ACTED tutorial Q10

[Gousgounis]

Stop writing business in the last 2 months of the year decreases the WP by 1/6 and the EP by 1/12. The solution says that the impact on the claims amount of the MCR is 1/72. Shouldn't it be 1/12 * 1/3= 1/36 ?

Thanks!

 

[Ian Senator]

It's only an approximation, but the premium in the last two months would on average be written half-way through, ie with one month to go. So you could argue that the exposure would be half of 1/36. You could of course use trapezium rules, or integration or something more complex to get a slightly different answer, but the conclusion is the same - that it will only make a small difference to average claims incurred.

 

[NeedToQualify]

I agree that the impact of the exposure\claims will be 1/72. But this will be for the current year only. Shouldn't we then divide this by 3 to get the 3 year average?

 

[Ian Senator]

Yes, you're right.

Let's do this by resorting to monthly calculations, just like my spreadsheet in another thread here somewhere.

Pols written in Jan will expose 11.5 months in this year.
Pols written in Feb will expose 10.5 months in this year.
...etc...down to...
Pols written in Dec will expose 0.5 months in this year.
This gives a total of 72 months of exposure in the current year (from business written in the current year).

If we stop writing business for the last two months, we lose 2 months of exposure (0.5 plus 1.5).
So exposure (and hence claims incurred) decreases by 1/36. But we've also got exposure from business written in the previous year, so yes, exposure goes down by 1/72.
The other two years of claims incurred won't change, so average claims incurred over last three years will only go down by 1/216.