Answers to Chapter 15
Questions:
1. The primary function of a life insurance company is to protect policyholders from adverse events. Insurance
companies accept premium payments in exchange for compensation in the event that certain specified, but
undesirable, events occur.
The primary function of depository institutions is to provide financial intermediation for individual and corporate
2. The adverse selection problem occurs because customers who are most in need of insurance are most likely to
acquire insurance. However, the premium structure for various types of insurance typically is based on an average
3. Life insurance companies have long-term liabilities because of the life insurance products that they sell. As a
result, the asset side of the balance sheet predominantly includes long-term government and corporate bonds,
A major similarity between depository institutions and insurance firms is the high degree of financial
leverage incurred by both groups of firms. Both groups solicit funds (from policyholders or depositors) and use them
to finance an asset portfolio predominately consisting of debt securities. A major difference between them is their
4. We can see in Table 15-2 that since the 1920s and 30s, life insurance companies have increased their holdings of
bonds and stocks and decreased their holdings of mortgage loans and policy loans. Government securities comprise
the next largest component and have recently increased back to their earlier levels after reaching very low levels in
5. The four basic lines of life insurance products are: (1) ordinary life, (2) group life, (3) credit life, and (4) other
activities. Ordinary life is sold on an individual basis and represents the largest segment (80%) of the life insurance
market. The insurance policy can be structured as pure life insurance (term life) or may contain a savings component
6. A typical life insurance contract requires a periodic payment by one party for a promised payment of either a
lump sum or an annuity if a particular event occurs, such as death or an accident. An annuity represents a reverse
7. A life insurance policy (whole life or universal life) requires regular premium payments which then entitle the
8. The primary change in the balance sheet of a life insurance company would be an increase in the liability
accounts that reflect these pension plans. Guaranteed investment contracts (GICs) and separate account categories
9. Insurance companies are more exclusively subject to state regulations compared to depository institutions.
Although there are national insurance organizations such as the National Association of Insurance Commissioners,
In 2009, the U.S. Congress considered establishing an optional federal insurance charter. The move behind
such a charter picked up steam following the failure of the existing state by state regulatory system to act in
preventing the problems at insurance giant AIG from becoming a systemic risk to the national economy. Those in
favor of an optional federal insurance charter noted that under the current state by state system, insurers face
obstacles such as inconsistent regulations, barriers to innovation, conflicting agent licensing, and education
10. State guarantee funds are different from deposit insurance in several ways. First, the insurance guarantee funds
are administered by the life insurance companies as opposed to a separate company like the FDIC for deposit
institutions. Second, insurance companies do not pay premiums into the guarantee fund until after the failure of an
insurance company. The FDIC requires annual premium payments from all depository institutions. Third, while the
11. Insurance companies earn profits by taking in more premium income than they pay out in policy payments.
Firms can increase their spread between premium income and policy payouts in two ways. The first way is to
decrease future required payouts for any given level of premium payments. This can be accomplished by reducing
the risk of the insured pool (provided the policyholders do not demand premium rebates that fully reflect lower
12. The two major lines of property-casualty insurance are property insurance (insurance compensating the insured,
fully or partially, for personal or commercial property damage as a result of accidents and other events) and liability
insurance (insurance compensating a third party, fully or partially, because its personal or commercial property was
damaged as a result of the accidental actions of the insured).
13. Product lines based on net premiums typically are included in the property-casualty insurance arena. The largest
decreases have been in the fire and allied categories, while the multiple peril (or umbrella) and liability policies have
14. The three sources of underwriting risk in the PC industry are: (a) unexpected increases in loss rates, (b)
unexpected increases in expenses, and (c) unexpected decreases in investment yields. Loss rates are influenced by
whether the product lines are property or liability (with the latter being less predictable), whether they are
15. The four characteristics or features of the perils insured against by property-casualty insurance, ranked by the
features in terms of actuarial predictability and total loss potential are:
16. Inflation generally has an adverse effect on the cost of providing benefits that have been purchased by the
insured, particularly if the policy is written in terms of the replacement cost of the asset and the premiums are not
17. Insurance companies have a more difficult time predicting the severity of losses for high– severity low-frequency
lines of business, such as earthquakes and hurricanes. In addition, these catastrophic events cause severe damage,
meaning the individual risks in the insured pool are not independent. As a result, premiums for high-severity
18. The balance sheet of a PC company is similar to that of a life insurance company. Long-term financial assets
such as bonds, common equities, and preferred stock comprise the majority of the assets, while loss reserves, loss
adjustment expenses, and unearned premiums dominate the liabilities. In contrast, short- and medium-term financial
19. The loss ratio measures the actual losses incurred on a line of insurance relative to the premiums earned on the
line. A ratio greater than 100 implies that the premiums earned did not cover the losses on the product line. The loss
20. The expense ratio measures the expenses incurred relative to premiums written. Expense risk is comprised
primarily of loss adjustment expenses, which relate to the cost surrounding the loss settlement process, and
21. The combined ratio is equal to the loss ratio plus the expense ratio. The ratio may be stated before or after
22. In cases where the combined ratio is greater than 100, the insurer must rely on investment income from
Problems:
1. a. The annual cash flows are given by X:
Solving for X, annual cash flows X = $117,459.62.
b. In this case, the first annuity is to be received five years from today. The initial sum today will have to be
compounded by five periods to estimate the annuities:
c. The required payment is the present value of $200,000 per year for 20 years at 10 percent.
2. a. The annual cash flows are given by X:
b. In this case, the first annuity is to be received six years from today. The initial sum today will have to be
compounded by five periods to estimate the annuities:
Solving for X, annual cash flows, X = $354,145.82
c. The required payment is the present value of $240,000 per year for 20 years at 7 percent.
3. The value of $10,000 deposited annually in a fund will amount to the following in ten years:
or using a financial calculator, N = 10, I = 8, PMT = 10,000, then compute FV = $144,865.62
The annuities per year over the next twenty years at 8% will be:
Solving for X, annual cash flows, X = $14,754.88
4. a. FV = $10,000{[(1 + 0.08)10 -1]/0.08}(1 + 0.08) = $10,000 (14.48656247)(1 + 0.06) = $156,454.87
b. In this case, the first annuity is to be received ten years from today. The amount of retirement funds at the end of
c. Deposit Value at Distribution Annual
Period 10 Years Period Payment
7 percent $147,835.99 7 percent $13,041.75
9 percent $14,857.72
9 percent $165,602.93 7 percent $14,609.11
9 percent $16,643.32
b. In this case, the first annuity is to be received 30 years from today. The amount of retirement funds at the end of
c. Deposit Value at Distribution Annual
Period 30 Years Period Payment
b. 15,000{[1 – (1/(1 + 0.05)30)]/0.05} = $230,586.77
or using a financial calculator, N = 30, I = 5, PMT = 15,000, then compute PV = $230,586.77
8. a. No, because the combined ratio is 73% + 12.5% + 18% = 103.5%.
9. Combined ratio = 77.5% + 12.9% + 16.0% = 106.40%.
10. Combined ratio = 64.8% + 25.6% + 6.0% = 96.4%.
11. Pure loss = $3.6 million – $1.96 million = $1.64 million
Expenses = 0.066 x $3,600,000 = $237,600
12. Pure loss = $12.75 million – $9.18 million = $3,570,000
Investment returns = $1,420,000
Net profits = $3,570,000 – $2,562,750 – $637,500 + $1,420,000 = $1,789,750
13. Loss ratio = $4,343,750/$6,250,000 = 69.5%
Expense ratio = $1,593,750/$6,250,000 = 25.5%
14. Loss ratio = $3,962,700/$5,550,000 = 71.4%
Expense ratio = $1,526,250/$5,550,000 = 27.5%