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April 2014 Q5 (ii)

M

maz1987

Member
This is clearly quite a difficult question, and I'm struggling to make sense of it even with the solution in front of me!

The examiners' report made it clear that the table of premiums was ambiguous, but that there was an explanation to be sure it was clear.

I don't see why the UPR for the return premium component is calculated as:

(1,375 + 2,175+ 3,127 + 3,174)/11 = 896

I would have calculated it simply as 3,174/11. This is because only 3,174 was written in 2013, and therefore this is the only premium amount for which there is the possibility of a return premium being paid. Why does the solution include the previous three years?

One explanation is that although only 3,174 worth of premium is exposed to return premium payment, the prior years' premium still contributed to the fund which will be paid back to policyholders. But then surely that would result in the calculation being:

(2,675 + 4,075 + 4,335 + 3,174)/11 i.e. the 10% component of the full written premium amounts paid each year.

I just don't like the idea of adding up the "written premium for policies still being renewed from previous years", since the earlier years are subsets of the later years.

:(
 
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Hi there

You are correct in that you need to allow for all (10 years eventually) of premiums in your fund that might be paid back to policyholders.

However, the guarantee only applies to those policyholders that renew their policy every year. So of the 2,675 of premium written originally in 2010 only 1,375 relates to policies which have been renewed continuously through to 2013, so only this part of the original written premium for 2010 can still be "exposed" to the guarantee.

Hence you need 1/11 * 1,375 as part of your UPR etc.
 
Ah yes, that makes sense now. If none of the policyholders from 2010 had renewed through to 2013 the 2010 component would be zero, but we would still include the 2011, 2012 and 2013 components (although they'd probably be reduced slightly).

Cheers
 
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I didn't understand there the 1/11 - 10/11 split came from. I understand you need to make something up, but why 1/11? It's just a bit of an awkward fraction. Why not go with 1/10, or 1/2?
 
Because there is a 10% loading to cover the premium return guarantee.

So of the total premiums written, 10%/110% (or 1/11) relates to the company's estimate of the cost of the guarantee.
 
still confused

Hi Darren
even with 1,375,2,175 etc being exposed to return of the premium guarantee, isn't 1,375a subset of 2,175 say in 2011?

Why is this not treated as such when question says 2,175 is for 2010 and 2011 policies still being renewed......
 
Ah,think I got it.what I was thinking is a double count is 2010 policy premiums renewed in 2011 i.e. 1,375[1.0572]= 1,454, the rest is new business underwritten in 2011 i.e. 2,175-1,454.
 
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