CAS Exam 8 Fall 2019, Question 18
Study guide: Exam 9
A property insurer has an existing Quota Share reinsurance treaty in place. The insurer would like to further reduce its net loss exposure by exploring a proposed Property Per Risk Excess reinsurance treaty. Given the following:
Existing Quota Share Reinsurance Treaty
- 25% Quota Share
- 15% Ceding Commission
Proposed Property Per Risk Excess Reinsurance Treaty
- Subject premium of $100 million net of the Quota Share reinsurance treaty
- Covers net losses in excess of $500,000, up to a limit of $500,000
- The Quota Share reinsurance treaty will inure to the benefit of this treaty
- Ceded Loss Ratio for this Excess layer is estimated to be 90%
The table below illustrates the insurer's historical experience data net of the Quota Share that is subject to the proposed Property Per Risk Excess layer:
| Historical Accident Year | On Level Subject Earned Premium ($ millions) | On Level Trended Ultimate Subject Loss Ratio | On Level Trended Ultimate Layer Loss Cost |
|---|---|---|---|
| 2014 | 100 | 75% | 25% |
| 2015 | 120 | 75% | 30% |
| 2016 | 150 | 90% | 45% |
| 2017 | 80 | 75% | 24% |
| 2018 | 100 | 80% | 36% |
Part a (0.5 points)
Calculate the loss cost of the Property Per Risk Excess layer using all 5 years of historical experience data provided.
Part b (1 point)
Assume that the following exposure curve definition applies to the Property Per Risk Excess layer:
G(x) = \frac{1 - 0.32428^x}{1 - 0.32428}
where G(x) represents the ratio of pure risk premiums retained by the insurer, and x represents the ground up loss normalized to the maximum possible loss of $1 million.
Calculate the loss cost of the Property Per Risk Excess layer retained by the reinsurer based on the exposure curve.
Part c (0.5 points)
Calculate the loss cost of the Property Per Risk Excess layer using a blend of the experience loss cost and the exposure loss cost based on a credibility weight of 80%.
Part d (2 points)
The insurer's historical gross expenses are estimated to be 15% of historical gross premiums.
Calculate the insurer's expected net underwriting profit after application of both the existing Quota Share reinsurance treaty and the proposed Property Per Risk Excess reinsurance treaty.
Part e (1 point)
The insurer is also exploring the following proposed modifications to the Quota Share reinsurance treaty:
- Option 1: Profit Commission equal to 100% of reinsurer profit above a 5% reinsurer margin
- Option 2: 20% Ceding Commission
Calculate the 5 year weighted average ratio of profit commission to ceded premium for the Quota Share reinsurance treaty using the historical experience data provided.
Part f (0.5 points)
Briefly describe one advantage and one disadvantage of implementing the proposed profit commission versus the higher ceding commission from the insurer's perspective.
Answer this question and see the worked solution