2015 spring 14 (c)

daviddavid
in W-11-SpecialClassification

I'm still confused after reading the sample answers as to why policy limits (loss data being capped) would be a problem in calculating deductible factors?

Suppose the company writes policies with a limit of 10k, with two deductible options 0 and 1000. The loss data would be capped at 10k, and admittedly, the loss elimination ratio calculated based on the capped losses would be different than if the loss data were ground-up. But I can't convince myself that this is an issue, because wouldn't we actually not want the LER based on uncapped data, since that's not how the loss payments are going to look like (the losses are capped in reality). Could you clarify on this? Thank you.

Comments

  • GrahamGraham
    edited August 2024

    You raise a valid point, and the sample answers for part (c) are all over the map. Here is the "official" explanation:

    • When calculating deductible factors, the purpose is to understand how much risk is being retained by the insurer versus how much is being transferred to the insured through the deductible. To do this accurately, we use the uncapped loss distribution because it provides a complete picture of the potential losses.

    Now, your point is that when losses are capped by the policy limits, the "complete picture of potential losses" would be better represented by the capped data since that's what the insurer actually pays out. The fact that the uncapped losses have a different distribution doesn't seem relevant. The text (and this exam question) seem to imply that the "true" distribution is the uncapped distribution, which I believe can legitimately be debated.

    I noticed from the sample answers (assuming that all these sample answers were given credit) that practically anything was accepted as the "issue". Then the "solution" could be anything half-way intelligent and that no in-depth explanation for why the solution worked was required. The solutions I've listed below are probably the best but they are rather generic:

    • fit theoretical severity distribution
    • use GLM approach
    • use industry data 

    I'm surprised this question was worth a full point because the answers were all very short. This should probably have been a 0.5 point question based on the lack of detail in the accepted answers. Note however that this question was from 2015, which is almost 10 years old and this questions has never reappeared.

    Conclusion: I think you raised a valid point but for the purposes of the exam, I would recommend simply giving the "official" explanation as I outlined above and leave it at that. If you have to do a calculation problem on deductibles, just follow the method in the text. That's really all you can do.

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