Limiting Losses to increase Credibility for Workers Compensation Loss Pick

[swpski]

I am not an actuary but I have been doing loss sensitive worker's compensation for a number of years and I have a question in regard to limiting losses to get a more credible loss pick for an insured. One model I have used in the past allowed the underwriting to limit the losses to various levels, i.e. $25k up to $500k. Based on the experience of the insured at that level the underwriter could develop a loss pick and then a combination of industry factors and insured experience were used to develop the layer between your choice and a $250k level. After that point industry factors basically took over.

The current model I am using only limits losses at $250k. I have some concerns with this as I am looking at companies with expected losses in the $500k to $2m level per year and payrolls in the $10m to $80m level. Here are my concerns:

- There is not enough credibility in their experience given the size of the insured to say that their experience below $250k is indicative of future performance.
- With the high loss limit we are then possibly over conservative on the excess factors to overcome any concerns with the accuracy of the limited pick.
- The model is overly developing losses under the $250k to compensate for lack of credibility.

I felt that my previous experience with the ability to limit losses and then develop based on those picks provided a more accurate pick for the insureds losses. By lowering the limited level I was able to get a more accurate idea of what their frequency losses looked like.

Am I missing something in this logic?

If not is NCCI my best bet for getting some LDF's at lower levels? My actuary has not been very helpful in exploring this approach

[Irish Blues]

When you say you're limiting losses to some threshold [25K, 50K, ... whatever] - are you limiting aggregate losses or individual losses? The latter makes much more sense than the former - if you limit aggregate losses, you're effectively imposing a policy limit and thus saying, "no matter how much loss I have and how many claims I might have, my total loss will never be over this amount" and so when you go to predict total loss, you've thrown out a critical chunk of data that has predictive value. If instead you limit individual losses, you recognize the frequency component [which is a key part of estimating total loss] but say "if I have a really big loss, it could be a fluke - so I'm only going to count $X of it in, the rest may be noise."

You'll have to clarify this point.

[swpski]

I am limiting individual losses.

[Irish Blues]

Ok, I'll try this for a 3rd time - this time, saving as I go.

A little bit of background: in a past life, I did WC pricing for a major WC carrier. One of the challenges we had was estimating excess losses, and we had a model to do that; however, in all the work we did and with all the data we had, we never felt like we could estimate excess losses with a threshold higher than $125K. We tried to put together something with a $250K limit, but could never get the model to make sense consistently. That work was with large accounts [payrolls were at least $500 million]; if we couldn't project excess losses using a $250K limit, I don't know how you'd do it using accounts that maybe have a handful percent of credibility.

Let's start from that point. If you're working with accounts with aggregate losses of $500K to $2M, chances are you don't see losses over $250K very often - and for some accounts, you probably don't see them at all. Thus, limiting losses to $250K is problematic off the bat; if you overestimate limited losses [which is likely when you use a higher limit than necessary], you're going to overestimate excess losses as well. So, you really need to figure out where you should be limiting losses in the first place. Ideally, you'll pick a limit where many [but not all] of the losses fall short of the threshold; you want some losses to pierce the limit you choose, but not too many [say, no more than 10% of your claims]. Once you select that point, you can develop limited losses and you know what threshold you have to start with to project excess losses.

Based on one of your comments about LDFs, though, it looks like you may have accounts that don't have enough data to develop losses reliably. If you have those situations, you have a couple of options to get LDFs:

1. Use NCCI data. I assume NCCI has LDF data; I never had to go retrieve that, since the accounts I worked with were large enough and had enough data to forecast on their own.
2. Use your own book of business. Yes, it's going to be a smaller volume of data than NCCI - but to the extent your book is different from NCCI, it's an acceptable substitute.

When you go to estimate excess losses, you'll want to use NCCI's excess factors. While your book may have enough information to estimate limited loss LDFs, that's because limited losses are mostly a frequency-driven event; excess factors are a reflection of severity, and unless you've got a large book of business [read: you're at least 5% of the industry book] you probably don't have enough information to say anything useful about excess losses [and even if you're up around 10%, one could put together an argument that you still don't have enough info].

So, to sum up: yes, at a $250K limit you're probably overestimating both limited and excess losses; if you limit losses to a more appropriate level, you can get more accurate estimates for both pieces. The key is still going to be picking a limit that is "appropriate" - that's not too high [giving the problem you described] or too low [where you now throw out much of the loss as excess and then underestimate both pieces].