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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.

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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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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/

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