IDEAS home Printed from https://ideas.repec.org/p/crs/wpaper/2004-12.html
   My bibliography  Save this paper

Aggregation oh Heterogeneous Beliefs, Asset Pricing and Risk Sharing in Complete Financial Markets

Author

Listed:
  • Laurent Calvet

    (Crest)

  • Jean-Michel Grandmont

    (Crest)

  • Isabelle Lemaire

    (Crest)

Abstract

We propose a method to aggregate heterogeneous individual beliefs, givena competitive equilibrium in complete asset markets, into a single "marketprobability" such that it generates, if commonly shared by all investors, thesame marginal valuation of assets by the market (the same equilibrium prices)as well as by each individual investor. As a result of the aggregation process,the market portfolio may have to be scalarly adjusted, upward or downward,a re‡ection of an "aggregation bias" due to the diversity of beliefs.From a "dual" viewpoint, the standard construction of an "expected utilitymaximizing aggregate investor" designed to "represent" the economy inequilibrium, is shown to be also valid in the case of heterogeneous beliefs,modulo the above scalar adjustment of the market portfolio, thereby generatingan "Adjusted" version of the "Consumption based Capital Asset PricingModel" (ACCAPM). The allocation of aggregate and individual risks (mutualization)is then analyzed in relation to deviations of individual beliefsfrom the aggregate "market probability". Finally, we identify the channelsthrough which the distributions, among investors, of individual beliefs and ofother microeconomic characteristics (incomes, attitudes toward risk), do affectpricing of risky assets and thus may, or may not, contribute to explainingsuch challenges as the so-called "equity premium puzzle".

Suggested Citation

  • Laurent Calvet & Jean-Michel Grandmont & Isabelle Lemaire, 2004. "Aggregation oh Heterogeneous Beliefs, Asset Pricing and Risk Sharing in Complete Financial Markets," Working Papers 2004-12, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2004-12
    as

    Download full text from publisher

    File URL: http://crest.science/RePEc/wpstorage/2004-12.pdf
    File Function: Crest working paper version
    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. Constantinides, George M & Duffie, Darrell, 1996. "Asset Pricing with Heterogeneous Consumers," Journal of Political Economy, University of Chicago Press, vol. 104(2), pages 219-240, April.
    3. Douglas T. Breeden & Robert H. Litzenberger & Tingyan Jia, 2015. "Consumption-Based Asset Pricing, Part 2: Habit Formation, Conditional Risks, Long-Run Risks, and Rare Disasters," Annual Review of Financial Economics, Annual Reviews, vol. 7(1), pages 85-131, December.
    4. Harjoat S. Bhamra & Raman Uppal, 2014. "Asset Prices with Heterogeneity in Preferences and Beliefs," Review of Financial Studies, Society for Financial Studies, vol. 27(2), pages 519-580.
    5. Miller, Edward M, 1977. "Risk, Uncertainty, and Divergence of Opinion," Journal of Finance, American Finance Association, vol. 32(4), pages 1151-1168, September.
    6. Angeletos, George-Marios & Calvet, Laurent-Emmanuel, 2006. "Idiosyncratic production risk, growth and the business cycle," Journal of Monetary Economics, Elsevier, vol. 53(6), pages 1095-1115, September.
    7. Lintner, John, 1969. "The Aggregation of Investor's Diverse Judgments and Preferences in Purely Competitive Security Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 4(04), pages 347-400, December.
    8. Angeletos, George-Marios & Calvet, Laurent-Emmanuel, 2005. "Incomplete-market dynamics in a neoclassical production economy," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 407-438, August.
    9. Abel, Andrew B, 1990. "Asset Prices under Habit Formation and Catching Up with the Joneses," American Economic Review, American Economic Association, vol. 80(2), pages 38-42, May.
    10. Andrea Buraschi & Fabio Trojani & Andrea Vedolin, 2014. "When Uncertainty Blows in the Orchard: Comovement and Equilibrium Volatility Risk Premia," Journal of Finance, American Finance Association, vol. 69(1), pages 101-137, February.
    11. Rubinstein, Mark, 1975. "Securities Market Efficiency in an Arrow-Debreu Economy," American Economic Review, American Economic Association, vol. 65(5), pages 812-824, December.
    12. Abel, Andrew B., 2002. "An exploration of the effects of pessimism and doubt on asset returns," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1075-1092, July.
    13. Wei Xiong, 2013. "Bubbles, Crises, and Heterogeneous Beliefs," NBER Working Papers 18905, National Bureau of Economic Research, Inc.
    14. Robert J. Shiller, 2014. "Speculative Asset Prices (Nobel Prize Lecture)," Cowles Foundation Discussion Papers 1936, Cowles Foundation for Research in Economics, Yale University.
    15. 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.
    16. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    17. J. Bradford De Long & Andrei Shleifer & Lawrence H. Summers & Robert J. Waldmann, 1989. "The Size and Incidence of the Losses from Noise Trading," Journal of Finance, American Finance Association, vol. 44(3), pages 681-696, July.
    18. Varian, Hal R, 1985. " Divergence of Opinion in Complete Markets: A Note," Journal of Finance, American Finance Association, vol. 40(1), pages 309-317, March.
    19. 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.
    20. Beber, Alessandro & Breedon, Francis & Buraschi, Andrea, 2010. "Differences in beliefs and currency risk premiums," Journal of Financial Economics, Elsevier, vol. 98(3), pages 415-438, December.
    21. repec:hrv:faseco:33077905 is not listed on IDEAS
    22. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    23. Weil, Philippe, 1992. "Equilibrium asset prices with undiversifiable labor income risk," Journal of Economic Dynamics and Control, Elsevier, vol. 16(3-4), pages 769-790.
    24. 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.
    25. Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March.
    26. Benhabib, Jess & Nishimura, Kazuo, 1979. "The hopf bifurcation and the existence and stability of closed orbits in multisector models of optimal economic growth," Journal of Economic Theory, Elsevier, vol. 21(3), pages 421-444, December.
    27. Mayshar, Joram, 1981. "Transaction Costs and the Pricing of Assets," Journal of Finance, American Finance Association, vol. 36(3), pages 583-597, June.
    28. Denis Gromb & Dimitri Vayanos, 2010. "Limits of Arbitrage: The State of the Theory," NBER Working Papers 15821, National Bureau of Economic Research, Inc.
    29. Benhabib Jess & Rustichini Aldo, 1994. "Introduction to the Symposium on Growth, Fluctuations, and Sunspots: Confronting the Data," Journal of Economic Theory, Elsevier, vol. 63(1), pages 1-18, June.
    30. De Long, J Bradford, et al, 1991. "The Survival of Noise Traders in Financial Markets," The Journal of Business, University of Chicago Press, vol. 64(1), pages 1-19, January.
    31. Andrea Buraschi & Alexei Jiltsov, 2006. "Model Uncertainty and Option Markets with Heterogeneous Beliefs," Journal of Finance, American Finance Association, vol. 61(6), pages 2841-2897, December.
    32. repec:oup:rfinst:v:30:y:2017:i:3:p:750-800. is not listed on IDEAS
    33. Campbell, John Y., 2003. "Consumption-based asset pricing," Handbook of the Economics of Finance,in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 13, pages 803-887 Elsevier.
    34. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
    35. Pok-sang Lam & Stephen G. Cecchetti & Nelson C. Mark, 2000. "Asset Pricing with Distorted Beliefs: Are Equity Returns Too Good to Be True?," American Economic Review, American Economic Association, vol. 90(4), pages 787-805, September.
    36. Jean-Michel Grandmont, 1998. "Expectations Formation and Stability of Large Socioeconomic Systems," Econometrica, Econometric Society, vol. 66(4), pages 741-782, July.
    37. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-1370, November.
    38. Barberis, Nicholas & Greenwood, Robin & Jin, Lawrence & Shleifer, Andrei, 2015. "X-CAPM: An extrapolative capital asset pricing model," Journal of Financial Economics, Elsevier, vol. 115(1), pages 1-24.
    39. Blume, Lawrence & Easley, David, 1992. "Evolution and market behavior," Journal of Economic Theory, Elsevier, vol. 58(1), pages 9-40, October.
    40. Francisco Gomes & Alexander Michaelides, 2008. "Asset Pricing with Limited Risk Sharing and Heterogeneous Agents," Review of Financial Studies, Society for Financial Studies, vol. 21(1), pages 415-448, January.
    41. Benhabib, Jess & Day, Richard H., 1982. "A characterization of erratic dynamics in, the overlapping generations model," Journal of Economic Dynamics and Control, Elsevier, vol. 4(1), pages 37-55, November.
    42. Robert J. Shiller, 2014. "Speculative Asset Prices," American Economic Review, American Economic Association, vol. 104(6), pages 1486-1517, June.
    43. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    44. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    45. Constantinides, George M, 1990. "Habit Formation: A Resolution of the Equity Premium Puzzle," Journal of Political Economy, University of Chicago Press, vol. 98(3), pages 519-543, June.
    46. Aloisio Araujo & Alvaro Sandroni, 1999. "On the Convergence to Homogeneous Expectations when Markets Are Complete," Econometrica, Econometric Society, vol. 67(3), pages 663-672, May.
    47. Rubinstein, Mark, 1974. "An aggregation theorem for securities markets," Journal of Financial Economics, Elsevier, vol. 1(3), pages 225-244, September.
    48. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    49. Lars Peter Hansen & Thomas J. Sargent & Thomas D. Tallarini, 1999. "Robust Permanent Income and Pricing," Review of Economic Studies, Oxford University Press, vol. 66(4), pages 873-907.
    50. De Long, J Bradford & Andrei Shleifer & Lawrence H. Summers & Robert J. Waldmann, 1990. "Noise Trader Risk in Financial Markets," Journal of Political Economy, University of Chicago Press, vol. 98(4), pages 703-738, August.
    51. Bernard Dumas & Alexander Kurshev & Raman Uppal, 2009. "Equilibrium Portfolio Strategies in the Presence of Sentiment Risk and Excess Volatility," Journal of Finance, American Finance Association, vol. 64(2), pages 579-629, April.
    52. Shleifer, Andrei & Summers, Lawrence H, 1990. "The Noise Trader Approach to Finance," Journal of Economic Perspectives, American Economic Association, vol. 4(2), pages 19-33, Spring.
    53. Friend, Irwin & Blume, Marshall E, 1975. "The Demand for Risky Assets," American Economic Review, American Economic Association, vol. 65(5), pages 900-922, December.
    54. Rajnish Mehra, 2012. "Consumption-Based Asset Pricing Models," Annual Review of Financial Economics, Annual Reviews, vol. 4(1), pages 385-409, October.
    55. Shiller, Robert J, 1981. "Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?," American Economic Review, American Economic Association, vol. 71(3), pages 421-436, June.
    56. Morin, Roger A & Fernandez Suarez, Antonio, 1983. " Risk Aversion Revisited," Journal of Finance, American Finance Association, vol. 38(4), pages 1201-1216, September.
    57. Péter Kondor, 2009. "Risk in Dynamic Arbitrage: The Price Effects of Convergence Trading," Journal of Finance, American Finance Association, vol. 64(2), pages 631-655, April.
    58. Nishimura, Kazuo, 1985. "Competitive equilibrium cycles," Journal of Economic Theory, Elsevier, vol. 35(2), pages 284-306, August.
    59. Narayana R. Kocherlakota, 1996. "The Equity Premium: It's Still a Puzzle," Journal of Economic Literature, American Economic Association, vol. 34(1), pages 42-71, March.
    60. Williams, Joseph T., 1977. "Capital asset prices with heterogeneous beliefs," Journal of Financial Economics, Elsevier, vol. 5(2), pages 219-239, November.
    61. Denis Gromb & Dimitri Vayanos, 2010. "Limits of Arbitrage," Annual Review of Financial Economics, Annual Reviews, vol. 2(1), pages 251-275, December.
    62. Jarrow, Robert A, 1980. " Heterogeneous Expectations, Restrictions on Short Sales, and Equilibrium Asset Prices," Journal of Finance, American Finance Association, vol. 35(5), pages 1105-1113, December.
    63. Rubinstein, Mark, 1976. "The Strong Case for the Generalized Logarithmic Utility Model as the Premier Model of Financial Markets," Journal of Finance, American Finance Association, vol. 31(2), pages 551-571, May.
    64. Alvaro Sandroni, 2000. "Do Markets Favor Agents Able to Make Accurate Predicitions?," Econometrica, Econometric Society, vol. 68(6), pages 1303-1342, November.
    65. Mayshar, Joram, 1983. "On Divergence of Opinion and Imperfections in Capital Markets," American Economic Review, American Economic Association, vol. 73(1), pages 114-128, March.
    66. Cass, David & Shell, Karl, 1983. "Do Sunspots Matter?," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 193-227, April.
    67. Azariadis, Costas, 1981. "Self-fulfilling prophecies," Journal of Economic Theory, Elsevier, vol. 25(3), pages 380-396, December.
    68. John G. Cragg & Burton G. Malkiel, 1982. "Expectations and the Structure of Share Prices," NBER Books, National Bureau of Economic Research, Inc, number crag82-1, July-Dec.
    69. Gonedes, Nicholas J, 1976. "Capital Market Equilibrium for a Class of Heterogeneous Expectations in a Two-Parameter World," Journal of Finance, American Finance Association, vol. 31(1), pages 1-15, March.
    70. Constantinides, George M, 1982. "Intertemporal Asset Pricing with Heterogeneous Consumers and without Demand Aggregation," The Journal of Business, University of Chicago Press, vol. 55(2), pages 253-267, April.
    71. John Geanakoplos & Ana Fostel, 2008. "Leverage Cycles and the Anxious Economy," American Economic Review, American Economic Association, vol. 98(4), pages 1211-1244, September.
    72. Sargent, Thomas J., 1993. "Bounded Rationality in Macroeconomics: The Arne Ryde Memorial Lectures," OUP Catalogue, Oxford University Press, number 9780198288695.
    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. Laurent Linnemer & Michael Visser, 2018. "Jean-Michel Grandmont A forthcoming mind," Working Papers 2018-06, Center for Research in Economics and Statistics.
    2. Angus A Brown & L C G Rogers, 2010. "Diverse Beliefs," Papers 1001.1450, arXiv.org.
    3. Branch, William A. & McGough, Bruce, 2008. "Replicator dynamics in a Cobweb model with rationally heterogeneous expectations," Journal of Economic Behavior & Organization, Elsevier, vol. 65(2), pages 224-244, February.

    More about this item

    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:crs:wpaper:2004-12. 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: (Sri Srikandan). General contact details of provider: http://edirc.repec.org/data/crestfr.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.