CAS Exam 9 Spring 2014, Question 22
Study guide: Exam 9
ABC Reinsurance Company is considering whether to write one of the following portfolios of property exposures:
- Portfolio A contains 100 locations with a combined total insured value of 45.
- Portfolio B contains 250 locations with a combined total insured value of 160.
Below is the distribution of events and corresponding loss amounts from a catastrophe model:
| Event | Prob p(i) | ABC Reinsurance Company | Portfolio A | Portfolio B | ABC + Portfolio A | ABC + Portfolio B |
|---|---|---|---|---|---|---|
| 1 | 0.010 | 350.00 | 2.00 | 150.00 | 352.00 | 500.00 |
| 2 | 0.020 | 200.00 | 0.50 | 50.00 | 200.50 | 250.00 |
| 3 | 0.010 | 1.00 | 40.00 | 2.50 | 41.00 | 3.50 |
| 4 | 0.030 | 75.00 | 0.40 | 24.00 | 75.40 | 99.00 |
| 5 | 0.015 | 160.00 | 1.40 | 80.00 | 161.40 | 240.00 |
| Average Annual Loss (Mean) | 12.16 | 0.46 | 4.45 | 12.62 | 16.61 | |
| Variance | 2,538.69 | 15.92 | 383.13 | 2,581.54 | 4,836.37 | |
| Coefficient of Variation | 4.14 | 8.62 | 4.40 | 4.03 | 4.19 | |
| Profit | 3.20 | 3.38 | 4.28 | |||
| Total Risk Adjusted Capital | 20.00 | 22.00 | 25.00 |
Below is the covariance share table between ABC Reinsurance and Portfolio A:
| Event | ABC | Portfolio A |
|---|---|---|
| 1 | Unknown | 0.079 |
| 2 | 3.910 | 0.010 |
| 3 | 0.019 | Unknown |
| 4 | 1.737 | 0.009 |
| 5 | 6.562 | 0.057 |
- ABC Reinsurance Company's share of the covariance with Portfolio B is 1,372.788.
- Portfolio B's share of the covariance with ABC Reinsurance Company is 541.762.
- The risk load multiplier,
\lambdais 0.005. - ABC Reinsurance Company only has enough capital to write one portfolio.
- ABC Reinsurance Company requires a 15% RAROC after adding the new portfolio.
Part a (2.25 points)
Using the covariance share method, calculate the renewal risk loads to complete the table below:
| Scenario | Risk Load Allocated To: ABC | Risk Load Allocated To: Added Portfolio | Risk Load Allocated To: Total |
|---|---|---|---|
| ABC + Portfolio A | |||
| ABC + Portfolio B |
Part b (2 points)
Using the information provided and outputs from the solution to part a. above, fully discuss the elements ABC Reinsurance Company should consider when deciding which portfolio to write.
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