Considerations Regarding Insurance Markets and Pooling of Risk: 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 7, pp. 7.9-7.26, 7.34-7.39.

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

Problem S5-21-1. Which of the following statements are true? More than one answer may be correct.

(a) The greater an insurer's investment income, the lower its present value of future losses.
(b) The greater an insurer's investment income, the greater its present value of future losses.
(c) An insurer will more investment income can afford to charge a lower premium for the same coverage.

(d) An insurer will more investment income can afford to charge a higher premium for the same coverage, because it can afford to survive the resulting flight of consumers away from the company.
(e) The insurer may only invest its own initial capital and earned premiums; it may not invest premiums that have been collected but have not yet been earned.
(f) Using reinsurance can increase an insurer's capacity to pay future claims and assume new business.
(g) Salaries paid to employees of the insurance company are considered a part of the production costs of providing insurance.
(h) Despite regulatory price limitations on insurance, consumers are always able to find the coverage they desire at some price.

Solution S5-21-1. The statements above are addressed in Nyce 2006, pp. 7.15-7.17. The following statements are correct:

(a) The greater an insurer's investment income, the lower its present value of future losses.

(c) An insurer will more investment income can afford to charge a lower premium for the same coverage.

(f) Using reinsurance can increase an insurer's capacity to pay future claims and assume new business.

(g) Salaries paid to employees of the insurance company are considered a part of the production costs of providing insurance.

Choices (b) and (d) are the opposites of (a) and (c), respectively, and so are incorrect. Choice (e) is incorrect, because the insurer may invest premiums as soon as they are collected. Choice (h) is incorrect; price limitations may mean that some consumers cannot get the coverage they want at any price, because insurers may not offer as much coverage as there is demand for the coverage.

Problem S5-21-2. Which of the following statements are true? More than one answer may be correct.

(a) Demand for insureds is always the result of voluntary choices on the part of potential customers.

(b) Only governments may mandate certain types of insurance.

(c) More risk-tolerant individuals will tend to purchase less insurance, all other things being equal.

(d) A given consumer's risk tolerance level and desire to purchase insurance are always going to be roughly the same.

(e) Insurance may be less lucrative for both individuals and organizations with highly limited financial resources and for extremely wealthy individuals and organizations.

(f) The decision regarding whether to retain losses or insure them is always made on the basis of financial considerations, where no mandates are present.

(g) By marketing new and original products, an insurer may increase the demand for insurance.

Solution S5-21-2. The statements above are addressed in Nyce 2006, pp. 7.17-7.20. The following statements are correct:

(c) More risk-tolerant individuals will tend to purchase less insurance, all other things being equal.

(e) Insurance may be less lucrative for both individuals and organizations with highly limited financial resources and for extremely wealthy individuals and organizations.

(g) By marketing new and original products, an insurer may increase the demand for insurance.

Choice (a) is incorrect, because both governments and private lenders often mandate the purchase of insurance that individuals would not necessarily have demanded on their own.

Choice (b) is incorrect, because private lenders often mandate the purchase of certain types of insurance (e.g. homeowners' insurance) as a condition of the loan.

Choice (d) is incorrect, because consumers' risk tolerance levels may change with age, wealth, and general economic circumstances.

Choice (f) is incorrect, because an insurer may attract consumers who would otherwise retain losses on the basis of a personable sales force, effective loss control services, and fast claims service.

Problem S5-21-3. Which of the following statements are true? More than one answer may be correct.

(a) Individuals' casualty losses are sometimes income-tax-deductible.

(b) Individuals' property insurance premiums are sometimes tax-deductible.

(c) If losses are tax-deductible and premiums are not tax-deductible, this gives individuals an incentive to purchase more insurance.

(d) Businesses' casualty losses are tax-deductible at the time they are paid.

(e) Businesses' casualty losses are tax-deductible at the time they are incurred.

(f) Businesses' insurance premiums are tax-deductible at the time they are paid.

(g) Purchasing insurance is likely to make businesses' after-tax earnings less stable.

Solution S5-21-3. The statements above are addressed in Nyce 2006, pp. 7.20-7.21. The following statements are correct:

(a) Individuals' casualty losses are sometimes income-tax-deductible.

(d) Businesses' casualty losses are tax-deductible at the time they are paid.

(f) Businesses' insurance premiums are tax-deductible at the time they are paid.

Choice (b) is incorrect, because individuals' property insurance premiums are not tax-deductible.

Choice (c) is incorrect, because if premiums are not tax-deductible but losses are, this gives individuals an incentive to retain more losses and get a deduction from their taxes for any losses incurred. This tends to motivate individuals to purchase no insurance, less insurance, or insurance with higher deductibles.

Choice (e) is incorrect, because casualty losses are tax-deductible at the time they are paid, not at the time they are incurred.

Choice (g) is incorrect, because purchasing insurance is likely to make businesses' after-tax earnings more stable - since the tax deduction for insurance premiums is spread more evenly over time, and the insurance costs are much more consistent from one year to another.

Problem S5-21-4. According to Nyce 2006, p. 7.21, four key issues that affect the functioning of insurance markets with regard to pricing are as follows:
1. Adverse selection;

2. Moral and morale hazard;

3. Actuarial equity vs. social equity;

4. Timing.

Each of the scenarios below pertains to one of the four issues above. Match each scenario to the issue of which it is an example.

(a) Wine Insurance Company offers coverage for a brand of wine that takes 100 years to mature. There is a risk that the wine will spoil or become contaminated during the maturation period, and the company will pay the market value of good wine for every unit of wine that gets contaminated.

(b) Data Dredging Insurance Company has proposed a new "finger-based insurance scoring" (FBIS) model, which is based on empirical studies that have been interpreted to suggest that individuals of differing finger lengths have different levels of likelihood of filing a claim. Regulators in State X disapprove the FBIS model's use in rating, arguing that individuals have little to no control over their finger length and that such discrimination would be contrary to public policy.

(c) Pi Insurance Company estimates that there is an average delay of 3.14159265 years between the time of a loss occurrence and the time of loss payment. Because the company can invest the premium in the meantime, it can afford to a charge a premium that is lower than the expected value of the loss.

(d) Individual Q knows that he is a careless driver, but he has been lucky and has not had any accidents in the past. He is able to purchase an extremely low-priced automobile insurance policy.

(e) Individual Θ is lazy and does not like to work; he deliberately sets himself on fire at work so as to sustain mild injuries that nonetheless prevent him from working. He stages the fire to look like an accident and collects a large percentage of his former salary in workers' compensation insurance benefits.

(f) An expert on earthquakes, floods, and hurricanes designs his own house to be virtually invulnerable to all of these perils. He discovers a way to construct this house at a reasonable cost, but the house is unique, and no insurer's rating plan can give enough discounts to account for its actual level of risk. Thus, the owner chooses to go without insurance, because his insurance premiums would be too expensive.

Solution S5-21-4. The following are the issues represented by each of these scenarios:
Scenario (a) is an example of timing;

Scenario (b) is an example of actuarial equity vs. social equity;

Scenario (c) is an example of timing;

Scenario (d) is an example of adverse selection;

Scenario (e) is an example of moral hazard;

Scenario (f) is an example of adverse selection.

Problem S5-21-5. In a certain neighborhood, houses are vulnerable to two types of perils - the Drill Monster (DM) and the Big Bouncy Monster (BBM). The DM lives in the ground, and it can only move vertically up or down. It has a tiny, but highly powerful drill using which it can puncture a hole inside the floor of a house and contaminate the house with a scent that requires considerable expense to remove but does not spread beyond the house. The DM cannot reproduce, and it never leaves its burrow. It is not known under which house the DM lives. The BBM is a giant sphere about the size of 12 houses that comes down at random times and destroys everything it touches. The residents are considering pooling their financial resources to pay for any losses occurring from the DM and the BBM. For which of these loss exposures in pooling most likely to reduce financial risk to each resident? For which of these loss exposures would the probability of every member paying out a positive amount be reduced by the pooling arrangement?

Solution S5-21-5. This question is based on the discussion of pooling in Nyce 2006, p. 7.34.

The financial risk due to the DM is more likely to be reduced because of the pooling arrangement. This is because loss exposures due to the DM are independent and uncorrelated, as a single contamination of a house by the DM does not spread to other houses. Pooling will be less effective at reducing financial risk due to the BBM, which can destroy up to 12 houses at a time - meaning that loss exposures due to the BBM are correlated.

Neither pooling arrangement would reduce the probability of paying out a positive amount for each member. Indeed, the probability of any one house being affected by one of these perils is always greater than the probability of a particular house being so affected. Thus, any given member of the pool will be more likely to pay out some amount in losses, but the average amount of the payout per individual will most likely be lower than if pooling did not exist.

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