Indicated Rate Change - Total

jj96gotthisjj96gotthis
in W-09-RiskClassification

Hi,

I would like to know how to calculate the indicated rate change:

Spring 2014 Q8 - Sample Solution 3 showed that the revenue-neutral rate change = normalized indicated relativity / normalized current relativity, where the total normalized current relativity = 0.9938 is calculated as the weighted average of the current relativity using the adjusted exposure.

Spring 2015 Q13 - Sample Solution 2 showed that the total % change = 6.6% is calculated as the weighted average of the % change using the adjusted exposure.

So the part that confused me is whether we should calculate the total indicated change as (total rebased indicated relativities / total current relativity) -1, OR the weighted average of the indicated change for each level.

To illustrate, please see the iteration below for Spring 2015 Q13. I calculated the total current relativity as the weighted average using adjusted exposure, I get 0.8215. Then I calculated the total rebased indicated relativities from the indicated relativities, I get 0.8713 (1/1.1478). Then I calculated the total indicated change as (total rebased indicated relativities / total current relativity) -1 = 6.06%, which is different from the solution of 6.6%.

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Could you please explain which method is the right way?

Thank you!

Comments

  • GrahamGraham

    Short answer:

    • I think both methods would be acceptable. What you did versus what was shown in the examiner's report are somewhat close but not algebraically equivalent. But as you noticed, the 2014.Spring exam seems to do it one way while the 2015.Spring exam seems to do it another way.
    • Unless you rerate every policy with current and proposed relativities and base rates, the results are only going to be approximate anyway. So the difference between 6.6% and 6.06% may not even be material since filed rate changes are often adjusted further for other reasons anyway.

    Here are a few more details about those questions which you might find helpful.

    2014.Spring #8:

    • Sample answers #1 and #2 do a direct calculation of the change in relativities without making any adjustments for a revenue-neutral change. They assume (without saying so) that the base rate will also need to be adjusted to make the change revenue-neutral. I'm a little surprised these answers got full credit. Not that there was an error, but that they didn't mention the assumption about the change to the base rate.
    • Sample answer #3 explicitly calculated the revenue-neutral change required for each territory without also needing a change in the base rate. That's why this sample answer had a different result for the relativity change in territory #3. The entire rate change was incorporated into the changes in relativities.

    2015.Spring #13:

    • This question was similar to 2014.Spring #8 but here they ask you to calculate the changes in relativities and the changes to the base rate to make the overall change revenue-neutral.
    • Your solution above is very close to sample answer #2. The only difference is how you calculate the final overall %-change. (The sample answer has 6.6% and you have 6.06%.) But as I stated as the top, I think both methods would be considered acceptable.
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