ST8 April 2017 Question 10

[randomWalker]

Hi, I have a few questions about this question; I haven't been able to find anyone else asking about this question which has me worrying my thinking is quite off.

Firstly the exposure - Turnover is given at $30m, growing by 5% except for one year. The Acted solutions give:

• AY1 Turnover = $30m (i.e. turnover at/during AY1)
• AY2 Turnover = $31.5m (i.e. turnover at/during AY2)
• AY3 Turnover = $33.075m (i.e. turnover at/during AY3)
• ..etc..

Howcome these figures are not "adjusted" to take them from their respective Accident Years to the midpoint of AY6? The precedent for this is from April 2011 Question 8 - when Payroll is inflated into the midpoint of the proposed Policy Year. What is the difference between turnover and payroll here? Both are monetary amounts - is it that Turnover is some sort of proxy for "sales" which doesn't make sense to inflate?

Secondly, assuming claims are occurring at the mid-point of the Accident year (not explicitly assumed by Acted..) should we not pro-rata the development factors? For AY5 $760,000 of Third Party death or bodily injury claims assumed halfway through the year... the Development table clearly says "Years of Development", (1) = 45% for Third-Party claims. Is it reasonable to assume 22.5% development here?

Finally, I managed to confuse myself around the deflation of 2%, when contrasting with similar questions like September 2011 Question 8, and the ILF Limit deflation calculation. How should I think about the following ways of adjusting for deflation of 2% (is that the same as "-2% growth").

• value * 0.98 ^ <periods>
• value * (1 / 1.02) ^ <periods>

Thanks in advance for any help or insights you can provide.

 

[randomWalker]

After digging through the notes I found of page 10 for Chapter 14 the following:

"If the exposure measure is expressed in monetary terms - for example wage-roll or turnover - then it is important that, w hen we apply trends to the historical frequencies, we also allow for inflation of this exposure measure"

This section specifically applies to the frequency & severity method, but I feel it's also appropriate for the burning cost method too.

 

[Ian Senator]

The turnover figure is adjusted later in the solution, where the estimated turnover for AY6 is multiplied by the expected burning cost percentage that was derived from looking at historic ratios, to get the expected claims cost for AY6. You could do it your way instead, inflating all the old exposures - you'd then get a different sequence of ratios, noticing a slightly different trend, but as long as you apply it correctly to AY6, you should get a very similar answer.

Development patterns: normally (as in triangulations, covered in SP7), we assume that the development pattern shown is at the end of each development year. To assume anything else would be very unusual so the assumption was not given credit. Watch out, though, for other questions where the latest diagonal is not complete - meaning you would need to do some sort of extrapolation.

Deflation: yes, I would say that deflation of 2% is like -2% inflation. Whether you multiply by 0.98 or divide by 1.02 depends on what you're adjusting. For example, if you're changing a loss ratio (claims/premiums) you would change the numerator to allow for claims inflation/deflation, but the denominator for price increases/decreases. eg if premiums had decreased by 2%, you'd multiply the denominator by 0.98. eg if claims inflation was 2%, then you'd multiply the numerator by 1.02.

Finally, your question about BC versus freq/severity. Yes, adjustments apply to both methods. Freq/Sev is just a slightly more granular method than the BC method.

 

[randomWalker]

Development patterns: normally (as in triangulations, covered in SP7), we assume that the development pattern shown is at the end of each development year. To assume anything else would be very unusual so the assumption was not given credit. Watch out, though, for other questions where the latest diagonal is not complete - meaning you would need to do some sort of extrapolation.

Thanks for the response Ian, I know you must be very busy currently.

I'm not sure if you are agreeing with me regarding the development factors?

I agree it would be normal to show development patterns at the end of the year, but we are also assuming that the claims-to-be-developed are occurring at the midpoint during each year. I stated my assumption of linear interpolation and carried on, but obviously, if my thinking is incorrect or I can save time by not making "useless" assumptions I should try to correct my exam technique.

 

[Ian Senator]

Yes, the claims occur across each accident year (so on average half-way though), but development patterns normally show the % developed at each calendar year-end. So I wouldn't use your approach....