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.
Which of the following is not a measure of risk sensitivity of some kind?
Measures of risk sensitivity include delta, gamma, vega, PV01, convexity and CR01, among others. They allow approximating the change in the value of a portfolio from a change (generally small) in one of the underlying risk factors.
Risk sensitivity measures are derivatives of the value of the portfolio, calculated with respect to the risk factor. Some risk sensitivity measures are second derivatives, and allow a more precise calculation of the change in the value of the portfolio. Many risk sensitivities are represented by Greek letter, but not all.
Delta () is a measure of the change in portfolio value based on a 1% change in the value of the underlying. Gamma () is a second order derivative that improves the calculation as part of a Taylor expansion. CR01 is a measure of the change due to a 1 basis point change in the credit spread. PL01 is not a measure of any kind of risk sensitivity, it does not mean anything.
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