1.1 Risk, Peril, Hazard, and the Law of Large Numbers

Every Life & Health exam opens with the vocabulary of risk. These terms appear directly on the test, and they reappear in disguised form throughout contract, underwriting, and ethics questions. Memorize the precise distinctions now.

Risk: The Possibility of Loss

Risk is uncertainty about whether a loss will occur. Insurance does not eliminate risk; it transfers the financial consequences of risk from an individual to an insurer in exchange for a premium.

The exam draws a hard line between two categories:

Death, disability, sickness, and fire are pure risks. Gambling, stock investing, and opening a business are speculative risks because they carry the possibility of profit. Insurers cover only pure risk.

Peril vs. Hazard

Students lose easy points by confusing these. A peril is the immediate cause of a loss, the thing that actually does the damage: heart attack, cancer, fire, flood. A hazard is a condition that increases the likelihood or severity of a loss but does not itself cause it.

Three categories of hazard appear on the exam:

• Physical hazard — a tangible condition: icy steps, smoking, high blood pressure, a hazardous occupation.
• Moral hazard — dishonesty or a tendency to cause a loss on purpose: a person who would fake a disability claim or commit arson for the payout.
• Morale hazard — indifference or carelessness because insurance exists: leaving doors unlocked, driving recklessly. Think "morale = lazy attitude."

Trap: Smoking is a physical hazard (a bodily condition), not a moral hazard. Faking a claim is moral; carelessness is morale.

Elements of an Insurable Risk

Not every pure risk can be insured. To be commercially insurable, a risk should meet these tests, which form the conceptual basis for underwriting:

1. The loss must be due to chance — accidental, outside the insured's control.
2. The loss must be definite and measurable — ascertainable time, place, and amount.
3. The loss must be predictable in the aggregate (the insurer must be able to estimate frequency and severity).
4. The loss cannot be catastrophic to the insurer — a single event cannot bankrupt the pool (war and nuclear events are excluded for this reason).
5. There must be a large number of homogeneous exposure units so the law of large numbers operates.
6. The premium must be economically feasible — affordable relative to the potential benefit.

The Law of Large Numbers

This is the mathematical engine of insurance and a frequent exam item. The law of large numbers states that the larger the number of similar (homogeneous) exposure units observed, the more closely actual loss experience will approach the expected (predicted) loss experience.

A single coin flip is unpredictable, but flip a coin 10,000 times and the result converges on 50% heads. Likewise, an insurer cannot predict whether you will die this year, but across 1,000,000 insureds of the same age and health it can predict the number of deaths with great accuracy. That predictability lets actuaries set adequate premiums.

Why "homogeneous" matters

The exposure units must be similar in their risk characteristics. Mixing 25-year-olds and 85-year-olds in one pool destroys predictability. This is why insurers classify and rate applicants — grouping like risks together so each class has stable, predictable loss experience.

A worked illustration

Suppose mortality tables show that out of 100,000 men aged 40, about 234 will die in the next year (a mortality rate of 0.00234, or 2.34 per 1,000). With 100,000 insureds the insurer can confidently budget for ~234 death claims and price the pure premium accordingly. With only 100 insureds, actual deaths might be 0 or 5 — wildly off the expected 0.234 — and the insurer could not price reliably. The larger the pool, the smaller the percentage deviation from expected results.

Adverse selection — the threat to the pool

Adverse selection is the tendency of those with the greatest probability of loss to seek insurance most aggressively (and to want the most coverage). A person who just received a terminal diagnosis is highly motivated to buy life insurance. If insurers did not screen, the pool would fill with high-risk insureds, claims would exceed premiums, and the system would collapse. Underwriting, waiting periods, and medical questions all exist to combat adverse selection.

Loss Exposure: Frequency and Severity

Actuaries describe each exposure using two measures the exam may name. Frequency is how often losses occur (the number of claims per period); severity is how large each loss is (the dollar amount). A young driver has high frequency but lower severity; a commercial fire has low frequency but catastrophic severity. Premiums must reflect both: pure premium roughly equals expected frequency multiplied by expected severity, spread across the pool.

Probability and the expected loss

Probability is the long-run relative frequency of an event, expressed from 0 (impossible) to 1 (certain). If 234 of 100,000 insureds are expected to die, the probability of death for one insured is 0.00234. Multiply that probability by the benefit to get the expected loss the insurer must fund. For a $250,000 policy, the expected mortality cost per insured is 0.00234 x $250,000 = $585 — the actuarial starting point before adding expenses and a margin. This is why precise classification matters: an error in the assumed probability multiplies straight through to the premium for every insured in the class.