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Actuary: Fap3-5

Module 3: Risk in Actuarial Problems

Section 5: Recognize Problem Commonalities

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Objectives

• Describe aspects of actuarial work that are both fundamental and common to all practice areas.
• Categorize commonalities in actuarial problems.
• In the reading m3s5-02_ActuarialConcepts.pdf, an actuary identified some of the key concepts about which you have already learned including:
  • Asset-liability management (ALM) (i.e., manage your assets and liabilities together).
  • Individual and collective models (i.e., each problem requires a consideration of data, assumptions and methods).
  • Assumptions, conservatism, and adjustments (i.e., materiality and approximation).
• A number of key, common concepts have been introduced. These concepts are common to actuarial problems in all areas of actuarial practice, including life insurance, health insurance, and retirement benefits. These include:
  • Economics of risk.
  • Selection of risk.
  • Random variables.
  • Actuarial equivalence.
  • Time value of money.
  • Individual and collective models
• Read Economics of Risk (m3s5-03_EconomicsofRisk.pdf) to see how financial security systems have been developed to cope with the financial consequences of economic risk that cannot be avoided by the individual.
• Matching elements of a DB pension plan with corresponding pedestal in the finiancial security system graphic:
  • Plan design - Selection of risk - by deciding which employees may enroll in the plan and the relative benefits offered.
  • Annuity purchase - Reinsurance - where the sponsor (who is providing insurance to the employees) transfers longevity risk to an insurance company.
  • Plan sponsor - Hedging strategy - by pre-funding future payments.
• Matching elements of a social insurance pension plan with corresponding pedestal in the finiancial security system graphic:
  • Plan design - Selection of Risk
  • Intergenerational transfer - Hedging Strategy
  • Reduction in coverage through mandated private pensions and tax breaks - Reinsurance

Common Actuarial Concepts: Selection of Risk

• All actuarial problems have elements of classification, selection, and anti-selection inherent in their solutions.
  • Actuaries classify individuals by age, sex and occupation, among other criteria. The categories into which individuals are sorted constitute the classification system.
  • Trowbridge: “The process by which a financial security system determines the category appropriate for each individual is a selection. The tendency for individuals to exploit, or select against, classification or selection is anti-selection. A constant interplay between selective and anti-selective forces is inherent in financial security systems.”=
  • Anti-selection occurs when an individual uses the classification system to personal benefit and against the provider.
  • Actuaries manage the problems associated with this interplay.
• Classification systems are constantly evolving through the work of actuaries. For example, smokers used to be able to buy life insurance for the same price as non-smokers. Modern classification systems set smokers and non-smokers into two separate classes with separate premium rates.
• Selection can result in a straight decline (i.e., the individual is not allowed coverage by the financial security system). In other instances, the individual may be covered but at substandard rates (i.e., higher prices).
• Anti-selection inevitably leads to a more refined classification system and selection process. As information becomes more widespread and as financial security systems compete for individual clients, the less refined system becomes uncompetitive. In employee benefit plans and pension plans, anti-selection is often controlled by the plan design.
• Actuaries work within financial security systems to manage the effect of the selection process. The selection process directly affects the actuary’s pricing work. The article "Evaluating Managed Care Effectiveness: A Societal Perspective" (m3s5-04_naaj0110_7.pdf) provides background to the external forces relevant to managed care within the United States. It also provides the overview of a model that demonstrates the interaction among the various stakeholders in the managed care environment.
• Managed care is offered and administered by entities known as managed care organizations (MCOs). Managed care plans offer financial incentives for enrolled participants to use health care providers that contract with the MCO. Characterized by such contractual arrangements between insurers and providers, managed care plans range from loosely controlled preferred provider organizations (PPOs) to tightly governed health maintenance organizations (HMOs).
• Managed care, in one form or another, has been around for more than 50 years. For example, prepaid employer-based health care coverage dates back to the late 1920s, when Blue Shield and Blue Cross Plans first agreed to reimburse physicians and hospitals for the cost of services provided to plan members. The market for health care coverage began to develop in earnest after World War II. Anxious to attract and keep good workers in a tight labor market and stymied by wage controls, employers looked for additional benefits they could offer employees.
• All of the following are stakeholders in the managed care system: Insurers, employers, providers, consumers, regulators and policymakers.
• The Stakeholder Relationship Model is premised on the following:
  • All stakeholders will support the diverse needs of the enrolled population.
  • Stakeholders will develop business strategies that do not negatively affect the success of the other stakeholders.
  • Stakeholders will share information and performance measures, and be held accountable for results.
  • Stakeholders will support the long-term needs of the entire managed care population.
• These trends could have a significant effect on the effectiveness of future managed care systems: Demographic change, changing employer funding and purchasing practices, consolidation among payers and providers, trends in performance measurement and regulatory activity.

Common Actuarial Concepts: Random Variables

• Probability models are common to all actuarial work. Learn more about this by reading Random Variables and Multi-Dimensional Cash Flows (m3s5-05_RandomVariables.pdf). Actuaries often replace a random variable with a constant in the formulas that form the basis for their models. The constant is often set to the expected value of the random variable. For which random variables and in which actuarial problems is this process common?
• Pension actuaries often rely heavily on the mean of the total claims random variable to establish funding recommendations for a pension plan. To estimate the benefits payable under a pension plan, a model and model parameters are required. The parameters involved in estimating the pension plan benefit cash flows include, salary increase rates, termination rates, mortality rates and retirement rates. For most pension plans, the expected value (mean) of the total claims is used.

Common Actuarial Concepts: Economics of Risk—Revisited

• Cash flow analysis and asset-liability management are common actuarial concepts in many actuarial problems. Read Economics of Risk: Revisited (m3s5-06_EconomicsofRiskRevisited.pdf) to learn more.
• Actuarial equivalence is often used to provide appropriate adjustments to the underlying liability cash flows. Many financial security systems allow the individual a choice in coverage by the financial security system or in payout from the financial security system. These choices are permitted on the basis of actuarial equivalence; that is, the value of each choice is said to have the same actuarial present value. The actuarial present value is the lump sum amount, discounted for interest, of the expected cash flows under each choice. This actuarial equivalence calculation depends on a specific set of actuarial assumptions (model parameters). The assumptions need not hold for an individual and anti-selection by an individual could result. For example, a member in poor health will trade a lifetime annuity for a current lump sum payout on an actuarial equivalence basis.
• Applications of actuarial equivalence used in practice areas include:
  • Life insurance: Non-forfeiture options, dividend options.
  • Retirement benefits: Optional annuity forms, early retirement reductions.
  • Group insurance benefits: Cafeteria plan options, medicare drug benefit.
  • Social insurance: Retirement age.

Common Actuarial Concepts: Time Value of Money

• Another commonality is the concept of the time value of money, which is central to most actuarial problems. The time value of money is, in fact, a building block for actuarial science. Read The Time Value of Money (m3s5-07_TimeValue.pdf). This material first appeared as chapter 4 in the “Fundamental Concepts of Actuarial Science” by Charles Trowbridge.
• In large measure, the time value of money arises from the natural human preference for present goods over future goods.
• In the long run, a business will be successful only if the return on capital employed is greater than the rate of interest.
• Lenders require adequate security, or raise the interest rate, to reflect the risk that the loan may not be repaid, or that the loan will be repaid in depreciated dollars.
• The concept of the time value of money (i.e., money today is worth more than money sometime in the future) leads to the practice of a lender charging a borrower for money. In essence, the borrower is paying “rent” (or interest) for the privilege of using the lender’s money.
• Although the preference for present money may explain some borrowing, such as borrowing to purchase a home, there are other reasons for borrowing. For example, businesses require capital goods in order to prosper. To get those capital goods, businesses will borrow money if the capital can be productive; that is, if the business can earn more by using the money it borrows than it spends in interest on the loans. On the other side of the transaction, the lender also finds his capital being productive…he earns more when he lends money than when he does not.

Common Actuarial Concepts: Individual and Collective Models

• The final concept that is common to all actuarial problems is that of the actuarial model. Read Individual and Collective Models (m3s5-08_IndividualAndCollectiveModels.pdf).
• Pricing is the determination of the premiums or contributions to be charged to an individual by the financial security system for future participation in the system. Through a pricing system, the actuary determines the appropriate balance between the individual’s liability and asset cash flows. This often involves analysis of the present value of the asset and liability cash flows at “point of sale” or, more generically, entry into the financial security system. Pricing also involves consideration of administrative expenses, enterprise risk, investment risk and profit (if any).
• In some instances, the aggregate liability is determined using the individual model applied on a client-by-client basis and summing the individually determined liabilities. In other instances, the aggregate liability may be determined directly for the whole group. Aggregate assets often come from two main sources. The first source is the financial assets currently held by the financial security system (e.g., cash, bonds, equities and real estate). The second source is the operational assets available to the financial security system from its clients (e.g., future premiums or contributions). Once current assets and liabilities have been estimated, the funding process is intended to deal with any imbalances; that is, surplus assets or funding deficiencies.
• Summary:
  • The individual model provides the framework for an individual’s relationship with a financial security system. Key concepts in the individual model are the liability cash flows (payments to the individual) and asset cash flows (payments by the individual). Cash flows are defined by at least three variables: the time at payment, the amount of payment, and the probability of payment.
  • The collective model, on the other hand, is used to manage risks related to the financial security system as a whole. The relationship between the financial security system and its clients is balanced on an aggregate or group, rather than individual, basis. Collective models include pension plans and blocks of life insurance. In many instances (pension plans, for example), aggregate liabilities are determined as the sum of individual liabilities.

Models and Modeling to Manage Risk

• Read Introduction to Models and Modeling to Manage Risk (m3s5-09_Models_v1.pdf).
• Deterministic component is defined as "a representation of an aspect of a given phenomenon expressed without the use of random variables."
• The core concepts of Risk Analysis and Management for Projects (RAMP) are 1) Identifying the risk; 2) Analyze the likelihood and seriousness of adverse events occurring; 3) Recognize options to mitigate; and, 4) Identify ways to control remaining risks.
• A stochastic component usually requires more information. Many actuaries start with a deterministic component and then construct a stochastic component when they have more information.
• It is better to have a vague or partial answer to the right question than to have a complete answer to the wrong question.
• All of the following should be considered when selecting a model:
  • Data available to create or validate your model
  • Models already available to address your question
  • The audience for your modeling results
  • Your understanding of the underlying assumptions