Probable Loss and the Law of Large Numbers

A Large, Homogeneous Group of Exposure Units

To facilitate the prediction of the probable loss through use of the law of large numbers, it is essential that there be a large number of similar units exposed to the same peril. If a company can insure only ten houses against damage by fire, very little prediction is possible. As noted in the discussion of the degree of risk, the larger the number of units involved, the less deviation there will be in the actual experience.

It is absolutely essential that there be a large group of exposure units. Not only is a large group of units necessary, but the units must be similar. In fire insurance, there must be a large number of similar properties. It is not possible to predict losses if the subjects for insurance present a hodgepodge of structures of various constructions, usages, and values. In life insurance, there must be a large number of persons in each age, health, and occupational classification.

Definite Loss

The loss must be difficult to counterfeit. Death, perhaps, comes closest to perfection in meeting this requisite. Death is so difficult to feign that few insureds will attempt it which is a big reason why so many different types of life insurance (http://www.equote.com/li/term-life-insurance-quote.html) are available. Only in cases in which the insured has disappeared can there be a suspicion of something other than death. In sickness insurance, however, it is sometimes difficult to tell if a loss has occurred. During the depression, it was found that sickness claims greatly increased.

Persons who could not find jobs either worried themselves sick or else, in order to collect benefits, decided to say they were indisposed. Inability to distinguish between real and fraudulent claims was in part responsible for the receivership of several insurance companies which wrote extensive amounts of disability insurance during the 1920's and the 1930's.

Disability insurance contracts today are much less liberal on the average than they were thirty years ago because of the adverse experience the companies had in those trying days. Companies are more careful both as to the kinds of disability contracts they will write and as to the people for whom they will be written.

Accidental Loss

The loss must not only be definite, but it must have been accidental, as distinguished from expected. Ideally, the loss should be beyond the control of the insured. Depreciation losses, for example, are uninsurable, since there is nothing accidental about their occurrence. Or if someone is killed in an unexpected accident at a younger age than expected, there are certain life insurance policies (http://www.equote.com/li/life-insurance.html) that compensate for that kind of tragedy.

These losses are expected. Also, when mercantile theft insurance is written, normal shoplifting losses are not covered. In credit insurance, normal credit losses are not covered; only the unexpected losses are insured. Death meets this requisite because, although death is certain, the time of death is uncertain.

Large Loss

The hazard to be insured against must be capable of producing a large loss which the insured could not pay without economic distress. Insurance against breakage of shoestrings is unknown. The loss involved is so small that it is not worth the time, effort, and expense to enter into an insurance contract to indemnify the loss. (And insureds would likely be furious at the company, since most shoestring breakage is due to wear and tear, which would not be covered by the policy.)

This example is a reductio ad absurdum, of course; but it illustrates the principle. There are, nevertheless, many coverages sold which insure small losses. Hospital policies which promise benefits of less than $150 although costing $15 a year are certainly in the small-loss class for many persons.

Automobile towing charges, with limits of $10 per disablement, seem to most insureds to involve such small losses as to make insurance inadvisable. It is uneconomic for a person to insure the small losses which he can very easily pay himself, for the cost of insurance includes not only the loss cost but also a rather substantial margin for expenses.