2016 Spring #10
When we do credibility weighting on relativities, why don't we need to ensure the two sets of relativities are normalized? If they are not normalized, ain't they in a different level?
I think I've seen a lot past exam questions where they do not normalize the relativities before doing credibility weighting. The 2016 Spring #10 is just one of them. Sample 1 answer from part (a) is an example of not doing the normalization before weighing by credibility. I got a different answer from normalizing the relativities before weighting by credibility. Is my answer (with normalization) also acceptable?
Thanks Graham in advance to your reply and for the amazingly consolidated study notes!
Comments
Thanks for the compliment! Glad you're enjoying the BA course! 😀
I tried first rebasing your 3rd last column (credibility weighted relativity normalized) as shown below, and although I didn't get the exact answer as in the examiner's report, it's very close, as was yours. Some of the differences are due to normalizing the relativities at each step as you did and some are due to rounding because that exam was in the paper and pencil days of taking exams. (So the examiners' report wouldn't have as many decimals as what you have in Excel thus leading to small differences versus the Excel version which keeps all the decimals.)
But the larger point is this: Problems like these don't always have a single, definitive answer like traditional math problems do. Actuarial methods for calculating rate changes are more like guidelines or rules of thumb, and the final selected rate change generally involves judgment and may differ slightly from the calculated result. As long as the numerical differences between different methods are minor, they typically don't result in any material impact on the final selected rate change.
For this type of problem on the exam, I would not do the normalizing steps because that only adds unnecessary work.
Hope that helps!