The Experts In Actuarial Career Advancement. Product Preview. For More Information: or call 1(800)

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1 P U B L I C A T I O N S The Experts In Actuarial Career Advancement Product Preview For More Information: Support@ActexMadRiver.com or call 1(800)

2 TABLE OF CONTENTS Section A Understanding the Principles of Risk Management LRM , The Theory of Risk Capital in Financial Firms A-1 to A-4 LRM , Rethinking Risk Management A- 5 to A- 10 LRM , The Theory of Risk Capital in Financial Firms A-11 to A-22 LRM , Rethinking Risk Management A-23 to A- 26 CIA: Dynamic Capital Adequacy Testing (DCAT) Educational Note, November 2007 (pp. 1-33) A-27 to A- 38 ERM Specialty Guide, May 2006, Chapters 1-6 A-39 to A- 50 Risk Appetite: Linkage with Strategic Planning A-51 to A- 58 Describing Risk Culture, The Actuary, August 2012 A-59 to A- 64 Section B Understanding the Various Sources of Risks faced by an Insurer Gregory, Chapter 8, Credit Exposure B-1 to B-4 Gregory, Chapter 9, Quantifying Credit Exposure B-5 to B-12 Gregory, Chapter 15, Wrong Way Risk B-13 to B-20 SN LRM , Mapping of Life Insurance Risks, AAA Report to NAIC B-21 to B- 24 SN LRM , Moody s Looks at RM & the New Life Insurance Risks 2000 B- 25 to B- 28 SN LRM , Liquidity Risk, Saunders and Cornett, Ch. 17, pp B- 29 to b- 36 A New Approach for Managing Operational Risk, SOA Research 2008 B- 37 to B- 50 Section C Understanding important risk management techniques along with their uses and limitations, and being able to perform risk measurement calculations LRM , Study Note on Parameter Risk C-1 to C-4 LRM , Value-at-Risk: Evolution, Deficiencies and Alternatives C- 5 to C- 8

3 LRM , Stress Testing, OSFI E-18 C- 9 to C-12 LRM , Value at Risk Uses and Abuses C-13 to C-16 LRM , Measures of Financial Risk, Dowd, Ch, 2, pp C-17 to C-20 LRM , A Short, Comprehensive, Practical Guide to Copulas, GARP, Oct C-21 to C-26 LRM , Stress Testing, A Robust End to End Approach, GARP, Oct C-27 to C-32 LRM , Diversification: Consideration of Modeling Approach & Related Fungibility and Transferability, CRO, Oct. 2013, pp. 4-14, C-33 to C-42 How Fair Value Measurement Changes RM Behavior in the Insurance Industry, SOA-Rosner 2013 C-43 to C-52 Economic Scenario Work Group Report C-53 to C-56 Academy Interest Rate generator: Frequently Asked Questions (FAQ) June 2014 C-57 to C-60 Summary of Variance of the CTE Estimator, Risk Management Newsletter, August 2008, Issue No. 13 C-61 to C-62 Getting to Know CTE, Ingram, Risk Management Newsletter, July 2004, Issue No. 2 C-63 to C-64 Section D Understanding of the principles of modeling, cash flow testing and asset-liability matching, and performing related calculations Asset Liability Management, Ch. 2, Defining Asset liability Management D- 1 to D- 8 Asset Liability Management, Ch. 3, Why Did ALM Become Important D-9 to D-14 LRM , ALM for Insurers D-15 to D-22 LRM , Life Insurance Forecasting and Liability Models, Exclude appendices D-23 to D-28 LRM , Key Rate Durations: Measures of Interest Rate Risk D-29 to D-32 LRM , Revisiting the Role of Insurance Company ALM w/in a RM Framework D-33 to D-36 LRM , Chapter 13 of Valuation of Life Insurance Liabilities, Lombardi D-37 to D-42 LRM , Chapter 14 of Life Insurance Products and Finance, Atkinson-Dallas Section 14.4 only on ALM Matching D-43 to D-44

4 Individual Life and Annuity Life Risk Management SECTION A

5 SN LRM A-1 SN LRM THE THEORY OF RISK CAPITAL IN FINANCIAL FIRMS Note from the author: It is important to understand what is risk capital, how risk capital is measured, how risk capital is accounted for in the calculation of profits and finally to learn the economic cost of risk capital. I. Introduction A. Features of principal financial firms 1. Credit-sensitivity of customers: Their customers can be major liability holders. 2. High costs of risk capital: Their opaqueness to customers and investors. 3. High sensitivity of profitability to cost of risk capital. B. What is Risk Capital? 1. Smallest amount that can be invested to insure value of firm s net assets against a loss in value relative to risk-free investment of those net assets. 2. Volatility of change in value of net assets is most important determinant of amount of risk capital. 3. Differs from regulatory capital that attempts to measure risk capital according to particular accounting standard. 4. Differs from cash capital that represents up-front cash required to execute a transaction. 5. Cash capital is component of working capital. C. Summary 1. Amount of risk capital depends only on riskiness of net assets. 2. Economics costs of risk capital are spreads on price of asset insurance arising from information costs and agency costs. 3. Full allocation of risk capital is generally not feasible. II. Measuring Risk Capital A. First 3 examples 1. Risk Capital and Asset Guarantees. 2. Risk Capital and Liability Guarantees. 3. Liabilities with Default Risk. B. Conclusions from these 3 examples 1. Different accounting balance sheet. 2. Very similar risk-capital balance sheets. 3. Same amount of risk capital because underlying asset is the same. 4. Only difference is which party bears the risk of insuring asset a. Example A: The insurance company. b. Example B: The parent. c. Example C: The note holder.

6 A-2 SN LRM C. A More General Case 1. Basic functions of capital providers a. All provide cash capital and all are sellers of asset insurance b. Provide risk capital: Cash required for purchase of asset insurance; almost always performed by equity holders. 2. Cash capital is determined by assets of firm. 3. Risk capital is determined by riskiness of net assets of firm. 4. Debt and equity represent the netting of asset insurance against provision of riskless cash capital and risk capital. D. Contingent Customer Liabilities 1. Riskiness of net assets will in general differ from riskiness of gross assets. 2. It determines type of insurance required to permit default-free financing. 3. It determines amount of risk capital. III. Accounting for Risk Capital in The Calculation of Profits A. Risk capital is used to purchase insurance on net assets. B. Insurance is a financial asset. C. Gains/losses on this asset should be included in calculation of profitability. D. Allocating costs of risk capital to individual businesses may be a problem. E. Any allocation must be imputed because highly risky principal transactions often require little or no up-front expenditure of cash. IV. The Economic Cost of Risk Capital A. Spread paid over fair market value firm pays in purchase of insurance. B. Reasons for spreads are adverse selection, moral hazard and agency costs. C. Spreads will be higher because of opaqueness of principal financial firms. D. Cost of risk capital will depend on form in which insurance is purchased. E. Spreads on each form are determined differently. F. Task for management is to weigh spread costs of different sources of asset insurance to find most efficient way of spending risk capital. G. In calculating expected profitability risk-capital costs should be expensed along with cash-capital costs.

7 SN LRM A-3 V. Hedging and Risk Management A. Hedging risk exposures reduces asset risk. B. Hedging market exposure reduces required amount of risk capital. C. If there are spread costs for risk capital and they depend on amount of risk capital, then reduction in risk capital from hedging will lead to lower costs of risk capital if hedges can be acquired at relatively small spreads. VI. Capital Allocation and Capital Budgeting A. Incremental cost of risk capital is proportional to incremental amount of risk capital. B. Diversification can dramatically reduce firm s overall risk capital. C. In effect, businesses coinsure one another requiring less external asset insurance. D. If marginal risk capital is used for allocation among businesses, some risk capital will not be allocated to any business. E. Conclusions 1. Full allocation of risk capital overstates marginal amount of risk capital. 2. Risk capital evaluated on a stand-alone basis overstates marginal risk capital. F. Risk capital is a function of 1. Riskiness of net assets affected by correlations among business units. 2. Value of net assets affected by their correlation with broad market. VII. Summary and Conclusions A. Amount of risk capital is uniquely determined and depends only on riskiness of net assets. B. Amount of risk capital is not affected by form of financing of net assets. C. Risk capital is used to purchase asset insurance. D. Economic costs of risk capital are spreads on price of asset insurance that stem from 1. Information costs. 2. Agency costs. E. Risk capital of multi-business firm is less than aggregate risk capital of businesses on stand-alone basis. F. Full allocation of risk capital across individual businesses is generally not feasible. G. Attempts can significantly distort true profitability of individual businesses.

8 A-4 SN LRM VIII. Technical Appendix A. Risk Capital = A 0 F(1,1,0,T,σ).4A 0 σ T where 1. F(S,E,r,T,σ) = Black-Scholes formula for European call option on stock. 2. S = Initial value of stock. 3. E = Exercise price. 4. r = Riskless rate. 5. T = Expiration date. 6. σ = Volatility of profits. IX. Questions A. Define what is risk capital and how it differs from regulatory capital and cash capital? B. How is risk capital determined? C. How is risk capital accounted for in the calculation of profits? D. What is the economic cost of risk capital?

9 ERM Specialty Guide A-39 ENTERPRISE RISK MANAGEMENT (ERM) SPECIALTY GUIDE, MAY 2006 CHAPTERS 1-6 Note from the author: It is important to understand the various definitions of ERM, the various elements of the COSO Report and the ways ERM can contribute to value creation. Also, it is important to learn the organizational objectives for pursuing ERM, the definition of risk appetite and how it can be measured and finally the way economic capital is calculated. I. Introduction A. Enterprise Risk Management Defined 1. Definition of the Casualty Actuarial Society a. Discipline by which an organization in an industry assesses, controls, exploits, finances and monitors risk from all sources for the purposes of increasing organization s short and long term value to its stakeholders. 2. Definition of COSO a. Process, effected by entity s board of directors, management and other personnel, applied in strategy setting and across the enterprise, designed to identify potential events that may affect the entity, and manage risk to be within its risk appetite, to provide reasonable assurance regarding the achievement of entity goals. 3. ERM is an ongoing generic process. 4. ERM applies broadly to all risks and to all organizations. 5. ERM definitions also stress the value creation. 6. Meaning of term Enterprise a. Auditing/Process Control nuance: control processes. b. Investments and Finance: portfolio. 7. It is the holistic aspect of enterprise that makes the difference: the contribution to overall portfolio risk rather than risk associated with each individual investment. B. A Context for Risk 1. Generally, appropriate context is that of entire enterprise because a. It aligns with Portfolio Theory. b. It is consistent with economic decisions facing organization. c. It aligns with stakeholders perspectives. 2. By reducing risk, enterprise may reduce capital and hence costs. 3. Investor is only concerned with risk and return of enterprise in total. C. A Case for Actuaries 1. Actuaries are experts in quantifying insurance risk. 2. By way of training, actuaries may quantify other types of risks and their interactions.

10 A-40 ERM Specialty Guide II. Why is ERM Important? A. Drivers of change and development of the discipline of ERM 1. Regulatory developments a. Basel Committee on Banking Supervision b. COSO Committee of Sponsoring Organizations c. In 1992, new regulations by London Stock Exchange. d. In 1995, US interpretive bulletin dealing with selection of annuity providers. e. In 1994, NAIC issued solvency regulation for P&C companies. f. In 2002, Sarbanes-Oxley Act aimed to keep internal controls up to date. g. Development of national standards on Risk Management h. COBIT: Control Objectives for Information and Related Technology. i. Supervisory authorities: OSFI, UK Financial Services Authority, US S&P and Moody s Financial Institutions. 2. Rating agency views a. They increased their surveillance on topic of ERM. b. They evaluate strengths of organization with respect to ERM. c. They ask questions about internally developed economic capital models. 3. Aspects of ERM upon which rating agencies are focusing most are Asset Liability Matching, Investment risks, Liability or pricing risk and Risk transfer. 4. The COSO Report a. Methodology inspires confidence by offering definite framework for ERM. b. COSO stresses ERM as iterative process that aligns risk response with strategic objectives of enterprise. 5. The 4 Categories of Objectives of the COSO Report a. Strategic: High-level, designed to support entity s mission/vision. b. Operations: Efficiency of operations. c. Reporting: Reliable financial and operational data and reports. d. Compliance: Compliance with laws and regulation. 6. The 8 Components of the COSO Report a. Internal Environment: structure, assignment of authority, development of personnel, risk appetite, management style, ethical values and culture. b. Objective Setting. c. Event Identification: Internal and external. d. Risk Assessment. e. Risk Response: Avoidance, Acceptance, Reduction and Sharing. f. Control Activities. g. Information and Communication. h. Monitoring.

11 ERM Specialty Guide A Limitations of ERM: Factors affecting quality of ERM a. Judgment. b. Breakdowns. c. Collusion. d. Cost versus Benefit. e. Management Override. 8. Actuaries Response to COSO: Greater emphasis on a. Risks external to entity and outside of management s control. b. Interdependent risks and cross-functional issues. c. Coordination of risk management within the entity. d. Transparency of the risk management system. e. Reputation of the firm. f. Quantification of risk. g. Long-term evaluation of risk: scenario planning and stress testing Basel Capital Accord a. Components of capital: equity capital and disclosed reserves. b. For supervisory purposes: second tier of capital: reserves and debt capital instruments Basel II Accord a. Pillar 1 : Augmenting minimum capital standards. b. Pillar 2 : Robust implementation of supervisory review of capital assessments. c. Pillar 3: Market discipline. 11. Economic Capital: Capital and risk management system must a. Use a basic risk-return framework. b. Be an integral part of corporate culture. c. Have management buy-in and support from stakeholders. d. Be consistent and coherent. e. Be dynamic and up to date. f. Be well researched and balanced. g. Be inclusive and cooperative across organization. 12. Conglomerates: Greater need for good corporate governance and coherent risk management. 13. Convergence of financial products, markets, globalization a. Banking has taken lead in risk management. b. P&C companies made significant advances. c. Important to learn and start with existing infrastructure.

12 A-42 ERM Specialty Guide 14. Board attention due to public s demands for certain assurances a. Sarbanes-Oxley Act of b. Established Public Company Accounting Oversight Board (PCAOB). c. Private, non-profit organization. d. All US accounting firms must register with PCAOB. e. Additional standards required by PCAOB. B. ERM Impact on Management Practices 1. Company s mindset toward ERM determines efficacy of risk management. 2. No single effort can produce greater results than developing risk management culture. 3. ERM must have a voice at executive management level: Chief Risk Officer (CRO). 4. CRO establishes channel for 2-way communication throughout organization. 5. RM responsibility must be independent of risk-taking functions. 6. ERM team affords company enterprise-wide view of opportunities and threats. 7. Ways a company can train for liquidity risk event a. Through crisis planning, modeling and stress testing. b. Liquidity crisis teams identify and manage risk events. C. Other ways that ERM can contribute to value creation 1. ERM can help enterprises to optimize capital and reduce exposure to risk. 2. Essential to survival. 3. First step: outline risks and quantify each one. 4. Next, a dynamic financial model is developed that recognizes all courses of capital available: equity, debt and insurance. 5. Total average cost of capital (TACC) a. Cost of debt x debt value/firm value, plus b. Cost of equity x equity value/firm value, plus c. Cost of insurance x insurance value/firm value. D. Organizational objectives for pursuing ERM 1. Competitive advantage. 2. ERM can influence business strategies. 3. ERM can help achieve business objectives and maximize shareholder value. 4. Transparency of management (reduction of agency costs): ERM involves a. Setting risk appetite and policy. b. Determining organizational structure. c. Establishing corporate culture and values. 5. Decision-making: Risk adjusted return plays important role. 6. Policyholder as a stakeholder: ERM can improve risk transparency to regulators, rating agencies and equity analysts.

13 ERM Specialty Guide A-43 III. Enterprise Risk Management Process A. Risk Control 1. Process of identifying, monitoring, limiting, avoiding, offsetting and transferring risks a. Identification of risks. b. Risk evaluation: frequency and severity. c. Monitoring of risks. d. Risk limits. e. Risk avoidance through design of products, investment programs and operational procedures. f. Offsetting risks through ALM and hedging. g. Transferring risks mainly through reinsurance. h. New product review. 2. Primary objective: To maintain risks retained at levels that are consistent with company risk appetites and company plans. B. Strategic Risk Management 1. Process of reflecting risk and risk capital in strategic choices that company makes a. Economic Capital: Realistic risk capital is calculated. b. Risk Adjusted Product Pricing. c. Capital Budgeting. d. Risk Adjusted Performance Measurement. 2. Primary objective: Optimization of risk adjusted results for the organization. C. Catastrophic Risk Management 1. Process of envisioning and preparing for extreme events that could threaten viability of enterprise a. Trend Analysis. b. Stress Testing: Impacts include financial, reputational, regulatory, credit ratings, etc. c. Contingency Planning. d. Active Catastrophic Risk Management. e. Problem Post Mortem. f. Catastrophic Risk Transfer. 2. Primary objective: To anticipate potential disasters in order to develop contingency plans to minimize their impact on enterprise.

14 A-44 ERM Specialty Guide D. Risk Management Culture 1. General approach of firm to dealing with its risks a. Risk Assessment. b. Best Practices. c. Support: Budget priority, access, authority and public statements. d. Communications and transparency. e. Reinforcement. 2. Primary objective: To create situation where Operational, Strategic and Catastrophic Risk Management take place without direct oversight of CRO or Risk Committee. IV. Decision-making A. Areas where ERM may cause changes in decisions 1. Asset/investment strategy. 2. Product pricing and design. 3. Annual business planning. 4. Reinsurance purchasing. 5. Strategic planning process. 6. Product/business mix. B. Key step is clarifying company s risk appetite. C. What is Risk Appetite? 1. Level of aggregate risk that a company can undertake and successfully manage over extended period of time. 2. Initially, establish corporate objectives: minimum surplus ratio, industry rating. 3. Establish range of possible future outcomes achieving risk-specific performance goals. D. How can Risk Appetite be Measured? 1. For regulatory or statutory basis: profits, capital and surplus, ability to pay claims. 2. For GAAP or IAS basis: profits, equity. 3. For economic basis: economic value, economic profits, embedded value, embedded value earnings. 4. Measures for risk tolerance a. Probability of ruin. b. Tail value at risk (TVAR) or conditional tail expectation (CTE). c. Below target risk. d. Economic cost of ruin. e. Value at risk.

15 ERM Specialty Guide A-45 E. How can a Company Define its Risk Appetite? 1. Board of Directors and Management ask for a. Good-risked based decision-making and effective use of capital. b. Identification of approach to determine capital position. c. Manage earnings volatility. d. Comply with regulatory changes. e. Improve corporate governance. f. Manage tail risk. g. Improve industry rating. h. Improve communications. 2. Methods and tools to identify risk appetite at executive level a. Survey and discussion. b. Analyze past and historical choices. c. Risk analysis on a single/multiple alternative(s). d. Delphi method. e. DFA-type stress analysis. f. Ask directly. 3. Employees Considerations a. Company culture. b. Physical workplace environment. c. Salary and benefits. d. Flexibility of work hours. e. Opportunities. f. Qualities of direct manager. g. Performance measures. h. Work/life balance flexibility. 4. Policyholders: Expectations a. Good standing with regulators and rating agencies. b. Payments of non-guaranteed elements at levels anticipated at time of sale. c. Attractive and competitive product offerings. d. Fair claim payment practices. 5. Rating Agencies a. Capital requirement is key criterion. b. Both quantitative and qualitative approaches are used. c. Economic Capital may become standard for all audiences. 6. Regulators: long-term solvency of company a. Operating limits. b. Minimum Capital Requirements: Risk-Based Capital in US. c. Supervisory Reviews: driven by risk mapping grid process.

16 A-46 ERM Specialty Guide F. How Do You Create the Strategies to meet these Demands? 1. Processes established for managing market and insurance risks a. Risk modeling and measurement. b. Economic capital calculation. c. Risk identification and prioritization. d. Internal risk monitoring and reporting. e. Risk control and mitigation. f. Risk aggregation. g. External risk communication. h. Risk-related performance measurement. 2. Risks insurer will measure a. Interest rate, equity, credit and currency. b. Liquidity, mortality, morbidity. c. Lapse/surrender. d. Property/real estate. e. Catastrophe. 3. Actions to take for better trade-off between risk and return a. More advanced ALM strategies. b. Strategies for hedging equity risk. c. Risk transfer vehicles. 4. Quantifying operational risk is more difficult and less developed. a. Stems from people, processes, systems and events. b. It can be managed using a control framework. 5. New tools that can be established a. Economic capital. b. Optimization routines. c. Fuzzy logic. d. Risk mapping and correlation. 6. Controls a. Limits on assets classes to ensure diversification. b. Individual name limits to control credit risk. c. Limits on certain types of business. d. Duration mismatch targets to mitigate interest rate risk.

17 ERM Specialty Guide A-47 G. How will decisions be made within a risk management control/committee framework? 1. Levels of integration of information: Global, Entity, Risk category, Function and Business. 2. Sources a. Enterprise Governance Getting the Balance Right. b. The Turnbull Report and Implementing the Turnbull Report. c. Restoring Trust The Breeden Report. H. What are the risks to succeeding at these strategies? 1. Support from the Board and upper management is essential. 2. Decisions must be made within established framework. 3. CRO, risk committee, line risk managers. 4. Additional up-front time and resources. 5. Roadblocks a. Resource issues. b. Modeling or measurement issues. c. Data or information system constraints. d. Level of complexity. e. Lack of clarity, of objections or benefits. f. Credibility of results. 6. Risk management must become part of performance management or incentive compensation plans a. Return on risk-based capital: actual versus target. b. Adherence to specific risk guidelines. c. Increase in risk-adjusted value. V. ERM Implementation A. Exercise in change management. B. An individual or a small team must have primary responsibility to implement ERM. C. What is important is the process. D. Risk adjusted ROE should become key component in executive compensation. E. Business unit managers must have close relationship with CRO. F. Accurate and consistent risk measurement is important. G. One key challenge in conglomerate is specifying a uniform time horizon 1. In banks, convention is to adopt a one-year horizon. 2. Insurance companies are typically capitalized for longer decision horizons.

18 A-48 ERM Specialty Guide H. Risk Management Structure 1. Link between central and local risk management should be clearly defined. 2. Group Risk Reporting a. Operating companies decide their risk appetite, measure their risks and decide how to manage risk/return. b. Group risk aggregates results. 3. Group Risk Quality Control a. Operating companies decide their risk appetite, measure their risks and decide how to manage risk/return. b. Group risk checks quality of risk measures and issues suggestions. 4. Group Risk Monitoring a. Group risk and operating companies decide risk appetite. b. Operating companies measure their risks, decide how to manage risk/return and address issues raised by group risk. c. Group risk analyzes results and raises issues. 5. Group Risk Management a. Group risk and operating companies decide risk appetite. b. Group risk measures all risks. c. Group risk analyzes results and makes recommendations. d. Operating companies decide how to maximize return given their risk limits. 6. Group Risk/Return Management a. Group risk decides risk appetite, measures all risks and decides what to do to change risk/return profile. b. Operating companies execute group risk s decisions. 7. Corporate Risk Department a. Should frequently test and monitor reserves and capital adequacy. b. Needs to be responsible for limit setting. I. Relationship Performance Measurement: Management must have incentive to use risk information to support better decision-making. J. Risk-Based Pricing 1. Rarely do prices consistently reflect risk. 2. Use of internal credit rating models is a step in right direction. 3. Important to look at a portfolio level. K. Transfer Pricing should be the responsibility of local business units.

19 ERM Specialty Guide A-49 VI. Situations in which implementing ERM has added value and/or avoided significant losses A. Recent failures 1. Highly rated insurer had to sell itself because it miscalculated financial risks associated with major reinsurance treaty. 2. Large multi-line carrier was unaware of its total exposure to a single natural catastrophe, until catastrophe occurred. 3. US insurers face fines, policyholder restitution and near-crippling damage to their reputations because of misleading sales practices. B. ERM has added value where management teams make decisions that 1. Exploit firm s true risk-taking capacity. 2. Complement existing risk profile. 3. Further overall strategic objectives. C. Recent situations where ERM has created value and/or avoided losses 1. Variable Annuity Risk Management a. Use of a hedge designed to offset losses due to potential decline in assets. b. Use of sophisticated dynamic hedging program. 2. Securitization: To raise capital and transfer risk a. Closed Block Securitizations. b. Regulation XXX Securitizations. c. UK recent securitizations utilize concept of Embedded Value. 3. Calculation of Economic Capital (EC) a. Based on calculations specific to company s risks. b. Different from Regulatory or Rating Agency Capital. c. Calculated on basis of expected future cash flows. d. EC models are often underpinned by explicit stochastic distribution models allowing more sophisticated calibration and interpretation. e. EC is sufficient surplus capital to cover potential losses at a given risk tolerance level and over a specified time horizon. f. Common methodology is to base EC on probability of ruin, amount of ruin or other expected shortfall measures. g. Probability of ruin is probability that liabilities will exceed assets on a PV basis at a given future valuation date. h. May use CTE measure or specified percentile approach. 4. Types of Risk Covered: SOA Survey a. Interest rate risk, pricing risk and credit risk. b. Equity market risk, liquidity risk and operational risk. c. Almost 60% of respondents were calculating EC and 24% plan to do so within the near future.

20 A-50 ERM Specialty Guide VII. Questions A. What is the CAS definition of ERM? B. What is the COSO definition of ERM? C. What are the 4 categories of objectives of the COSO Report? D. What are the 8 components of the COSO Report? E. Identify ways ERM can contribute to value creation. F. What are the organizational objectives for pursuing ERM? G. What is risk appetite and how can it be measured? H. How is economic capital being calculated?

21 SN LRM D-29 SN LRM KEY RATE DURATIONS: MEASURES OF INTEREST RATE RISKS Note from the author: It is important to learn the definition and advantages of the key rate durations concept, the profiles of various types of bonds and the 3 propositions identified in the document. I. Introduction A. Yield curve movements affect each type of bond differently. B. Most commonly used measure of interest rate risk exposure is effective duration 1. Proportional change in security value / Infinitesimal parallel shift of the spot curve. 2. When effective duration is high, security is exposed to significant interest rate risk. 3. Often inadequate because spot curve rarely moves in a parallel fashion. C. Key rate durations 1. Vector representing price sensitivity of a security to each key rate change. 2. Advantages a. Key rate durations can identify the price sensitivity of an option-embedded bond to each segment of the spot yield curve. b. It recognizes that yield curve movement is driven by multiple market factors. c. It is easy to use it to create a replicating portfolio of a bond with embedded options using zero-coupon bonds. 3. It has broad applications to fixed-income portfolio management. 4. It is useful in analyzing more complex option-embedded securities.

22 D-30 SN LRM II. Key Rate Durations A. Modeling Non-Parallel Yield Curve Shifts 1. The sum of key rate durations is identical to the effective duration. 2. S(t) = R*(t) - R(t). 2. S(t) = Shift (t), R(t) is the initial spot curve and R*(t) the shifted spot curve. 3. Author chooses a set of 11 key rates t(i): 3 months, 1 year, 2 years,..., 30 years. 4. The yield curve shift can be approximated by linear interpolation of key rate shifts. B. Basic Key Rate Shifts 1. b[t;1,d(1)] = d(1) for 0.00 < t < 0.25 = d(1) x (1 t) / ( ) for 0.25 < t < 1.00 = 0 for 1.00 < t < b[t;i,d(i)] is the i th basic key rate shift of term t with the level of shift being d(i). 3. The 11 independent basic key rate shifts can approximate all the small yield curve shifts. 4. S[t;d(1),..., d(11)] = b[t;1,d(1)] b[t;11,d(11)]. C. Kay Rate Durations 1. P* - P = - P D(i) d(i). 2. P is the security price initially and P* is the price with the shift of the key rate. 3. D(i) is the i th key rate duration and d(i) the shift defining the i th basic key rate shift. 4. P* - P = - P D(1) d(1) P D(11) d(11). 5. Proposition 1: Key rate durations are in fact a linear decomposition of effective duration. 6. D = D(1) D(11). D. Numerical Example. E. Key Rate Durations and Alternative Schemes 1. 3 types of yield curve movements a. Level: Represented by all key rates moving by the same amount. b. Steepness: Represented by short rates moving more than long rates. c. Curvature: Represented by short rates dropping while long rates rise. 2. Much of the yield curve movements can be explained by these 3 movements. F. The Link Between Key Rate Durations and Pricing Models 1. Models entail changes in spot rates over time that result in arbitrage-free price movements for all securities in the market. 2. Valuation takes the spot yield curve as a given. 3. AR models directly specify subsequent arbitrage-free movements. 4. AR models are uniquely capable of motivating key rate durations of bonds with embedded options.

23 SN LRM D-31 III. Key Rate Duration Profiles A. Key rate duration profile: plot of key rate durations against the terms of all the key rates. B. Zero-Coupon Bond 1. All key rate durations are 0 except on maturity date. 2. Key rate duration of a zero-coupon bond must lie on the 45 o line. C. Coupon Bond 1. Key rate durations increase and decrease with the term. 2. Significantly large key rate duration at maturity. D. Callable Corporate Bond 1. Callability greatly changes the interest rate risk exposure of the bond. 2. Clearly callability shortens the effective duration. 3. Callable bonds are more sensitive to shorter-term key rate changes. 4. Callable bond with lower coupon rate has less probability of being called. E. Callable Bond with a Sinking Fund 1. Sinking fund clearly reduces the effective duration of the bond. 2. Sinking fund makes the bond more sensitive to shorter-term key rates. 3. Analysis shows crucial difference between pricing and risk exposure of publicly traded bond and private placements. F. European Call Option 1. Option is insensitive to changes of any key rates with a term before expiration date. 2. Key rate duration for expiration date is negative. G. European Put Option 1. Key rate duration profile is almost the mirror image of European call option. 2. Magnitude of key rate durations is not the same. H. Embedded Option in a Callable Bond 1. Option is insensitive to short-term key rate movements. 2. For American options there is no longer only one expiration date but a range of them. I. GNMA Pass-Through 1. Prepayment option significantly affects key rate durations. 2. Key rate duration profile is a smooth bell-shaped curve.

24 D-32 SN LRM J. Principal-Only (PO) and Interest-Only (IO) GNMAs 1. Key rate duration profile shows high interest rate risk exposure of a PO. 2. PO performs like a call option. 3. Key rate duration profile of IO is mirror image of PO except in magnitude. K. Summary: Key rate durations must be actively monitored when used for bond strategies. IV. Key Rate Durations in a Portfolio Context A. Key Rate Durations of a Portfolio 1. w(j) = V(j) / V for j = 1... m. 2. w(j) is the proportion of the bond position to the portfolio value, or weight. 3. V(j) is the value of the j th bond position. 4. The sum of all the bond position values must equal the portfolio value V. 5. The bond portfolio consists of m bond positions. 6. Proposition 2: D(i) = w(1) D(1,i) + w(2) D(2,i) w(m) D(m,i), for each i = D(i) is the portfolio i th key rate duration. 8. D(j,i) is the j th bond position i th key rate duration. B. Identifying Interest Rate Bets using Key Rate Durations 1. If a portfolio is constructed to have the same key rate durations as a bogey or index, the portfolio must have the same interest rate risk exposure as the bogey or index. 2. If assets have same key rate durations as liabilities, portfolio is immunized against any yield curve shifts, as long as the shifts are sufficiently small. C. Constructing Hedge Ratios for Option-Embedded Bonds 1. Proposition 3: Given the key rate durations of a bond or a portfolio, a portfolio of zerocoupon bonds can be constructed such that the portfolio has the same value and interest rate risk exposure of the underlying bond or portfolio. 2. A portfolio of option-free bonds is needed and a set of hedge ratios are needed. 3. Portfolio of option-free bonds must be revised dynamically. V. Conclusions. VI. Appendix Adjusted Key Rate Durations. VII. Questions A. What is the definition and the advantages of the key rate durations concept? B. Give the various key rate duration profiles of different types of securities. C. What are the 3 propositions that were derived by the author of this document?