1.1 Risk, Peril, Hazard, and the Law of Large Numbers
Key Takeaways
- Risk is uncertainty regarding loss; only pure risk (loss or no loss, no chance of gain) is insurable, while speculative risk is not.
- A peril is the cause of loss (fire, death); a hazard is a condition that increases the chance or severity of loss.
- Moral hazard involves dishonesty/intent; morale hazard involves carelessness or indifference because coverage exists.
- The law of large numbers makes losses predictable across large groups, enabling adequate yet competitive premiums.
- The five risk-management methods are avoidance, retention, sharing, reduction, and transfer; insurance is transfer, and deductibles represent retention.
Risk, Peril, Hazard, and the Law of Large Numbers
Insurance exists to manage risk — defined on the exam as uncertainty regarding loss. Notice the definition centers on uncertainty, not on the loss itself. If a loss were certain (it will definitely happen) or impossible (it can never happen), there would be no risk to insure. The whole business of insurance is built on situations where loss might occur but the timing or severity is unknown.
The exam distinguishes two categories of risk, and only one is insurable:
- Pure risk — only two outcomes exist: loss or no loss. There is no possibility of gain. A house may burn down (loss) or not (no loss); you never profit from owning it against fire. Only pure risk is insurable.
- Speculative risk — three outcomes exist: loss, no loss, or gain. Gambling, stock investing, and starting a business are speculative. Speculative risk is never insurable.
A reliable test trap: insurance handles pure risk. If a scenario contains a chance of profit, it is speculative and uninsurable.
Peril vs. Hazard
Students constantly confuse these two. Memorize them precisely:
- Peril — the cause of a loss. Fire, illness, premature death, theft, and earthquake are perils. A peril is the thing that actually destroys value.
- Hazard — a condition that increases the likelihood or severity of a loss. A hazard does not cause the loss directly; it raises the odds that a peril will occur.
There are three classic hazard types tested on the national exam:
| Hazard | Definition | Example |
|---|---|---|
| Physical hazard | A tangible physical condition | Oily rags in a basement; icy steps; a heart murmur |
| Moral hazard | A dishonest tendency that increases loss | An insured who burns property to collect proceeds |
| Morale hazard | Indifference or carelessness because insurance exists | Leaving doors unlocked since theft is "covered" |
The single most common trap: moral hazard involves intent and dishonesty (arson, fraud), while morale hazard involves carelessness and a careless attitude ("who cares, I'm insured"). One letter, two very different ideas.
An insured leaves the keys in an unlocked car because "the insurance company will pay if it's stolen." This careless attitude is an example of which hazard?
The Law of Large Numbers
Insurers cannot predict whether one particular person will die or get sick this year. But they can predict, with remarkable accuracy, how many out of a large group will. This is the law of large numbers: as the number of similar, independent exposure units increases, the actual loss experience moves closer to the expected (probable) loss experience.
This principle is the mathematical engine of insurance. It lets actuaries set premiums that are adequate to pay claims yet competitive. A simple worked illustration:
- Suppose mortality data shows 2 deaths per 1,000 insureds aged 40 each year.
- An insurer covers 100,000 such insureds, each carrying a $100,000 policy.
- Expected deaths: 100,000 × (2 / 1,000) = 200 deaths.
- Expected claims: 200 × $100,000 = $20,000,000.
- Pure mortality cost per insured: $20,000,000 / 100,000 = $200.
The insurer adds expense and profit loading on top of that $200 pure premium. With only 10 insureds, a single death would devastate the math; with 100,000, the result is dependable. More exposure units = more predictable losses = lower relative risk to the insurer.
Risk Management Techniques
Individuals and businesses handle risk in one of several ways. The exam expects you to recognize all five and to know that insurance is a form of transfer:
- Avoidance — eliminate the exposure entirely (never fly to avoid air-crash risk).
- Retention — accept the risk and pay losses yourself (a deductible is partial retention).
- Sharing — spread risk among a group (a partnership, or pooling).
- Reduction — lower frequency or severity (sprinklers, seat belts).
- Transfer — shift the financial consequence to another party. Insurance is the most common transfer method.
A frequently missed point: choosing a higher deductible increases the amount of risk retained by the insured (and lowers premium), while a lower deductible transfers more risk to the insurer. Deductibles are best understood as the line between retention and transfer.
Elements of an Insurable Risk
Not every pure risk is something an insurer will accept. To be commercially insurable, a risk should satisfy a set of conditions the exam summarizes with the acronym CANHAM (or similar). Master these because scenario questions hinge on whether a risk qualifies:
- Calculable / Predictable: the chance and cost of loss must be measurable so a premium can be set. Mortality and morbidity tables make life and health losses calculable.
- Accidental and Unintentional: the loss must be due to chance, outside the insured's control. Intentional losses (suicide in year one, arson) are excluded.
- Definite (Measurable): the loss must be definite in time, place, and amount. Death is a clearly definite event, which is why life insurance pools work so well.
- Not Catastrophic to the insurer: the loss cannot be so widespread that it bankrupts the pool (war, nuclear events, floods are often excluded or specially handled).
- Large number of homogeneous units: enough similar exposure units must exist for the law of large numbers to operate.
- Affordable / Economically feasible: the premium must be reasonable relative to the potential benefit; insuring a $50 item for a $40 premium is pointless.
A related concept is adverse selection — the tendency of poorer-than-average risks to seek insurance more aggressively. Underwriting, waiting periods, and pre-existing-condition rules exist to counter adverse selection so that the calculable, homogeneous pool the actuaries priced does not skew toward unhealthy applicants.
An insurer covers 50,000 lives with an expected mortality rate of 3 per 1,000. How many deaths should the insurer expect this year, and what principle supports this prediction?