Fall 2014 Q7
Hi,
In order to calculate the Average Acc Date in this question, the formula i.e mid-pt of historical period + 0.5*policy term, fails for CY 2011 as the company began writing business in 2011 only. So, with uniformity assumption, logically the AWD for 2011 must be 1/7/2011 making 1/10/2011 to be the AAD for the 6-monthly policies written in 2011 (according to me!)
However, the examiners' report mentions that as the AAD is shifting due to growing book, the trend period for applying loss trend to 2011 loss must be 3.375 i.e from mid-point of Qtr 3 of 2011 to 1/1/2015.
How did they come up with AAD of 2011 to be the mid-point of Qtr 3 of 2011 i.e 15/8/2011 ?
Thanks
Comments
I think the AAD of the mid-point of quarter 3 was related to the policy term being 6 months and the insurer starting at the beginning of that year, not that fact that the book of business was growing.
In any case, I think it was a bit of an unfair question and the graders did accept either 3.375 (correct) or 3.5 (incorrect) for the trend period. I did a quick spreadsheet to calculate the AAD for 6-month policies written uniformly starting at the beginning of a year, and it does work out to pretty close to the mid-point of Q3, Aug 13. I don't it was reasonable to expect people to do this however:
Just a small follow up query.
Going by your logic, wouldn't it be correct to conclude that these monthly time periods you selected in the spreadsheet instead of a year and the assumption that policies are written in the middle of each month are essentially accounting for the fact that due to growing book of business, the average accident date is shifting and thus investigation must be done using smaller time periods?
In fact, if we chose quarterly time periods analogous to what you suggested, we would exactly arrive at 7.5th month i.e ~15th august of the year.
You are conveying the same thing right?
If the volume is growing, you generally get more accurate estimates using shorter time periods, but my example isn't trying to incorporate growth. (Unless you think of "growth" as going from zero earned premium prior to January to something non-zero starting in January.) It's just a way to calculate the AAD using January as the start of the insurer's operations. Your method of using quarters should work just as well.