Fatal flaw in auto ratemaking

[Grandpa]

I do not know what the reason is. But actuaries have been making a simple mistake that if corrected they could make a good deal of money. The basic problem is that policies that have more than one car, the older car does not get used as much, especially if there is only one driver on the policy. Consider the following example.

You have 100 policies (policies A) with one car and one driver all of the drivers have a 5% frequency. The cars on these policies are all 8 years old. You have 25 policies (policies B) with two cars and one driver. Each policy has a 1 year old car and an 8 year old car. The 8 year old car is driven 4% of the time and the 1 year old car is driven 96% of the time. All of the drivers on these policies have a 5% frequency as well. In a traditional actuarial analysis you would combine all the 8 year old cars together. You then have this problem. You have 5 (100*5%) claims from policies A and .05 (25*5%*.04) claims from policies B. So your frequency for 8 year old cars is (5+.05)/125 = .0404. THE RESULT IS THAT YOU UNDERCHARGE FOR POLICIES WITH ONLY ONE CAR AND YOU OVERCHARGE FOR POLICIES WITH MORE THAN ONE CAR.. YOU CAN MAKE MONEY HERE IF YOU FIX THIS AND YOUR COMPETITORS DO NOT. And, NO, using a multi-car discount does not solve this problem.

If you have GLM software create a variable such as “1-1” for one car one person, “1-2” for one car two people, “1-3+” for one car and three or more people on the policy. Do the same for all car and people combinations where there is sufficient data. Create an interaction term with vehicle age and you will see that vehicle age goes completely flat. For every vehicle age the “1-1” factor will equal 1.00. For every vehicle age “1-2” will all be a little higher (around 1.05) but still all the same number. This is because there is more exposure because there are more people available to drive the car. For every vehicle age “1-3” will be a little higher still (around 1.07) because there is a little more exposure. There is still a lot of fixing to be done on the policies that have two or more cars but if recognize this than you will be able to figure those policies out. A final word of caution, make sure you have one variable for sex and that you combine your married variable into the “#cars-#vehicles” variable otherwise your factors will look weird.

Simpsons paradox is a good paper for explaining this situation.
http://www.casact.org/pubs/proceed/proceed04/04133.pdf

[careerchanger]

The 8 year old car is driven 4% of the time and the 1 year old car is driven 96% of the time.

Is it?

[Commander Keen]

Originally Posted by careerchanger

Is it?

Probably true if there's only one driver on the policy, but it's more likely that the person under the policy doing less driving will get the older car. I'd say it's probably closer to 60%-40%, though with my parents, my dad drives his 10 year old car MUCH more than my mom drives her 6 month old car...

It's also probably false with policies with young drivers. For the most part, kids aren't going to be driving newer cars, yet they'll still be doing > 4% of the driving.

I'm confused as to why this is in the C5 forum, perhaps the P&C forum would be a better place?

[stealthy]

What about if there are two cars on the policy, the car with better gas mileage will be driven more than the other, regardless of how old the car is? With gas prices where they are, why not charge more premium for the car with better gas mileage because it will have a higher exposure because it is on the road more? If I had an insured with a Hummer and a VW, I would bet that the VW is driven a lot more.

If you can clearly evaluate driving frequency to track what percentage of use the vehicles get, great! Until recently with the advent of various software that tracked vehicle usage (as well as how/where the vehicle was used), it was difficult if not impossible to track vehicle usage except for commercial auto policies where the exposure basis happened to be miles driven (and even then, auditing to ensure the mileage correct was difficult and could easily be manipulated by the insured). For private passenger, the cost to attempt to do this was prohibitively more than the potential savings, not to mention potential manipulation by the insured; even now, whether it's cost-effective (or even possible) to trace what percentage of use a vehicle gets in order to get a more accurate rate plan is open to debate. Just because it can be more accurate doesn't necessarily mean it will be used - if the cost to maintain the plan exceeds the expected profit, it's very likely that no one is going to use it.

There's still a huge missing factor here: where and when were the vehicles used? Was that 4% out in rural areas in mid-morning with hardly anyone else on the road? Was the 96% on major highways during rush hour to and from congested urban areas? Things like that aren't reflected in your discussion, and they can have a significant impact on the actual results.

In theory, yes - you're correct. In reality? Unless you're going to get a ton of customers to let you track how much they actually drive their vehicles to get accurate information on usage (an assumption that's doubtful because a lot of people have "right to privacy" concerns about stuff like this), getting enough data to establish sufficient credibility may be a very real, insurmountable problem.