# What's driving the rate change

Hello,

So I’ve completed a complex rate revision where some segmentation is being added, and there are a number of moving parts. To understand what’s going on, I’ve got my policy level before and after premiums and the most important field, percent change.

Then the leadership asks, quite reasonably, what’s driving the change? When changes are simple, explanations are too, base rate only revisions lead to uniform changes. Revisions where base rates and one or two segments change can be explained by big changes to policies who had big factor changes.

But this time, I made many changes, so I’m not entirely certain what is driving the changes. So the fun idea is, build a model!

The setup would be simple, policy level attributes readily available from the data, and a response variable, the percent change.

And the question, and the reason for the post, is what is the best model to build?

In my head, I thought classification and regression trees would be fine, but say you had 2000 policies, and want to build something to predict the biggest driver of premium increase/decrease, how would you do it?

I’m thinking something in R studio because I’ve worked in this platform before. I’m in the process of using the rpart function, but am not sure if anything else is good out there, and not to difficult to use.

Any recommendations? Thanks!

Till All are One,

Epistemus

Couldn’t you literally just pull the 5 policies with the biggest changes and do a waterfall of the new classification contributions to the impacts?

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Not sure how to do it in R, but you can pretty quickly create a GBM with response variable being an indicator. Indicator would be 1 if rate change of a risk was above a specific threshold say 20%.

GBM would then identify the most predictive variables that drive your rate change.

I’ve done this before using Willis towers software (Radar)

I would never say “I ran a model” to leadership, i’d just use model results to gain insight, then look into whatever was coming out of the model to see if i agreed with it. I’m not sure leadership cares how i answer the question of “what’s driving the results” just that i can answer the question with a response tailored to them.

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This rate revision … is it an indication or a rate impact?

If it’s a rate indication, do a waterfall exhibit that shows how much the indication changed by changing various inputs along the way. Period.

If it’s a rate impact [we’re taking these changes, it’s going to impact all policies, here’s how much], @John.S.Mill is right: look at the largest policies, step through the changes being made, see what’s driving changes in those. If loss costs for certain classes went up and you write quite a bit in those classes, that’s probably your answer. If ILFs changed substantially for some table, again - that could be it.

A model isn’t necessary here. Critical analysis of your data is. That’s what actuaries are paid to do, because other people won’t or don’t know where to start.

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How extensive is the list of “changes to the rating plan”?

You might look those aspects of the rating plan with the “largest changes” and see what the distribution of “before” premiums look like for that part. You might also look at the “average before premium” for these. (I.e., perform a univariate analysis on elements that are likely to have larger impacts)

You might also look at both policies with the largest percent change as well as policies with the largest dollar change.

In a situation where a rate change has a complex set of moving parts (e.g. implementing a new predictive model / changing from one model to another), I’d agree that looking at a sampling of most-impacted risks would be a simple way to build a report to describe the situation.

(I’d also pick some least-impacted risks, for comparison purposes.)

You could also build a predictive model using an appropriate set of characteristics to predict the rate change (on a dollar and/or percentage basis), using the results to select/create example risks to profile, and generate a set of univariate plots to describe the impacts to different groups along major/easily understood rating/underwriting characteristics…but that might require time that you may not have. Profiling some example risks would probably get you what you need in less time.

DANGEROUS

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Dangerous if presented in isolation. But if you’re presenting a multidimensional change to an audience that struggles with more than one dimension, they may be needed to help round out the picture if you’re presenting profiles of impacted risks.

Perhaps it also depends on the product. In my last pricing role, I was working with a business that had few enough (large) accounts that when we updates to our rating structure, I was able to generate a list of accounts, tagged with a couple of high-level descriptive variables, current rate, current schedule mod, new rate. The underwriters and their managers got lists for “their” accounts, and we were able to go back-and-forth to help them understand what the change meant to them.

But because of the nature of that business, there were few enough risks, and the underwriters were familiar enough with their accounts, that it worked.

Knowing one’s audience is a key part of communicating.

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I agree with others that a key part is knowing what your audience wants to do with this. Is this for the ceo or for a line manager wanting to know how policyholders will be impacted ? These are very different answers.

But it sounds like OP maybe knows this, and instead of as looking for advice about how to get some insight for themselves before deciding on an answer.

I would say just using gbm in R, and looking at variable importance plots and partial dependence plots. The hyper parameters probably aren’t going to matter that much if you just want some ideas about the big drivers of change. All of these would almost surely be for just OP to look at, not to share.

Thank you, the problem is i had to go through a complex rating process and even looking at segments that are changing or being added is not easy. As other have said, looking at policies with large  or percent changes is actually something I’ve done already, and have commented in my initial submission of results. I just don’t know if in this instance what it will take for me to have comfort with being able to both explain big changes, and even provided actionable/digestible incites for the non actuarial leadership more involved in sales.

I agree and have done what others have suggested as a good starting point. Look at policies with big changes, explain those.

Thanks /u/magillaG ! thanks everyone!

Another thought . . . along the lines of the univariate analysis:

I’d imagine that you know the “percent change” for various elements in your rating plan; Create a display showing:

“level” of rating element component % Dist of Pre-Prem Avg Pre-Prem Amt %chg of rating element \alpha %chg in total prem \beta \frac{1+\beta}{1+\alpha}-1.0
xxx %x \$yyy %\alpha %\beta %\gamma

%\gamma would then show what impact “other changes” had on an element that might have a “large” change.

That is, you might have a policy showing “significant” changes due to a particular rating element, but this can help show that for the book overall, whether that change is “pervasive” or “mitigated” by other changes.

1. This looks like a simple question, but it’s not really that simple: when you say “leadership asks, quite reasonably, what’s driving the change?” do you understand what they’re wanting for an answer? It sounds like maybe you don’t. If you don’t, or if you’re not entirely clear, go ask now. Understanding that is really critical to getting the right answers the first time around.