Characteristics of Ideally Insurable Loss Exposures: Practice Questions and Solutions

This section of the study guide is intended to provide practice problems and solutions to accompany the pages of Foundations of Risk Management and Insurance, cited below. Students are encouraged to read these pages before attempting the problems. This study guide is entirely an independent effort by Mr. Stolyarov and is not affiliated with any organization(s) to whose textbooks it refers, nor does it represent such organization(s).

Some of the questions here ask for short written answers based on the reading. This is meant to give the student practice in answering questions of the format that will appear on Exam 5. Students are encouraged to type their own answers first and then to compare these answers with the solutions given here. Please note that the solutions provided here are not necessarily the only possible ones.

Source:

Nyce, C.M. Foundations of Risk Management and Insurance (Second Edition). 2006. American Institute for Chartered Property Casualty Underwriters. Chapter 8, pp. 8.3-8.27.

Original Problems and Solutions from The Actuary's Free Study Guide

Problem S5-23-1. Nyce 2006, p. 8.4, lists six characteristics of ideally insurable loss exposures:

1. Pure risk;

2. Fortuitous losses from the insured's standpoint;

3. Definite and measurable losses;

4. Large number of similar exposure units;

5. Independent and non-catastrophic losses;

6. Affordable premiums.

Each of the situations below does not meet one of the above criteria. Identify which characteristic is absent in each situation.

(a) A large number of houses are clustered together in a neighborhood. The Big Bouncy Monster (BBM), whose size is equivalent to that of twelve houses, can touch down on the ground at any time and will destroy anything it touches.

(b) Ms. Ψ wants to start an insurance company whose only product would be a package policy offering coverage on property damage to a particular kind of Chinese teapot, property damage liability arising from the insured's expeditions to the Moon, and pet grooming liability. There are approximately four people in the world who would be potential customers for this kind of policy.

(c) Mr. Δ eats cookies with his tea. However, he often drops cookies into the tea and refuses to eat the wet cookies afterward. He wishes to obtain insurance coverage on his cookies, so that he would be refunded the purchase price every cookie he deems inedible.

(d) Ms. Θ wants to obtain insurance coverage against her own acts of vandalism to her hovermobile.

(e) Mr. Ω has invested money in the stock of a startup high-tech firm. He wants to purchase insurance coverage that would refund any of his losses on his investment.

(f) Mr. Ξ sometimes feels depressed and wants to purchase insurance coverage that indemnifies him for the "emotional cost" of his depression.

Solution S5-23-1.

Situation (a) lacks the characteristic of independent and non-catastrophic losses, since the BBM can destroy a large number of houses at the same time and can inflict considerable damage at once.

Situation (b) lacks the characteristic of a large number of similar exposure units, as there are not many potential insureds who would want this kind of coverage, and the exposures covered within the package policy are extremely different from one another,.

Situation (c) lacks the characteristic of affordable premiums. It would be prohibitively expensive to insure frequent small losses such as Mr. Δ's cookie drops, as the loss adjustment expenses would likely far exceed the losses.

Situation (d) lacks the characteristic of fortuitous losses from the insured's standpoint, since Ms. Θ has full control over whether she vandalizes her own hovermobile.

Situation (e) lacks the characteristic of pure risk. A stock investment is a speculative risk, with the possibility of gains for the investor.

Situation (f) lacks the characteristic of definite and measurable losses. "Emotional cost" is highly subjective, difficult to identify, and virtually impossible to measure using any external standard.

Problem S5-23-2. Fire typically poses a pure risk of loss, and the loss is fortuitous from the standpoint of the owner of the building that catches on fire. What situation poses an exception to this rule? (See Nyce 2006, p. 8.12.)

Solution S5-23-2. Fire may not be a pure risk or a cause of fortuitous loss if the owner of the building commits arson for profit. For instance, the owner may want to set fire to an obsolete or run-down building, collect insurance money, and build a structure that brings in more revenue using the proceeds. The fact that the owner set fire to the property means that the fire loss was not fortuitous; the fact that the owner may gain financially from the fire means that the risk is now speculative and is no longer pure.

Problem S5-23-3. For both the windstorm cause of loss and the flood cause of loss, explain why these causes of loss sometimes may not meet the following criteria where commercial property is concerned:

(a) Large number of similar exposure units;

(b) Independent and not catastrophic losses;

(c) Economically feasible premiums.

(See Nyce 2006, pp. 8.13-8.15.)

Solution S5-23-3.

(a) With regard to windstorms, buildings located in different areas may face substantially different loss exposures. For instance, buildings in hurricane-prone coastal states may face substantially greater windstorm loss exposures than buildings in landlocked areas. The same applies to floods. A dry area with little precipitation faces a significantly lower probability of flood than an area near a large body of water. Commercial buildings also serve a wider variety of functions that individual homes, which may make comparison of exposure units more difficult than in the case of residences owned by individual.

(b) A windstorm - especially a hurricane - can devastate an entire geographic area, destroying large amounts of property. Thus, windstorm losses can be catastrophic, and they may not be independent if the buildings affected are located in the same area. Flood losses are also geographically concentrated and so are seldom independent. Large floods may cause catastrophic losses - as happened, for instance, in New Orleans in the aftermath of Hurricane Katrina in 2005.

(c) In areas which are at a high risk for windstorms, improved catastrophe modeling may be able to more accurately evaluate that risk, leading to correspondingly higher premiums that may become economically infeasible for many insureds. Flood premiums for property and fixed locations have typically been considered economically infeasible by private insurers because of the geographically concentrated loss exposures, the potential for catastrophic damage, and the virtual certainty that a flood would occur within a given area during a longer time period (e.g. 100 years).

Problem S5-23-4. According to Nyce 2006, pp. 8.17-8.18, premises and operations liability has all six characteristics of an ideally insurable loss exposure. Products liability, however, may lack four of these characteristics. Which four are they, and why might products liability lack them?

Solution S5-23-4. The characteristics that products liability may lack in some situations are as follows:
1. Definite and measurable losses: The cause of the an injury allegedly due to the insured's product may not always be definite; there may be several possible causes, only one of which might be the product. The loss may also not be measurable, as an injury often involves non-financial damage (e.g. pain and suffering, emotional distress, disfigurement, etc.) that is difficult to put a monetary value on.

2. Large number of similar exposure units: It is possible that a product may cause injuries in only rare cases - as when most users react favorably to a medicinal drug, but a small percentage of the population experiences severely negative side effects. Products liability may also arise from a customer who uses a product in an unusual fashion and thereby damages himself.

3. Independent and non-catastrophic losses: It is possible that a product could adversely affect large numbers of individuals and organizations, if it has been widely distributed. This could result in substantial and even catastrophic liability losses for the maker of the product.

4. Affordable premiums: The possibility of losses that are difficult to measure, unusual losses and dissimilar exposure units, and catastrophic losses may render premiums for products liability economically infeasible.

Problem S5-23-5. Which of the following statements about personnel loss exposures are true? More than one answer may be correct.

(a) The retirement cause of loss has typically been found to be uninsurable.
(b) The severity of a personnel cause of loss is about the same, irrespective of the member of the organization whose loss occurs.
(c) There is a wide variety of property-casualty insurance products available for personnel loss exposures.
(d) Because of the possibility of employee suicides, the death cause of loss may not be fortuitous.
(e) One characteristic that the death cause of loss sometimes may not meet is the definite and measurable nature of losses.
(f) The retirement cause of loss may not be fortuitous, because an employee can choose when to retire.
(g) The retirement cause of loss may not be fortuitous, because organizations can influence employees' retirement decisions through a variety of incentives and disincentives.
(h) One reason why the death cause of loss may not be an ideally insurable loss exposure is because it sometimes may not have a large number of similar exposure units.
(i) One reason why the death cause of loss may not be an ideally insurable loss exposure is because it often may not be independent and non-catastrophic.

Solution S5-23-5. The following answers are correct:
(a) The retirement cause of loss has typically been found to be uninsurable.

(e) One characteristic that the death cause of loss sometimes may not meet is the definite and measurable nature of losses.

(g) The retirement cause of loss may not be fortuitous, because organizations can influence employees' retirement decisions through a variety of incentives and disincentives.

(h) One reason why the death cause of loss may not be an ideally insurable loss exposure is because it sometimes may not have a large number of similar exposure units.

Choice (b) is incorrect; an organization may have key members whose death, retirement, or resignation could have a substantially more adverse impact than the loss of other employees.

Choice (c) is incorrect; property-casualty insurers typically do not insure personnel loss exposures.

Choice (d) is incorrect; an employee suicide is still a fortuitous cause of loss from the standpoint of the insured organization for which the employee works.

Choice (f) is incorrect, because an employee's choice to retire may still be fortuitous from the standpoint of the insured organization for which the employee works. Although it is true that the retirement cause of loss may not be fortuitous, the reason given is not correct in cases where the organization exerts no positive or negative influence on the employee's choice to retire.

Choice (i) is incorrect; employee deaths are independent and non-catastrophic in the vast majority of cases.

See other sections of The Actuary's Free Study Guide for Exam 5.