Divergent Reference-Dependent Risk-Attitudes and Endogenous Collateral Constraints

The booms preceding financial crises typically feature high exposure to risky assets, high leverage, asset price growth and low debt margins, which are then followed by sharp de-leveraging after the crisis. We build a model that endogenously generates such heightened leverage/deleverage cycle and asset price boom/bust with three elements. First borrowers exhibit gain-loss preferences around a time-varying reference level, hence they are increasingly risk tolerant at the upper tails and this fosters debt and risky asset demand, while they are loss-averse on the lower tails, something which fosters de-leveraging. Second they are subject to occasionally binding collateral constraints and third, there is heterogeneity in risk-attitudes between borrowers and lenders. The latter implies that the debt margin varies endogenously and countercyclically to close the gap between lenders/borrowers evaluations (namely debt demand and supply). We solve the model analytically and numerically, through a global method, namely policy function iterations with endogenously Markov-switching regimes. Numerically the model matches well several moments for asset prices, returns, equity premia and Sharpe ratio, the volatility of leverage, its procyclicality and the counter-cyclicality of the debt margins.