ICP 19A: Statistical Basis for Insurance

Transcription

1 A Core Curriculum for Insurance Supervisors ICP 19A: Statistical Basis for Insurance Basic-level Module

2 Copyright 2006 International Association of Insurance Supervisors (IAIS). All rights reserved. The material in this module is copyrighted. It may be used for training by competent organizations with permission. Please contact the IAIS to seek permission. This module was prepared by Julian Gribble. Mr. Gribble qualified as an actuary in 1991, holding qualifications from the Society of Actuaries (FSA), the Canadian Institute of Actuaries (FCIA), and the Institute of Actuaries of Australia (FIAA). He has more than 25 years of business experience in the private sector in insurance and funds management. Since 1993, he has been a consulting actuary and is director of his own consulting practice. He was instrumental in implementing the capacity-building program for regulators Managing Regulatory Change in Life Insurance and Pensions Program (MRC), which was endorsed by the Asia Pacific Economic Cooperation (APEC) finance ministers. His professional activities with the Institute of Actuaries of Australia include chairing a review of the actuarial control cycle syllabus and sitting on the International Relations Committee. The module was reviewed by Arup Chatterjee, Monika Jurášová, and Michael Oliver. Arup Chatterjee is deputy director of the Insurance Regulatory and Development Authority, Hyderabad, India, and has occupied the position for six years. He is a member of the Asia Pacific Risk and Insurance Association, Singapore, as well as the Global Association of Risk Professionals in the United States. He is currently working in the IAIS Secretariat. Monika Jurášová is working in the insurance sector. She spent 10 years with the Office of State Supervision of Insurance and Pension Funds in the Ministry of Finance of the Czech Republic, where she was a member of the Inspection Department, the International Department, and the Helsinki Protocol Working Group on Supervision of Insurance Groups. She held a short-term appointment with the European Bank for Reconstruction and Development in London in Michael Oliver is the director of insurance at the Financial Services Commission in the British Virgin Islands, a major center for captive insurance companies. He has more than 30 years of experience in the insurance industry and is a fellow of the Chartered Insurance Institute (FCII). He has worked as an advisor to the Insurance Division of the U.K. Financial Services Authority and as senior vice president of the property and casualty division of a U.S. insurer. Earlier he underwrote international general insurance business in the United Kingdom.

3 Contents About the Core Curriculum v Note to learner vii Pretest ix A. Introduction B. Basic characteristics of insurance C. Types of risk insured D. Quantification of insurable risks E. Key elements of strategic underwriting and pricing policy F. Underwriting G. Setting premiums H. Systems and processes used by insurers I. Supervisory approaches to premium adequacy iii

4 J. Broader context K. Conclusion L. References Appendix I. ICP Appendix II. Glossary of key terms Appendix III. Insurance pooling Appendix IV. Answer key

5 About the Core Curriculum A financially sound insurance sector contributes to economic growth and well-being by supporting the management of risk, allocation of resources, and mobilization of longterm savings. The insurance core principles (ICPs), developed by the International Association of Insurance Supervisors (IAIS), are key international standards relevant for sound financial systems. Effective implementation of the ICPs requires skilled and knowledgeable insurance supervisors. Recognizing this need, the World Bank and the IAIS partnered in 2002 to develop a core curriculum for insurance supervisors. The Core Curriculum Project, funded and supported by various sources, accelerates the learning process of both new and experienced supervisors. The ICPs provide the structure for the core curriculum, which consists of a set of modules that summarize the most relevant aspects of each topic, focus on the practical application of supervisory concepts, and cross-reference existing literature. The core curriculum is designed to help those studying it to: Recognize the risks that arise from insurance operations Know the techniques and tools used by private and public sector professionals Identify, measure, and manage these risks Operate effectively within a supervisory organization Understand the ICPs and other IAIS principles, standards, and guidance Recommend techniques and tools to help a particular jurisdiction observe the ICPs and other IAIS principles, standards, and guidance Identify the constraints and identify and prioritize supervisory techniques and tools to best manage the existing risks in light of these constraints. v

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7 Note to learner Welcome to the ICP 19A: Statistical basis for insurance module. This is a basic-level module on statistical concepts that underlie insurance activity that does not require specific prior knowledge of this topic. The module should be useful to either new insurance supervisors or experienced supervisors who have not dealt extensively with the topic or are simply seeking to refresh and update their knowledge. Start by reviewing the objectives, which will give you an idea of what a person will learn as a result of studying the module, and answer the questions in the pretest to help gauge your prior knowledge of the topic. Then proceed to study the module either on an independent, self-study basis or in the context of a seminar or workshop. The amount of time required to study the module on a self-study basis will vary, but it is best addressed over a short period of time, broken into sessions on sections if desired. To help you engage and involve yourself in the topic, we have interspersed the module with a number of hands-on activities for you to complete. These exercises are intended to provide a checkpoint from time to time so that you can absorb and understand the material more readily and can apply the material to your local circumstances. You are encouraged to complete each of these activities before proceeding with the next section of the module. If you are working with others on this module, develop the answers through discussion and cooperative work methods. An answer key in appendix IV sets out some of the points that you might consider when tackling the exercises and suggests where you might look for the answers. As a result of studying the material in this module, you will be able to do the following: vii

8 Insurance Supervision Core Curriculum 1. Explain the basic characteristics of insurance that enable insurers to take on risks 2. Outline the types of risks that insurers take on as a result of their insurance activities 3. Discuss some of the difficulties in quantifying some types of risks for example, due to uncertainties regarding the frequency, amount, or timing of payment of claims or the existence of embedded options in the insurance contracts 4. Describe the essential elements of a strategic underwriting and pricing policy 5. Describe the systems that insurers typically use to control their (a) pricing levels, (b) underwriting practices, (c) claim payment processes, and (e) administrative expenses 6. Explain the most significant factors considered by an insurer in setting its premiums, including (a) insurance risks, (b) investment risks and expected returns, (c) persistency, (d) policy acquisition and administrative expenses, and (e) target return on capital 7. Outline the techniques that a supervisor can use to assess the reasonableness of the methods and assumptions used by a particular insurer to set its premiums 8. Summarize the requirements of ICP 19, focusing on essential criteria a, b and c. viii

9 ICP 19A: Statistical Basis for Insurance Pretest Before you study this module, attempt to answer the questions in this pretest. This exercise is intended to help you to assess your level of knowledge of this topic. Appendix IV provides answers and comments on the questions in this pretest and on the exercises found throughout the text. 1. Is the following statement an appropriate description of insurance: Insurance is a wager for example, I bet my premium of $500 against the insurance company s $150,000 if my house burns down? a. Yes b. No 2. An insurer currently offers a life insurance product for which the premium makes no distinction as to whether the insured is a smoker or not. The insurer has proposed the introduction of a preferred insurance premium to insureds already holding policies in the current product if they can demonstrate that they do not smoke. Is this an appropriate approach? a. Yes b. No ix

10 Insurance Supervision Core Curriculum 3. Two small insurance companies, with the same insured risk profile, offering identical products, and using identical policies and procedures, are seeking supervisory approval to merge. Both hold sufficient capital to have 95 percent confidence that they will be able to meet the next year s claims (as required by current solvency requirements). One of the reasons given to support the merger is that the combined company will be able either to release capital while maintaining the 95 percent confidence level of meeting claims payment or to have a higher level of confidence of meeting claims payments as a direct consequence of the merger. a. True b. False. x

11 ICP 19A: Statistical Basis for Insurance Basic-level Module A. Introduction This is a basic-level module that focuses on IAIS Insurance Core Principle (ICP) 19 on the statistical basis for insurance (see appendix I for the full text of ICP 19). The emphasis is on insurable risks and aspects of their direct management. A separate module dealing with ICP 19 module 19B focuses on reinsurance. The broader spectrum of risk management for insurers is addressed in other ICPs, in particular those relating to the supervised entity and the prudential requirements group: ICP 9 on corporate governance ICP 10 on internal controls ICP 18 on risk assessment and management ICP 20 on liabilities ICP 21 on investments ICP 22 on derivatives and similar commitments ICP 23 on capital adequacy and solvency. Other mechanisms are available to transfer risk in addition to insurance, and these are often called alternate risk transfer mechanisms. These alternatives are not considered in this module. In this module, it is assumed that insurers, their clients, and their potential clients are agreed in principle that the risks they consider are insurable. The ICPs are generally specified to be applicable to life and non-life insurance. The discussion in this document is applicable to both life and non-life insurance, unless spe- 1

12 Insurance Supervision Core Curriculum cifically indicated otherwise. While written in the context of insurance, this module is applicable in both the insurance and reinsurance contexts, unless specifically indicated otherwise. Many terms take on specific meanings in the context of insurance. Some of these terms are explicitly included in the IAIS Glossary of Terms (IAIS 2006) and are reproduced in appendix II. Some further terms are defined in the text, and further references are also provided. Several points should be noted when reading this module. First, the content is well established and should not be expected to vary by jurisdiction. There may be some variation in the specific terms used in different areas, but the terms used in this module are commonly accepted. References are made, in particular, to Black and Skipper (1999), Booth and others (2004), Hart, Buchanan, and Howe (1996), and Vaughn and Vaughn (2003). Second, some exercises for self-testing and further review are included in the module, and the suggested responses are presented in appendix IV. Third, a number of references have been included to provide further sources of information on a self-study basis. The International Association of Insurance Supervisors (IAIS) updated its Insurance Core Principles and Methodology in October 2003 (IAIS 2003a). The 28 core principles are intended to cover all aspects of a supervisory framework and should be considered as a whole. In summary, ICP 19 states: Since insurance is a risk-taking activity, the supervisory authority requires insurers to evaluate and manage the risks they underwrite, in particular, through reinsurance, and to have the tools to establish an adequate level of premiums. The explanatory notes for ICP 19 are as follows: Insurers take on risks and manage them though a range of techniques, including pooling and diversification. Every insurer should have an underwriting policy that is approved and monitored by the board of directors. Insurers use actuarial, statistical, or financial methods for establishing liabilities and determining premiums. If these amounts are materially understated, the consequences for the insurer can be significant and in some cases fatal. In particular, premiums charged could be inadequate to cover the risk and costs, insurers may pursue lines of business that are not profitable, and liabilities may be understated, masking the true financial state of the insurer. There is a need to ensure that embedded options have been identified and properly priced and that an appropriate reserve has been established. Insurers use a number of tools to mitigate and diversify the risks they assume. The most important tool to transfer risk is reinsurance. An insurer should have

13 ICP 19A: Statistical Basis for Insurance a reinsurance strategy, approved by its board, that is appropriate to its overall risk profile and its capital. The reinsurance strategy will be part of the insurer s overall underwriting strategy. Further, to support ICP 19, a number of essential criteria are specified. In relation to this module, these criteria indicate that: Insurers have strategic underwriting and pricing policies in place, and these policies are approved and reviewed regularly by the board of directors. Insurers evaluate the risks they underwrite and establish and maintain an adequate level of premiums. For this purpose, insurers should have systems in place to control their expenses related to premiums and claims, including the handling of claims and administrative expenses. These expenses should be monitored by management on an ongoing basis. The supervisory authority is able to review the methodology used by the insurer to set premiums to determine that they are established on reasonable assumptions to enable the insurer to meet its commitments. This module focuses on criteria a, b, and c. For discussion of the remaining essential criteria d, e, and f see module 19B on reinsurance. To support the core principles, the IAIS provides further principles, standards, and guidance papers. These documents should be considered as an integrated body of work. Exercises 1. To what extent do insurers in your jurisdiction satisfy essential criteria a and b of ICP 19? 2. To what extent does your supervisory agency have in place methodologies, processes, and the expertise to assess the practices of insurers in your jurisdiction with regard to essential criteria a, b, and c of ICP 19? 3. To the extent that an insurer does not satisfy some of the essential criteria a, b, or c of ICP 19, what powers and practices does your supervisory body have in place to direct and assure compliance with them?

14 Insurance Supervision Core Curriculum B. Basic characteristics of insurance At an intuitive level, the word risk implies uncertainty of outcomes, results, events, or actions. In some cases, individuals have some control or choice over the events, and in other cases they do not. For example, individuals have no control over tsunamis or earthquakes, but they can choose not to engage in hazardous activities. A key characteristic of risk is that the outcomes of the events are uncertain: they cannot be known ahead of time. This implies that risk is inherently statistical in nature and also that there must be more than one possible outcome for the events. In general, some outcomes will be positive, in that they exceed expectations, and some will be negative, in that they do not meet expectations. The way in which outcomes are measured may also vary, depending on the events being considered. For example, one may be disappointed with the quality of a recommended book, or one may make financial gains through investing in the stock market. All aspects of human endeavor involve some aspect of risk. Risk may be assessed differently by different parties, relative to their particular position and circumstance. The impact of risk is often asymmetric and nonlinear. There is evidence from the field of behavioral finance that individuals do not react in the same way when presented with potential gains or losses of equal magnitude and that, as the magnitude of potential losses increases, individuals become increasingly risk averse. For example, positive outcomes are accepted, but negative outcomes with losses above a certain level may be catastrophic to the particular insured. In general, only risks with consequences above a material threshold (initially assessed by the party seeking insurance) are insured, while trivial risks are not. That is, an individual typically only seeks insurance when he or she believes that it is necessary to transfer the risk in order to avoid catastrophic consequences. The business of insurance is intimately connected with risk, its assessment, and its management. Consequently, the risks that are relevant to the insurance industry need to be characterized. The focus here is on products the commercial insurance industry offers to its clients, not on the risks involved with management of the business. Insurance restricts its focus to covering those risks that have economic or financial consequences and to addressing the adverse impacts of those financial consequences. There are two main types of economic risk: Speculative risks. These risks involve the possibility of either financial gain or loss. Such risks are often entered into deliberately (and so voluntarily). Examples include gambling, hedging, and business (entrepreneurial) risks. Pure risk. In this there is only the possibility of financial loss or of no financial loss. Examples include the loss of value of a house destroyed by fire or the loss of earning power by an individual due to death or disability. The business of insurance is only concerned with pure risks, and even then not all pure risks. Some other categorizations of risk are also useful.

15 ICP 19A: Statistical Basis for Insurance Static and dynamic risks. Dynamic risks result from changes in the economy and are often considered to benefit society in the long run through adjustment in the allocation of resources. Examples include changes in price, consumer tastes, and technology. While they typically affect many individuals, dynamic risks are difficult to predict. Static risks occur in the absence of changes to the economy and are usually not a source of gain to the community. They typically involve some sort of individual loss and occur with some regularity over time. As such, static risks are more predictable and more suited to management via insurance. An example of a static risk is the destruction of dwellings (for example, due to fire). Fundamental and particular risks. Fundamental risks involve losses that are impersonal in origin and consequence. They are group risks that affect many individuals and may be caused by social, economic, political, or physical phenomena. Examples include hurricanes, inflation, and the like. Particular risks are losses from individual events that affect individuals or small groups. Examples include fire and theft. Fundamental risks are often addressed at a governmental level for example, through social insurance. Particular risks are the responsibility of individuals and so can be addressed via insurance. The distinction between fundamental and particular risks changes over time, as highlighted by reactions to the September 11, 2001, terrorist attack on the World Trade Center in New York. The terms peril and hazard are often used in conjunction with risk. Peril. A peril identifies the cause of a risk for example, fire, theft, or injury. Hazard. A hazard is a factor contributing to the risk, increasing or decreasing the probability or size of a loss arising from a given peril. Hazards can be classified as physical, moral, or other hazards. Physical hazards include the construction materials of a building, the location of a residence, the brakes on a car, and so on. Moral hazards relate to the attitudes of individuals and cover the range from dishonesty through to carelessness and lack of concern. The consequences of moral hazard can often be seen in an increase in physical hazards. Issues that may arise under moral hazard include insurance fraud, where individuals seek to fabricate or exaggerate claims, increased carelessness toward loss prevention from people who have purchased insurance, or a tendency of providers to increase services or costs when those costs are known to be covered by insurance. Moral hazard tends to increase both the frequency and severity of losses when the loss events are insured, so the minimization of moral hazard is an important consideration in the management of an insurance business. Sometimes a distinction is made between dishonesty (moral hazard) and changes in behavior or indifferent attitudes (morale hazard). Other hazards include, for example, legal hazard, which is the hazard of the consequences of changes in laws, regulations,

16 Insurance Supervision Core Curriculum or precedents for example, if building regulations are updated, then the cost of replacing a building may be increased. At an overview level, the risks that can be addressed though the mechanism of insurance that is, insurable risks have a number of characteristics: Circumstances capable of definition. The nature of the loss, and the criteria under which the loss is assessed, must be specified before the loss occurs. This highlights the importance of having proper and completed contracts in place prior to the event. Assessable risk. There must be sufficient information available so that the frequency and severity of the potential losses can be assessed. The expertise to interpret the information and its consequences properly is also required. This emphasizes the statistical nature of insurance and the need for sufficient experience to be available to provide a starting point for developing appropriate covers. It also implicitly requires that the risks be sufficiently similar so that their treatment as a group pooling is appropriate. Assessable financial loss. The event insured against must result in a loss that can be determined and quantified in financial terms. This leads to the underwriting requirements of insurable interest that is, clarifying that the insured may realistically suffer a loss of the size to be insured. Indemnity. The insurance payment should only indemnify the insured for the loss. That is, it should not be possible for the insured to make a profit from the insurance coverage. In some cases, assessing the loss can be subjective for example, in assessing reasonable wear and tear on machinery. However, in other cases, there is sometimes the possibility that the amount of financial loss to the insured could be less than the benefits provided for under the policy for example, under an insurance policy that provides a fixed monetary benefit for each day of hospitalization. These examples highlight the importance of assessing and managing underwriting and claims of insurers. This is modified somewhat for life insurance, since the usual legal position is that a financial value cannot be placed on human life and generally individuals can, in principle, seek to take out as much life insurance on their own lives as they wish. Also, there is no possibility of partial loss with insurance on the life of a person: the person is either dead or alive. As a consequence, life insurance policies provide cash payments for sums that are agreed (or the mechanism for computing them is agreed) at inception of the policy. While death is ultimately unavoidable, in life insurance the risk insured against is the timing of the death. As such, strictly speaking, a life insurance contact is not an indemnity contract. Fortuitous loss. The loss must be fortuitous and uncertain. That is, the insured should not be able to increase the chances of the loss occurring, and the prob-

17 ICP 19A: Statistical Basis for Insurance ability of the loss occurring cannot be certain. The management of moral hazard is important. Public interest. The insurance cover must not threaten the public interest. For example, it should not encourage criminal activity. It should be clear that, as a consequence of these requirements, not all risks, and not all pure risks, are insurable. This is highlighted by the treatment of terrorism risk since the September 11, 2001, attacks on the World Trade Center in New York. In the development of a commercial insurance portfolio, a number of other considerations also need to be taken into account: Losses not catastrophic to the insurer. The insurer must be able to sustain the losses incurred. This raises the issues of concentration: geographic (for example, weather events), demographic (for example, gender, age, socioeconomic status), and the like. Affordable premiums. In a practical setting, if the purchasers do not consider the premiums charged to be affordable, then the cover will not be purchased or will be purchased in insufficient quantities to validate statistical assumptions. Consequently, the issue of costs other than pure risk costs, including administrative costs and profit expectations, are important. The role of competition here is also important. Avoidance of adverse selection. Care needs to be taken to ensure that insurance policies are not designed in such a way that policyholders can exploit opportunities offered in the policy to their advantage and to the detriment of the insurer. Offering some sort of guarantees in a policy should be considered with care, as they potentially provide legitimate avenues for the policyholders to select against the insurer. Avoidance of excessive exposure to loss. The insurer should give careful consideration to potential accumulation of risk and cover limits offered to policyholders. An aspect of this is the question of whether a policyholder is overinsured (perhaps through covers with more than one insurer). See also the comments regarding concentration of risk. From a legal perspective, some principles that underlie insurance are reflected in the insurance laws in many countries. These include the following: Insurable interest. The individual seeking the insurance cover must have a legitimate and valid risk of financial loss should the event insured against occur. Utmost good faith. Both the insurer and the (potential) insured must reveal to each other all material facts relating to the proposed insurance cover in a timely manner. This stands in contrast to the more common principle of buyer beware when making purchases.

18 Insurance Supervision Core Curriculum Indemnity. In most cases, only financial losses actually incurred can be recovered through an insurance policy. Subrogation. In the circumstances where an insured collects an indemnity, the insured then relinquishes any further rights of redress to the insurer. Subrogation may cover rights such as salvage rights on property indemnified for or the right to collect damages from a third party. Subrogation occurs in non-life insurance and (sometimes) in health insurance, but not in life insurance. Proximate cause. The linkage between the adverse results and the causes of an event must be sufficiently direct and clear. Insurance is based on providing coverage against the consequences of specified perils, and so the mere fact that a loss occurs does not automatically trigger the insurance payment. It needs to be demonstrated that the adverse outcome can be attributed to a peril that was insured against. Binding contracts. Insurance contracts are defined by law and are normally instigated by the payment of a specified consideration (the initial premium) by the insured; in return, the insurer takes on a binding obligation to pay, subject to the conditions of the contract. In some cases, there may be a need for particular clauses or conditions to be included in or excluded from insurance contracts. Generally, this is done from a market conduct regulatory perspective, with the objective being to protect the policyholder, recognizing the ongoing and significant information asymmetry that exists between the insured and the policyholder. In summary, insurance can be viewed as an economic device whereby the individual substitutes a small certain cost (the premium) for a large uncertain financial loss (the contingency insured against) that would exist if it were not for the insurance contract. That is, the basic purpose of insurance is to provide individual policyholders with a means to spread or diversify risk that might otherwise be unacceptable or unmanageable for the individual. Pooling An argument sometimes advanced against taking out insurance is that it can be expensive due to the costs of administration and the profits the insurer may make. This argument is usually supported by reference to average or expected costs of loss to an individual. The logic is fundamentally flawed since it relies on applying a statistically based result (average costs) at the level of an individual. Statistical results are only appropriate in a group or pooled setting. At the individual level, either the event occurs or it does not: if it occurs, the full loss is incurred; if it does not, then no loss is incurred. The proposal of the individual retaining insurance premiums over a period of time to cover the cost of the event is also flawed in that it presumes that the event will not hap-

19 ICP 19A: Statistical Basis for Insurance pen until sufficient monies have been accumulated. If the timing of the event were that well known, then the need for insurance would be removed, at least partially. The mathematical justification for how the insurance process can succeed in practice lies in the law of large numbers and the pooling of risk among a group of individuals. Since risks are inherently uncertain, they need to be approached from a statistical perspective. The probability of a risk event occurring is generally considered in terms of a random variable with a given probability distribution. The random variable then has properties, such as mean and variance, which are derived from the probability distribution, that are used to understand its expected behavior. When such risks are pooled, the behavior of the pool is driven by the new random variable, which is the sum of the random variables of the individual risks. The behavior of the pool is then determined from the properties of this new random variable. If all the individual risks in the pool have the same behavior, then key aspects of the behavior of the pool can be deduced from knowing the behavior of any one of the individual risks. The following is not intended to be a rigorous mathematical derivation; rather it is a descriptive summary to illustrate the key principle. Assume that a claim either occurs or does not occur for each insured in a single time period. The extension of this illustration to variable numbers of claims or multiple time periods is not pursued. Two key characteristics of a random variable, X, are its expected value or mean and its variance: Expected value or mean. This is commonly written as μ or as μ X when it is necessary to clarify that the mean is of the random variable X. Theoretically, the mean is the value of the random variable with a 50 percent probability that a value of the random variable will exceed μ and a 50 percent probability that a value of the random variable will be less than μ. So, loosely, the mean is a measure of the center of the set of possible values of the random variable. Variance. Variance is a measure of the dispersion of the values the random variable may take around the mean, and it is commonly written σ 2. The larger the variance of a random variable, the larger the spread of results around its mean. Formally, it is the expected value of the new random variable (X μ) 2. The standard deviation, σ, is the square root of the variance. The standard deviation is perhaps the most commonly used measure of dispersion about the mean. Other important properties of random variables have useful applications in the mathematics of insurance, but these are not pursued here. In practice, means and variances often need to be estimated based on a set of observed values of the random variable. There is a large body of knowledge around such processes, but this is not pursued here. In insurance, a key issue is the management, and reduction, of the variability of results. For a single random variable, the only way to be certain of protecting against the variability of the results is to hold funds in an amount equal to the largest value the ran- 9

20 Insurance Supervision Core Curriculum dom variable can take. For large risks with relatively low probabilities of occurring, this typically is not feasible (hence the need for insurance!). More generally, funds in addition to the expected value of the loss (the mean) should be, and typically are required to be, held to reduce the probability of an insurer s failure to an acceptable level. One version of the law of large numbers concludes that, when statistically identical risks are pooled together, as the size of the pool increases, the relative variability in results decreases. That is, the larger the pool, the more likely it is that the total amount of claims will converge to expectations (presuming no errors in the underlying assumptions). This convergence permits the insurance concept to work. At the level of the pool, the insurer has to hold relatively fewer additional funds than an individual to achieve the same level of comfort (the probability of failure or claims exceeding assets). The gap between the additional funds the insurer has to hold and the sum of the additional funds the individual insureds would collectively have to hold provides the funding for the insurer s expenses and profit. It is also important to note that as the potential risk increases, insureds become increasingly risk averse and consequently become more willing to pay a premium for insurance that can protect them from situations that may be catastrophic to them (but are not to the insurer). A measure of the relative variability of a random variable is its coefficient of variation, defined to be the standard deviation divided by the mean. The coefficient of variation allows a comparison of the relative variability of results of two random variables even though their numerical values may be very different. The conclusion from the preceding paragraph can be put another way: as the size of the pool of identical risks increases, an individually large coefficient of variation due to a single risk is reduced to an acceptably small coefficient of variation for the pool once it contains a sufficient number of risks. See, for example, Hart, Buchanan, and Howe (1996). The impact of pooling can also be seen directly through a mathematical derivation supporting this discussion. This is pursued further in appendix III. Also, the central limit theorem provides the basis for computational tools. While noted in appendix III, this is not pursued further here. It is also important to note that pooling should not be expected to reduce variance of the result to nil (or close to nil) for very large portfolios. This is because, while pooling can reduce the diversifiable variance of the group outcome, it does not reduce its systemic variance (that is, variance in the underlying claims rate parameters). Again, see appendix III. It is important to recognize the following: Homogeneity of risks. The assumption that all risks in a pool are identical is often not met in practice. It is a matter of judgment, usually by actuaries, as to the level of variance acceptable in a given pool. A balance must be struck between the size of the pool and the variety of risks within it. Independence of risks. Similarly, the assumption of independence of risks may not always be met. If risks are too well correlated (for example, in a war situa- 10

21 ICP 19A: Statistical Basis for Insurance tion) or a small number of large risks dominate a pool, then the variability of the pool is not adequately reduced and the pooling principle will fail. Again, it is a matter of judgment and underwriting to retain sufficient independence of risks in a pool. The conclusions reached under the assumptions of homogeneity and independence of risks remain essentially valid, as these assumptions are progressively relaxed or not fully met in a practical environment. From the supervisory perspective, the level of understanding that supervised entities have with regard to the risk profiles and structures of their insured pools and portfolios before and, especially, after the application of any reinsurance is a significant matter. In summary, the mathematical justification for insurance is that the pooling of (similar) risks reduces the variability of the overall outcome. Insurable risk management Insurers face many risks in addition to those directly related to the insurable risks taken on as part of the insurance business. While it is outside the scope of this module to consider all these risks, a useful overview of the risks facing insurers is provided in IAA (2004, ch. 5) and in the modules on ICP 18, risk management. The approaches to risk management generally fall into one of the following categories: Avoidance. By the nature of their business, insurers take on risk. However, they need not take on all risks that may be insurable and should be making coherent business decisions as to the areas from which they will, and will not, accept risks. If an insurer does not have the capacity financial, expertise, or operational to understand, manage, and administer risks, then it is perhaps better off not taking them on. From a supervisory perspective, when insurers enter new lines of business or exit current lines of business, it may be opportune to review their capacities. Acceptance. The pooling of (ideally) uncorrelated risks has been discussed. Diversification of risks for example, in a geographic, product, or group sense is often presumed and so is important to monitor. The role of both underwriting and claims management should not be underestimated. Also, the availability of appropriate reinsurance may play an important role in prudent acceptance of risks by the insurer. Control or reduction. There are many ways in which insurers can seek to control the insured risks they take on. They may limit the volume of insurance cover sold. The underwriting use of specific exclusions and policy loadings may be 11

22 Insurance Supervision Core Curriculum appropriate. The insurer may actively and financially encourage prevention and safety programs for example, among employers with dangerous machinery. Transfer. In cases where the insurer does not have the expertise or capacity to retain a risk, then it may be transferred. The most common risk transfer mechanism is reinsurance, although there are other options as well. Catastrophe insurance is a good example of where reinsurance may be used. In general, it is important for an insurer to retain a significant interest in any risks that may be reinsured. Not only should this ensure that the insurer retains a strong interest in proper underwriting, pricing, and claims management, but it also allows the supervisory authority to address the risk that the insurer is fronting for the reinsurer. Exploitation. In some cases, risks may provide an insurer with an opportunity. Since risks are not additive, it may be possible for risks to offset each other. For example, increased mortality may be beneficial to annuity business but detrimental to traditional life insurance business. In practice, some additional issues need to be borne in mind from both the supervisory and business perspectives: Competition. In general, insurers operate in a competitive environment and cannot be judged in isolation. Policyholders generally have the option at least to change insurers (if the cover is compulsory) or, more typically, to choose whether or not to purchase insurance coverage. Embedded options and guarantees. When present in products, embedded options and guarantees need to be identified, measured, appropriately priced, and provided for in the insurer s balance sheet. The assessment of such options or guarantees may be a difficult task. In summary, the general approaches to risk management are also applicable to the management of insured risks. Solvency and premium adequacy From a prudential supervisory perspective, the key issue is for insurers to remain solvent and to meet their future commitments. Appropriate pricing practices and adequate premiums are obviously important considerations, but other issues are of at least equal importance. A number of other things also need to be in place to ensure long-term solvency of an insurer. These include the following: 12

23 ICP 19A: Statistical Basis for Insurance Risk management. To achieve long-term success, appropriate risk management needs to be in place throughout an insurer s operations. This is in addition to the risk management and assessment that take place for insured risks. This covers all aspects of the business, from underwriting being consistent with pricing assumptions through to appropriate expense and claims management being in place. There are many potential immediate causes of failure of insurers. See Sharma and others (2002). However, MacDonnell (2002) ultimately assigns the root cause of almost all failures to poor management. Appropriate liability assessment. If the outstanding obligations of an insurer are not assessed properly, especially for long-term or long-tail business, then the apparent adequacy of the insurer s premiums will not be able to sustain the business in the long term. Adequate capital. Insurers should hold adequate capital to protect them against adverse deviations in various types of experience. Prudential regulators typically mandate the holding of minimum levels of capital and encourage insurers to hold capital in excess of these minimums. In many cases, capital requirements may seek to reflect a supervisor s perspective on the risk involved with particular lines of business written by the insurer, and in other cases, the capital requirements may not be so risk adjusted for example, when minimum capital requirements or additional margins are specified. While premium adequacy is a valuable objective, long-term solvency depends on a number of things. Where the supervisory authority and insurers choose to place the most emphasis in this chain needs to be balanced with the ultimate need for the whole chain to hold up, not just for isolated individual links to appear adequate. This emphasizes the need for early-warning flags to provide time for remedial actions, such as increasing premiums and closing products or lines of business, to be effective. In summary, premium adequacy is a valuable objective, but it does not ensure solvency. Exercises 4. The so-called deep pocket syndrome, in which legal juries may make larger awards when losses are covered by insurance is an example of moral hazard. a. True b. False 5. A product guarantee is not a contract of insurance since the outcome is under the control of the manufacturer. a. True b. False 13

24 Insurance Supervision Core Curriculum 6. In your jurisdiction, are maximum or minimum premium rates specified in some way by the supervisory authority or another authority for any classes of insurance? If so, what is the rationale supporting these imposed limits, and how are they adjusted (for example, to take into account the impact of inflation)? What risk does the supervisor take on by setting such limits? 7. In your jurisdiction, what investigations do insurance supervisors conduct to assess whether the theoretically expected convergence of actual toward expected claims results occurs as insurance portfolios, reported to cover like risks, increase in size? Where such convergence is not observed, what steps may the supervisory authority (or insurer) take? If the supervisory authority does not conduct such analyses, how does it determine whether claims behavior is showing reasonable or unreasonable volatility? 14

25 ICP 19A: Statistical Basis for Insurance C. Types of risk insured The driver for insurance coverage is that individuals seek to transfer risks that they feel are too large to carry on an individual basis. The primary mechanism that permits insurance to work is that of pooling of risk. However, not all risks are insurable. Private insurance Generally, private organizations provide insurance covers. These organizations may operate on a mutual basis or on a for-profit basis as companies that may or may not be listed on stock exchanges. The insurance covers offered by such organizations usually have some common characteristics. See, for example, Vaughn and Vaughn (2003): Voluntary participation. Usually individuals or entities have a choice as to whether or not to take out an insurance cover and have an opportunity to choose (and change) their insurance provider. In some cases, insurance covers may be required, but still be provided by companies in a competitive setting, as opposed to by a monopoly provider. Risk transfer via individual contract. The transfer of risk is formally accomplished by the exchange of a contract between the insured and the insurer. Individual equity. The coverage, its premiums, and benefits typically are based on the concept of individual equity. That is, benefits are commensurate with the individual premium paid to address the specific risks being insured. Fully funded. The provider of the insurance cover needs to have the capacity and capital to provide adequate confidence that the insurance contracts made can be honored. Supervisory bodies typically seek, on behalf of the general public, to impose a regulatory regime that will provide such assurance, at least to a specified minimum level of confidence. In almost all circumstances, the liabilities taken on by the insurer must be fully funded. In summary, the focus in this module is on voluntary insurance, provided under the above conditions. Other insurance Some other types of insurance may be encountered, and the supervisory authority may well be required to take an interest in their provision or administration for example, when administration is outsourced to the private sector. Apart from the brief descriptions that follow, these types of insurance are not pursued further. 15

26 Insurance Supervision Core Curriculum Self-insurance. Some large entities, governmental or private, have the option of using insurance principles to manage their own risks. The option to self-insure for certain classes of risk may be subject to supervisory approval. Among other things, such approval may depend on appropriate assurances and ongoing demonstrations that the risk pool is sufficiently large, the insurance program is funded adequately and securely, the entity has sufficient expertise to administer the program on a long-term basis, and the risks are sufficiently diversified and independent. Some large entities may be driven to self-insurance by a desire to reduce costs, especially in times of good experience, without having a sufficient understanding of the potential impact of adverse experience. In the extreme, funding of claims costs from ongoing cash flows could pose a serious risk to the entity. Social insurance. Typically, governments administer a number of so-called insurance schemes. These typically are compulsory, with standard benefits determined by law, and, in some cases, are based on a no fault principle. In addition, elements of social adequacy and redistribution of assets may be driving these programs. While some such programs are adequately funded based on short-term and long-term actuarial projections for example, the Canada Pension Plan many are not. Such insurance programs have their own characteristics that may well reflect their compulsory nature and, in some cases, monopoly provision. Common examples of social insurance programs may include (a) workers compensation, where employers are required to have insurance coverage to provide benefits to employees and their dependents when an employee suffers an occupational injury or disease; (b) accident compensation, such as motor vehicle bodily injury or death; (c) unemployment insurance; (d) government pensions, such as old age, disability, and the like; and (e) government medical, health care, and aged care. Many countries have some form of a government Medicare program, and some governments provide or support ongoing assistance in managing other risks, such as flood, crop failure, public guarantee insurance programs for financial institutions, and, more recently, terrorism. In some cases, insurance coverages are required by law but are provided through private insurers. This is often the case with compulsory liability insurance of professional groups, such as doctors, lawyers, accountants, and so on. Classes of private insurance The set of risks covered by insurance is evolving. As a result of technological progress and increasing wealth, new risks are being identified and managed. Examples in- 16

27 ICP 19A: Statistical Basis for Insurance clude identity fraud, information security, risks from the Internet and e-commerce, and emerging legal risks such as environmental damage, discrimination, and so on. Moreover, while insurance policies typically are classified according to their primary class, they may well include coverage for a variety of risks. The breadth of the risks covered is particularly apparent in non-life insurance. From a supervisory and legal perspective, insurance covers are usually divided into three main types: Life insurance. This type of insurance is long established and usually focuses on risks flowing from the loss of earning power by an individual and reflects the continuity or cessation of human life. Health insurance. This type of insurance focuses on the financial loss to an individual due to accident and sickness. Non-life insurance. Sometimes known as general insurance or property and casualty insurance. This type of insurance may cover a broad range of contingencies. It can be thought of as encompassing all types of insurance not included in life or health insurance. Indeed, in Australia, this is the essence of the legal definition of general insurance. There may be significant variations in the legal definitions of these types of insurance between jurisdictions. Some insurance products may be tax-advantaged that is, governments may encourage the use of insurance products through tax incentives. For example, the purchase of annuities on retirement may be tax-advantaged in order to encourage their use. In some cases, insurance covers may be provided through group insurance, often via policies held by employers for employees. The next three sections outline the main types of products in life, health, and nonlife insurance. These comments are indicative and high level only; they do not include all possible types of insurance covers or follow any particular regulatory categorization (for example, from the European Union or elsewhere). Life insurance The four main types of life insurance are traditional whole-of-life or endowment policies, universal life-style policies, pure risk policies, and annuities: Traditional whole-of-life or endowment policies. These may last until death, may contain a significant savings element (hence a surrender value), and may be participating policies. Pure endowment policies depend on survival to the end of a specified period, but endowment insurance typically also pays a death benefit during the period of the policy. These long-term policies typically have level 17

28 Insurance Supervision Core Curriculum premiums and, as with other policies with level premiums over an extended period, typically develop significant technical provisions. Universal life-style policies. This type of policy has a significant savings element and is characterized by its flexibility and transparency. Within specified constraints, the policyholder typically can vary premiums (for example, take premium holidays) and vary life insurance coverage. Reporting itemizes investment earnings, administrative fees, and charges for insurance risk. In some cases, policyholders may be able to choose how monies are invested. Pure risk policies. These have no surrender value and may cover death, disability, disability income, or trauma (critical illness or dread disease). In many jurisdictions, non-life or health insurers may also provide these products, or similar ones. Such policies typically have premiums that increase with age and are guaranteed renewable and so do not develop large technical provisions. Annuities. In exchange for an initial lump sum, the annuitant receives a regular income stream for life or for a defined period. Large technical provisions are required in respect of annuities. An immediate annuity commences payment of the income stream immediately, and a deferred annuity has an accumulation phase (perhaps with multiple premium payments) before the income stream commences. In some countries for example, Australia life insurance companies may sell investment products, in which no element of insurance cover is required. In summary, life insurance business is generally long term in nature and quite capital intensive, with varying degrees of exposure to the following risks, depending on the particular coverage: mortality and morbidity, expenses, lapses (policyholders deciding not to continue with the policy and ceasing premium payments), investment experience, and claims management (especially when benefits may be paid to living policyholders). Health insurance The three main types of health insurance include disability income insurance, medical expenses and ancillary benefits, and long-term care: Disability income insurance. Disability insurance provides coverage, often dependent on loss of income, due to disability, injury (accident), or sickness. Medical expenses and ancillary benefits. These may be in the form of annually renewable policies (analogous to annual renewable-term life policies) or longerterm permanent health policies. 18

29 ICP 19A: Statistical Basis for Insurance Long-term care. These insurance policies are intended to provide care to the elderly (typically over age 65), covering a range of benefits, including in-home care, institutional care, and sickness. Health insurance can vary greatly among jurisdictions and can be a complex area for a number of reasons: changing societal expectations and patterns of use, medical inflation and other expense management, longevity (since health care costs increase greatly toward the end of life), difficulty in obtaining good data for insurance purposes, interaction with social security health and governmental medical care programs, and claims control to address anti-selection and overuse. Where participation in health insurance is voluntary, there is also a risk of anti-selection where policyholders may seek to take out policies only when they have concluded that they have an immediate need for insurance. In summary, health insurance is an evolving and potentially complex area. Non-life insurance Non-life insurance is often classified into one of several groups (see, for example, Hart, Buchanan, and Howe 1996). The main classes of non-life insurance include stationary property, moving property, liability, and other: Stationary property, such as (a) domestic building and contents, (b) commercial building and contents, including fire or ISR (industrial special risk) covers, (c) engineering, including things like machinery breakdown and the consequences of a breakdown (traditionally boiler explosions and their consequences), (d) electronic equipment breakdown and its consequences (including loss of records), (e) money, (f) fidelity (misappropriation of goods or monies by employees), and (g) consequential loss, also known as loss of profits or business interruption cover Moving property (including property being transported), such as (a) motor vehicles, including comprehensive motor vehicle insurance, third-party bodily injury or death (often compulsory), and third-party property damage, (b) ships and boats (typically for commercial vessels, policies have internationally agreed wording), (c) aircraft, covering both own damage and third-party property and personal injury, and (d) cargo being moved by conventional means Liability, such as (a) public liability, covering claims by third-party bodily or property damage, (b) product liability coverage for manufacturers against claims arising from the use of their products, (c) professional indemnity, covering professional persons against legal liability for claims caused by professional negligence (typically professionals cannot legally practice without having such insurance in place), and (d) workers compensation, whereby employers are re- 19

30 Insurance Supervision Core Curriculum quired to compensate employees for accidental injury at work and certain workrelated illnesses and to compensate the dependents of employees who die as a result of an employment accident or injury Other, such as sickness and accident covers (typically only cancelable covers), extended warranty insurance, mortgage insurance, consumer credit insurance, and trade credit insurance. Non-life insurance is a complex and broad business, with multiple covers needed to protect a business or individual from a corresponding range of risks and their consequences. Many non-life insurance benefits are living benefits that is, the claimant remains alive and this increases the risks of fraud and moral hazard in claims management. In contrast to life insurance, non-life insurance typically is written on an annual and cancelable basis, which permits changes and concepts such as bonus-malus schemes (where individual experience can be reflected annually in the individual premiums charged), no claims bonuses, and so on. Non-life insurance typically is also more sensitive to economic conditions and exhibits the so-called insurance cycle between hard and soft markets. Reinsurance is generally a more important consideration in non-life insurance than in life insurance. Non-life insurance claims are also often subject to a severity assessment that is, the sum insured provides an upper limit on the benefit paid. Claims assessment needs to take into account things like wear and tear and age when assessing actual financial loss, and this assessment is often made only after the claim is notified. Claims in some non-life insurance classes may be very long tailed. That is, the time lag between the insured incident occurring and the insurer being notified may be significant, and the time lag between notification and payment of the claim may also be significant. Finally, changing public and legal perception and precedent may affect final claims payments. Good examples of this are asbestos and environmental claims. Examples of long-tailed non-life insurance business include public and professional liability, which typically develop significant technical provisions. Examples of short-tailed (almost commodity) non-life insurance include domestic home and content insurance and motor vehicle third-party property insurance. In summary, non-life insurance is a broad and complex area, typically encompassing all insurance covers that are not life or health covers. 20

31 ICP 19A: Statistical Basis for Insurance Exercises 8. What are the legal definitions of life insurance, health insurance, and non-life (general or property and casualty) in your jurisdiction? Can any insurance covers be written under more than one of these definitions? Are all life insurance products required to include some minimum level of life contingency risk coverage? 9. You are the founder and sole owner of a small manufacturing entity, with 10 permanent employees and a number of casual employees in peak periods. The entity owns its premises. You also have a manufacturing plant, a public showroom, and a fleet of trucks for local delivery of orders. Consider what your insurance requirements may be. 10. The insurance needs of individuals often move through a life cycle. Consider the insurance needs of (a) a student whose only possessions are a low-limit credit card and an old car and (b) a young married person who has taken out a mortgage on a new house, has a new high-paying job, a dependent spouse, two young children, and a new car. 21

32 Insurance Supervision Core Curriculum D. Quantification of insurable risks To provide insurance, the insurer needs to define the perils to be covered, since these define the benefits promised and should be accurately reflected in the policy conditions. While not pursued here, the consistency among the perils covered for pricing, the benefits promised during marketing, and legal contractual conditions is an important matter, which may be addressed, in part, through market conduct regulation. Risks usually are assessed on two criteria: Frequency of occurrence of the event. Depending on the event, multiple occurrences may be covered (for example, burglary). Severity of the event given that it has occurred. Some benefits are income streams as opposed to lump-sum payments, so the question of duration of the payment stream also arises. An example of this is disability income insurance and other forms of disability benefit. In life insurance, particularly for death benefits, the situation is generally simpler, as the severity of the event is known at inception of the policy, when the sum insured is defined. In non-life insurance, health insurance, and some life insurance (with living benefits), the benefit payment is generally determined on a strict indemnity principle, and the sum insured provides an upper limit on the benefit payable. In summary, the most common approach to insurance risks is to consider frequency of event and severity of event separately. Modeling Experience data, and claims data in particular, should be interpreted as observations of random variables. When data are then analyzed using models, various risks need to be recognized and managed: Parameter statistical variability. The parameters of the model may themselves be random variables and so subject to random fluctuations. This is the case even if the appropriate model and its parameters are known with certainty. Parameter estimation. Model parameters are usually estimated from observed data. Since they are statistics based on observations, they will not be the precise underlying parameters. Model variability. No model completely reproduces the real world. Since models are approximations and simplifications of the real world, there will be differences between model results and real-world experience. The goal is to understand how such differences may occur and whether they may be material. 22

33 ICP 19A: Statistical Basis for Insurance In summary, modeling techniques change and develop over time, and so there will be occasions when reviewing previously completed work and its supporting data can be productive and offer new insights. Historical experience The usual starting point for quantifying insurable risks is to examine historical experience. The extent to which this experience is, or should be, relied upon varies, depending on how reliable it is considered to be and the extent to which past experience is expected to repeat in the future. Judgment is required in assessing both of these matters, which implies that a range of reasonable opinions and results may emerge. Various issues need to be considered when assessing historical experience: Availability. This covers the simple matter of whether the data are available and have been recorded systematically and in sufficient volume. If not, then it may be impossible, or prohibitively expensive, to seek the data out, and all that can be done is to record the relevant data in the future and wait for sufficient data to accumulate for future analysis. Reliability and consistency. When data sets are available, they need to be tested to determine whether they are consistent, both internally and with any other data, indicators, or validation checks that may be available. They also need to be assessed to determine whether they are complete or whether only some of the relevant data have been recorded (for example, only events over a certain size or only from certain sources at certain periods). Relevance. When using data already collected, the purpose for which data was collected should also be understood, as it may be different from the current purpose. For example, medical data on conditions diagnosed may significantly understate the insured incidences of a disease, since from a claimant s perspective, the objective is to satisfy a set of criteria, whereas from a medical perspective, some judgment may be exercised, and only the real cases may be included for medical purposes. Collectively, the impact of these three points is referred to as the pedigree of the data. Modeling. A variety of techniques can be used to analyze data. Different tools may produce different results, so it is important to understand the strengths and limitations of the analysis tools used. Results. In general, results will be estimates of underlying true variables. Consequently, these estimates may be incorrect. The most common risk here is misestimation of the mean, meaning that an estimate of the mean of a distribution 23

34 Insurance Supervision Core Curriculum is not correct. A consequence of this will be misestimation of the variance and other parameters. Similarly, if trends are estimated from data for example, the trend of a change in the mean (say, mortality data reflecting improved mortality) then the reliability of this analysis also needs to be considered. The issue then is whether the possible extent of the misestimations is material or not to the outcomes of the computations. The volume of data, the pedigree, and the tools used in the analysis are important considerations in determining the level of confidence attributable to the results of the analysis. In general, individual insurers should seek to use their own data when possible, on the basis that they should have an intimate understanding of the data and their specific features. However, the volume of data often is not statistically reliable, or there are no data to support new products. In this case, insurers should consider using industry data, if available, after making due allowance for consistency and reliability. Data from the general populations for example, for medical matters may also be used but should be used with care, as insured populations differ from the general populations and the purpose for which the data were collected may be very different from the insurance purpose at hand. The large reinsurers are also potentially valuable sources of data and often have expertise in their analysis. In any event, it must always be recognized that the bases and environments in which historical data were collected may not remain valid in the future. The consequence is that projections based on historic data and patterns may not be valid in the future, not because the modeling is inappropriate, but simply because the underlying environment has changed. This highlights the ongoing need to review historical data, analyses, and conclusions reached, as their validity may fade over time. Regardless of the source of data, insurers should explicitly recognize their own specific objectives, capacities, and risk management in the development and management of new products. In summary, while historical data are a good starting point for analysis, they need to be interpreted in the context of future expectations and the specifics of the particular insurer s products and objectives. An uncertain future Insurers are essentially in business to manage the risks for which they provide cover. Insurance is an intrinsically statistical business that seeks to manage future results. The prospective nature of insurance means that the quantification of the risks involved cannot provide certainty, either for the individual obtaining the insurance or for the insurer providing the cover. However, as discussed in the previous section, the pooling mechanism is a key to the insurer s ability to manage its insurance business. 24

35 ICP 19A: Statistical Basis for Insurance A separate aspect of future uncertainty is that there may be changes in the external environment, especially in health and non-life insurance. These issues are largely outside the control of the insurer (unless it withdraws from the affected lines of business) or the supervisory authority, although sometimes they influence debates and typically are one-sided against the insurer (in that benefit payments increase). Examples include the following: Judicial changes and precedents. In some situations, the legal system provides guidance as to insurance benefit payments for example, in cases of employee injury or death. Juries and courts may set (increasing) compensation-level precedents that become the future norm. Superinflation. This occurs when, on an ongoing basis, benefit costs rise faster than inflation. Many medical and related costs show this behavior. This phenomenon tends to drive up premium rates. Overuse or increased use. This occurs when public expectations or other circumstances change, and more claims are made than historically expected. Examples of this are increased use of medical procedures, at least partly driven by fear of litigation if they are not used. Changing knowledge. For example, increased awareness and significantly changed work and usage practices have been associated with asbestos-related injuries and illness. Changing societal expectations. For example, this includes the increased awareness of the far-reaching impact of environmental damage and the need to remedy it. Changing societal habits. For example, in the so-called first world, changing eating habits are purported to be generating epidemic levels of obesity and rapidly rising rates of diabetes. Knock-on effects from these life-style changes may be expected in morbidity and mortality figures and in heath insurance results. Longevity. Average life expectancies are increasing worldwide. From an insurance perspective, this poses potential risks for living benefits, morbidity rates, and health rates (both of incidence and duration). For annuity providers, there is the risk that annuitants will live longer than expected and that their funds will not be adequate to support the promised benefits. In summary, significant influences often suggest that future experience will diverge from past experience. 25

36 Insurance Supervision Core Curriculum Risk management tools for insurers A consequence of the inherent uncertainty in developing expectations of future experience is the importance of the insurer having some tools with which to manage deviations from future expected experience. This highlights the risk to the insurer of the provision of guarantees, since guarantees may leave no opportunity to manage variations in future experience. In the same way, including options in insurance contracts also poses a risk to the insurer, as options provide an opportunity for insureds to select against the insurer when they perceive it to be in their interest to do so. In developing products, insurers should consider including the potential need to make changes, and adequate flexibility should be reflected in the policy conditions. A supervisory issue is whether these tools are used appropriately and equitably. Examples include the following: Inflation-linked policy fees. These are common in life insurance. Long-term insurance contracts include an annual policy fee, designed to offset ongoing administrative costs. This fee is linked to inflation in order to match the inflation in the costs. Premium reviews. For long-term (multi-year) contracts, policies may only be guaranteed renewable for the group of policyholders. This permits the insurer to change premiums at the group level in light of experience. For annual policies (typical in non-life and group life insurance), premiums are reset for each continuing (renewing) policy. An extreme example of this is the significant withdrawal of terrorism insurance covers following the September 11, 2001, terrorist attacks on the World Trade Center in New York. Participating policy bonuses. Participating insurance contracts have a mechanism with which to share the impact of experience between the insured and the insurer. Supervisory input and legislation may be needed to ensure that the sharing is equitable. Similar results flow through with profit sharing on other policies, such as group life or group health policies. Investment earnings. Many modern life insurance policies that offer a savings component have explicit sharing mechanisms that pass the investment risk to the policyholders. The most extreme example of this is unitized investment products, where the unit price moves directly in line with the performance of the underlying assets. Underwriting tools. When the insurer is considering offering a policy to an insured, underwriting tools provide the basis for assigning policyholders to the appropriate category of risk. Such tools include the use of policy loadings or exclusions for individuals and, in a non-life setting, the use of bonus-malus schemes, especially in motor vehicle insurance. Diversity of risk. Maintaining diversity of risk means avoiding the concentration of risk for example, avoiding geographic concentration for non-life insurance 26

37 ICP 19A: Statistical Basis for Insurance (house and content insurance) or a particular socioeconomic group in life insurance and health insurance. Reinsurance. The appropriate use of reinsurance is also a powerful tool in rebalancing and diversifying risk portfolios and reducing the potential consequences of catastrophe risks. Catastrophes are, from the perspective of the insurer, large single events, perhaps with multiple impacts on an insurer. Examples include hailstorms (house and car damage in a concentrated geographic area) and aircraft crashes in which a (relatively) large number of passenger lives are insured by one insurer. The large international reinsurers also tend to have developed deep expertise in risk management, underwriting, and claims management and so can be in a position to assist insurers with their management of these things. This can be of considerable benefit to insurers. Proper technical provisioning for guarantees and policy options. Insurers may choose to include guarantees or options in policies. Examples of the difficulties that guarantees can induce when not managed properly include Equitable Life in the United Kingdom and the impact of low interest rates on the Japanese insurance industry in the period around When guarantees and options are priced properly and provided for in the balance sheet, they are not intrinsically bad. Established control cycle management approach. Insurers should have in place ongoing processes to collect, review, and analyze experience and compare emerging experience to pricing assumptions on a regular and planned basis. Following from this, they should also have in place the processes to make the required product changes to respond to emerging experience. This may move beyond the issues of strict pricing and financial modeling. For example, if demographic assumptions underlying product development are not met, then either product changes or sales practices may need adjustment. A common case is that of products being developed with certain assumptions regarding average sum insured (used to allocate fixed costs on a relative basis). Then, when experience shows the average premium size to be significantly smaller than the presumed size, a deficiency between expenses incurred and expense allowances is generated. In summary, a wide variety of risk management tools are available to insurers. Supervisory considerations Ultimately, it is the responsibility of the insurer to manage insured risks. If an insurer is at risk of failure due to its inability to manage itself, then supervisory intervention may be required. Consideration of supervisory intervention is beyond the scope of this module. The supervisory authority can assist by prescribing and requiring minimum standards to be met and explicitly reported on. It should consider identifying early-warn- 27

38 Insurance Supervision Core Curriculum ing signals that may assist in alerting insurers and the authority of impending problems while there may still be time to address them. The supervisory authority can also assist through the collection, analysis, and dissemination of industry-wide information to the industry. Exercises 11. An insurer in your jurisdiction is proposing to develop a new insurance product. This product provides a living benefit in an annually renewable product, and the insurer intends to distribute it in a niche market. Data to support premium development have been provided by a reinsurer and are based on experience in developed first world countries. To gain public confidence, the insurer is proposing to offer guaranteed premiums (and has included a 5 percent premium loading to provide a contingency allowance for this). What is your response to this proposal? 12. Outline how future changes in the environment may affect risk factors and may affect both current and future insurance products in your jurisdiction. 13. As the supervisor in your jurisdiction, what powers do you have to require insurers to take specified actions regarding the sale of products that you consider to be priced inappropriately? 28

39 ICP 19A: Statistical Basis for Insurance E. Key elements of strategic underwriting and pricing policy At a high level, commercial insurers are generally in business to make a profit by providing an insurance service. Just as with other organizations, the corporate governance of insurers is important. It can be argued that, along with the rest of the financial services industry, insurers have an obligation to hold to higher standards of corporate governance than the norm since they have, to varying degrees, a fiduciary duty to their policyholders. This is emphasized by the long-term nature of many insurance and other financial service products. Consequently, insurers should have set corporate objectives. Boards define strategies to achieve these objectives, and the management and staff of the insurer implement the strategies. The pricing objectives of an insurer will depend on its overall strategic objectives and choices made about competitive positioning and so on. The rate of growth of an insurer, in terms of premium written, should also be managed, as overly rapid growth may imply inadequate pricing and the consequent risks of undercapitalization, inadequate risk management, or inadequate reinsurance. Underwriting strategies, at a high level, will determine the types of risk covered by the insurer and the extent to which particular types of risk are covered. The role of reinsurance in both pricing and underwriting is also important. While claims will reflect the results of the underwriting, pricing, and distribution efforts of the insurer, the efficient and effective administration of legitimate claims is also a key determinant in the success of the insurer. These strategies and choices should be contained explicitly in written and current board policies. Corporate governance is discussed in the module on ICP 9 and not pursued here. It should be expected that pricing and related strategies and policies are documented as they are propagated from the board and implemented by the insurer. These policies should become more detailed as they reach lower levels of staff in the insurer. The lower-level policies should remain consistent with higher-level policies at all times. In summary, consistent with overall good corporate governance, insurers should have in place current board-approved policies regarding insurer pricing and underwriting strategies. Pricing policy Pricing policy has three main aspects, among others (see Hart, Buchanan, and Howe 1996): Rate of return on capital. The objective is to achieve a desired or specified rate, perhaps measured over a specified period. Often called a hurdle rate of return, different product lines may have different hurdle rates. 29

40 Insurance Supervision Core Curriculum Profits. The objective is to maximize these where possible. However, this objective requires the insurer to balance the potentially competing objectives of market share and shareholder expectations and to manage both the long-term and short-term expectations of shareholders and other stakeholders. Higher-level strategic considerations also may come into play for example, if the insurer is part of an international or more broadly based financial services entity. In this case, the profit objectives and marketing opportunities of the group may interact with the profit objectives and marketing opportunities of the particular insurer (for example, in the case of captive insurers). It is important to express profits in relation to the business written for example, as a percentage of premiums written or received or, for investment products, perhaps as a percentage of funds under management. In practice, short-term profit levels achieved will vary due to many factors, some outside the control of the insurer. Consequently, it is important to understand the sources of profits as well as simply their size when assessing the longer-term profitability of an insurer. It is also important not only to consider profits from a single period but also to assess the longer-term trends in profits and their sources. So an assessment of an insurer s target profit levels is more meaningful when made in a longer-term context that includes understanding the underlying drivers of the profits. When examining future profit expectations, it is important to consider the likelihood of their achievement in light of the historical experience of the insurer as well the insurer s history of achieving its profitability objectives. Market share. The objective is to maintain or extend the current position. Often the view is taken that there are economies of scale to be realized, so the size of the insurer is a relevant consideration. However, care needs to be taken not to view any premium received as being good just because it has been received. A key question is whether the premium received generates a profit for the company or not. There is a potential risk that significant ongoing sales of unprofitable business will undermine the financial security of the insurer in the long term. The concepts of loss leader or marginally costed products fall into this category of risk. In general, the higher the required rate of return on capital, the higher the risk tolerance of the board will need to be. At a strategic level, insurers need to ensure that their expectations are consistent with their tolerance and appetite for risk. Their risk tolerance and appetite should be determined explicitly by the board and well understood by the management and staff of the insurer. These objectives may not be fully compatible with each other, so insurers will focus on specific aspects in a way that changes over time. For example, the view may be that market expansion, while costly in the shorter run, will generate overall benefits in the longer run. 30

41 ICP 19A: Statistical Basis for Insurance At any point in time, an insurer should be able to articulate the extent to which it is focusing on each of these objectives, its criteria for success in achieving its objectives, how it is assessing and monitoring progress toward its objectives, and what processes it has in place to review and reassess objectives in the long term. In some cases, insurers may deliberately cross-subsidize between products. Marginal costing is potentially an example of this. If the subsidy comes from the insurer s capital, through lower profits or depleted capital, then this is the choice of the insurer. However, if the subsidy arises through contributions from other policyholders, then the question arises of the overall equity of treatment of policyholders. For example, it is usually considered inequitable to overallocate expenses into participating products with the result that these policyholders then bear higher expenses (relative to the nonparticipating policyholders or the insurer s shareholders) and suffer lower bonuses. Even when cross-subsidies are acceptable, they are difficult to manage. As a general rule, cross-subsidies should not be encouraged. It should be clear that a pricing policy cannot exist in isolation. As discussed in more detail later, pricing depends critically on understanding the risks being covered and on ensuring that only those benefits that should be paid are actually paid. In other words, pricing, underwriting, and claims management are tightly intertwined. Policy, for one, has impacts on the others. Consistent policy, and its implementation among these three areas, is crucial to the long-term success of the insurer. In summary, an insurer s pricing, underwriting, and claims management policies should be interlinked and consistent. Underwriting policy A key technical aspect of an insurer s risk management is the control and management of underwriting risk. Underwriting is the process by which an insurance company determines whether or not and on what basis it will accept a proposal for insurance, thus offering coverage against the specific identified risks. A key tool used by underwriters is the proposal (or application) form. Proposal forms should therefore include as much of the relevant information as the underwriter needs. The principle of utmost good faith underpins the ability of the underwriter to rely on this information. In practice, not all information can be collected about all risks, so underwriters need to focus on the important information. As the size of the sum insured increases, underwriters may seek more information to improve their assessment of the risk. The quality of the proposal form, and the care with which it is completed, can have a significant effect on the quality of underwriting. Supervisors may become involved with the design of proposal forms, perhaps disallowing certain questions or perhaps insisting on the inclusion of others. Supervisory views may also be influenced by specific legal requirements. Such requirements may arise from a va- 31

42 Insurance Supervision Core Curriculum riety of sources, not only those related directly to the insurance being applied for but also broader requirements, such as anti-money-laundering initiatives. Insurers need to establish their own explicit underwriting policies. Often reinsurers provide expert assistance. Typical underlying principles include the following (see Black and Skipper 1999): Size. Groups need to be large enough to be statistically significant, especially for standard rates of premium. This usually presumes independence of members of the group. In practice, this may not always be fully achieved. A key issue is the understanding of how much the independence assumption can be compromised without seriously violating underlying principles and results. Homogeneity. Groups need to remain sufficiently homogeneous so that individuals contribute in proportion to their expected losses. There is a natural tension between these size and homogeneity requirements. In practice, a key issue is the understanding of how much the homogeneity assumption can be breached without seriously violating underlying principles and results. Balance within classes. Balance must be maintained within classes. There is a natural tendency to include poorer risks with the standard class. If this occurs, the composition of the class will change over time, and its claims experience will likely deteriorate. From a management perspective, the insurer should have in place the appropriate documentation, training, review, authorization, and monitoring procedures. There should be procedures for checking large or unusual cases. There should be clear policies regarding the use of reinsurance, both facultative and obligatory. Also, underwriters should have access to external expertise to improve their ability to address risks that are unusual in their experience. Underwriting is a complex and continually evolving discipline. It is based on the interpretation of large volumes of data and relies on statistical tools and analysis. As such, it is not an exact science, and judgment and experience are called for. It is only with the wisdom of hindsight that trends and changes become apparent. In summary, an insurer s underwriting policy should include things like the following: Lines of insurance that may be written Prohibited exposures Limits on the amount of coverage permitted by various criteria, such as individuals, geographic area, and type of insurance Criteria under which additional information is sought Approaches to defining and dealing with nonstandard risks Authorization, checking, and review procedures. 32

43 ICP 19A: Statistical Basis for Insurance The right to underwrite The private insurance industry is built on the principle of actuarial equity. This means that individuals are treated fairly in accordance with their individual characteristics. In the context of insurance, this translates to the premiums charged to an individual being proportionate to the risk that the individual poses for the insurer. In such a context, the critical importance of underwriting is apparent, as its permits like risks to be grouped together and unlike risks to be separated by underwriters using appropriate indicators and risk classification factors or tools. Other concepts of equity also exist for example, the group-oriented concept of social equity. The classification factors that insurers use should be socially acceptable. However, sometimes other views of equity lead to positions that contradict actuarial equity and may lead to the actuarial equity position becoming socially unacceptable. An example of this is the debate as to whether it is acceptable to use gender as a differentiator in determining annuity payments. That is, whether it is appropriate for males and females each with the same age and the same lump-sum deposit to receive different annual annuity payments. From the perspective of actuarial equity, there is no doubt that different life expectancies should generate different payment amounts. From the perspective of social equity, however, the view may be that, with age and lump sum being equal, annual payments should be the same. Another aspect of the need to underwrite is driven by the fact that most private insurance covers are voluntary. That is, individuals can choose whether or not to take out an insurance cover, and they can move between insurance providers. If individuals perceive that they are not getting a fair deal usually assessed in terms of actuarial equity then they can leave the insured pool. However, when the good risks leave, this degrades the risk profile of the groups remaining in the pool. The consequence of this may be that claims increase, leading to future increases in premium. When this phenomenon occurs in life insurance, it is known as a mortality spiral. Other examples of risk classification factors that are used, but may not generally be considered socially acceptable, include gender, age, place of residence, marital status, and occupation. In many countries, specific anti-discrimination laws are in place to prevent discrimination on socially unacceptable grounds. The insurance industry and its supervisors need to be aware of the need to underwrite on actuarially justified grounds and, therefore, the need to educate those with the power to grant exclusions from anti-discrimination laws (see, for example, IAAust 1997). If insurance is compulsory for a group, then the risk of mortality spirals diminishes. A community rating system, which allocates the same premium to each member of the group independent of differences in risk profiles, can work, because those who feel they are being overcharged cannot leave. However, such a system does not provide incentives either for the better risks to maintain their quality or for the poorer risks to improve their risk profile. In principle, a community rating approach in a voluntary environment probably will fail. 33

44 Insurance Supervision Core Curriculum The questions surrounding the possible use of individual genetic information in the underwriting process are not pursued here. In summary, the right to underwrite is a key to the ongoing successful existence of the insurance industry. Claims management The flip side of underwriting is claims management. The direct linkage between the two is through the policy wording. Care needs to be taken to ensure that the policy wording is precise, clear, and relevant to the policies and markets being sold into. In many cases, as with underwriting, the final judgments as to which claims should be admitted, and the extent to which they should be admitted, will contain an element of judgment. Claims management needs to be fair and firm. It needs to reflect the intent of the policy and be consistent with the intent of the underwriting. Claims payment policies and procedures need to be documented and followed. Appropriate control authorizations and sign-offs need to be in place to reduce the risk of claims mismanagement or fraud. For large claims that may take considerable time to settle, the impact of interest on initial claim amounts may be significant. The efficiency of claims payment processes is also a matter worth monitoring. In non-life insurance, in particular, claims estimates may be required pending a final settlement that may be years in the future. Claims estimation (and review) guidelines should be documented clearly and followed. In summary, good claims management is crucial to the long-term success of insurers and is linked to underwriting and pricing through the wording of policies. Exercises 14. What, if any, anti-discrimination laws or regulations are current in your jurisdiction that may affect the underwriting of insurance policies? What, if any, specific exemptions are in place, or should be in place, to permit effective insurance underwriting? 15. In your jurisdiction, what powers do you, as the insurance supervisor, have over the content of insurance proposal forms (content, change, and so forth)? 16. It has been stated that pricing and underwriting (and claims management) of policies should be consistent with each other. Discuss how this consistency can be implemented in practice. 34

45 ICP 19A: Statistical Basis for Insurance F. Underwriting Underwriting is inherently statistical in nature. The importance of good underwriting to the long-term success of an insurer is paramount. However, there may be a long time lag between the execution of poor underwriting and its manifestation through poor claims experience, and even then the link may not be clear. In practice, underwriters use a set of classification factors to assess risks. This set of factors may not include all possible factors. As the set of factors increases, the granularity of the risk classification increases, the complexity of the task increases, and the statistical validity of conclusions decreases. This introduces practical constraints, and judgment is needed in assessing where to draw the line. A key criterion is that, when the underwriters have made their classification, this information needs to be accessible and usable by others within the insurer. For example, the actuaries need to set appropriate premium scales based on the classification results, and intermediaries need to be able to explain the results to policyholders. Different levels of underwriting may be used for different businesses. Provided the risks being taken are understood, this is acceptable, but the danger is that risk information or expectations will be taken from one context and then applied in another context. The issue of simplified underwriting reflects this issue. In summary, underwriting is a discipline in its own right and is a key to the longterm success of an insurer. Life insurance: Risk factors In life insurance, the factors that influence the degree of risk for a particular insured are relatively well understood, reasonably stable over time, and easily and robustly measured. The emphasis may change, depending on the specifics of the cover sought, but the usual set of risk factors includes the following: Age (there is a very strong correlation between age and mortality) Gender Medical issues (to varying degrees of detail depending on the cover sought), such as smoking habits, personal history and current state of health, family history, and alcohol and drug use Occupation Life style, including hazardous sports and activities and other risky behaviors Financial status and risk of speculation (by the potential insured). For proposals involving large sums insured, insurers may undertake independent verification of facts and the character of the potential policyholder. All of these risk factors, which directly influence the frequency and severity of claims for a given exposure, 35

46 Insurance Supervision Core Curriculum are robust. That is, they typically are independently verifiable and so difficult for the potential policyholder to change or camouflage. The essential set of risk factors for health insurance is similar, although with different emphases. However, there is an increased potential for moral hazard in a health insurance scenario, and the underlying behavior of the risks and resulting claims is much less stable than for life insurance. In summary, the major risk factors for life insurance are typically stable and well defined. The same risk factors are generally applicable to health insurance, but with different emphases and less stability. Non-life insurance: Risk versus rating factors In non-life insurance, a distinction is drawn between risk and rating factors. Risk factors are those that are believed to influence directly the frequency and severity of claims. However, these factors may be hard to measure, or their measurement may be unreliable and open to manipulation by policyholders (exposing the insurer to the risk of deliberate anti-selection). To address this issue, insurers seek to identify other attributes of the prospective policyholder or the risks to be insured that are felt to be closely related to the underlying risk factors, but easier to measure and manage and more robust. Risks are then classified based on a combination of the reliable risk factors and other rating factors. The analysis is immediately complicated by the use of rating factors, as they are only proxies or approximations for the underlying risk factors. An example of a risk factor that cannot be identified is traffic density. This would be an expected risk factor in assessing motor insurance. A proxy, rating factor, that is commonly used is residential address, on the premise that the closer the residence is to the center of the city, the denser the traffic will be. An example of an unreliable risk factor would be the use of car color given evidence that drivers of red cars are more accidentprone than others. This risk factor can be too easily camouflaged, either by changing car colors or by changing cars! Non-life insurance, typically having to do with living benefits, is often more complex and broader in scope than life insurance, with more risk factors influencing claims behaviors. As a result, processes for calculating premiums can become quite complex, and the insurer must balance having a workable computation, on the one hand, with accuracy, on the other. As an example of how complex non-life insurance can become, the following list of factors may be relevant to private car insurance: Relating to the proposed policyholder. Age, gender, address, car usage (distance and purpose), length of time holding a driver s license, driving record, occupa- 36

47 ICP 19A: Statistical Basis for Insurance tion, level of no-claims discount achieved, whether the policyholder owns the car or not, level of deductible prepared to accept, and marital status Relating to the vehicle. Age, make, and model of car, modifications made to car, tracking devices, seatbelts or other significant safety features, color of car Coverage sought. Third-party personal liability (may be compulsory), thirdparty property damage, and comprehensive (both third-party cover and own damage). Although there is a well-developed body of knowledge around the relevant risk and rating factors for motor vehicle insurance, the business evolves and changes, reflecting different characteristics in different jurisdictions. In summary, non-life insurance is typically more complex and diverse than life insurance and often relies more heavily on a (often limited) set of rating factors. Diversity of non-life insurance A line of non-life insurance can be characterized as being either long or short tailed or as either personal or commercial. In either case, specific characteristics of the insurance covers must be considered. Particularly in the case of commercial non-life insurance, the role of the underwriters and risk managers can be important, as the risks encountered may be less homogeneous than in other circumstances and quite specific to industries or occasions. In such cases, the role of the underwriter s judgment and experience become critical, and more traditional statistically based approaches may be less applicable. The Lloyds of London syndicates have exemplified this issue in the past, and some of their failures have highlighted the significant risks that can be undertaken. Group insurance In some cases, insurance covers may be offered to a group, as opposed to the individuals in that group. In this case, the underwriting is usually done at the level of the group, not at the level of the individuals making up the group. Different criteria are used to reflect the group characteristics. Groups in life insurance are usually formed by persons who have a business or professional relationship with the owner of the contract and are then provided with insurance coverage under a single contract. A standard example is an employer taking out group life or group health coverage for its employees. Black and Skipper (1999) identify the major differences between individual and group life insurance as follows: 37

48 Insurance Supervision Core Curriculum Group underwriting (at the group, not an individual member, level) Use of a single master contract to cover the group Lower costs (due to mass distribution and mass administration) Ongoing flexibility (which increases as the size of the group increases) Experience rating (in which group experience affects future premiums). We do not consider group insurance further. The underwriting cycle An observed phenomenon in non-life insurance is called the underwriting cycle. This refers to a seeming cycle of about six years in duration during which non-life insurers profits, in aggregate, travel from being strong to being weak and back to being strong. The common explanation of this phenomenon is that increasing profits lead to business optimism and so to increased capacity and perhaps new entrants. Then the marketing efforts become more aggressive, with insurers lowering their underwriting standards as they seek to maintain their market shares. This then leads to lower profits, a decline in capacity, and stricter underwriting; the cycle begins again. Other hypotheses can also explain this observed cycle. See, for example, Booth and others (2004). This issue is not pursued further except to note that it does not relate to the earlier discussion regarding underwriting. Exercises 17. Simplified underwriting (a short standardized questionnaire) is often used for insurance products that are sold though a mass marketing approach. Discuss the risks involved with such an approach and how they may be mitigated. 18. Substandard risks are those that do not fall into the standard category. In the context of life insurance, discuss the underwriting options that may be available to increase premiums to allow polices to be issued to substandard risks. 19. In the context of non-life house and contents insurance, identify a list of factors that may be relevant in determining appropriate premiums. (Suggestion: It may be useful to obtain a copy of a typical house and contents insurance policy in your jurisdiction and review it.) 38

49 ICP 19A: Statistical Basis for Insurance G. Setting premiums While much effort is put into setting premiums, a significant element of judgment will be involved. Future experience is not certain, and different insurers take different competitive positions. Consequently, there is no single right way to determine premiums, and the setting and management of premiums can be a complex task. An insurer cannot know with certainty the extent of premium adequacy until the last policy in the block of business under consideration has been terminated and all experience on the block of policies has been defined. There is a growing trend to have actuaries set and review premiums. In some jurisdictions, this trend is well established and may be required by law, in some cases driven by precedent, supervisory encouragement, or the adoption of an increasingly professional approach by insurers, while in other jurisdictions the practice is still developing. Basic principles At a high level, the objectives when setting premiums are to ensure that they are adequate, equitable, and reasonable: Adequacy. For a block of policies, the premium payments collected plus investment earnings attributable to retained funds (technical provisions, in particular) are expected to be adequate to fund current and future benefit payments and all related expenses. This does not imply that adequacy is required for each individual policy. Equity. For a block of policies, the premiums charged should be equitable to policyholders. Premiums charged should also be consistent with the expected benefits and other costs attributable to that block of policies. This raises the issue of the appropriate allocation of expenses that cannot be linked directly to specific policies. Often these overhead expenses can be a significant proportion of the total expenses incurred by the insurer, so the matter of their allocation is material. Underwriting is the primary mechanism that insurers use when seeking to achieve equity among premiums charged to policyholders. Reasonable. Insurance premiums should not be excessive when compared to the benefits they may provide. Opinions of how to interpret excessive may vary. In some instances, the view is held that a competitive market will protect policyholders from excessive premiums. The extent to which this is valid depends on many things, including the level of true competition in the insurance market and the level of sophistication of the insurers understanding of the drivers of premiums. In many countries, the trend is for life insurance rates not to be regulated. In health insurance, premium rates are more commonly subject to 39

50 Insurance Supervision Core Curriculum regulation. For non-life insurance, the situation varies both by jurisdiction and by class of business. An important point is the meaning of expected in the first bullet point above. In general, pricing assumptions will differ from liability valuation assumptions. Where valuation assumptions are more conservative than pricing assumptions, the intent is for the insurer to hold additional provisions. These provisions then can address adverse experience in claims results, especially where this adverse experience is due to volatility in results as opposed to underlying changes in parameters. In order for premium rates to be adequate, they should include appropriate profit margins and margins to compensate for the holding of more conservative technical provisions. It is prudent, especially if there are guarantees (related to premiums or other features of the product), to include some provision for contingencies. In summary, the basic objectives when setting premiums are adequacy, equity, and reasonableness. Approaches to setting premiums At one extreme, an insurer may not conduct any analysis and instead simply adopt a premium scale used by a competitor or mandated by a supervisor. At the other extreme, insurers, especially the larger ones, can analyze (their own and others ) experience data, determine their marketing objectives, and then, through their understanding of the drivers of premium rates, seek to hone their premium rates to be competitive. The extent to which this honing process may be applied depends on the volatility and variability of expected experience, with larger contingency margins retained as the expected variation in experience increases. Traditionally, premiums have been set using deterministic formulas. The longer the term of the insurance contract, the more complex the premium-setting process becomes and the greater the involvement of the actuarial profession. For long-term, multi-year insurance contracts, the premium payment options include a single premium paid up-front, ongoing level premiums, limited-term level premiums, and increasing premiums. More modern techniques for setting premiums now extend to using projections and discounted cash flows that permit future assumptions to vary. These deterministic approaches can also be extended to statistical models. While more complex and difficult to use, statistical models may also generate a deeper understanding of the impact of deviations from expected experience. These complexities are not pursued here. In summary, there are many approaches to setting premiums. Traditionally, deterministic methods have been used, but more recently statistical approaches are being employed. 40

51 ICP 19A: Statistical Basis for Insurance The starting point for setting premiums is to identify the pure premium. The pure premium is the expected total amount of claims incurred by the group taking out the insurance cover divided by the number of members in the group, assuming that all members of the group suffer the same loss. More generally, Pure_Premium = Total_Expected_Claims / Exposed_To_Loss. For example, if experience shows that, last year, 20 deaths occurred, generating $1 million of claims in a group of 2,500 identical people (from an underwriting perspective), each with $50,000 of coverage, then the pure life insurance premium per policy would be the total amount of claims divided by the exposure, or $1,000,000 / 2,500 = $400. As explained, determining expected claims based on historical data can be difficult. In general, frequency and severity of claims need to be estimated, and severity may depend on the duration of benefit payments made. To provide the insurance cover, the insurer will incur expenses for things like commissions and other acquisition expenses, ongoing administrative and management expenses, claims-processing expenses, and perhaps taxes and other charges. Additionally, the recovery of product development expenses may warrant consideration. In theory, expenses incurred to maintain additional technical provisions or reserves and capital charges should also be allowed for. Such expenses are often expressed or determined in relative terms as a percentage of either pure premiums or expected claims. Pure premiums can then be scaled up to include an expense allowance on a proportionate basis. This gives: Office_Premium = Pure_Premium + Expenses (Initial, Ongoing, Claims/Exit, etc). Insurers are entitled to make a commercial profit and may also need to include an allowance for contingency funds in the final premium charged to the policyholder. This gives: Gross_Premium = (1 + Profit_Margin + Contingency) * Office_Premium. This simplistic derivation presumes only a single premium for a single year s worth of cover. When the cover extends over a number of years, then the terms above need to be replaced by present values of future streams of monies. When using present values, the question arises regarding the appropriate discount rates, reflecting the time value of money. In non-life insurance, a claims ratio is often used, and limits may be prescribed for claims ratios (for example, the claims ratio may not be less than 50 percent). For annual contracts, this can be a useful measure, and it is defined as: 41

52 Insurance Supervision Core Curriculum Claims_Ratio = Incurred_Claims / Earned_Premiums. In the context of the above pricing discussion, the pricing claims ratio is the ratio of the pure premium divided by gross premium. For policies under which not all the premiums received are paid out relatively quickly, the insurer must recognize its liability for such future obligations. These technical provisions arise in life insurance when the premium pattern does not match the underlying expected claims pattern and in non-life insurance when there is a significant lag between payment of the premium and resolution of the claim so-called long-tailed business. The time lags involved may cover many years. For example, in non-life insurance, asbestos claims may remain active for as much as 50 years, and in life insurance whole-of-life policies may stay in force for more than 50 years. In life insurance, where technical provisions build up to assist in providing future benefits, the issue of ownership of the assets backing these provisions arises if the policy is discontinued prior to the benefit being needed. This leads to the issue of surrender values and other non-forfeiture benefits. This is not pursued here. The determination, investment, and management of the technical provisions are major issues for insurers and supervisors. See the modules on ICP 20 and ICP 21, in particular. The question arises of the main drivers in the determination of premiums. In cases where components of the premium are intended for savings or are in the context of longer-term policies with level premiums, the development of technical provisions becomes important. In cases where initial expenses incurred exceed initial premiums received (so effectively the insurer, or its shareholders, makes a loan to the policyholder), then the issue of discontinuances arises, as the remaining policyholders need to contribute to both their own loan repayments and those for the exited policyholders. If the mortality, morbidity, or other contingency being insured against has a stronger incidence than expected, then the remaining policyholders will need to contribute premiums to support the expected new claims. If the expenses incurred by the insurer exceed those expected and priced into the premiums, then either the remaining policyholders or the shareholders-owners will need to fund these increased costs. If underwriting practices are not adequate, then the quality of the risk being undertaken by the insurer will be of a lower standard than was assumed in the premium-setting basis. If claims control is inadequate, then claims paid out may exceed those expected. Depending on the insurance cover in place and its administration, the main drivers of results, funding, and profitability will vary. For example, long-term endowment insurance products depend strongly on investment performance, whereas yearly renewable term insurance results are driven more by the impact of the mortality assumptions. These factors will affect different insurers in different ways, depending on their current position and the controls in place. In summary, premiums need to reflect the underlying contingency insured against (the pure premium), expenses, profit, and a contingency allowance. 42

53 ICP 19A: Statistical Basis for Insurance Premium and product management Independent of whether supervisory approvals are required for premiums either for new products or for changes in existing products insurers should have in place processes for controlling and managing the development of new products and the review of existing products. While the development or review of premiums is a key element of the development and maintenance of insurance products, it is not the only element to be considered. Insurers should have in place a methodology covering all aspects of product development. From the perspective of pricing, it should include documentation of the full process of premium development, such as data used, analyses done, assumptions made, models used, results, sensitivity analyses, and so on. In the broader process of product development, all other facets of the process, including the proper approvals and sign-offs, should be recorded. A product review process should exist, which would consider the prior product development process and the rationale for the decisions taken and evaluate them in light of subsequent experience. Supervisors should be able to request access to the records of product development or review processes and, based on this information, form views as to the appropriateness of not only the premiums charged but also the control process around the overall product development, management, implementation, and experience monitoring. In summary, strong management processes are needed in addition to adequate premium setting and review practices. Drivers in premium setting In summary, there are a number of drivers of insurance premiums. These can be observed from the discussion of the premium formulas. For a specific product offered by an insurer, the relative importance of these drivers will vary. Contingency insured against The starting point for premium development is the pure premium. As already discussed, the assessment of the pure premium may not be an easy task. Expenses Insurers incur expenses in the running of their business. These are often split in a number of ways: 43

54 Insurance Supervision Core Curriculum Direct and indirect. Direct expenses are those directly attributable to policies for example, commissions on sales. Indirect expenses include overhead, systems, and so on. Allowance for both direct and indirect costs should be made in premium development. Acquisition, maintenance, investment, and claims. Expenses may be treated differently depending on their source, both in general and in premium development. One-off. Some expenses are (or can be) treated as unusual and not expected to recur. While these may be treated in various ways, they generally are not included in premium considerations. The analysis of expenses and their attribution at the product level is complex and can be matter of judgment, with no single right answer. Insurers and supervisors should address the equity and consistency of expense allocations both at particular times and over time. It is not uncommon for auditors to be asked to review expense allocations, which are typically done by actuaries, to assure their appropriateness. Supervisors should review the apportionment of expenses and taxes as part of their regular inspections. Investment experience When products build up significant technical provisions, the investment of the corresponding assets is a key to the overall success of the product. Investments need to reflect the underlying characteristics of the expected liability flows and expected investment returns. This should drive considerations regarding liquidity and control of the volatility of asset values, depending on the potential variability in liability flows under different and varying circumstances. This can become critical if economic shocks reduce the value of assets, but the value of the liabilities does not change. For example, if significant proportions of assets supporting fixed benefits (such as life insurance obligations) are invested in the stock market and there is a stock market crash, there is a risk that the liabilities may exceed the assets following the crash. Hence this resilience aspect of asset-liability management (ALM) is important to both insurers and the supervisory authority. There is an important trade-off between seeking maximum investment returns and ensuring that the pricing and valuation of expected rates of return are met with an appropriate level of certainty at all times. See ICP 21. Persistency For policies that are priced on the assumption that they will stay in force for more than one premium payment, there is the risk that the policyholder will cease making pay- 44

55 ICP 19A: Statistical Basis for Insurance ments earlier than expected. Where policies go out of force because the policyholder either ceases paying the expected premiums or specifically requests a surrender (if surrender values are involved), but the insured contingency has not taken place (thereby generating a claim), the policy is said to have lapsed or discontinued. The rate at which policies discontinue can be computed as the lapse rate, and the rate at which they stay in force can be computed as the persistency rate. Then the relationship of persistency rates being one minus the corresponding lapse rates will hold. Where all expenses are not covered directly from the initial premium, then discontinuances, or lack of persistency, can be a problem for the insurer. This is because the expense recoveries expected from future premiums by the discontinuing policyholder will not be realized, and so either the insurer or other policyholders will need to support these expenses. Premium development should reflect expected discontinuance rates, and discontinuance experience should be monitored carefully. It is often the case that the pattern of discontinuance is affected by broader economic conditions. A similar issue can also arise with short-term annual policies (many non-life policies) that are allowed to be paid at higher frequencies than annually, such as monthly. Persistency can also be affected by the method of payment (for a given frequency) for example, direct debit, credit card, or direct billing. Insurance products can be structured so that poor persistency generates increased profit for the insurer. Such lapse-supported policies should be discouraged. An extreme example of this would be products that build up significant technical provisions, and so potential surrender values, but on discontinuance no surrender value is paid out. Consequently, in life insurance, it is common to find minimum surrender values for appropriate products specified in law or regulation. Economic and other external forces In particular, inflation both in general and in the context of super-inflation of benefits for long-term policies and long-tailed business may be a significant business and pricing risk. However, other factors may also intrude; see the discussion regarding the uncertainty of the future. Profit margin The insurer is entitled to expect a reasonable return on capital invested. Typically a hurdle rate of return is set as a matter of policy, and product profitability is managed to this target. The hurdle rate may vary by product or product line. As noted, the insurer cannot determine final profits until the last policy in a block has finished. For long-term policies, the insurer s capital can be tied up for long periods, so it is not unreasonable for this to be considered when setting profit margins. 45

56 Insurance Supervision Core Curriculum Competition The competitive environment places practical restrictions on the premiums that may be charged to policyholders, since for otherwise equivalent coverage and reliability there will be a tendency to seek out the lowest premium. From a supervisory perspective, if an insurer is undercutting a market, this may be cause for concern for both the longterm stability of the insurer and the viability of the market. Confidence Insurers need to hold contingency margins in case of ongoing deviations from expected results that is, errors in underlying assumptions that emerge with experience. Another aspect of confidence may be the level of experience that the insurer has with the cover being offered. When the insurer is offering covers that are new, either to the insurer or to the market as a whole, then contingency margins may also be appropriate to address the risks of poor underwriting or poor claims management until the relevant expertise is developed. It might also be expected that an insurer with no experience with a particular product may use the services of reinsurers, not only to provide risk reinsurance but also to contribute expertise for example, in underwriting and claims management. In summary, there is a common set of drivers of premiums, with different relative importance for different insurance covers. 46

57 ICP 19A: Statistical Basis for Insurance Exercises 20. You are asked to review the pricing of a yearly renewable term life insurance product. Premiums increase annually in line with expected mortality. At inception of the policy, a high up-front commission is paid to the sales agent. What are the major drivers of the pricing process? Would your answer change if the structure of commissions changed to become a level, low commission paid annually for the first six years of the policy? 21. You have been asked to review the pricing of an annual environmental damage cover for an industrial rubbish dump. What are the major drivers of the pricing process? Does it make a difference if the policy is on a claims-notified basis or a claimsincurred basis? 22. A small, recently established insurer has proposed basing its premium scales on those of a large, well-established, and highly respected insurer (for the same products). The basis for this approach is that this large insurer has access to good experience and has the capacity to perform all the necessary analysis in determining a good premium scale. As supervisor, you have been asked to decide whether this is acceptable and to justify your decision. 47

58 Insurance Supervision Core Curriculum H. Systems and processes used by insurers There are two key elements in assessing the systems and processes used by insurers to manage their business: Documentation and management. The documentation and management of the individual processes as they unfold. This includes the appropriate governance regime, accountabilities, sign-offs, and so on. Monitoring regime. Once processes are completed for example, the development of a new product the key to long-term management is regular review and assessment of experience with the ability to make corrections as necessary. This feedback loop or control cycle approach is a key to the successful management of long-term products. This is noted in the section discussing risk management tools. See also the discussion regarding reliance on independent reviews. Experience analyses To support the monitoring process, experience analyses is needed to compare expected results with actual results. Then the ongoing relevance of pricing assumptions can be assessed and, if necessary, remedial actions can be taken in a controlled manner. The depth of review will depend on the importance of the assumption being reviewed. Depending on the volume of the insurer s data available, external data from other companies, industry, or more broadly may also be assessed. This experience provides a basis on which to review and revise the assumptions needed for any revised premium calculations. In summary, well-established insurers, especially those subject to a regime similar to an annual financial condition report, have in place an ongoing annual review cycle. Pricing It is not uncommon for the roles of pricing and valuation to be carried out by separate areas within an insurer. Consistency checks between pricing and valuation assumptions should be explicitly in place. In principle, pricing assumptions will be best estimate assumptions, with valuation assumptions being more conservative as best estimate assumptions plus some margin. In some jurisdictions, the valuation assumptions are specified externally, but in others they are not. In either case, pricing and valuation assumptions should be reconciled and monitored over time. When changes to either pricing or valuation assump- 48

59 ICP 19A: Statistical Basis for Insurance tions are made, these should be managed through a secure process of change control and then used consistently going forward for example, in both new and review pricing work. A key test of the reliability of prior work is whether sufficient information is available to reproduce the prior results before moving on to their review. Where valuation or pricing assumptions are set externally, the potential for inconsistencies arises, and this should be monitored. In summary, it is important to maintain consistency between pricing and valuation assumptions. Administrative expenses Insurers should have an established budgeting process in place and then monitor experience against these budgets on an ongoing basis. Accountability should be expected at all levels and should be supported by internal and external audit work. In many cases, expenses cannot be attributed directly to products. Such overhead expenses are incurred, and their allocation between product lines for future pricing purposes may be a matter of judgment and management via an insurer s expense allocation model or process. This raises the question of whether the allocations are equitable and consistent over time. Examples include the allocation of head-office expenses, systems-support expenses, income tax expenses, and advertising expenses. In summary, the analysis and equitable allocation of expenses can be a difficult task. Management processes Supervisors should be able to review documented operating procedures governing the activities of the insurer and assess their adequacy and completeness. Supervisors should also be able to examine and establish whether the prescribed procedures are actually being followed in practice (if they are not, this indicates a lack of control). In general, internal operating procedures, followed by staff, should include functions such as the following: Segregation of duties, such as underwriting, policy issuance, and claims management Documented and enforced limits of authority Documented and enforced review and authorization procedures, especially when financial matters are involved, such as the drawing of checks for benefit payments Exception reporting on new acceptances and claims behavior Peer and manager review as expected operating practice 49

60 Insurance Supervision Core Curriculum Use of external experts for example, to assess unusual underwriting or claims situations (reinsurers are often available for this role, but the ongoing use of other experts would also be likely) Consistent reporting for all levels of reporting, the data included in the report should be reconciled over time and with other relevant data Management information, which should be produced in a regular, timely, and reliable manner and be presented in a format that is informative to the senior management receiving it. These points should be considered in the broader context of the overall management and governance of the insurer, a topic beyond the scope of this module. See ICPs 9, 10, and 18. In summary, the key to an insurer s long-term success is sound management in line with established principles of good governance. Exercises 23. In setting pricing assumptions, are insurers in your jurisdiction expected to reflect recent experience, or are they able to set these assumptions based on future (budgeted?) expectations? 24. Outline the role that independent auditors in your jurisdiction play in assessing the appropriateness of the systems and processes used by insurers to manage their business. 25. As a supervisor, what mechanisms do you have available to assess the consistency, or otherwise, of the pricing and valuation assumptions used by insurers in your jurisdiction? 50

61 ICP 19A: Statistical Basis for Insurance I. Supervisory approaches to premium adequacy Before considering adequacy, some thought should be given to the meaning of the word. Insurance is an inherently statistical business, and future experience is intrinsically uncertain. So adequate cannot be a definitive statement and must, ultimately, be a probabilistic statement. A more appropriate approach is to treat adequacy as an initial assessment of (expected) reasonableness. Premium adequacy considerations are as applicable to products already in the marketplace as to new products. In some sense, since existing products already have a block of business in force (perhaps with large premium volumes), the ongoing review of existing premium rates could be considered to be more important than the review of proposed premium rates for new products. This observation is less applicable for many non-life insurance products, which typically are renewed annually under new premium scales, although the development of new premium scales can generate significant annual workloads, for both insurers and regulators, if a proper review process reflecting recent experience is in place. The key issue from a prudential supervisory perspective is seeking to ensure the ongoing solvency of insurers so that their commitments to policyholders can be met. Other aspects of financial management affect solvency, such as capital held, risk management, liquidity, and so on. Premium rates that are expected to cover claims, expenses, loadings, and target profit margins are desirable, but they are not, by themselves, a sufficient condition to assure the ongoing solvency of insurers. In practice, such expectations may not be met each year due to variability of experience. The issue of whether it is appropriate, and if so at what level, for supervisors to review premium rates cannot be answered categorically. In an established and competitive insurance environment, with strong supporting infrastructure, it can be argued that a more effective approach to ensuring insurer solvency is for insurers to hold sufficient risk-based capital to reduce the probability of failure to a level that the supervisor considers to be acceptably low. In this context, if low premiums are charged, the insurer should be required to address the risk by holding a larger amount of risk-based capital. The appropriate approach will depend on the characteristics, history, and capacities of players in individual jurisdictions. As insurance industries and their supervisors develop in a particular jurisdiction, it is likely that the regulatory emphasis will move toward risk-based capital and appropriate risk management practices as the supervisory and business management tools. In summary, premium adequacy by itself cannot ensure ongoing solvency, but premium inadequacy poses a significant threat to ongoing solvency. 51

62 Insurance Supervision Core Curriculum Accounting data At a summary level, the after-the-event underwriting result, derived from accounting information, may be useful. The underwriting result is usually given as: Earned premium Incurred claims Associated expenses and commissions. If investment income on technical provisions is identified, then an insurance result can be obtained as: Underwriting result + Investment income on technical provisions. A positive underwriting or insurance result may encourage the perception of premium adequacy. However, these results have the inherent deficiency of being deterministic point estimates of statistical quantities and also reflect variations in accounting treatments. They implicitly assume that the business is in a steady state, since the data represent cash flows over a period. At the level of a product line, issues related to the allocation of expenses also have to be considered. Similarly, poor claims management may generate negative results. The impact of reinsurance can also be significant. Trends over time may give more insight into the ongoing experience of the insurer. In summary, relying on this style of historical accounting analysis, as it is summary and after the event, may not provide strong, reliable, or timely information to the supervisory authority. Direct review The supervisory authority may take a number of approaches to the direct review of premium rates: Reproduction. This approach involves the independent recalculation of premium rates by the supervisor. Such an approach may have initial appeal. However, it can be of limited usefulness for a number of reasons. (a) It often implies that a specific methodology must be used when determining premiums, which can inhibit the introduction of new approaches or parameters (for example, updated mortality or morbidity tables). (b) It is a time-consuming process for the supervisory authority and can inhibit development of the industry. (c) It presumes that the authority is at least as well placed as the insurer to assess both the premiums computed and the supporting data and model parameters, within the context in which the insurer intends to market the product. This can be a questionable assumption, depending on the capacity of the supervisor. 52

63 ICP 19A: Statistical Basis for Insurance Certificates of adequacy. Another approach is for the supervisory authority to require some form of certificate of adequacy of premiums. The authority can then specify the form or the certification and so require that certain issues be addressed. Such certifications may be required explicitly or implicitly as part of other reporting. These certificates may be required from the insurer or from independent third parties. This may relieve the insurer of the need to reproduce all of the premiums, but still require the authority to have the specific capacity to analyze the certificates provided, perhaps in a limited time frame. A number of jurisdictions require that premium rates for certain lines of business be subject to specific supervisory approval or notification before they may be marketed by an insurer. In other jurisdictions, if the insurer files premium scales with the supervisory authority, and the authority makes no comment or does not prohibit the use of the premiums within a certain period, then there is a default approval of the premiums for use. In such a file and proceed regime, the key supervisory issue is to determine the degree of reliance that the authority can reasonably place on the competency with which proposed premiums have been derived. Where self-regulatory mechanisms are in place for example, the use of industry bodies the supervisory issue becomes the reliability of that mechanism. The supervisory authority, through a process of reviewing premiums or a more general process of collecting industry data, should be in a position to form views on appropriate ranges for premiums and overall trends in premium for particular products (allowing for legitimate differences between insurers). This should permit the supervisor to identify outliers, perhaps for review with a higher priority, and also permit the supervisor to feed back to the industry valuable information regarding high-level industry experience. The level of the reviews undertaken, both by the insurer and by the supervisory authority, need to be sufficiently focused to ensure that specific product issues are identified, rather than lost in more general reviews of overall results and experience. Supervisors should be aware of supervisory risk when they review insurance premiums. By the very act of reviewing the premiums, when the premiums are determined to be acceptable by some criteria, there is an element of endorsement by the supervisor. Should future experience be adverse for the insurer, there is a risk of the supervisor being (or being sought to be) blamed for any losses experienced by the insurer owing to inadequate premiums, because of the supervisor s prior approval of the premium. Supervisors need to exercise care when choosing to review premiums and to ensure that they have the capacity, time, and processes in place to justify their results. More subtly, detailed approval processes by the supervisor may inhibit industry initiative. Supervisors also need to remain aware that, in principle, it is not their role to manage the insurers they regulate. That is the role of the management of the insurers. Supervisors need to avoid inadvertently crossing the boundary between supervision and management. This can be difficult, especially if there is a low level of expertise within 53

64 Insurance Supervision Core Curriculum the insurer. However, this issue should be addressed at a more general level through the licensing and intervention regime; see ICPs 6 through 10. As with other aspects of regulation and supervision, supervisors should seek to develop links with other supervisors and exchange information and experiences. Especially with the development of products new to a particular jurisdiction, the ability to draw on experience from other jurisdictions can be valuable. In summary, various approaches are available to supervisors in assessing premium adequacy. These range from performing a direct review through some form of certification to not reviewing premiums directly but focusing on risk-based capital adequacy. Impact of environment Premiums are set at a point in time and reflect assumptions about the future made at that time. It is rare for all pricing assumptions to be borne out in practice, even if they are genuine best estimates at the time (leaving aside the commercial impact of other pressures, such as competitive positioning). In some cases, the differences can be major, such as the impact of changing knowledge and expectations around issues like asbestos claims, legal precedents, and environmental matters. In a changing environment, the ability of insurers to react to changes in expectation should be considered. In this context, the risk of guarantees and policyholder options for example, guaranteed premium rates (in contrast to guaranteed renewability of cover) should be considered. If the insurer has the opportunity to make changes to premiums (levers), such as changing premium rates, operating bonus-malus schemes, allocating bonuses for participating products, and so forth, then it is important for the supervisor to understand under what conditions and to what extent the insurer actually takes remedial actions using these levers. An insurer s marketing plans may also affect the assessment of premium adequacy, depending on the level at which the assessments are made. At a company level, it should be expected that long-term premium adequacy is maintained. However, at the level of a product line or specific product, loss leaders may be used explicitly. A supervisory view on the appropriateness of this practice will strongly influence this lower-level assessment of premium adequacy. The importance of maintaining the quality of underwriting and having strong processes of claims control and management should not be underestimated. Both directly affect the assessment of premium adequacy through their impact on whether pricing assumptions are achieved in practice. In some circumstances, insurers may legitimately delay the payment of claims. However, the undue delay of claims payments should be discouraged, and supervisors should monitor paid claims development. This may be a serious issue if an insurer deliberately delays claims payments in order either to maintain solvency ratios or to enhance (apparent) profits artificially. 54

65 ICP 19A: Statistical Basis for Insurance In summary, the potential for environmental change highlights the need for insurers to maintain adequate documentation of pricing assumptions and processes and to conduct experience analyses to provide a basis for monitoring experience. Such processes and documentation should be available for the supervisor to inspect should it become appropriate. Outsourcing In some jurisdictions, it is not uncommon for insurers to outsource aspects of their product development, underwriting, or claims management. In particular, some aspects of underwriting and claims management may be outsourced to brokers. Where administrative or other back-office services are outsourced for example, within a group care needs to be taken to ensure that appropriate outsourcing arrangements are in place and that costs are accounted for appropriately and fully. See APRA Insight (2001); Joint Forum (2005). Reliance on independent reviews The actuarial profession, when developed in a jurisdiction, should provide a strong and professionally independent body of expertise that can be utilized by both the insurance industry and its supervisors. Supervisors should then expect to be able to rely on the professional expertise and competency of the actuarial profession in (among other things) the development of adequate premiums for products. See IAIS (2003c). The actuarial role can extend to all aspects of the premium-setting process, including: Reflecting and reviewing insurer objectives Ensuring the adequacy of data Setting assumptions regarding anticipated experience Adopting appropriate modeling and determination of premium scales Including appropriate contingency and profit margins Understanding the risks being taken Using product management tools to permit responses to changes in expectation as experience unfolds. In the context of ongoing review and product management, the concept of requiring a financial condition report, prepared annually for the board of the insurer, with a confidential copy supplied to the supervisor, is a strong model. The actuary who prepares the report (often termed the appointed actuary or something similar) is required to avoid conflicts of interest and to report impartially. This model is well entrenched 55

66 Insurance Supervision Core Curriculum in more established markets, where the actuarial profession is well developed. The strength and independence of the actuarial profession underpin the success of this approach. The financial condition report should cover a broad range of matters, including pricing and repricing of products, as part of assessing the current and future financial condition of the insurer. The preceding comments should not be taken to imply that actuaries are the only independent experts who can assist both insurers and supervisors. While the actuarial profession can be well versed in issues relating to technical insurance matters, such as pricing, provisioning, and capital management, other professionals can also provide valuable assistance. For example, there will likely be legal, accounting, and taxation issues to consider, underwriting and claims management are separate expert disciplines in their own right, management expertise is an effective precondition for the long-term success of insurers, and many aspects of risk management need to be addressed other than those within the traditional actuarial focus. In summary, no matter what standard processes may be in place for determining and approving premiums prior to the sale of products, supervisors should always retain the legal right to require an independent review of premiums to be carried out at their direction. This right should be a component of more extensive legal powers that permit the supervisory authority to intervene in the running of an insurer, should this be required. Exercises 26. In your jurisdiction, what processes are in place to review the adequacy of insurance premiums charged by insurers? Consider the question from the separate perspectives and responsibilities of the supervisor and the insurer. 27. In your jurisdiction, does the supervisor have the power to require independent reviews of pricing (and other) insurer functions? If so, when was this power last invoked, and how effective was the supervisory intervention? 28. What analyses does the insurance supervisor in your jurisdiction undertake to monitor industry trends in the specific context of trends in premiums and claims rates? 56

67 ICP 19A: Statistical Basis for Insurance J. Broader context Many texts are available that address the basics of insurance, typically written for university undergraduates. While most of these texts go well beyond the scope of this module, they usually include chapters addressing the basics of insurance and may also consider issues from a perspective sympathetic to a supervisory position with regard to the management of insurers. The reference list includes some well-known works: Vaughn and Vaughan (2003), Black and Skipper (1999), and Outreville (1998). The readers of these texts need to distinguish between the principles being developed and the details of their application in a particular national environment; they also need to recognize that, as the environment changes, so may the relative importance of the particular application. Other sources of information are also available. In many countries, there is an insurance institute of some form. While these bodies are typically industry based and provide qualifications to members of the insurance industry, and so may be locally focused, they also often provide education on insurance matters on a commercial basis. For example, the Chartered Insurance Institute (CII), based in England, provides a range of good educational programs and has links to more than 65 other insurance institutes worldwide (see the CII website, located at Other uses of statistics in insurance The use of statistical analysis and techniques is becoming increasingly widespread in insurance. While most topics are beyond the scope of this module, we note some areas in which statistical approaches and the resulting stochastic models are currently being applied, including: Liability calculations. See ICP 20. The Hong Kong supervisory standard for providing for investment guarantees requires stochastic modeling. See OCI (2001). Investments and asset-liability management. See ICP 21 and 22. See also Booth and others (2004). Solvency and capital adequacy calculations. See ICP 23. Australia recently introduced a general (non-life) insurance prudential regulatory regime. See, for example, APRA (2002a). Operational risk. See the comments on banking developments. Capital management. Target surplus is typically held by insurers, based on their internal assessments of probabilities of failure over specified time frames, in addition to minimum supervisory requirements. Large insurers typically apply more stringent requirements than the regulatory minimums. 57

68 Insurance Supervision Core Curriculum Pricing. The fundamental frequency and severity approach is more pronounced in non-life than in life insurance. Enterprise risk management. The intent of enterprise risk management is to manage risks, both individually and together at a holistic level. The rationale is that understanding the interrelationships between risks is as important as understanding the risks individually. This is driving the development of overall risk management strategies, sometimes with supervisory input. See, for example, APRA (2002b). Much of the theory behind enterprise risk management is statistical. Model risk Models have the potential to provide deeper insights into issues and to provide information on variability of results. With the increasing influence of statistical ideas and models in actuarial and financial mathematics, there is a commensurate increase in the complexity of the models available. The trade-off in using more complex models is that a higher level of expense and expertise is required. Typically more data and parameters are needed, and more assumptions are required to support the model. A key risk in the use of more sophisticated models is to assure that the models are set up properly and validated, the input data and model parameters are appropriate, and outputs are reviewed carefully and communicated clearly. This risk applies both to supervisors in assessing the use of such models in their industry and to the industry itself. There is a place in the business and supervisory environments for both the simpler and more complex models, provided their limitations are recognized. If the Basel II approach for banking is adopted in the insurance environment, then the assessment and acceptance of the use of supervised entities own internal risk assessment models will become increasingly important. Under this approach, models may be, or may be expected to be, developed by the industry players and then, subject to supervisory review, accepted as providing appropriate results (see Basel Committee on Banking Supervision 2004). The IAIS has taken initial steps in this direction in a recent discussion paper (see IAIS 2005). Life and non-life insurance As noted in the introduction, discussions in this module are applicable to both life and non-life insurance unless specifically indicated otherwise. Several differences have been noted, and they are summarized as follows: 58

69 ICP 19A: Statistical Basis for Insurance Single-year versus multi-year contracts Living versus death benefits Range of events generating claims Variability of non-life indemnity payments Use of rating (versus risk) factors in non-life insurances Volatility of non-life insurance results. 59

70 Insurance Supervision Core Curriculum K. Conclusion The management of direct risks in insurance is inherently statistical in nature. The insurance mechanism works due to the advantages of the pooling approach. The future is uncertain, and insurance is focused on the management of future risks. Product pricing, underwriting, and other aspects of insurance business (such as asset liability management) all are supported by the use of statistical models. Certainty cannot be achieved, and both the supervised businesses and supervisors need to recognize this. New and more sophisticated tools and models may well increase understanding of the range of possible future outcomes. However, the increased sophistication of models has to be supported by the capability of users to interpret the results. Statistical methods can provide insight into expected results and assist in quantifying the risk of business failure, whereas traditional deterministic methods and judgment based on experience may provide less insight. The insurance business is complex, with many risks to be managed in a changing environment. Data on which to base pricing, underwriting, and ongoing product and related decisions often are based on historical experience. However, the past is not a predictor of the future, so judgment and expertise are needed in order to interpret the historical experience. Many risk management skills are needed to develop an understanding of insurable risk and to develop products that provide the public with viable long-term insurance covers. In the context of this module, the roles of underwriters, claims managers, and actuaries are at the forefront of this risk management process. 60 Exercises 29. Why is it common to have suicide clauses in life insurance policies? Are these clauses appropriate? 30. The criteria used to underwrite group insurance are typically the same as those used to underwrite the corresponding individual insurance. True or false? 31. As the supervisor, you have been approached by an insurer seeking approval of the following proposal. The insurer has been asked to insure a large (for the insurer) single risk on an annually renewable basis. This risk is in a line of business that is new to the insurer. The insurer has received independent expert advice as to the appropriate actuarial premium for this risk. This premium includes a profit loading that is twice the normal profit loading used by the insurer and a further contingency margin. What is your reaction regarding the appropriateness of this? 32. For a non-life insurance policy that is an indemnity contract, explain why the insurance payouts in the event of a successful claim may be less than the sum insured. Is it always the case that such contracts may pay out less than the sum insured?

71 ICP 19A: Statistical Basis for Insurance 33. As a high-level summary statement, it has been suggested that the moral hazard is greater in health insurance than in life insurance. Explain why you either agree or disagree with this. 34. In your jurisdiction, what policies, procedures, and rights does the supervisor have to access records of an insurer to support the premium computations and product development procedures of insurers? Having accessed this information, what processes are in place within the supervisory authority to review and assess the premium adequacy? 35. It is always better to use a risk factor than a rating factor for underwriting purposes, if the risk factor can be identified. True or false? 61

72 Insurance Supervision Core Curriculum L. References APRA (Australian Prudential Regulatory Authority) Outsourcing: Issues and Risk Management. APRA Insights (4th quarter). Available at a. Actuarial Opinions and Reports on General Insurance Liabilities. Guidance Note GGN Sydney, July. Available at b. Prudential Standard GPS 220: Risk Management for General Insurers. Sydney, July. Available at Basel Committee on Banking Supervision International Convergence of Capital Measurement and Capital Standards: A Revised Framework. Basel, June. Available at Black, Kenneth Jr., and Harold D. Skipper Jr Life and Health Insurance, 13th ed. Prentice-Hall. [North American focused in detail and application of principles] Booth, Philip, Robert Chadburn, Deborah Cooper, Steven Habeman, and Dewi James Modern Actuarial Theory and Practice. London: Chapman and Hall/CRC. Hart, D. G., R. A. Buchanan, and B. A. Howe Actuarial Practice of General Insurance. Institute of Actuaries of Australia. Hossack, I. B., J. H. Pollard, and B. Zehnwirth Introductory Statistics with Applications in General Insurance, 2d ed. New York: Cambridge University Press. IAA (International Actuarial Association) A Global Framework for Insurer Solvency Assessment: A Report by the Insurer Solvency Assessment Working Party. Ottawa. Available at IAAust (Institute of Actuaries of Australia) Insurance and Risk Classification Policy: An Equitable System for All. Sydney. IAIS (International Association of Insurance Supervisors). 2003a. Principles 1: Insurance Core Principles and Methodology. Basel, October. Available at org b. The Use of Actuaries as Part of a Supervisory Model. Guidance Paper 7. Basel, October. Available at Towards a Common Structure and Common Standards for the Assessment of Insurer Solvency: Cornerstones for the Formulation of Regulatory Financial Requirements. Draft consultation paper. Basel, February. Available at www. iaisweb.org Glossary of Terms. Basel, March. Available at Joint Forum (of the Basel Committee for Banking Supervision, International Association of Insurance Supervisors, and International Organization of Securities Commissions) Outsourcing in Financial Services. Basel, February 2005, Available at Klugman, S. A., H. H. Panjer, and G. E. Willmot Loss Models, from Data to Decisions, 2d ed. Wiley-Interscience. 62

73 ICP 19A: Statistical Basis for Insurance MacDonnell, W Managing Risk: Practical Lessons from Recent Failures of EU Insurers. FSA Occasional Paper 20. London: Financial Services Authority, December. OCI (Office of the Commissioner of Insurance) Reserving Standards for Investment Guarantees. Guidance Note 7. Hong Kong, January. Available at gov.hk/oci. Outreville, J. François Theory and Practice of Insurance. Massachusetts: Kluwer Academic Publishers. Sharma, Paul, and others Prudential Supervision of Insurance Undertakings: Report of the London Working Group on Solvency II. Paris: Conference of the Insurance Supervisory Authorities of the Member States of the European Union. Vaughn, Emmett J., and Therese M. Vaughan Fundamentals of Risk and Insurance, 9th ed. John Wiley and Sons. [North American consumer focus, particularly after first chapters in section on risk management.] 63

74 Insurance Supervision Core Curriculum Appendix I. ICP 19 ICP 19 Insurance activity Since insurance is a risk taking activity, the supervisory authority requires insurers to evaluate and manage the risks that they underwrite, in particular through reinsurance, and to have the tools to establish an adequate level of premiums. Explanatory notes Insurers take on risks and manage them through a range of techniques including pooling and diversification. Every insurer should have an underwriting policy that is approved and monitored by the board of directors Insurers use actuarial, statistical, or financial methods for estimating liabilities and determining premiums. If these amounts are materially understated, the consequences for the insurer can be significant and in some cases fatal. In particular, premiums charged could be inadequate to cover the risk and costs, insurers may pursue lines of business that are not profitable, and liabilities may be understated, masking the true financial state of the insurer. There is a need to ensure that embedded options have been identified and properly priced and that an appropriate reserve has been established Insurers use a number of tools to mitigate and diversify the risks they assume. The most important tool to transfer risk is reinsurance. An insurer should have a reinsurance strategy, approved by its board, that is appropriate to its overall risk profile and its capital. The reinsurance strategy will be part of the insurer s overall underwriting strategy. Essential criteria a. The supervisory authority requires insurers to have in place strategic underwriting and pricing policies approved and reviewed regularly by the board of directors. b. The supervisory authority checks that insurers evaluate the risks that they underwrite and establish and maintain an adequate level of premiums. For this purpose, insurers should have systems in place to control their expenses related to premiums and claims, including claims handling and administration expenses. These expenses should be monitored by management on an ongoing basis. c. The supervisory authority is able to review the methodology used by the insurer to set premiums to determine that they are established on reasonable assumptions to enable the insurer to meet its commitments. 64

75 ICP 19A: Statistical Basis for Insurance d. The supervisory authority requires that the insurer has a clear strategy to mitigate and diversify risks by defining limits on the amount of risk retained and taking out appropriate reinsurance cover or using other risk transfer arrangements consistent with its capital position. This strategy is an integral part of the insurer s underwriting policy and must be approved and regularly monitored and reviewed by the board of directors. e. The supervisory authority reviews reinsurance arrangements to check that they are adequate and that the claims held by insurers on their reinsurers are recoverable. This includes that: The reinsurance program provides coverage appropriate to the level of capital of the insurer (taking into account the real transfer of risk) and the profile of the risks it underwrites The reinsurer s protection is secure. This might be addressed through different means, such as relying on a system of direct supervision of reinsurers or obtaining collateral (including trusts, letters of credit, or funds withheld). f. The supervisory authority checks that risk transfer instruments are properly accounted for in order to give a true and fair view of the insurer s risk exposure. 65

76 Insurance Supervision Core Curriculum Appendix II. Glossary of key terms In the interests of brevity, the sources provided in the IAIS glossary for each term have been omitted here (see IAIS 2006). Casualty insurance: A classification of insurance coverages used in the monoline era consisting of workers compensation, liability, crime, glass, and boiler coverages, used to distinguish such coverages from fire or property coverages. Catastrophe loss: A loss of unusual size; a shock loss; a very large loss. Class rating: An approach to rate making in which a price per unit of insurance is computed for all applicants with a given set of characteristics. For example, the rate may apply to all persons of a given age and sex, to all buildings of a certain type of construction, or to all businesses of a certain type. Excess: That which goes beyond, as excess insurance, over and above a primary amount. Experience rating: An insurance pricing system in which the insured s past experience determines the premium for the current protection. Fiduciary: A person or corporation having the duty created by undertaking to act primarily for another s benefit in matters connected with such undertaking or an agent handling the business of another when the business he or she transacts or the money or property being handled is not his or her own or for his or her own benefit. Gross premium: The premium for insurance that includes the provision for anticipated losses (the pure premium) and for anticipated expenses (loading). Equivalent term: office premium. Group insurance: Any insurance plan under which a number of employees and their dependants are insured under a single policy, issued to their employer, with individual certificates given to each insured employee; the most commonly written lines are life and accident and health. Health insurance: A generic term applying to all types of insurance indemnifying or reimbursing for losses caused by bodily accident or sickness or for expenses of medical treatment necessitated by sickness or accidental bodily injury. 66

77 ICP 19A: Statistical Basis for Insurance Indemnity principle: Of a general legal principle related to insurance, which holds that the individual recovering under an insurance policy should be restored to the approximate financial position he or she was in prior to the loss. Insurable interest: An interest that might be damaged if the peril insured against occurs: the possibility of a financial loss to an individual that can be protected against through insurance. Insurance: An economic device whereby the individual substitutes a small certain cost (the premium) for a large uncertain financial loss (the contingency insured against) that would exist if it were not for the insurance contract; an economic device for reducing and eliminating risk through the process of combining a sufficient number of homogeneous exposures into a group in order to make the losses predictable for the group as a whole. Judgment rating: The process of determining the rate for a coverage without the benefit of extensive loss experience or statistical information. Law of large numbers: Theory of probability that is the basis for insurance; the larger the number of exposure units, the more closely will the actual results obtained approach the probable results expected from an infinite number of exposures. Equivalent term: central limit theorem. Loading: That part of an insurance rate designed to cover expenses, profit, and a margin for contingencies; in some instances, an additional amount added to an insurance rate because of some extraordinary hazard or expense. Material fact: Information about the subject of insurance that, if known, would change the underwriting basis of the insurance and that would cause the insurer to refuse the application or charge a higher rate. Mispricing risk: The risk that miscalculations have led to premiums that are too low to cover the insurer s expenses related to claims, claims handling, and administration. Equivalent terms: mispricing risk, risk of insufficient tariffs, product design, and pricing risk. Moral hazard: A careless attitude on the part of an insured that increases the chance of loss or causes losses to be greater than would otherwise be the case. Nonparticipating insurance: Policy insurance on which the premium is calculated to cover as closely as possible the anticipated cost of the insurance protection and on which no dividends are payable to the insured. 67

78 Insurance Supervision Core Curriculum Participating insurance: Policies that entitle the policyholder to receive dividends reflecting the difference between the premium charged and the actual operating expenses and mortality experience of the company; if expenses and mortality are better than anticipated, so that an excess of premium has been collected, a portion of the excess then so available is returned to the insured in the form of dividends the premium is calculated to provide some margin over the anticipated cost of the insurance protection. Peril: The event insured against; the cause of possible loss. Physical hazard: A condition of the subject of insurance that creates or increases the chance of loss, such as structural defects, occupancy, or similar conditions. Pool: A risk-sharing mechanism in which the members of a group agree to be collectively responsible for losses. Postselection underwriting: An insurer s practice of reevaluating the desirability of insureds at or prior to the renewal of their policies. Prudent person approach: An approach requiring the insurer to act in the way that a prudent person would for example, by considering the risks involved, obtaining and acting on appropriate professional advice, and suitably diversifying the investments. Pure premium: The part of the premium that is sufficient to pay claims and claims-adjustment expenses, but not other expenses; also, the premium developed by dividing claims by exposure, disregarding any loading for commission, taxes, and expenses. Pure risk: A condition in which there is the possibility of loss or no loss only. Rated policy: An insurance policy issued at a higher than standard premium rate to cover the extra risk involved in certain instances where the insured does not meet the standard underwriting requirements; for example, impaired health or a particularly hazardous occupation. Retrospective rating: The process of determining the cost of an insurance policy after expiration of the policy, based on the loss experience under the policy while it was in force. Risk: In the abstract, used to indicate a condition of the real world in which there is a possibility of loss; also used by insurance practitioners to indicate the property insured or the peril insured against. 68

79 ICP 19A: Statistical Basis for Insurance Risk management: A scientific approach to the problem of dealing with the pure risks facing an individual or an organization in which insurance is viewed as simply one of several approaches for dealing with such risks. Self-insurance: A risk retention program that incorporates elements of the insurance mechanism. Speculative risk: A condition in which there is a possibility of loss or gain. Subrogation: An assignment or substituting of one person for another by which the rights of one are acquired by another in collecting a debt or a claim, as an insurance company stepping into the rights of a policyholder indemnified by the company. Substandard (impaired risk): Risks that have some physical impairment requiring the use of a waiver, a special policy form, or a higher premium charge. Suicide clause: A life insurance policy provision that limits the insurer s liability to the return of premiums if the insured commits suicide during the first two years of the policy. Uberrimae fides: Literally, of the utmost good faith. The basis of all insurance contracts both parties to the contract are bound to exercise good faith and do so by a full disclosure of all information material to the proposed contract. Underwriting: The process by which an insurance company determines whether or not and on what basis it will accept an application for insurance. 69

80 Insurance Supervision Core Curriculum Appendix III. Insurance pooling This appendix introduces the mathematics supporting the validity of the fundamental insurance principle of pooling. It is this principle that permits the insurance industry to exist. The mathematics permits quantification of risks and can lead to the assessment of probabilities and confidence intervals. The topic is approached sequentially, beginning with an individual risk model and then addressing the law of large numbers and the central limit theorem, topics that may be of interest to more advanced readers. For further details on the derivations, see, in particular, Booth and others (2004) and also Hart, Buchanan, and Howe (1996); Hossack, Pollard, and Zehnwirth (1999); Klugman, Panjer, and Willmot (2004). Coefficient of variance Assume there are n identical, but independent, policyholders. Define X i to be the random variable representing the claims made by the ith policyholder in a policy year. So the X i forms a set of independent and identically distributed random variables. Let the Expected value of X i be E(X i ) = μx i = 1,, n Variance of X i be Var(X i ) = σx 2 i = 1,, n. For future reference, note the assumption that the mean and variance of the X i are all exactly known. For completeness, also note that the expected value of X i represents the pure premium for the insurance cover. Let Y = Σ X i. That is, Y is the random variable representing the total claims for the year. The coefficient of variance (CV) of each of the X i is, by definition, CV[X] = σ X / μ X. An interpretation of the CV is that it measures the uncertainty (via standard deviation σ) relative to the expected size of the risk (via the mean μ). Now consider the random variable Y, reflecting the independence of the X i : 70 Expected value of Y is μ Y = E(ΣX i ) = Σμ X = nμ X Variance of Y is σ Y 2 = Var(ΣX i ) = Σσ X 2 = nσ X2. Hence CV(Y) = (σ Y2 )0.5/μ Y = [Var(ΣX i )]0.5 / E(ΣX i )=(1 / n0.5)*σ X /μ X =(1 / n0.5) * CV(X). As n increases, so 1 / n0.5 decreases, and the relative uncertainty of Y decreases compared to the relative uncertainty of each of the X i.

81 ICP 19A: Statistical Basis for Insurance In practice, it is unlikely that all the X i will be completely independent. Assume that any pair of the X i has a correlation coefficient less than ρ, 0 < ρ < 1. Assuming that the X i all have the same mean and variance, then it can be shown that, where Y = Σ X i, then CV(Y) is bounded above by ρ0.5cv(x). Clearly, if some of the correlations are negative, this upper bound could be significantly reduced in particular cases. That is, even after allowing for some degree of correlation between the individual claims, the relative variability of the portfolio is less than that of the individual claims. Note that CV(Y) tends not to zero as n increases, but to a number larger than zero. As ρ increases, the effectiveness of the insurance pooling declines. This demonstrates that correlated risks, such as in war, cannot be insured effectively. This analysis also supports the importance of the insurer seeking to maintain, to the extent possible, the independence of its insureds. This approach is that of an individual risk model. Large claims It is unlikely that all (potential) claims in the portfolio will be of equal size. Assume the probability of the claim of size X i, i = 1,..., n, occurring is p. That is, in this simple case, the claim amount is known for each risk in the insurance period and so is represented by a binomial probability distribution. It follows, assuming independence of the X i, that Y = Σ X i over the portfolio of the n risks considered has E(Y) = μ Y = p ΣX i Var(Y) 2 = σ Y = p(1 p) ΣX i2. It follows, therefore, that, for a fixed sum insured in the portfolio, the variance is minimized when all the claims are equal in size. Rephrased, the greater the variability of the individual claim sizes, the greater the variability of the overall portfolio and the greater the impact of the (potentially) larger claims. This supports the increased use of reinsurance when the number of relatively larger risks in a portfolio is small. In non-life insurance, due to the stricter application of the indemnity principles, which implies that a sum insured only gives an upper limit of the claim payment, the issue of this variability of size is more important than in traditional life insurance, where the size of the claim payments typically is known from inception of the policy. 71

82 Insurance Supervision Core Curriculum Variable claims frequency The previous section assumes that the probability of a claim occurring, p, is known. Now assume that the likelihood of a claim occurring is itself not known with certainty and is a random variable. Assume that the likelihood of a claim occurring is a random variable, C, with expected value E(C) = μ C = p, and variance Var(C) = σ C2. (In the previous section σ C 2 = 0) Note that C is only dealing with whether or not the claim occurs, not with the size of the claim should it occur. The size of the claim, given that it occurs, is addressed by the random variables X i. It is assumed that the occurrence and size of the claim are statistically independent of each other. With this separation of claim occurrence and claim size, a collective risk model approach has been taken. When the X i are independent and identically distributed, the individual risk model can be considered as a special case of a collective risk model. Consider an insurance portfolio with n of these identical risks, X i that is, an extension of the situation in the first section of this appendix. As before, we are interested in the total claims cost Y = ΣX i. Now there are two probability distributions to consider: the size of the claim once it occurs and the likelihood of the claim occurring. This is addressed by introducing a new random variable, N, the number of claims made. Assume that N is independent of all the claim amounts, X i, i = 1,, n. For the insurance portfolio containing n identical policies, we have the following: E(N) = μ N = nμ C = np Var(N) = σ N 2 = n 2 σ C2. Then, using the conditional probability, we get: E(Y) = E[E(Y N)] = E(Nμ X ) = μ N μ X Var(Y) = E[Var(Y N)] + Var[E(Y N)] = E[NVar(X)] + Var(Nμ X ) 2 2 = E(N)Var(X) + μ X2 Var(N) = μ N σ X + μ X σ N2. The relative variance for the insurance portfolio is seen from the coefficient of variance to be: CV(Y) = (μ N σ X 2 + μ X 2 σ N2 )0.5/μ N μ X = [(σ X2 /μ N μ X2 ) + (σ N2 /μ N2 )]0.5. Now, as n increases, the first term in the expression for CV(Y) tends to zero, since the μ N grows with N, but the second term remains fixed at n 2 σ C 2 / n 2 μ C 2 = σ C 2 / μ C2. The first term should be interpreted as variability due to the variability of the amount of claims between policies. The assumption of independence between policies leads this variability to tend to zero, as the number of policyholders increases. The second 72

83 ICP 19A: Statistical Basis for Insurance term, however, is driven by the variability in the frequency of claims. This has been assumed to be the same for all policyholders, so policyholders are not independent with regard to this, and this uncertainty does not tend to zero as the size of the portfolio increases. This second term can only be zero if Var(C) = σ C 2 = 0. That is, the likelihood of a claim is known with certainty, which in practice is not the case. Law of large numbers A slightly different view is obtained by examining the behavior of the average claim that is, Y/n. We get E[Y/n] = E(Y) / n = E [E(Y N)] / n = E(Nμ X ) / n = μ N μ X / n = μ C μ X Var(Y/n) = Var(Y) / n 2 = {E[Var(Y N)] + Var[E(Y N)]} / n 2 = 2 2 = (μ N σ X + μ X σ N2 ) / n 2 2 = (nμ C σ X + μ X2 n 2 σ C2 ) / n 2 2 = μ C σ X2 / n + μ X σ C2. As n increases, the first term tends to zero, but the second term remains constant, reflecting the systemic variance of C. See the comments regarding CV(Y). From a theoretical perspective, a version of the law of large numbers states that Limit n infinity [Probability( Y / n μ X < ε)] = 1, where ε is any arbitrary small constant. That is, the average claim cost per policy will tend toward the expected claim cost as n increases. Central limit theorem Although it is not pursued further here, the powerful central limit theorem can be used as the basis for approximate computations. Following Hossack, Pollard, and Zehnwirth (1999), if Y is the sum of n identically distributed independent random variables (X i, i = 1,, n), each with mean μ X and variance σ X2, then the distribution of the standardized random variable T = (S nμ X ) / n0.5 σ X = n0.5(s / n μ X ) / σ X has a limiting distribution, which is a normal distribution with mean 0 and variance 1. This result holds whatever the distribution of the independent random variable X may be. 73

84 Insurance Supervision Core Curriculum That is, even if the distribution of the X i is unknown, the behavior of the aggregate (S) becomes known as n increases. There is, of course, the question of how large n should be before the behavior of S is reasonably approximated by the normal distribution. In many classes of insurance, particularly in non-life insurance, the distribution of the X i is often skewed, and this tends to imply that the behavior of the tails of the distributions (for example, for reinsurance purpose) will be more difficult to deal with than is the behavior of the distribution overall. These issues are not pursued further here. Conclusion The key points to take from this discussion relate to pooling and its limits: Pooling. If the likelihood of claims is known with certainty, then pooling of homogeneous (like) claims leads to ever-decreasing relative variance of total claims for the pool. That, is the behavior of the pool becomes increasingly predictable. Limits to pooling. The assumptions underlying the first point are not fully met in practice. As a consequence, the variance of an insurance portfolio, no matter how large, will be bounded away from zero for the following reasons: (a) lack of independence (the impact of not having complete independence between the risk insured); (b) variability of the size of the risks insured (the impact of large policies in a portfolio is heightened ); (c) inherent variability in the probabilities of claims being incurred (this systemic risk cannot be diversified away by increasing the size of the portfolio). 74

85 ICP 19A: Statistical Basis for Insurance Appendix IV. Answer key Pretest 1. Is the following statement an appropriate description of insurance: Insurance is a wager for example, I bet my premium of $500 against the insurance company s $150,000 if my house burns down? No. Insurance is a means of pooling risks. 2. An insurer currently offers a life insurance product for which the premium makes no distinction as to whether the insured is a smoker or not. The insurer has proposed the introduction of a preferred insurance premium to insureds already holding policies in the current product if they can demonstrate that they do not smoke. Is this an appropriate approach? No. Those who do not smoke are likely to move to the new product, so most of those who continue to hold the current product will be smokers. The premium rates of the current product are unlikely to be sufficient to cover the higher mortality rates of a group comprised largely of smokers. 3. Two small insurance companies, with the same insured risk profile, offering identical products, and using identical policies and procedures, are seeking supervisory approval to merge. Both hold sufficient capital to have 95 percent confidence that they will be able to meet the next year s claims (as required by current solvency requirements). One of the reasons given to support the merger is that the combined company will be able either to release capital while maintaining the 95 percent confidence level of meeting claims payment or to have a higher level of confidence of meeting claims payments as a direct consequence of the merger. True. The increase in the size of the pool of risks is beneficial. Exercises 1. To what extent do insurers in your jurisdiction satisfy essential criteria a and b of ICP 19? The response depends on the specifics of the particular jurisdiction. Discuss with colleagues. 75

86 Insurance Supervision Core Curriculum 2. To what extent does your supervisory agency have in place methodologies, processes, and the expertise to assess the practices of insurers in your jurisdiction with regard to essential criteria a, b, and c of ICP 19? The response depends on the specifics of the particular jurisdiction. Review supervisory manuals and discuss with colleagues. 3. To the extent that an insurer does not satisfy some of the essential criteria a, b, or c of ICP 19, what powers and practices does your supervisory body have in place to direct and assure compliance with them? The response depends on the specifics of the particular jurisdiction. Review ICP 14 on preventive and corrective measures for information on such powers and practices and discuss those of your supervisory authority with colleagues. 4. The so-called deep pocket syndrome, in which legal juries may make larger awards when losses are covered by insurance is an example of moral hazard. True. 5. A product guarantee is not a contract of insurance since the outcome is under the control of the manufacturer. True. However, if a product guarantee is broad for example, extending beyond failures caused by design or manufacturing deficiencies it may have insurance characteristics. 6. In your jurisdiction, are maximum or minimum premium rates specified in some way by the supervisory or another authority for any classes of insurance? If so, what is the rationale supporting these imposed limits, and how are they adjusted (for example, to take into account the impact of inflation)? What risk does the supervisor take on by setting such limits? The response to both questions depends on the specifics of the particular jurisdiction. However, the supervisor runs the risk of being attributed with the setting of premiums, especially if premiums turn out to be inappropriate for some reason. 7. In your jurisdiction, what investigations do insurance supervisors conduct to assess whether the theoretically expected convergence of actual toward expected claims results occurs as insurance portfolios, reported to cover like risks, increase in size? Where such convergence is not observed, what steps may the supervisory authority 76

87 ICP 19A: Statistical Basis for Insurance (or the insurer) take? If the supervisory authority does not conduct such analyses, how does it determine whether claims behavior is showing reasonable or unreasonable volatility? The response to both questions depends on the specifics of the particular jurisdiction. Discuss with colleagues. 8. What are the legal definitions of life insurance, health insurance, and non-life (general or property and casualty) in your jurisdiction? Can any insurance covers be written under more than one of these definitions? Are all life insurance products required to include some minimum level of life contingency risk coverage? The responses depend on specifics of the particular jurisdiction. Review the insurance law. 9. You are the founder and sole owner of a small manufacturing entity, with 10 permanent employees and a number of casual employees in peak periods. The entity owns its premises. You also have a manufacturing plant, a public showroom, and a fleet of trucks for local delivery of orders. Consider what your insurance requirements may be. The responses should be the outcome of group discussions. Insurance requirements may include workers compensation, group life and health, pensions, motor vehicle, property, general liability, and product liability covers. 10. Individuals insurance needs often move through a life cycle. Consider the insurance needs of (a) a student whose only possessions are a low-limit credit card and an old car and (b) a young married person who has taken out a mortgage on a new house, has a new high-paying job, a dependent spouse, two young children, and a new car. The responses should be the outcome of group discussions. The student may need only motor vehicle third-party liability and health insurance cover. The married person is likely to need life, health, disability, property, liability, motor vehicle third-party liability and physical damage, and savings products. 11. An insurer in your jurisdiction is proposing to develop a new insurance product. This product provides a living benefit in an annually renewable product, and the insurer intends to distribute it in a niche market. Data to support premium development have been provided by a reinsurer and are based on experience in developed first world countries. To gain public confidence, the insurer is proposing 77

88 Insurance Supervision Core Curriculum to offer guaranteed premiums (and has included a 5 percent premium loading to provide a contingency allowance for this). What is your response to this proposal? The proposal is high risk. The data supplied may be inappropriate for pricing, and the guarantee is risky. 12. Outline how future changes in the environment may affect risk factors and may affect both current and future insurance products in your jurisdiction. The responses should be the outcome of group discussions. 13. As the supervisor in your jurisdiction, what powers do you have to require insurers to take specified actions regarding the sale of products that you consider to be priced inappropriately? The responses depend on the specifics of the particular jurisdiction. Review the insurance law. 14. What, if any, anti-discrimination laws or regulations are current in your jurisdiction that may affect the underwriting of insurance policies? What, if any, specific exemptions are in place, or should be in place, to permit effective insurance underwriting? The responses depend on the specifics of the particular jurisdiction. Review the insurance, employment, and human rights laws. A common exemption would be the ability to base premium rates on the age of the insured. 15. In your jurisdiction, what powers do you, as the insurance supervisor, have over the content of insurance proposal forms (content, change, and so forth)? The responses depend on the specifics of the particular jurisdiction. Review the insurance law; in some jurisdictions, all such forms must be filed with or approved by the supervisory authority. 16. It has been stated that pricing and underwriting (and claims management) of policies should be consistent with each other. Discuss how this consistency can be implemented in practice. The responses should be the outcome of group discussions, but they should address the need for the participation of underwriting and claims experts in the product development process and the ongoing monitoring of experience compared to the pricing assumptions. 78

89 ICP 19A: Statistical Basis for Insurance 17. Simplified underwriting (a short standardized questionnaire) is often used for insurance products that are sold though a mass marketing approach. Discuss the risks involved with such an approach and how they may be mitigated. The responses should be the outcome of group discussions, but they should address anti-selection by poor risks, the need to limit the number of policies or units sold to a given individual, the tendency of mass market products to perform worse than standard insured mortality, and low takeup rates, which may imply high expenses and so reduced profitability. 18. Substandard risks are those that do not fall into the standard category. In a life insurance context, discuss the underwriting options that may be available to increase premiums to allow polices to be issued to substandard risks. Your answer should address the following issues: rate up by age, various types of loadings, and exclusions. 19. In the context of non-life house and contents insurance, identify a list of factors that may be relevant in determining appropriate premiums. (Suggestion: It may be useful to obtain a copy of a typical house and contents insurance policy in your jurisdiction and review it.) The responses should be the outcome of group discussions. Relevant factors might include the size of the house, nature of construction, distance from a fire hydrant and the fire department, nature of the contents, existence of fire and burglary alarm systems, and so forth. 20. You are asked to review the pricing of a yearly renewable term life insurance product. Premiums increase annually in line with expected mortality. At inception of the policy, a high up-front commission is paid to the sales agent. What are the major drivers of the pricing process? Would your answer change if the structure of commissions changed to become a level, low commission paid annually for the first six years of the policy? The responses should be the outcome of group discussions. The major drivers of pricing would include mortality and lapse rates, expense levels, profit objectives, and competition. A level commission would decrease the risk of loss due to high lapse rates. 21. You have been asked to review the pricing of an annual environmental damage cover for an industrial rubbish dump. What are the major drivers of the pricing 79

90 Insurance Supervision Core Curriculum process? Does it make a difference if the policy is on a claims-notified basis or a claims-incurred basis? The responses should be the outcome of group discussions. The major drivers of pricing would include the nature of the materials being dumped, the physical design of the dump site, and the proximity of the dump to homes and businesses. The insurer would be liable for a much longer period under a policy written on a claims-incurred basis than under a claims-notified basis. 22. A small, recently established insurer has proposed basing its premium scales on those of a large, well-established, and highly respected insurer (for the same products). The basis for this approach is that this large insurer has access to good experience and has the capacity to perform all the necessary analysis in determining a good premium scale. As supervisor, you have been asked to decide whether this is acceptable and to justify your decision. The responses should be the outcome of group discussions. The comfort that you may derive from the work done by the large insurer should be tempered by the possibility that the new insurer may have different levels of operating expenses and commissions, market its product to different types of consumers, and apply different underwriting standards than those of the established insurer. Each of these factors might mean that the premium scale is inadequate. 23. In setting pricing assumptions, are insurers in your jurisdiction expected to reflect recent experience, or are they able to set these assumptions based on future (budgeted?) expectations? The responses depend on the specifics of the particular jurisdiction. 24. Outline the role that independent auditors in your jurisdiction play in assessing the appropriateness of the systems and processes used by insurers to manage their business. The responses depend on the specifics of the particular jurisdiction. Independent auditors typically focus their assessment on the systems and processes that affect the reliability of the financial statements. 25. As a supervisor, what mechanisms do you have available to assess the consistency, or otherwise, of the pricing and valuation assumptions used by insurers in your jurisdiction? 80

91 ICP 19A: Statistical Basis for Insurance The responses depend on the specifics of the particular jurisdiction. Review supervisory manuals and discuss with colleagues. 26. In you jurisdiction, what processes are in place to review the adequacy of insurance premiums charged by insurers? Consider the question from the separate perspectives and responsibilities of the supervisor and the insurer. The responses depend on the specifics of the particular jurisdiction. Review supervisory manuals and discuss with colleagues. 27. In your jurisdiction, does the supervisor have the power to require independent reviews of pricing (and other) insurer functions? If so, when was this power last invoked, and how effective was the supervisory intervention? The responses depend on the specifics of the particular jurisdiction. Review the insurance law and discuss with colleagues. 28. What analyses does the insurance supervisor in your jurisdiction undertake to monitor industry trends in the specific context of trends in premiums and claims rates? The responses depend on the specifics of the particular jurisdiction. Discuss with colleagues. 29. Why is it common to have suicide clauses in life insurance policies? Are these clauses appropriate? They are included to prevent anti-selection, so they are appropriate (but only for a limited period, such as two years). 30. The criteria used to underwrite group insurance are typically the same as those used to underwrite the corresponding individual insurance. True or false? False. Group underwriting criteria would include the size of the group, the age distribution of group members, the nature of work performed by members of the group, and the extent to which individuals are able to determine the amount of insurance; the health of an individual may be assessed only for those with high amounts of coverage. 31. As the supervisor, you have been approached by an insurer seeking approval of the following proposal. The insurer has been asked to insure a large (for the insurer) single risk, on an annually renewable basis. This risk is in a line of business that 81

92 Insurance Supervision Core Curriculum is new to the insurer. The insurer has received independent expert advice as to the appropriate actuarial premium for this risk. This premium includes a profit loading that is twice the normal profit loading used by the insurer and a further contingency margin. What is your reaction regarding the appropriateness of this? The approach is risky and likely viewed with disfavor. 32. For a non-life insurance policy that is an indemnity contract, explain why the insurance payouts in the event of a successful claim may be less than the sum insured. Is it always the case that such contracts may pay out less than the sum insured? The payouts in the event of a successful claim may be less than the sum insured because the value of the item may have declined over time (for example, due to wear and tear). However, such contracts do not inevitably pay out less than the sum insured. An agreed amount policy may have been entered into. 33. As a high-level summary statement, it has been suggested that the moral hazard is greater in health insurance than in life insurance. Explain why you either agree or disagree with this. It is true. Health insurance is (generally) a living benefit. 34. In your jurisdiction, what policies, procedures, and rights does the supervisor have to access records of an insurer to support the premium computations and product development procedures of insurers? Having accessed this information, what processes are in place within the supervisory authority to review and assess the premium adequacy? The responses to both questions depend on the specifics of the particular jurisdiction. Review the insurance law and discuss with colleagues. 35. It is always better to use a risk factor than a rating factor for underwriting purposes, if the risk factor can be identified. True or false? False. 82