CIA PremLiab Excel Exhibit
I don't understand how the trend factor is calculated in column F, Appendix B Sheet 4 GrossMisc tab.
- The footnote says the trend factor = (1+trend) ^ [AAD of UPR less AAD of accident year] however the formula in the cell seems to be doing (1+trend) ^ (1/3 plus 0.5) for the current year.
- In Exam 5, if I remember correctly, we would trend from average accident date of the historical year to the average accident date of the year for which we are doing rate indication. Why are we adjusting for AAD of UPR here? I would think there would be no unearned premium remaining for historical accident years. I did not find any explanation of this in the source reading.
Thank you!
Comments
Yes, there is something wrong in that exhibit. The formula listed below the table doesn't match what was used in the table. But I don't think either is correct.
When you're calculating AAD for claims liabilities, we usually assume a uniform loss distribution over the year so the AAD is mid-year or 0.5. Then to trend those accidents to year-end, we would use exponents 0.5, 1.5, 2.5, etc, adding 1 for each accident year that you go back.
But for premium liabilities the AAD is 1/3. This is explained in the premium liabilities source reading. It works out like that because the AAD for premium liabilities (versus claim liabilities) is a weighted average of time and the proportion of UPR remaining.
Anyway, because the AAD for premiums is earlier, you have to trend it more to get it to the end of the year. In particular, there's an extra (0.5-1/3) or 1/6 that should be added to the exponent. So I believe the exponents in column F should be (0.5+1/6), (1.5+1/6), and so on. If you do that, you get a slightly lower total loss ratio in column (9) which is cell K20. I got 89.7% instead of 90.3%. (Their exhibit seems to use (0.5+1/3), (1.5+1/3) and so on which I don't think is correct.)
And finally, it's true that the UPR goes away a year after a policy is written, but that doesn't change the fact that the AAD for the premium liabilities is 1/3 not 0.5. That difference has to be accounted for in all years, not just the most recent year.
That makes perfect sense. I couldn't figure it out even after reading the source reading. Thank you so much!