Optimal Housing, Consumption, and Investment Decisions over the Life-Cycle

We provide explicit solutions to life-cycle utility maximization problems involving dynamic decisions on investments in stocks and bonds, consumption of perishable goods, and the rental and the ownership of residential real estate. House prices, stock prices, interest rates, and the labor income of the decision-maker follow correlated stochastic processes. The explicit consumption and investment strategies are simple and intuitive and are thoroughly discussed and illustrated in the paper. A calibrated version of the model exhibits many interesting and realistic features. For example, due to a positive correlation between house prices and labor income, young individuals want little (or even negative) exposure to house price risk and tend to rent their home. Later in life, when human wealth declines, the desired housing investment increases and will eventually reach and exceed the desired housing consumption, suggesting that the individual should buy his home---and buy either additional housing units (for renting out) or house price linked financial assets. In the final years, preferences shift back to home rental. While our model involves continuous adjustments of the consumption of housing services and the exposure of wealth to house price risk, we demonstrate that the derived strategies are still useful if the housing positions are only reset infrequently. Our results suggest that markets for REITs or other financial contracts linked to house prices will lead to non-negligible improvements of welfare