Answers to Chapter 15 Questions
1. The primary function of a life insurance company is to protect policyholders from adverse events. Banks accept deposits from people and companies looking for a fairly safe, liquid place to put their money and make loans to people and companies who need more money.
2. 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 composition of the liabilities, which is fixed for depository institutions but stochastic for insurance firms. While the face value of bank deposits is fixed, the insurance company's net policy reserves depend on expected future required payouts which can be highly uncertain. The other difference is that insurance companies are allowed to invest in equity instruments, which currently are prohibited for depository institutions.
3. We can see in Table 15-1 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 the 60s and 70s.
4. The four basic lines of life insurance products are: (1) ordinary life; (2) group life; (3) industrial life; and (4) credit life. Ordinary life is sold on an individual basis and represents the largest segment of the life insurance market. The insurance policy can be structured as pure life insurance (term life) or may contain a savings component (whole life or universal life). Group policies are similar to ordinary life insurance policies except that they are centrally administered, providing cost economies in evaluating, screening, selling, and servicing the policies. Industrial life has largely been replaced by group life since cost economies have made group life more affordable. Industrial life was historically marketed to individuals who would make small, very frequent payments and would require personal collection services. Credit life typically is term life sold in conjunction with some debt contract.
5. 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 contract where the party invests money to liquidate a fund, that is, to receive periodic payments depending on the market conditions. It may be initiated by investing a lump sum or making periodic payments before the annuity payments are begun.
6. A life insurance policy (whole life or universal life) requires regular premium payments which then entitle the beneficiary to a single lump sum. Upon receipt of such a lump sum, a single annuity could be obtained which would generate regular cash payments until the value of the insurance policy is depleted.
7. The pension fund constitutes a liability for the insurance company since it would now be obligated to pay the pensioners of the fund according to some agreed upon contract. It would be shown on the right hand side of the balance sheet in the form of reserves or a guaranteed investment contract (GIC). The money paid into the fund by the company and/or its employees would be invested by the insurance company, thus affecting the amount and composition of the assets.
8. 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, the companies themselves are regulated by the state agencies. Depository institutions are typically subject to both national and state oversight. While both banks and insurance companies receive regulatory scrutiny as to the quality of their assets and liabilities, bank regulations also dictate minimum reserve and capital requirements. Banks have more geographic restrictions. Both insurance companies and banks are limited in the products that they can offer, although recent regulations (such as the Financial Services Modernization Act of 1999) are change this mix.
9. a. The annual cash flows are given by X:
$1,000,000 = X(PVIFA 10%, 20)
where PVIFA is obtained from the present value annuity tables with i = 10% and n = 20 years.
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:
$1,000,000(1+0.10)5 = X(PVIFA 10%, 20)
Solving for X, annual cash flows, X= $189,169.90
10. The value of $10,000 deposited annually in a fund will amount to the following in ten years:
FV = 10,000(FVIFA 8%, 10) = $144,865.62
The annuities per year over the next twenty years at 8% will be:
$144,865.62 = X(PVIVA 8%, 20)
Solving for X, annual cash flows, X= $14,754.88
11. In the first case, the insurance company should charge an amount such that
Lump sum = $20,000(PVIFA 6%, 15) = $194,245.
In the second case, the company should charge
Lump sum = $20,000(PVIFA 6%, 20) = $229,398.
This problem raises the issue of whether it is fair for one individual to be charged a higher amount than another because of differences in life expectancy, especially if these differences have their basis in gender or race.
12. Insurance firms 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 payout in two ways. One 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 expected future payouts). The other way is to increase the profitability of interest income on net policy reserves. Since insurance liabilities typically are long term, the insurance company has long periods of time to invest premium payments in interest earning asset portfolios. The higher the yield on the insurance company's investments, the greater the policy payout (in the case of variable life insurance) and the greater the insurance company's profitability. Since junk bonds offer high yields, they offer insurance companies an opportunity to increase the return on their asset portfolio. However, junk bonds are much more risky and as result of the recent failures of some life insurance firms, the NAIC=s proposed laws limiting insurance company holdings of junk bonds in their asset portfolios.
13. Since 1960 the biggest decreases have been in the fire, accident and health, and allied categories, while the multiple peril policies have shown the biggest increases. The changes are related in that much change in the number of policies that have decreased can be attributed to the subsuming of these policies into the multiple peril policies.
14. 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).
In many cases, property and liability insurances are sold together, such as personal or commercial multiple peril and auto insurance. Fire and allied lines usually are sold as property insurance only. Liability insurance is sold separately for coverages such as malpractice or product liability hazards. In addition, reinsurance provides a means for primary insurers to pool their risk by transferring some of the risk and premium to a reinsurer.
15. 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 low-severity high- frequency lines or high-severity low-frequency lines (with the latter being more difficult to estimate), and whether they are long-tail or short-tail lines (with the former being more difficult to estimate). Loss rates also are affected by product inflation and social inflation. Unexpected increases in expenses are a result of increases in commission costs to brokers, general expenses, taxes and other expenses related to acquisitions. Finally, investment yields depend on the stock and bond markets as well as on the asset allocations of the portfolios.
16. The answer to this S&P question will vary depending on the date of the assignment
17. Generally, the effect is an adverse one, particularly if the policy is written in terms of the replacement cost of the asset and the premiums paid are not adjusted for inflation. Moreover, the investment value of the assets of insurers, particularly bonds and other fixed rate securities, are likely to be fall in value from unexpected inflation.
18. a. No, because the combined ratio is 73% + 12.5% + 18% = 103.5%.
b. Yes, because the combined ratio adjusted for investment yield is 103.5% - 8% = 95.5%.
19. Combined ratio = 77.5% + 12.9% + 16.0% = 106.40%.
In order to be profitable, the yields on investments have to be greater than 6.40%.
20. The answer to this S&P question will vary depending on the date of the assignment.
21. 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 low-frequency lines will be charged higher premiums than low-severity high-frequency lines.
Similarly, long-tail lines of businesses are harder to predict than short-tail lines because claims can be made years after the premiums have been made. Thus, premiums in this category of business will be higher. Modern day examples of such lines include coverage for product liabilities, such as exposure to asbestos or chemicals like agent orange.
22. Pure loss = $3.6 million - $1.96 million = $1.64 million
Expenses = 0.066 x $3,600,000 = $237,600
Dividends = 0.012 x $3,600,000 = $43,200
Investment returns = $170,000
Net profits = 1,640,000-237,600-43,200+170,000 = $1,529,200
23. The answer to this S&P question will vary depending on the date of the assignment.