Retirement Income Adequacy With Immediate and Longevity Annuities

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1 May 2011 No. 357 Retirement Income Adequacy With Immediate and Longevity Annuities By Youngkyun Park, Employee Benefit Research Institute UPDATING EARLIER EBRI ANALYSIS: This Issue Brief updates with recent information and estimates on retirement and health care expenditures a previous EBRI analysis (from 2006), which quantified how different types of risk (investment income, longevity, and long-term care risk), asset allocation, and percentage of annuitization affect retirement income adequacy. IMPACT OF IMMEDIATE AND LONGEVITY ANNUITIES ON RETIREMENT INCOME ADEQUACY: This report analyzes how differently immediate and longevity annuities can affect probable income adequacy in retirement by taking into account long-term health care expenditures. Specifically, it attempts to find the optimal level of annuitization and asset allocation that would provide a desired level of confidence that individuals will have sufficient retirement income, based on the three different types of risk: investment income, longevity, and long-term care. Immediate annuities, as the name implies, begin distributions to the owner as soon as they are purchased; longevity annuities delay distributions to a specified later age, to help protect the owner against the risk of outliving his or her assets. KEY FINDINGS: Annuitization by using either immediate or longevity annuities appears to be more effective for retirees with low income than those with high income to reach a desired level of retirement income adequacy under certain conditions. As previous research has shown, adding in retiree health and long-term care costs to the retirement calculation dramatically increases estimated retirement costs and the initial retirement wealth needed to finance those costs. The impact of an immediate annuity on retirement income adequacy: Simulation results show that for a male retiring at 65 facing investment and longevity risk, who desires a 90 percent chance of retirement income adequacy with an immediate annuity, could optimally achieve that target by fully annuitizing his initial retirement wealth regardless of different equity allocations in his portfolio. However, if he is assumed to be facing investment, longevity, and long-term care risk, he would need to annuitize percent (not 100 percent) of his initial retirement wealth; some portion of his initial retirement wealth should be reserved to finance unexpected long-term care costs. The impact of a longevity annuity on retirement income adequacy: To achieve the same (90 percent) chance of retirement income adequacy with a longevity annuity, simulation results show that when the retiree faces all the three types of risk (investment, longevity, and long-term care risk), he should increase the allocation of his initial retirement wealth to both a longevity annuity and equities in his portfolio, compared with when he faces only investment and longevity risk. The increased allocations to a longevity annuity and equities are to cover the unexpected significant long-term care costs. A research report from the EBRI Education and Research Fund 2011 Employee Benefit Research Institute

2 Youngkyun Park is research associate the Employee Benefit Research Institute. This Issue Brief was written with assistance from the Institute s research and editorial staffs. Any views expressed in this report are those of the author, and should not be ascribed to the officers, trustees, or other sponsors of EBRI, EBRI-ERF, or their staffs. Neither EBRI nor EBRI-ERF lobbies or takes positions on specific policy proposals. EBRI invites comment on this research. Copyright Information: This report is copyrighted by the Employee Benefit Research Institute (EBRI). It may be used without permission but citation of the source is required. Recommended Citation: Youngkyun Park, Retirement Income Adequacy With Immediate and Longevity Annuities, EBRI Issue Brief, no. 357, May Report availability: This report is available on the Internet at Table of Contents Introduction... 4 Methodology... 4 Three Building Blocks... 6 Results... 7 Building Block Building Block Immediate and Longevity Annuities: Building Blocks 2 and Retirement Income Adequacy Under Building Block Retirement Income Adequacy Under Building Block Conclusion References Endnotes Figures Figure 1A-B, Impact of Initial Retirement Wealth on the Probability of Retirement Income "Adequacy," by Equity Allocation... 8 Figure 2A, Necessary Final Earnings Multiple for Retirement Income "Adequacy," by Retirement Income Category and Equity Allocation... 9 B. Necessary Replacement Rates for Retirement Income "Adequacy," by Retirement Income Category and Equity Allocation... 9 Figure 3A B, Impact of Initial Retirement Wealth on the Probability of Retirement Income "Adequacy," by Equity Allocation With No Annuitization Figure 4A D, Impact of Initial Retirement Wealth on the Probability of Retirement Income "Adequacy," by Annuitization Figure 5A, Replacement Rates Required for a Chance of "Adequacy": Building Block 2 and Lowest Income Category B. Replacement Rates Required for a 75% Chance of "Adequacy": Lowest Income Category C. Replacement Rates Required for a Chance of "Adequacy": Lowest Income Category Figure 6A, Replacement Rates Required for a Chance of "Adequacy": Building Block 2 and Highest Income Category B. Replacement Rates Required for a 75% Chance of "Adequacy": Highest Income Category ebri.org Issue Brief May 2011 No

3 C. Replacement Rates Required for a Chance of "Adequacy": Highest Income Category Figure 7, Impact of Final Earnings on Probability of "Adequate" Retirement Income, by Income Category, Equity Allocation, and Annuitization Figure 8A D, Impact of Initial Retirement Wealth on the Probability of Retirement Income "Adequacy," by Annuitization Figure 9A, Replacement Rates Required for a Chance of "Adequacy": Building Block 3 and Lowest Income Category B. Replacement Rates Required for a 75% Chance of "Adequacy": Lowest Income Category C. Replacement Rates Required for a Chance of "Adequacy": Lowest Income Category Figure 10A, Replacement Rates Required for a Chance of "Adequacy": Building Block 3 and Highest Income Category B. Replacement Rates Required for a 75% Chance of "Adequacy": Highest Income Category C. Replacement Rates Required for a Chance of "Adequacy": Highest Income Category Figure 11, Impact of Final Earnings on Probability of "Adequate" Retirement Income, by Income Category, Equity Allocation, and Annuitization: Building Block Figure 12, Multiple of Final Earnings for a Chance of Adequacy in Building Block 2: Immediate and Longevity Annuities, For: Males Retiring at Age 65 in the Lowest Income Category Figure 13, Multiple of Final Earnings for a Chance of Adequacy in Building Block 2: Immediate and Longevity Annuities, For: Males Retiring at Age 65 in the Highest Income Category Figure 14, Multiple of Final Earnings for a Chance of Adequacy, by Equity Allocation and Annuitization With Longevity Annuity: Building Block Figure 15, Multiple of Final Earnings for a Chance of Adequacy in Building Block 3: Immediate and Longevity Annuities, For: Males Retiring at Age 65 in the Lowest Income Category Figure 16, Multiple of Final Earnings for a Chance of Adequacy in Building Block 3: Immediate and Longevity Annuities, For: Males Retiring at Age 65 in the Highest Income Category Figure 17, Multiple of Final Earnings for a Chance of Adequacy, by Equity Allocation and Annuitization With Longevity Annuity: Building Block ebri.org Issue Brief May 2011 No

4 Introduction Measuring retirement income adequacy has been done in a variety of ways. One of them is a replacement rate, which is defined as a ratio of retirement income to preretirement income (or final earnings). VanDerhei (2006) conducted an in-depth study on replacement rates, considering three different types of risk (investment income, longevity, and longterm care risk), which a retiree needs to consider for retirement income adequacy. His research used the EBRI Ballpark E$timate Monte Carlo. This Issue Brief updates his previous analysis (VanDerhei, 2006) with recent information/estimates on retirement and health care expenditures. In addition, this report also examines retirement income adequacy of retirees facing the three types of risk listed above, but for those who have immediate and longevity annuities. The previous Issue Brief (2006) explored retirement income adequacy with an immediate annuity, whereas this report extends the analysis by including a longevity annuity as well as an immediate annuity. Longevity annuities are similar to immediate annuities in that they provide a stream of fixed benefits over time (usually until death). Unlike other annuities, however, a longevity annuity starts to distribute its payments only when the retiree reaches an advanced age, such as 80 or 85. Because of this, a longevity annuity is often referred to as an advanced life deferred annuity (Milevsky, 2005). The price of a longevity annuity is lower than that of an immediate annuity, because it is mainly determined by conditional survival, which declines with age. In other words, a longevity annuity distributes higher payments per premium dollar compared with an immediate annuity, because the payments are deferred until a commencement age at which the chance of survival declines. This Issue Brief analyzes the influence of longevity annuities on retirement income adequacy by incorporating retirement expenditures (including long-term health care costs) based on nationwide survey estimates into simulation models. This approach differs from previous studies on longevity annuities (e.g., Webb, Gong, and Sun, 2007; Scott, 2008). Scott calculated additional spending available by purchasing a longevity annuity instead of an immediate annuity but did not explicitly include retirement expenditures in his models. Webb, Gong, and Sun (2007) assumed that retirees would undertake an optimal spending of unannuitized wealth that maximizes expected discounted utility or a simple rule of thumb by setting annual consumption equal to some percentage of initial wealth; thus, they were not able to include long-term care costs, which can be financially catastrophic to retirees. Therefore, inclusion of more realistic retirement expenditures (including potential catastrophic long-term care costs) would provide a meaningful comparison of the benefits from immediate and longevity annuities. There is one caveat to the simulation results presented in this Issue Brief. The simulations are conducted for a male retiring at age 65 with specific assumptions on the long-term capital market and investment expenses, the long-term inflation rate, and the mortality table. The first section of this Issue Brief briefly discusses methodology, which includes retirement income adequacy, retirement expenditures and income, long-term capital market assumptions, and three building blocks. The following sections discuss retirement income adequacy with simulation results based on recent information/estimates, a comparison of the benefits of immediate and longevity annuities, and a conclusion. Methodology This analysis of retirement income adequacy starts with a male who is retiring at age 65. As for his retirement income adequacy, it uses the definition adopted in the 2006 Issue Brief (VanDerhei, 2006). If the sum of the simulated investment income, amounts paid from Social Security, and the annuitized portion of the initial retirement wealth (if any), is more than the simulated expenditures for the year, the excess amounts are invested. However, if any deficits occur, the deficit is removed from the accumulated retirement wealth. A large number of simulated life-paths (e.g., 10,000 paths) are run with the specified initial retirement wealth. If there is a non-negative amount at the end of the simulated life-path, this path is regarded as one generating adequate retirement income. After the simulation runs, a ebri.org Issue Brief May 2011 No

5 probability of adequate retirement income is computed. This value is interpreted as the percentage of simulated lifepaths with adequate retirement income. Following the previous study of VanDerhei (2006), retirement expenditures are assumed to consist of two components: (a) basic retirement expenses net of health care that the elderly incur in their life, and (b) health care costs. Retirement expenditures net of health care include food, apparel and services, transportation, entertainment, reading and education, and housing. Specifically, the retirement expenditures net of health care are determined based on the following final earnings categories (in 2009 dollars) for single male retirees: Those with final income less than $16,932 (Category 1) Those with final income less than $34,860 (Category 2) Those with final income less than $58,764 (Category 3) Those with final income $58,764 or more (Category 4). 1 Based on the 2008 Consumer Expenditure Survey (CES), retirement expenditures in 2009 dollars (net of health care) by income categories are used as follows: $14,209 for Category 1, $15,433 for Category 2, $20,328 for Category 3, and $26,239 for Category 4. As for health care expenditures, two types of estimated expenditures are used deterministic and stochastic which are discussed in detail in the section on the three building blocks. For purposes of this analysis, a retiree is assumed to receive annual retirement income from three sources: first, annuitized income from an immediate or longevity annuity purchased with his initial retirement wealth; second, initial Social Security benefits; and third, investment income from the initial retirement wealth or the remaining wealth after annuitization, if any. For simplicity, payments from defined benefit retirement plans are not included. 2 For annuitized income at retirement, two types of annuities are considered: immediate and longevity annuities. Specifically, a male retiring at age 65 is assumed to purchase an annuity that starts immediately to distribute lifetime payments, or a longevity annuity that starts to distribute lifetime payments beginning at age 85. The prices of an immediate annuity and a longevity annuity are calculated by using the quotes from the website at the end of 2009, and from MetLife s Longevity Income Guarantee (maximum income version) as of September 18, 2009, respectively. 3 Initial Social Security benefits are calculated for the four income categories from the 2008 Current Population Survey (CPS) data. All the 2008 values were brought forward to 2009 by decreasing the values by 0.4 percent, because the CPI inflation in 2009 was 0.4 percent. In addition to annuitized income at retirement, investment income from initial retirement wealth or remaining wealth after annuitization (if any) is assumed to be generated from a portfolio consisting of three asset classes: U.S. equity, non-u.s. equity, and fixed income. An equity portfolio is constructed with a ratio of 67 percent U.S. equity to 33 percent non-u.s. equity. The expected rate of return and volatility of each asset class, and correlations between the classes, are assumed to follow those of three assets extracted from JP Morgan s long-term capital market return assumptions as of November 30, 2009 (JP Morgan, 2009). 4 Based on the long-term capital market assumptions, simulated portfolio returns are generated annually, which follow a joint log-normal independent and identical distribution. In addition, investment expenses for equities and fixed income are assumed to be 99 basis points and 75 basis points, respectively (Collins, 2010). 5 For this Issue Brief, a general inflation rate (with the exception of health care cost inflation) is assumed to be 2.8 percent, which was used as a long-term inflation rate by the 2009 Annual Report of the Board of Trustees of the Federal Old-Age and Survivors Insurance and Federal Disability Insurance Trust Funds (OASDI) for intermediate-cost assumptions. Health care cost inflation is discussed in the section on Building Block 3. ebri.org Issue Brief May 2011 No

6 Three Building Blocks The 2006 Issue Brief introduced three building blocks to describe appropriate replacement rates for retirement planning (VanDerhei, 2006). This section briefly reviews these building blocks with updated information and estimates. Building Block 1: Investment Risk Building Block 1 focuses on investment risk related to equity allocation. As a retiree increases his equity allocation, he may benefit from a higher-than-expected investment income, but also faces a larger downside risk from investment losses. Regarding longevity, a retiree is assumed to have the average life expectancy (or average longevity). For example, a male retiring on his 65 th birthday is assumed to live to his 82 nd birthday, based on the 2001 Commissioners Standard Ordinary (CSO) mortality table. 6 (However, it should be noted that 50 percent of the population will live beyond the average life expectancy.) As well as average longevity, Building Block 1 also assumes average health care costs. Two types of health care expenses are discussed in this article: deterministic (or single-point estimate) and stochastic (or probabilistic). Building Block 1 includes only deterministic health care expenses. Deterministic health care costs for retirees consist of two parts insurance premium estimates, such as Medicare Part B and Part D and Medigap premiums, and out-of-pocket expenditures that are not fully reimbursed (or not covered) by Medicare and/or private Medigap health insurance. For simplicity, however, this analysis does not consider Medicaid, which could partly cover the deterministic health care expenses. The exclusion of Medicaid (for those who meet the income and asset tests) from the model would underestimate a probability of adequate retirement income (in particular, for retirees with low income), which is determined by whether there is a non-negative balance at the end of the simulated life-path. For this analysis, the annual Medicare Part B premium is assumed to be $1,157 adjusted for future inflation at 3.5 percent, and the Medicare Part D premium is assumed to be $364 adjusted for future inflation at 7.0 percent. 7 The annual Medigap premium is assumed to be $1,479, adjusted for future inflation at 3.5 percent, which is the same as that of the Medicare Part B premium. 8 Lastly, out-of-pocket expenditures are estimated by the four income categories based on the 2008 CES, and its annual growth rate is assumed to be 7.0 percent, which is the same as that of the Medicare Part D premium. 9 Building Block 2: Investment and Longevity Risk Building Block 2 incorporates both investment income and longevity risk into the planning process. Longevity risk refers to the risk of a retiree outliving his assets. The assumption of the average life expectancy used in Building Block 1 is relaxed in Building Block 2 by reflecting the full mortality table. To deal with longevity risk, a retiree may buy a life annuity upon retirement. A retiree under Building Block 2, therefore, is assumed to be able to purchase an immediate annuity at the end-of-year 2009 price. 10 As for health care costs, Building Block 2 assumes deterministic health care expenses, as does Building Block 1. Building Block 3: Investment, Longevity, and Long-term Care Risk Unlike Building Blocks 1 and 2, Building Block 3 deals with stochastic health care costs that include (1) nursing home or home-based health care and (2) prescription drug costs. First, long-term care costs are simulated based on the incidence of nursing home and home health care expenses, which are estimated from the 1999 and 2004 National Nursing Home Surveys (NNHS) and the 2000 and 2007 National Home and Hospice Care Surveys (NHHCS), respectively. 11 A retiree at age 65 is assumed to be in one of four possible health states: (1) home health care patient, (2) nursing home care patient, (3) not receiving either home care or nursing home care, and (4) death. For the four states, a transition probability matrix is constructed, which determines whether a retiree stays in the current state or moves to one of the other states. A transition continues until death. 12 A transition probability matrix is constructed based on the estimates of two surveys, the 1999 NNHS and the 2000 NHHCS. Since the four states are related to age, the transition probability matrix is dependent on age. The transition probability matrix is built up to the age at which a survival rate is equal to zero. 13 ebri.org Issue Brief May 2011 No

7 For those who are in a state of nursing home or home health care, stochastic long-term care expenses are determined by a product of two factors: the length of stay/number of days of care, and costs of the long-term care. The duration of care is simulated based on the distribution of the length of stay/care found in the 1999 NNHS and the 2000 NHHCS. For costs of the long-term care, estimated monthly costs are used from the 2004 NNHS and the 2009 NHHCS. 14 However, it should be noted that this analysis does not consider Medicaid, as mentioned earlier. The exclusion of Medicaid-covered long-term health care costs for low-income individuals would underestimate the probability of adequate retirement income for retirees in the lowest-income category. Second, prescription drug costs are simulated based on the distribution of the prescription medicine costs from the 2004 Medical Expenditure Panel Survey by five age groups: 65 69, 70 74, 75 79, 80 84, and 85 or older. The simulated prescription drug costs are adjusted with the annual growth rates of Medicare Part D premiums for 2006 to In sum, stochastic health care costs in Building Block 3 consist of Medicare Part B, Part D, and Medigap premiums, simulated prescription drug costs, and simulated long-term care costs of home care or nursing home care. As for long-term care inflation, nursing home, and home health care fees are assumed to be adjusted annually by 5.0 percent and 3.0 percent, respectively, which are the average annual growth rates of the daily base rate for 2003 to 2008 (Prudential Long-Term Care Cost Study, 2008). Prescription drug costs, on the other hand, are assumed to be adjusted for future inflation at 7.0 percent, the same as that of Medicare Part D premium. Results This section discusses retirement income adequacy in terms of a probability of adequate retirement income in relation to initial retirement wealth. Initial retirement wealth is specified as a dollar amount, a multiple of final earnings, or a replacement rate which is defined as a ratio of the annual amount of an individual s retirement income to final earnings just prior to retirement. Retirement income adequacy is discussed by locating the highest probability of adequacy (or the highest success rate) for a given initial retirement wealth or the lowest multiple of final earnings (or the lowest replacement rate) for a given probability of adequacy. Building Block 1 Building Block 1 focuses on retirement income adequacy against only the investment income risk that is related to equity allocation. Panel A of Figure 1 shows simulation results for a male retiring at age 65 and living to age 82 in the lowest-income category. Different equity allocations lead to different probabilities of adequacy for a given level of initial retirement wealth. For example, if a worker were to retire with an account balance of $150,000 and allocated 5 percent to equities, he would have no chance of having adequate retirement income. However, if he increased his investment in equities to 95 percent, he would have a 39 percent probability of success because of the possibility that he could derive higher investment income from equities. Panel B of Figure 1 provides similar results for the stylized retiree but in the highest-income category. Since retirement expenditures are assumed to increase with income, the retiree in the highest-income category would need a larger initial retirement wealth to get the same probability of success, or have a lower probability of success with the same level of initial retirement wealth. For a retiree with an account balance of $150,000, for example, the success rate with a 95 percent equity allocation is 30 percent, which is lower than the retiree in the lowest-income category. Alternatively, retirement income adequacy can be discussed in terms of multiple final earnings or replacement rates by locating its lowest value in a given probability of adequacy. Panels A and B of Figure 2 demonstrate final earnings multiples and replacement rates, respectively, by the probability of adequacy and equity allocation in different income categories. ebri.org Issue Brief May 2011 No

8 Figure 1 A. Impact of Initial Retirement Wealth on the Probability of Retirement Income "Adequacy," by Equity Allocation For: Males Retiring at Age 65 in the Lowest Income Category Building Block 1: investment income stochastic, and longevity and health care expenses deterministic Probability of Adequacy 8 $0 $50,000 $100,000 $150,000 $200,000 $250,000 $300,000 $350,000 $400,000 $450,000 $500,000 Initial Retirement Wealth 5% Equity Allocation 25% Equity Allocation Equity Allocation 75% Equity Allocation 95% Equity Allocation Probability of Adequacy 8 B. Impact of Initial Retirement Wealth on the Probability of Retirement Income "Adequacy," by Equity Allocation For: Males Retiring at Age 65 in the Highest Income Category Building Block 1: investment income stochastic, and longevity and health care expenses deterministic $0 $50,000 $100,000 $150,000 $200,000 $250,000 $300,000 $350,000 $400,000 $450,000 $500,000 Initial Retirement Wealth 5% Equity Allocation 25% Equity Allocation Equity Allocation 75% Equity Allocation 95% Equity Allocation Source: Simulations from Ballpark E$timate Monte Carlo, Employee Benefit Research Institute. ebri.org Issue Brief May 2011 No

9 Figure 2 A. Necessary Final Earnings Multiple for Retirement Income "Adequacy," by Retirement Income Category and Equity Allocation Retirement Income Category Probability of Retirement Income Equity Allocation 5% 25% 75% 95% "Adequacy" % % % % B. Necessary Replacement Rates for Retirement Income "Adequacy," by Retirement Income Category and Equity Allocation Retirement Income Probability of Retirement Income For: Males Retiring at Age 65 Building Block 1: Investment income stochastic, and longevity and health care expenses deterministic For: Males Retiring at Age 65 Building Block 1: Investment income stochastic, and longevity and health care expenses deterministic Equity Allocation 5% 25% 75% 95% Category "Adequacy" % % % 75% 133.8% 130.7% 130.9% 133.1% 136.4% 138.2% 136.6% 140.9% 148.8% 158.5% % 62.1% 60.9% 60.1% 59.9% 75% % 65.9% 66.5% 65.9% 67.3% % % 45.2% 44.7% 44.5% 75% 48.1% 47.4% 47.4% 47.9% 48.6% 49.1% 48.7% 49.7% 51.5% 53.6% % 33.7% % 32.4% 75% 35.2% 34.7% 34.7% 35.1% 35.7% % 36.5% 37.9% 39.6% Source: Simulations from Ballpark E$timate Monte Carlo, Employee Benefit Research Institute. ebri.org Issue Brief May 2011 No

10 Figure 2 shows that different retirement income adequacy targets need different equity allocations. For example, if a lowest-income retiree desires a 50 percent probability of adequacy, a 95 percent equity allocation (combined with a 5 percent fixed income investment) would lead to the lowest necessary initial retirement wealth for adequacy, in terms of a multiple of final earnings (Panel A) or a replacement rate (Panel B). This 95 percent equity allocation is valid across different income categories. However, if the retiree aims for a 90 percent probability of adequacy, a 25 percent equity allocation would be relatively optimal compared with other equity allocations. The 25 percent equity allocation also applies to the other income categories. Building Block 2 In contrast to Building Block 1, which assumes average life expectancy, Building Block 2 incorporates longevity risk into the model by reflecting the full mortality table. Figure 3 provides the same analysis for the lowest-income retiree (Panel A) and the highest-income retiree (Panel B) as in Figure 1. However, longevity risk leads to different results from those of Figure 1. Specifically, longevity risk results in a non-zero probability of adequacy with low initial retirement wealth (because there is a chance of dying before exhausting the initial retirement wealth). For example, if a worker were to retire with an account balance of $150,000 and had allocated 5 percent of his account balance to equities, he would have a zero probability of adequacy under Building Block 1, but about a 32 percent probability of adequacy under Building Block 2. At the same time, however, longevity risk requires larger initial retirement wealth to meet a higher probability of retirement income adequacy. For example, if the retiree sought a 90 percent probability of adequacy, he would need initial retirement wealth of about $210,000 under Building Block 1, but about $350,000 under Building Block 2. Figure 4 demonstrates the value of purchasing an immediate annuity at retirement (at age 65) to achieve a higher probability of retirement income adequacy. For example, a retiree in the lowest-income category who has a 5 percent equity allocation (Panel A) would be better off annuitizing his initial retirement wealth, if he desires more than a 40 percent probability of retirement adequacy. Panel B shows the retiree having a 50 percent equity allocation would be better off annuitizing, for at least a 50 percent probability of adequacy. For retirees in the highest-income category, Panels C and D demonstrate results similar to those of Panels A and B. Figure 5 (a retiree in the lowest-income category) and Figure 6 (a retiree in the highest-income category) show that an optimal level of annuitization would vary by equity allocations as well as the probability of target retirement income adequacy. If a retiree in the lowest-income category desires a 50 percent chance of adequacy, he would achieve this target adequacy with a combination of no annuitization and a 95 percent equity allocation. However, if he desires a 75 percent or 90 percent chance of adequacy, a full annuitization would be optimal. Then equity allocations would marginally influence the optimality. Similar results are also found for the retiree in the highest-income category (Figure 6). Figure 7 demonstrates final earnings multiples by different probabilities of adequacy, equity allocations, degrees of annuitization, and income categories. An optimal level of annuitization and equity allocation is found by locating the lowest multiples of final earnings in a given target of retirement income adequacy. For example, if a retiree in the lowest-income category desires a 50 percent chance of adequacy, he would optimally achieve the target adequacy by selecting a combination of no annuitization and a 95 percent equity allocation. However, if he desires a 90 percent chance of adequacy, he should choose a combination of a full annuitization and a 95 percent equity allocation. Building Block 3 Building block 3 includes two stochastic components related to health care costs: long-term care (nursing home or home-based care) and prescription drug costs. Long-term care costs can be financially catastrophic and, thus, devastate retirement income adequacy. Building Block 3 deals with this long-term care risk. The following tables provide a simple example of the impact of adding stochastic long-term care costs on retirement income adequacy in the lowest- and highest-income categories in terms of replacement rates. The table is constructed by assuming a 50 percent equity allocation and no annuitization at retirement. ebri.org Issue Brief May 2011 No

11 Figure 3 A. Impact of Initial Retirement Wealth on the Probability of Retirement Income "Adequacy," by Equity Allocation With No Annuitization For: Males Retiring at Age 65 in the Lowest Income Category Building Block 2: investment income and longevity stochastic, health care expenses deterministic Probability of Adequacy 8 $0 $50,000 $100,000 $150,000 $200,000 $250,000 $300,000 $350,000 $400,000 $450,000 $500,000 Initial Retirement Wealth 5% Equity Allocation 25% Equity Allocation Equity Allocation 75% Equity Allocation 95% Equity Allocation B. Impact of Initial Retirement Wealth on the Probability of Retirement Income "Adequacy," by Equity Allocation With No Annuitization Probability of Adequacy For: Males Retiring at Age 65 in the Highest Income Category Building Block 2: investment income and longevity stochastic, health care expenses deterministic 8 $0 $50,000 $100,000 $150,000 $200,000 $250,000 $300,000 $350,000 $400,000 $450,000 $500,000 Initial Retirement Wealth 5% Equity Allocation 25% Equity Allocation Equity Allocation 75% Equity Allocation 95% Equity Allocation Source: Simulations from Ballpark E$timate Monte Carlo, Employee Benefit Research Institute. ebri.org Issue Brief May 2011 No

12 Figure 4 A. Impact of Initial Retirement Wealth on the Probability of Retirement Income "Adequacy," by Annuitization 5% Equity Allocation For: Males Retiring at Age 65 in the Lowest Income Category Building Block 2: investment income and longevity stochastic, health care expenses deterministic Probability of Adequacy 8 $0 $50,000 $100,000 $150,000 $200,000 $250,000 $300,000 $350,000 $400,000 $450,000 $500,000 Initial Retirement Wealth Annuitization 25% Annuitization Annuitization 75% Annuitization Annuitization B. Impact of Initial Retirement Wealth on the Probability of Retirement Income "Adequacy," by Annuitization Equity Allocation For: Males Retiring at Age 65 in the Lowest Income Category Building Block 2: investment income and longevity stochastic, health care expenses deterministic Probability of Adequacy 8 $0 $50,000 $100,000 $150,000 $200,000 $250,000 $300,000 $350,000 $400,000 $450,000 $500,000 Initial Retirement Wealth Annuitization 25% Annuitization Annuitization 75% Annuitization Annuitization Source: Simulations from Ballpark E$timate Monte Carlo, Employee Benefit Research Institute. ebri.org Issue Brief May 2011 No

13 Probability of Adequacy 5% Equity Allocation For: Males Retiring at Age 65 in the Highest Income Category Building Block 2: investment income and longevity stochastic, health care expenses deterministic 8 Figure 4 (cont'd.) C. Impact of Initial Retirement Wealth on the Probability of Retirement Income "Adequacy," by Annuitization $0 $50,000 $100,000 $150,000 $200,000 $250,000 $300,000 $350,000 $400,000 $450,000 $500,000 Initial Retirement Wealth Annuitization 25% Annuitization Annuitization 75% Annuitization Annuitization Probability of Adequacy D. Impact of Initial Retirement Wealth on the Probability of Retirement Income "Adequacy," by Annuitization Equity Allocation For: Males Retiring at Age 65 in the Highest Income Category Building Block 2: investment income and longevity stochastic, health care expenses deterministic 8 $0 $50,000 $100,000 $150,000 $200,000 $250,000 $300,000 $350,000 $400,000 $450,000 $500,000 Initial Retirement Wealth Annuitization 25% Annuitization Annuitization 75% Annuitization Annuitization Source: Simulations from Ballpark E$timate Monte Carlo, Employee Benefit Research Institute. ebri.org Issue Brief May 2011 No

14 Lowest-Income Category Probability of Adequate Retirement Income Replacement Rate Needed Under Building Block 1 Building Block 2 Building Block % 123.1% 152.2% 75% Highest-Income Category Probability of Adequate Retirement Income Replacement Rate Needed Under Building Block 1 Building Block 2 Building Block % 36.3% 75% Replacement rates needed to meet a 50 percent probability of retirement income adequacy do not vary significantly across three building blocks. However, when a retiree targets a 90 percent adequacy, the replacement rate for that adequacy dramatically increases under Building Block 3. For example, a retiree in the lowest-income category needs a replacement rate of percent under Building Block 2, which is about a 30 percent increase over the rate of the Building Block 1. However, when the retiree is under Building Block 3, he needs a replacement rate of percent, which is a 65 percent increase over the rate of Building Block 2. A similar pattern is also found for a retiree in the highest-income category. As presented in Figure 4 (Building Block 2), Figure 8 also demonstrates the value of purchasing an immediate annuity at retirement to reach a higher probability of retirement income adequacy. However, the retiree who wants to achieve the same target retirement adequacy under Building Block 3 now needs more initial retirement wealth to cover potential catastrophic long-term care costs. For example, if a retiree in the lowest-income category who adopts a full annuitization and a 5 percent equity allocation targets a 90 percent chance of adequacy, he needs an initial retirement wealth of $224,000 under Building Block 2 (Panel A of Figure 4). 15 However, if the retiree is under Building Block 3, he needs an initial retirement wealth of $542,000 to get the same probability of adequacy (Panel A of Figure 8). Similar results are also found for a retiree in the highest-income category (Panel C of Figure 4 vs. Panel C of Figure 8). An optimal level of annuitization in Building Block 3 varies in different equity allocations as well as target retirement income adequacy. Figures 9 and 10 present replacement rates required for a certain chance of adequacy by different degrees of annuitization and equity allocations. Compared with Building Block 2 (Figures 5 and 6), Building Block 3 needs a higher replacement rate to meet a target retirement adequacy. In addition, equity allocations under Building Block 3 become more crucial than those under Building Block 2, because of the potential catastrophic long-term care costs. For example, when a retiree who desires a 90 percent chance of adequacy chooses a full annuitization under Building Block 2, equity allocations do not matter relatively: The difference between the highest and lowest replacement rates is only 3.2 percentage points under Building Block 2 (Panel C of Figure 5). However, when the retiree is under Building Block 3, the difference increases to 20.8 percentage points (Panel C of Figure 9). Figure 11 demonstrates different optimal level of annuitization by income category as well as equity allocation and target retirement income adequacy. Different from Building Block 2 (Figure 7), the results of Building Block 3 show that a 95 percent equity allocation is optimal in any degree of annuitization except no annuitization. The same optimal ebri.org Issue Brief May 2011 No

15 equity allocation is found across income categories. Thus, the high equity allocation under Building Block 3 would be sufficient to cover potentially catastrophic long-term care costs. Immediate and Longevity Annuities: Building Blocks 2 and 3 To examine retirement income adequacy against longevity risk, two types of annuities are considered: immediate and longevity annuities. Longevity annuities are basically immediate annuity contracts without the initial payments (Scott, 2007). For example, a longevity annuity purchased at age 65 starts to distribute payments at age 85; an immediate annuity purchased at age 65 begins payments at age 65. For this analysis, a male retiring at age 65 is assumed to purchase an immediate annuity at a price quoted at the end of 2009 from or a longevity annuity commencing payments at age 85 at a price quoted as of 9/18/2009 in MetLife s Longevity Income Guarantee. 16 For example, a $50,000 premium for an immediate annuity (the immediate annuity price) is assumed to purchase annual payments of $3,791, and the same premium for a longevity annuity (the longevity annuity price) would make annual payments of $39,501 starting at age 85. Retirement Income Adequacy Under Building Block 2 Figures 12 and 13 demonstrate that if a retiree in the lowest or the highest income category targets a 90 percent chance of adequacy, he should fully annuitize the initial retirement wealth with an immediate annuity regardless of equity allocations. The lowest multiple of final earnings is found in a full annuitization (or 100 percent annuitization of the assets). The full annuitization with an immediate annuity is consistent with the findings of Scott, Watson, and Hu (2006) and Gong and Webb (2010). They state that retirees interested in fully annuitizing their assets should select an immediate annuity instead of a longevity annuity. 17 Pashchenko (2010) also documented that full annuitization would be optimal in the case of deterministic health care costs. As for a longevity annuity, in contrast, the figures show that a retiree would be able to reach a 90 percent probability of adequacy by allocating only about 15 to 20 percent of his initial retirement wealth to a longevity annuity. 18 The lowest multiple of final earnings is found in a range of percent annuitization with a longevity annuity. 19 An allocation of the small fraction of the initial retirement wealth to the longevity annuity would enable the retiree to preserve liquidity. Thus, the longevity annuity may overcome a potentially important psychological barrier to annuitization (Gong and Webb, 2010). In addition, the figures show that the positive effects of immediate and longevity annuities on retirement income adequacy are stronger for retirees in the lowest-income category than for those in the highest-income category. The slopes of immediate and longevity annuities for a retiree in the lowest-income category (Figure 12) are steeper than those for his counterpart in the highest-income category (Figure 13). For example, a retiree with no annuitization and a 50 percent equity allocation in the lowest-income category (Panel C of Figure 12) needs 18.3 times final earnings to get a 90 percent chance of adequacy. If the retiree fully annuitizes his retirement wealth with an immediate annuity or allocates about a 20 percent of his retirement wealth to a longevity annuity, he needs 12.9 or 15.3 times final earnings, each of which saves 5.4 or 3.0 times his final earnings, respectively. However, if a retiree in the highest-income category annuitizes in the same way as his counterpart in the lowest-income category, he needs 2.3 or 2.7 times final earnings (Panel C of Figure 13), each of which saves 1.0 or 0.6 times final earnings, respectively. These savings are relatively small compared with the savings for the retiree in the lowest-income category. In sum, Figures 12 and 13 demonstrate that retirees in the lowest-income category who desire a 90 percent chance of adequacy are likely to be relatively much better off annuitizing than those in the highest-income category. For a retiree in Building Block 2, Figure 14 presents final earnings multiples for a 90 percent chance of adequacy by equity allocation and the degree of annuitization with the longevity annuity. A retiree in the lowest-income category is able to achieve the 90 percent adequacy with a combination of a percent equity allocation and a 20 percent allocation to the longevity annuity (Panel A). Similarly, a retiree in the highest-income category can reach the target adequacy with a combination of a 35 percent equity allocation and a 20 percent allocation to a longevity annuity (Panel B). ebri.org Issue Brief May 2011 No

16 20 Figure 5 A. Replacement Rates Required for a Chance of "Adequacy" For: Males Retiring at Age 65 in the Lowest Income Category Building Block 2: Investment income and longevity stochastic, health care expenses deterministic Replacement Rate 175% 1 125% 25% 75% 20 B. Replacement Rates Required for a 75% Chance of "Adequacy" For: Males Retiring at Age 65 in the Lowest Income Category Building Block 2: Investment income and longevity stochastic, health care expenses deterministic Replacement Rate 175% 1 125% 25% 75% 20 C. Replacement Rates Required for a Chance of "Adequacy" For: Males Retiring at Age 65 in the Lowest Income Category Building Block 2: Investment income and longevity stochastic, health care expenses deterministic Replacement Rate 175% 1 125% 25% 75% Degree of Annuitization 5% Equity Allocation 25% Equity Allocation Equtiy Allocation 75% Equity Allocation 95% Equity Allocation Source: Simulations from Ballpark E$timate Monte Carlo, Employee Benefit Research Institute. ebri.org Issue Brief May 2011 No

17 Figure 6 A. Replacement Rates Required for a Chance of "Adequacy" For: Males Retiring at Age 65 in the Highest Income Category Building Block 2: Investment income and longevity stochastic, health care expenses deterministic Replacement Rate 25% 75% B. Replacement Rates Required for a 75% Chance of "Adequacy" For: Males Retiring at Age 65 in the Highest Income Category Building Block 2: Investment income and longevity stochastic, health care expenses deterministic Replacement Rate 25% 75% C. Replacement Rates Required for a Chance of "Adequacy" For: Males Retiring at Age 65 in the Highest Income Category Building Block 2: Investment income and longevity stochastic, health care expenses deterministic Replacement Rate 25% 75% Degree of Annuitization 5% Equity Allocation 25% Equity Allocation Equtiy Allocation 75% Equity Allocation 95% Equity Allocation Source: Simulations from Ballpark E$timate Monte Carlo, Employee Benefit Research Institute. ebri.org Issue Brief May 2011 No

18 Income Category Probability of % of Equity Annuitization Income Probability of % of Equity Annuitization Adequacy Investment 25% 75% Category Adequacy Investment 25% 75% 1 5% % % 25% % % % % % % % 5% % % % % % % % % % % % % % % % % % Figure 7 Impact of Final Earnings on Probability of "Adequate" Retirement Income, by Income Category, Equity Allocation, and Annuitization For: Males Retiring at Age 65 Building Block 2: Investment income and longevity stochastic, health care expenses deterministic 25% % % % % % % % 5% % % % % % % % % % % % % % % Source: Simulations from Ballpark E$timate Monte Carlo, Employee Benefit Research Institute. ebri.org Issue Brief May 2011 No

19 Probability of Adequacy 8 Figure 8 A. Impact of Initial Retirement Wealth on the Probability of Retirement Income "Adequacy," by Annuitization 5% Equity Allocation For: Males Retiring at Age 65 in the Lowest Income Category Building Block 3: investment income, longevity, and health care expenses stochastic Initial Retirement Wealth Annuitization 25% Annuitization Annuitization 75% Annuitization Annuitization Probability of Adequacy 8 B. Impact of Initial Retirement Wealth on the Probability of Retirement Income "Adequacy," by Annuitization Equity Allocation For: Males Retiring at Age 65 in the Lowest Income Category Building Block 3: investment income, longevity, and health care expenses stochastic Initial Retirement Wealth Annuitization 25% Annuitization Annuitization 75% Annuitization Annuitization Source: Simulations from Ballpark E$timate Monte Carlo, Employee Benefit Research Institute. ebri.org Issue Brief May 2011 No

20 Probability of Adequacy 8 Figure 8 (cont'd.) C. Impact of Initial Retirement Wealth on the Probability of Retirement Income "Adequacy," by Annuitization 5% Equity Allocation For: Males Retiring at Age 65 in the Highest Income Category Building Block 3: investment income, longevity, and health care expenses stochastic Initial Retirement Wealth Annuitization 25% Annuitization Annuitization 75% Annuitization Annuitization Probability of Adequacy 8 D. Impact of Initial Retirement Wealth on the Probability of Retirement Income "Adequacy," by Annuitization Equity Allocation For: Males Retiring at Age 65 in the Highest Income Category Building Block 3: investment income, longevity, and health care expenses stochastic Initial Retirement Wealth Annuitization 25% Annuitization Annuitization 75% Annuitization Annuitization Source: Simulations from Ballpark E$timate Monte Carlo, Employee Benefit Research Institute. ebri.org Issue Brief May 2011 No