SOCIETY OF ACTUARIES Advanced Portfolio Management Exam APMV MORNING SESSION Date: Friday, May 9, 2008 Time: 8:30 a.m. – 11:45 a.m. INSTRUCTIONS TO CANDIDATES General Instructions Written-Answer Instructions 1. This examination has a total of 120 points. It consists 1. Write your candidate number at the top of each sheet. of a morning session (worth 60 points) and an afternoon Your name must not appear. session (worth 60 points). 2. Write on only one side of a sheet. Start each question a) The morning session consists of 10 questions on a fresh sheet. On each sheet, write the number of numbered 1 through 10. the question that you are answering. Do not answer more than one question on a single sheet. b) The afternoon session consists of 12 questions numbered 11 through 22. 3. The answer should be confined to the question as set. The points for each question are indicated at the 4. When you are asked to calculate, show all your work beginning of the question. Questions 1 through 5 including any applicable formulas. pertain to the Case Study, which is enclosed inside the front cover of this exam booklet. 5. When you finish, insert all your written-answer sheets into the Essay Answer Envelope. Be sure to hand in all 2. Failure to stop writing after time is called will result in your answer sheets since they cannot be accepted later. the disqualification of your answers or further Seal the envelope and write your candidate number in disciplinary action. the space provided on the outside of the envelope. Check the appropriate box to indicate morning or 3. While every attempt is made to avoid defective afternoon session for Exam APMV. questions, sometimes they do occur. If you believe a question is defective, the supervisor or proctor cannot 6. Be sure your written-answer envelope is signed because give you any guidance beyond the instructions on the if it is not, your examination will not be graded. exam booklet. Tournez le cahier d’examen pour la version française. © 2008 by the Society of Actuaries Printed in the U.S.A. 475 N. Martingale Road Exam APMV-Front Cover Schaumburg, IL 60173-2226 CASE STUDY INSTRUCTIONS The case study will be used as a basis for some examination questions. Be sure to answer the question asked by referring to the case study. For example, when asked for advantages of a particular plan design to a company referenced in the case study, your response should be limited to that company. Other advantages should not be listed, as they are extraneous to the question and will result in no additional credit. Further, if they conflict with the applicable advantages, no credit will be given. **BEGINNING OF EXAMINATION** MORNING SESSION Questions 1 – 5 pertain to the Case Study 1. (4 points) You are a consulting actuary for a rating agency. Particular Motors is considering a purchase of $500 Million in Separate Account Institutional GICs from LifeCo, and has engaged your company to assign a credit rating to this line of business as a stand alone entity using the internal risk rating system methodology as described in Crouhy. The term to maturity that Particular Motors is looking for is 10 years. (a) Describe the purpose and the criteria for the following elements of the internal risk rating system: (i) Financial Assessment (ii) Management and other qualitative factors (b) Evaluate LifeCo’s management and other qualitative factors with respect to the proposed GIC purchase. EXAM APMV: Spring 2008 - 1 - GO ON TO NEXT PAGE Advanced Portfolio Management Morning Session Questions 1 – 5 pertain to the Case Study 2. (7 points) (a) Describe the concept of a benchmark in performance measurement. (b) Describe the properties of a valid benchmark. (c) Construct an appropriate benchmark to measure the performance of LifeCo’s GIC block of business. Available Benchmarks are: Yield Duration Money market 4.5% 0.25 Medium-term Treasury bonds 5 3 Real Estate I (50% pass-through / 50% CMOs) 6 3.5 Real Estate II (50% pass-through / 50% CMOs) 5.3 1.3 Corporate Bonds I (70% inv. grade / 30% non-inv. grade) 7.5 4.15 Corporate Bonds II (70% inv. grade / 30% non-inv. grade) 6.5 3.2 Corporate Bonds III (50% inv. grade / 50% non-inv. grade) 6 3.1 Equity I (15% in foreign securities) 8 8 Equity II (15% in foreign securities) 6.8 5.2 (d) Compare the yield of LifeCo’s GIC portfolio to that of the benchmark recommended in (c). EXAM APMV: Spring 2008 - 2 - GO ON TO NEXT PAGE Advanced Portfolio Management Morning Session Questions 1 – 5 pertain to the Case Study 3. (6 points) LifeCo has revised downward the effective duration of the accumulation annuity block of business from 4.7 years to 4.1 years. You are responsible for reviewing the portfolio of assets backing the block of business (Appendix A to the Case Study). (a) (1 point) Demonstrate that the assets backing the accumulation annuity block of business do not comply with LifeCo’s ALM guidelines after the revision of effective liability duration. (b) (4 points) Analyze the characteristics of each asset class in the portfolio that should be considered in rebalancing the portfolio to be in compliance with the ALM guidelines. (c) (1 point) Recommend changes to the portfolio to bring it in compliance with the ALM Guidelines, given that the yield curve is expected to shift upward and the accumulation annuity block of business is coming out of its surrender charge period. EXAM APMV: Spring 2008 - 3 - GO ON TO NEXT PAGE Advanced Portfolio Management Morning Session Questions 1 – 5 pertain to the Case Study 4. (12 points) The management of LifeCo has asked you to select a stochastic equity model to use for consistent modeling of all equity-linked products. It is expected that the model would be used mainly for valuation and capital modeling purposes. The implementation would be similar to the one recommended by the Canadian Institute of Actuaries Research Paper on the “Use of Stochastic Techniques to Value Actuarial Liabilities under Canadian GAAP”. (a) (2 points) Identify the LifeCo products with equity exposure and describe that equity exposure. (b) (3 points) Describe the following stochastic equity models: (i) lognormal (ii) regime-switching lognormal (iii) AAA stochastic log-volatility model (iv) GARCH(1,1) (c) (1 point) Recommend a stochastic equity model appropriate for LifeCo’s equity exposure. (d) (3 points) Describe the following techniques to estimate parameters: (i) Maximum likelihood estimation (ii) Left-tail calibration method (iii) Markov Chain Monte Carlo estimation (e) (1 point) Recommend a parameter estimation technique for the model recommended in (c). (f) (1 point) Assess whether or not the recommended model in (c) would be appropriate to price hedging strategies. (g) (1 point) Describe how results across products should be aggregated to ensure a consistent CTE measure at the company level. EXAM APMV: Spring 2008 - 4 - GO ON TO NEXT PAGE Advanced Portfolio Management Morning Session Questions 1 – 5 pertain to the Case Study 5. (6 points) LifeCo’s ALM Committee decided to fully hedge the guarantee risk in the Equity Linked GIC portfolio effective Dec. 31, 2000. You are to prepare a static hedge proposal using only options. S&P Price Index, Dec. 31, 2000 1378 S&P Total Return Index, Dec. 31, 2000 1590 Interest (annual) 12% S&P Index dividend yield 3% Volatility (annual) S&P Price Index = 18% S&P Total Return Index = 18% Assume that the Equity Linked GIC asset portfolio has tracked the S&P Total Return Index performance very well since issue. Options with the following parameters are available in the over-the-counter market: S&P Total Return Underlying S&P Price Index Put Option Call American Exercise European (a) Determine option(s) for LifeCo’s Equity Linked GIC portfolio; specify type of underlying, option, and exercise. (b) Determine the term, strike rate, and notional amount of the option(s) recommended in (a). (c) Calculate the premium of the option(s) recommended in (a) using the information given. (d) Demonstrate how the option(s) purchased will hedge the risk if the S&P Price Index and Total Return Index drop to 1170 and 1350, respectively, ignoring premium paid for the option(s) in (c). EXAM APMV: Spring 2008 - 5 - GO ON TO NEXT PAGE Advanced Portfolio Management Morning Session 6. (8 points) In-House, a large financial institution, is currently paying a rate of 3.00% to its depositors and charging a 7.25% loan rate. It has the following three subsidiaries: A – Consumer bank B – Mortgage lender C – Derivatives trading company Subsidiary C earned 11.25% on its trades last year. At the beginning of last year, In-House has the following available data (in millions): A B C Loans 1 22 0 Deposits 30 1 0 Investments 0 0 8 Expenses 0.175 0.405 0.550 In order to more accurately measure the financial performance of each subsidiary, In- House decides to revise its net income statement, by adding a transfer pricing charge to account for the loans A made to B and C to fund their transactions. (a) (2 points) Calculate the net income for each subsidiary before the transfer pricing adjustment. (b) (3 points) Calculate the transfer pricing charge used and the revised net income for each subsidiary, assuming that after the transfer pricing adjustment, subsidiary A’s revised net income is $597,720. (c) (1 point) Describe the concept of transfer pricing for a life insurance company. (d) (2 points) Describe the advantages and disadvantages of the use of transfer pricing for a life insurance company.