HASENMILLER: Predictable Risks

Blake Hasenmiller

With the U.S. Senate and the House both having passed a health care bill, it seems almost inevitable that the federal government will soon have a greater say in the way health insurance works. One of the major problems with the current situation, according to many lawmakers, is that insurance companies often will not cover preexisting conditions. In other words, if you’re sick or in need of medical care in some way and don’t already have insurance, it’s very possible that nobody will sell you any, or will charge you significantly more if they do. 

I have a few related examples that I’d like to share with you before I comment on this further, so please bear with me for a moment. I promise I’m going somewhere with this. 

Say I flip a coin X number of times, and then ask you to come as close as possible to predicting what fraction of the time you believe the coin will land on heads. You would probably guess around half the time, and that would be a good guess. But if X = 1, you won’t even be close. Your chance of being correct, or at least closer to correct would increase significantly if I flipped the coin twice. And the more I flip, the better your guess is.  For example, the sample standard deviation — which is a measure of the amount of variability in the outcomes — of the fraction of times the coin lands on heads for only one flip is .71. If I flip it twice, this number falls to .41. For 20 flips, it’s .11 and after 100 flips of a coin, the sample standard deviation is only .05. 

Another example: If I flip a coin 10 times, the chance of heads coming up between four and six times is 66 percent. If I flip a coin 100 times, the chance of heads coming up 40-60 times is 96 percent.

The purpose of these examples is simply to show that the more times you repeat a process, the more likely you are to be close to the average result.

Keeping that in mind, imagine that, at the end of each year, everyone is forced to roll a die. If you roll a six, you lose $12,000. If not, you lose nothing. Now imagine that you are given a choice: For $2,000 per year, you don’t have to roll. Would you do it? 

On average, the cost to you is equal in both scenarios. But chances are you would prefer the “pay $2,000 each year” option. The first option would force you to continually save your money just in case you rolled a six. The second option allows you to accurately predict your outflow and spend your money accordingly. In other words, it eliminates the risk.

But what if you weren’t offered the second option? What would you do? What I would do is this: Get a bunch of people together and offer to cover costs if they roll a six on the condition that they each give me $2,100 per year. For an extra $100 per year, on average, I would allow people to predict their die-rolling expenditures. For many people this would be worth $100 more per year. For some it might not, and they would save money on their own instead. 

But what about my level of risk? After all, couldn’t I lose a lot of money if enough people rolled sixes all at once? Well, technically, it is possible, but it is statistically very unlikely. That’s because, as I explained earlier, once you get enough people together, it will become much easier to predict the fraction of people who will roll a six. 

This is known as risk-pooling, and it is what insurance companies do: They are paid to assume your risk for you. That catch is, if done on a large enough scale, it’s not risky at all. Of course, this assumes that the insurance companies can accurately predict your level of risk, which is considerably more difficult than predicting the rolls of a die. 

That being said, certain conclusions about risk levels can be reached. For example, statistically speaking, people who have gotten a DUI are more likely to be in a car accident. People who smoke are more likely to get emphysema. People who wrestle bears for a living are more likely to die an early death. People who have appendicitis are more likely to need their appendix removed.

Now back to the die rolling example for a minute. If you knew that someone was going to roll a six, how much would you charge that person for insurance? You’d charge at least $12,000 if you don’t want to lose money. Of course, that would kind of defeat the purpose of insurance. 

If you have appendicitis, the chances needing an appendectomy are pretty darn close to 100 percent. That’s not what we call a risk. That’s what we call an inevitability. So how much do you think an insurance company is going to charge to insure someone with appendicitis? Probably pretty close to the price of an appendectomy. 

That’s the problem with the whole “pre-existing condition” debate that’s going on. The point of insurance is to insure a risk. Pre-existing conditions are not risks. They are conditions. You know about them, thus no uncertainty and therefore no risk. 

If insurance companies are forced to insure pre-existing conditions, they will charge people with pre-existing conditions a much higher rate. If they cannot do this, they will charge everyone a higher rate to offset it. If they cannot do that either, they will likely go out of business. 

Our elected officials need to come to their senses and realize that to insure a risk, a risk must first exist.

Blake Hasenmiller is a senior in industrial engineering and ecomonics from DeWitt.