Actuaries and underwriters love large groups. The bigger the better. Small groups and individuals are almost impossible to accurately price. Big groups allow statistical approximations to approach population realities while the error bars on a small group are massive. Massive error bars make underwriters and actuaries cry.
The following will have some math and more importantly a lot of statistical intuition, so please bear with me.
Let us imagine that Mayhew Insurance company has 1,000 employees in a single group. This is a good size group. The group premiums are precisely enough to cover medical and administrative expenses for the year. Let us also assume that 10% or 100 employees are expensive to cover. The other 900 are in reasonably decent health or in good health. Their premiums cover the expenses of the expensive 10%.
Each work group has to buy all of their own services in order to promote internal competition (thus destroying the theory of the firm as an institution). That means 20 managers are now buying insurance for their employees independently as a small group. It will be the same 1,000 people getting covered with the same 100 people who are expensive but what happens with rate structures?
Two things will happen. First, the administrative costs will increase. Some tasks are scale invariant while other tasks scale with membership. As I’ve mentioned before, my work is basically scale invariant. It takes me the same amount of time and thus costs if I work on a group of three members or three thousand members. The first group has a cost attribution of several dollars per member while the second group has a cost attribution of pennies. The medical loss ratio of 80% for small groups and individual markets and 85% for large groups recognizes this difference in group structure.
The second pricing reality is when statistics become important. We know the general population risk of someone being expensive is 10%. We would expect 5 people in each group of 50 to be expensive. That is a naive and incorrect modeling of the situation.
A 50 person group that has complete statistical independence in a binomial distribution will have precisely 5 high cost people in the group 18% of the time. 43% of the time, that group will have less than 5 high cost people (including a 3% chance that either no or one person is high cost). Conversely, there is a 12% chance that there are 8 or more high cost people in that group. There is roughly a 50% chance that between 4 and 6 people in this group are high cost individuals.
Now we can make life a little bit more complicated for the actuaries. Let us assume that health status is not randomly distributed throughout the company. The health economics, actuaries and underwriters are reasonably representative of company health status. Customer service and government compliance offices have quite a few people who have well known tales of woe. Doctor outreach is the company version of Pharma girls where they seem to exclusively recruit former Division 1 scholarship soccer players and swimmers.
The twenty groups of fifty people apiece would have seven groups with no more than two expensive people in it. There are another six groups with at least eight particularly sick people in it. Then there would be seven groups with four to six people who are high cost individuals.
So what does this mean?
Seven groups would see roughly the same premiums that they saw when there was a single 1,000 member Mayhew Insurance group. Seven groups that have very few high cost individuals in it, would see significantly lower premiums than they would under the 1,000 member company wide group. Six groups would see significantly higher prices as they have more than average number of sick people in these small sub-groups. One of these groups would see at least a doubling of premiums.
Slicing and dicing Mayhew Insurance from a single group to 100 groups would produce an even wider spread of premiums dependent on health status. Breaking Mayhew Insurance from one group with a thousand members to a thousand groups with one member creates even more variance. Random noise becomes more important in small group sizes.
A large group smooths out the random noise and makes the cost of covering the sick lower due to both lower administrative costs and lower variance costs. This point will be important on the next post on small group underwriting changes and the potential for rate shock next fall.
