ILA-LP Sample Study Manual You have downloaded a sample of our ILA- LP detailed study manual. The full version covers the entire syllabus and is included with the online seminar. Each portion of the detailed study manual is available in PDF with a clickable table of contents. Each reading (and sub-chapters if applicable) are also bookmarked in the PDF for ease of navigation in your favorite desktop, tablet, or smartphone PDF viewer. Though not shown in the sample material, we also offer a highly condensed version of the detailed study manual (the condensed outline mentioned in the product description). The condensed outline is in the same format as the detailed study manual. If you have additional questions about the detailed study manual or any aspect of the exam, please email me. J. Eddie Smith, IV, FSA, MAAA eddie@theinfiniteactuary.com www.theinfiniteactuary.com
The Infinite Actuary s Detailed Study Manual for the SOA s ILA Life Pricing Exam J. Eddie Smith, IV, FSA Fall 2017 / Spring 2018
Life Pricing Study Manual Introduction About This Study Manual This detailed study manual is just one component of our ILA-LP online seminar, which also includes video lessons and condensed outlines for all of the syllabus material, practice problems, commentary on previous SOA exams, and ash cards. This study manual is intended to help you get through the source material faster than if you had no study manual. Some of the readings are very dicult to absorb on the rst attempt. The study manual will help you pick out important information more quickly. This study manual is organized in exactly the same order as the online seminar, which is not necessarily the same order as the ocial syllabus. The layout of the seminar reects what I believe is the most logical order for learning the material start to nish: A. Products and Markets B. Pricing Assumptions C. Performance Measurement and Risk Management D. Modeling and Hedging E. Regulatory and Tax Considerations How to Use This Study Manual With the Online Seminar This detailed study manual will provide you with a detailed foundation and reference guide for the rest of the online seminar. It s the most detailed and verbose outline we provide with the seminar. Unlike condensed outlines and ash cards, which are design to aid memorization, this detailed study manual is designed with readability in mind. You will not be able to memorize everything in this guide, nor should you. As I explain in the Introduction section of the online seminar, ideally you ll have 3 4 months to prepare for the exam. You ll want to spend the rst half of that time reading as much as you can and trying to learn concepts. Don t worry about memorization until the last 1-2 months before the exam. Each summary in this detailed study manual starts with a section called Overview of This Reading. These overviews show you the contents and most testable topics 2016 The Innite Actuary, LLC
Life Pricing Study Manual Introduction in each chapter at a glance. I recommend reviewing these sections before and after you tackle the readings on your own. After going through the detailed study manual for a given reading, it s a good idea to watch the accompanying video lesson, which will further reinforce the big picture for that reading and provide illustrative examples to reinforce quantitative concepts. Good Luck! It s critically important to keep a couple of things in mind as you go through the material: 1. Keep moving forward. Don t get bogged down! 2. Remember that you are not trying to become an expert in the material. You are trying to identify and master testable material suciently to pass the exam. If you study regularly and put in the time, you will be amazed at how much material you can pack into your head by exam day especially if you prioritize concept learning over memorization in the early stages of studying. That said, a good deal of memorization is needed. Use the condensed lesson handouts and ash cards as a guide for that. And remember one of the most important features of our online seminar is customer support. Our course forum is a great place to post questions about any of the material because it gives other students a chance to answer and see answers. You can also email me anytime with any questions. Your Instructor, J. Eddie Smith, IV, FSA, MAAA eddie@theinniteactuary.com 2016 The Innite Actuary, LLC
LP Detailed Study Manual: Section A LP-102: EIAs LP-102: Equity Indexed Annuities Rhonda Ahrens (2004) Overview of This Reading This study note introduces a lot of testable material on EIAs: both quantitative and written Key topics include: Point-to-point vs. averaging The eects of annual ratcheting Features that control the cost of options How to calculate index-based interest Funding the GMAV and index interest Static vs. dynamic hedging Regulatory considerations that aect EIA design This study note also relates closely to Chapter 13 of the Hardy text, which also covers many of the same EIA mechanics Basic EIA Product Design EIAs are deferred annuities that provide a guaranteed minimum rate of return, but also allows the policyholder to participate in an equity index during the index period During the index period (7-10 years), money allocated to the index account value is credited with index-based interest The S&P 500 is a commonly used index Basic EIA Account Values During the index period, cash values are oored at the the guaranteed minimum account value (GMAV), which subject to standard nonforfeiture law The study note assumes the following GMAV: GMAV t 0.90 SinglePrem (1.03) t This GMAV formula is based on the old valuation law, but it is used extensively in the book s examples. Other readings on the syllabus (e.g. Ch. 13 of the Hardy text) use an even dierent formula for the GMAV. If an exam problem doesn t specify the formula, I would assume the minimum value under current SNL, which is shown toward the end of this reading and also in LP-122. 2016 The Innite Actuary, LLC Page A-53
LP Detailed Study Manual: Section A LP-102: EIAs The index account value (IAV) is based on the index return: IAV t SinglePrem ty (1 + IndexBasedInterest t ) i 1 If the GMAV is higher than the IAV at the end of the index period, T, the IAV is set equal to the GMAV: IAV T max(gmav T, IAV T ) Basic Index Growth Methods 1. Point-to-Point (PTP) No Ratcheting Based on rst and last days of the time period IndexGrowth% FinalClosingLevel InitialClosingLevel 1 2. Point-to-Point (PTP) Annual Ratchet Same mechanics as #1, but the PTP calculation is done annually The annual returns are compounded over the entire index period This will produce the same return as the no-ratchet version unless index growth limiting features are present (discussed shortly) 3. Average Index Growth Based on average closing level over the time period with n trading days (e.g. n = 12 for a monthly average based on a one-year timeframe) IndexGrowth% 1 np ClosingLevel n t t InitialClosingLevel 1 Results in smaller growth than PTP, so less expensive Example: Non-Ratcheting PTP vs. Averaging 4-Year Index Period Year Closing Level 0 105 1 101 2 106 3 107 4 115 2016 The Innite Actuary, LLC Page A-54
LP Detailed Study Manual: Section A LP-102: EIAs PTP IndexGrowth% 115 105 Avg IndexGrowth% 1 9.5% 1 (101 + 106 + 107 + 115) 4 105 1 2.1% The averaging results in smaller growth because the interim values in years 1-3 are given as much weight as the nal closing value in the numerator. The study note says that typically the average index growth will be 55-60% of the PTP growth. Managing the Cost of the Index Interest Index Call Options Insurers buy call options to fund index interest credits Factors that Increase the Cost of Call Options: Higher volatility Longer maturity dates EIA designs that allow for higher index returns Low interest rates increase the cost of the GMAV (harder to nd bonds with sucient yield), which leaves less money available to buy options The combination of low interest rates and high equity volatility is especially bad Features that Limit Index Growth To control (lower) option expense, EIA designs often limit the range and magnitude of raw index growth available to the policyholder through the following features 1. Participation Rate Percentage factor applied to the raw index growth For example, if the participation rate is 80% and the index returns 10%, the policyholder s index-based interest would be 8% 2. Floor Return Most EIAs oor the policyholder s index return at 0% This ensures that the IAV will never decrease 3. Margin An amount subtracted from the raw index return For example, if the margin is 3% and the index returns 10%, the policyholder s index-based interest would be 7% 2016 The Innite Actuary, LLC Page A-55
LP Detailed Study Manual: Section A LP-102: EIAs 4. Cap The maximum amount of raw index return available to the policyholder For example, if the cap is 9% and the index returns 10%, the policyholder s index-based interest would be 9% The examples in the book focus only on the PTP design (with and without annual ratchet) The calculations are done in this order: 1. Calculate raw index return 2. Apply participation rate 3. Subtract margin 4. Apply cap or oor 5. Credit nal index interest to IAV 6. Cash surrender value = max(iav, GMAV) Example with More Features (Builds on Previous Example) Participation rate = 90% Margin = 1% Cap = 5% Floor = 0% For PTP with annual ratchet, the returns must be calculated and compounded annually: (1) (2) (3) (4) (5) Closing Raw Apply Apply Apply Cap Year Level Return PR Margin or Floor IAV 0 105 100.00% 1 101 3.81% 3.43% 4.43% 0.00% 100.00% 2 106 4.95% 4.46% 3.46% 3.46% 103.46% 3 107 0.94% 0.85% 0.15% 0.00% 103.46% 4 115 7.48% 6.73% 5.73% 5.00% 108.63% For PTP without annual ratchet, the only dierence is that the raw return is based on the current closing level relative to the initial level; all other calculations are the same (1) (2) (3) (4) (5) Closing Raw Apply Apply Apply Cap Year Level Return PR Margin or Floor IAV 0 105 100.00% 1 101-3.81% -3.43% -4.43% 0.00% 100.00% 2 106 0.95% 0.86% -0.14% 0.00% 100.00% 3 107 1.90% 1.71% 0.71% 0.71% 100.71% 4 115 9.52% 8.57% 7.57% 5.00% 105.00% 2016 The Innite Actuary, LLC Page A-56
LP Detailed Study Manual: Section A LP-102: EIAs Comparing each approach to the GMAV: IAV With IAV Without Year Ratchet Ratchet GMAV 0 100.00% 100.00% 90.00% 1 100.00% 100.00% 92.70% 2 103.46% 100.00% 95.48% 3 103.46% 100.71% 98.35% 4 108.63% 105.00% 101.30% Observations: The annual ratchet approach will always result in higher returns, especially when caps, oors, participation rates, and margins are present because of the compounding eect For example, in year 2, the closing level of 106 is barely above the initial level of 105; after applying the margin to the non-ratcheted return, the oor comes into eect And so with the non-ratchet approach, the return is zero in year 2 However, with the annual ratchet, the year 2 return is relative to the much lower year 1 level of 101 resulting in a return of 3.46%; not only is this a higher return, it s locked in for future periods In this example, the IAV stays above the GMAV at all levels because the index period illustrated is fairly short; the GMAV doesn t get above the 100% level until years 4+ Additional Features Intended to Control Costs 1. Annual Resets The insurer can reset features like caps each year in response to changing volatility During periods of high volatility, the insurer would lower the cap If volatility lessens, the insurer could increase the cap 2. Flexible Premium EIAs Requires a lower GMAV (e.g. 75% of premium instead of 90%) Allow for higher participation rates since GMAV cost is lower (i.e. more money for options) 3. Lower GMAV Interest Rates The 3% minimum rate initially required by SNL has been recognized as unreasonable Current SNL now allows down to a 1% minimum if certain requirements are met 4. Index Growth Measurement An insurer might use the averaging method instead of PTP since average results in smaller and more stable index credits (cheaper options) Monthly averaging is common 2016 The Innite Actuary, LLC Page A-57
Life Pricing Study Manual: Section C LP-113: The Economics of Insurance LP-113: The Economics of Insurance Swiss Re (2001) Overview of This Reading The economic approach described in this study note has many similarities with risk based or market consistent approaches elsewhere on the syllabus This is a very large study note in terms of testability; it is rich with quantitative, conceptual, and listy topics that could be tested Perhaps the most fundamental thing to understand from this reading is that economic methods are designed to link prots to insurance risk, not investment risk Key topics for the exam include: Shortcomings of traditional measurement systems How and why insurers can borrow cheaply to create value Base cost of capital Frictional costs both from the shareholders and insurer s perspective Franchise value How to create a replicating portfolio and how it changes through time How to calculate the economic value of liabilities How to calculate economic prot Why economic prot is immune to interest rate changes How emerging insurance experience aects economic prot The purpose of the treasury function Considerations for incentive compensation Problems with alternative methods like embedded value 3 main decisions of risk and capital management 3 techniques for reducing balance sheet risk Note: The video lesson series in the online seminar includes extensive numerical examples to illustrate key concepts in this chapter. Going through those examples is critical to fully understanding the framework in this study note, which often intimidates people at rst. The good news is that once you master a few fundamentals, it s actually not that bad! 2016 The Innite Actuary, LLC Page C-45
Life Pricing Study Manual: Section C LP-113: The Economics of Insurance Introduction: Why Economic Capital? Prerequisites for Maximizing Shareholder Value 1. Understand the value creation process 2. Ability to measure value creation 3. Incentive systems that align management interests with value creation How the Insurance Industry is Changing Until the 1990s, competition was low and prot margins were high Changes in the 1990s: Deregulation and globalization Increased competition from inside and outside the industry (banking) Higher competition! lower prot margins! higher volumes now required Increased value awareness across the industry Shortcomings of Articial Value Measurement Systems Articial traditional, non-economic approaches 1. Mask true value in a company 2. Mislead managers about key risks 3. Vary greatly across product lines and countries! comparisons are dicult 4. Overly conservative Leads to hidden reserves Allows companies to smooth/control prot emergence (U.S. GAAP) Smoothing masks volatility and true economic condition May hide the need for corrective actions The Economic Perspective Assets should be valued at market values Liability cash ows should be valued using best estimates and time value of money How Insurers Are Financial Intermediaries 1. Liability-Driven Financial Intermediaries Borrow money from policyholders (premiums) 2016 The Innite Actuary, LLC Page C-46
Life Pricing Study Manual: Section C LP-113: The Economics of Insurance Invest premiums in nancial markets Pay benets to policyholders if claim event occurs 2. Reduce Policyholder s Credit Exposure Insurers hold extra capital to reduce risk of default (from policyholder s perspective) How Insurers Di er From Leveraged Investment Funds 1. Competitive Disadvantage with Investing Less favorable tax and regulatory environment Double taxation (more on this later) 2. Insurers Can Borrow More Cheaply It s cheaper to borrow from policyholders than in capital markets Insurers can sell policies for more than their economic cost Policyholders are willing to pay for protection How Insurers Create Value 1. Selling contracts for more than the production and frictional costs 2. Achieving investment returns greater than base CoC benchmark Franchise value = intangible part of a company s market value that represents expected value from future business = Total Company Market Value Economic Net Worth In other words, a company is worth more to investors than simply taking the dierence between current assets and current liabilities Cost of Capital (CoC) for Insurers Investors (shareholders) can invest in an insurance company or in some other investment opportunity Total Opportunity Cost of Capital = Base CoC + Frictional Costs + Liquidity Value + Option to Default Value Base CoC = Benchmark Return on Investment Portfolio Replicating Portfolio Return I.e. the premium required if shareholders invested directly in the assets held by the insurer Do not use CAPM because it doesn t capture frictional costs 2016 The Innite Actuary, LLC Page C-47
Life Pricing Study Manual: Section C LP-113: The Economics of Insurance Liquidity Value and Option to Default 1. Insurer s Option to Default Insolvent insurers may default on liabilities Cost is based on credit spread resulting from insurer s rating Add the extra spread to the risk-free rate rate used in the EVL calculation 2. Liquidity Value Insurers may choose to hold less liquid assets if they can hold them to maturity Higher yield on illiquid assets lowers the production value Add the extra liquidity spread to the risk-free rate rate used in the EVL calculation Frictional Capital Costs Frictional capital costs = costs specic to investing in an insurer 1. Agency Costs Shareholders require compensation for lack of transparency and control Insurance companies are less transparent than other investments a shareholder could make Insurance company may not act in the shareholders best interest Cost ranges from 5-200 bps of capital held 2. Cost of Financial Distress Shareholders require extra return for the company-specic risk of ruin (insolvency) Cost ranges from 10-20% of market value (shouldn t exceed franchise value) 3. Regulatory Restriction Costs Cost of holding extra regulatory capital that can t be used for other purposes (like a liquidity risk) Cost ranges from 0-200 bps of restricted capital 4. Double Taxation on Investment Income Insurer s investment income is taxed when it ows through earnings, then it gets taxed again when distributed to shareholders Cost = Tax Rate Taxable Income Taxable income includes eects of statutory/tax reserve changes and the total investment income on capital Try to make yourself look at all of this from the shareholder s perspective. As an investor, you want to know that the return for your investment is consistent with the risks taken. By choosing to invest in an insurance company, you need to be compensated for these insurance-company-specic frictional costs that aren t found in alternative investments. 2016 The Innite Actuary, LLC Page C-48
Life Pricing Study Manual: Section C LP-113: The Economics of Insurance The Replicating Portfolio The portfolio that matches the best estimate of future liability cash ows Provides cash ows to pay claims, expenses, and capital costs Produces the liability Value of liabilities = market value of replicating portfolio Best estimate liability cash ows are easily replicated with risk-free assets The risk in pure insurance (e.g. term life) best estimate cash ows is non-systemic and can be diversied away by shareholders Products with interest rate risk have systemic risk (cannot be diversied away) Requires more sophisticated hedging Replication Risk Inability to nd a portfolio that replicates liability cash ows (e.g. liabilities too long) Treated as a frictional cost Calculating the Economic Value of Liabilities (EVL) 1. Project liability cash ows (premiums, claims, expenses, etc.) 2. Project frictional costs 3. Calculate net liability cash ow at each future point in time Net CF = Premiums Claims Expenses Frictional Costs 4. EVL = PV(Net CF) at risk-free rate The EVL is based on risk-free rates because the cash ows can be replicated with risk-free assets Buy zero-coupon bonds to match years with negative net CF Borrow (short) zero-coupon bonds to match years with positive net CF EVL = Market Value of Long Bonds Market Value of Short Bonds EVL Example Year Premiums Claims Expenses Frictional Costs Net CF 0 100 87 0 13 1 100 50 5 2 43 2 50 5 2 57 The company will receive 43 in year 1 and will have to pay out 57 in year 2 Build a replicating portfolio: 2016 The Innite Actuary, LLC Page C-49
Life Pricing Study Manual: Section C LP-113: The Economics of Insurance Buy zero-coupon bonds maturing for 57 in 2 years Short zero-coupon bonds maturing for 43 in year 1 The long 2-year bonds will fund the net liability payment in year 2, and the borrowed 1-year bonds will be repaid with the positive cash ow in year 1 Assume the risk-free rate is 3% all years: EVL 0 43 1.03 + 57 1.03 2 41.75 + 53.73 11.98 This is the net market value of the risk-free replicating portfolio at time 0 Economic Profit and IRR Economic Prot at Issue Economic Prot = Net CF Change in EVL From the previous example: Economic Prot at Issue 13 11.98 1.02 In other words, the company collected 13 upfront but only had to spend 11.98 to set up the replicating portfolio The IRR of the cash ows is: 13 IRR 1.44% 43 1 + IRR + 57 (1 + IRR) 2 The IRR is the company s cost of borrowing from the policyholder along with the cost of other expenses and frictional costs Since the company borrowed at a rate of 1.44%, then invested in assets yielding 3%, the company earned a spread of 1.56% This illustrates the 2nd way that insurers dier from leveraged investment funds: the borrowing advantage IRR is a ckle animal, especially if the cash ow signs switch a lot. As such, the authors recommend focusing on the absolute economic prot. However, in simple cases like the one above, you might be asked to calculate it on the exam. 2016 The Innite Actuary, LLC Page C-50