403 Paper 2 2004

A04 Paper 2 Q2: You're adjusting the old data for the rate changes so that you can get a new ULR. The difficult bit is coming up with the weightings used, as follows:

Take earned premium for 2004, for example (ie the top part of the equation): then half the earned premium in that year will be from pols written on the current rates (so 0.5*1.05*1.06*.92).
For the other half, pols written mid-jan03 will expose 1/24 in 2004, mid-feb will expose 3/24, etc, mid-june will expose 11/24. Add this up gives 1.5.
For later pols, pols written mid-jul03 expose 13/24, ....., mid-Dec expose 23/24. Add this up gives 4.5.
So exposure from the mid-policies gives three times as much as that from early policies. And the total must equal half. So you have 1/8, 3/8, 1/2 total weighting on each.

Also, note that when you actually do the calculation, the answer comes to 1.028 and not 1.059 as the examiners' report suggests. The examiners are aware of this error but didn't correct it.

Sept 04 P2 Q2: We too ended up with different answers from the examiners; we used different DAC assumptions too. They told us that any reasonable and consistent allowance for DAC would have been accepted.

Interesting to note that in a recent ST3 exam, there was an accounts question and the examiners chose to ignore DAC completely, which makes life a little easier! I wouldn't suggest you do this, though, as in all other prior exams (ST3 and SA3), they generally do want you to allow for DAC, although the exact approach they take does vary. As always, as long as you state your assumptions and don't over-simplify your approach, you should be ok.

Hope this helps.

 

Because the loss ratios you've been given are for the market, not the insurer in question. You therefore need to adjust them for the rate changes that have been made in 2003 so that you get an adjusted earned premium for 2003 too.

So, start with 76% loss ratio for 2003, (claims incurred/premiums earned), then increase the claims incurred by 8% inflation (or whatever else you choose), then increase the denominator by the change in earned premium from 2003 to 2004.

 

You're adjusting the loss ratios you've got for the market, to allow for the one insurer's rate changes you've been given, to come up with a market loss ratio for 2004.

I think what you've done in your calculation, is to assume that the 76% 2003 loss ratio already allows for the rate changes that you've been given, in which case your calculation would make sense. Hopefully as long as you stated that you were doing it this way, you'd have got the marks.

 

Half the earned premium in 2004 will be from policies written on the current rates, and for the other half, policies written mid‑Jan 2003 will expose 1/24 in 2004, mid-Feb will expose 3/24, … , mid-June will expose 11/24. Add this up gives 1.5. For later policies, those written mid‑July 2003 expose 13/24, ....., mid-Dec expose 23/24. Add this up gives 4.5.

So exposure from the middle group of policies gives three times as much as that from early policies. And the total must equal half. So you have 1/8, 3/8, 1/2 total weighting on each.