Felix Salmon explains the bad bargain known as "index annuities" very well indeed. In the beginning, these annuities are pretty good investment products:
You hand over a lump sum, and an insurance company promises to pay you an income so long as you’re alive. If you die early, you lose out (but don’t need the money any more); if you live long, you win, and do need the money.
Then, these products got ruined when the sellers introduced an early cashout provision which allows buyers to "take out up to 100% of your money penalty-free if you are diagnosed with a terminal illness or enter a nursing home."
As Felix explains:
The reason for me to buy an annuity is that I want to be subsidized by the short-lived if I turn out to be one of the long-lived. What I don’t want is for the short-lived to be able to get their money back in full, because then my subsidy goes away, and there’s no point in buying an annuity at all.
This is the same point I try to get across in Chapter 3 of Numbers Rule Your World. The term "subsidy" has a terribly negative connotation in the U.S. but insurance only works because of subsidies. The arrangement, in the case of disaster insurance, is for the lucky to subsidize the unlucky, and it only works if there is uncertainty as to who will be the lucky one. The participants have to feel that the subsidy arrangement is "fair" or else they wouldn't join the scheme.