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

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  • Institut for Økonomi
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.
UdgiverInstitut for Økonomi, Aarhus Universitet
Antal sider50
StatusUdgivet - 2008

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