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

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Author Info
Thomas Q. Pedersen () (School of Economics and Management, University of Aarhus, Denmark and CREATES)

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Abstract

In this paper we derive an approximate analytical solution to the optimal con- sumption 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 ap- proach 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 ev- idence from the asset pricing literature. We show that accounting for habit a¤ects 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.

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

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Date of creation: 01 Dec 2008
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Handle: RePEc:aah:create:2008-60

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Related research
Keywords: Intertemporal consumption and portfolio choice; habit formation; time-varying expected returns; time-varying risk aversion;

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Find related papers by JEL classification:
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions
G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing

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    Other versions:
  2. 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. [Downloadable!] (restricted)
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    Other versions:
  7. Campbell, John Y. & Chan, Yeung Lewis & Viceira, Luis M., 2003. "A multivariate model of strategic asset allocation," Journal of Financial Economics, Elsevier, vol. 67(1), pages 41-80, January. [Downloadable!] (restricted)
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  8. Tom Engsted & Thomas Q. Pedersen, 2008. "Return predictability and intertemporal asset allocation: Evidence from a bias-adjusted VAR model," CREATES Research Papers 2008-27, School of Economics and Management, University of Aarhus. [Downloadable!]
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  11. 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. [Downloadable!] (restricted)
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  20. Sydney Ludvigson & Martin Lettau, 1999. "Consumption, aggregate wealth and expected stock returns," Staff Reports 77, Federal Reserve Bank of New York. [Downloadable!]
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  22. 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. [Downloadable!]
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    Other versions:
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