The Basel II standards for banking specify procedures for estimating the exposure to risk. In particular, Basel II specifies how much cash banks must keep on hand to cover bad loans. One element of these standards is the following formula, which expresses the expected amount lost when a borrower defaults on a loan:
Expected Loss = PD × EAD × LGD
where PD is the probability of default on the loan, EAD is the exposure at default (the face value of the loan), and LGD is the loss given default (expressed as a percentage of the loan).
For a certain class of mortgages, 6% of the borrowers are expected to default. The face value of these mortgages averages $250,000. On average, the bank recovers 80% of the mortgaged amount if the borrower defaults by selling the property.
(a) What is the expected loss on a mortgage?
(b) Each stated characteristic is a sample estimate. The 95% confidence intervals are [0.05 to 0.07] for PD, [$220,000 to $290,000] for EAD, and [0.18 to 0.23] for LGD. What effect does this uncertainty have on the expected loss?
(c) What can be said about the coverage of the range implied by combining these intervals?