On-Level On the Level

Let’s say, hypothetically, you are working at a commercial insurance company which has been abandoned by competent actuarial staff for some ten years. During this time, the only impact to policyholder rates were at an underwriter’s discretion - giving credits and debits (of course only where justified), as well as flat 5% increases to LCMs each year. Also during this time, this company’s competitors have been refining their rating algorithms and skimming the cream that is your low risk ex-policyholders.

This company hires you to create an indication. How do you on-level this premium? Filed rates have increased, but not at an actuarially justifiable pace. Underwriting credits and debits have been applied haphazardly, and are quantifiable only on persisting business. Anti-selection has run amok, causing high risk groups to stay while overpriced better business has gone elsewhere. The rate increases you have achieved are invariably correlated to the survivorship bias that is your current portfolio of sticky risks.

At this point, would it make sense to only use historical data given that those historical policies are still in force? Is there another way to adjust for a rapidly changing cohort of business that optimistically will return to its profitable ways of ten years ago?

How about extension of exposures? How would you rate those historical exposures today?

I’m in personal lines, so I realize I’m surely oversimplifying.

You only need to on-level to what is currently being charged, so it doesn’t matter if those changes were justifiable or not. If your company has been abusing LCMs to get rate increases without adjusting loss costs, then you only need to adjust for the LCM changes.

There are a lot of things that an actuary would need to do to clean up that situation though. Good luck.

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This . . . whether or not this is “actuarially sound.”

And you can also ignore debits/credits that are “at the underwriter’s discretion” since this reflects some sort of business decisions and not what might be actuarially sound.

Hi @GamblinMan . Interesting question. My thoughts:

1.) Do you need to On-Level the EP to create an indication? Would you want to create a Pure Premium/Loss Cost indication instead of Loss Ratio? If so, no need to consider EP at all.
2.) Similar to points others have raised, is your goal to create an indication for manual rates? If so, then even if you do Loss Ratio, I’d think you’d use manual premium (excluding Schedule Rating). So historical credits/debits irrelevant.
3.) Including only policies in force is a tricky question. Often you’d want to include everything to improve credibility (esp. in Commercial). Either way, just keep your choice (of how you are accounting for this mix shift) in mind when you make your trend selects.

Are you looking to update overall rate only or can you also update relativity factors at the same time? Hopefully it’s the latter case.

Along the lines of what some others are saying i think you have 4 things you have to do:

  1. figure out what is, in other words on level to current rates regardless of their justification.

  2. figure out what ought to be, in other words the indicated rates which don’t really depend on current rates.

  3. figure out if you have buy-in from others on fixing things. If not then you might need to put together some simpler illustrations of what is going on, even if they are less sophisticated from an actuarial perspective. like just comparing CY premiums and losses among certain policy types.

  4. try to separate trend due to anti selection from other trend sources. this might involve looking at trends after having removed policies that left, but i’d be super careful about that since it can create strange biases in your data set.

This is a good question! I’ve done loads of indications but have never restricted my data(claims and losses) to only be of those still on the books. There must be a reason this isn’t common, and core actuarial literature has not proposed it. Generally speaking you could be biasing your data by only including survivors. I think your on-leveling would be the same regardless, but am not sure what your premium trend would be. The downside (or the whole point) to restricting your dataset to current policies on the books is you could get lots of adverse development and loss trends. You’re also not necessarily reflecting the types of risks you could be writing. If you expected your book to be unchanged your prospective premium trend should be flat, i think.

So i’ll piggyback your question, what are the formal reasons to not restrict experience to types of policies currently on the books?

Is it a closed book? That might be a reason to keep it to policies currently on the books.
But if it is an open book, the new policies could be of any type of person, Best to use as much experience as possible of people who buy that policy.

(DISCLAIMER: Not a P&C Actuary, but I’ve seen discussions like this for my area, which acts in similar ways to P&C.)