Insurance Expected Value Audit
Example: Annual premium for the coverage: 400 $ · Maximum claim payout: 10000 $ · Annual probability of a covered loss: 1.5 % · Annual value you assign to peace of mind: 100 $ · Years of coverage to evaluate: 10
| Annual expected value gain/loss from coverage | $-150 |
| Expected annual claim payout | $150 |
| Loss probability needed to break even | 4.00% |
| Total premiums over coverage period | $4,000 |
| Expected payout per dollar of premium | 0.38 |
Worked example
A $400/year appliance warranty covers up to $10,000 with an estimated 1.5% annual failure rate. Expected annual payout: $150. After adding $100 of peace-of-mind value, the annual expected value gain is $150 + $100 − $400 = −$150 per year. Over 10 years you pay $4,000 and expect to receive $1,500 — a $2,500 expected loss. The warranty only breaks even if the failure rate exceeds 4% annually.
Frequently asked questions
What is expected value in insurance?
Expected value is the probability of a loss multiplied by the loss amount. If a covered event has a 2% annual probability and pays $5,000, the expected value is $100. A rational buyer only pays a premium above expected value when the loss would cause genuine financial hardship — catastrophic risk — not routine inconvenience.
Should any insurance have a negative expected value for me?
Yes — some insurance should. Life insurance for a breadwinner, disability insurance, homeowners insurance, and major medical are all examples where the catastrophic downside justifies paying above expected value. The rule applies to small, frequent, predictable losses.
What is the break-even loss probability for my premium?
The break-even probability is your annual premium divided by the coverage amount. For a $400 premium on $10,000 coverage, you need a 4% annual loss probability to break even on expected value alone. Most extended warranties and add-on policies have actual failure rates below their break-even.
How do insurers know the right premium to charge?
Insurers use actuarial tables, historical claims data, and risk modeling to price premiums above their expected loss. The difference pays for overhead, profit, and reserves. Individual buyers almost never have better loss data than the insurer — which is why the expected value test nearly always favors dropping low-stakes coverages.