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

Risk is the foundation of insurance. Risk is uncertainty regarding financial loss. Insurance exists so that individuals can trade an uncertain, potentially catastrophic loss for a small, certain cost (the premium). The exam will not ask you to merely define terms; it gives a fact pattern and asks you to classify it correctly.

Pure Risk vs. Speculative Risk

Only pure risk is insurable. Pure risk has exactly two outcomes: loss or no loss, with no opportunity for gain. Speculative risk adds the possibility of gain (and is therefore uninsurable, because it resembles gambling).

Exam trap: If a choice involves any chance of profit, it is speculative and not insurable. The correct "insurable" answer is always the pure-risk option.

Peril vs. Hazard

A peril is the direct cause of loss (the event itself). A hazard is a condition that increases the likelihood or severity of a peril. Hazards lead to perils, which cause losses.

• Physical hazard — a tangible condition: high blood pressure, hazardous occupation, obesity, icy steps.
• Moral hazard — intentional dishonesty: lying on an application, arson to collect, faked claims.
• Morale hazard — carelessness or indifference because insurance exists: not locking doors, reckless driving.

Memory aid: Moral = morality (right/wrong, intentional). Morale = attitude (careless). Do not confuse the two; the exam tests this directly.

The Law of Large Numbers

The law of large numbers states that the larger the number of similar exposures (homogeneous units), the more accurately the insurer can predict the group's actual loss experience. The insurer cannot predict which insured will die or get sick, but across thousands of similar lives it can predict the proportion with high reliability. This is why insurers seek large pools: predictability lets actuaries set adequate, equitable premiums.

Characteristics of an Insurable Risk

For a risk to be commercially insurable it generally must meet six tests:

1. Due to chance — accidental, outside the insured's control.
2. Definite and measurable — clear time, place, cause, and amount.
3. Statistically predictable — losses can be estimated in the aggregate.
4. Not catastrophic — not so large or correlated it bankrupts the insurer (war, nuclear loss are typically excluded; floods/earthquakes need special handling).
5. Large number of homogeneous exposures — enough similar units for the law of large numbers to operate.
6. Not against public policy — paying the loss must not reward illegal or harmful acts.

Insurers reduce catastrophe and concentration risk by transferring part of their own risk to reinsurance companies.

Adverse Selection

Adverse selection is the tendency of higher-risk individuals to seek insurance more aggressively than lower-risk individuals. A person who knows they are seriously ill is more motivated to buy a large life policy. Left unchecked, adverse selection skews the pool toward bad risks, drives up claims, and forces premiums up until healthy insureds drop out — a "death spiral."

Insurers fight adverse selection with underwriting (screening applicants), pre-existing condition limits, waiting/probationary periods, and rate classification. Recognizing it in a fact pattern is a frequent exam task: if the scenario describes someone buying coverage because they expect a loss, the concept is adverse selection.

Loss, Frequency, and Severity

Two measurements drive pricing. Frequency is how often losses occur; severity is how large each loss is. A risk that is low-frequency but high-severity (premature death, total disability) is the classic candidate for risk transfer through insurance, because the insured cannot easily absorb a rare but devastating loss. A high-frequency, low-severity risk (minor dental cleanings) is often better retained through deductibles and copays. Combining these ideas, insurers price a policy so that pooled premiums cover expected losses (the pure premium) plus a loading for expenses, reserves, and profit.

Worked Numeric: Loss Prediction

Suppose an insurer covers 100,000 similar 40-year-old males and mortality tables predict 2.5 deaths per 1,000 per year. Expected deaths = 100,000 x 2.5/1,000 = 250 deaths. If each policy pays a $100,000 benefit, expected claims = 250 x $100,000 = $25,000,000. Dividing by 100,000 insureds yields a pure mortality cost of $250 per policy before expenses.

The law of large numbers is what makes that 250-death estimate reliable; with only 100 insureds the actual count could swing wildly, but across 100,000 lives the prediction is dependable. This is precisely why insurers seek large, homogeneous pools and why a small or non-homogeneous book of business is harder to price.

Handling Risk: The Five Methods

Before transferring risk to an insurer, people manage it in five recognized ways. The exam asks you to classify a scenario into one of these.

Insurance is the primary method of risk transfer. Deductibles, copays, and elimination periods are forms of risk retention — the insured keeps the first slice of loss. A sound program usually combines methods: reduce what you can, retain the small/predictable losses, and transfer the catastrophic ones.

Exam Application Drill

Watch for these recurring traps: (1) any answer with a chance of gain is speculative, never insurable; (2) moral = intentional dishonesty, morale = carelessness; (3) the law of large numbers makes losses predictable, it does not prevent them; (4) a deductible is retention, not transfer. When a question describes someone buying coverage because they already expect a loss, name adverse selection, and remember underwriting is the insurer's primary defense against it.