Price Increases on Individual Health Plans: Deductible Leveraging

I was intrigued by the mention of "deductible leveraging" in Wellpoint's response to criticisms of their on-average 25% premium increases for individual customers in the California market.

How important an effect might this leveraging idea be? Well, pretty significant. The basic idea is that as underlying expenses increase, the company bears a larger portion of the total expense, so long as the deductible remains fixed. This increase in cost is going to be reflected in premiums. Here's the simple math.

Let x, a random variable, be an individual's actual health care expenses for a year. Let the deductible be D and we will call the premium P. All these will be annual amounts.

Then the expected value of the individual's insurance expenses are E(x) and the insurance company's portion of that would be:

I = insurance company's costs = E(x) - D

since the individual pays the deductible first. I am ignoring any coinsurance.

With fair insurance (I wonder if Sec. Sebelius can imagine such a concept!) the premium would be set at:

P = I = E(x) - D

Now let's just see what happens to P when we experience inflation at the rate of "i" in underlying insurance expenses.

Expenses will become (1+i)x, and therefore the insurance company's costs become (1+i)E(x) - D. This means that the premium increases to

P' = (1+i)E(x) - D

Then the percentage increase in the premium is

P'/P = {(1+i)E(x) - D}/{E(x) - D}

= {E(x)-D}/{E(x)-D} + {iE(x)/(E(x)-D)}

= 1 + i{E(x)/(E(x)-D)}

Note that the term multiplying the inflation rate is greater than 1, since the denominator is smaller than the numerator. There is the basic leveraging effect.

Let's use some numbers to see how it might work out. Suppose underlying inflation in health costs to be 10%, and let's take a policy with a $2500 deductible with a premium of $3600 per year. This implies, from the above equation, that total expected costs must be $6100.

Using that last equation up above, it follows that the rate of increase in the premium will not be 10% but instead 16.9%. Using the kind of rhetoric that Sec. Sebelius (fast becoming my least favorite person in Washington), the premium increases 1.69 times faster than the underlying rate of inflation.

As will be obvious from the last equation, this leveraging effect is greater for higher deductible policies.

Note that while the individual feels a 16.9% increase in their premium, their total expected cost still only increases by the rate of inflation, that is, 10%. This is a trivial point, but one that not a single reporter or story has made.

There are many problems in the individual health insurance market that need fixing and that can be fixed. I just wish that Obama, and the Republicans too, would hold true to their pledges to stop the rhetoric and focus on the real issues. Blaming the insurance companies and their "excess profits" as dear Sec. Sebelius has been doing, is shameful.