I'd like to respond to several posts in detail, but I don't have time right now if I want to propose a new model, which I do.
Letsgobobby, with respect to what you currently view as a practical guess at what the decision model for umbrella insurance should be, I am on the exact same page. Almost to the letter. That said, one item on which we might disagree is on what to do with low probabilities. Your attitude seems to be that low is low, so don't think too much about it. I say there is a big difference between a 1 percent chance of something, and a 0.1 percent chance of something, and 0.01 percent chance of something. It's one in a hundred, versus one in a thousand, versus one in ten thousand. I'd care about the distinctions between those probabilities when I was making this kind of decision.
Msilenus, I like your model, but I have a feeling the data might be too complex to define, or at least to have much confidence in without large sample sizes...which, as has been mentioned, would be difficult to arrange for by zip code.
Let me propose a different approach that might work out to be simpler. Keep in mind as you read it that I am making simplicity a high priority. Another big motivation for the model is the difficulty in obtaining (or even defining, to some extent) the data needed for the models I and msilenus suggested. I may not be able to improve on those suggestions, but I'll throw this out there and see what others think.
With respect to any insurance, what I ultimately care about are the outcomes for people who actually buy the coverage. In particular, if I'm trying to decide whether buying umbrella insurance is a good idea, and if it is, then how much would be optimal for me, I want to study the outcomes realized by holders of umbrella policies. I don't care about judgments in general--now that I think about it, that information might be better for a sales pitch than for this decision process. I care about what happens--the bottom line--to those who have umbrella insurance.
Take the $1M level of coverage, for example. I want to know how many people in my zip code (yes, sample size--hang on) had umbrella insurance each year, and how many times during each year one of those individuals (yet another issue, which I'll get to in a moment) had to pay out money from their own pockets as the result of a court judgment. For simplicity, I won't worry about how much they had to pay, or whether they had to pay because the matter was outside the scope of the policy. (I'm iffy on both parts there, but a case can be made for each, especially assuming they make data availability much more likely. I'm trying to formulate an approach that's actually possible, not one that is theoretically ideal.) The bottom line I'd come up with would be an estimate of the probability that an individual with a $1M umbrella policy would have to pay a court award in spite of the insurance in a given year.
Do this for all amounts of umbrella coverage, including $0 (no coverage at all)--and we should probably say liability coverage, not specifically umbrella). This would give us a distribution (or density function--whatever
) on which to base our decision. The decision would still be arbitrary, but at least we could see what we were getting for our money. A sampling of estimates (which I am fabricating from thin air) might appear something like:
$300K of auto liability -> 1% chance annually of paying out of pocket on an auto-related court judgment
$1M of auto liability -> 0.1% chance
$2M -> 0.04% chance
$5M -> 0.01% chance
Again, this approach is not necessarily more appealing theoretically than has already been suggested. I'm just thinking that the data might be easier to define and gather.
Regarding the two items I said I'd come back to...first, there's the matter of sample size. I agree that breaking the data out by zip code might result in samples that are too small, although it is also possible that even with sparse data for the larger awards, we might still be able to fit a curve to the distribution. Assuming the samples would be too small even for curve fitting, we could look at all-U.S. data, and then cleverly scale is some coarse way for each state, zip code, or whatever. I don't want to think about the details of that at the moment
, but I suspect it could be done. There would be some problems with a simple scaling strategy, but perhaps it would be good enough for almost everybody.
The other issue that came immediately to mind as I was typing the word "individuals" was that I think we'd need to break this out by the number of people in the household, since more family members means more likelihood of something going wrong. Or maybe the output variable could be annual percentage chance of out-of-pocket payout, per dollar of premium paid. That would factor in additional risk from a variety sources, including family size. I figure insurance companies have that stuff worked out pretty well already.
So, what do you think? Good? Bad? Or is everyone asleep at this point?