Spring 2017 - Q10 Part B

Comments

• Graham

  March 2022

  No, the loss ratio method is for calculating an indicated rate change. That's different from calculating indicated relativities for territories.

  To calculate relativities, we need the loss costs for each territory so we can compare them. Then territories with higher loss costs get higher relativities and those with lower loss costs get lower relativities. This is done by dividing each territory's loss cost by the base territory (territory B.)
• pactuary

  March 2022

  Are loss costs and total losses analogous? Or do loss costs imply loss / exposure?
• Graham

  March 2022

  In the Werner text, "loss cost" means "losses / exposures". It's synonymous with "pure premium". (So "loss costs" and "losses" are different things.)
• pactuary

  March 2022

  Thanks Graham :)
• Graham

  March 2022

  You're welcome!
• srinandhegde

  September 2024

  I did not understand how to account for the policy fee in this problem. How is the policy fee of $50 different from fixed expense of $55? Particularly, say the give the above details and ask us to calculate the indicated average rate change. Do we just take 50+55=105 as the fixed expense in the numerator (pure premium method) or do we account for the policy fee in a different manner?

  One more conceptual doubt. I have understood why we need to find an indicated base rate after finding the indicated rate relativities. But why are we asked to find indicated policy fee, which I feel is like asking the indicated fixed expense? Isn't that taken care of when we project fixed expense? Here I am thinking policy fee is similar to fixed expense, so please correct me if I am wrong.
• Graham

  September 2024 edited September 2024

  The policy fee and fixed expense are treated differently in ratemaking because they have distinct purposes and are accounted for in separate parts of the calculation.

  1. Policy Fee vs Fixed Expense: 

  • The fixed expense is a cost incurred for each exposure and is included in the premium calculation. It is adjusted to account for the variable expense ratio and the underwriting profit provision (as noted in the Werner document).
  • The policy fee, on the other hand, is an additive amount applied at the last step of the rate calculation. It is not subject to variable expenses or underwriting profit provisions.

  2. How to Account for the Policy Fee:

  • In calculating the indicated average rate change using the pure premium method, you do not simply add the policy fee to the fixed expense. Instead, the fixed expense is adjusted for the variable expenses and profit margin, whereas the policy fee is added as a flat fee at the end, after all other premium components have been determined. 
  • For example, the indicated fixed expense is adjusted using the formula ( Fixed Expense ) / (1 - V - Q), where V is the variable expense ratio and Q is the underwriting profit provision. The policy fee remains a flat additive amount.

  3. Indicated Policy Fee vs Fixed Expense:

  • The reason you calculate an indicated policy fee is to ensure it reflects the actual cost structure. It is not necessarily redundant with the fixed expense. While fixed expenses represent costs related to the handling of the exposure, the policy fee often reflects administrative costs not directly related to the exposure count (e.g., policy issuance or servicing costs).
  • The indicated policy fee is calculated to ensure that it is sufficient to cover those additional costs, independent of exposure.

  Therefore, you should not combine the policy fee with the fixed expense in the numerator of the pure premium method. The fixed expense is adjusted within the premium calculation, and the policy fee is added at the end as a separate component.
• srinandhegde

  September 2024

  Thank you very much Graham!! It's very clear now.