PAK Study Manual Foundations of CFE (CFE) Exam Fall 2015 Edition

Transcription

1 PAK Study Manual Foundations of CFE (CFE) Exam Fall 2015 Edition CTE Hull-White Ito s Lemma Agency Theory Reinsurance Risk Neutral Corporate Finance Stochastic Simulation Efficient Market Hypothesis Regime Switching Lognormal Dynamic Hedging Economic Capital Behavioral Finance Martingale Value at Risk Dividend WACC Delta

2 PAK Study Manual for CFE Fall 2015 PRODUCT FEATURES Features PAK Study Manual PAK Exam Aid PAK Memorization Aid PAK Test Aid PAK Video of the Week PAK Study Manual Basic Package Summaries X X X Relevant Past Questions (List) X X X 150+ Practice Questions X X X Case Study Analysis X X X 10 Mock Questions X X X Suggested Schedule (Detailed) X X X Support X X X Mock Questions X X X 150+ Practice Questions X X X Past Questions (Sorted PDFs) X X X Condensed Summary X X Electronic Flash Cards X X Mock Exam X X X Weekly Videos X X X Bonus materials Online Videos Videos for Past Questions Practice Question Set PAK Study PAK Online Manual Premium Seminar Package X X X X 1

3 PAK STUDY MANUAL 1. Summary The PAK Study Manual covers the entire Foundations of CFE (CFE) syllabus. Not only does it give you the detailed explanations on conceptual, calculation, and exam materials, but it also fills in the gaps among the topics that are not covered in the source readings. It helps you better understand and master the confusing logics and difficult materials. In addition, it links the similar topics across readings together and connects them to the syllabus so that you can see the whole picture of this exam. 2. Relevant Past CFE/FETE SOA Exam Questions (List) For each reading, we compose a list of relevant past exam questions (if any) so that you can locate the questions quickly and practice them immediately. This saves your time on searching what materials are relevant to this exam. 3. Case Study Analysis (New) This set connects the case study materials to the study materials so that you can see the picture on how they can be tested Practice Questions One key point to pass this exam is to "practice" (Practice makes perfect!). Due to this reason, we include many practice questions in each reading to refresh the materials just learnt and to strengthen your knowledge. More practice will be available in the PAK Exam Aid Mock Exam Questions The mock exam questions mimic the same difficulty level of the real exam questions. 10 mock exam questions and solutions are included in the PAK Study Manual to challenge your understandings. More practice will be available in the PAK Exam Aid. 6. Suggested Study Schedule (Detailed) The syllabus is huge. It is very easy to lose track on your study. A clearly defined study schedule and some useful tips are included to help you better manage your schedule. 7. Support Get questions? Please send me an NOTES 1. The availability date of the case study analysis may be different. It depends on when the SOA releases the new case study. 2. If the SOA do not release the case study, an additional 5 mock questions will be used to replace the case study analysis. The study materials were very helpful in preparing me for the exam. Most importantly I was better able to apply the things that I learned to exam style questions. By Marc Roberts Read the whole story DO YOU KNOW? The PAK Study Manual and related aids are updated EVERY exam sitting. You will see the most updated materials, examples, and explanations to help you master the concepts and pass this exam in the first attempt. PAK MEMORIZATION AID 1. Electronic Flash Cards Summarize the key points (with mnemonics) (PDF version is also available) Work best for any big-screen cellular phone or mp3 player (e.g. iphone, HTC, Android, Nook, etc) 2. Condensed Summary Summarize the key points in outline format Quickly refresh all the important topics in the readings PAK TEST AID 2 1. Mock Exam This set of mock exam is different from those mock questions available in the PAK Exam Aid. You can write down your answers and send them to me. I will give you detailed feedbacks on how to improve your exam score

4 PAK EXAM AID Mock Exam Questions and Solutions The mock exam questions mimic the same difficulty level of the real exam questions. 30 mock exam questions and solutions are included to challenge your understandings Practice Questions (New) One key point to pass this exam is to "practice" (Practice makes perfect!). Due to this reason, we include many practice questions in each reading to refresh the materials just learnt and to strengthen your knowledge. They are different from the practice question set in the manual. 3. Past SOA Exam Questions (from All FSA Tracks) Relevant to This Exam This set not only includes the past exam questions from the CFE/FETE exam, but also includes the past exam questions from all the other FSA exam tracks (e.g. FETE, APM, CSP, DP, etc). It helps you better understand how the materials were tested and gets you familiar with the SOA exam question style. PAK VIDEO OF THE WEEK (NEW) DO YOU KNOW? You can find the most updated information about the PAK Study Manual and related aids under the Announcement section on the front page of the PAK website. 1. Videos discussing confusing topics and concepts. 2 Videos explaining calculation-related examples. 3. Video reviewing the case study. 4. Weekly video answering common students' questions. 5. It will be launched on 5/30. The PAK study package is fantastic! Paul and Eddy are very helpful and quick to answer any questions By Sarah Bryant Read the whole story RELEASE SCHEDULE Summaries Features PAK Study Manual 5/15 and 6/30 PAK Exam Aid PAK Memorization Aid PAK Test Aid PAK Video of the Week PAK Study Manual Basic Package PAK Study PAK Online Manual Premium Seminar Package 5/15 and 6/30 5/15 and 6/30 Relevant Past Questions (List) 6/30 6/30 6/ Practice Questions 6/30 6/30 6/30 Case Study Analysis 6/30 6/30 6/30 10 Mock Questions 6/30 6/30 6/30 Suggested Schedule (Detailed) 5/15 5/15 5/15 Support Anytime Anytime Anytime Mock Questions 8/30 8/30 8/ Practice Questions 8/30 8/30 8/30 Past Questions (Sorted PDFs) 7/30 7/30 7/30 Condensed Summary 8/15 8/15 Electronic Flash Cards 8/15 8/15 Mock Exam 9/15 9/15 9/15 Weekly Videos 5/30 5/30 5/30 Bonus materials To Be Announced Online Videos 5/30 and 6/30 Videos for Past Questions 8/30 Practice Question Set 8/30 3

5 PAK ONLINE SEMINAR 1. Over 80 videos to clarify and explain the key concepts/calculations in the readings of the entire syllabus 2. Discuss the past exam questions and what questions might be asked on the upcoming exam 3. Videos reviewing exam tips and techniques that can help you to maximize your score 4. Review the new version of the case study and discuss which sections are important, and how they might be tested 5. Contain condensed outlines for each reading 6. Practice Question Set (150 questions) to test your knowledge 7. Review the lectures and study at your own pace, on any PC, Mac, smartphone, and/or tablet device 8. All videos are available in MP3 (audio) format 9. Instructor support via and PAK Forum support to help you to clarify any section of the syllabus 10. Free access for 2nd attempt (only for those who scored 2-5) SAMPLES? You can find more samples on the PAK website. IMPORTANT NOTES 1. Please note that all products are in electronic (PDF) format. No hard copy is provided. 2. Once you make a purchase (please use your work address), we will send you a confirmation within 1 business days Once the files are available, we will send them to you through . Please make sure that you put the correct address when you purchase the PAK products. If you do not receive the confirmation , please send us an (services@pakstudymanual.com). 3. Please check your junk mailbox. Sometimes, our is blocked. DO YOU KNOW? If you are not sure which exam track to take, or how it can advance your career, you can send an to Paul or Eddy and discuss your situation with them. They will share their work experience with you so that you can make your decision informatively. MORE INFORMATION Want more information? Please contact us at eddy.chan@pakstudymanual.com, paulpeterson@pakstudymanual.com, or visit COMMENTS FROM THE PAST CANDIDATES You can find more comments from the past candidates here: PAK Testimonials. WHERE TO PURCHASE PAK PRODUCTS The PAK products are available at Actex, Actuarial Bookstore, and SlideRule Books. 4

6 Frequent Answer Questions Do You Need to Read the Source Readings? Unlike the preliminary exams, reading the source readings (textbooks, SOA study notes, and online readings) is a must in the FSA exams. PAK Study Manual can help you understand the materials faster and memorize them quickly so that in the time-limited environment, you can be well-prepared for the exam. How Much Time is Needed to Study for This Exam? This varies by person. Usually it will take one hours to study for a FSA exam (5-hour). Please expect to spend the same amount of time for the CFE exam. Study Schedule From the date the SOA release the new syllabus to the exam date, there are around 4 months to study. How to plan your study schedule? T=2.5 months T=0 T=3.5 months T=4 months Read the Source Readings Review Again Practice Read the Source Readings Assume you take the SDM exam in this exam sitting. In general, it will take one 2 to 2.5 months to finish them. To study more efficiently, I highly suggest you following the steps below: Step 1: Define Your Own Study Schedule - Use the suggested study schedule as a reference - Prepare your own study schedule (Target and Expect to read the whole syllabus and the past exams 2 or 3 times before the exam Step 2: Read the Source Readings Together with the PAK Study Manual - Write down your notes in the study manual - Highlight all the key points there (Will be used for memorization later) - Label any calculations that you will go over again later - Go over the related past exam questions once you finish that reading Step 3: Read the SOA Past Papers - Read them once you finish your first-round of readings (use the PAK Exam Aid) - Understand how the topics were tested and how the questions were answered Review Again After completing the three steps above, you probably have a general idea about how the exam looks like. Now you should review the source readings again but this time focus more on the key topics, clarify the confusing concepts/calculations, think of what can be tested and read them carefully (use my mock exam questions) Practice The last month is the most critical month. Here are the steps: - Practice the past exams and my mock questions to identify what you still do not know - Go back to the readings and find your answers (or send me an if you need help) - Start memorizing the key points (use the PAK Memorization Aid) - Use the PAK Test Aid to test your knowledge (Send me your answers and I will give you detailed feedbacks on how to improve your score in the exams) More Information I will explain how to prepare for this exam in much more details in the PAK Study Manual. Any Questions? I know you probably have a lot of questions in your mind regarding the exam or choosing study aids. Please feel free to contact me at eddy.chan@pakstudymanual.com 2015 PAK Study Manual 1 SOA CFE Exam (Study Manual)

7 F : A Market Cost of Capital Approach to Market Value Margins (by CFO Forum) Key Points 1. Understand the economic balance sheet structure 2. Understand how to use the market cost of capital approach to calculate the market value margin 1. Executive Summary Two Common Approaches to Calculate the Market Value Margins (MVMs) - Percentile approach - Market cost of capital (MCoC) approach Market Cost of Capital (MCoC) Appaoch - The CRO Forum prefers the MCoC approach - This approach works for both life and non-life business Main Reasons for the CRO Forum s Preference 1. Support appropriate risk management actions 2. Appropriate reflection of risk 3. Better response to a potential crisis 4. Easy to implement 5. Transparent, easily verifiable and understandable 6. Pass the use test Figure 2: Economic Balance Sheet SAMPLE Components of Market Consistent Value of Liabilities (MVL) 1. Expected PV of future LCFs 2. MVM for non-hedgeable risks (An explicit cost of risk for non-hedgeable risk) MVL - It represents the market consistent value at which the liabilities could be transferred to a willing, rational, diversified counterparty in an arms length transaction under normal business conditions Note Arms Length Transaction means the transaction made by two totally independent parties 2015 PAK Study Manual 2 SOA CFE Exam (Study Manual)

8 MVM - It is the cost of risk (risk margin) in addition to the expected PV of future LCFs required to manage the business on an ongoing basis - It is estimated by the PV of the cost of future capital requirements for non-hedgeable risks - Calculation of MVMs using a MCoC approach is straightforward given that the majority of the calculation is prescribed under the standard SCR 2. Introduction Purpose of This Paper - The MCoC approach to MVMs is the CFO Forum s preferred method Calculate the Liability Value - The assets and liabilities should be measured on a consistent basis for solvency purposes o This basis should be market value - In order to determine the MVL, a MVM is added to the expected PV of future LCFs o The CRO Forum does not agree with using the percentile method to calculate the MVM since it is not consistent with the aim of introducing a risk based solvency assessment o The MCoC approach to MVMs is the CFO Forum s preferred method 3. Why Take a MCoC Approach to MVMs? Two Common Approaches to Calculate the Market Value Margins (MVMs) for Non-Hedgeable Risks 1. Percentile approach o Sufficient capital is needed to ensure that the liabilities can be met with a predefined confidence level 2. Market cost of capital (MCoC) approach o Sufficient capital is needed to be able to run-off the business Main Reasons for the CRO Forum s Preference 1. Support appropriate risk management actions 2. Appropriate reflection of risk 3. Better response to a potential crisis 4. Easy to implement 5. Transparent, easily verifiable and understandable 6. Pass the use test Supports Appropriate Risk Management Actions - MCoC approach o It more appropriately differentiates between risks similar to the way in which capital markets differentiate between risks (equity investment vs. equity option) o It ensures that the cost of risk is measured purely based on the economic cost of holding capital to support non-hedgeable risks The cost of risk and any allowance for prudence are clearly separated The reserve reflects the best estimate of the cost of managing risk Margins for prudence should only be reflected in the capital held (SCR) and not in the technical provision (MVL) - Percentile approach o Prudence may be incorporated in both the reserves and capital which can lead to inefficient management of risks and double counting of risks 2015 PAK Study Manual 3 SOA CFE Exam (Study Manual)

9 Appropriate Reflection of Risk - MCoC approach o The MVMs will always reflect the risk inherent in the product - Percentile approach o The MVMs will not always reflect the risk inherent in the product because there is no link between the arbitrary percentile value chosen and the market price o Also, the percentile approach does not refer to each risk type separately Figure 1: Percentile vs. MCoC Figure 1 - For the long tailed gamma distribution ( more-severity risks: catastrophic risk, terrorist risk, etc) o The percentile approach underestimates the price of non-hedgeable risk - For the normal distribution (regular insurance risks: mortality risk, etc) o The percentile approach greatly overestimates the market price of risk - The MCoC approach ensures that insurers consider the tails of the distributions o No consideration is given to the shape of the distribution using the percentile approach Experiences of the Australian and the Swiss Regulators - Australian regulators o It is difficult to reasonably explain the spread of risk margins using the percentile approach - Swiss Regulators o The MVMs under a MCoC approach appropriately reflect the risk inherent in the business The calculation is stable from period to period Life insurers writing mainly savings products have relatively small MVM since insurance risk is small Life insurers writing risk products have relatively large MVM since they have a large exposure to biometric risk and a long duration of the run-off portfolio 2015 PAK Study Manual 4 SOA CFE Exam (Study Manual)

10 Response to a Potential Crisis - MCoC approach o It ensures that after a stressed event, the company will be able to appropriately remunerate either a third party accepting the liability or new capital providers o It achieves this through the SCR for non-hedgeable risks needed to support the liability in future years and hence the MVM, which represents a provision for the cost of holding this capital - Percentile approach o It implicitly forces the insurer to hold part of the capital needed to support the business in future years in the form of a prudence margin o This prudence margin will not suffice to run-off the liabilities with the level of confidence implied by the SCR o It does not ensure that there will be sufficient financial resources to cover future capital costs needed to remunerate either a third party accepting this liability or new capital providers Ease of Implementation - Percentile approach o It is complex (for small entities) to implement since it requires stochastic calculations over the whole run-off period to determine the appropriate percentile on the distribution of liability values - MCoC approach o It is easier to implement since there is only one unknown item (the SCR for non-hedgeable risks) and this can be calculated with ease using the standard SCR Transparent, Verifiable and Comprehensible - MCoC approach o Supervisors can easily replicate and verify the MVM calculation (using standard SCR and internal model) - Percentile approach o It is not so easily verified because it is not possible for the regulator to use the standard SCR to benchmark the internal models used to determine the percentile value o Australian regulators experienced a wide variation in the results from insurer to insurer, when adopting a percentile approach - The MCoC approach has been used for some 20 years The Use Test - It already passes the use test envisioned in the Solvency II framework 2015 PAK Study Manual 5 SOA CFE Exam (Study Manual)

11 4. Theory Underpinning the MCoC Approach: The Economic (Solvency) Balance Sheet Figure 2: Economic (Solvency) Balance Sheet Note In the general accounting framework, we know that assets = liabilities + equities. Assume that assets = MVA and liabilities = MVL. Then equities = SCR + Excess capital Economic (Solvency) Balance Sheet - It distinguishes between the asset and liability values and the capital required for solvency purposes - Capital requirements consider risks emanating from both sides of the balance sheet - It does not explicitly identify the cost of capital Market Value of Assets (MVA) - The capital markets provide the MVA - It is derived from the cost of managing the risks underlying the business on an ongoing basis Market Consistent Value of Liabilities (MVL) - It represents the market consistent value at which the liabilities could be transferred to a willing, rational, diversified counterparty in an arms length transaction under normal business conditions - Market values should be used where available to value the MVL - Where market values are not available, the MVL must be explicitly calculated using market consistent valuation techniques 2015 PAK Study Manual 6 SOA CFE Exam (Study Manual)

12 Figure 3: Components Parts of the MVL Calculation Expected Present Value of Future Liability Cash Flows - It includes premiums, fees, policyholder claims, expenses and commissions - The market consistent value of these future CFs may be determined as the cost of setting up a replicating portfolio Replicating (Hedge) Portfolio - The portfolio of assets that most closely matches the corresponding liability CFs - In the absence of arbitrage, and if the liability CFs could be matched exactly, the market consistent value of the liabilities will exactly equal the market value of the replicating portfolio Note To the simplest form, the expected PV of future LCFs is the same as the reserve that we learnt in FAP. Remember the formula? Reserve = PV(Expenses/Claims) PV(Premiums) Figure 4: Replicating Portfolio 2015 PAK Study Manual 7 SOA CFE Exam (Study Manual)

13 MVM for Non-Hedgeable Risk - The MVM is defined as the cost of risk (risk margin) in addition to the expected PV of future LCFs required to manage the business on an ongoing basis - It is only necessary to calculate an explicit MVM for non-hedgeable risks Figure 5: Types of Risk Affecting the Liability Cash Flow Hedgeable Risks - A hedgeable risk is a risk which can be pooled or hedged using a replicating portfolio o Hedging costs are implicit in the observed market price of those instruments o Thus, it is not necessary to calculate an explicit MVM for hedgeable risks Non-Hedgeable Risks - Risks for which a deep and liquid market is not available are referred to as non-hedgeable o They are risks for which a market price cannot be observed - To compensate an investor for the cost of taking non-hedgeable risks, an explicit MVM is demanded o Under the MCoC approach, the MVM is the compensation required for the cost of holding capital against non-hedgeable risks over the life of the policy Figure 6: Flowchart for Determining the Appropriate Method for Calculating the MVL 2015 PAK Study Manual 8 SOA CFE Exam (Study Manual)

14 Solvency Capital Requirement (SCR) - It can be determined by the Standard Approach or the Internal Model Approach under Solvency II - The projection of what the SCR is for non-hedgeable risk is needed to calculate the MVM Cost of Capital (CoC) - It refers to the capital charge on fully diversified capital held to cover non-hedgeable risks only o This should not be seen as a total company CoC Note In the embedded value framework, the CoC means the cost of holding the capital needed to support the businesses of the whole company. In the MVM calculation here, we just focus on the capital held to cover non-hedgeable risks only. 5. The MCoC Approach to MVMs MCoC Approach to MVMs - The MVM for non-hedgeable risk is calculated as the PV of the cost of future capital requirements for non-hedgeable risks Steps to Calculate the MVM for Non-Hedgeable Risks 1. Project the SCR for non-hedgeable risks o Using the standard model or internal models, the projected SCR can be determined via an underlying driver that is indicative of the risk level (e.g. PV of benefit) (See Appendix C) o The required SCR at time 0 for non-hedgeable risk types would be set at 99.5% Value at Risk for a holding period of one year and calculated net of full diversification effects (see Appendix B) 2. Calculate the capital charge o The capital charge for non-hedgeable risks can be explicitly calculated by multiplying the future SCR at each point in time by the CoC for non-hedgeable risk o This cost of capital charge only applies to capital that is required for the non-hedgeable risk 3. Discount the projected capital charge o The projected capital charge stream is then discounted at the risk free rate (swap rate) to get the MVM Figure 7: Calculating the MVM for Non-Hedgeable Risk 2015 PAK Study Manual 9 SOA CFE Exam (Study Manual)

15 Illustrative Example Data and Assumptions - An insurer has sold 500 term policies and the premium on each policy is 50 - If the policyholder dies within a 5 year period, then a benefit of 1000 is paid - The probability of dying within any one year is 1% - The swap rate is 5% (yield curve is assumed to be flat) - The CoC for non-hedgeable risks used to illustrate the approach in this example is 4% Step 1: Project the SCR for Non-Hedgeable Risks Time No. of policies (start of year) Premium (beginning of year) 25,000 Claims 5,000 4,950 4,901 4,851 4,803 PV Claims (Discounted at mid-year) 21,764 17,729 13,543 9,199 4,687 2,176 = 10% x 21,764 SCR SCR as % of PV of benefits 10% 1,773 = 10% x 17,729 1,354 = 10% x 13, = 10% x 9, = 10% x 4,687 Step 2: Calculate the Capital Charge Time SCR 2,176 1,773 1, = 4% x 2,176 Capital Charge Capital Charge / SCR 4% 71 = 4% x 1, = 4% x 1, = 4% x = 4% x 469 Step 3: Discount the Capital Charge Time SCR 2,176 1,773 1, Capital Charge (mid-year) Discounted Capital Charge 85 = 87/1.05^0.5 Total MVM 245 PV Liabilities 21,764 MVL 22, = 71/1.05^ = 54/1.05^ = 37/1.05^ = 19/1.05^ Frequently Asked Questions Circularity - The issue of circularity in the calculation arises because the MVM is calculated directly from the SCR o But it also makes up part of the MVL and is assumed to be included in the SCR calculation - The relative size of the MVM in comparison to the total MVL is small so the impact of including the MVM in the SCR calculation would be insignificant o Thus, it is assumed that the MVM will have little or no effect on the SCR Asset Liability Mismatching - The acquiring insurer should not be compensated for any avoidable asset liability mismatch (ALM) taken by the defaulting insurer o ALM risk is a hedgeable risk so it is assumed that the acquiring insurer can swap back to the replicating portfolio instantaneously and hedge any ALM taken by the defaulting insurer 2015 PAK Study Manual 10 SOA CFE Exam (Study Manual)

16 Level of Risk Margin Relative to Overall Liability - Some regulators and supervisors are concerned about the relatively low level of MVMs - The explicit MVM only corresponds to the MVM charged for non-hedgeable risks o Low margins are also observed using a percentile approach so this is not purely a MCoC issue Tax - The liabilities and the MVM should be set on a pre-tax basis since this is analogous to how market values are set for assets Operational risk - Since operational risk is a non-hedgeable risk, it should be included in the calculation of the MVM Harmonization - The MVM calculation is based on the projected capitals but various insurers have various internal models o The CRO Forum has also formulated recommended approaches of benchmarking internal models to address these concerns o The proportion of the MVL that corresponds to the explicit MVM is relatively small so any discrepancies will have a relatively small impact on the results Total Portfolio vs. Different Business Line - The MVM is calculated for each LoB for each risk type and then added to the best estimate liability value o This will improve transparency and facilitate companies analysis of the risks they take o The MVL is then aggregated to a company level Non-Life Business - The MCoC approach applies for non-life business o For in-force business, a SCR for non-hedgeable risk will be set up for the current year to support the insured risk o In addition to this, SCR for the non-hedgeable reserve risks will be held after the expiration of the contract o This capital is held to cover the risk that reserves may not be sufficient to cover claims either because ultimate claims or the pay out pattern had been incorrectly estimated Small Entities - The Swiss Solvency Field Test showed that this MCoC approach works well in smaller entities due to its simplifying assumptions - The standard SCR approach can be adopted to determine the SCR for non-hedgeable risks Variation in CoC - The CoC for non-hedgeable risks reflects the excess return over risk free rates that an acquiring company would require to compensate them for the cost of holding capital to run-off the business - The CRO Forum suggests that the risk margin (MCoC) should not vary by risk type or business o Since the SCR for non-hedgeable risk will differ between risk types, the MVM will automatically differ under the MCoC approach thereby better reflecting risk - With regard to the reference market in which the products are sold, it is possible that the price of risk may vary between countries due to uncertainty in the market o Most of this uncertainty is due to the difficulties in hedging unwanted risk and will already be factored into the SCR and MVM, as these risks are not hedgeable 2015 PAK Study Manual 11 SOA CFE Exam (Study Manual)

17 Time Horizon - One common misconception regarding the MCoC approach o The MVM only considers one year worth of risk and everything after the first year is ignored because the SCR is measured using a one-year shock approach o This is incorrect - The SCR calculation does consider the expected LCFs over periods o The SCR represents the change in liability value between expected future liability cash flows and worst-case (99.5% percentile) cash flows o These worst-case cash flows reflect not what we can observe in any one year but rather how far off we can be in estimating our expected liability cash flows over their entire life Appendix A. Expected Present Value of Future Cash Flows Products without Optionality - All cash flows that occur with certainty are totally risk free and can be replicated with risk-free assets of a similar term Diversifiable Risk - The market consistent framework assumes that there is no reward for holding diversifiable risk o This assumption implies that any cash flows that are not risk free but where risk is diversifiable should be treated as risk free and hence discounted at the swap rate o This assumption flows through to the treatment of the MVM for non-hedgeable risks Non-Diversifiable Risk - This assumption also implies that expected cash flows that are subject to non-diversifiable risk should be discounted at a rate that reflects the risk inherent in the cash flow o The risk-adjusted rate contains a risk premium that investors would demand for o The greater the expected return driving such a risky cash flow, the greater the discount rate applied to the cash flow Certainty Equivalent Approach - This is a form of risk-neutral valuation where the risky cash flows are adjusted and projected assuming that all underlying assets earn the risk-free rate Note 1. Discount risky cash flows using risk-adjusted rate: 2. Discount risk-free cash flows using risk-free rate: 3. Adjust risky cash flows and discount at risk-free rate: V V V = = = CF risky, t (1 + r + r ) CF f risk free, t t + rf (1 ) CF risky, t (1 + r ) f t p Z t t Products with Embedded Options or Guarantees - For products with options/guarantees, using the certainty equivalent approach becomes a very complex process due to the non-linear, asymmetric relationships with market returns that exist in these products o It is necessary to determine the liability value using option pricing or Monte Carlo simulation o In order to achieve market-consistency, both methods should be calibrated to reproduce the prices of traded assets that best reflect the characteristics of the liabilities being valued 2015 PAK Study Manual 12 SOA CFE Exam (Study Manual)

18 Appendix B. Diversification Four Levels of Diversification Diversification Levels Level 1 (Within risk types) Level 2 (Across risk types) Level 3 (Across entities, within a given geography) Level 4 (Across geographies or regulatory jurisdictions) Example Adding more unrelated risks to the portfolio Combining two classes of insurance Two or more insurance companies in the same geography within an insurance Group Two or more insurance companies in different geographies within an insurance Group Appendix C: Proxy Measures for Projecting Capital Products Non-Hedgeable Risk Type Death Protection Survivorship Protection Savings Accident & Health Mortality Net amount at risk PV of benefits Economic liability Net amount at risk Life Morbidity N/A N/A N/A Net amount at risk Insurance Persistency Economic liability Economic liability Economic liability Economic liability Note There is a long list in the reading. You should read it once. I personally think the life insurance line is more important so I put it here. Practice Question List the considerations of calculating the MVM 1. Circularity 2. Asset Liability Mismatching 3. Level of Risk Margin Relative to Overall Liability 4. Tax 5. Operational risk 6. Harmonization 7. Total Portfolio vs. Different Business Line 8. Non-Life Business 9. Small Entities 10. Variation in CoC 11. Time Horizon Past CFE/FETE SOA Questions Related To This Reading 2013 Fall CFE Q8 (Must Read) 2015 PAK Study Manual 13 SOA CFE Exam (Study Manual)