# P1.T4.24.15. CreditMetrics, Euler’s Theorem, Derivative Risk Capital

#### Nicole Seaman

##### Director of CFA & FRM Operations
Staff member
Subscriber
Learning Objectives: Describe and apply the Vasicek model to estimate default rate and credit risk capital for a bank. Describe the CreditMetrics model and explain how it is applied in estimating economic capital. Describe and use the Euler’s theorem to determine the contribution of a loan to the overall risk of a portfolio. Explain why it is more difficult to calculate credit risk capital for derivatives than for loans.

Questions:

24.15.1.
Using the CreditMetrics model how many bonds will be rated “B” or better if five random draws are conducted and the draws result in the below values? Given that there is an 8% chance the bond rating will change from B to A over the next year, a 50% chance the bond rating will remain a B, a 34% chance the bond rating will decrease to a C, and an 8% chance the bond will default.

Random Draws: “-1.5, -0.5, 0.0, 1.5, 2.5.”

a. 1
b. 2
c. 3
d. 4

24.15.2. The standard deviation of losses for three loans is each 2.5.
• Loan 1 and Loan 2 are uncorrelated.
• Loan 1 and Loan 3 have a correlation of 0.3
• Loan 2 and Loan 3 have a correlation of 0.7
Calculate the standard deviation of the loss on the portfolio using Euler’s method. Then, determine the increase in the portfolio's standard deviation if the size of Loan 1 increases by 10%.

a. 1.6875
b. 0.1923
c. 0.1489
d. 0.0146

24.15.3. You are the Chief Risk Officer at a major financial institution. Your task is to explain to the board of directors why calculating credit risk capital for derivatives is more complex than for traditional loans. Which of the following reasons best explains why it is more difficult to calculate credit risk capital for derivatives than for loans?

a. Loans have simple counterparty risk management, while derivatives involve complex and dynamic counterparty risk due to multiple cash flows and changing market exposures.
b. Exposure measurement for loans is based on the outstanding balance, which is predictable, whereas for derivatives, sophisticated modeling is required to estimate potential future exposure (PFE).
c. Regulatory capital requirements for loans are clear and standardized, whereas derivatives require advanced approaches to account for credit valuation adjustment (CVA) and wrong-way risk.
d. All of the above.