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

Risk is the foundation of every life and health insurance question. The exam expects you to classify a fact pattern correctly before you ever reach a number or a provision. Master these definitions first, because every later chapter assumes them.

What Is Risk?

Risk is uncertainty about whether a financial loss will occur. Note that risk is the uncertainty itself, not the loss. Insurance does not eliminate the underlying event; instead it transfers the financial consequence of that event to an insurer in exchange for a premium.

The industry exists because individuals dislike uncertainty. People will pay a small, fixed, known cost (the premium) to avoid a large, uncertain, potentially devastating cost (the loss). That trade is the economic engine behind every policy you will sell.

Pure Risk vs. Speculative Risk

Only pure risk is insurable. Pure risk offers two outcomes only: loss or no loss. Speculative risk adds a third outcome, the chance of gain, and is never insurable because covering it would resemble gambling and would encourage the insured to pursue the loss.

Exam trap: If a question asks which risk an insurer will cover, the answer is always pure risk. A second trap distinguishes risk (the uncertainty) from exposure (the unit at risk, such as an insured life).

Perils and Hazards

Students constantly confuse perils with hazards, so the exam tests the difference repeatedly. A peril is the immediate cause of a loss: death, sickness, accident, fire, or theft. A hazard is a condition that increases the probability that a peril will occur or increases the severity of the resulting loss. A peril causes the loss; a hazard merely raises the odds.

• Physical hazard — a tangible, measurable condition: obesity, heart disease, a hazardous occupation such as mining, or living in a flood zone.
• Moral hazard — intentional dishonesty rooted in a character defect: lying on an application, faking a disability claim, or arson to collect.
• Morale hazard — indifference or carelessness because insurance exists: skipping prescribed medication or driving recklessly because a claim will pay.

Memory hook: moral = morality (right vs. wrong, an intentional choice); morale = attitude or spirit (a careless, indifferent state of mind).

The Law of Large Numbers

The law of large numbers states that the larger the number of similar, independent exposure units observed, the more closely actual loss experience will match the predicted (expected) loss. Insurers cannot predict whether any single insured will die this year. Across 100,000 similar lives, however, they can predict aggregate deaths within a tight margin, and that predictability is what allows accurate premium pricing.

This principle is why insurers want large, homogeneous pools. Homogeneous means the exposures are similar enough that one mortality table fairly describes them all. Mixing wildly different risks in one rate class would make predictions unreliable.

Worked example: A mortality table shows that among 35-year-old standard males, 1.8 deaths per 1,000 are expected annually. For a $250,000 policy, the pure mortality cost per insured is calculated as follows:

• Expected claims per insured = (1.8 / 1,000) x $250,000 = $450 (before expenses, interest earnings, and profit loading).

With only 50 insureds the actual result could swing wildly above or below $450; with 500,000 insureds the result converges toward the expected $450 cost. Larger pools reduce the volatility around the average, not the average itself. The insurer then adds expense and profit loadings and subtracts assumed interest to reach the gross premium.

Adverse Selection

Adverse selection is the tendency of those with the highest probability of loss to seek insurance most aggressively. A diabetic applicant is more motivated to buy health coverage than a healthy applicant who feels invincible. Left unchecked, adverse selection floods the pool with bad risks, drives up claims, forces premium increases, and chases away the good risks, a spiral insurers call the death spiral.

Insurers counter adverse selection through underwriting, requiring evidence of insurability, imposing waiting and probationary periods, attaching exclusions, and using contestable periods. Each tool exists to keep the insured pool close to the average risk the rates assume.

Elements of an Insurable Risk

For a risk to be insurable, it should generally meet these conditions:

1. The loss must be due to chance (accidental, outside the insured's control).
2. The loss must be definite and measurable in time, place, and amount.
3. The loss must be predictable for the group (law of large numbers).
4. The loss must not be catastrophic to the insurer (avoid mass simultaneous claims).
5. There must be a large number of homogeneous exposure units to pool.
6. The premium must be economically feasible relative to the potential loss.

War and intentional self-inflicted loss fail the chance requirement, which is exactly why policies exclude them. A risk that fails any single element is generally uninsurable in the standard market.

From Pure Cost to Gross Premium

The pure mortality cost is only the starting point of a premium. Insurers build the gross premium in three steps:

1. Start with the net premium, the cost of expected claims discounted for assumed interest the insurer will earn on reserves.
2. Add a loading for operating expenses, agent commissions, and a profit margin.
3. The result is the gross premium the policyholder actually pays.

Worked illustration: Suppose expected claims are $450 per insured and the insurer assumes it will earn interest that reduces the present-value net cost to $420. If loading for expenses and profit adds $130, the gross premium is $420 + $130 = $550. Lower mortality, higher assumed interest, or tighter expenses all push the gross premium down, which is why a healthier insured pool and efficient operations matter to pricing.

Morbidity vs. Mortality

Finally, distinguish the two tables insurers rely on. A mortality table predicts the rate of death by age and is the basis for life insurance pricing. A morbidity table predicts the rate and duration of sickness and disability and is the basis for health and disability insurance pricing. Both depend on the law of large numbers, and both can be skewed by adverse selection if underwriting fails.