Learning Objectives: Explain the distinctions between economic capital and regulatory capital and describe how economic capital is derived. Describe the degree of dependence typically observed among the loan defaults in a bank’s loan portfolio and explain the implications for the portfolio’s default rate. Estimate the mean and standard deviation of credit losses assuming a binomial distribution.
Questions:
24.14.1. A bank has a $20,000,000 portfolio of loans. The portfolio has a probability of default of 0.6%, a correlation parameter of 0.3, and a recovery rate of 40%. Using the Vasicek model and the 99.9 percentile of the default rate, what is closest to the required regulatory capital?
a. 1,891,800
b. 9,459,000
c. 2,035,800
d. 1,261,200
24.14.2. When using the Vasicek model during the financial crisis in 2008, how would the model have accounted for the economic conditions?
a. The Vasicek model uses interest rates as a proxy for the general health of the economy.
b. The Vasicek model does not specifically account for the current health of the economy.
c. The Vasicek model would account for a recession with a low F variable in Vasicek’s default rate model.
d. The Vasicek model would account for a recession with a high F variable in Vasicek’s default rate model.
24.14.3. A bank has a portfolio that consists of 1,000 loans that are each worth $5 million, and each has a 2% probability of default over the next year. The recovery rate is assumed to be 60% with a correlation coefficient of 0.2. Determine the standard deviation, α, of the loss for the loan portfolio as a percentage of its total value.
a. 0.0267
b. 0.0145
c. 0.0307
d. 0.0180
Answers here:
Questions:
24.14.1. A bank has a $20,000,000 portfolio of loans. The portfolio has a probability of default of 0.6%, a correlation parameter of 0.3, and a recovery rate of 40%. Using the Vasicek model and the 99.9 percentile of the default rate, what is closest to the required regulatory capital?
a. 1,891,800
b. 9,459,000
c. 2,035,800
d. 1,261,200
24.14.2. When using the Vasicek model during the financial crisis in 2008, how would the model have accounted for the economic conditions?
a. The Vasicek model uses interest rates as a proxy for the general health of the economy.
b. The Vasicek model does not specifically account for the current health of the economy.
c. The Vasicek model would account for a recession with a low F variable in Vasicek’s default rate model.
d. The Vasicek model would account for a recession with a high F variable in Vasicek’s default rate model.
24.14.3. A bank has a portfolio that consists of 1,000 loans that are each worth $5 million, and each has a 2% probability of default over the next year. The recovery rate is assumed to be 60% with a correlation coefficient of 0.2. Determine the standard deviation, α, of the loss for the loan portfolio as a percentage of its total value.
a. 0.0267
b. 0.0145
c. 0.0307
d. 0.0180
Answers here:
