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

Intertemporal Asset Allocation with Habit Formation in Preferences: An Approximate Analytical Solution

  • Thomas Q. Pedersen

    ()

    (School of Economics and Management, University of Aarhus, Denmark and CREATES)

In this paper we derive an approximate analytical solution to the optimal consumption and portfolio choice problem of an infinitely-lived investor with power utility defined over the difference between consumption and an external habit. The investor is assumed to have access to two tradable assets: a risk free asset with constant return and a risky asset with a time-varying premium. We extend the approach proposed by Campbell and Viceira (1999), which builds on log-linearizations of the Euler equation, intertemporal budget constraint, and portfolio return, to also contain the log-linearized surplus consumption ratio. The "difference habit model" implies that the relative risk aversion is time-varying which is in line with recent evidence from the asset pricing literature. We show that accounting for habit affects both the myopic and intertemporal hedge component of optimal asset demand, and introduces an additional component that works as a hedge against changes in the investor's habit level. In an empirical application, we calibrate the model to U.S. data and show that habit formation has significant effects on both the optimal consumption and portfolio choice compared to a standard CRRA utility function.

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: ftp://ftp.econ.au.dk/creates/rp/08/rp08_60.pdf
Download Restriction: no

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2008-60.

as
in new window

Length: 50
Date of creation: 01 Dec 2008
Date of revision:
Handle: RePEc:aah:create:2008-60
Contact details of provider: Web page: http://www.econ.au.dk/afn/

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. John Y. Campbell & Luis M. Viceira, 1996. "Consumption and Portfolio Decisions When Expected Returns are Time Varying," NBER Working Papers 5857, National Bureau of Economic Research, Inc.
  2. John Y. Campbell, 1992. "Intertemporal Asset Pricing Without Consumption Data," NBER Working Papers 3989, National Bureau of Economic Research, Inc.
  3. Kim, Tong Suk & Omberg, Edward, 1996. "Dynamic Nonmyopic Portfolio Behavior," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 141-61.
  4. Campbell, John Y, 1996. "Understanding Risk and Return," Journal of Political Economy, University of Chicago Press, vol. 104(2), pages 298-345, April.
  5. John Y. Campbell & Robert J. Shiller, 1988. "Stock Prices, Earnings and Expected Dividends," NBER Working Papers 2511, National Bureau of Economic Research, Inc.
  6. John H. Cochrane, 1999. "Portfolio Advice for a Multifactor World," NBER Working Papers 7170, National Bureau of Economic Research, Inc.
  7. Campbell, John Y, 1991. "A Variance Decomposition for Stock Returns," Economic Journal, Royal Economic Society, vol. 101(405), pages 157-79, March.
  8. Samuelson, Paul A, 1969. "Lifetime Portfolio Selection by Dynamic Stochastic Programming," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 239-46, August.
  9. Abel, A.B., 1990. "Asset Prices Under Habit Formation And Catching Up With The Joneses," Weiss Center Working Papers 1-90, Wharton School - Weiss Center for International Financial Research.
  10. Munk, Claus, 2008. "Portfolio and consumption choice with stochastic investment opportunities and habit formation in preferences," Journal of Economic Dynamics and Control, Elsevier, vol. 32(11), pages 3560-3589, November.
  11. Hindy, Ayman & Huang, Chi-fu & Zhu, Steven H., 1997. "Optimal consumption and portfolio rules with durability and habit formation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(2-3), pages 525-550.
  12. Valery Polkovnichenko, 2007. "Life-Cycle Portfolio Choice with Additive Habit Formation Preferences and Uninsurable Labor Income Risk," Review of Financial Studies, Society for Financial Studies, vol. 20(1), pages 83-124, January.
  13. Engsted, Tom & Pedersen, Thomas Q., 2012. "Return predictability and intertemporal asset allocation: Evidence from a bias-adjusted VAR model," Journal of Empirical Finance, Elsevier, vol. 19(2), pages 241-253.
  14. G. Constantinides, 1990. "Habit formation: a resolution of the equity premium puzzle," Levine's Working Paper Archive 1397, David K. Levine.
  15. Campbell, John Y & Chan, Yeung Lewis & Viceira, Luis M, 2001. "A Multivariate Model of Strategic Asset Allocation," CEPR Discussion Papers 3070, C.E.P.R. Discussion Papers.
  16. R. Mehra & E. Prescott, 2010. "The equity premium: a puzzle," Levine's Working Paper Archive 1401, David K. Levine.
  17. Nicholas Barberis, 2000. "Investing for the Long Run when Returns Are Predictable," Journal of Finance, American Finance Association, vol. 55(1), pages 225-264, 02.
  18. Bekaert, Geert & Hodrick, Robert J. & Marshall, David A., 1997. "On biases in tests of the expectations hypothesis of the term structure of interest rates," Journal of Financial Economics, Elsevier, vol. 44(3), pages 309-348, June.
  19. Epstein, Larry G & Zin, Stanley E, 1989. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework," Econometrica, Econometric Society, vol. 57(4), pages 937-69, July.
  20. R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers 58, Massachusetts Institute of Technology (MIT), Department of Economics.
  21. Sydney Ludvigson & Martin Lettau, 1999. "Consumption, aggregate wealth and expected stock returns," Staff Reports 77, Federal Reserve Bank of New York.
  22. Gomes, Francisco J & Michaelides, Alexander, 2003. "Portfolio Choice with Internal Habit Formation: A Life-Cycle Model with Uninsurable Labour Income Risk," CEPR Discussion Papers 3868, C.E.P.R. Discussion Papers.
  23. Kocherlakota, N., 1995. "The Equity Premium: It's Still a Puzzle," Working Papers 95-05, University of Iowa, Department of Economics.
  24. Wachter, Jessica A., 2002. "Portfolio and Consumption Decisions under Mean-Reverting Returns: An Exact Solution for Complete Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 37(01), pages 63-91, March.
  25. Lynch, Anthony W., 2001. "Portfolio choice and equity characteristics: characterizing the hedging demands induced by return predictability," Journal of Financial Economics, Elsevier, vol. 62(1), pages 67-130, October.
  26. Epstein, Larry G & Zin, Stanley E, 1991. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 263-86, April.
  27. Sundaresan, Suresh M, 1989. "Intertemporally Dependent Preferences and the Volatility of Consumption and Wealth," Review of Financial Studies, Society for Financial Studies, vol. 2(1), pages 73-89.
  28. 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 551-71, May.
  29. Balduzzi, Pierluigi & Lynch, Anthony W., 1999. "Transaction costs and predictability: some utility cost calculations," Journal of Financial Economics, Elsevier, vol. 52(1), pages 47-78, April.
  30. Ingersoll, Jonathan Jr., 1992. "Optimal consumption and portfolio rules with intertemporally dependent utility of consumption," Journal of Economic Dynamics and Control, Elsevier, vol. 16(3-4), pages 681-712.
  31. Bodie, Zvi & Detemple, Jerome B. & Otruba, Susanne & Walter, Stephan, 2004. "Optimal consumption-portfolio choices and retirement planning," Journal of Economic Dynamics and Control, Elsevier, vol. 28(6), pages 1115-1148, March.
  32. Fama, Eugene F. & French, Kenneth R., 1989. "Business conditions and expected returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 25(1), pages 23-49, November.
  33. Fama, Eugene F. & French, Kenneth R., 1988. "Dividend yields and expected stock returns," Journal of Financial Economics, Elsevier, vol. 22(1), pages 3-25, October.
  34. 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.
  35. 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.
  36. Brennan, Michael J. & Schwartz, Eduardo S. & Lagnado, Ronald, 1997. "Strategic asset allocation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1377-1403, June.
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:aah:create:2008-60. 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: ()

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.