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

Risk: The Foundation of Insurance

Insurance exists to manage risk, defined on the exam as uncertainty regarding financial loss. The key word is uncertainty. If a loss is certain to occur (such as the eventual death of an insured), only the timing and amount are uncertain. That residual uncertainty is what insurers price and pool.

The exam draws a sharp line between two categories of risk:

• Pure risk — only two outcomes: loss or no loss. There is no chance of gain. A house either burns or it does not. Pure risk is the only insurable type.
• Speculative risk — three outcomes: loss, no loss, or gain. Gambling, stock trading, and starting a business are speculative. Speculative risk is never insurable because the chance of profit defeats the purpose of indemnity.

Memorize the trap: insurers cover pure risk only. A question describing a chance of profit is describing speculative risk.

Peril vs. Hazard

Students confuse these two constantly, and the exam exploits it.

• A peril is the actual cause of a loss — fire, illness, premature death, accident, flood.
• A hazard is a condition that increases the likelihood or severity of a peril.

There are three hazard types:

The distinction tested most: moral = dishonesty; morale = carelessness. Both increase loss probability, but only moral hazard involves intent to deceive.

The Law of Large Numbers

Insurers cannot predict whether one person will die or fall ill this year. But across a large group, outcomes become statistically predictable. The Law of Large Numbers states that the larger the number of similar exposure units, the more closely the actual loss experience will match the predicted (expected) loss experience.

This is why insurers want large pools of homogeneous risks. A small or poorly diversified pool produces volatile, unpredictable results; a large pool lets actuaries set premiums with confidence.

Worked example: An actuary studies a mortality table showing that out of 100,000 men age 45, about 400 are expected to die within the year — a rate of 4 per 1,000. With only 50 insureds, actual deaths might be 0 or 3, wildly off the 0.2 expected. With 1,000,000 insureds, actual deaths will land very near the predicted 4,000. The pure premium per insured is calculated as expected losses divided by exposure units; the law of large numbers makes that figure reliable.

Adverse Selection

Adverse selection is the tendency of higher-than-average risks to seek insurance more aggressively than standard risks. A person who knows they are seriously ill is far more motivated to buy a large life policy. If insurers did nothing, the pool would fill with bad risks, claims would exceed premiums, and the company would fail.

Underwriting, medical exams, waiting periods, and pre-existing-condition provisions all exist to control adverse selection. The exam frequently asks why a given provision exists — the answer is almost always "to protect against adverse selection."

Six Requirements of an Insurable Risk

For a pure risk to be commercially insurable, it should meet these criteria — a high-yield list:

1. Due to chance — the loss must be accidental and outside the insured's control.
2. Definite and measurable — clear in time, place, cause, and amount.
3. Predictable — a large pool lets the insurer estimate future losses (Law of Large Numbers).
4. Not catastrophic — not so widespread that the insurer cannot cover all claims at once (war and nuclear risks are typically excluded).
5. Randomly selected and large loss exposure — many similar, independent exposure units.
6. Economically feasible — the premium must be affordable relative to the potential benefit.

If a fact pattern describes a loss the insured can cause at will, or a single catastrophic exposure, it fails these tests and is not insurable.

Methods of Handling Risk: STARR

Before risk is transferred to an insurer, individuals and businesses can handle it five ways, tested under the acronym STARR:

• Sharing — spreading risk among a group (a corporation's many shareholders absorb a loss together; reciprocal insurers).
• Transfer — shifting the financial burden to another party; insurance is the primary risk-transfer device, and a hold-harmless agreement is another.
• Avoidance — eliminating exposure entirely (not flying to avoid an air-crash risk). Effective but impractical for most exposures.
• Reduction — lowering loss frequency or severity (sprinklers, wellness programs, seatbelts).
• Retention — knowingly keeping the risk, funded by deductibles, self-insurance, or savings.

The exam frames a deductible as risk retention (the insured retains the first layer) and the policy itself as risk transfer. A self-insured employer plan is retention; buying stop-loss on top of it adds transfer.

Loss Exposure, Frequency, and Severity

Underwriters and actuaries describe risk in two measurable dimensions that drive premium:

• Frequency — how often a loss is expected to occur in the pool.
• Severity — how large each loss is when it occurs.

A high-frequency, low-severity exposure (routine doctor visits) is priced very differently from a low-frequency, high-severity exposure (catastrophic illness). Insurance is most efficient for low-frequency, high-severity events, which is why catastrophic medical and large life policies are economical while first-dollar coverage of small, frequent costs is expensive. A loss exposure is simply any condition that presents the possibility of loss, whether or not a loss actually occurs, and the count of similar exposures is what the Law of Large Numbers requires to make predictions reliable.