Enterprise Risk Management (ERM) Exam Spring 2015 Edition CTE VaR Solvency II Reinsurance Risk Aggregation Coherence Risk Measure Tail Dependency Strategic Risk Management Operational Risk Principles-Based Reserves and Capital Extreme Value Theory Economic Capital Stress Testing Copula KRD
for ERM Spring 2015 PRODUCT FEATURES Purposes Features PAK Study Manual PAK Exam Aid PAK Flash Cards PAK Test Aid PAK Study Manual Package Study Summaries X X PAK Online Seminar Study Relevant Past Questions (List) X X Study Practice Questions X X Study Application-Type Question Set X X Study Mock Questions X X Study Online Tutorial X X Study Suggested Schedule (Detailed) X X Study Email Support X X Practice Mock Questions X X Practice Case Study Analysis X X Practice Past Questions (Sorted PDFs) X X Review Flash Cards X X Review Condensed Summary X X Evaluation Mock Exam X X Bonus Bonus materials X Study Online Video Seminar (New) X Study Practice Questions X 1
PAK STUDY MANUAL (ERM CORE + EXT.) 1. Summary (ERM Core + ERM Extension) The covers the entire Enterprise Risk Management (ERM) syllabus (The ERM extension is included). 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 ERM 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. 200+ Practice Questions (200+ in total) One key point to pass this exam is to "practice" (Practice makes perfect!). Due to this reason, I include many practice questions in each reading (200+ in total) to refresh the materials just learnt and to strengthen your knowledge. More practice will be available in the PAK Exam Aid. 4. Application-Type Practice Question Set (New) This practice question set gives you an idea on how to apply the materials into a scenario/ situation. This item will be released on 12/30. 5 Mock Exam Questions The mock exam questions mimic the same difficulty level of the real exam questions. 5 mock exam questions and solutions are included in the 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. Online Tutorial Starting from 3/30, we will upload weekly tutorial videos online to clarify some confusing concepts and discuss some important topics for this exam sitting. Don't miss out! 8. Email Support Get questions? Please send me an email 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. It was very organized and valuable. By Marc Roberts Read the whole story DO YOU KNOW? The 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. 2 PAK FLASH CARDS 1. Electronic Flash Cards Summarize the key points (with mnemonics) (PDF version is also available) Contain around 300+ flash cards (front and back) Work best for any big-screen cellular phone (e.g. iphone, HTC, Android, etc) 2. Bonus: Condensed Summary Summarize the key points in outline format Quickly refresh all the important topics in the readings PAK TEST AID 1. Mock Exam (New) 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
PAK EXAM AID 1. 30 Mock Exam Questions and Solutions (New) 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. 2. 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. 3. Past SOA Exam Questions (from All FSA Tracks) Relevant to This Exam This set not only includes the past exam questions from the ERM 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. NOTES 1. The availability date of the 1 st and 2 nd items above may be different. It depends on when the SOA releases the new case study. 2. 1 st release will contain item #3 and will be released on 12/15/14. The 2 nd release will contain item #1 -#2 and will be released on 2/1/14. 3. If the SOA do not release the case study, an additional 5 mock questions will be used to replace the case study analysis. 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. The Mock questions, Mock exam and Exam Aid are also very beneficial to make sure you're abilities are up to par before the real exam. By Wes Smith Read the whole story RELEASE SCHEDULE Purposes Features PAK Study Manual PAK Exam Aid PAK Flash Cards PAK Test Aid PAK Study Manual Package Study Summaries 11/15 11/15 Study Relevant Past Questions (List) 11/15 11/15 Study Practice Questions 11/15 11/15 Study Application-Type Question Set 12/30 12/30 Study Mock Questions 11/15 11/15 Study Suggested Schedule (Detailed) 11/15 11/15 Study Online Tutorial 3/30 (Weekly) 3/30 (Weekly) Study Email Support Anytime Anytime Practice Mock Questions 2/1 2/1 Practice Case Study Analysis 2/1 2/1 Practice Past Questions (Sorted PDFs) 12/15 12/15 Review Flash Cards 12/15 12/15 Review Condensed Summary 12/15 12/15 Evaluation Mock Exam 3/1 3/1 Bonus Bonus materials To Be Announced PAK Online Seminar Study Online Video Seminar (New) 11/30 and 3/15 Study Practice Questions 11/30 3
PAK STUDY MANUAL PACKAGE 1. (Release on 11/15) 2. PAK Exam Aid (Release on 12/15 and 2/1) 3. PAK Memorization Aid (Release on 12/15) 4. PAK Test Aid (Release on 3/1) 5. Bonus materials PAK ONLINE SEMINAR (NEW) 1. Clarify and explain the key concepts/calculations in each reading in the syllabus 2. Discuss the past exam questions (e.g. exam techniques, how to score) 3. Review the new case study 4. Review the ERM Extension materials in both video and webinar format 5. Contain condensed outlines for each reading on the syllabus 6. Include practice questions to test your knowledge 7. Review the lectures and study at your own pace 8. Email support 9. Free access for 2nd attempt (only for those who scored 2-5) NOTE 1. The online seminar will be released on 11/30 and 3/15. 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. DO YOU KNOW? If you are not sure which exam track to take, or how it can advance your career, you can send an email to Eddy and discuss your situation with him. He will share his work experience with you so that you can make your decision informatively. 2. Once you make a purchase (please use your work email address), we will send you a confirmation email within 1 business days Once the files are available, we will send them to you through email. Please make sure that you put the correct email address when you purchase the PAK products. If you do not receive the confirmation email, please send us an email (services@pakstudymanual.com). 3. Please check your junk mailbox. Sometimes, our email is blocked. MORE INFORMATION Want more information? Please contact me at eddy.chan@pakstudymanual.com or visit www.pakstudymanual.com 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
Economic Capital Modeling Practical Considerations
Economic Capital is the amount of capital that is needed to cover unexpected losses at a certain risk tolerance level Credit: Economic Capital Modeling: Practical Considerations p.4 (by Milliman)
Income Statement Year-End 20X0 20X1 20X2 20X3 20X4 20X5 20X6 20X7 20X8 20X9 (+) Premium Income 247.2 282.6 320.5 361.2 405.1 452.6 504.1 560.1 621.1 687.6 (+) Investment Income 60.5 71.8 85.0 99.9 116.7 135.4 156.1 179.0 204.4 232.3 (=) Total income 307.7 354.4 405.5 461.1 521.8 588.0 660.2 739.1 825.5 919.9 ( ) Death Benefits 23.0 26.7 31.2 36.4 42.4 49.7 59.0 69.9 81.5 93.6 ( ) Annuity, Surrender, and Other Benefits 43.1 52.0 62.0 73.2 85.6 99.5 114.9 131.9 150.7 171.5 ( ) Premium Taxes 4.9 5.7 6.4 7.2 8.1 9.1 10.1 11.2 12.4 13.8 ( ) Reserve Increase (Changes in Stat Res) 155.5 180.3 205.2 232.2 258.2 287.9 319.4 353.1 389.7 429.3 ( ) Other Expense 8.5 12.9 14.3 15.9 17.6 19.5 21.5 23.8 26.3 29.0 ( ) Commission 51.2 55.5 62.1 69.2 76.9 85.0 93.7 103.1 113.6 125.0 (=) Total Benefits and Expenses 286.2 333.1 381.2 434.1 488.8 550.7 618.6 693.0 774.2 862.2 PAK (+) Statutory Profit on Existing and New Business 21.5 21.3 24.3 27.0 33.0 37.3 41.6 46.1 51.3 57.7 ( ) Unallocated Expense 5.5 1.8 1.1 0.3 0.0 0.0 0.0 0.0 0.0 0.0 (+) Interest on Capital 3.3 3.6 4.3 5.0 5.7 6.6 7.5 8.6 9.7 11.0 (=) Total Pre-Tax Earnings 19.3 23.1 27.5 31.7 38.7 43.9 49.1 54.7 61.0 68.7 ( ) Federal Income Tax 8.6 10.9 13.0 15.7 18.6 20.7 23.0 25.5 28.3 31.6 (=) After-Tax Earnings (Net Income) 10.7 12.3 14.4 16.0 20.2 23.2 26.1 29.2 32.7 37.1 PV(Net Income) = 100
Income Statement Year-End 20X0 20X1 20X2 20X3 20X4 20X5 20X6 20X7 20X8 20X9 (+) Premium Income 247.2 282.6 320.5 361.2 405.1 452.6 504.1 560.1 621.1 687.6 (+) Investment Income 60.5 71.8 85.0 99.9 116.7 135.4 156.1 179.0 204.4 232.3 (=) Total income 307.7 354.4 405.5 461.1 521.8 588.0 660.2 739.1 825.5 919.9 ( ) Death Benefits 23.0 26.7 31.2 36.4 42.4 49.7 59.0 69.9 81.5 93.6 ( ) Annuity, Surrender, and Other Benefits 47.4 57.2 68.2 80.5 94.2 109.5 126.4 145.1 165.8 188.7 ( ) Premium Taxes 4.9 5.7 6.4 7.2 8.1 9.1 10.1 11.2 12.4 13.8 ( ) Reserve Increase (Changes in Stat Res) 155.5 180.3 205.2 232.2 258.2 287.9 319.4 353.1 389.7 429.3 ( ) Other Expense 8.5 12.9 14.3 15.9 17.6 19.5 21.5 23.8 26.3 29.0 ( ) Commission 51.2 55.5 62.1 69.2 76.9 85.0 93.7 103.1 113.6 125.0 (=) Total Benefits and Expenses 290.5 338.3 387.4 441.4 497.4 560.7 630.1 706.2 789.3 879.4 PAK (+) Statutory Profit on Existing and New Business 17.2 16.1 18.1 19.7 24.4 27.4 30.1 32.9 36.2 40.6 ( ) Unallocated Expense 5.5 1.8 1.1 0.3 0.0 0.0 0.0 0.0 0.0 0.0 (+) Interest on Capital 3.3 3.6 4.3 5.0 5.7 6.6 7.5 8.6 9.7 11.0 (=) Total Pre-Tax Earnings 15.0 17.9 21.3 24.3 30.2 33.9 37.7 41.5 46.0 51.6 ( ) Federal Income Tax 7.1 9.0 10.9 13.1 15.6 17.2 19.0 20.9 23.1 25.6 (=) After-Tax Earnings (Net Income) 7.9 8.9 10.4 11.2 14.6 16.7 18.7 20.6 22.9 25.9 PV(Net Income) = 90
Difference = 100 90 = 10 1 Data Point Difference 100th 60 99th 58 98th 55 97th 52 96th 50 95th 49 94th 48 93rd 47 92nd 45 91st 42 TVaR(95%) = (60+58+55+52+50)/5 = 55 VaR(95%) = 50 1. Take the difference 2. Rank them 3. Calculate the VaR
PV(Net Loss) 100th 70 99th 78 98th 65 97th 62 96th 60 95th 59 94th 58 93rd 57 92nd 55 Prob. Expected Loss Reserve Mean Loss 50 VaR(95%) Economic Capital 95 th 10 60 Percentile VaR(95%) = Quantile Expected Value = 60 10 = 50 1. Rank them 2. Take the difference 3. Calculate the VaR Loss
Total Major Risks Underwriting Risk Credit Risk Total Risk Market Risk Operational Risk Liquidity Risk
Risk Sources Market Risk Descriptions The risk that market levels, interest rates, or volatility change, result in losses Credit Risk Liquidity Risk Underwriting / Demographic Risk Operational Risk The risk that an asset held experiences either a default or a significant fall in its credit quality The risk that reduced liquidity constrains the ability to buy and sell assets, resulting in losses The risk that actual demographic experience turns out worse than expected The risk that there is a failure in the operational aspects of the business people, process, or system
Practical Concerns 1 2 3 4 5 6 7 VaR vs. Tail VaR Stochastic Analysis vs. Stress Test Real World vs. Risk Neutral Diversification Effect Time Horizon Negative Cumulative Surplus Future New Business
Economic Capital Underwriting Risk 10 Credit Risk 20 Market Risk 30 Operational Risk 40 Liquidity Risk 50 Underwriting Risk Economic capital w/o diversification = 10 + 20 + 30 + 40 + 50 = 150 Credit Risk Market Risk Operational Risk Liquidity Risk Underwriting Risk 1 0 0 0.5 0.5 Credit Risk 0 1 0.5 0 0.5 Market Risk 0 0.5 1 0 0.5 Operational Risk 0.5 0 0 1 0.5 Liquidity Risk 0.5 0.5 0.5 0.5 1 Economic capital with diversification 1 0 0 0.5 0.5 10 0 1 0.5 0 0.5 20 = [ 10 20 30 40 50] 0 0.5 1 0 0.5 30 = 107 0.5 0 0 1 0.5 40 0.5 0.5 0.5 0.5 1 50 0.5 Diversification benefit = 150 107 = 43
Market Credit Liquidity Insurance Operational Group Aggregate 5% 1203 1173 1183 1056 1356 1215 7186 5% VaR 203 173 183 56 356 215 1186 Credit Liquidity Market Operational Insurance Group Credit 1.00 0.30 0.40 0.20 0.25 0.10 Liquidity 0.30 1.00 0.50 0.25 0.10 1.00 Market 0.40 0.50 1.00 0.10 0.10 0.50 Operational 0.20 0.25 0.10 1.00 0.10 0.50 Insurance 0.25 0.10 0.10 0.10 1.00 0.40 Group 0.10 1.00 0.50 0.50 0.40 1.00 Economic capital with diversification 1 0.3 0.4 0.2 0.25 0.1 173 0.3 1 0.5 0.25 0.1 1 183 0.4 0.5 1 0.1 0.1 0.5 203 = [ 173 183 203 356 56 215] = 816 0.2 0.25 0.1 1 0.1 0.5 356 0.25 0.1 0.1 0.1 1 0.4 56 0.1 1 0.5 0.5 0.4 1 215 0.5
Benefits 1 2 3 4 5 Determine the appropriate level of capital needed Understand the capital requirements Measure performance based on capital usage Assess the return on capital Understand how well capitalized companies are
Economic Capital Modeling Key points Define economic capital Understand how it is calculated Know the aggregation calculation Describe the practical concerns List the benefits
Practice Questions ERM-106-12: Economic Capital Modeling: Practical Considerations Q1: You are given these two definitions: A. The capital that is required to support a business with a certain probability of default B. The capital that is the excess of the value of the company s assets over the value of its liabilities on a realistic or marketconsistent basis Recognize which types of economic capital they are. Data for Q2-Q6 Credit Market Operational Economic Capital 100 200 50 Credit Market Operational Credit 1 0.8 0.3 Market 0.8 1 0.2 Operational 0.3 0.2 1 Q2: Calculate the aggregated (total) economic capital without diversification benefit. Q3: Calculate the aggregated (total) economic capital with diversification benefit. Q4: Calculate the amount of diversification benefit. Q5: Describe what will happen on your aggregated economic capital if the correlation between market risk and operational risk increases. Q6: Describe what will happen on your aggregated economic capital if the correlations among the risks become zero. 1 SOA ERM Exam
Practice Questions ERM-106-12: Economic Capital Modeling: Practical Considerations S1: A Required Economic Capital and B Available Economic Capital S2: Total EC (without diversification) = 100 + 200 + 50 = 350 S3: 0.5 1 0.8 0.3 100 100 200 50 0.8 1 0.2 200 0.3 0.2 1 50 0.5 100 100 1+ 200 0.8 + 50 0.3, 100 0.8 + 200 1+ 50 0.2, 100 0.3 + 200 0.2 + 50 1 200 = 298.75 50 S4: Diversification benefit = 350 298.75 = 51.25 S5: If the correlation between market risk and operational risk increases, the total economic capital calculated based on the correlation matrix will increase. This will decrease the diversification benefit. S6: If the correlations among risks become zero, the total economic capital = (100 2 + 200 2 + 50 2 ) 0.5 = 229.13. The total economic capital decreases and the diversification benefit increases. 2 SOA ERM Exam