ENDOGENOUS DEFAULTS, VALUE-AT-RISK AND THE BUSINESS CYCLE

The procyclical leverage cap compounds the procyclical behaviour of the bank’s equity, restricting credit supply in the trough of the business cycle and easing it when the economy is booming. [...] Note also that the fluc- tuation of the return on capital RIt+1 is the only source of changes in the default rates beyond what is expected at the time of loan issuance; all other variables affecting the distance to default ξt+1 are known at the time of issuance. [...] The inability of the bank to immediately replenish its equity capital is in line with the empirical observations in Adrian and Shin (2010, 2014), where the authors show that the first variable of adjustment used by brokers/dealers when adjusting leverage is the assets’ side of the balance sheet as opposed to equity capital that remains stable in the short term. [...] A good measure of the risk of the bank’s portfolio would depend on the size of the portfolio Xt, the loans’ interest rate Rt, and the distribution of distance-to-defaults ξt+1 affecting the performance of the bank’s portfolio at time t+ 1. [...] These factors are the bank equity EBt = (1− dt−1)πBt , which is determined by the performance of the bank’s portfolio; the loan demand driven by the variable E RI Dt t+1/Rt ; and the credit spread reflecting the riskiness of the VaR scenario SV aRt.