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

We derive explicit solutions to life‐cycle utility maximization problems involving stock and bond investment, perishable consumption, and the rental and ownership of residential real estate. Prices of houses, stocks and bonds, and labor income are correlated. Because of a positive correlation between house prices and labor income, young individuals want little exposure to house price risk and tend to rent their home. Later in life the desired housing investment increases and will eventually reach and exceed the desired consumption, suggesting that the individual should buy his home–and either additional housing units (for renting out) or house price–linked financial assets. In the final years, preferences shift back to home rental. The derived strategies are still useful if housing positions are only reset infrequently. Our results suggest that markets for real estate investment trusts or other house price–linked contracts lead to nonnegligible welfare gains.