Risk-based capital requirements and optimal liquidation in a stress scenario

We develop a simple yet realistic framework to analyze the impact of an exogenous shock on a bank's balance-sheet and its optimal response when it is constrained to maintain its risk-based capital ratio above a regulatory threshold. We show that in a stress scenario, capital requirements may force the bank to shrink the size of its assets and we exhibit the bank's optimal strategy as a function of regulatory risk-weights, asset market liquidity and shock size. When financial markets are perfectly competitive, we show that the bank is always able to restore its capital ratio above the required one. However, for banks constrained to sell their loans at a discount and/or with a positive price impact when selling their marketable assets (large banks) we exhibit situations in which the deleveraging process generates a death spiral. We then show how to calibrate our model using annual reports of banks and study in detail the case of the French bank BNP Paribas. Finally, we suggest how our simple framework can be used to design a systemic capital surcharge