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

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  • Thomas Q. Pedersen

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

Abstract

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.

Suggested Citation

  • Thomas Q. Pedersen, 2008. "Intertemporal Asset Allocation with Habit Formation in Preferences: An Approximate Analytical Solution," CREATES Research Papers 2008-60, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2008-60
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    File URL: ftp://ftp.econ.au.dk/creates/rp/08/rp08_60.pdf
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    More about this item

    Keywords

    Intertemporal consumption and portfolio choice; habit formation; time-varying expected returns; time-varying risk aversion;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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