Chapter 21
Insurance Companies and Pension Funds
Insurance Companies
Fundamentals of Insurance
Adverse Selection and Moral Hazard in Insurance
Selling Insurance
Mini-Case Box: Insurance Agent: The Customer’s Ally
Growth and Organization of Insurance Companies
Types of Insurance
Life Insurance
Health Insurance
Property and Casualty Insurance
Insurance Regulation
The Practicing Manager: Insurance Management
Screening
Risk-Based Premium
Restrictive Provisions
Prevention of Fraud
Cancellation of Insurance
Deductibles
Coinsurance
Limits on the Amount of Insurance
Summary
Credit Default Swaps
Conflicts of Interest Box: The AIG Blowup
Pensions
Conflicts of Interest Box: The Subprime Financial Crisis and the Monoline Insurers
Types of Pensions
Defined-Benefit Pension Plans
Defined-Contribution Pension Plans
Private and Public Pension Plans
Mini-Case Box: Power to the Pensions
124 Mishkin/Eakins • Financial Markets and Institutions, Eighth Edition
Regulation of Pension Plans
Employee Retirement Income Security Act
Individual Retirement Plans
The Future of Pension Funds
◼ Overview and Teaching Tips
Insurance companies and pensions are two ways people are saving in nonbank institutions. Since most
people are risk-averse, they prefer to buy insurance and take the risk away from themselves. This chapter
explains the fundamentals of insurance by discussing several basic principles. Life insurance and property
and casualty insurance are the two most common types of insurance. The section on life insurance provides
an in-depth look at the different types and parts of life insurance. One must decide what type they desire to
have either for their retirement, death, or both. The largest health insurance company in the nation is Blue
Cross/Blue Shield which covers hospital care and doctor services. Property and casualty insurance protect
against losses from fire, theft, storm, explosion, and neglect. This type of policy is short term compared to
life insurance which is long term. The characteristics of property and casualty insurance are laid out in detail.
People are retiring earlier and living longer, so pension plans have become a growing investment vehicle.
Pension plans can either be defined-benefit or defined-contribution plans and either public or private.
Social Security is the largest public pension plan. All plans must follow a set of standards called the
Employee Retirement Income Security Act. The Pension Benefit Guarantee Corporation insures most
private pension plans.
◼ Answers to End-of-Chapter Questions
2. Insurance companies do not want people to use insurance as a form of gambling.
3. Information asymmetry exists when one party to a transaction knows more about the situation than
4. Adverse selection occurs when a person elects to buy insurance because she knows her risk is greater
6. Independent agents do not represent any particular insurance agency but sell products from a large
number of companies. Exclusive agents sell the products of one company exclusively.
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11. Reinsurance allocates a portion of the risk to another company in exchange for a portion of the
premium.
12. Defined-benefit plans specify precisely what payment will be made to the plan’s beneficiaries.
13. A more sophisticated public, greater awareness of providing for retirement, and a lack of confidence
in Social Security have led to growth in private pension plans.
◼ Quantitative Problems
1. Research indicates that the 1,000,000 cars in your city experience unrecoverable losses of
$250,000,000 per year from theft, collisions, etc. If 30% of premiums are used to cover expenses,
what premium must be charged to car owners?
2. Assume that life expectancy in the United States is normally distributed with a mean of 73 years and
a standard deviation of 9 years. What is the probability that you will live to be over 100 years old?
Solution: The Z-score is calculated as follows:
100 73 27 3
99
Z−
= = =
The age of 100 years old is 3 standard deviations to the right of the mean. Using a standard
normal probability chart, this suggests that the probability is less than 1%.
3. Your rich uncle dies, leaving you a life insurance policy worth $100,000. The insurance company
also offers you an option to receive $8,225/year for 20 years, with the first payment due today. Which
option should you use?
Solution: Since the options are either $100,000 immediately or $8,225/year, you can calculate the
rate your are “paying” as:
126 Mishkin/Eakins • Financial Markets and Institutions, Eighth Edition
With this information, the answer depends on many factors. Do you “need’ the $100,000
today? Can you personally invest the $100,000 at a higher rate with the same level of risk?
Is there any risk that the insurance company will not pay in the future? Etc.
4. A home products manufacturer estimates that the probability of being sued for product defects is
1% per year per product manufactured. If the firm currently manufacturers 20 products, what is the
probability that the firm will experience no lawsuits in a given year?
Solution: The probability of not being sued is 99%. If we assume that the probabilities are
independent, then the probability of no lawsuits over all 20 products is:
5. Kio Outfitters estimated the following losses and probabilities from past experience:
0.25%
0.75%
1.50%
5.00%
15.00%
Loss
Probability
$30,000
0.25%
$15,000
0.75%
$10,000
1.50%
$ 5,000
2.50%
$ 1,000
5.00%
$ 250
15.00%
$ 0
75.00%
What is the probability Kio will experience a loss of $5,000 or greater? If an insurance company
offers a loss policy with $1,500 deductible, what is the most Kio will pay?
Chapter 21: Insurance Companies and Pension Funds 127
Copyright © 2015 Pearson Education, Inc.
Solution: Compute the future value at $1,000 per month:
N = 44 12; PMT = 1,000; I = 8/12; PV = 0
Compute FV. FV = $4,858,811
Dave is clearly close to his goal already. To determine what he needs to have the $5 M:
FV = 5,000,000; I = 8/12; N = 528; PV = 0
Compute PMT. PMT = $1,029.
7. When opening an IRA account, investors have two options. With a regular IRA account, funds added
are not taxed initially, but are taxed when withdrawn. With a Roth IRA, the funds are taxed initially,
but not when withdrawn. If an investor wants to contribute $15,000 before-tax to an IRA, what will
be the difference after 30 years between the two options. Assume that the investor is currently in the
25% tax bracket, and the IRA will earn 6%/year.
8. An employee contributes $200 a year (at the end of the year) to her pension plan. What would be the
total contributions and value of the account after 5 years? Assume that the plan earns 15% per year
over the period.
9. Paul’s car slid off the icy road causing $2,500 in damage to his car. He was also treated for minor
injuries, costing $1,300. His car insurance has a $500 deductible, after which the full loss is paid.
His health insurance has a $100 deductible and covers 75% of medical cost (total). What was
Paul’s out-of-pocket costs from the incident?