SP2017 Q7

[Actuarial]

Hey y’all,

Had a couple questions on the following exam problem:

• What does “Normalized” mean, e.g. in the context of Normalized Current Relativities? I know we calculate that by dividing the current relativity per class by the exposure weighted average of the current relativities, but am lacking the conceptual aspect.
• After we calculate the Credibility Weighted Indicated Relativites, why do we need to normalize again?
• Finally, what is the purpose of the Off Balance? My guess is that we calculate a total relativity change and because we would like a revenue-neutral overall change, we need to divide by our total relativity change. Is that true?

Here’s the solution I was looking at for reference:

Sorry for the long question. I’m constantly confused on these types of questions so any help is appreciated.

[lofi_actuary]

• for me normalizing is when you try to measure against the total avg, here, curr rel is measured against ClassA,we want to normalize it, i.e measure against the avg relativity of the entire group, so calculate the(weighted) avg first, then divide each class rel by the avg rel.

• for the pure premium method (as opposed to the loss ratio method), when credibility is involved, you always have to normalize the current and proposed relativity, before finding the final relativity. for loss ratio method, there is no need to normalize.

• off balance is needed when the avg indicated relativity is different from the avg rel of the current, this is causing an impact to the total premium, off balance factor is used to offset this impact to the premium by modifying the base rate.