1.1 Risk, Hazards, Perils, and the Law of Large Numbers

Insurance exists to manage risk, defined as the uncertainty or possibility of financial loss. Every life and health exam opens here because the words risk, peril, and hazard are tested relentlessly and are easy to confuse.

Two Kinds of Risk

Insurers distinguish two categories. Pure risk involves only the chance of loss or no loss — never a gain (a house burning, a disabling injury, premature death). Speculative risk involves a chance of loss, no change, OR gain (gambling, stock trading, opening a business).

The rule to memorize: only pure risk is insurable. Speculative risk is uninsurable because the insured could profit, which violates the purpose of indemnity and invites manipulation.

Perils Versus Hazards

A peril is the immediate cause of a loss — the event that actually destroys value. Fire, heart attack, car collision, and flood are perils.

A hazard is a condition that increases the likelihood or severity of a loss arising from a peril. Hazards do not cause loss directly; they make a peril more probable or more damaging. The exam tests three hazard types:

A classic trap: moral hazard is intentional dishonesty; morale hazard is an attitude of carelessness. Both raise loss probability, but only morale stems from the false security of being insured.

The Law of Large Numbers

Insurers cannot predict whether one person will die or fall ill this year. The Law of Large Numbers states that as the number of similar, independent exposure units increases, the actual loss experience moves closer to the expected (probability-based) loss experience.

• The larger and more homogeneous the insured pool, the more accurately an insurer predicts aggregate losses.
• Accurate prediction lets actuaries set premiums that cover expected claims plus expenses and profit.
• This is why insurers want many similar policyholders, not a handful of unique ones.

Worked numeric: why scale matters

Suppose the true annual death probability for a group is 1%. Expected deaths:

• Pool of 100 lives: expected 1 death, but actual could easily be 0 or 3 — a swing of up to 300% of expected.
• Pool of 100,000 lives: expected 1,000 deaths; actual results cluster tightly (e.g., 980-1,020), a swing under 2%.

The insurer charging premiums on the large pool can price with confidence; the small pool is statistically unstable.

Characteristics of an Insurable Risk

Not every pure risk can be insured. To be commercially insurable, a risk generally must meet these standards:

• Due to chance — the loss is accidental and outside the insured's control.
• Definite and measurable — the time, place, cause, and amount can be determined.
• Predictable — a large enough pool lets the insurer estimate future losses (Law of Large Numbers).
• Not catastrophic to the insurer — losses are not so correlated that one event ruins the company (war and floods are often excluded for this reason).
• Economically feasible — the premium is affordable relative to the potential loss; the loss is large enough to matter but the chance small enough to price.

A scenario the exam loves: insuring against the certainty of a worn-out roof fails the "due to chance" test (it is wear, not accident), so it is uninsurable maintenance, not a covered peril.

Elements of Risk and the Insurer's Job

Every exposure can be broken down into elements the insurer evaluates:

• Frequency — how often a loss occurs (e.g., minor dental claims are frequent).
• Severity — how large each loss is (e.g., a major illness is severe but rare).

Insurers price both. A peril with low frequency but high severity (premature death) is ideal for insurance because premiums are modest while the protection is large. A high-frequency, low-severity event (eyeglasses) is better budgeted than insured, since administrative cost can exceed the loss.

Loss exposure terminology

• Exposure — any condition or situation that presents a possibility of loss, whether or not loss actually occurs.
• Loss — the reduction, decrease, or disappearance of value.
• Proximate cause — the peril that sets in motion an unbroken chain of events leading to the loss; insurers pay only when a covered peril is the proximate cause.