Learning Objectives: Compare agencies’ ratings to internal credit rating systems. Describe linear discriminant analysis (LDA), define the Altman’s Z-score and its usage, and apply LDA to classify a sample of firms by credit quality. Describe the relationship between borrower rating and probability of default. Describe a rating migration matrix and calculate the probability of default, cumulative probability of default, and marginal probability of default.
24.13.1. Considering the internal ratings-based (IRB) approach utilized by banks for assessing the creditworthiness of companies, especially those that do not have external ratings from agencies, which of the following best describes an advantage of internal ratings systems over traditional agency ratings?
a. Internal ratings can provide a more detailed evaluation of a company's ability to service its debt through specific financial metrics and cash flow analysis.
b. Agency ratings offer more consistent results since they are applied uniformly across various industries and geographic regions.
c. Internal ratings are generally more accessible to the public and provide a broader understanding of a company's financial health.
d. Agency ratings are quicker to update and reflect recent market changes more efficiently than internal systems.
24.13.2 Everina Grande Corp, the borrower, has undergone a financial review using both Altman’s Z-score and an internal ratings system developed by its primary bank. The financial ratios from the borrower's recent financial statements provided the following data for the Z-score calculation:
How does Altman's Z-score differ from the bank's internal rating system in assessing Everina Grande Corp's credit quality?
a. Altman’s Z-score suggests low risk of default, while the bank’s internal system indicates potential risk, highlighting the importance of current market conditions in internal assessments
b. Both the Z-score and the internal system suggest a high risk of default, reflecting a consistent evaluation across different methods.
c. Altman’s Z-score identifies the company as high risk, whereas the bank’s internal system gives it a stable outlook.
d. Both methods indicate that the company is unlikely to default soon, showing a consistent outcome despite different analytical focuses.
24.13.3 Abbot Castello, a financial analyst examining historical default probabilities and rating migration matrices for various bond ratings over a multi-year period. The data provided reflects typical transitions and default experiences for bonds with initial ratings. For example, bonds initially rated at BBB show an annual increase in the probability of default over the first few years, demonstrating a characteristic increase in risk over time for investment-grade bonds. The probabilities are as follows:
Given that a bond initially rated BBB has not defaulted by the end of the second year, which of the following BEST describes the calculated probability of default during the third year, and what does this illustrate about the rating migration matrix?
a. 0.75%, assuming the year three default rate applies without previous years’ consideration.
b. 0.43%, using the cumulative probability up to the end of year two as the third year’s rate.
c. 0.32%, taking the annual increase from year two to three as the conditional probability
d. 0.321%, factoring in the survival rate up to year two and the increase in default probability.
Answers here:
24.13.1. Considering the internal ratings-based (IRB) approach utilized by banks for assessing the creditworthiness of companies, especially those that do not have external ratings from agencies, which of the following best describes an advantage of internal ratings systems over traditional agency ratings?
a. Internal ratings can provide a more detailed evaluation of a company's ability to service its debt through specific financial metrics and cash flow analysis.
b. Agency ratings offer more consistent results since they are applied uniformly across various industries and geographic regions.
c. Internal ratings are generally more accessible to the public and provide a broader understanding of a company's financial health.
d. Agency ratings are quicker to update and reflect recent market changes more efficiently than internal systems.
24.13.2 Everina Grande Corp, the borrower, has undergone a financial review using both Altman’s Z-score and an internal ratings system developed by its primary bank. The financial ratios from the borrower's recent financial statements provided the following data for the Z-score calculation:
- Working capital/Total assets (X1): 0.254
- Retained earnings/Total assets (X2): 0.448
- Earnings before interest and taxes/Total assets (X3): 0.0896
- Market value of equity/Total liabilities (X4): 1.583
- Sales/Total assets (X5): 3.284
How does Altman's Z-score differ from the bank's internal rating system in assessing Everina Grande Corp's credit quality?
a. Altman’s Z-score suggests low risk of default, while the bank’s internal system indicates potential risk, highlighting the importance of current market conditions in internal assessments
b. Both the Z-score and the internal system suggest a high risk of default, reflecting a consistent evaluation across different methods.
c. Altman’s Z-score identifies the company as high risk, whereas the bank’s internal system gives it a stable outlook.
d. Both methods indicate that the company is unlikely to default soon, showing a consistent outcome despite different analytical focuses.
24.13.3 Abbot Castello, a financial analyst examining historical default probabilities and rating migration matrices for various bond ratings over a multi-year period. The data provided reflects typical transitions and default experiences for bonds with initial ratings. For example, bonds initially rated at BBB show an annual increase in the probability of default over the first few years, demonstrating a characteristic increase in risk over time for investment-grade bonds. The probabilities are as follows:
- Year 1: 0.16%
- Year 2: 0.43%
- Year 3: 0.75%
Given that a bond initially rated BBB has not defaulted by the end of the second year, which of the following BEST describes the calculated probability of default during the third year, and what does this illustrate about the rating migration matrix?
a. 0.75%, assuming the year three default rate applies without previous years’ consideration.
b. 0.43%, using the cumulative probability up to the end of year two as the third year’s rate.
c. 0.32%, taking the annual increase from year two to three as the conditional probability
d. 0.321%, factoring in the survival rate up to year two and the increase in default probability.
Answers here:
