Immediate Annuities and Retirement Income Portfolios

Transcription

1 Prepared by: Milliman, Inc. Timothy E. Hill FSA Susan J. Sell FSA Immediate Annuities and Retirement Income Portfolios

2 , whose corporate offices are in Seattle, serves the full spectrum of business, financial, government, and union organizations. Founded in 1947 as Milliman & Robertson, the company has 48 offices in principal cities in the United States and worldwide. Milliman employs more than 2,100 people, including a professional staff of more than 1,000 qualified consultants and actuaries. The firm has consulting practices in employee benefits, healthcare, life insurance/ financial services, and property and casualty insurance. For further information visit

3 Table of Contents executive summary 2 Methodology 4 Results 9 Case #1: Affluent households 9 Case #2: High net worth/upper affluent households 13 Case #3: Middle/mass market households 17 Assumptions 22

4 EXECUTIVE SUMMARY NAVA and Milliman, Inc. conducted joint research to demonstrate and quantify the potential advantages of incorporating lifetime guaranteed income streams into a retirement-income plan. This report documents the methodology, assumptions, and results of the analysis performed. The analysis included three case studies representative of particular segments of the retirement-income market. The segments included affluent households (Case 1), high net worth/upper affluent households (Case 2), and middle/mass market households (Case 3) and they were differentiated by retirement savings and annual income goals. The characteristics of the three case studies are outlined in Table 1: Table 1 Wealth Profile at Age 65 affluent High Net Worth/ Middle/ Upper Affluent Mass Market Net Worth $3.5 million $11.0 million $700,000 Assets Available for Retirement $2.5 million $8.0 million $500,000 Pre-Retirement Income $175,000 $500,000 $65,000 Post-Retirement Income Goal $140,000 $324,00 $50,000 Amount from Social Security ($29,000) ($24,000) ($30,000) Net of Social Security Benefits $111,000 $300,000 $20,000 The study assumed that retirement-income was funded via a single premium immediate annuity (SPIA) and/or mutual-fund withdrawals. The assets available for retirement were allocated to a SPIA first with the remaining amount allocated to mutual funds. The mutual-fund allocation consisted of a mix of equity and bond allocations. The analysis assumed that the retirement-income requirement increased annually at 2.5% and that Social Security benefits also increased at 2.5%. Social Security benefits were not considered in the stochastic calculations that are described in this report; they were simply used to reduce the income level required. Income levels from the SPIA assumed joint annuitants, both age 65, and a joint and last survivor payout option. Any remaining income requirements were withdrawn from mutual funds. The appreciation/depreciation of the mutual fund was based on 10,000 stochastic equity/bond returns, net of fund expenses. We ran stochastic scenarios for each SPIA/equity/bond allocation and determined the probability of meeting the income goal for each allocation. The stochastic scenarios also included a bequest (death benefit) calculation. We assumed the death benefit equaled the mutual-fund value at the end of the year of death. The table below summarizes the probability of meeting the income goal for each of the case studies and includes calculations both with and without a SPIA in the asset allocation mix. Note that in this table and throughout the report we use a notation for SPIA/Equity/Bond Allocation. For instance, the first entry is 70%/55%/45%. In other words, 70% of the retirement savings is used to buy a SPIA. The remaining 30% is invested in mutual funds with a 55% equity and 45% bond mix. Table 2 Withdrawals from Mutual Funds OnlY adding SPIA to the Mix Case Probability of equity/ Probability of SPIA/Equity/ Meeting bond Allocation Meeting bond Allocation Income goal Income goal 1 69% 85%/15% 84% 70%/55%/45% 2 82% 65%/35% 97% 60%/45%/55% 3 78% 65%/35% 94% 60%/50%/50% 2

5 We developed an index to compare the relative value of alternate asset allocations based on meeting income goals and on leaving a bequest. The bequest (death benefit) was assumed to equal the mutualfund value at the end of the year of death. We based the index on an income component and a death benefit component, with each component weighted equally. The scenario with the highest index was considered the optimal asset allocation solution for meeting income and bequest requirements. The study also considered maintaining a minimum amount of liquidity in determining an optimal assetallocation solution. We defined the minimum liquidity requirement in terms of a minimum mutual-fund balance at the end of each year during the first 20 years of the projection. The table below shows the optimal solution based on the index and the impact of an additional liquidity requirement. Table 3 Without Minimum With Minimum Liquidity Requirement liquidity Requirement Case spia/equity/ Minimum LiquidITY spia/equity/ bond Allocation bond Allocation 1 70%/85%/15% $1 million 55%/80%/20% 2 60%/60%/40% $3.5 million 55%/50%/50% 3 60%/60%/40% $215,000 55%/65%/35% We ran sensitivity tests under alternative allocations, liquidity needs, and index component weights. Note: The results contained in this report are dependant on assumptions made. These assumptions include but are not limited to equity returns, bond fund returns, inflation rates, and mortality assumptions. Different assumptions will lead to different results, and may lead to different conclusions. The results are intended to be illustrative only. Milliman does not intend the results to benefit any specific parties. In particular, Milliman is not recommending any particular insurance purchase, and is not offering advice with respect to retirement planning or investment strategy Retirement planning decisions must reflect an individual s specific circumstances, risk tolerance, and view on the future economic environment. The assumptions contained in this report may or may not be consistent with a particular view. In reading this report, the recipient acknowledges that this report contains complex, technical analysis, and that Milliman recommends that the recipients be aided by their own actuary or other qualified professional when reviewing the report. 3

6 Methodology The objective of this study was to compare common investment strategies and income requirements and to show how they may be modified or improved by the inclusion of a single premium immediate annuity (SPIA). The methodology underlying the analysis is described in this section of the report. Three case studies representative of the diverse retirement-income market were analyzed. The case studies are illustrative examples that are consistent with the segments described in the report, Target Marketing: The Watchwords for Capturing Retirement Income Opportunities, authored by Noel Abkemeier, Douglas J. Bennett, and Brent Hamann. (The report is available online at Watchwords-RR pdf or by searching on "target marketing" from the Milliman home page at Each case study covers a particular segment of the retirement-income market. The segments likely have distinct needs and desires for advice, as well as distinct needs for products and services. The analysis differentiated the segments by retirement savings and annual income goals as follows: Table 4 Case Segment Retirement Annual Income Study S savings Goal #1 Affluent Households $2.5 million $140,000 #2 High Net Worth/ $8 million $324,000 Upper Affluent Households #3 Middle/Mass Market Households $500,000 $50,000 The affluent segment represents about six million households in the United States. They are within the 80th and 95th percentiles of the most affluent Baby Boomers. The study determined a wealth profile at age 65 for this group as shown in the following table. Table 5 Affluent Wealth Profile at Age 65 amount Net worth Assets available for retirement $3.5 million $2.5 million Pre-retirement income $175,000 Post-retirement income goal $140,000 Amount from Social Security ($29,000) Net of Social Security benefits $111,000 For all case studies, it was assumed that the net post-retirement income goal will grow at 2.5% inflation. The high net worth/upper affluent segment represents about two million households in the United States. They are in the top 5% of Baby Boomers and control about 50% of total current net worth. A wealth profile at age 65 was determined in the same manner as that for the affluent households. 4

7 Table 6 Upper Affluent Wealth Profile at Age 65 amount Net worth Assets available for retirement $11.0 million $8.0 million Pre-retirement income $500,000 Post-retirement income goal $324,000 Amount from Social Security ($24,000) Net of Social Security benefits $300,000 The middle/mass market segment represents the remaining Baby Boomers (80%), about 32 million households in the United States. The wealth profile for this segment is shown in the table below: Table 7 Middle/Mass Market Wealth Profile at Age 65 amount Net worth $700,000 Assets available for retirement $500,000 Pre-retirement income $65,000 Post-retirement income goal $50,000 Amount from Social Security ($30,000) Net of Social Security benefits $20,000 The study assumed that retirement income was funded via a SPIA and/or mutual-fund withdrawals. The assets available for retirement were allocated to a SPIA first (with allocations ranging from 0% to 100%), with the remaining amount allocated to mutual funds. The mutual-fund allocation consisted of a mix of equity and bond allocations with the equity share ranging from 5% to 100% and the remainder allocated to bond funds. The equity/bond mix remained constant throughout the projection period. It was assumed that the retirement-income requirement increased annually by an inflation rate of 2.5%. Social Security benefits were also assumed to increase annually at 2.5%. These benefits were not considered in the stochastic calculations that are described in the following paragraphs, as they were simply used to reduce the income level required. The amount of annual income from the SPIA was determined by applying a SPIA income rate to the amount allocated to a SPIA. The SPIA income rate was based on joint annuitants, both age 65, and a joint and last survivor payout option (no period certain). The SPIA payment amount remained level throughout the joint lifetime of the annuitants. The SPIA income rate used in the study was determined by taking an average of the top current annual SPIA rates from the CANNEX SPIA database dated November 28, Following are the joint and last survivor SPIA rates for a male age 65 and female age 65 that were averaged: Table 8 CompanY spia Annual Income Rate per $100,000 Applied A $6, B $6, C $6, D $6, E $6, Average $6, For example, under Case #1 if 50% of the assets available for retirement were allocated to a SPIA, the annual SPIA income amount would be about $84,240 (.50 x $2.5 million x 6,739/100,000). 5

8 Any remaining income requirements were withdrawn from mutual funds. In the Case #1 example above, $26,760 ($111,000 - $84,240) would be withdrawn the first year from mutual funds. In the second year, $111,000 x $84,240, or $29,535, would be withdrawn from mutual funds. The mutual-fund balance at the end of each year of the projection period equaled the fund balance at the beginning of the year, less any required withdrawals taken at the beginning of the year, plus appreciation/depreciation of the mutual funds. The appreciation/depreciation of the mutual fund was based on 10,000 stochastic equity/bond returns, net of fund expenses. The projection was run until age 115 (the end of the mortality table). The stochastic scenarios were run for each of the assumed SPIA/equity/bond allocations. The income shortfall was calculated for each scenario. A shortfall occurred if the mutual-fund balance was less than the amount of the required annual withdrawal from the mutual funds (while at least one of the annuitants was alive). The amount of the shortfall was equal to the total retirement income (net of Social Security benefits) less the SPIA payment and less the mutual-fund balance. For each SPIA/equity/bond allocation, the probability of meeting the income goal was determined by dividing the number of scenarios that did not have an income shortfall by the total number of scenarios (10,000). The baseline for each case was the scenario with the highest probability of meeting the income goal without an allocation to a SPIA, i.e., income needs were met from Social Security and withdrawals from mutual funds. The next step was to look at the scenarios with a SPIA added to the asset allocation to determine its impact on the probability of meeting the income goal. The SPIA annual payment amount was determined by multiplying the amount allocated to a SPIA by the SPIA income rate. For Case #1, the probability of meeting the income goal of $111,000 with a 5% equity/95% bond mix was about 40%. This probability was highest at 69% with an 85% equity/15% bond mix. If a SPIA was added to the mix and 70% was allocated to the SPIA, with a 55% equity/45% bond allocation in mutual funds, the probability of meeting the income goal was approximately 84%. A bequest (death benefit) was also calculated for each stochastic scenario. The death benefit equals the mutual-fund value at the end of the year of death. The incidence of the payment of the death benefit was based on the same stochastic mortality and stochastic mortality improvement factors that drove the determination of longevity. For each of the 10,000 SPIA/equity/bond allocation scenarios, an average death benefit was calculated. A comparison of the tradeoff between meeting the income goal (probability of success) with the amount of any bequest was made. The following table shows the tradeoff between the probability of success and the amount of a bequest for Case #1. Table 9 equity Share = 85% SPIA Allocation Average Probability of Success Average Bequest ($ millions) 0% 68.60% % 71.80% % 76.10% % 82.70% 3.18 An index was developed for the purpose of comparing scenarios on a relative basis. The index was based on an income component and a death benefit component, with equal weights (50%) for each component. The income component was determined by first calculating the present value of any income shortfalls (PVIS) over the projection period. The income index was derived by the following formula: [1 - PVIS / (5 x initial retirement-income amount)]. The intent of this formula was to normalize the results. The income index was not allowed to fall below a value of zero. No income shortfalls would result in an income index value of one. A value close to zero occurs in scenarios where there were substantial income shortfalls. 6

9 Assuming the initial retirement-income amount in Case #1 ($111,000), an income shortfall of $100,000 results in an income-index value of When the income shortfall increases to $400,000, then the income-index value equals The following graph illustrates income-index values at various levels of income shortages. 1 Income Index Relative to Income Shortages 0.8 Income Index Present Value of Income Shortfall The death benefit component was based on the following formula: 1 (e 1-D x.375) where D = 2 x minimum(4 x total initial retirement assets, death benefit) total initial retirement assets The death benefit index was constrained to values between zero and one. Scenarios with high deathbenefit amounts would result in a death-benefit index close to one. A value close to zero would occur under scenarios with low death-benefit amounts. For example, using the total initial retirement-income assets of Case #1 ($2.5 million), if the average death benefit is $1.2 million, then the death-benefit index is An average death benefit of $4.7 million results in a death-benefit index of The higher the average death benefit, the greater the deathbenefit index. The following graph shows the death-benefit index for a range of average death benefits. 1 Death-Benefit Index Relative to Average Death Benefit 0.9 Death-Benefit Index , , , , , , , ,7 0 0 Average Death Benefit ($ millions) 7

10 The scenario with the highest index was considered to be the optimal solution to meeting income and bequest requirements. The following characteristics of the optimal solution based on the index were then reviewed: Portion of retirement assets allocated to SPIA and resulting SPIA annual lifetime income Total allocated to mutual funds Mutual-fund asset allocation Probability of not meeting income goal Average bequest The scenario with the highest index value (.7947) for Case #1 occurred with 70% of total retirement assets allocated to a SPIA. The SPIA allocation of $1.75 million produced $118,000 in annual lifetime income. The remaining $750,000 was allocated to mutual funds with an 85% equity/15% bond mix. Under the optimal solution, there is a 17% chance of not meeting the income goal and an average bequest of $3.5 million. A scenario similar to the optimal solution was run, assuming no allocation to a SPIA but using the same equity/bond allocation to mutual funds. The probability of not meeting the income goal and the average bequest under this scenario were compared with the comparable results of the optimal solution. For Case #1, if all retirement assets are allocated to mutual funds with an 85% equity/15% bond mix, there is an increase in the probability of not meeting the income goal (31%), but the average bequest increases to $4.1 million. The study also determined the optimal asset-allocation solution to meeting retirement-income needs (not outliving one s assets), leaving a bequest, and maintaining a minimum amount of liquidity. The minimum liquidity requirement was defined in terms of a minimum mutual-fund balance at the end of each year during the first 20 years of the projection. The index was calculated as described above, but with the elimination of those combinations that did not meet the minimum liquidity requirement. The following characteristics of the optimal solution with a minimum liquidity requirement were then reviewed: Portion of retirement assets allocated to SPIA and resulting SPIA annual lifetime income Total allocated to mutual funds Mutual-fund asset allocation Probability of not meeting income goal Average bequest Minimum liquidity For Case #1, a minimum liquidity requirement of $1 million during the first 20 years was assumed. Under this scenario, the optimal solution was a 55% SPIA allocation and 80% equity/20% bond mix in mutual funds. On average there was a 22% chance of not meeting the income goal and the average bequest was $3.6 million. Other scenarios were also run with varying assumptions regarding SPIA/equity/bond allocations, minimum liquidity requirements, and initial invested assets. 8

11 Results Case #1: Affluent Households Income Mutual fund allocations only The probability of meeting the income goal ($111,000 net of Social Security benefits) based on a systematic withdrawal program from mutual funds only is shown below, based on equity allocations from 5% to 100%. 7 0 % $2.5 Million in Retirement Assets: Probability of Meeting Income Goal by Asset Mix Probability of Meeting Income Goal 6 0 % 5 0 % 4 0 % 3 0 % 0 % 2 0 % 4 0 % 6 0 % 8 0 % % Equity % The success of the program was measured by target income lasting as long as at least one of the two joint annuitants is still alive. The highest probability of meeting the income goal was 69% with an 85% equity/15% bond allocation. In general, the probability of success increased up to the optimal equity allocation and then tapered off slightly. The study then analyzed the amount of income generated assuming withdrawals from mutual funds with an 85% equity/15% bond allocation, plus Social Security benefits. The following graph shows the annual income from Social Security and from the mutual funds. The total income requirement increased 136%, from $140,000 to about $330,300 at age 100. The line in the graph below shows that the mutual-fund balance is depleted at age 110. The line represents the balance of the mutual funds based on a 7% return. $2.5 Million in Retirement Assets: 85% Equity / 15% Bond in Mutual Funds $ $ 3.0 Annual Income (000s) $ $ $ $ $ 2.5 $ 2.0 $ 1.5 $ Mutual Fund Balance (millions) Age Social Security Systematic Withdrawal Mutual Fund Balance 9

12 Income Mutual fund and SPIA allocations The result of adding a SPIA to the allocation, with the remaining assets in mutual funds, is shown in the graph below. The SPIA allocation was assumed to range from 0% through 75%. The graph shows three equity/bond asset allocations for the portion in the mutual funds (55%, 70%, and 85% in equities). The addition of a SPIA increased the highest probability of meeting the income goal from 69% (see above) to 84%. This probability occurred under the scenario with 70% of retirement savings allocated to a SPIA and a 55% equity/45% bond allocation in mutual funds. 8 5 % $2.5 Million in Retirement Assets: Probability of Meeting Income Goal with SPIA and Varying Asset Mix Probability of Meeting Income Goal 8 0 % 7 5 % 7 0 % 6 5 % 8 5 % E q u i ty 7 0 % E q u i ty 5 5 % E q u i ty 6 0 % 0 % 1 0 % 2 0 % 3 0 % 4 0 % 5 0 % 6 0 % 7 0 % Percent of Retirement Assets Used to Purchase SPIA The amount of income generated assuming a 70% allocation to a SPIA, withdrawals from mutual funds with a 55% equity/45% bond allocation, and Social Security benefits is shown in the following graph. The amount of annual SPIA income under this scenario equals about $118,000. The mutual-fund balance under this scenario is depleted at age 115. $2.5 Million in Retirement Assets: 70% of Retirement Assets in SPIA, 55% Equity / 45% Bond in Mutual Funds $ $ 3.0 Annual Income (000s) $ $ $ $ $ 2.5 $ 2.0 $ 1.5 $ Mutual Fund Balance (millions) Mutual Fun Age Social Security SPIA Systematic Withdrawal Mutual Fund Balance Index An index was developed to allow comparison of the relative value of alternate asset allocations based on meeting income goals and on leaving a bequest (death benefit). The following three-dimensional graph shows the average index derived based on a 50% weight on not outliving assets (meeting income needs) and a 50% weight on the death benefit. The average index was determined over a range of SPIA and equity/bond allocations and 10,000 scenarios. The optimal solution occurred when 70% was allocated to a SPIA and the equity/bond allocation was 85%/15%. 10

13 $2.5 Million in Retirement Assets: Average Index Based on 50% Not Outliving Assets and 50% Bequest 7 5 % 5 0 % 2 5 % SPIA % 0 % % 8 0 % 6 0 % 4 0 % 2 0 % Equity % Index Optimal solution Under the optimal solution determined above, 70% of the total retirement assets ($2.5 million) were allocated to a SPIA. The SPIA allocation of $1.75 million produced $118,000 in annual lifetime income. The remaining $750,000 was allocated to mutual funds with an 85% equity/15% bond mix. During the first three years, the income requirements are met by Social Security benefits and SPIA benefit payments. In the fourth year, the income needs (excluding Social Security benefits) are about $120,000. This is the first year under this scenario that the mutual funds must be tapped for income (the SPIA payment equals $118,000). The mutual funds were largely left to grow to cover inflation and to provide a bequest. Under the optimal solution, there is a 17% probability of not meeting the income goal and the average bequest is $3.5 million. If $2.5 million was allocated entirely to mutual funds with an 85% equity/15% bond mix, the probability of not meeting the income goal increases to 31%, but the average bequest increases to $4.1 million. The graph below shows the annual income from Social Security, from the SPIA, and withdrawals from mutual funds based on the optimal solution. $2.5 Million in Retirement Assets: 70% of Retirement Assets in SPIA, 85% Equity / 15% Bond in Mutual Funds $ $ 3.0 Annual Income (000s) $ $ $ $ $ 2.5 $ 2.0 $ 1.5 $ Mutual Fund Balance (millions).0 Mutual Fund Balance (millions) Age Social Security SPIA Systematic Withdrawal Mutual Fund Balance 11

14 Index Minimum liquidity Another common need during retirement is liquidity. The following graph shows the index recalculated, reflecting a minimum liquidity requirement of $1 million during the first 20 years. The index was derived based on a 50% weight on not outliving assets (meeting income needs) and a 50% weight on the bequest (death benefit). The average index was determined over a range of SPIA and equity/bond allocations and 10,000 scenarios. $2.5 Million in Retirement Assets: $1 Million in Minimum Liquidity 6 0 % 3 0 % % 8 5 % 7 0 % 5 5 % 4 0 % 2 5 % 1 0 % Equity % 0 % SPIA % Index Minimum liquidity optimal solution When minimum liquidity was an additional requirement during retirement, the optimal solution was a 55% SPIA allocation and an 80% equity/20% bond mix in mutual funds. The SPIA allocation of $1.375 million produced about $93,000 in annual lifetime income. The income amount was $25,000 lower than that resulting from the optimal solution without a minimum liquidity requirement. The remaining $1.125 million was allocated to mutual funds. Under this scenario, on average there was a 22% chance of not meeting the income goal and the average bequest was $3.6 million. The minimum liquidity requirement was assumed to be $1 million during the first 20 years. Under this scenario, the mutual funds were tapped for income immediately ($18,000). The following graph shows the average annual income and average mutual-fund balance based on the optimal solution. $2.5 Million in Retirement Assets: 55% of Retirement Assets in SPIA, 80% Equity / 20% Bond in Mutual Funds $ $ 3.0 Annual Income (000s) $ $ $ $ $ 2.5 $ 2.0 $ 1.5 $ Mutual Fund Balance (millions) Age Social Security SPIA Systematic Withdrawal Mutual Fund Balance 12

15 Case #2: High Net Worth/Upper Affluent Households Income Mutual fund allocations only The probability of meeting the income goal ($300,000 net of Social Security benefits) based on a systematic withdrawal program from mutual funds only is shown below based on various equity allocations % $8 Million in Retirement Assets: Probability of Meeting Income Goal by Asset Mix Probability of Meeting Income Goal 9 0 % 8 0 % 7 0 % 6 0 % 0 % 2 0 % 4 0 % 6 0 % 8 0 % % Equity % The success of the program was measured by target income lasting as long as at least one of the two joint annuitants is still alive. The highest probability of meeting the income goal was 82%, with a 65% equity/35% bond allocation. Reasonable mortality assumptions resulted in an average life expectancy of 31 years with a 42% probability of living to age 100. The study then analyzed the amount of income generated assuming withdrawals from mutual funds with a 65% equity/35% bond allocation, plus Social Security benefits. The following graph shows the income needs from Social Security and from the mutual funds. The income requirement increased 137%, from $324,000 to $768,919 at age 100. The line in the graph below shows that the average mutual-fund balance continues to appreciate despite withdrawals from the mutual funds. $8 Million in Retirement Assets: 65% Equity / 35% Bond in Mutual Funds $ 1,5 0 0 $ 1 2 Annual Income (000s) $ 1,2 5 0 $ 1,0 0 0 $ $ $ $ 1 0 $ 8 $ 6 $ 4 $ 2 Mutual Fund Balance (millions) Age Social Security Systematic Withdrawal Mutual Fund Balance 13

16 Income Mutual fund and SPIA allocations The result of adding a SPIA to the allocation, with the remaining assets in mutual funds, is shown in the graph below. The SPIA allocation was assumed to range from 0% through 60%. The graph shows three asset allocations for the portion in the mutual funds (45%, 65%, and 85% in equities). The addition of a SPIA increased the highest probability of meeting the income goal from 82% (see above) to nearly 97%. This probability occurred under the scenario with 60% of retirement savings allocated to a SPIA and a 45% equity/55% bond allocation in mutual funds % $8 Million in Retirement Assets: Probability of Meeting Income Goal with SPIA and Varying Asset Mix Probability of Meeting Income Goal 9 5 % 9 0 % 8 5 % 8 5 % E q u i ty 6 5 % E q u i ty 4 5 % E q u i ty 8 0 % 0 % 1 0 % 2 0 % 3 0 % 4 0 % 5 0 % 6 0 % Percent of Retirement Assets Used to Purchase SPIA The amount of income generated assuming a 60% allocation to a SPIA, withdrawals from mutual funds with a 45% equity/55% bond allocation, and Social Security benefits is shown in the following graph. The amount of annual SPIA income under this scenario equals $323,472. Withdrawals are not taken from the mutual fund until the fifth year and the mutual-fund balance continues to appreciate. $8 Million in Retirement Assets: 60% of Retirement Assets in SPIA, 45% Equity / 55% Bond in Mutual Funds $ 1,2 0 0 $ 1 0 Annual Income (000s) $ 1,0 0 0 $ $ $ $ $ 8 $ 6 $ 4 $ 2 Mutual Fund Balance (millions) Age Social Security SPIA Systematic Withdrawal Mutual Fund Balance Index The following three-dimensional graph of the average index is derived based on a 50% weight on not outliving assets (meeting income needs) and a 50% weight on the bequest (death benefit). The average index was determined over a range of SPIA and equity/bond allocations and 10,000 scenarios. The optimal solution occurred when 60% was allocated to a SPIA and the equity/bond allocation was 60%/40%. 14

17 $8 Million in Retirement Assets: Average Index Based on 50% Not Outliving Assets and 50% Bequest 6 0 % 3 0 % % 7 5 % 5 0 % 2 5 % Equity % 0 % SPIA % Index Optimal solution Under the optimal solution, 60% of the total retirement assets ($8 million) were allocated to a SPIA. The SPIA allocation of $4.8 million produced about $323,500 in annual lifetime income. The remaining $3.2 million was allocated to mutual funds with a 60% equity/40% bond mix. During the first four years, the income requirements are met by Social Security benefits and SPIA benefit payments. In the fifth year, the income needs (excluding Social Security benefits) are about $331,000. This is the first year under this scenario that the mutual funds must be tapped for income (the SPIA payment equals $323,500). The mutual funds were largely left to grow to cover inflation and to provide a bequest. Under the optimal solution, there is a 3.2% probability of not meeting the income goal and the average bequest is $16.7 million. If $8 million was allocated entirely to mutual funds with a 60% equity/40% bond mix, the probability of not meeting the income goal increases to 17.8% and the average bequest decreases to $15.5 million. The graph below shows the annual income from Social Security, from the SPIA, and withdrawals from mutual funds based on the optimal solution. $ 1,2 0 0 $8 Million in Retirement Assets: 60% of Retirement Assets in SPIA, 60% Equity / 40% Bond in Mutual Funds $ 1 4 Annual Income (000s) $ 1,0 0 0 $ $ $ $ $ 1 2 $ 1 0 $ 8 $ 6 $ 4 $ 2 Mutual Fund Balance (millions) Mutual Fund Balance (millions) Age Social Security SPIA Systematic Withdrawal Mutual Fund Balance 15

18 Index Minimum liquidity The following graph shows the index reflecting a minimum liquidity requirement of $3.5 million during the first 20 years. The index was derived based on a 50% weight on not outliving assets (meeting income needs) and a 50% weight on the bequest (death benefit). The average index was determined over a range of SPIA and equity/bond allocations and 10,000 scenarios. $8 Million in Retirement Assets: $3.5 Million in Minimum Liquidity 6 0 % 3 0 % 0 % SPIA % % 8 5 % 7 0 % 5 5 % 4 0 % 2 5 % 1 0 % Equity % Index Minimum liquidity optimal solution When minimum liquidity is an additional requirement during retirement, the optimal solution is a 55% SPIA allocation and 50% equity/50% bond mix in mutual funds. The SPIA allocation of $4.4 million produced about $296,500 in annual lifetime income. The income amount is about $27,000 lower than that resulting from the optimal solution without a minimum liquidity requirement. The remaining $3.6 million was allocated to mutual funds. Under this scenario, on average there is a 3.6% chance of not meeting the income goal and the average bequest is $16.1 million. The minimum liquidity requirement was assumed to be $3.5 million during the first 20 years. Under this scenario, the mutual funds must be tapped for income immediately ($3,500). The following graph shows the average annual income and average mutual-fund balance based on the optimal solution. $8 Million in Retirement Assets: 55% of Retirement Assets in SPIA, 50% Equity / 50% Bond in Mutual Funds $ 1,2 0 0 $ 1 0 Annual Income (000s) $ 1,0 0 0 $ $ $ $ $ 8 $ 6 $ 4 $ 2 Mutual Fund Balance (millions) Age Social Security SPIA Systematic Withdrawal Mutual Fund Balance Other alternatives Two additional alternatives were analyzed for Case #2. The first assumed the client wants to stay with a 70% equity/30% bond allocation in the mutual funds. The second assumes the client wants to spend $1 million immediately, and allocate half of the remaining $7 million to a SPIA and half to mutual funds 16

19 with a 75% equity/25% bond mix. The annual SPIA payment under this scenario is nearly $236,000. The results of these scenarios are summarized in the table below: Table 10 Alternative 70% Equity/30% Bond 50% SPIA/50% Mutual Funds (75% Equity/25% Bond) Invested Assets $8 million $7 million Probability of not 18.1% 18.1% (but will get $236,000 meeting income goal Case #3: Middle/Mass Market Households for life from SPIA) Average bequest $16.3 million $11.8 million Minimum liquidity $6.6 million $3.2 million Income Mutual fund allocations only The probability of meeting the income goal ($20,000 net of Social Security benefits) based on a systematic withdrawal program from mutual funds only is shown below based on various equity allocations. The success of the program was measured by target income lasting as long as at least one of the two joint annuitants is still alive. The highest probability of meeting the income goal was 78% with a 65% equity/35% bond allocation. Reasonable mortality assumptions resulted in an average life expectancy of 31 years with a 42% probability of living to age % $500,000 in Retirement Assets: Probability of Meeting Income Goal by Asset Mix Probability of Meeting Income Goal 7 0 % 6 0 % 5 0 % 0 % 2 0 % 4 0 % 6 0 % 8 0 % % Equity % The study then analyzed the amount of income generated assuming withdrawals from mutual funds with a 65% equity/35% bond allocation, plus Social Security benefits. The following graph shows the income needs from Social Security and from the mutual funds. The income requirement increased 137%, from $50,000 to $118,660 at age 100. The line in the graph below shows that the average mutual-fund balance continues to appreciate despite withdrawals from the mutual funds. 17

20 $500,000 in Retirement Assets: 65% Equity / 35% Bond in Mutual Funds $ $ Annual Income (000s) $ $ $ $ 7 5 $ 5 0 $ 2 5 $ $ $ $ $ Mutual Fund Balance (000s) Age Social Security Systematic Withdrawal Mutual Fund Balance Income Mutual fund and SPIA allocations The result of adding a SPIA to the allocation, with the remaining assets in mutual funds, is shown in the graph below. The SPIA allocation was assumed to range from 0% through 60%. The graph shows three asset allocations for the portion in the mutual funds (50%, 65%, and 85% in equities). The addition of a SPIA increased the highest probability of meeting the income goal from 78% (see above) to nearly 94%. This probability occurred under the scenario with 60% of retirement savings allocated to a SPIA and a 50% equity/50% bond allocation in mutual funds % $500,000 in Retirement Assets: Probability of Meeting Income Goal with SPIA and Varying Asset Mix Probability of Meeting Income Goal 9 5 % 9 0 % 8 5 % 8 0 % 8 5 % E q u i ty 6 5 % E q u i ty 5 0 % E q u i ty 7 5 % 0 % 1 0 % 2 0 % 3 0 % 4 0 % 5 0 % 6 0 % Percent of Retirement Assets Used to Purchase SPIA The amount of income generated assuming a 60% allocation to a SPIA, withdrawals from mutual funds with a 50% equity/50% bond allocation, and Social Security benefits is shown in the following graph. The amount of annual SPIA income under this scenario equals about $20,200. Withdrawals are not taken from the mutual fund in the first year, but begin in the second year when the income requirement (net of Social Security benefits) equals $20,

21 $500,000 in Retirement Assets: 60% of Retirement Assets in SPIA, 50% Equity / 50% Bond in Mutual Funds $ $ $ Annual Income (000s) $ $ $ 9 5 $ 7 5 $ 5 5 $ 3 5 $ $ $ $ Mutual Fund Balance (000s) $ 1 5 -$ Age Social Security SPIA Systematic Withdrawal Mutual Fund Balance Index The following three-dimensional graph of the average index is derived based on a 50% weight on not outliving assets (meeting income needs) and a 50% weight on the bequest (death benefit). The average index was determined over a range of SPIA and equity/bond allocations and 10,000 scenarios. The optimal solution occurred when 60% was allocated to a SPIA and the equity/bond allocation was 60%/40%. $500,000 in Retirement Assets: Average Index Based on 50% Not Outliving Assets and 50% Bequest 6 0 % 3 0 % 0 % SPIA % % 7 5 % 5 0 % 2 5 % Equity % Index Optimal solution Under the optimal solution, 60% of the total retirement assets ($500,000) were allocated to a SPIA. The SPIA allocation of $300,000 produced about $20,200 in annual lifetime income. The remaining $200,000 was allocated to mutual funds with a 60% equity/40% bond mix. During the first year, the income requirements are met by Social Security benefits and SPIA benefit payments. In the second year, the income needs (excluding Social Security benefits) are $20,500. This is the first year under this scenario that the mutual funds must be tapped for income (the SPIA payment equals $20,200). Under the optimal solution, there is a 7.0% probability of not meeting the income goal and the average bequest is $892,000. The graph below shows the annual income from Social Security, from the SPIA, and withdrawals from mutual funds based on the optimal solution. 19

22 $500,000 in Retirement Assets: 60% of Retirement Assets in SPIA, 60% Equity / 40% Bond in Mutual Funds $ Annual Income (000s) $ $ $ 5 0 $ $ $ $ $ Mutual Fund Balance (000s) Age Social Security SPIA Systematic Withdrawal Mutual Fund Balance Index Minimum liquidity The following graph shows the index reflecting a minimum liquidity requirement of $215,000 during the first 20 years. The index was derived based on a 50% weight on not outliving assets (meeting income needs) and a 50% weight on the bequest (death benefit). The average index was determined over a range of SPIA and equity/bond allocations and 10,000 scenarios. $500,000 in Retirement Assets: $215,000 in Minimum Liquidity 6 0 % 3 0 % 0 % SPIA % % 8 5 % 7 0 % 5 5 % 4 0 % 2 5 % 1 0 % Equity % Index Minimum liquidity optimal solution When minimum liquidity is an additional requirement during retirement, the optimal solution is a 55% SPIA allocation and 65% equity/35% bond mix in mutual funds. The SPIA allocation of $275,000 produced about $18,500 in annual lifetime income. The income amount is $800 lower than that resulting from the optimal solution without a minimum liquidity requirement. The remaining $225,000 was allocated to mutual funds. Under this scenario, on average there is a 9% chance of not meeting the income goal and the average bequest is $914,000. The minimum liquidity requirement was assumed to be $215,000 during the first 20 years. Under this scenario, the mutual funds must be tapped for income immediately ($1,500). The following graph shows the average annual income and average mutual-fund balance based on the optimal solution. 20

23 $500,000 in Retirement Assets: 55% of Retirement Assets in SPIA, 65% Equity / 35% Bond in Mutual Funds $ $ Annual Income (000s) $ $ $ $ $ $ $ $ $ Mutual Fund Balance (000s) Age Social Security SPIA Systematic Withdrawal Mutual Fund Balance Alternate index For the middle/mass market (Case #3), it may be more important to meet income needs rather than leave a bequest (death benefit). The following results assume a greater weight on the income component of the index (75%) than on the death benefit component (25%). Following is a graph of the average index derived based on a 75% weight on not outliving assets (meeting income needs) and 25% weight on the death benefit. The optimal solution with these weights also occurred when 60% was allocated to a SPIA and the equity/bond allocation was 60%/40%. $500,000 in Retirement Assets: Average Index Based on 75% Not Outliving Assets and 25% Bequest 6 0 % 3 0 % 0 % SPIA % % 8 5 % 7 0 % 5 5 % 4 0 % 2 5 % 1 0 % Equity % 21

24 Assumptions The assumptions used in this study are summarized below: Table 11 IteM assumption Case #1: Affluent #2: High Net #3: Middle/Mass households Worth/Upper Market Households affluent Households Age Age 65 for Male and Female Projection Period To end of mortality table (age 115) Starting Assets $2.5 million $8 million $500,000 Post-retirement annual $111,000 $300,000 $20,000 Income (net of Social Security benefits) Percent to SPIA Varies from 0% to 100% SPIA Income Rate per $1,000 of premium based on average of the top five SPIA rates from CANNEX SPIA Payout Option joint and Last Survivor SPIA Certain Period none Equity Share Varies from 0% to 100% Equity Returns american Academy of Actuaries C-3 Phase 2 diversified Large Capitalized U.S. Equity scenarios Bond Returns american Academy of Actuaries C-3 Phase 2 U.S. Long-Term Corporate Bonds Fund Expense 75 bps Inflation Rate 2.50% Mortality Table annuity 2000 Mortality Table frasierized Joint Mortality Past Mortality Projected from 2000 to 2007 at 2% annual improvement Improvement (q x * (1 -.02) 7 ) Stochastic Future Random improvement factors from a normal distribution Mortality Improvement WITh a mean of 2% and a standard deviation of 1% Stochastic Mortality Random numbers are generated based on a Uniform (0,1) distribution If the random number is greater than the Frasierized joint mortality rate, then death is assumed to occur Average Life Expectancy 31 years based on the above mortality assumptions 42% probability of living to age 100 Index Weights 50% meeting income needs 50% bequest Minimum Liquidity $1 million $3.5 million $215,000 Requirement 22

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