About PrARI By Anna Abaimova Background In the early years of our financial life the most important piece of economic wisdom that guides wealth accumulation is the concept of portfolio diversification and asset allocation. Long term financial success, at this stage, is contingent upon one s ability to allocate current and ongoing financial and human capital across many diverse and uncorrelated asset classes. This has guided the financial industry and modern asset management for the last 30 years. However, once the time comes to retire and start withdrawing income from a nest egg and with the ongoing demise of Defined Benefit pensions -- a new set of risks such as longevity, inflation and sequence-of-returns risk 1 threaten chances of financial retirement success. As a result, the famed role of asset allocation diminishes and product allocation becomes the critical component of an effective retirement income risk management strategy. With a myriad of investment and insurance products available to retirees, the new challenge is answering the question: which of these products are suitable for a particular client, and in what proportions? 1 The 2006 paper written by M. Milevsky and T. Salisbury Asset Allocation and the Transition to Income: The Importance of Product Allocation in the Retirement Risk Zone outlines retirement risks in detail. The paper can be downloaded from The IFID Centre s website: www.ifid.ca 1
PrARI: Product Allocation for Retirement Income PrARI 2 -- which is an acronym for Product Allocation for Retirement Income -- is a proprietary methodology that was developed by the QWeMA Group, Toronto, Canada and is a module within QWeMA VIEW Version 1.0. The algorithmic core of this program does not rely on cumbersome computer (a.k.a. Monte Carlo) simulations to arrive at optimal product allocations and probabilities. Rather, the underlying algorithms calculate all relevant probabilities and expectations using unique and novel analytic approximations as well as PDE-based methods. Aside from offering a fast and efficient methodology of assessing and optimizing retirement product and asset allocation strategies, PrARI is based on a developing economic philosophy. This is the view that while there are seemingly countless options when it comes to retirement products and product features, they can typically be classified under one of PrARI s three retirement product silos. In other words, the PrARI approach is about decomposing retirement income products into their respective silos, and then determining how much of one s wealth should be allocated to these silos, all using unique mathematical algorithms. Specifically, the PrARI program considers three principal financial and insurance categories for the construction of a comprehensive product allocation strategy: 1) The systematic withdrawal plan (SWiP), or a method by which a portfolio of mutual funds or a managed account is periodically liquidated to generate a fixed and predicable income. 2) The guaranteed living income benefit (GLiB), which includes guaranteed minimum withdrawal benefits (GMWB) for life and/or guaranteed minimum income benefits (GMIB). This category captures the benefit and value of the market contingent life annuities. 2 PrARI is a registered trademark of the QWeMA Group Inc. 2
3) Lifetime payout income annuities (LPIA) such as single premium immediate annuities (SPIA) or advanced life delayed annuities (ALDA). In general, this product category captures the benefit and value of longevity protection within a retirement strategy. And, while this product category is currently the least favored or popular in the retirement income space, QWeMA group and the PrARI algorithm consider it to be deserving of its own retirement income silo. Each product varies in its effectiveness at addressing the above-mentioned retirement risks and retirement goals which may include maintaining liquidity for varying cash needs, maximizing estate value and addressing behavioral weaknesses. A valuable benefit offered by a product is typically offered at the expense of another risk management or goal achievement attribute. Consequently, economic tradeoffs are at the heart of the retirement product allocation problem. For instance the lifetime payout annuity (LPiA) completely hedges longevity risk by guaranteeing income for life but at the expense of liquidity, bequest, and flexibility. On the other hand the SWiP offers full flexibility with respect to liquidity and bequest but fails to address longevity and sequence-of-returns risks. The optimal product allocation is therefore driven by one s diametrically opposed priorities: 1) security and sustainability of the desired retirement income versus 2) the maximization of the estate value for heirs and beneficiaries. For each set of individual and economic parameters and product allocation the PrARI program calculates the Retirement Sustainability Quotient (RSQ), which is the overall probability that a given product allocation and asset allocation will generate the desired level of income for the remainder of one s life. As well, a corresponding Expected Discounted Bequest (EDB) value will be generated; this is the current value of the projected amount that is expected to be left to the client s estate upon death. We can not emphasize enough how critical it is for retirees and their advisors to understand that RSQ and EDB are the two most important dimensions of retirement income planning, and that it is incomplete and misleading to focus on only one of these two dimensions. Strategies that maximize sustainability will inherently reduce the discounted value of bequest, and vice versa. 3
Inputs As a starting point, a number of client-specific input variables must be entered. The required demographic characteristics include: the client s (and the spouse s, if applicable) current age, gender, health and the number of years that remains until retirement. The client s starting financial position is also gauged through inputs including: the starting liquid wealth available for investment and the amount of inflationadjusted desired annual income. The inflation-adjusted amount of any defined benefit pension income (that is guaranteed for life) must also be specified within the Preexisting Pension Income field. This income will be subtracted from the desired retirement income value to arrive at the income gap, which will be bridged or funded using a combination of the three retirement product categories. The user is also welcome to modify the settings or the default assumptions regarding expected asset class performance as well as the swap yield curve (to be used for annuity and EDB pricing) within the Capital Market panel. Here, a cost of living adjustment (COLA) rate can also be specified, which will serve as a proxy for personal retirement inflation. In the Mortality Rates panel, the user can modify mortality assumptions that are used for annuity payment and RSQ calculations, if an alternate mortality table is preferred. The program automatically recalculates the probability that this individual survives to age 90. Annual LPIA payout rates, promised in return for an initial deposit of $100,000 are also automatically generated within the Immediate Annuity panel based on mortality and swap curve input values. Once again, the user is free to modify these payouts if needed. Finally, the GLiB Parameters panel captures the characteristics of the available living benefit. The annualized asset-based insurance fee charged for the elected rider is specified as well as the bonus rate that may be credited on the invested sum if no withdrawals are made prior to retirement. Finally, the withdrawal rate that will be applied to the account base to calculate the income guaranteed for the client s life is also entered. Once the user makes all desired changes within the settings panels, clicking OK will save these preferences for the current and subsequent PrARI session. 4
Varying all of the above assumptions and settings will lead to unique points on the retirement income frontier illustrated below: 1) Universe of Available Products 2) Universe of Available Assets Product/Asset Mix 1 Product/Asset Mix 2 Product/Asset Mix 3 Retirement Wealth Age Gender Health Pension & Social Security Summary Input Variables Desired Spending Plan EDB Capital Market Projections & Assumptions 0% RSQ 100% PrARI Analyzer This section of the PrARI module assesses the sustainability of a particular userspecified product allocation and the underlying asset allocation. The user enters the percentage of the portfolio that is to be allocated to each of the three main product classes and estimates what fraction of these investments are equity-based and bondbased. Note that in QWeMA VIEW 1.0, the PrARI module does not allow for allocations to equity and cash-based LPIAs. Taking into account client and portfolio characteristics, the program computes the RSQ or overall probability that the client s allocation and spending strategy is sustainable and will not result in income shortfall. As well, the program computes the current value of the expected estate value or the EDB. 5
PrARI Optimizer In contrast to the PrARI Analyzer, the PrARI Optimizer determines a unique and optimal product and asset allocation for the client based on demographic characteristics, financial circumstances and most importantly his criteria or priorities. The user should select the option to Maximize RSQ subject to EDB> x if the objective is to obtain the greatest possible protection against longevity risk and to maximize retirement income sustainability while leaving the minimum specified EDB of x dollars. Alternatively, the client may have other sources of guaranteed retirement income and can tolerate a lower probability of retirement income sustainability in order to maximize the value to be left to his or her beneficiaries. In this case, the user should choose to Maximize EDB subject to RSQ> x. The PrARI Optimizer will then return a product and asset allocation that maximizes the EDB while achieving the minimum desired RSQ of x percent. Note that in QWeMA VIEW 1.0, the PrARI Optimizer presents allocations with a granularity of 5%. Future program version will allow for greater flexibility. 6
Once again, the user is reminded of underlying economic tradeoff that will be apparent within the optimized solution and the resulting RSQ and EDB values. A high overall income sustainability probability may come at the expense of an estate goal and vice versa. When interpreting a given product allocation, note that from a financial engineering perspective, the main difference between a SWiP-based retirement income product and GLiB-based product is that although both products behave similarly in the first few years of their life, the GLiB contains a long-dated put option that kicks in if and when the underlying account hits zero. Thus, while a SWiP would terminate and cease providing income, a GLiB would continue, for life. Stated differently, this means that a family unit that relies exclusively on a SWiP to fund a parent s retirement is essentially "short" this long dated put option, which exposes the family unit to risk and reduces the potential for any bequest or estate transfer. We call this put option an RCLA, which stands for ruincontingent life annuity. On a slightly more technical level, the difference between the expected discounted bequest (EDB) of the funds allocated to a SWiP versus the EDB for funds allocated to GLiB, is precisely the RCLA value 3. Of course, the ongoing fee for GLiB-like product is higher than a SWiP-like product, which essentially "pays" for this RCLA. 3 For a detailed explanation of the RCLA, please refer to the following paper: A Different Perspective on Retirement Income Sustainability: Introducing the Ruin Contingent Life Annuity (RCLA)" (H. Huang, M.A. Milevsky, T.S. Salisbury). The paper can be downloaded from The IFID Centre s website: www.ifid.ca 7
Numerical Example For an illustration of PrARI s optimizer process, consider the following hypothetical example. Michael, who is in excellent health is about to turn 62 years old and take an early retirement. He has been self-employed throughout his working years and has accumulated $1.5 million in retirement savings. In planning his retirement product allocation strategy, he identifies his main goal to be achieving a spending of $87,000 per year, after inflation. He is not concerned with leaving a large sum to his estate and hopes to leave only a portion of his nest egg to cover any remaining expenses. Given Michael s good health and the fact that he does not have a pension that will last for the remainder of his life, he is most concerned with maintaining a substantial spending rate and hedging against longevity risk. His criteria, therefore, is to maximize his RSQ while achieving a minimum EDB of $225,000 (or $15 per initial deposit of $100). The economic and financial settings 4 are summarized below: 4 Please note that this set of parameters was prepared for illustrative purposes only. The example was conducted in real or inflation-adjusted terms. 8
The optimal product and asset allocation, given Michael s financial circumstances and retirement priorities, is displayed below. He will spend $87,000 per year in real dollars, and achieve an expected discounted bequest value of $226,195. The RSQ, or probability of meeting his spending goal is approximately 88%. 9
Michael s financial circumstances and criteria are reflected in his optimized allocation: The 40% allocation to the LPIA can be attributed to the product s excellent ability to hedge against longevity risk Michael s main concern. Similarly the solution involves a large allocation to the SWiP to provide liquidity that is needed for a high withdrawal rate. Note that along with the allocation among the three retirement income product categories, the PrARI Optimizer derives Michael s asset allocation: 40% of his portfolio value will be allocated to bonds and 60% to equity. While this hypothetical example should not be taken as actual investment and insurance recommendations, it illustrates the use of PrARI as a tool for thinking about the variables that affect the economic tradeoffs in retirement. It is the beginning of a discussion rather than the end of a process. In Sum Today there is little if any disagreement among financial professionals regarding the existence and relevance of unique risks that await clients in the retirement income phase. And, rather than trying to predict the outcomes of the inflation, longevity and sequence-of-returns variables, one should insure against adverse outcomes by adapting an appropriate product allocation strategy. Relying upon traditional asset allocation alone will not be enough. Rather, all three product categories income annuities, mutual funds within a systematic withdrawal plan, and guaranteed living income benefit riders -- should be mixed and matched in various combinations to maximize one s retirement sustainability quotient. The PrARI program a module within QWeMA VIEW 1.0 offers its users a fast and reliable analytic methodology which provides guidance and a basis for discussion for advisors and their clients as they plan the allocation of their retirement nest egg. In future versions of QWeMA VIEW the scope of PrARI will be broadened to assess other dimensions of an optimal product portfolio at advanced ages including the role of taxes, life and long term care insurance, personal debt and refined asset allocations. 10
Contact and Support To review research papers on the topic of retirement income risk management and product allocation, please visit: www.qwema.ca For technical support, please contact a QWeMA group representative at: support@qwema.ca 11