# Question: The Basel II standards for banking specify procedures for estimating

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?

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?

## Answer to relevant Questions

Catalog sales companies such as L.L. Bean encourage customers to place orders by mailing seasonal catalogs to prior customers. The expected profit from each mailed catalog can be expressed as the product Expected profit = p ...Suppose that for budget planning purposes the city in Exercise 39 needs a better estimate of the mean daily income from parking fees. (a) Someone suggests that the city use its data to create a 95% confidence interval ...Direct mail advertisers send solicitations (junk mail) to thousands of potential customers hoping that some will buy the product. The response rate is usually quite low. Suppose a company wants to test the response to a new ...An auto manufacturer leases cars to small businesses for use in visiting clients and other business travel. The contracted lease does not specify a mileage limit and instead includes a depreciation fee of $0.30 per mile. The ...A consumer interest group buys a brand-name kitchen appliance. During its first month of use, the appliance breaks. The manufacturer claims that 99% of its appliances work for a year without a problem. (a) State the ...Post your question