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FRM一級每日一題 【估值與風(fēng)險(xiǎn)模型】
Consider two portfolios. One with USD 100 million credit exposure to a single B-rated counterparty. The second with Euro 100 million on credit exposure split evenly between 50 B-rated counterparties. Assume that default probabilities and recovery rates are the same for all B-rated counterparties. Which of the following statements is not wrong?
A. The expected loss of the first portfolio is greater than the expected loss of the second portfolio and the unexpected loss of the first portfolio is greater than the unexpected loss of the second portfolio.
B. The expected loss of the first portfolio is greater than the expected loss of the second portfolio and the unexpected loss of the first portfolio is equal to the unexpected loss of the second portfolio.
C. The expected loss of the first portfolio is equal to the expected loss of the second portfolio and the unexpected loss of the first portfolio is equal to the unexpected loss of the second portfolio.
D. The expected loss of the first portfolio is equal to the expected loss of the second portfolio and the unexpected loss of the first portfolio is greater than the unexpected loss of the second portfolio.
Answer: D
Unexpected loss is the volatility of the expected loss. Therefore, there is diversified effect.
|
Frequency Distribution |
Severity Distribution |
||
|
Probability |
Frequency |
Probability |
Severity |
|
0.6 |
0 |
0.5 |
USD 1,000 |
|
0.3 |
1 |
0.4 |
USD 100,000 |
|
0.1 |
2 |
0.1 |
USD 1,000,000 |
Based on this information, what is your estimate of the expected loss due to operational risk?
A. USD 20,000
B. USD 70,250
C. USD 130,600
D. USD 140,500
Answer: B
|
Scenario |
Loss |
Probability |
Loss×Probability |
|
0 |
- |
0.60 |
- |
|
1 |
1,000 |
0.15 |
150 |
|
1 |
100,000 |
0.12 |
12,000 |
|
1 |
1,000,000 |
0.03 |
30,000 |
|
2 |
2,000 |
0.03 |
50 |
|
2 |
200,000 |
0.02 |
3,200 |
|
2 |
2,000,000 |
0.00 |
2,000 |
|
2 |
101,000 |
0.04 |
4,040 |
|
2 |
1,001,000 |
0.01 |
10,010 |
|
2 |
1,100,000 |
0.01 |
8,800 |
|
|
|
EL |
70,250 |
