1.1 Risk, Hazards, Perils, and the Law of Large Numbers
Key Takeaways
- Pure risk (loss or no loss) is insurable; speculative risk (includes chance of gain) is not.
- A peril is the cause of loss; a hazard is a condition that increases the chance or severity of a peril.
- Moral hazard is intentional dishonesty; morale hazard is carelessness or indifference toward loss.
- Insurable risks must be accidental, definite, measurable, predictable, non-catastrophic, and economically feasible.
- The law of large numbers makes group losses predictable, so larger, more homogeneous pools yield more accurate premiums.
Insurance exists to manage risk, defined as uncertainty about whether a financial loss will occur. The exam separates two categories. Pure risk offers only two outcomes — loss or no loss — with no chance of gain; it is the only risk insurers will cover. Speculative risk adds a third outcome, the chance of gain, and is uninsurable.
Memorize the distinction: dying prematurely, becoming disabled, or a house fire are pure risks. Buying stock, gambling, or launching a business are speculative. If a scenario describes any path to profit, it is speculative and outside an insurance contract.
Perils vs. Hazards
A peril is the direct cause of a loss — the event that actually produces the damage. A hazard is a condition that increases the likelihood or severity of a peril. Candidates routinely confuse these, so anchor the chain: a hazard makes a peril more likely, and the peril causes the loss.
| Term | Definition | Life & Health Example |
|---|---|---|
| Peril | The cause of loss | Death, sickness, accidental injury |
| Physical hazard | A tangible condition raising risk | High blood pressure, obesity, dangerous occupation |
| Moral hazard | Dishonesty or character flaw inviting loss | Faking a disability claim, lying on an application |
| Morale hazard | Indifference or carelessness from having coverage | Reckless behavior because "insurance will pay" |
Distinguish moral hazard (intentional dishonesty) from morale hazard (an indifferent or careless attitude). Both raise the insurer's expected payout but stem from different roots.
Elements of an Insurable Risk
Not every pure risk is insurable. To issue a policy, an insurer needs a risk that satisfies a set of standards. The classic checklist:
- Due to chance — the loss must be accidental and outside the insured's control.
- Definite and measurable — the loss must be verifiable in time, place, and amount.
- Statistically predictable — the insurer must estimate future losses from past data.
- Not catastrophic — losses cannot strike a huge share of the pool at once (war, nuclear events are excluded).
- Large number of similar exposures — the pool must be big enough to spread risk.
- Economically feasible premium — the premium must be affordable relative to the potential loss.
The Law of Large Numbers
The law of large numbers is the mathematical engine of insurance. It states that as the number of similar, independent exposure units grows, the actual loss experience of the group moves closer to the predicted (expected) loss. Predicting whether one specific person dies this year is impossible; predicting how many of 1,000,000 insured 40-year-olds will die is highly accurate.
A worked illustration: suppose mortality tables show that 2 of every 1,000 insured 40-year-old men die in a year. With only 10 insureds, actual deaths might be 0 or 2 — wildly off the prediction. With 1,000,000 insureds, the expected 2,000 deaths will be very close to actual. Larger pools shrink the percentage error, letting actuaries set premiums with confidence.
This is why insurers want a large number of homogeneous (similar) exposures. The larger and more similar the pool, the more reliable the loss prediction and the more accurately premiums reflect true cost.
Risk Management Techniques
Individuals and insurers handle risk through five recognized techniques. Insurance itself is transfer.
| Technique | Description | Example |
|---|---|---|
| Avoidance | Eliminate the activity entirely | Never flying to avoid plane crashes |
| Reduction | Lower frequency or severity | Installing smoke detectors |
| Retention | Accept the risk yourself | A health plan deductible |
| Sharing | Spread among a group | Partners pooling business risk |
| Transfer | Shift to a third party | Buying an insurance policy |
Reinsurance is how insurers themselves transfer risk: a primary insurer (the ceding company) passes part of a large risk to a reinsurer, protecting against catastrophic single losses.
Frequency, Severity, and Why Predictability Matters
Actuaries price risk by estimating two dimensions of loss. Frequency is how often a loss is expected to occur in the pool; severity is how large each loss is expected to be. A risk with low frequency but high severity — premature death — is exactly what life insurance is built to handle, because the law of large numbers makes the group frequency predictable even though any single death is not.
Consider why catastrophic and speculative risks break the model. A war or pandemic violates the "not catastrophic" rule because losses strike a huge share of the pool simultaneously, so independence between exposures collapses and the prediction fails. Speculative risk fails because the chance of gain attracts people for reasons unrelated to protection, distorting the pool. These constraints are not arbitrary — each one keeps the loss distribution stable enough for the law of large numbers to work, which is why every insurable-risk element traces back to keeping predictions reliable.
An applicant lists scuba diving and a history of high blood pressure on a life application. The high blood pressure is best classified as which of the following?
Why does an insurer want a large number of similar exposure units in its pool?