Sure Johnnie, here ya go.
When I refer to "adverse selection", I'm suggesting that an individual retiree may have information that the insurance company doesn't have, then rationally acts on that information in a way that is not beneficial to the insurer. From Investopedia:
The term adverse selection was originally used in insurance. It describes a situation where an individual's demand for insurance (either the propensity to buy insurance, or the quantity purchased, or both) is positively correlated with the individual's risk of loss (e.g. higher risks buy more insurance), and the insurer is unable to allow for this correlation in the price of insurance. This may be because of private information known only to the individual (information asymmetry)...
The standard example is a smoker being more likely to buy insurance than a non-smoker if the product is offered at a rate equal for all applicants, regardless of smoking history.
I'm probably not using the term precisely enough to describe this particular situation, but the principle is very relevant.
Looking at the information from the insurer's position first...
GM calls Prudential and asks "what will you charge me to take this bundle of 40,000 pensions off my books? I'll send you the list":
- 1212 males age 57: 12 at $1000/ month, 27 at $1100/mo.....
- 755 females age 57: 16 at $900 / mo., 39 at $1000 / mo....
- 1345 males age 58....
- etc., etc. until all 40,000 lines of the spread sheet are filled
Prudential then uses their standard mortality / life expectancy measures and premium calculation methods to arrive at a premium for each of the 40,000 lines, then provides the individual premiums and the bottom line total to GM.
GM then makes an offer to all 40,000 retirees on equal terms for all, adjusted only for age, marriage, gender and pension payment. I assumed (and now contradicted by Rodi's post) that the offer to that first 57-year-old on the list (Joe) was: "keep $1000 a month or take a lump sum equal to the premium Prudential will charge us for taking the $1000-a-month-for-life off our hands."
Now from Joe's perspective. He may be anywhere in this range:
a. "Mom and Dad lived to over 95. I'm in perfect health. I'm taking the security of a $1000 per month pension that provides longevity insurance."
Or...
b. "Daddy and Momma both had heart attacks at age 60. Doc tells me that my cancer is spreading and I've got about 6 months to live. The way I figure it, GM says I can get $6000 (6 x $1000) if I keep taking the monthly payment vs. $200,000 lump sum. DD has college debt up to her eyeballs and I want to help her anyway I can. I'm taking the lump sum."
Joe has acted on asymmetric information. He knows the lump sum is a much better deal for him because he has information not made available to Prudential.
Back to Prudential...
If 10,000 of the "Joe B's" with excellent odds of coming out ahead monetarily by taking the lump sum choose to do so, then the premium calculations Prudential used for the remaining 30,000 are not accurate.
Prudential comes out behind, a victim of adverse selection, because they have charged a premium based on the average life expectancy of a pool of 40,000 people of average health. The liability they will get, however, will be to make payment for life to a pool of 30,000 healthier-than-average individuals.