I propose a life-cycle model where a finitely lived risk averse agent finances her housing investment choosing to provide a down payment. After signing the mortgage contract, the agent may strategically default and move into the rental market. Risk neutral lenders efficiently price mortgages charging a default premium to compensate themselves for expected losses due to default on a mortgage. As a result, mortgage value and amount of leverage are closely linked. An alternative is for the agent to rent the same house, paying a rent fully adjustable to house prices. The rent risk premium is set such that the agent is indifferent ex ante between owning with a mortgage and renting. Three main results arise. First, the optimal down payment and the house price volatility are positively related. The higher the house price volatility, the higher the down payment the agent provides to decrease the volatility of the equity share in the house. Second, in the presence of borrowing constraints, a higher risk of unemployment persistence and/or a substantial drop in labor income decreases the leveraged position the agent takes. Third, ruling out the effect of taking costly leverage on owning a house significantly biases the results in favor of owning over renting.
Default premium loan to income ratio and loan to value ratio negative home equity rent risk premium