Which of the following statements are true:
1. A transition matrix is the probability of a security migrating from one rating class to another during its lifetime.
2. Marginal default probabilities refer to probabilities of default in a particular period, given survival at the beginning of that period.
3. Marginal default probabilities will always be greater than the corresponding cumulative default probability.
4. Loss given default is generally greater when recovery rates are low.
Statement I is incorrect. A transition matrix expresses the probabilities of moving to a given set of ratings at the end of a period (usually one year) conditional upon a given rating at the beginning of the period. It does not make a reference to an individual security and certainly not to the probability of migrating to other ratings during its entire lifetime.
Statement II is correct. Marginal default probabilities are the probability of default in a given year, conditional upon survival at the beginning of that year.
Statement III is incorrect. Cumulative probabilities of default will always be greater than the marginal probabilities of default - except in year 1 when they will be equal.
Statement IV is correct. LGD = 1 - Recovery Rate, therefore a low recovery rate implies higher LGD.
The probability of default of a security during the first year after issuance is 3%, that during the second and third years is 4%, and during the fourth year is 5%. What is the probability that it would not have defaulted at the end of four years from now?
The probability that the security would not default in the next 4 years is equal to the probability of survival at the end of the four years. In other words, =(1 - 3%)*(1 - 4%)*(1 - 4%)*(1 - 5%) = 84.93%. Choice 'd' is the correct answer.
For credit risk calculations, correlation between the asset values of two issuers is often proxied with:
Asset returns are relevant for credit risk models where a default is related to the value of the assets of the firm falling below the default threshold. When assessing credit risk for portfolios with multiple credit assets, it becomes necessary to know the asset correlations of the different firms. Since this data is rarely available, it is very common to approximate asset correlations using equity prices. Equity correlations are used as proxies for asset correlation, therefore Choice 'c' is the correct answer.
Which of the following are valid approaches for extreme value analysis given a dataset:
1. The Block Maxima approach
2. Least squares approach
3. Maximum likelihood approach
4. Peak-over-thresholds approach
For EVT, we use the block maxima or the peaks-over-threshold methods. These provide us the data points that can be fitted to a GEV distribution.
Least squares and maximum likelihood are methods that are used for curve fitting, and they have a variety of applications across risk management.
Which of the following statements are true:
1. A high score according to Altman's Z-Score methodology indicates a lower default risk
2. A high score according to the Probit or Logit models indicates a higher default risk
3. A high score according to Altman's Z-Score methodology indicates a higher default risk
4. A high score according to the Probit or Logit models indicates a lower default risk
A high score under the probit and logit models indicates a higher default risk, while under Altman's methodology it indicates a lower default risk. Therefore Choice 'd' is the correct answer.
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