Portfolio and Consumption Choice with Stochastic Investment Opportunities and Habit Formation in Preferences

We study the dynamic consumption and portfolio choice of an investor who has habit formation in preferences and access to a complete financial market. For general, possibly non-Markov, dynamics of market prices, we provide an exact characterization of the optimal behavior in terms of two relatively simple and intuitively interpretable stochastic processes. We study in more detail the optimal strategies in two concrete examples of time-varying investment opportunities. Firstly, we derive a closed-form solution of the optimal consumption and portfolio choice with mean-reverting stock returns. Secondly, with Cox-Ingersoll-Ross interest rate dynamics we can express the optimal strategies in terms of the solution to a partial differential equation, which has an explicit solution for time-additive preferences, but not with habit formation. Our numerical examples show that, while hedging demands for various assets are affected differently by habit persistence, the main effect on relative asset allocations stems from the fact that some assets (bonds and cash) are better investment objects than others (stocks) when it comes to ensuring that future consumption will not fall below the habit level. The implications of habit persistence in models with labor income are also addressed