Habit formation and lifetime portfolio selection
A life cycle model in which an investor (a) faces i.i.d. asset returns, (b) receives no non-asset income, and (c) has an iso-elastic period utility function, predicts that the investor will allocate a constant fraction of his wealth to risky securities over his lifetime. This result is at odds with both economic intuition and the empirical evidence on asset allocation of individuals. In this work we investigate the effect that habit formation has on life cycle portfolio allocation. This amounts to relaxing assumption (c) by making period utility dependent on past consumption. We derive the optimal consumption and investment policies for a finitely-lived investor in discrete time and find that habit formation can explain increasingly conservative as well as hump-shaped investment patterns over the life cycle, both of which have been documented empirically. The crucial element determining which pattern obtains is the initial habit of a young investor. Furthermore we find that habit formation induces much stronger life cycle effects than those obtained by relaxing either assumptions (a) or (b): Return predictability is of negligible importance in a habit formation model, and labor income alone cannot generate hump-shaped investment patterns. Next we show that our basic results are robust to whether habit formation is introduced into the utility function as a difference or ratio, and to whether the habit stock consists of only one lag or a distributed lag of consumption. In contrast, the endogeneity of habit is crucial to our results--a model with a constant subsistence level, which is nested in our more general model, cannot produce the same life cycle investment patterns. Finally, we show that a continuous-time version of our habit model yields qualitatively different results.
|Year of publication:||
|Authors:||Lax, Yoel E|
|Type of publication:||Other|
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