Spring 2015 Q3 parts a. and b.
Hi,
I am a bit confused as to whether "written car years" numbers given in the question are "car years" or "car half-years" for PY 2013 time periods when 6 month policies were sold. Assuming they are already car years (as we did not multiply 107.5 by an extra 0.5 to account for 6 month policy term in part a. and it was also mentioned as a common mistake by the examiners if candidates did multiply by the extra 0.5), then why should we multiply 107.5 car years (and not car half-years!) by 2 to get 215 car years that should be up for renewal in first half year of PY 2014 for the purposes of part b. ?
I mean if it wasn't for renewal, then 107.5 car years would have been 107.5*2= 215 car years with our assumption change (from uniform writings within each half year to uniform writings throughout the year), but, according to me, as these are renewals of the old 6 month policies only and will occur only in first half of 2014, so either there should be only 107.5 car years renewed in part b. or in part a. we must treat 107.5 as car half-years and multiply by 0.5.
Kindly clear this confusion.
Comments
1 written car-year always means the same thing. It's the equivalent of 1 policy for 1 year, but it can come about in different ways:
In this problem there are 107.5 written car-years in the second half of 2013 but since they are six-month policies, that means 107.5 x 2 = 215 people are insured. (Each person writing a six-month policy would contribute only 0.5 written car-years.) And all 215 people will be up for renewal in the first half of 2014. This time however, if all of them renewed, there would be 215 written car-years for this same group of people because they are now annual policies. (In this problem, they don't all renew and that's essentially what being asked in part b.)
The solution in the examiner's report is well written. If you're still confused, take a break and come back to it tomorrow or in a few days. That usually helps clear your brain so you can get a fresh look at it.
Hello,
Just a follow up question for part b. I understand that at the beginning of 2014, there's a potential of 215 policies being renewed.
I'm not sure I understand why for the policies renewed, the solution removes the 45 written policies in the second half of 2014 from the 210 new policies written in the first half of 2014.
If it's because it says that the policies are written uniformly over the year, shouldn't we have added the 210 and 45 together because over the year of 2014 we have 255 policies written?
There was a trick in this problem. They tell you the retention ratio was 77% when the company wrote 6-month policies and are essentially asking you to calculate (or rather estimate) the retention ratio after they switched to annual policies. If you were working at this company, you would have the data to calculate the retention ratio directly using the formula:
But in this problem, you only know the denominator, not the numerator. The denominator is 215 but you have to estimate the numerator. So what we know is that there were 45 new policies in the second half of 2014. (They must be new because the policies written in the first half of 2014 would not be up for renewal until at least Jan 1, 2015.)
Anyway, the BIG ASSUMPTION you have to make is that the first half of 2014 would ALSO have had 45 NEW policies. Then the implication is that of the 210 policies that were written in the first half of 2014, we would have 45 NEW policies and 210-45 = 165 RENEWAL policies. So you use 165 in the numerator of the retention ratio formula.
Could you explain solution for part c which is asking about the appropriateness of the uniform assumption?
In particular, what does it mean when in sample 1 when it says renewals all occur in the first half? Don't renewals happen every 6 months prior to 2014 and every year after 2014?
Also, in sample 2, for renewals being heavy at the beginning of the year and the next wave of written car years being CY 2015, is this related to the fact that there are 210 written car years for the first half of 2014 but only 45 for the second half of 2014?
I don't think either of the sample answers is a good answer. Here is how I thought about it:
So my conclusion (based on the limited information) is that an assumption of uniform writings over the entire year 2014 is not appropriate because there are more writings in the first half of the year. But it's possible that the assumption holds for both 6-months periods. There isn't enough information provided to say anything more specific.
I think the examiners' were looking for logical reasoning based on the given information, not necessarily a definitive answer.