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I'm struggling to understand why we would apply 10% to the UEP and not 90%. I thought within this formula we were looking to get the amount of UEP that the company was retaining, but this seems to imply it's the amount subject to reinsurance.
IRIS 4, and in particular surplus aid, is looking at liabilities that are being removed from the company's balance sheet. Removing liabilities is what "aids" the surplus. Since UEP is a liability, we are interested in the amount that's going to the reinsurer not the amount the company retains. I've written out the full solution below.
Take a look at the IRIS 4 formula in the practice template for IRIS 1,2,3,4 in quiz 1 of the NAIC.IRIS wiki article. I wrote out the formulas there in a slightly simpler way that I think is easier to follow than the formulas in the source text. I've also inserted all the intermediate steps:
The last line is obtained by canceling (300,000 x 10%) in the numerator and denominator.
Because the company expects it's prior-year surplus to increase by the amount of ceding commission it receives in 2013, we have:
where as above:
And if you do all the arithmetic, you get the final answer of 6.6% for IRIS 4, which matches the examiner's report.
I guess where I get confused is there isn't always an distinction on what the Unearned Premium they are giving us is. So for example Question 16 a on Spring 2018 just gives Unearned Premium. Is there something I am missing in this question that would make me assume all of this UEP is ceded to non-affiliates? I can see they accepted a bunch of responses here, so it's kind of unclear when I need to do additional work vs just use the value given.
I understand what you mean and unfortunately the exam questions are sometimes ambiguous. In 2016.Spring Q16a, there are 5 different sample solutions provided with the following answers:
It's obvious that everyone was confused about how to interpret the given information. In particular, the UEP of 30 was interpreted several different ways in the different sample solutions:
They seemed to accept both. So I guess, just do what you think is best. Sorry, that's not a great answer but I can't really say anything more definitive. In these types of annual statement problems, it's often quite difficult to get full credit but there are things you can do to make sure to maximize partial credit:
So, that's my overall advice. Work those old problems several times until you can do them very easily. They often repeat questions (or portions of questions) so if you can do all these old problems, you'll be in good shape for the exam. Also remember that everyone else is facing these same issues so even though it's very frustrating, you won't be at any particular disadvantage versus other exam-takers.