Insurance is a mechanism for pooling low-probability, high-cost events across a large group. Each participant pays a small premium; the pool pays the few who experience the event. The economics are honest — households come out slightly worse on average — but the reason to buy it is that the tail risk without it is unbearable.
- 01State the pooling logic in one sentence.
- 02Distinguish tail risks worth insuring from ordinary variance worth self-insuring.
- 03Explain why insurance is a negative-expected-value transaction that households should still make.
The mechanism
A thousand households each pay $500 a year into a pool. In a normal year, ten of them experience a loss of $30,000. The pool pays the losses; the insurer's premium income covers claims, expenses, and a modest profit. Each participant transforms a 1% chance of a $30,000 loss into a certain $500 cost.
What to insure
Insure what would ruin you. A house fire, a serious injury, a lawsuit, the death of the primary earner. Do not insure what you can absorb — a cracked phone screen, a two-week vacation, a warranty on a mid-range appliance. Extended warranties are the archetypal negative-expected-value transaction with no tail-risk justification.
The math is honest
Insurance is negative expected value for the household. The insurer must cover claims, operating expenses, and a return to shareholders. The transaction is worth it not because the expected value is positive but because the distribution has a tail the household cannot survive. Understand the transaction; do not resent it.
- Insure the tail. Self-insure the middle.
- Extended warranties fail the tail test.
- The transaction is negative expected value on purpose.