Spring 2018 (Makeup) Q11 d)

judyohjudyoh
edited October 2023 in W-14-Implementation
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When normalizing the current relativity, it looks like the sample solution takes a weighted average of the current relativities using the premium as weights to get the total current relativity and normalized. I don't understand why this is valid because my understanding is that premium is a function of the current relativities and thus you should use exposures as weights rather than premium. For example, exposure = premium / current relativity, then use the resulting exposures to get a weighted average of the current relativities to use to normalize the relativities. Can you explain why the sample solution does it like this?


Also could you explain the solution? It appears that the indicated change compares (current premium) * (indicated change) to (new premium). So essentially, is the change in base rate making up for the premium shortfall? Does this mean territory relativities should be adjusted? (BR adjustment should be backed out)

Comments

  • GrahamGraham

    Using Premium as Weights vs. Using Exposure:

    • When using premiums as weights, you're weighting each territory's (or class's) relativity based on the premium volume they contribute. However, as you've rightly pointed out, if the premium is a function of the relativity, there could be circular logic here. Adjusting the relativities based on premiums which are themselves influenced by relativities may not provide a clear understanding of underlying risk differences.
    • When using exposures as weights, you're giving each territory (or class) a weight based on the number of units (e.g., number of policies, policy-years, etc.) they contribute. This approach is more straightforward because it's not influenced by the price (i.e., the premium), but rather by the volume or count of the exposure unit.

    If the goal is to truly understand the risk (or loss potential) differences among territories or classes without the influence of price, then using exposures as weights is more appropriate. If, however, the intention is to understand how much each class or territory contributes to the total premium, then premiums could be used as weights.

    Is the change in base rate making up for the premium shortfall?

    • Yes, essentially the indicated rate change aims to ensure that the premiums charged adequately cover the expected claims and expenses.

    Should territory relativities be adjusted?

    • Yes. From the table, the "normalized indicated relativity" shows that territories B and C should have their relativities adjusted. If the relativity is greater than 1, it means that the territory has a higher loss experience than expected and rates should be increased. On the other hand, if it's less than 1, it means the opposite.

    Base Rate (BR) adjustment backed out?

    • Yes, if you're adjusting the base rate (overall rate change) then you'd need to adjust the territory relativities to ensure that the combined effect (base rate change + relativity change) results in the desired overall rate change.


  • judyohjudyoh

    Thank you for your detailed explanation. In this question do you think it is valid to be using premium as weights? In other similar questions, typically relativities are exposure weighted. Do you think it be considered incorrect on my exam if I calculated the exposures using exposure = premium / current relativity and used these to weight the relativities?

  • GrahamGraham

    No, don't do that. If they didn't give you the exposures then I wouldn't try to estimate them. That's just making the problem unnecessarily complicated.

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