Spring 2015 Q11

keshav1996keshav1996
in W-12-Credibility

Hi,

In the sample solution 1 (PFA the required part for reference) for this question, if they are intending to apply the trended present rates method, shouldn't "1.069" they have calculated as complement be actually the "trend factor" that should be applied to the indicated rate change factor without credibility (i.e 1.0256) and not the trended indicated rate itself that they wrongly (according to me!!) have used as the complement in the final step??

Thanks

Attachment for reference.JPG


Comments

  • GrahamGraham

    I believe what they did is correct. Here's the formula for trended present rates:

    image.png

    For the values in the formula, we have:

    • present rate = 1.0000 (this is a relative rate because we're using the loss ratio method)
    • loss trend factor = (loss trend) / (premium trend) = 1.07 / 1.05
    • prior indicated loss cost (change) = 1.07
    • loss cost (change) implemented with last review = 1.025

    Substituting these values gives:

    • C = 1.069 (as shown in the examiner's report)

    We now calculate the weighted average of 1.069 with the current indicated rate change, which in sample answer 1 is 2.56% or 1.0256. The credibility of this estimate was 0.855 so the final answer is as shown in your original post above.

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