The Role of Default and Asset-Backed Securities for Sharing Idiosyncratic Risk

I develop a highly tractable, heterogeneous agent, incomplete markets dynamic stochastic general equilibrium model with collateralized lending and asset-backed securities. Agents who face aggregate and idiosyncratic investment risk can borrow by putting up their investments as collateral. Borrowers can default at any time, with the only penalty being the confiscation of collateral. The debt contracts are pooled and issued as asset-backed securities. Under a natural loan-to-value (LTV) constraint I prove the existence of equilibrium. The equilibrium allocation weakly Pareto dominates the autarky allocation, but strictly Pareto dominates only if there is active default. Assets in zero net supply or tranching are irrelevant for risk sharing when agents have a common relative risk aversion coefficient. In a numerical example with risk aversion 2, expected investment return 8%, and volatility 15%, as the collateral requirement loosens the welfare approaches that in complete markets, the borrowing rate sharply increases from −1% to 20%, while the risk-free rate stays below 2%. Therefore the model predicts realistic equity premium and risk-free rate.