Asset Pricing with Stochastic Habit Formation

Abstract

This paper examines optimal consumption/portfolio choices under stochastic habit formation in which it is uncertain how deep consumers would become in the habit of consuming in future. By extending Shroder and Skiadas [1] to stochastic habit formation, the optimization problem with stochastic habit forming preferences is transformed into that with simple time-additive preferences. Optimal portfolios are composed of the tangency portfolio and habit hedging portfolio. Resulting risk premia are characterized by consumption beta, which is proportionate to the covariance with consumption changes, and habit beta, defined by using the covariance with habit.