Risk, Loss Exposures, and Hazards in Insurance: 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 1, pp. 1.3-1.17.

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

Problem S5-18-1. Nyce 2006, p. 1.6 discusses three necessary elements of loss exposures:
1. An asset exposed to loss;

2. Cause of loss (peril);

3. Financial consequences of the loss.

Apply these concepts to the following situation:

Amenhotep is growing spherical blue crops on his land. It is possible that a Perilous Purple Monster (PPM) will appear on his land and eat the crops. If this happens, Amenhotep has probability 0.5 of losing his entire crop (worth $60,000) and a probability of 0.5 of only losing one-tenth of his crop. Identify the elements of the loss exposure Amenhotep faces.

Solution S5-18-1. The elements of the loss exposure are as follows:
Asset exposed to loss: The spherical blue crops owned by Amenhotep;
Cause of loss: The PPM eating the crops;
Financial consequences of the loss: Provided that a loss occurs, the financial consequences are either a loss of $60,000 with probability 0.5 or a loss of $10,000 with probability 0.5.

Problem S5-18-2. Nyce 2006, p. 1.4, describes the two elements of risk as being the following:

1. Uncertainty of outcome;

2. Possibility of a negative outcome.

Which of the following situations exhibit risk under these criteria? More than one answer may be correct.

(a) You are given a free lottery ticket for a drawing where you have a small chance of winning $50,000,000. Otherwise, you win or lose nothing.

(b) You purchase a lottery ticket for $5 for a drawing where you have a small chance of winning $50,000,000. Otherwise, you win or lose nothing.

(c) Your friend tells you the following: "If you can spell the name of the capital of Madagascar backwards, I will give you $50. Otherwise, I will give you $25."

(d) You know with certainty that, if you go swimming, you will either be eaten by a shark or catch a contagious disease.

(e) You know with certainty that, if you go swimming, you will either be eaten by a shark or find a hidden treasure.

(f) You know with certainty that, if you go swimming, you will either be eaten by a shark.

Solution S5-18-2.

Choice (a) fails to meet the definition of risk, because there is no possibility of a negative outcome. You can win the lottery, but you cannot lose any money, and you have not even paid for the ticket.

Choice (b) meets the definition of risk, because if you do not win the $50,000,000 prize, you will have lost the purchase price of the ticket.

Choice (c) does not meet the definition of risk, because there is no possibility of a negative outcome. Irrespective of whether you answer correctly, you get some amount of money in excess of what you originally had.

Choice (d) meets the definition of risk, as the outcome is uncertain, and negative outcomes are possible. (Both of the possible outcomes are negative.)

Choice (e) meets the definition of risk, as the outcome is uncertain, and a negative outcome is possible. (There is only one negative outcome - being eaten by a shark.)

Choice (f) does not meet the definition of risk, because there is no uncertainty of outcome. If you go swimming, you will get eaten.

Thus, (b), (d), and (e) are correct answers.

Problem S5-18-3. Amenhotep is growing spherical blue crops on his land. It is possible that a Perilous Purple Monster (PPM) will appear on his land and eat the crops. Amenhotep has purchased PPM insurance coverage against this peril.

Nyce 2006, pp. 1.8-1.9 identifies four types of hazards that can occur in insurance:

1. Moral hazard;

2. Morale hazard;

3. Physical hazard;

4. Legal hazard.

Classify each of the following scenarios under one of the hazard categories described above.

(a) Amenhotep's spherical blue crops have genetically mutated to give off a scent that is particularly appealing to the PPM.

(b) Amenhotep, confident that insurance will pay for his losses, decides to go fishing all the time instead of looking after his crops.

(c) The Spherical Crop Regulation Authority (SCRA) issues a new bulletin, stating that PPMs must not be interfered with at any time, even when they trespass on property or eat farmers' crops.

(d) Amenhotep hires a friend to dress up as a PPM and pretend to devour the crops. In reality, the friend stores the crops inside his large costume and sells them on the market, giving the proceeds to Amenhotep. Amenhotep files a claim on his insurance policy.

(e) The courts in Amenhotep's jurisdiction have consistently found in favor of insureds in coverage disputes between the insurers and insureds. In particular, the courts have always awarded "pain and suffering" damages to insureds whose crops have been eaten by PPMs. The courts have insisted that these damages are covered under all PPM insurance policies.

Solution S5-18-3.

Scenario (a) poses a physical hazard; the scent of the mutated crops is a condition of property that increases the frequency - and possibly the severity - of losses.

Scenario (b) poses a morale hazard; Amenhotep is more negligent, now that he has insurance.

Scenario (c) poses a legal hazard; the bulletin prevents Amenhotep from interfering with the PPM whenever the PPM decides to eat Amenhotep's crops. This is likely to increase the severity of any loss that occurs.

Scenario (d) poses a moral hazard; Amenhotep has colluded with his friend to defraud the insurer.

Scenario (e) poses a legal hazard; the courts in Amenhotep's jurisdiction have ruled in such a way as to increase the likely insurance payout in the event of a loss. This makes it more costly for the insurer to offer coverage.

Problem S5-18-4. Nyce, on p. 1.11, classifies loss exposures into four types:

1. Property loss exposures;

2. Liability loss exposures;

3. Personnel loss exposures;

4. Net income loss exposures.

Property loss exposures can be classified as either tangible property loss exposures or intangible loss exposures. Tangible property is further divided into real property and personal property.

Apply the above classifications to each of the following situations, pertaining to Superwidgets, Inc. More than one classification may apply to each scenario.

(a) The CEO of Superwidgets, Inc. has 600 years of management experience that could not be replaced in the event of the CEO's death, retirement, or resignation.

(b) Superwidgets, Inc. owns a large and highly valuable art collection that is on display inside the corporate headquarters. The company does not plan to ever sell the collection and claims that it serves purely to enhance the employees' esthetic enjoyment of the workplace. The art is vulnerable to fire, flood, and paint-eating bugs.

(c) A branch office of Superwidgets, Inc. is the primary revenue generator for the company. The building sits on top of an earthquake fault and would be completely destroyed in the event of an earthquake.

(d) Superwidgets, Inc. owns a patent on a superwidget design that has been the blueprint for its major product. Several competitors have been alleging that the design is too simple and obvious to be patentable, and there are rumors that lawsuits may be filed, alleging illegitimate and injurious conduct on the part of Superwidgets, Inc. for holding back information that should be in the public domain.

(e) Superwidgets, Inc. uses a trade secret formula for the fuel used to power its superwidgets. The formula cannot be patented, no legal recourse exists to protect its trade secret status, and competitors will readily adopt it if its existence becomes known. This formula has thus far allowed Superwidgets, Inc. to substantially exceed its competitors in revenue and profitability.

(f) Superwidgets, Inc. markets its products to particularly sensitive consumers who will file lawsuits if the bouncing dodecahedron inside each superwidget does not bounce a sufficient number of times per minute. Each of these "nuisance lawsuits" is usually settled and constitutes a one-time expense for the company. The lawsuits do not damage the company's revenue-generating capacity or reputation, as the general public dismisses the lawsuits as being filed by cranks.

Solution S5-18-4.

Situation (a) presents both a personnel loss exposure (due to the possibility that the CEO might at some time no longer remain with the company) and a net income loss exposure (as the company's ability to generate income is likely to be hampered without the CEO's management experience).

Situation (b) presents a tangible, personal property loss exposure (due to the possibility that art owned by the company may be lost). There is no net income loss exposure, since the art does not contribute to the company's income generation abilities.

Situation (c) presents both a tangible, real property loss exposure (due to the possibility of loss to the branch office building) and a net income loss exposure (as the branch office is the primary revenue generator for the company, and its operations would be interrupted if its building were destroyed).

Situation (d) presents an intangible property loss exposure (due to the possibility of loss of the patent), a liability loss exposure (due to the possibility of lawsuits pertaining to the patent), and a net income loss exposure (due to the possibility of diminished income for the company if the patent is lost).

Situation (e) presents an intangible property loss exposure (due to the possibility of loss of the trade secret), and a net income loss exposure (due to the possibility of diminished income for the company if the trade secret is lost). There is no liability loss exposure, since no legal action is possible regarding the trade secret formula.

Situation (f) presents a liability loss exposure from the possibility of lawsuits filed against the company. There is no net income loss exposure, as the lawsuits are one-time losses and do not affect subsequent income of the company.

Problem S5-18-5. Nyce 2006, p. 1.17, describes some possible types of net income losses, including the following:
1. Loss of goodwill;
2. Failure to perform;
3. Missed opportunities.

Classify each of the following causes of net income loss under one of the categories listed above. Assume that the company has suffered a decrease in net income in each of these situations.

(a) Superwidgets, Inc. promises to deliver 300 superwidgets to a retailer, but only delivers 30 superwidgets due to a decimal point error made by one of the company's employees.
(b) Despite studies that show that solid blue superwidgets have been consistently more profitable while costing no extra money to produce, Superwidgets, Inc. has continued to produce superwidgets in the traditional stripes-with-polka-dots pattern.
(c) One of the pet chickens of the CEO of Superwidgets, Inc. has run amok on a public walkway and mildly pecked 80 pedestrians. No lawsuits have been filed, but several newspaper editorials have chided Superwidgets, Inc. for irresponsible behavior toward the general public. The CEO has staunchly refused to issue an apology, alleging special pecking rights for his chickens.
(d) Superwidgets, Inc. has decided to replace customer service representatives with automated telephone answering systems that were designed to lead consumers in circles until the consumers hang up in disgust. As a result, consumers are finding themselves practically unable to call the company with questions or complains and are thus more reluctant to purchase superwidgets.
(e) Superwidgets, Inc. has refused to invest in a new oil refining operation despite having the capital and expertise to do so. The CEO has stated that "Superwidgets is what we do, and we will not stray from our fundamental purpose."
(f) Superwidgets, Inc. has been consistently late on its mortgage payments for the commercial real estate it owns. As a result, no lenders are willing to make any future loans to the company.

Solution S5-18-5.

Situation (a) is an example of failure to perform.

Situation (b) is an example of missed opportunities.

Situation (c) is an example of loss of goodwill.

Situation (d) is an example of loss of goodwill.

Situation (e) is an example of missed opportunities.

Situation (f) is an example of failure to perform.

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