Learning Objectives: Describe the use of a single-factor model to measure portfolio credit risk, including the impact of correlation. Define beta and calculate the asset return correlation of any pair of firms using the single factor model. Using the single-factor model, estimate the probability of a joint default of any pair of credits and the default correlation between any pair of credits. Describe how Credit VaR can be calculated using a simulation of joint defaults. Assess the effect of granularity on Credit VaR.
Questions:
24.12.1. Under the assumptions of a single-factor credit model, two firms, Firm X and Firm Y, have betas of 1.5 and 0.9, respectively. What is the covariance between the returns of the firms?
a. 0.068
b. 1.350
c. 0.302
d. 0.003
24.12.2. Malz praises copulas for estimating portfolio credit risk as they "permit the model to generate quite detailed results—the entire probability distribution of portfolio credit outcomes—with a very light theoretical apparatus and requiring the estimation of only one additional parameter, the correlation, beyond those used in single-credit modeling." Despite these benefits, Malz highlights several potential drawbacks associated with using copulas. However, one of these options is not cited by him as a pitfall:
a. The marginal distributions must be normal, so we are forced to accept a multivariate normal of defaults.
b. The choice of copula is arbitrary, and we simply do not know enough to reliably estimate the copula correlation.
c. It is difficult enough to estimate default correlations and the copula correlation is only related to, not identical to, it.
d. Once a copula parameter value is assigned, it is tempting to rely on a wide range of consequently generated model results, but this is dangerous.
24.12.3. Bastrop Bank specializes in making commercial loans to large real estate developments. However, management is considering reducing its exposure to any one development and making smaller average loans to more small businesses. How would this likely affect the granularity on credit VaR?
a. Granularity would decrease as the bank focuses on fewer loans with higher exposure.
b. Granularity would increase as the bank analyzes a larger number of smaller loans.
c. Granularity would not be affected by the loan size or number of borrowers.
d. It's impossible to determine the impact without knowing the current Credit VaR.
Answers here:
Questions:
24.12.1. Under the assumptions of a single-factor credit model, two firms, Firm X and Firm Y, have betas of 1.5 and 0.9, respectively. What is the covariance between the returns of the firms?
a. 0.068
b. 1.350
c. 0.302
d. 0.003
24.12.2. Malz praises copulas for estimating portfolio credit risk as they "permit the model to generate quite detailed results—the entire probability distribution of portfolio credit outcomes—with a very light theoretical apparatus and requiring the estimation of only one additional parameter, the correlation, beyond those used in single-credit modeling." Despite these benefits, Malz highlights several potential drawbacks associated with using copulas. However, one of these options is not cited by him as a pitfall:
a. The marginal distributions must be normal, so we are forced to accept a multivariate normal of defaults.
b. The choice of copula is arbitrary, and we simply do not know enough to reliably estimate the copula correlation.
c. It is difficult enough to estimate default correlations and the copula correlation is only related to, not identical to, it.
d. Once a copula parameter value is assigned, it is tempting to rely on a wide range of consequently generated model results, but this is dangerous.
24.12.3. Bastrop Bank specializes in making commercial loans to large real estate developments. However, management is considering reducing its exposure to any one development and making smaller average loans to more small businesses. How would this likely affect the granularity on credit VaR?
a. Granularity would decrease as the bank focuses on fewer loans with higher exposure.
b. Granularity would increase as the bank analyzes a larger number of smaller loans.
c. Granularity would not be affected by the loan size or number of borrowers.
d. It's impossible to determine the impact without knowing the current Credit VaR.
Answers here:
