1.1 Risk, Hazards, Perils, and the Law of Large Numbers
Key Takeaways
- Risk is uncertainty about loss; only pure risk (loss or no loss) is insurable, never speculative risk.
- A peril is the immediate cause of loss; a hazard is a condition that increases the chance or severity of that peril.
- Hazards come in three flavors: physical (tangible), moral (intentional dishonesty), and morale (carelessness because coverage exists).
- The Law of Large Numbers lets insurers predict aggregate losses accurately as the pool of similar exposure units grows.
- An insurable exposure must be due to chance, definite and measurable, predictable across many similar units, and non-catastrophic.
Why Risk Sits at the Center of Insurance
Risk is uncertainty about whether a financial loss will occur. Every life and health policy exists to convert that uncertainty into a fixed, budgetable cost called a premium. The exam expects you to classify the risk in a fact pattern before you reason about coverage.
Note the order of cause and effect that the test rewards: a hazard raises the odds of a peril, and the peril produces the loss. Keep that chain straight and most vocabulary questions answer themselves.
Pure Risk vs. Speculative Risk
Pure risk offers only two outcomes — loss or no loss — with no chance of gain. Speculative risk adds a third outcome: profit. Insurers underwrite only pure risk, because covering a chance of gain would be gambling.
| Attribute | Pure Risk | Speculative Risk |
|---|---|---|
| Possible outcomes | Loss or no loss | Loss, gain, or break-even |
| Insurable? | Yes | No |
| Life & Health examples | Premature death, disability, sickness | Day-trading, opening a clinic, betting |
Exam shortcut: if a choice contains a chance to come out ahead financially, it is speculative and therefore not insurable.
Perils and Hazards
A peril is the direct cause of a loss — death, sickness, injury, fire. Life insurance covers the peril of death; health insurance covers the perils of sickness and injury.
A hazard is any condition that makes a peril more likely or more severe. There are three:
- Physical hazard — a tangible condition: uncontrolled diabetes, obesity, a hazardous occupation such as crop-dusting.
- Moral hazard — intentional dishonesty: lying about tobacco use, faking a disability claim, arranging a loss to collect benefits.
- Morale hazard — indifference or carelessness because coverage exists: skipping checkups or driving recklessly since insurance will pay.
| Hazard | Driver | Life & Health example |
|---|---|---|
| Physical | Real-world condition | High blood pressure on an application |
| Moral | Deliberate deceit | Concealing a cancer diagnosis |
| Morale | Lax attitude | Ignoring doctor's orders once insured |
Memory hook: moral = morality (right vs. wrong, intentional). Morale = attitude (lazy, careless).
An applicant deliberately omits a recent heart-attack diagnosis from her life insurance application so she can qualify at standard rates. What does her conduct represent?
The Law of Large Numbers
The Law of Large Numbers is the statistical principle that as the number of similar, independent exposure units increases, actual results move closer to expected (predicted) results. It is what lets an insurer set a premium today for losses that have not yet happened.
Worked example. Suppose mortality data show that, for a class of 45-year-old non-smokers, 2 deaths per 1,000 lives are expected each year.
- Insure only 10 lives: zero deaths and two deaths are both realistic outcomes — wildly unpredictable.
- Insure 100,000 lives: about 200 deaths are expected, and the actual count will land very close to 200.
With a $250,000 face amount on each of the 100,000 policies, expected claims are 200 x $250,000 = $50,000,000. Spread across 100,000 policyholders, that is a $500 pure (mortality) premium per policy before expenses and profit loading. The larger the pool, the more reliably $500 covers the year's claims.
| Pool size | Expected deaths (2 per 1,000) | Predictability |
|---|---|---|
| 10 | 0.02 | Useless |
| 1,000 | 2 | Rough |
| 100,000 | 200 | Strong |
| 1,000,000 | 2,000 | Very strong |
Elements of an Insurable Risk
Not every pure risk can be written. To be commercially insurable, an exposure should satisfy these tests:
- Due to chance — accidental and outside the insured's control (this is why early suicide is excluded).
- Definite and measurable — identifiable as to time, place, and dollar amount so a claim can be valued.
- Statistically predictable — enough similar exposure units exist for the Law of Large Numbers to work.
- Not catastrophic — one event should not bankrupt the pool, which is why war and pandemic clauses appear.
- Economically feasible — the premium must be small relative to the potential loss, or no one will buy.
Trap to watch: a candidate answer that says an insurable risk must "guarantee a profit for the insurer" is always wrong — insurance accepts that some pooled premiums will be paid out as losses.
An insurer reviews mortality statistics on millions of insureds and finds it can predict the number of annual deaths in a large risk class with great accuracy, while it cannot predict deaths in a group of only five people. This reliability of large-group predictions reflects: