Optimal Consumption and Portfolio Choices with Risky Housing and Borrowing Constraints

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Abstract
We examine the optimal dynamic portfolio decisions for investors who acquire housing services from either renting or owning a house. Our results show that when indifferent between owning and renting, investors owning a house hold a lower equity proportion in their net worth (bonds, stocks, and home equity), reflecting the substitution effect, yet hold a higher equity proportion in their liquid portfolios (bonds and stocks), reflecting the diversification effect. Furthermore, following the suboptimal policy of always renting leads investors to overweigh in stocks, while following the suboptimal policy of always owning a house causes investors to underweigh in stocks.