2016 Q19
Can you explain why the capital held under the QS is $100M – ($50M)*(0.2)*(1.5) = $85M?
Does the ($50M)*(0.2)*(1.5) represent the capital relief given by the QS so the company only needs to hold an additional 85? And is the capital relief given by a QS always equal to the maximum loss payout? If that is the case how would we calculate the capital relief if there was no Maximum ceded loss ratio?
Comments
The graph is hard to read; different sample answers use different 1-in-100 year PMLs. I'll assume the 1-in-100 year PML is $100 million.
With a 20% quota share the ceded premium is 0.2*50m = 10million.
The terms of the quota share treaty limit the ceded loss to 150% of the ceded premium, so the maximum amount of loss that can be ceded is 150%*10m = 15m.
So under the quota share treaty, to cover a 1-in-100 year loss they need to hold 100m - 15m = 85m in capital.
Without the maximum ceded loss ratio constraint, the quota share loss ratio will follow/match the primary insurer's loss ratio. The capital relief is the amount recoverable under the reinsurance treaty. Without the maximum ceded loss ratio constraint this is the quota share ceding percentage multiplied by the 1-in-x year PML.
1) So if there hadn't been a max ceded loss, the Capital Required would have bee 100M*(1-.2) = 80M instead of 85M?
2) If so and the max ceded loss had been 25M, would the capital required have been 75M or 80M?
Yes, for a 20% quota share without the max ceded loss constraint, the 1-in-100 year ceded loss would be 20%*100m = 20m and so the company needs 100m - 20m = 80m in capital to meet the 1-in-100 year requirement.
I'm not entirely sure where you're getting the 25m figure from. Assuming we're still talking about a 20% quota share, we have 50m in premium, of which 10m goes to the quota share reinsurer. Assuming we're still looking to meet the 1-in-100 year capital requirement means we need enough capital to meet a 100m loss. The quota share covers 20% of this, up to some maximum ceded loss. So the quota share covers up to 20m which corresponds to a maximum ceded loss ratio of 200%. Under this set up, there's no way for the insurer to cede more than 20m. So the capital requirement is still 80m.
Let me know if I misinterpreted your question please.