IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

Equilibrium in securities markets with heterogeneous investors and unspanned income risk

  • Christensen, Peter Ove
  • Larsen, Kasper
  • Munk, Claus

In a finite time horizon, incomplete market, continuous-time setting with dividends and investor incomes governed by arithmetic Brownian motions, we derive closed-form solutions for the equilibrium risk-free rate and stock price for an economy with finitely many heterogeneous CARA investors and unspanned income risk. In equilibrium, the Sharpe ratio is the same as in an otherwise identical complete market economy, whereas the risk-free rate is lower and, consequently, the stock price is higher. The reduction in the risk-free rate is highest when the more risk-averse investors face the largest unspanned income risk.

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.sciencedirect.com/science/article/pii/S0022053112000087
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 147 (2012)
Issue (Month): 3 ()
Pages: 1035-1063

as
in new window

Handle: RePEc:eee:jetheo:v:147:y:2012:i:3:p:1035-1063
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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. Milton Friedman, 1957. "Introduction to "A Theory of the Consumption Function"," NBER Chapters, in: A Theory of the Consumption Function, pages 1-6 National Bureau of Economic Research, Inc.
  2. John Y. Campbell, 2006. "Household Finance," NBER Working Papers 12149, National Bureau of Economic Research, Inc.
  3. Lars Nielsen & Maria Vassalou, 2006. "The instantaneous capital market line," Economic Theory, Springer, vol. 28(3), pages 651-664, 08.
  4. Alexander David, 2008. "Heterogeneous Beliefs, Speculation, and the Equity Premium," Journal of Finance, American Finance Association, vol. 63(1), pages 41-83, 02.
  5. John Heaton & Deborah Lucas, 2000. "Portfolio Choice and Asset Prices: The Importance of Entrepreneurial Risk," Journal of Finance, American Finance Association, vol. 55(3), pages 1163-1198, 06.
  6. Phillippe Weil, 1997. "The Equity Premium Puzzle and the Risk-Free Rate Puzzle," Levine's Working Paper Archive 1833, David K. Levine.
  7. Steven J. Davis & Felix Kubler & Paul Willen, 2006. "Borrowing Costs and the Demand for Equity over the Life Cycle," The Review of Economics and Statistics, MIT Press, vol. 88(2), pages 348-362, May.
  8. Dirk Krueger & Hanno Lustig, 2006. "When is Market Incompleteness Irrelevant for the Price of Aggregate Risk (and when is it not)?," NBER Working Papers 12634, National Bureau of Economic Research, Inc.
  9. George M. Constantinides, 2002. "Rational Asset Prices," Journal of Finance, American Finance Association, vol. 57(4), pages 1567-1591, 08.
  10. S Rao Aiyagari & Mark Gertler, 1997. "Asset Returns with transaction costs and uninsured individual risk," Levine's Working Paper Archive 648, David K. Levine.
  11. George M. Constantinidies & John B. Donaldson & Rajnish Mehra, 1998. "Junior Can't Borrow: A New Perspective on the Equity Premium Puzzle," NBER Working Papers 6617, National Bureau of Economic Research, Inc.
  12. Storesletten, Kjetil & Telmer, Chris & Yaron, Amir, 2002. "Asset pricing with idiosyncratic risk and overlapping generations," Seminar Papers 703, Stockholm University, Institute for International Economic Studies.
  13. Bernard Dumas & Alexander Kurshev & Raman Uppal, 2007. "Equilibrium Portfolio Strategies in the Presence of Sentiment Risk and Excess Volatility," NBER Working Papers 13401, National Bureau of Economic Research, Inc.
  14. Duffie, Darrell & Jackson, Matthew O., 1990. "Optimal hedging and equilibrium in a dynamic futures market," Journal of Economic Dynamics and Control, Elsevier, vol. 14(1), pages 21-33, February.
  15. Wouter J. Denhaan, 2000. "The Importance Of The Number Of Different Agents In A Heterogeneous Asset-Pricing Model," Computing in Economics and Finance 2000 349, Society for Computational Economics.
  16. Chris I. Telmer, 1991. "Asset Pricing Puzzles and Incomplete Markets," Working Papers 806, Queen's University, Department of Economics.
  17. Zvi Bodie & Robert C. Merton & William F. Samuelson, 1992. "Labor Supply Flexibility and Portfolio Choice in a Life-Cycle Model," NBER Working Papers 3954, National Bureau of Economic Research, Inc.
  18. S. Rao Aiyagari & Mark Gertler, 1990. "Asset Returns with Transactions Cost and Uninsured Risk: A Stage III Exercise," NBER Working Papers 3481, National Bureau of Economic Research, Inc.
  19. Lucas, Deborah J., 1994. "Asset pricing with undiversifiable income risk and short sales constraints: Deepening the equity premium puzzle," Journal of Monetary Economics, Elsevier, vol. 34(3), pages 325-341, December.
  20. Gourinchas, Pierre-Olivier & Parker, Jonathan A, 2000. "Consumption Over the Life-Cycle," CEPR Discussion Papers 2345, C.E.P.R. Discussion Papers.
  21. Orazio P. Attanasio & Monica Paiella, 2006. "Intertemporal Consumption Choices, Transaction Costs and Limited Participation to Financial Markets: Reconciling Data and Theory," NBER Working Papers 12412, National Bureau of Economic Research, Inc.
  22. Henderson, Vicky, 2005. "Explicit solutions to an optimal portfolio choice problem with stochastic income," Journal of Economic Dynamics and Control, Elsevier, vol. 29(7), pages 1237-1266, July.
  23. Per Krusell & Anthony A. Smith, Jr., . "Income and Wealth Heterogeneity, Portfolio Choice, and Equilibrium Asset Returns," GSIA Working Papers 1997-45, Carnegie Mellon University, Tepper School of Business.
  24. Szpiro, George G, 1986. "Measuring Risk Aversion: An Alternative Approach," The Review of Economics and Statistics, MIT Press, vol. 68(1), pages 156-59, February.
  25. 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.
  26. Malinvaud, E., 1972. "The allocation of individual risks in large markets," Journal of Economic Theory, Elsevier, vol. 4(2), pages 312-328, April.
  27. Harald Uhlig, 2010. "A Law of Large Numbers for Large Economies," Levine's Working Paper Archive 2070, David K. Levine.
  28. Wang, Neng, 2009. "Optimal consumption and asset allocation with unknown income growth," Journal of Monetary Economics, Elsevier, vol. 56(4), pages 524-534, May.
  29. Neng Wang, 2003. "Caballero Meets Bewley: The Permanent-Income Hypothesis in General Equilibrium," American Economic Review, American Economic Association, vol. 93(3), pages 927-936, June.
  30. Milton Friedman, 1957. "A Theory of the Consumption Function," NBER Books, National Bureau of Economic Research, Inc, number frie57-1, January.
  31. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
  32. Joao F. Cocco, 2005. "Consumption and Portfolio Choice over the Life Cycle," Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 491-533.
  33. Duffie, J Darrell & Huang, Chi-fu, 1985. "Implementing Arrow-Debreu Equilibria by Continuous Trading of Few Long-lived Securities," Econometrica, Econometric Society, vol. 53(6), pages 1337-56, November.
  34. David K. Levine & William R. Zame, 2002. "Does Market Incompleteness Matter?," Econometrica, Econometric Society, vol. 70(5), pages 1805-1839, September.
  35. Ralph S. J. Koijen & Theo E. Nijman & Bas J. M. Werker, 2010. "When Can Life Cycle Investors Benefit from Time-Varying Bond Risk Premia?," Review of Financial Studies, Society for Financial Studies, vol. 23(2), pages 741-780, February.
  36. Wang, Neng, 2004. "Precautionary saving and partially observed income," Journal of Monetary Economics, Elsevier, vol. 51(8), pages 1645-1681, November.
  37. Christian Gollier & Richard Zeckhauser, 2005. "Aggregation of Heterogeneous Time Preferences," Journal of Political Economy, University of Chicago Press, vol. 113(4), pages 878-896, August.
  38. John Heaton & Deborah Lucas, 1993. "Evaluating the Effects of Incomplete Markets on Risk Sharing and Asset Pricing," NBER Working Papers 4249, National Bureau of Economic Research, Inc.
  39. Hui Guo & Robert F. Whitelaw, 2006. "Uncovering the Risk-Return Relation in the Stock Market," Journal of Finance, American Finance Association, vol. 61(3), pages 1433-1463, 06.
  40. Svensson, L.E. & Werner, I., 1990. "Nontraded Assets in Incomplete Markets: Pricing and Portfolio Choices," Papers 477, Stockholm - International Economic Studies.
  41. Malinvaud, E, 1973. "Markets for an Exchange Economy with Individual Risks," Econometrica, Econometric Society, vol. 41(3), pages 383-410, May.
  42. Munk, Claus & Sørensen, Carsten, 2010. "Dynamic asset allocation with stochastic income and interest rates," Journal of Financial Economics, Elsevier, vol. 96(3), pages 433-462, June.
  43. Wei Xiong & Hongjun Yan & Review Financial, 2007. "Heterogeneous Expectations and Bond Markets," Yale School of Management Working Papers amz2614, Yale School of Management, revised 01 Jun 2009.
  44. Jérôme B. Detemple & René Garcia & Marcel Rindisbacher, 2000. "A Monte-Carlo Method for Optimal Portfolios," CIRANO Working Papers 2000s-05, CIRANO.
  45. Constantinides, George M & Duffie, Darrell, 1996. "Asset Pricing with Heterogeneous Consumers," Journal of Political Economy, University of Chicago Press, vol. 104(2), pages 219-40, April.
  46. Michael Gallmeyer & Burton Hollifield, 2008. "An Examination of Heterogeneous Beliefs with a Short-Sale Constraint in a Dynamic Economy," Review of Finance, European Finance Association, vol. 12(2), pages 323-364.
  47. Lynch, Anthony W. & Tan, Sinan, 2011. "Labor income dynamics at business-cycle frequencies: Implications for portfolio choice," Journal of Financial Economics, Elsevier, vol. 101(2), pages 333-359, August.
  48. Wang, Neng, 2006. "Generalizing the permanent-income hypothesis: Revisiting Friedman's conjecture on consumption," Journal of Monetary Economics, Elsevier, vol. 53(4), pages 737-752, May.
  49. Tano Santos & Pietro Veronesi, 2006. "Labor Income and Predictable Stock Returns," Review of Financial Studies, Society for Financial Studies, vol. 19(1), pages 1-44.
  50. 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.
  51. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-57, August.
  52. Calvet, Laurent E., 2001. "Incomplete Markets and Volatility," Journal of Economic Theory, Elsevier, vol. 98(2), pages 295-338, June.
  53. 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.
  54. Luis M. Viceira, 1999. "Optimal Portfolio Choice for Long-Horizon Investors with Nontradable Labor Income," NBER Working Papers 7409, National Bureau of Economic Research, Inc.
Full references (including those not matched with items on IDEAS)

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

When requesting a correction, please mention this item's handle: RePEc:eee:jetheo:v:147:y:2012:i:3:p:1035-1063. 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: (Zhang, Lei)

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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.