JasonScandopolous

04-06-2011, 04:29 PM

I am struggling to see why a premium or exposure trend should be necessary to consider.

Assume a book has various rating variables, and all combinations of rating variables are priced such that the expected loss ratio is equal for every combination. If we see a trend emerge, where higher deductibles are being adopted, we will still achieve the same overall loss ratio as we did before (because deductible relativities will have been properly priced).

If deductible relativites were *not* properly priced to begin with, and hence the loss trend and premium trend from this move to higher deductibles are not equal, then we get a different answer. However, if this is the case, we should adjust our deductible pricing, as it was clearly based on faulty or old assumptions (otherwise, prem trend and loss trend resulting from higher deductible writings would be equal). However, realizing that our pricing is off, the number of policyholders with a given deductible should have nothing to do with how we go about fixing the relativity; this is all about losses. Premium trend again isn't necessary; as we fix the deductible relativities, premium trend cancels out with loss trend again (well, prem trend + on-level factor, where pricing is adjusted to the correct level).

Nevermind, I think I figured out why we need it: I correctly (I think) reasoned that premium trend should be matched by loss trend from the same thing that caused the premium trend, if pricing was correct... however, if other loss trends exist (using my original example, say this is personal auto, accident frequencies increase), we won't be able to know what part of loss trend is from deductible changes and what is from accident frequencies. We can only measure total loss trend, and then cancel out the deductible effect via premium trend.

Assume a book has various rating variables, and all combinations of rating variables are priced such that the expected loss ratio is equal for every combination. If we see a trend emerge, where higher deductibles are being adopted, we will still achieve the same overall loss ratio as we did before (because deductible relativities will have been properly priced).

If deductible relativites were *not* properly priced to begin with, and hence the loss trend and premium trend from this move to higher deductibles are not equal, then we get a different answer. However, if this is the case, we should adjust our deductible pricing, as it was clearly based on faulty or old assumptions (otherwise, prem trend and loss trend resulting from higher deductible writings would be equal). However, realizing that our pricing is off, the number of policyholders with a given deductible should have nothing to do with how we go about fixing the relativity; this is all about losses. Premium trend again isn't necessary; as we fix the deductible relativities, premium trend cancels out with loss trend again (well, prem trend + on-level factor, where pricing is adjusted to the correct level).

Nevermind, I think I figured out why we need it: I correctly (I think) reasoned that premium trend should be matched by loss trend from the same thing that caused the premium trend, if pricing was correct... however, if other loss trends exist (using my original example, say this is personal auto, accident frequencies increase), we won't be able to know what part of loss trend is from deductible changes and what is from accident frequencies. We can only measure total loss trend, and then cancel out the deductible effect via premium trend.