1.1 Risk, Hazards, Perils, and the Law of Large Numbers
Key Takeaways
- Only pure risk (loss-or-no-loss, no chance of gain) is insurable; speculative risk like gambling or investing is not.
- A peril is the cause of loss (fire, theft, wind); a hazard increases the chance or severity of that peril.
- The three hazard types are physical, moral, and morale - exam questions hinge on telling them apart.
- The law of large numbers lets insurers predict aggregate losses accurately as the insured pool grows, enabling sound rates.
- The ideal insurable exposure is one of a large group of homogeneous, independent units facing measurable, accidental loss.
Defining Risk
Risk is uncertainty about whether a loss will occur. Insurance manages this uncertainty by transferring it from an individual to an insurer in exchange for a premium.
There are two broad categories:
- Pure risk - involves only the chance of loss or no loss, with no possibility of gain (a house burns or it does not). This is the only insurable type.
- Speculative risk - involves the chance of loss, no change, or gain (gambling, starting a business, buying stock). Insurers will not cover it.
Exam trap: any answer choice describing a chance to profit is speculative and therefore uninsurable.
Perils vs. Hazards
A peril is the actual cause of a loss - fire, windstorm, theft, collision, or lightning. A hazard is any condition that increases the likelihood or severity of a peril.
The three hazard types are tested constantly:
| Hazard | Definition | Example |
|---|---|---|
| Physical hazard | A tangible condition increasing loss chance | Oily rags in a basement; an icy sidewalk |
| Moral hazard | Dishonesty or character creating intent to cause loss | Insured arsons a failing business for the proceeds |
| Morale hazard | Carelessness or indifference because insurance exists | Leaving a car unlocked because "it's covered" |
Memory aid: moral = intent to be dishonest; morale = an indifferent attitude.
A policyholder stops locking the doors of an insured warehouse because losses are covered anyway. This best illustrates which condition?
The Law of Large Numbers
The law of large numbers is the statistical principle that the larger the number of similar exposure units observed, the more closely actual loss experience will match the predicted (expected) loss. A single fire is unpredictable, but among 100,000 similar homes the annual fire frequency is highly stable.
This predictability lets actuaries set rates that are adequate (cover losses and expenses), not excessive, and not unfairly discriminatory - the three legal rate standards. Without enough homogeneous units, the insurer cannot price the product reliably.
Worked illustration: if historical data show 1 fire per 1,000 dwellings per year and the average fire loss is $40,000, the pure premium per dwelling is (1/1,000) x $40,000 = $40. Loading for expenses and profit is added on top to reach the gross rate.
Elements of an Insurable Risk
For a risk to be commercially insurable it should generally meet these characteristics (often called CANHAM):
- Calculable - loss frequency and severity can be estimated.
- Accidental - the loss is unexpected and outside the insured's control.
- Non-catastrophic - not so widespread it bankrupts the insurer (war and flood are typically excluded for this reason).
- Homogeneous and large in number - many similar units share the pool.
- Affordable - the premium is economically feasible.
- Measurable - the loss is definite in time, place, cause, and amount.
Exam trap: catastrophic perils such as flood, war, and nuclear hazard are commonly excluded precisely because they violate the non-catastrophic requirement.
Methods of Handling Risk
Insurance is only one of several risk management techniques. The national exam expects you to recognize all five:
- Avoidance - eliminating the exposure entirely (not buying a motorcycle avoids motorcycle accident risk).
- Retention - keeping the risk, planned (a deductible) or unplanned (self-insuring small losses).
- Sharing - spreading risk across a group, as a pool or partnership does.
- Reduction (control) - lowering loss frequency or severity with sprinklers, alarms, and safety programs.
- Transfer - shifting the financial burden to another party; insurance is the most common form of transfer.
Deductibles use both retention (the insured keeps the first dollars) and transfer (the insurer covers the excess). Recognizing each method by its description is a recurring question type.
Loss Exposures and Adverse Selection
A loss exposure is any condition that presents the possibility of loss, whether or not a loss actually occurs - a warehouse exposes its owner to fire, theft, and liability exposures. Underwriters classify exposures so that similar units pay similar rates, supporting the homogeneity the law of large numbers requires.
Adverse selection is the tendency of higher-risk applicants to seek insurance more aggressively than lower-risk ones. Left unchecked, it skews the pool toward bad risks and forces rates up. Insurers fight adverse selection through underwriting, exclusions, and policy conditions.
Exam trap: do not confuse adverse selection (a pool-composition problem) with a morale hazard (an individual attitude). Both raise losses but for different reasons.
Frequency, Severity, and Why Predictability Matters
Actuaries describe losses along two axes. Loss frequency is how often a loss is expected to occur, and loss severity is how large each loss is expected to be. A fleet of taxis has high frequency but low severity per claim; a chemical plant explosion has low frequency but extreme severity.
The law of large numbers stabilizes frequency far more than it tames severity, which is why catastrophic, high-severity perils strain the model and are reinsured or excluded.
A second worked example shows the payoff of scale. With 10 insured homes, one fire produces a 10% loss rate; the predicted rate could easily be off by hundreds of percent. With 1,000,000 homes, the observed annual fire rate converges tightly on the expected 0.1%, so the insurer can charge the calculated $40 pure premium with confidence. This convergence - more units, more accuracy - is the entire economic justification for insurance.
Which characteristic explains why standard property policies exclude flood and war?