Income for the Retirement Years: A New Model for Seeking Stable Retirement Income

As workers begin the transition from asset accumulation to retirement, they face a wide array of complex and inter-related decisions that will affect their ability to enjoy the “golden years.” Unfortunately, these decisions – such as how to allocate assets, when to take Social Security benefits and whether to buy an annuity – often befuddle the most sophisticated minds in finance, let alone individuals with modest savings and limited financial knowledge. To help unravel the inter-relationships, we set forth a unified framework that aims to optimize decisions collectively and present potential strategies designed to seek the most stable and consistent income stream possible for a given retiree’s wealth and Social Security income. We examine two hypothetical case studies – one for an individual with a moderate income and low wealth and another for someone with high income and high wealth. Based on our model, we conclude that the mix of stocks and bonds one should hold at retirement depends significantly on their level of wealth and that the decision to annuitize is relatively consistent across the wealth spectrum.

The need to make multiple and inter-related decisions is a daunting one for retirement planners. For example, determining the mix of fixed income and equities at retirement affects both the level and sustainability of income that a retiree can generate from their investment portfolio. Social Security can be an excellent hedge against longevity risk, yet the magnitude of Social Security income may be insufficient to maintain one’s quality of life should they live longer than expected. As such, a deferred annuity can be used to help insulate the retiree from the risk of outliving their assets. But how much exposure to a deferred annuity is appropriate?

One of the main issues that makes retirement planning so complex is that each decision affects every other decision. If one chooses to delay receiving Social Security, for instance, a larger fraction of the investment portfolio may need to be used for consumption in the intervening years. This, in turn, may have implications for asset allocation – the mix of stocks and bonds.

Our work expands upon previous PIMCO analysis on retirement planning. In “Investing in Retirement,” we showed how the decision to allocate to an immediate or deferred annuity is conditional on the choice of whether or not to defer Social Security, assuming a fixed asset allocation of 40% equity and 60% bonds.

We build upon these findings by explicitly seeking to solve for both the deferral and asset allocation decisions simultaneously. To highlight the important role of Social Security in the asset allocation decision, we show how the optimal mix of stocks and bonds changes based on one’s view on the future of the Social Security system. Additionally, we allow for constraints on one’s wealth level, which prevents retirees from fully drawing down their savings. This modification is intended to produce results more consistent with real-world behavior. Lastly, rather than assuming a static stock-bond mix, we allow the asset allocation to evolve through the retirement years (although, based on our model, we conclude that the optimal stock-bond mix does not materially change over time). We find that both the decision of whether or not to defer receiving Social Security benefits as well as the optimal mix of stocks and bonds depends significantly, according to our model, on one’s starting wealth and the magnitude of their Social Security benefit.

Social security

Social Security is highly beneficial to retirees not only because it provides a stable retirement income stream, but also because it hedges against both inflation and longevity risk. This makes decisions around Social Security particularly critical. A key choice for recipients is when, between age 62 and 70, to start taking Social Security benefits. Naturally, starting earlier eases the burden of retirement by providing immediate income. However, delaying can meaningfully increase one’s monthly payout. For example, delaying benefits from age 65 to 70 boosts benefit payments by 43%.1

Figure 1 shows the multiplier applied by the Social Security Administration depending on when an individual chooses to start taking benefits. The multiplier is defined relative to the full retirement age of 67, when recipients born in 1960 or later become eligible to receive their full benefit payment.

Figure 1 is a table that shows the Social Security multiplier as a percentage of full retirement benefit, for U.S. retirees ages 62 to 70. The multiplier increases each year the retirement start is delayed. For age 62, the multiplier is 70%, increasing to 100% by age 67, which is the full retirement benefit for individuals born in 1960 or later. By age 70, the multiplier is at its highest, at 124%. More data as of 31 December 2017 is detailed within the table.

The deferral decision is, in part, a trade-off between the advantages of higher income from deferral versus the cost of financing consumption from one’s personal savings, investment portfolio or other sources in the interim. Individuals who have sufficiently high savings balances can better afford to finance spending via their savings until Social Security payments commence.

Figure 2 shows the optimal deferral decision as a function of salary2 and savings based on our model. It concludes that individuals with low savings are better off taking their benefit immediately, whereas those with high wealth balances gain by deferring. However, for savings between $75,000 and $150,000, an individual’s salary – a proxy for the level of the Social Security benefit – matters. As the savings balance increases, one is more likely to gain by deferring but only if the Social Security benefit is “small” relative to their wealth. The reason is that, in our framework, retirees prefer a smooth consumption stream to a volatile one. When one’s benefit payment is high relative to their wealth, deferring Social Security will result in a large “bump” in retirement income at age 70. If the bump is sufficiently large, deferring Social Security will undermine the objective of generating a relatively smooth income path. Regardless, our research indicates that even moderately affluent individuals (with investment assets above $175,000), would likely be better off deferring Social Security benefits until age 70.3

Figure 2 is a table showing wealth horizontally and salary vertically. The table shows a hypothetical example in which, for someone with a salary of $25,000, deferral is more beneficial if their wealth is $75,000 or above. As income increases, the deferral is more beneficial at higher amounts of wealth. For a salary of $50,000, it’s at $100,000. For salaries $125,000 and above, the deferral is more beneficial at wealth starting at $175,000. Squares shaded green show the intersection of salary and wealth where the deferral is more beneficial, and red indicates the deferral is less so.

Deferred annuities

A key risk for retirees is longevity risk – the risk of outliving one’s assets. It may seem strange to think of living long as a risk, but in the context of retirement savings, it means running out of money too soon and a substandard retirement. And while Social Security explicitly protects against this risk, for many retirees the fraction of income that Social Security generates is generally insufficient to meaningfully hedge against the risk of outliving one’s savings. Particularly for wealthier retirees, the progressive nature of Social Security means that hedging longevity risk must entail more than basic reliance on Social Security.

Annuities may help in this regard as they are an insurance contract that can provide a guaranteed stream of income for life. Deferred annuities tend to be far less expensive than immediate annuities for a given notional exposure. This is because deferred annuities don’t pay out until a future date and are conditional on the recipient being alive at the time the annuity payments commence.4 As such, for certain individuals, an allocation to a deferred annuity can help to hedge longevity risk without unduly burdening consumption between retirement age and the start of annuity payments. Immediate annuities, on the other hand, combine bond-like features with a longevity hedge, and so effectively encapsulate two dimensions of the retirement problem.

Therefore, and consistent with results of Gong and Webb (2007), in this analysis we focus only on deferred annuities as a way to isolate decisions related to longevity risk from the overall asset allocation. Specifically, we evaluate a 20-year deferred real annuity purchased by a 65-year-old who begins accruing payments, in real dollars, at age 85.5 Accordingly, the deferred annuity in our model hedges not only longevity risk, but inflation risk as well.6 (The use of deferred annuities in this analysis should not be considered a recommendation for one annuity contract over another.)

Asset allocation

In addition to the Social Security and annuity decisions, the prospective retiree must also determine how to invest the non-annuitized portion of their savings. We focus on the high-level allocation between a higher-volatility equity asset and a lower-volatility fixed income asset.7 The decision of how much to allocate to each is critical because an overly aggressive asset allocation can lead to losses and reduce savings to a level that cannot sustain one’s income needs, whereas too conservative an allocation may not provide enough income in general.

Perhaps surprisingly, one of the key variables affecting a retiree’s asset allocation is the value of their Social Security benefit relative to their savings. Social Security can be thought of as similar to a real bond because it pays a fixed inflation-adjusted coupon. In terms of its contribution to the factor risks of the overall retirement pie in our model, Social Security can effectively occupy the space held by bonds in the retiree’s asset allocation. To the extent the contribution of Social Security reflects a relatively high fraction of the retiree’s income, the individual effectively has a large allocation to fixed income. Conversely, for those whose Social Security benefit is relatively small, the effective bond allocation is low.

Low wealth individuals therefore have much more effective fixed income exposure as a percentage of their assets than their wealthier peers. As such, our model indicates that these investors may be able to take greater equity risk in the non-annuitized portion of their asset allocation. Conversely, wealthier retirees in our model need to hold a greater allocation to fixed income in order to compensate for the smaller bond-like contribution of Social Security.

Importantly, we are not assuming that wealthy investors are somehow more risk averse than those who have less wealth; in our model, all investors are characterized by a constant level of risk aversion.8 Wealthier retirees hold more fixed income because the contribution of Social Security to retirement income is relatively small. In fact, if we do not consider the Social Security benefit in our optimization, all retirees would hold the same stock-bond allocation.

Model results: Two case studies

Case 1: Moderate salary/Low savings

Consider an individual who has accumulated $75,000 in savings by age 65 and receives Social Security benefits based on average earnings of $75,000 throughout their working career.9 This individual can expect to earn around $24,500/year (real) by taking Social Security immediately, corresponding to an income replacement of 33%. Assuming he is healthy enough to live for 30 more years, a back-of-the-envelope calculation might predict that the investment portfolio could contribute an additional $2,500 ($75,000/30) before investment returns, yielding an overall retirement income of around $27,000 per year.10 Of course, he is still subject to longevity risk if he lives beyond age 95.

Our optimization model, however, shows that our retiree can actually do better, including by taking steps that include mitigating the risk of outliving his assets. Figure 3 shows his optimal decisions and the resultant expected income.11

Our hypothetical retiree chooses to take his Social Security payment immediately at age 65, invests $10,425 in a deferred annuity that pays out in 20 years, and allocates 100% of his assets to equities.12 The aggressive equity allocation may seem counterintuitive for someone with such a small savings balance. However, because of the high fraction of consistent real income provided by Social Security, a high level of equity risk contributes only a modest amount of volatility to his retirement income, based on our assumptions.

Figure 3 is a table showing a hypothetical example of  the optimal decisions for a 65-year-old U.S. retiree with $75,000 in savings and Social Security benefits based on average earnings of $75,000 throughout their working career. The table includes the percentage allocation decision, dollars allocated and retirement and real income for the first 20 years for five income sources: social security, deferred annuity, stocks, bonds and drawdown. Data is detailed within. Figure 4 is a bar chart showing a hypothetical retiree’s sources of income for someone with at retirement having averaged $75,000 salary and having $75,000 savings. Retirement income is about $30,000 at age 65, and declines slightly over time to age 84, after which a deferred annuity payment begins, raising income to a steady amount annually thereafter, around $28,500. The bars for each year mostly comprise social security income, represented in blue, of $24,500. The first 20 years involve a drawdown of savings, represented by orange. A black dotted line sloping downward shows anticipated savings balance over time, expressed in nominal dollars, starting at $50,000, declining to zero by age 83. Deferred annuity payments, shown in teal, take over at age 85 to replace the lost savings.

The bars in Figure 4 show the retiree’s sources of income, expressed in real dollars. The black dotted line shows his anticipated savings balance over time, expressed in nominal dollars.13 As expected, the vast majority of his yearly income comes from Social Security, with an additional $4,000 on average coming from the investment portfolio. Of the $4,000, approximately $3,150 comes from drawing down principal and $850 from investment returns. The portfolio is spent down entirely between age 65 and 85, with an average principal drawdown of 4.2%. This is possible because at age 85 his deferred annuity will start paying approximately $3,400/year in real dollars. From age 85 on, our retiree derives all consumption from Social Security and annuity payments. The combination of generating income via the investment portfolio in the first 20 years and via an annuity thereafter allows our retiree to generate a stable retirement income stream and mitigate longevity risk.

Case 2: High Salary/High Savings

At the other extreme of the distribution, we optimize for someone who has amassed a rather large savings pool of $2 million and accrued a Social Security benefit based on average annual earnings of $200,000. This hypothetical individual is fortunate to have a high savings balance, allowing him to defer Social Security and finance the first five years of retirement via the investment portfolio. Also, because the majority of his income will be derived from investments, rather than Social Security, the bump in income at age 70 induces relatively little income volatility, further justifying the deferral decision. Figure 5 shows the optimal decisions for this hypothetical retiree.

Figure 5 is a table showing a hypothetical example of  the optimal decisions for a 65-year-old U.S. retiree with $2 million in savings and Social Security benefits based on average earnings of $200,000 throughout their working career. The table includes the percentage allocation decision, dollars allocated and retirement and real income for the first 20 years for five income sources: social security, deferred annuity, stocks, bonds and drawdown. Data is detailed within.

Unlike the hypothetical retiree in Case I who invests 100% of his portfolio in equities, the wealthy retiree invests 71% in fixed income. The higher allocation to bonds is intended to compensate for the relatively small impact of Social Security on his income stream. The wealthier individual draws down 4.4% of his principal balance on average and depletes his savings by age 85. Interestingly, the retiree allocates 13% of his investable assets to a 20-year deferred annuity – about the same percentage as the lower-wealth retiree. Figure 6 shows the sources of income for the Case II retiree.

Although at age 70 our hypothetical wealthy retiree experiences a “jump” in income when Social Security begins paying out, his average real income remains fairly steady throughout retirement at around $131,000 per year (real). He accomplishes this by spending a relatively large fraction of his investment portfolio between age 65 and 70, but then significantly reduces spending from the investment portfolio when Social Security begins paying out. This highlights the fact that wealthy individuals can smooth consumption by drawing down more of their investment portfolio between age 65 and 70, an option not necessarily afforded to their less fortunate peers. The wealthy retiree also spends down his assets through age 85 when the deferred annuity begins paying around $80,000/year, keeping his income stream largely intact and mitigating longevity risk. Although not shown, our retiree maintains a relatively stable stock-bond allocation throughout his retirement years of about 30/70.

Figure 6 is a bar chart showing a hypothetical U.S. retiree’s sources of income, for the scenario of someone having had an average salary of $200,000 and $2 million in savings. Income averages around $131,000 from age 65 to 84, with it dipping to $120,000 by age 69, and rising at 70, when Social Security papyments begin. The first five bars, or years, are made up entirely of slightly declining withdrawals, shaded in orange. At age 70, when the Social Security payments of $32,400 begin, shaded in blue, income rises to more than $150,000, which slowly declines to $120,000 by age 84. After that, deferred annuity payments begin, shaded in teal, keeping income steady amount annually thereafter, around $131,000. A black dotted line slopes down for the first 20 years, showing the decline in savings to zero by age 83.

Maintaining positive wealth balances

While understanding the optimal retirement planning decisions for an individual who is comfortable fully spending down their savings balance is insightful, it’s highly unlikely that most retirees would be willing to do this in practice. Unforeseen financial risks such as an illness or the desire to pass on wealth to heirs are obvious reasons for maintaining a positive savings balance. In fact, recent research by the Employee Benefit Research Institute (EBRI) shows that, regardless of the retiree’s starting savings level, individuals retain about 75% of their starting balance after 20 years, on average.14

In this section, we repeat the optimization exercise for our two hypothetical retirees, but – consistent with empirical findings – we constrain their average nominal wealth balance at age 85 to 75% of their starting balance at age 65. This has obvious implications for consumption, because a smaller fraction of wealth can be used to generate income. Additionally, because less principal balance is spent each year, annuity and asset allocation decisions may also be affected. Figure 7 shows how retirement planning decisions differ for the hypothetical Case I retiree when the savings balance is constrained.

The decisions made by the hypothetical Case I retiree look broadly similar when wealth is constrained. In both cases, he takes Social Security immediately and invests 100% of his portfolio in equities. He invests less in the deferred annuity (9.4% versus 13.9% of his starting balance) because longevity risk is diminished by spending down less of his savings. In terms of consumption, the Case I retiree is able to spend $27,500/year for the next 20 years compared to $28,500 when wealth is unconstrained – a reduction of only 3.5%. The Case I retiree experiences little change in lifestyle because the majority of his retirement income comes from Social Security, which is unaffected by the wealth constraint. When wealth is constrained, the retiree also generates substantially more income via the investment portfolio ($1,523 versus $855) due to having drawn down less principal, leaving a higher principal balance that generates greater income over time. As a result, he gives up only $1,000 per year in income by constraining principal to 75% of its starting level. Figure 8 shows the sources of income for the Case I retiree.

Figure 9 compares the decisions for the high wealth/high income retiree. Our hypothetical Case II retiree continues to defer his Social Security benefit given his high wealth balance, but invests a much smaller fraction in the deferred annuity – 3.2% versus 12.7% – and holds a slightly higher equity allocation of 34% versus 29%.

The model allocates a slightly greater allocation to equity risk because he draws down less savings over time. For the same reasons as the Case I retiree, the wealthier individual assumes less annuity exposure because his longevity risk is reduced via lower spending. The biggest difference is in spending. For the first 20 years, he spends about $103,000/year versus $131,000/ year in the unconstrained case, or a 21% reduction in consumption. These values reflect principal drawdowns of 2.3% and 4.4%, respectively. Hence, a wealth balance constraint has a much larger impact on wealthy individuals than it does for those who are less fortunate because a much larger fraction of their consumption is financed via their investment portfolio. Figure 10 shows the income sources for the Case II retiree.

Figure 7 has two tables showing how retirement planning decisions differ for the hypothetical U.S. retiree of having had an average salary of $75,000 and having $75,000 in savings at retirement. The first table shows a full drawdown, whereas the other table shows the effects of constraining the savings drawdown. Data as of 31 December 2017 are detailed within. Figure 8 is a bar chart showing a hypothetical U.S. retiree’s sources of income for someone at retirement having averaged $75,000 in salary and having $75,000 savings, under a wealth-constrained scenario. Retirement income over the first 20 years, from ages 65 to 84, averages $27,500 and is fairly even, declining slightly over time, due to a declining withdrawal amount from savings, shaded as orange in the bars. Most of the income over the retiree’s lifespan is from Social Security, shaded blue, at $24,500 each year. Annuity payments start at age 85, shaded in teal, bringing income up to around $29,000, up from $27,000 the previous year.  A black dotted line showing the average wealth slopes downward over time, from around $65,000 at retirement, slowly approaching the $50,000 level, but never dipping below it. Figure 9 has two tables showing how retirement planning decisions differ for the hypothetical U.S. retiree of having had an average salary of $200,000 and having $2 million in savings at retirement. The first table shows a full drawdown, whereas the other table shows the effects of constraining the savings drawdown. Data as of 31 December 2017 are detailed within. Figure 10 is a bar chart showing a hypothetical U.S. retiree’s sources of income for someone at retirement with having averaged $200,000 in salary and having $2 million savings, using a wealth-constrained approach. The first five bars, or years, are made up entirely of withdrawals, shaded in orange. Withdrawals start at $100,000 at age 65, declining to around $80,000 at age 69. After that, Social security payments of $32,400 are added in, raising income to $120,000. For the next 15 years, withdrawals continue to decline, lowering income to about $98,000 by age 84. At age 85, annuity payments start, raising income up to about $118,000. With the continued reduction in withdrawals, income declines to about $98,000 by age 104. Savings are still at around $1.3 million at age 100.

The stock-bond allocation

The mix of stocks and bonds one holds at retirement is a key decision for investors. As shown in the previous section, our model indicates that the optimal asset allocation can change rather dramatically depending on one’s wealth level with wealthier individuals holding significantly more fixed income than those with smaller account balances. The role of Social Security is critical in this consideration, and our framework takes this as given. In other words, the asset allocation optimization results in the prior section were predicated on the notion that Social Security benefit payments continue without interruption throughout one’s life. In this section, we dig deeper into the asset allocation decision. First, we show how the optimal asset allocation changes as a function of one’s wealth. Then we relax the assumption that Social Security will exist with certainty, and show how the stock-bond mix changes with one’s confidence in the persistence of benefit payments.

Figure 11 shows the relationship between the optimal equity allocation and the starting savings balance. To make the results as consistent as possible, we base the inputs on real-world data. Specifically, we assume that the investor has accumulated a Social Security benefit comparable to someone who has earned an average real wage of $56,000 through their working careers, takes their Social Security benefit immediately at age 65, and does not invest in an annuity (either immediate or deferred).15 As before, we set the wealth constraint to 75% of its starting value. As expected, Figure 11 shows, based on our model and underlying assumptions, that investors with low levels of wealth allocate significantly to equities as a counterbalance to their bond-like Social Security benefit. At the other end of the wealth spectrum, the equity allocation levels off at around 30%. Beyond $2 million in assets, we find that the optimal allocation to equities slowly declines, but remains close to 30%. These results assume that the retiree’s Social Security benefit remains unfettered.

Figure 11 is a graph of a hypothetical optimal equity allocation, shown on the Y-axis, versus starting savings at retirement, shown on the X-axis. The optimal allocation for someone with $30,000 in savings at retirement is 100%, shown on the left of the graph, and declines with increases in starting savings at retirement, represented by a downward (negative) sloping line.  For someone with $385,000 at retirement, the optimal equity allocation is around 55%, and for someone with $2 million, it is around 30%.


Of course, there is no guarantee that Social Security will continue in its current state. Financial advisors often speak about the need to consider a future in which one’s Social Security benefit is either significantly diminished or, in the worst case scenario, ceases to exist at all. To better understand the role that the investor’s confidence in Social Security plays in the asset allocation decision, we modify our model to allow for a potential cessation of one’s Social Security benefit by assuming a particular default rate for Social Security and then re-computing the stock-bond allocation. Figure 12 shows the optimal equity allocation versus Social Security default intensity.16 Our parameter values are the same as those in Figure 9 and the starting wealth balance is $385,000.17 Figure 12 shows that even a modest expectation of default dramatically reduces the equity allocation. For example, the equity allocation falls from 53% to 34% for a 0% and 5% default intensity, respectively. While a 5% default intensity corresponds to an expected default time of 20 years, it still has a significant impact on the optimal equity allocation. This result highlights how important the perception of Social Security’s solvency is to the asset allocation decision. If one believes in even a slight chance of default, the optimal equity allocation falls dramatically. When one views Social Security’s survival as highly unlikely, our results show that the equity allocation falls to as low as 20%, irrespective of one’s starting wealth level.

Figure 12 is a graph of a hypothetical optimal equity allocation, shown on the Y-axis, versus the Social Security default hazard rate, shown on the X-axis. The graph shows that even a modest expectation of default dramatically reduces the equity allocation. For a default rate of 0%, the optimal equity allocation is 54%. Yet for a default rate of 5%, it drops to 34%. The line continues to slope downward, but decreasingly so, as the default rate increases. At a default rate of 10%, allocation is about 26%. At 100%, allocation is 21%.

Model summary

While there is, of course, no one-size-fits-all solution to the highly complex problem of retirement, we believe the results of our model allow us to put forth a few heuristics that retirees and their advisors may find useful in their retirement planning. Figure 13 summarizes our hypothetical case studies.

Figure 2 shows that beyond $75,000 in assets, the optimal Social Security decision implied by our model is to defer. For asset levels below this level, the model implies that one needs to consider the size of the benefit in relation to their assets. But for individuals with relatively low balances, one should consider leaning toward taking Social Security benefits immediately and avoiding financing consumption via savings. Both high-wealth and low-wealth retirees in our model allocate up to around 13% to a deferred annuity, with a wider range for high-wealth individuals. By deferring Social Security, our model indicates that high-wealth retirees have a higher effective longevity hedge than those who take their benefit immediately. As a result, the model assumes a lower allocation to a deferred annuity. The mix of stocks and bonds within the model are quite different between the two cohorts, with high-wealth retirees allocating only about 30% of their portfolio to equities versus their lower-wealth counterparts, who hold nearly their entire portfolio in equities. Finally, depending on one’s desire to retain a positive principal balance throughout retirement, the case studies indicate a real principal drawdown of between 2% and 4% to finance consumption. The principal drawdown range derived from our model case studies is consistent across the wealth spectrum.

Figure 13 is a table summarizing the hypothetical case studies of a low-wealth U.S. retiree with $75,000 at retirement, compared with a high-wealth retiree with $2 million. Data as of 31 December 2017 from the Social Security Administration is included within.


Retirement planning decisions are complex. Furthermore, choices are often viewed in isolation without consideration for the impact on other key decisions. Our model provides a framework that seeks to solve collectively for the optimal choices in terms of Social Security deferral, annuitization, asset allocation and consumption. We show that these decisions depend critically on a retiree’s level of savings, their Social Security benefit and their tolerance for spending down savings. While there is no single solution for all situations, our framework allows us to put forth concepts that may help solve for determining the most consistent retirement income stream one can obtain given starting conditions and drawdown preferences.


“Investing in Retirement”, PIMCO Quantitative Research, April 2015.

Banerjee, Sudipto, Asset Decumulation or Asset Preservation? What Guides Retirement Spending, EBRI Research Institute, April 3, 2018, Issue 447.

Brown, Jeffrey, Olivia Mitchell, and James Poterba, “Mortality Risk, Inflation Risk, and Annuity Products,” NBER Working Paper, July 2000.

Gong, Guan, and Anthony Webb, “Evaluating the Advanced Life Deferred Annuity: An Annuity People Might Actually Buy,” Center for Retirement Research at Boston College, September 2007.

Milevsky, Moshe, “Real Longevity Insurance With a Deductible: Introduction to Advanced-Life Delayed Annuities (ALDA),” North American Actuarial Journal, Vol. 9, No. 4, pp 109-122.

The models, scenarios and decisions included here are not based on any particular financial situation, or need, and are not intended to be, and should not be construed as a forecast, research, investment advice or a recommendation for any specific PIMCO or other strategy, product or service. Individuals should consult with their own financial advisors to determine the most appropriate allocations for their financial situation, including their investment objectives, time frame, risk tolerance, savings and other investments. Investors should speak to their financial advisors regarding the investment mix that may be right for them based on their financial situation and investment objectives.

1 At the full retirement age of 67, the beneficiary receives 100% of their Social Security benefit. Receiving benefits at age 65 and 70 results in payments of 86.7% and 124%, respectively, relative to the full retirement benefit.

2 Social Security benefits are based on average indexed monthly earnings during the 35 years in which the participant earned the most. See

3 We have modeled the deferral decision as a choice between taking the Social Security benefit at age 65 or 70. We have not considered whether or not retirees should take their benefit in between this age range. However, the general rule should still apply: individuals with high wealth balances should defer.

4 Additionally, purchasers of deferred annuities may benefit from the pooling of longevity risk, which occurs when insurance companies diversify their exposure across many individuals.

5 The deferred real annuity was first described in the academic literature in Milevsky (2005), who termed it the Advanced Life Deferred Annuity (ALDA).

6 Although we focus on real annuities, in results not shown here we find that the allocation to a deferred annuity is not particularly sensitive to whether the instrument is modelled as real or nominal, under our long-term inflation assumptions of 2.1%. In general, to the extent realized inflation is materially different from breakeven inflation, participants can strongly prefer either a real or nominal annuity. However, that is not the case under our baseline assumptions.

7 Equities are proxied by the S&P 500 and bonds by the Bloomberg Barclays US Aggregate index.

8 In our model, retirees are defined by a constant relative risk aversion (CRRA) utility function with a risk-aversion level of 4. One of the main properties of CRRA utility is that the optimal asset allocation is invariant to the level of wealth. Using alternative utility functions in which the level of relative risk aversion is an explicit function of wealth will yield different stock-bond allocations for different levels of savings.

9 This corresponds approximately to the median IRA account balance of a 65-69 year old of $78,612. Source: as of January 2018.

10 We use the pronoun “he” throughout this paper. We do so because our modelling is based on life expectancy assumptions for a typical male, using data from the Social Security Administration. Because females have slightly longer life expectancy than males, in general this will increase the allocation to a deferred annuity. However, one should not expect broad differences in results between male and female life expectancy assumptions.

11 In our income calculations we do not distinguish between income coming from yield versus capital gains.

12 The deferred annuity is valued using life expectancy data for a 65-year-old male from the Social Security Administration. We apply a 20% reduction to the “fair” annuity value to reflect real world pricing of annuities. The haircut we apply is based on Brown, Mitchell, and Poterba (2000), who show a money’s-worth range of 0.75 to 0.87 for inflation-indexed annuities.

13 The income stream is shown in real dollars whereas the savings balance is shown in nominal dollars. We have chosen to present the data in this fashion because retirees care about consumption and hence real dollars are the correct measure for income. We show the savings balance in nominal dollars because retirees tend to think about a nominal dollar balance as opposed to a real balance. Hence, the reader should keep in mind that the nominal portfolio balance shown is not reflective of true purchasing power.

14 “Asset Decumulation or Asset Preservation? What Guides Retirement Spending,” EBRI Research Institute, Sudipto Banerjee, April 3, 2018, Issue 447.

15 $56,000 is approximately the average salary rate of workers with a 401k plan from age 25 to 65, as sourced from EBRI. The vast majority of retirement savers do not annuitize and most individuals take their benefit before age 70 (United States Government Accountability Office (GAO-11-400), June 2011).

16 1/default intensity is the expected time to default. For example, a default intensity of 5% implies an expected default horizon of approximately 20 years.

17 Source: EBRI Brief, March 13, 2018, No. 445.
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Figures are provided for illustrative purposes and are not indicative of the past or future performance of any PIMCO product.

All investments contain risk and may lose value. Investing in the bond market is subject to risks, including market, interest rate, issuer, credit, inflation risk, and liquidity risk. The value of most bonds and bond strategies are impacted by changes in interest rates. Bonds and bond strategies with longer durations tend to be more sensitive and volatile than those with shorter durations; bond prices generally fall as interest rates rise, and the current low interest rate environment increases this risk. Current reductions in bond counterparty capacity may contribute to decreased market liquidity and increased price volatility. Bond investments may be worth more or less than the original cost when redeemed.  Equities may decline in value due to both real and perceived general market, economic and industry conditions.  Annuity guarantees are backed by the claims-paying ability of the issuing insurance company. PIMCO does not offer insurance guaranteed products or products that offer investments containing both securities and insurance features. PIMCO does not provide legal or tax advice. Please consult your tax and/or legal counsel for specific tax or legal questions and concerns.

This material contains the opinions of the manager and such opinions are subject to change without notice. This material has been distributed for informational purposes only and should not be considered as investment advice or a recommendation of any particular security, strategy or investment product. Information contained herein has been obtained from sources believed to be reliable, but not guaranteed. No part of this material may be reproduced in any form, or referred to in any other publication, without express written permission. PIMCO is a trademark of Allianz Asset Management of America L.P. in the United States and throughout the world. ©2018, PIMCO.