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A Class of Tractable Incomplete-Market Models for Studying Asset Returns and Risk Exposure

Author

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  • François Le Grand

    (EM - EMLyon Business School, D-ERDW - Departement Erdwissenschaften [ETH Zürich] - ETH Zürich - Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich])

  • Xavier Ragot

    (ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique, CNRS - Centre National de la Recherche Scientifique, OFCE - Observatoire français des conjonctures économiques (Sciences Po) - Sciences Po - Sciences Po)

Abstract

We present a class of tractable incomplete-market models, where agents face both aggregate risk and limited participation in financial markets. Tractability relies on the assumptions of small asset volumes and of a period utility function that is linear beyond a threshold, in line with Fishburn's (1977) contribution in decision theory. We prove the existence of an equilibrium and derive theoretical results regarding asset prices and consumption choices. This small-trade model is able to reproduce a low safe return and a high equity premium, together with a realistic representation of household exposure to both idiosyncratic and aggregate risks.

Suggested Citation

  • François Le Grand & Xavier Ragot, 2018. "A Class of Tractable Incomplete-Market Models for Studying Asset Returns and Risk Exposure," Post-Print hal-03949545, HAL.
    • Handle: RePEc:hal:journl:hal-03949545
    DOI: 10.1016/j.euroecorev.2018.01.003
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    1. Challe, Edouard & Le Grand, François & Ragot, Xavier, 2013. "Incomplete markets, liquidation risk, and the term structure of interest rates," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2483-2519.
    2. Kevin M. Murphy & Finis Welch, 1992. "The Structure of Wages," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(1), pages 285-326.
    3. 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.
    4. Robert E. Hall, 2010. "Basic Analysis of Forward-Looking Decision Making," Introductory Chapters, in: Forward-Looking Decision Making: Dynamic Programming Models Applied to Health, Risk, Employment, and Financial Stability, Princeton University Press.
    5. Duffie, Darrell, et al, 1994. "Stationary Markov Equilibria," Econometrica, Econometric Society, vol. 62(4), pages 745-781, July.
    6. Basak, Suleyman & Cuoco, Domenico, 1998. "An Equilibrium Model with Restricted Stock Market Participation," The Review of Financial Studies, Society for Financial Studies, vol. 11(2), pages 309-341.
    7. Annette Vissing-Jorgensen, 2000. "Towards an Explanation of Household Portfolio Choice Heterogeneity: Nonfinancial Income and Participation Cost Structures," Econometric Society World Congress 2000 Contributed Papers 1102, Econometric Society.
    8. YiLi Chien & Harold Cole & Hanno Lustig, 2012. "Is the Volatility of the Market Price of Risk Due to Intermittent Portfolio Rebalancing?," American Economic Review, American Economic Association, vol. 102(6), pages 2859-2896, October.
    9. Mark Aguiar & Mark Bils, 2015. "Has Consumption Inequality Mirrored Income Inequality?," American Economic Review, American Economic Association, vol. 105(9), pages 2725-2756, September.
    10. John Moore & Nobuhiro Kiyotaki, 2008. "Liquidity, Business Cycles, and Monetary Policy," 2008 Meeting Papers 35, Society for Economic Dynamics.
    11. Mukoyama, Toshihiko & Sahin, Aysegul, 2006. "Costs of business cycles for unskilled workers," Journal of Monetary Economics, Elsevier, vol. 53(8), pages 2179-2193, November.
    12. Judd, Kenneth L., 1985. "The law of large numbers with a continuum of IID random variables," Journal of Economic Theory, Elsevier, vol. 35(1), pages 19-25, February.
    13. Kubler, Felix & Schmedders, Karl, 2002. "Recursive Equilibria In Economies With Incomplete Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 6(2), pages 284-306, April.
    14. Fishburn, Peter C, 1977. "Mean-Risk Analysis with Risk Associated with Below-Target Returns," American Economic Review, American Economic Association, vol. 67(2), pages 116-126, March.
    15. Becker, Robert & Zilcha, Itzhak, 1997. "Stationary Ramsey Equilibria under Uncertainty," Journal of Economic Theory, Elsevier, vol. 75(1), pages 122-140, July.
    16. Jonathan Heathcote & Kjetil Storesletten & Giovanni L. Violante, 2009. "Quantitative Macroeconomics with Heterogeneous Households," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 319-354, May.
    17. Walentin Karl, 2010. "Earnings Inequality and the Equity Premium," The B.E. Journal of Macroeconomics, De Gruyter, vol. 10(1), pages 1-23, November.
    18. Yannis Bilias & Dimitris Georgarakos & Michael Haliassos, 2010. "Portfolio Inertia and Stock Market Fluctuations," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 42(4), pages 715-742, June.
    19. van Rooij, Maarten & Lusardi, Annamaria & Alessie, Rob, 2011. "Financial literacy and stock market participation," Journal of Financial Economics, Elsevier, vol. 101(2), pages 449-472, August.
    20. Miao, Jianjun, 2006. "Competitive equilibria of economies with a continuum of consumers and aggregate shocks," Journal of Economic Theory, Elsevier, vol. 128(1), pages 274-298, May.
    21. Ricardo Lagos & Randall Wright, 2005. "A Unified Framework for Monetary Theory and Policy Analysis," Journal of Political Economy, University of Chicago Press, vol. 113(3), pages 463-484, June.
    22. Yili Chien & Harold Cole & Hanno Lustig, 2011. "A Multiplier Approach to Understanding the Macro Implications of Household Finance," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(1), pages 199-234.
    23. Mankiw, N. Gregory & Zeldes, Stephen P., 1991. "The consumption of stockholders and nonstockholders," Journal of Financial Economics, Elsevier, vol. 29(1), pages 97-112, March.
    24. Tri Vi Dang & Gary Gorton & Bengt Holmström & Guillermo Ordoñez, 2017. "Banks as Secret Keepers," American Economic Review, American Economic Association, vol. 107(4), pages 1005-1029, April.
    25. Giacomo De Giorgi & Luca Gambetti, 2017. "Business Cycle Fluctuations and the Distribution of Consumption," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 23, pages 19-41, January.
    26. Campbell, John Y., 1999. "Asset prices, consumption, and the business cycle," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 19, pages 1231-1303, Elsevier.
    27. Greg Kaplan & Giovanni L. Violante & Justin Weidner, 2014. "The Wealthy Hand-to-Mouth," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 48(1 (Spring), pages 77-153.
    28. Polkovnichenko, Valery, 2004. "Limited stock market participation and the equity premium," Finance Research Letters, Elsevier, vol. 1(1), pages 24-34, March.
    29. Tom Krebs, 2006. "Recursive equilibrium in endogenous growth models with incomplete markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(3), pages 505-523, November.
    30. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    31. Favilukis, Jack, 2013. "Inequality, stock market participation, and the equity premium," Journal of Financial Economics, Elsevier, vol. 107(3), pages 740-759.
    32. Bruce D. Meyer & James X. Sullivan, 2013. "Consumption and Income Inequality and the Great Recession," American Economic Review, American Economic Association, vol. 103(3), pages 178-183, May.
    33. Nobuhiro Kiyotaki & John Moore, 2005. "2002 Lawrence R. Klein Lecture Liquidity And Asset Prices," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 46(2), pages 317-349, May.
    34. Robert Shimer, 2005. "The Cyclical Behavior of Equilibrium Unemployment and Vacancies," American Economic Review, American Economic Association, vol. 95(1), pages 25-49, March.
    35. Fatih Guvenen, 2009. "A Parsimonious Macroeconomic Model for Asset Pricing," Econometrica, Econometric Society, vol. 77(6), pages 1711-1750, November.
    36. Krusell, Per & Mukoyama, Toshihiko & Smith Jr., Anthony A., 2011. "Asset prices in a Huggett economy," Journal of Economic Theory, Elsevier, vol. 146(3), pages 812-844, May.
    37. George M. Constantinides & Anisha Ghosh, 2017. "Asset Pricing with Countercyclical Household Consumption Risk," Journal of Finance, American Finance Association, vol. 72(1), pages 415-460, February.
    38. Jonathan A. Parker & Annette Vissing-Jorgensen, 2009. "Who Bears Aggregate Fluctuations and How?," American Economic Review, American Economic Association, vol. 99(2), pages 399-405, May.
    39. François Grand & Xavier Ragot, 2016. "Incomplete markets and derivative assets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(3), pages 517-545, August.
    40. Satyajit Chatterjee & Dean Corbae & Makoto Nakajima & José-Víctor Ríos-Rull, 2007. "A Quantitative Theory of Unsecured Consumer Credit with Risk of Default," Econometrica, Econometric Society, vol. 75(6), pages 1525-1589, November.
    41. Markus K. Brunnermeier & Stefan Nagel, 2008. "Do Wealth Fluctuations Generate Time-Varying Risk Aversion? Micro-evidence on Individuals," American Economic Review, American Economic Association, vol. 98(3), pages 713-736, June.
    42. Greg Kaplan & Giovanni L. Violante, 2014. "A Model of the Consumption Response to Fiscal Stimulus Payments," Econometrica, Econometric Society, vol. 82(4), pages 1199-1239, July.
    43. repec:hal:pseose:halshs-00944920 is not listed on IDEAS
    44. Jonathan Heathcote & Fabrizio Perri & Giovanni L. Violante, 2010. "Unequal We Stand: An Empirical Analysis of Economic Inequality in the United States: 1967-2006," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 13(1), pages 15-51, January.
    45. Greg Kaplan & Giovanni L. Violante & Justin Weidner, 2014. "The Wealthy Hand-to-Mouth," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 45(1 (Spring), pages 77-153.
    46. Harald Uhlig, 1996. "A law of large numbers for large economies (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 41-50.
    47. Wen, Yi, 2015. "Money, liquidity and welfare," European Economic Review, Elsevier, vol. 76(C), pages 1-24.
    48. Francisco Gomes & Alexander Michaelides, 2008. "Asset Pricing with Limited Risk Sharing and Heterogeneous Agents," The Review of Financial Studies, Society for Financial Studies, vol. 21(1), pages 415-448, January.
    49. Coleman, Wilbur John, II, 1991. "Equilibrium in a Production Economy with an Income Tax," Econometrica, Econometric Society, vol. 59(4), pages 1091-1104, July.
    50. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 867-896, October.
    51. Allen, Franklin & Gale, Douglas, 1994. "Limited Market Participation and Volatility of Asset Prices," American Economic Review, American Economic Association, vol. 84(4), pages 933-955, September.
    52. Feldman, Mark & Gilles, Christian, 1985. "An expository note on individual risk without aggregate uncertainty," Journal of Economic Theory, Elsevier, vol. 35(1), pages 26-32, February.
    53. Gârleanu, Nicolae & Kogan, Leonid & Panageas, Stavros, 2012. "Displacement risk and asset returns," Journal of Financial Economics, Elsevier, vol. 105(3), pages 491-510.
    54. Moritz Kuhn, 2013. "Recursive Equilibria In An Aiyagari‐Style Economy With Permanent Income Shocks," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 54, pages 807-835, August.
    55. Huggett, Mark, 1993. "The risk-free rate in heterogeneous-agent incomplete-insurance economies," Journal of Economic Dynamics and Control, Elsevier, vol. 17(5-6), pages 953-969.
    56. Scheinkman, Jose A & Weiss, Laurence, 1986. "Borrowing Constraints and Aggregate Economic Activity," Econometrica, Econometric Society, vol. 54(1), pages 23-45, January.
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    More about this item

    Keywords

    Incomplete markets; Risk sharing; Consumption inequalities;
    All these keywords.

    JEL classification:

    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution

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