting Procedures," Journal of Benefit-Cost Analysis, De Gruyter, vol. 2(2), pages 1-56, April.
    15. Hara, Chiaki & Huang, James & Kuzmics, Christoph, 2011. "Effects of background risks on cautiousness with an application to a portfolio choice problem," Journal of Economic Theory, Elsevier, vol. 146(1), pages 346-358, January.
    16. Toda, Alexis Akira & Walsh, Kieran James, 2014. "The Equity Premium and the One Percent," MPRA Paper 79009, University Library of Munich, Germany, revised 28 Feb 2017.
    17. Carlier, G. & Lachapelle, A., 2011. "A numerical approach for a class of risk-sharing problems," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 1-13, January.
    18. Felix Kubler & Karl Schmedders, 2010. "Non-parametric counterfactual analysis in dynamic general equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 181-200, October.
    19. Christian Ghiglino & Alain Venditti, 2008. "The role of the wealth distribution on output volatility," Working Papers halshs-00281379, HAL.
    20. Chiaki Hara, 2006. "Heterogeneous Risk Attitudes In A Continuous-Time Model," The Japanese Economic Review, Japanese Economic Association, vol. 57(3), pages 377-405.
    21. Gollier, Christian, 2003. "Who Should we Believe? Collective Risk-Taking Decisions with Heterogeneous Beliefs," IDEI Working Papers 201, Institut d'Économie Industrielle (IDEI), Toulouse.
    22. Christian Gollier, 2003. "Collective Risk-Taking Decisions with Heterogeneous Beliefs," CESifo Working Paper Series 909, CESifo Group Munich.
    23. Flåm, Sjur Didrik, 2016. "Borch’s theorem, equal margins, and efficient allocation," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 162-168.

    More about this item

    Keywords

    Aggregation; heterogeneous consumers; absolute risk tolerance; mutual fund theorem;

    JEL classification:

    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D58 - Microeconomics - - General Equilibrium and Disequilibrium - - - Computable and Other Applied General Equilibrium Models
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hit:piedp2:323. 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: (Digital Resources Section, Hitotsubashi University Library). General contact details of provider: http://edirc.repec.org/data/cihitjp.html .

    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 CitEc recognized a reference but did not link an item in RePEc 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 RePEc Author Service 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.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.