Fall 2018 Q12 b)

judyohjudyoh
in W-14-Implementation

Hi, could you help me understand this solution?

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Screen Shot 2023-10-12 at 7.44.06 PM.png

It's not clear to me which section of Werner14 this solution refers to so I am having trouble understanding. What I was thinking is, the current is 1.36 (from sample 1) and selected is 1.31. However, it asks for a overall rate level change of 0%. So current is 1.36 but it is too high compared to the selected of 1.31 so you adjust the base rate by 1.36/1.31 to get 1035?

Comments

  • GrahamGraham
    edited October 2023

    Yes, you are correct. In simple terms you can think of it like this:

    • (overall change) = (base rate change) x (relativity change)

    So if you want 0% overall change and the relativity change is 10% then to compensate, the base rate change needs to be 1/(1+10%):

    • 1.0 = (base rate change) x 1.1
    • base rate change = 1.0 / 1.1

    It works the same way with that exam problem:

    • 1.0 = (base rate change) x 1.031/1.036

    Now solve for the base rate change:

    • base rate change = 1.036/1.031 = 1.035

    (It is slightly more complicated if there are additive expense fees in the rating formula. It's always easier if everything is multiplicative.)

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