You can't diversify them away is what matters about those. All very well to say they are boring but you previously said they were zero.
Not on purpose I didn't.
Adding more people eliminates precisely the non systematic risk that you are, erm, not bored by. That part can be diversified away. Beyond a relatively small pool I suspect it shrinks to negligible for the insurer. But for the insuree, it is eliminated for every person that joins so there is no fall off in utility from the perspective of more and more people joining.
No, it cannot. This is what I'm trying to explain. And I'm doing it very poorly, apparently

.
Look - if it were true that the non-systemic risk in health insurance could be diversified away, then insurers wouldn't care which policyholders they got, they'd only care that they had
more of them. They would only care that they had a large number of policyholders.
But we don't - we need enough to make our fixed operating costs reasonable in the marketplace, but beyond that, we'd be happiest if we had a smaller number of the right kind of people than a large number that included some of the wrong kind.
The systemic variance in health insurance - the variance in negotiated rates, utilization, new technologies and treatments entering the market, regional variations in price and behavior, and the variance in cost associated with age and gender and smoking status - these are all very predictable. These are not problems for insurers. This is not where our worry is.
Our worry is around the variance of claims at the individual person level. It's the combination of the expected cost level for person A and the length of the claim cost tail on person A's distribution.
And that variance doesn't get diversified away.
If we have a pool that consists of 100 healthy people, and we add one hemophiliac... the likelihood of having a claim of $1M or higher does NOT reduce. It increases. It increases because the hemophiliac's variance is NOT offset by the variances of the other 100 healthy people.
My understanding is that with stocks, every time you add a new stock to your portfolio, the variance of the portfolio is reduced, correct? So the more you add, the lower the variance. The more you add, the lower the likelihood of experience a return that is more than X standard deviations from the mean.
This is not the case for health insurance. When you add more people, it does NOT necessarily reduce the variance of the pool. It does not necessarily reduce the likelihood of experiencing a claim more than X standard deviations fro the mean. Even more than that, it can increase the likelihood that the
aggregate claim level of the pool is further away from the predicted mean.
In stocks, it is often the case that the non-systemic portion of the risk is negatively correlated with a different stock, right? When domestic stocks perform well, foreign stocks perform poorly, and vice-versa. They are both reacting to the same underlying stimuli, but they move in opposite directions. My understanding is that this is why diversification works.
This does not happen with health insurance. No two peoples' non-systemic risks move in opposite directions. When Bob gets unexpectedly sicker, Joe does NOT get unexpectedly healthier. That's NOT how it works. They do NOT offset. The non-systemic portion of the risks are NOT correlated with each other - they are nearly perfectly uncorrelated.