Chapter 15 Homework
Q17. Which of the insurance lines listed below will be charged a higher premium by insurance companies and why? a) low-severity, high frequency lines versus high-severity, low frequency lines. b) long-tail versus short-tail lines.
a) a. In general, loss rates are more predictable on low severity, high-frequency lines than on high-severity, low-frequency lines. For example, losses in fire, auto, and homeowners peril lines tend to be expected to occur with high frequency and to be independently distributed across any pool of insured customers. Thus, only a limited number of customers are affected by any single event. Furthermore, the dollar loss of each event in the insured pool tends to be relatively small. Applying the law of large numbers, the expected loss potential of such lines—the frequency of loss times the extent of the damage (severity of loss)—may be estimable within quite small probability bounds. Other lines, such as earthquake, hurricane, and financial guarantee insurance, tend to insure very low-probability (frequency) events. Here, many policyholders in the insured pool are affected by any single event (i.e., their risks are correlated) and the severity of the loss could be potentially enormous. This means that estimating expected loss rates (frequency times severity) is extremely difficult in these coverage areas. As a result, premiums for high-severity low-frequency lines will be charged higher premiums than low-severity high-frequency lines. b)Some liability lines suffer from a long-tail risk exposure phenomenon that makes estimation of expected losses difficult. This long-tail loss arises in policies for which the insured event occurs during a coverage period but a claim is not filed or made until many years later. The delay in the filing of a claim is in accordance with the terms of the insurance contract and often occurs because the detrimental consequences of the event are not known for a period of time after the event actually occurs. Losses incurred but not reported have caused insurers significant problems in lines such as medical malpractice and other liability insurance where product damage suits. Because long-tail lines of businesses are harder to predict than short-tail lines because, premiums in this category of business will be higher.
P8. Calculate the following: a) IF the loss ratio on a line of property insurance is 73%, the loss adjustment expense is 12.5%, and the ratio of commissions and other acquisitions expenses is 18%, is this line profitable? b) How does your answer to part (a) change if investment yields of 8% are added?
a) a. No, because the combined ratio = loss ratio + expense ratio + dividend ratio = 73.00% + (12.50% + 18.00%) + 0.00% = 103.50% > 100%. b) b. Yes, because the operating ratio = combined ratio - investment yield = 103.50% - 8.00% = 95.50% < 100%.
Q2. What is the adverse selection problem? How does adverse selection affect the profitable management of an insurance company?
Adverse selection is the problem that customers who apply for insurance policies are more likely to be those most in need of insurance (i.e., someone with chronic health problems is more likely to purchase a life insurance policy than someone in perfect health). Thus, in calculating the probability of having to pay out on an insurance contract and, in turn, determining the insurance premium to charge, insurance companies' use of health (and other) statistics representing the overall population may not be appropriate (since the insurance company's pool of customers is likely to be more prone to health problems than the overall population). Insurance companies deal with the adverse selection problem by establishing different pools of the population based on health and related characteristics (such as income). By altering the pool used to determine the probability of losses to a particular customer's health characteristics, the insurance company can more accurately determine the probability of having to pay out on a policy and can adjust the insurance premium accordingly.
Q9. How does the regulation of insurance companies compare with that of depository institutions?
An important piece of legislation affecting the regulation of life insurance companies is the McCarran-Ferguson Act of 1945, which confirms the primacy of state over federal regulation of insurance companies. Thus, unlike the depository institutions, which can be chartered at either the federal or state levels, a life insurer is chartered entirely at the state level. In addition to chartering, state insurance commissions supervise and examine insurance companies using a coordinated examination system developed by the National Association of Insurance Commissioners (NAIC). Regulations cover areas such as insurance premiums, insurer licensing, sales practices, commission charges, and the types of assets in which insurers may invest. In 2009, the U.S. Congress considered establishing an optional federal insurance charter. Support for such a charter increased 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 requirements. The Wall Street Reform and Consumer Protection Act of 2010 established the Federal Insurance Office (FIO), an entity that reports to Chapter 15 - Insurance Companies HWSolutions_FMI_Saunders7e_Ch15 3 of 7 Congress and the President on the insurance industry. While the industry continues to be regulated by the states, the FIO has the authority to monitor the insurance industry, identify regulatory gaps or systemic risk, deal with international insurance matters and monitor the extent to which underserved communities have access to affordable insurance products. The Wall Street Reform and Consumer Protection Act also called for the establishment of the Financial Stability Oversight Council (FSOC), which is charged with designating any financial institution (including insurance companies) that presents a systemic risk to the economy and subjecting them to greater regulation. Also the result of the Wall Street Reform and Consumer Protection Act, the Federal Reserve has become a major supervisor of insurance firms. The Fed extended much of its authority over the insurance industry through the designation of three of the largest insurers (American International Group, Prudential Financial, and MetLife) as "systemically important financial institutions." However, with the closure of the Office of Thrift Supervision in 2011, the Fed also supervises 14 insurance companies that own savings institutions. In total, the Fed supervises about one-third of U.S. insurance industry assets. This increased oversight by the Fed has incited concern among insurance companies and state regulators that the Fed will enact onerous capital rules and supervise insurance firms like banks. Promoting the concerns are cases like that of MetLife that failed the Fed's "stress tests" in 2012 despite the firm's protests the Fed misunderstood its business model. In 2015, MetLife sued the U.S. to overturn its designation as a nonbank systemically important financial institution. The insurer argued that its failure would not pose a risk to the financial system. MetLife further argued that, because it is harder for a customer to pull money from an insurance contract than it is for a depositor to withdraw money from a bank deposit account during a crisis, the insurance industry is safer than banking. Not counting on the courts to agree, in 2016 MetLife announced that it would divest a large piece of its life insurance unit: a unit that had been the core of the company's business for decades. However, shortly after this, a federal judge ruled that MetLife did not deserve to be labeled too big to fail and as such was allowed to shed its designation as a systemically important financial institution and the increased regulatory oversight that went along with that designation.
Q6. Explain how annuities represent the reverse of life insurance activities.
Annuities represent the reverse of life insurance principles. While life insurance involves different contractual methods to build up a fund and the eventual payout of a lump sum to the beneficiary, annuities involve different methods of liquidating a fund over a long period of time, such as paying out a fund's proceeds to the beneficiary. The contract may be initiated by investing a lump sum or by making periodic payments before the annuity payments begin.
P9. An insurance company's projected loss ratio is 77.5%, and its expense ratio is 23.9%. It estimates that dividends to policyholders will add another 5%. What is the minimum yield on investments required in order to maintain a positive operating ratio?
Combined ratio = loss ratio + expense ratio + dividend ratio = 77.50% + 23.90% + 5.00% = 106.40%. In order to be profitable, the yields on investments have to be greater than 6.40%.
Q22. What is the investment yield on premiums earned? Why has this ratio become so important to property-casualty insurers?
In cases where the combined ratio is greater than 100 percent, overall profitability can be ensured only by a sufficient investment return on premiums earned. That is, P&C firms invest premiums in assets between the time they receive the premiums and the time they make payments to meet claims. For example, in 2016, net investment income to premiums earned (or the P&C insurers' investment yield) was 8.5 percent. As a result, the overall average profitability (or operating ratio = combined ratio after dividends minus investment yield) of P&C insurers was 91.5 percent. It was equal to the combined ratio after dividends (100.0%) minus the investment yield (8.5%). Since the operating ratio was less than 100 percent, P&C insurers were profitable overall in 2016. Net returns on investments can have a big impact on industry profitability. For example, in 2012 P&C insurers' investment yield was 10.5 percent. As a result, the operating ratio of P&C insurers was 92.7% (the combined ratio after dividends (103.2%) minus the investment yield (10.5%)). While the combined ratio after dividends corresponds to net losses, the high investment yield resulted in an operating ratio that was less than 100%. That is, P&C insurers were profitable in 2012. However, lower net returns on investments (e.g., 2.8 percent rather than 10.5 percent) would have meant that underwriting P&C insurance was marginally unprofitable (i.e., the operating ratio of insurers in this case would have been 100.4%).
Q11. How do life insurance companies earn profits?
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 expected future payouts). The second 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 is the yield on the insurance company's investments, the greater is the difference between the premium income stream and the policy payouts (except in the case of variable life insurance) and the greater is the insurance company's profitability.
Q3. Contrast the balance sheets of depository institutions with those of life insurance firms.
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, corporate equities, and a declining amount of mortgage products. The asset side of a depository institution's balance sheet is comprised primarily of short- and medium-term loans to corporations and individuals and some liquid investment securities (e.g., Treasury securities). 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
P13. A property-casualty insurer brings in $6.25 million in premiums on its homeowners MP line of insurance. The line's losses amount to $4,343,750, expenses are $1,593,750, and dividends are $156,250. The insurer earns $218,750 in the investment of its premiums. Calculate the line's loss ratio, expense ratio, dividend ratio, combined ratio, investment ratio, operating ratio, and overall profitability.
Loss ratio = $4,343,750/$6,250,000 = 69.50% Expense ratio = $1,593,750/$6,250,000 = 25.50% Dividend ratio = $156,250/$6,250,000 = 2.50% Combined ratio = loss ratio + expense ratio + dividend ratio = 69.50% + 25.50% + 2.50% = 97.50% Investment yield = $218,750/$6,250,000 = 3.50% Operating ratio = combined ratio - investment yield = 97.50% - 3.50% = 94.00% Overall profitability = 100.0% - 94.0% = 6.0%
P11. An insurance company collected $3.6 million in premiums and disbursed $1.96 million in losses. Loss adjustment expenses amounted to 6.6% and dividends paid to policyholders totaled to 1.2%. The total income generated from their investments was $170,000 after all expenses were paid. What is the net profitability in dollars?
Pure loss = $1,960,000 Expenses = 0.066 x $3,600,000 = $237,600 Dividends = 0.012 x $3,600,000 = $43,200 Investment returns = $170,000 Net profits = $3,600,000 - $1,960,000 - $237,600 - $43,200 + $170,000 = $1,529,200
Q21. How is the combined ratio defined? What does it measure?
The combined ratio is equal to the loss ratio plus the expense ratio. It is a measure of the overall underwriting profitability of a line, which includes the loss, loss adjustment expenses, and expense ratios. Technically, the combined ratio is equal to the loss ratio plus the ratios of LAE to premiums written and commissions and other expenses to premiums written. The combined ratio after dividends adds dividends paid to policyholders as a portion of premiums earned to the combined ratio. If the combined ratio is less than 100 percent, premiums alone are sufficient to cover both losses and expenses related to the line. As seen in Table 15-6, this was the case from 2013-2016. The combined ratio before dividends was 95.7%, 96.5%, 97.6%, and 99.5%, respectively, over this period.
Q20. What does the expense ratio measure? Identify and explain the two major sources of expense risk to a property-casualty insurer. Why has the long-term trend in this ratio been decreasing?
The expense ratio measures the expenses incurred relative to premiums written. The two major sources of expense risk to P&C insurers are (1) loss adjustment expenses (LAE) and (2) commissions and other expenses. LAE relate to the costs surrounding the loss settlement process. For example, many P&C insurers employ adjusters who determine the liability of an insurer and the size of an adjustment or settlement to make. The other major area of expense involves the commission costs paid to insurance brokers and sales agents and other operating expenses related to the acquisition of business. The expense ratio includes the commission and other expenses for P&C. In contrast to the increasing trend in the loss ratio, the expense ratio decreased over recent years. Despite this trend, expenses continued to account for a significant portion of the overall costs of operations. In 2015, for example, commission and other expenses amounted to 27.8 Chapter 15 - Insurance Companies HWSolutions_FMI_Saunders7e_Ch15 6 of 7 percent of premiums written. Clearly, sharp rises in commissions and other operating costs can rapidly render an insurance line unprofitable.
Q5. What are the similarities and differences among the four basic lines of life insurance products?
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 (77.8% in 2015) 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 (21.6%) are similar to ordinary life insurance policies except that they cover a large number of insured persons under a single policy, providing cost economies in evaluating, screening, selling, and servicing the policies. Credit life (<1%) typically is term life sold in conjunction with some debt contract. Their cost per unit of coverage is usually much higher than other methods of covering these liabilities in the event of unexpected death. Thus, they are a rarely used type of life insurance. Other major activities of life insurance companies are the sale of annuities, private pension plans, and accident and health insurance.
Q15. Identify four characteristics or features of the perils insured against by property-casualty insurance. Rank the features in terms of actuarial predictability and total loss potential.
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: 1) Property versus liability: In general, maximum levels of losses are more predictable for property lines than for liability lines. 2) Severity versus frequency: In general, loss rates are more predictable on low severity, high-frequency lines than they are on high-severity, low-frequency lines. 3) Long Tail versus Short Tail: Some liability lines suffer from a long-tail risk exposure phenomenon that makes estimation of expected losses difficult. This long-tail loss arises in policies for which the insured event occurs during a coverage period but a claim is not filed or made until many years later. The delay in the filing of a claim is in accordance with the terms of the insurance contract and often occurs because the detrimental consequences of the event are not known for a period of time after the event actually occurs. 4) Product Inflation versus Social Inflation: Loss rates on all P&C property policies are adversely affected by unexpected increases in inflation. The inflation risk of property lines is likely to reflect the underlying inflation of the economy, while the inflation risk of liability lines may be subject to the changing values or social risk of the society (e.g., juries' willingness to award punitive and other damages at rates far above the underlying rate of inflation). Such social inflation has been particularly prevalent in commercial liability and medical malpractice insurance and has been directly attributed by some analysts to faults in the U.S. civil litigation system.
Q19. What does the loss ratio measure? What has been the long-term trend of the loss ratio?
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 ratio has increased from the 60 percent range in the 1950s to the 70 and 80 percent range in the 1990s into the early 2010s. A turnaround started in 2013, as the loss ratio dropped to 67.4 percent and values stayed below 70 percent through 2015 when the loss ratio was 69.8 percent. Over the first six months of 2016, the loss ratio rose back to 71.9 percent.
Q8. If an insurance company decides to offer a corporate customer to a private pension fund, how would this change the balance sheet of the insurance company?
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 likely would increase, depending on the type of pension plans provided to the customers. The premiums and contributions would be invested in the normal asset categories of the insurance company, except in cases where the pension fund requires aggressive investment strategies. In this case, the funds may be invested in specific equity mutual funds.
Q1. How do the primary function of an insurance company compare with that of a depository institution?
The primary function of an insurance company is to protect policyholders (both individuals and corporations) 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 savers. By accepting deposits and making loans, depository institutions allow savers with predominantly small, short-term financial assets to benefit from investments in larger, longer-term assets. These long-term assets typically yield a higher rate of return than short-term assets.
Q14. What are the three sources of underwriting risk in the P&C industry?
The three sources of underwriting risk in the PC industry are: (a) unexpected increases in loss rates, (b) unexpected increases in expenses, and/or (c) unexpected decreases in investment yields or returns. Loss risk is 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 are also 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.
Q12. What are the two major lines of property-casualty (P&C) insurance firms?
The two major lines of property-casualty insurance are property insurance (insurance coverage related to the loss of real and personal property) and casualty—or perhaps more accurately, liability (insurance coverage that offers protection against legal liability exposures). In many cases, property and liability insurance coverages are sold together in single policy packages - for example, homeowners multiple peril 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.
