Question

Q3: Suppose ExBank’s risk analysts have estimated that the expected default rate on a commercial loan portfolio is 10%. The portfolio currently contains $500 million in commercial loan assets. Estimated recovery rates on the portfolio are 65%. The volatility associated with commercial defaults is 6%. Assume the adverse volatility factor is 1.96 and a 10 day VaR. Using what you know already for how to calculate VaR, what is the economic capital of the commercial loan portfolio?

Answer 1

Economic capital = VaR - EXPECTED loss

expected loss = PD * LGD * EAD

PD = probability of default = 10%

LGD = loss given default = 1- recovery rate = 1 - .65 = 0.35 = 35%

EAD = EXPOSURE at default = $500 million

Expected loss = 0.10 * 0.35 * 500

= 17.5 million

VALUE AT RISK

VaR = Standard deviation * volatility factor * exposure

= 1.96 * 0.06 * 500

= 58.8

Ten day VAR = 58.8 * ?10

= 185.9

Economic capital = value at risk - expected loss

= 185.9 -17.5

= $168.4 million