Week 50 Day 1: Insurance as Risk Transfer: What It Is and Is Not

The rule: insure against catastrophes, self-insure against inconveniences. A $500 phone screen repair is an inconvenience -- do not insure it. A $300,000 house fire is a catastrophe -- insure it. A $200,000 medical bill is a catastrophe -- insure it. A $100 copay is an inconvenience -- accept it. This means choosing higher deductibles (which lower your premiums) and pocketing the savings. A $500 deductible on your car insurance costs far more in premiums over time than a $1,000 or $2,000 deductible. The higher deductible saves you money in the long run because most years you have no claim. The insurance company sets premiums to make a profit -- on average, you pay more in premiums than you receive in claims.

The economics of insurance are straightforward once you understand the business model. Insurance companies collect premiums from millions of policyholders, invest the 'float' (premiums collected but not yet paid out), and pay claims from the combined pool. They set premiums so that total premiums collected exceed total claims paid plus operating costs -- this is their profit margin (the 'combined ratio'). For the individual policyholder, this means insurance is always a negative expected value proposition: on average, you will pay more in premiums than you receive in benefits. So why buy it? Because the expected value is not the right framework for catastrophic risk. A $300,000 house fire has a low probability (about 0.1% per year) but a devastating financial impact. The expected loss is $300 per year, but the actual loss if it occurs is financial ruin. You are paying a premium ($1,000-$2,000/year) that exceeds the expected value ($300) in exchange for eliminating the risk of ruin. This is rational for catastrophic risks and irrational for small risks. The insurance industry profits most from policies covering small, frequent losses (extended warranties, phone insurance, dental insurance, pet insurance) where the markup over expected claims is 30-50%. These are the policies you should avoid. The policies where insurance provides genuine value are those covering large, rare events: homeowners, auto liability, health, disability, umbrella liability, and (if you have dependents) life insurance.

The theoretical foundation for optimal insurance purchasing was established by Arrow (1963) and refined by Raviv (1979), who proved that the optimal insurance contract for a risk-averse individual features a deductible -- the insured retains small losses and transfers large losses to the insurer. The size of the optimal deductible increases with the individual's wealth (wealthier people can absorb larger losses) and decreases with the individual's risk aversion. This result has been robustly confirmed in applied work: Sydnor (2010) found that homeowners systematically overpay for low-deductible policies, paying $100 or more annually to reduce their deductible from $1,000 to $500 -- implying a willingness to pay $100 to avoid a $500 loss that occurs with approximately 5% probability (expected savings of $25). This five-to-one ratio of premium to expected benefit reveals the behavioral bias driving the insurance industry's profits on small-loss policies: loss aversion and probability neglect cause people to overweight the pain of paying for small losses, even when self-insurance dominates economically. Barsky, Juster, Kimball, and Shapiro (1997) measured risk aversion in a large sample and found that the median American has a coefficient of relative risk aversion of approximately 4 -- high enough to justify insurance against catastrophic losses (medical, home, liability) but not high enough to justify the premiums charged for small-loss policies (extended warranties, low deductibles). The practical implication: raise your deductibles to the highest level your emergency fund can cover, eliminate insurance on replaceable items, and redirect the premium savings to building wealth.