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by Manish Malhotra

Manish Malhotra is the founder and CEO of Income Discovery, a firm focusing on building new approaches for generating retirement income and new tools to help planners build an appropriate income strategy for their clients. (

Executive Summary

  • Even though retirement distribution is the most actively researched area in the world of financial planning, the profession still lacks a comprehensive analysis framework for comparing retirement distribution strategies.
  • Such a framework should do an apples-to-apples comparison among various retirement distribution strategies such as the appropriate time to claim Social Security or the use of systematic portfolio withdrawals in combination with fixed annuities, variable annuities, and bond ladders.
  • The proposed framework in this paper includes two reward and three risk metrics. The widely used metric of probability of success is complemented with two additional risk metrics: a view into what happens when the plan fails and the amount of income generated from fixed sources of cash flow. The proposed reward metrics are retirement income and average legacy.
  • A general outline of the effect of various income strategies on the metrics is provided, which can help planners practice the art of building an income plan mixing a systematic withdrawal portfolio with a fixed source of cash flow such that the plan provides acceptable confidence and reasonable protection in unfavorable markets with a potential to leave a legacy (if so desired) in favorable markets.

Even though retirement distribution is the most actively researched area in the world of financial planning, we still lack a comprehensive analysis framework for comparing retirement distribution strategies. The majority of the research primarily focuses on safe withdrawal rates from a total-return-based systematic withdrawal portfolio (SWP). There are many alternative income strategies that can be used in isolation or in combination with total-return-based SWP, such as time segmentation, bond ladders, and life or period-certain fixed annuities or variable annuities with guaranteed lifetime withdrawal benefits (GLWB). There are additional decisions to make, such as when to take Social Security.

How does a planner judge which strategy is better? If it is better, by how much is it better? An analysis framework that helps guide these decisions is needed. This paper proposes such a framework. After explaining the framework, case studies will demonstrate the power of the framework in constructing an appropriate retirement distribution strategy based on the unique situation of the client.

Literature Review

The safe withdrawal rate (SWR) has been a very active research area since the seminal work using historical sequence of returns-based analysis by William Bengen (1994). Philip Cooley et al., in their two studies, showed success rates for different withdrawal rates and asset allocations (Cooley 1998), and recommended stock allocations for maximizing success rates for 30 years of real retirement income (Cooley 2011) using historical sequence of returns-based analysis. More recently, Wade Pfau has made significant contributions to the field of safe withdrawal rates by first showing that a 4 percent SWR is not safe when looked at in the international context of 17 developed economies (Pfau 2010). He developed further Michael Kitces’s work (Kitces 2008) on sensitivity of SWR to market valuation levels by analyzing the SWR sensitivity to two additional factors: dividend yield and nominal bond yields (Pfau 2011a). In his latest paper, he examined the sensitivity of withdrawal rates to capital market expectations and provided guidelines for withdrawal rates for a given failure rate and retirement duration (Pfau 2012). Pfau also proposed to shift the discussion from SWR to “safe savings rates” and developed guidelines for how to determine the safe savings rate (Pfau 2011c).

Few studies move beyond the SWR by incorporating annuities or other real life situations such as changing income needs during retirement or flexible withdrawals based on portfolio performance. John Ameriks et al. (2001) showed how adding a nominal immediate annuity to the retirement portfolio can improve the risk profile—increase certainty and the period for which income is generated. William Bengen extended his prior work by proposing a framework for adjusting the withdrawal rate based on different types of withdrawal schemes, tax status of the portfolio, time horizon, asset allocation, and rebalancing frequency (Bengen 2006). Jonathan Guyton, meanwhile, built an approach for flexible withdrawal strategies where withdrawals are adjusted based on portfolio performance (Guyton 2004). Wade Pfau examined the weakness of variable annuities (VA) with GLWB in providing inflation-adjusted income (Pfau 2011b), and Joe Tomlinson compared the VA with GLWB to an immediate income annuity and found VA-GLWB to be a costly way to provide the income guarantees (Tomlinson 2012). S. Gowri Shankar (2009) explored the strategy of using a TIPS ladder and longevity insurance to generate safe lifelong retirement income.

Retirement Income Analysis Framework

Because the decisions about retirement income strategy interact in a complex way, an effective way to do an apples-to-apples comparison among different strategies, such as the ones outlined in the paper introduction, is to analyze each strategy using Monte Carlo simulation (called simulation hereafter) through the same set of future scenario paths, and observe the outcome of each strategy in meeting the objective of generating inflation-adjusted income over the planning horizon. Although the industry practices the use of simulation to analyze income withdrawals from an SWP, use of simulation to analyze a complete income strategy covering use of bond ladders, Social Security claim strategies, and different tax drawdown strategies, etc., is not heavily practiced. The simulation can be done using scenario paths (a scenario path, also known as iteration, is a sequence of inflation and asset class returns in future years) generated from either the historical sequence or future expectations of inflation and asset class returns.1

Framing the decision among the distribution strategies in terms of risk-reward trade-off, similar to existing practice in the wealth management industry, helps both the client and the adviser. There can be multiple risk and reward metrics for the framework, with the objective that each metric brings out a unique perspective, and all of them collectively aid in making a decision. Ideally, the metrics should be understandable by an average retiree so that the adviser has an opportunity to involve the retiree in the trade-off decisions.

Consider the following risk and reward metrics as part of the retirement income analysis framework.

Reward No. 1: Retirement Income. The first potential reward for a retiree is the level of inflation-adjusted retirement income. Because an investor’s goal changes upon retirement and the focus shifts to retirement income as the primary factor for decision making (rather than portfolio return, a reward sought by an investor in the accumulation phase), the analysis framework should use retirement income as the first reward metric.

Risk No. 1: Confidence. The first risk that a retiree is concerned about is the chance (probability) that the desired income will not be generated successfully over the planned horizon. Rather than present the probability of failure, it has been well accepted protocol to present the probability of success. The probability of success in generating the desired income over the planning horizon is termed confidence—the first proposed risk metric in the framework.

Risk No. 2: Years of Income in Bad Markets. Although the confidence metric is very helpful, it still doesn’t give a complete picture of the risk. It is not sufficient to know just the chance of achieving success; it is equally important to evaluate what happens if the plan fails. A good analogy is the use of a seatbelt in a car. Use of the seatbelt doesn’t change the probability of getting into an accident. The only thing it changes is the level of injury sustained in a bad car crash. Similarly, it is important to look at what happens in an unfavorable market for the retirement income plan and to develop strategies that function as a seatbelt. A view into what happens when the plan fails can be developed from the number of years over which full desired retirement income was generated successfully for all scenario paths in the simulation, and finding the bottom 2nd percentile2 number of years of income generation. This becomes the second risk metric in the analysis framework.

Risk No. 3: Fixed Source Coverage. In this paper, I will explore many strategies that provide fixed sources of cash flow. In this context, fixed means the sources for which future cash flow is fixed in either nominal terms or real terms. Examples of fixed sources are: Social Security, pensions, fixed annuities, and a ladder of bonds held to maturity. A retirement income cash-flow source based on assets with uncertain returns (as is the case with a systematic withdrawal portfolio) is clearly perceived as having different risk characteristics than a source providing a fixed source of cash flow. It is extremely comforting for the retiree to know that some percentage of the desired income over the planning horizon comes from fixed sources. That is the final risk metric in the analysis framework. This metric is considered a risk metric because it communicates approximately the percentage of retirement income over the planning horizon that is not exposed to investment risk and thus provides a psychological comfort to the retiree. Additionally, it serves as an aid for the planner in structuring an income plan, as will be explained later in sample case studies.

Fixed source coverage over the planning horizon is calculated as a ratio of the sum of the cash flows from all the fixed sources to the sum of the desired income. For the above calculation, the real cash flows (in today’s dollars) are taken over the least successful scenario path, a path where the systematic withdrawal portfolio has the least amount left at the end of the planning horizon.

Reward No. 2: Average Legacy. After having satisfied the primary goal of generating retirement income within acceptable risk, the secondary goal for the retiree is leaving a legacy. The median of the terminal value of the portfolio at the end of the planning horizon captures the secondary goal and becomes the second reward metric in the proposed analysis framework. The median is calculated across the terminal value on all scenario paths, with zero terminal value attributed to those paths where the systematic withdrawal portfolio was exhausted before the end of the planning horizon. Average legacy is determined in real dollars measured in today’s dollars.
Figure 1 gives a visual representation of all the metrics explained above.

A comparison among different income strategies along these metrics provides an appropriate frame of reference for making a choice. A software tool that implements the framework can identify a set of efficient strategies, where each efficient strategy either minimizes the risk measured along one of the metrics for a desired reward or maximizes the reward within acceptable risk. The proposed framework doesn’t extend itself to making a choice between multiple efficient strategies, a decision that is left to the adviser and retiree, who evaluate the trade-offs involved in the decision. Because all the above metrics, especially the risk metrics, are easily understandable by an average retiree, it gives an opportunity for the retiree to be involved in the trade-off decision. The metrics capture some of the key concerns retirees have regarding portfolio sustainability, and help the adviser and the retiree collectively make better decisions about the retirement distribution strategy.

AUG12 Malhotra Figure 1

Analyzing Retirement Distribution Strategies

First, let’s define what I mean by a retirement distribution strategy. Retirement distribution portfolios can be arranged in more ways than having just one systematic withdrawal portfolio. For example, in the book Retirement Income Redesigned (Evensky 2006), Harold Evensky explains a distribution strategy in which a cash-flow reserve is set up alongside an investment portfolio. This reserve can hold two to five years of retirement income needs in money market and low-maturity bonds, which allows the client to avoid sales from the main portfolio during market declines. Use of a reserve portfolio is an example of a retirement distribution strategy with two time segments.
A retirement distribution strategy defines the following elements:

  • Income Withdrawal Rules. For example, a constant real income, real income level adjusted over time based on a predetermined schedule, or real income adjusted based on portfolio performance—or similar income schedules based on nominal income needs.
  • Portfolio Configuration. For example, into multiple buckets such as one total-return-based SWP, or using SWP with a ladder of bonds held to maturity or fixed life annuities, or segmented buckets with replenishment rules across the buckets.
  • Withdrawal Order Rules. Set of rules for withdrawing income across multiple tax type accounts. Rules could have fixed order or performance-dependent order.
    In the next section, I will use three case studies to demonstrate how the analysis framework and the metrics can be used in choosing appropriate distribution strategies. While working with the cases, I will explain why all three risk metrics are needed for a comprehensive analysis.

Early Retiree Case Study: Davis Family

AUG12 Malhotra Sidebar

The first case study involves an early retiree couple, for whom the adviser recommends a TIPS ladder and also analyzes the decision on the appropriate age to claim Social Security (see Early Retiree Case Study sidebar). Peter and Linda are age 56 and 51, respectively. Because a TIPS ladder is used in the analysis, the income plan has to be based on a specific start year, which is assumed to be 2013.

Full retirement age (FRA) for Peter, who was born January 10, 1956, is 66 years and 4 months. FRA for Linda, who was born on January 12, 1961, is 67 years. Peter’s benefit amount on FRA is $2,000 per month. The benefit amount is reduced to 91.1 percent if he claims it at age 65. He gets an 8 percent per annum benefit increase for deferring until age 70—a period of 3.67 years. Linda’s FRA benefit amount is $1,650 per month. She gets 86.7 percent of the FRA benefit at age 65 and can increase the benefit by 8 percent per annum for three years by deferring the claim until age 70.
Let’s first analyze the strategy of Peter and Linda claiming Social Security when each one of them reaches age 65. I will also create a ladder of TIPS that uses the coupon and the maturing principal to generate retirement income. I will consider multiple ladder options: 50 percent of the retirement income from year 2014 until year 2020 (the year before the first Social Security stream starts) and 80 percent of the retirement income over the same period. TIPS, rather than nominal bonds, are used because the objective is to generate real (after-inflation) income. TIPS price quotes used for this analysis are as of February 8, 2012.

All strategies are analyzed using Monte Carlo simulation on the same set of 1,000 scenario paths (iterations). Each scenario path is a 60-year sequence of inflation and asset class real returns. Inflation and asset class real returns for each scenario path are generated based on the assumption of normal distribution of logarithmic real return and logarithmic inflation. Standard mathematical steps are used to generate correlated annual inflation and real returns: Cholesky decomposition of the correlation matrix, use of the decomposed matrix to generate correlated standard normal random variables, conversion of the standard normal variables to normally distributed logarithmic return and inflation based on mean and standard deviation of inflation and the asset class, and conversion from logarithmic values to decimal values. Inflation and returns for each year are generated independently (random walk assumption is used, which implies that each period’s returns are independent of the prior period) till a 60-year scenario path is complete. Only relevant years of a scenario path, for example 50 years in this case study, are used for the simulation.

All calculations are done in real dollars. The first income withdrawal is made in January 2013, followed by 49 more annual withdrawals in every January thereafter. Cumulative annual real cash flow from fixed sources (Social Security, pensions, and a TIPS ladder, in this case) is subtracted from the real income need in the year (adjusted based on phases) to determine the withdrawal from the annually rebalanced constant allocation SWP. If fixed sources provide more cash flow than the income need in any year, the excess amount is deposited into the SWP. The post-disbursal real value of SWP is rebalanced to the target model allocation and then real returns for each asset class are applied to the balance for the asset class to arrive at the pre-disbursal real value of SWP for the next year.

The Social Security real amount stays constant except in periods of deflation. Because the Social Security nominal payout stays constant on deflation until the inflation index rises above its last peak, the real value of Social Security will increase for that period. The inflation index for each scenario path is determined by setting it to 1.0 at the beginning and compounding the inflation on the scenario path thereafter for every subsequent year. The nominal value of the pension is converted to real value by dividing the nominal value by the inflation index for that year on each scenario path.

Performance of Different Strategies

Peter and Linda’s risk profile suggests that the maximum volatility portfolio that they would be comfortable with is a moderate risk allocation. Thus, I would explore both a conservative and moderate portfolio (the model allocations are defined in Table 8; the phrase inflation-protected refers to relatively high use of TIPS and other real assets producing inflation-adjusting income). I analyze all combinations of the two model allocations mentioned above and three configurations for bond ladders (not building a ladder and two other configurations mentioned earlier) to short-list two plans, one that provides the highest confidence and another that provides the longest years of income in bad markets. Those two plans are presented in Table 1.

AUG12 Malhotra Table 1

The analysis framework metrics clearly bring out the implications of each strategy, helping the adviser and retiree reach a decision, as explained below:

  • Compared to the first plan, the lesser volatile strategy of the second plan provides income for two more years in bad markets, though it reduces the confidence of achieving the full income over 50 years by 3 percentage points.
  • The TIPS ladder provides an inflation-adjusted income source backed by the U.S. government, providing a psychological comfort that 50 percent of income till Social Security starts is coming from a safe source with no volatility. Fixed source coverage for the safer strategy is higher, reflecting the use of the TIPS ladder.
  • Some advisers and retirees may prefer the first plan while others may prefer the second plan. The trade-off that the retiree needs to consider for the safety of the second plan (lesser volatility in SWP and locked cash flow from TIPS ladder) represents a significant drop, over 60 percent, in the average legacy the clients can expect to leave behind, and a slight drop in confidence. Although the drop in average legacy is high in relative terms, in absolute terms the average legacy of $1.6 million may be acceptable to Peter and Linda.

Now, let’s look at an alternative strategy: taking Social Security at age 70 with a similar portfolio of SWP and TIPS ladder. For the TIPS ladder, I change the configurations to provide 50 percent or 80 percent of income over 12 years, as Social Security is assumed to be claimed at age 70. After analyzing all combinations of previously defined model allocations and the TIPS ladder, the same strategy performs best on both risk metrics—Plan 2 in Table 2.

AUG12 Malhotra Table 2
Let’s analyze the performance of the strategies in Table 2:

  • By delaying Social Security, Peter and Linda are able to cover the tail risk, the probability of a worst case scenario developing, in their retirement plan. They don’t need to explore buying additional life annuities, as their existing lifelong sources provide over 95 percent of the income in the last phase of their retirement.
  • The second plan reduces risk along all metrics with significantly longer years of income in bad markets—an additional 10 years compared to the first plan. Fixed source coverage also increases to 76 percent compared to 58 percent in the previous plan, reflecting the use of a longer TIPS ladder and higher Social Security benefit.
  • The second plan in the case of claiming Social Security at 70 performs well on all three risk metrics compared to both the plans for the case of claiming Social Security at 65 (see Table 1).

A planner who is new to the analysis framework may mistakenly expect that both the confidence and years of income in bad markets metrics will move together; that is, when one improves, the other also improves. For some strategies, the metrics may move together and for other strategies they may move in opposite directions.

As seen in Table 1, a higher-volatility strategy using a moderate allocation has higher confidence but lower years of income in bad markets (better on one and worse on the other) compared to a conservative allocation coupled with a TIPS ladder. Generally, as the volatility of a systematic withdrawal portfolio increases from conservative to moderate to aggressive, the confidence of achieving a goal increases but the sequence of return risk of a higher volatility portfolio reduces the years of income in bad markets.

Let me explain this in detail using Figure 2. The chart shows the cumulative probability distribution of years of real income of $50,000 generated from a $1 million SWP with balanced and conservative inflation-protected models (see Table 8 for the model details) when simulated under the same capital market assumptions as used in the prior case study. Scenario paths of 200 years were used for the analysis, to effectively capture the distribution of years of income. The x-axis of the chart shows the probability that income will be generated for at least the number of years on the y-axis. The high volatility, high return balanced portfolio has over 45 percent probability of generating income for at least 200 years, and completely dominates the other portfolio in favorable markets. But in unfavorable markets, the balanced portfolio does worse than the conservative portfolio—11 years versus 15 years of income on the worst scenario path. From the same chart, you can also read the confidence metric. If the planning horizon were 20 years, the conservative portfolio would provide higher confidence at around 90 percent compared to about 86 percent for the balanced portfolio.

AUG12 Malhotra Figure 2

A hypothetical TIPS ladder that provides the desired real income of $50,000 would appear as a flat horizontal line because that provides income for a constant number of years. Fixed sources like a TIPS ladder and life annuities will generally protect the retiree in unfavorable markets by improving the tail represented in Figure 2. To build that protection, some degree of upside is given up by moving part of the SWP to the strategies providing fixed sources of cash flow. The art of building an income plan lies in finding the right balance of SWP and fixed sources of cash flow that provide acceptable confidence and reasonable protection in unfavorable markets with a potential to leave a legacy (if so desired) in favorable markets.

In the above case study, I have built an income plan for the Davis family that performs well on all risk metrics by reaping the benefit of deferring Social Security and building a safe source of inflation-adjusted cash flow using a TIPS ladder until Social Security starts. With the TIPS ladder and pension providing safety in the early years of the plan, and Social Security providing safety in the later years of the plan, plus a conservative inflation-protected SWP providing the remaining part of the retirement income, the Davis family can enjoy a retirement with peace of mind.3

Mid-retiree Case Study: Jones Family

AUG12 Malhotra Sidebar 2
Our next case study is the Jones family. Ron, age 75, and Carol, age 70, are at a serious risk of running out of money while they are still alive. This case study will explore strategies that use fixed immediate annuities and a reverse mortgage to see how they can help the Jones family achieve a safe income over the remaining lifespan (see Mid-retiree Case Study sidebar).

Annual inflation and real returns are generated using rolling 360-month windows over historical monthly total return data available in Ibbotson’s Classic Yearbook. Different capital market assumptions are being used in every case study to demonstrate that the framework is independent of the type of capital market assumptions used in the analysis. In practice, each adviser will use custom capital market assumptions or the adviser may choose to analyze a strategy against different capital market assumptions.

As the Jones family faces a significant risk of running out of money during their lifetime, an immediate fixed life annuity will be incorporated into the retirement plan. Based on the Jones family’s risk profile, a moderate allocation (60 percent U.S. large-cap stocks and 40 percent intermediate-term government bonds) for the SWP is being considered.

A similar method as defined in the previous case study is used where all analysis is calculated in real dollars. An inflation-linked life annuity is modeled by keeping its real payouts constant, except in periods of deflation. The inflation-linked annuity product reduces the nominal payout in proportion to the level of deflation, but the payout doesn’t fall below the initial nominal amount of payout. Reverse mortgage nominal payments are converted to real amounts by dividing the nominal amount by the value of the inflation index.

AUG12 Malhotra Table 3

The analysis of alternative plans in Table 3 illustrates several things:

  • The Jones family will have to base the rest of their retirement on the lower end of their income expectation: $30,000 of annual income. Even to generate that income, a significant part of their retirement assets (60 percent) should be invested in an inflation-linked life annuity. Purchase of the annuity increases their fixed source coverage from 64 percent to 87 percent and improves other risk metrics as well: confidence increases by 14 percentage points and the strategy produces full income for an additional three years in an unfavorable market.
  • Their plan is highly sensitive to the income level. An increase of 10 percent in the income using a strategy that uses just the SWP will have only 32 percent confidence and produce just 12 years of income in an unfavorable market. The safer income level for the Jones family would be approximately $30,000 unless other strategies such as the use of a reverse mortgage are introduced.

Table 4 shows the strategy of using a reverse mortgage on their house that pays them a monthly nominal amount of $643 over their joint lifespan. By adding a reverse mortgage to their income plan that was based on a fixed annuity and SWP, Ron and Carol are able to enjoy a higher retirement income of $34,000 at an acceptable risk level: 87 percent of income covered from fixed sources, confidence of 88 percent, and 24 years of income in bad markets. The strategy of using a fixed annuity performs better than not using the annuity on all risk metrics, even after adding a reverse mortgage to the income plan. For the Jones family the primary concern is running out of money, so I am not analyzing the average legacy, which is a secondary outcome. If the
average legacy were to be compared across the plans that use or don’t use a reverse mortgage, the real value of the house would have to be added to the average legacy from the investment portfolio.

AUG12 Malhotra Table 4

Using a fixed annuity and a reverse mortgage with the balance invested in an SWP, $34,000 of annual income—still $1,000 less than the upper limit of the desired income range—can be safely generated for the Jones family. That is the recommended plan for them.

In this case study, a plan was created with an income level that is less than desired, but the risk of the plan was kept at a level comfortable to the client. Similarly, the planner will try to find strategies to produce desired income within acceptable risk, and if none are found, builds plans with reduced income levels.

Significance of Fixed Source Coverage

Using the above case, consider the importance of the fixed source coverage metric. Having high fixed source coverage, such as the 87 percent seen in the last case study, reduces the significance of the other two risk metrics. Even if the systematic withdrawal portfolio bottoms out, the client still has 87 percent of his income locked. For the client, the metric provides a simple view of the amount of retirement income exposed to investment risk. For example, in the second plan in Table 4, the client knows that the other two risk metrics are pertinent only for 13 percent of the income, which may give the client confidence in proceeding with the plan even if the other two risk metrics are relatively lower.

The fixed source coverage metric is also important from an analytical standpoint for the planner. Fixed sources are most effective at reducing the tail risk—they usually increase the years of income in unfavorable markets. If a plan has low confidence and low years of income in bad markets and the plan doesn’t have many fixed sources of cash flow, the planner may add some fixed sources of cash flow to cover the tail risk and improve the confidence of the plan.

Retiree in 60s Case Study: Robert Smith

AUG12 Malhotra Sidebar 3

Next, consider the case of Robert Smith, who is 65. In this case, I will analyze the use of fixed immediate and variable annuities with guaranteed lifetime withdrawal benefits (see Retiree in 60s Case Study sidebar).

Robert has a very low risk profile, so the only model allocation considered for his SWP is a conservative one. However, for the variable annuity (VA) with GLWB, a balanced model, the most aggressive model supported in Vanguard’s VA with GLWB, is considered because the downside protection provided by the VA makes it acceptable for the low risk profile client. Also, it is not advisable to have a low return, low volatility portfolio in the VA while paying the GLWB fees for downside protection.

The same methodology is used for running simulations as was used for the Early Retiree case study, but with different capital market assumptions (see Tables 6 and 7). The VA is assumed to be purchased in January of the start year. To model the performance of the variable annuity contract, I first assume that it pays out the guaranteed amount of benefits as a percentage of the benefit base from the start year of the plan. The contract value represents the value of all the underlying investments in the annuity. The benefit base is the same as the contract value at the time of the contract purchase and is adjusted in later years as explained below. The benefit base is tracked in nominal dollars and the contract value is tracked in real dollars. At the end of each simulation year, the benefit base is stepped-up to the nominal amount of the contract value, if the nominal amount of the contract value is higher than the benefit base. The updated benefit base is used to determine guaranteed lifetime withdrawal, which along with mortality, expense, and admin (MEA) fees and GLWB rider fees, is deducted from the contract value before the next year’s simulated returns are applied to the portfolio underlying the VA. The nominal amount of guaranteed lifetime withdrawal and GLWB rider fees are converted to real dollars before they are subtracted from the contract value. The guaranteed lifetime withdrawal continues to be paid even after the contract value falls to zero. No withdrawals over and above the lifetime benefit are taken from the VA, even if the systematic withdrawal portfolio is exhausted. The contract value remaining after the last withdrawal is added to the terminal value of the portfolio, which is used in average legacy calculations.

AUG12 Malhotra Table 5

The performance of three different strategies is presented in Table 5:

  • Besides the obvious increase in fixed source coverage from the purchase of annuities (up to 68 percent in the third plan), an improvement is also observed in the confidence metric—15 percentage points for the second plan and 9 percentage points for the third plan.
  • In unfavorable markets, the income is generated for an additional four years in the second plan that uses fixed annuities and one year in the third plan that uses fixed and variable annuities.
  • Contrary to popular expectation, use of fixed annuities can improve the average legacy in some cases. If the investor were to rely solely on an SWP with the conservative model, as in the first plan, the average legacy at the end of the plan is relatively small because of low returns in the conservative portfolio. However, in the second plan based on a fixed life annuity, the annuity and Social Security provide approximately $45,900 of cash flow in the last phase of retirement, leaving only about $11,700 to be withdrawn from the SWP. The low level of withdrawal from the SWP in the last phase of retirement lets the SWP grow to a higher terminal value on favorable scenario paths, thereby increasing the average legacy metric.
  • Although the fixed annuity in the second plan improves the confidence significantly, the decision to purchase a fixed immediate annuity using a significant percentage of the assets requires the client to give up access to a large capital base. The third plan, based on a mix of fixed annuities and VA, provides an attractive alternative. It has a better risk profile and higher average legacy amount than the first plan that relies only on an SWP. At the same time, Robert will be losing access to only 15 percent of his capital, an amount he may find acceptable. (An alternative strategy of systematic purchase of fixed immediate annuities can also be used to navigate around the concern of losing access to a large capital base.)

In this case, the third plan that balances multiple objectives of safety and access to capital by using a fixed annuity and a VA will be the recommended plan for Robert Smith.
The above analysis is based on the unique situation of Robert Smith and specific capital market assumptions; a different set of assumptions would lead to a different recommendation. For example, a high inflation capital market assumption, as used in the Davis family case study, would reduce the attractiveness of the VA (see Pfau 2011b for the weakness of a VA in providing inflation-adjusted income). Also, another investor who is able to withstand more volatility in the SWP can generate relatively higher confidence in their income plan by using a moderate or moderate-aggressive portfolio, so he may not need to consider annuities to increase the confidence.

Summary and Future Work

This paper has demonstrated the use of an analysis framework to identify appropriate income strategies using three different case studies. Using this framework, advisers can incorporate a variety of income-producing strategies and products, and decisions about Social Security benefits, into their withdrawal analyses—lacking in much of the past research focused purely on withdrawals from a total return portfolio. Advisers who wish to offer more creative solutions to the retirement planning and withdrawal challenges may find this to be a more comprehensive “real world” modeling process. Current financial planning software will have to be upgraded to support the proposed analysis framework and upcoming retirement income planning software has an opportunity to embody the proposed framework.

Future articles could cover the evaluation of different distribution strategies such as drawdown order across different tax types of accounts with an eye to meeting a desired post-tax income need, plus various time segmentation strategies and distribution strategies using flexible withdrawal rules. The comprehensive model for retirement withdrawals has not yet appeared in our literature, but it may now be possible to outline its general parameters.


  1. Most financial planners take Monte Carlo simulation to mean simulation using scenario paths generated based on the random walk assumption. Historical sequence-based analysis is not termed Monte Carlo simulation by planners. Because the definition of Monte Carlo simulation refers to an analysis of a decision or strategy based on repeated trials, irrespective of how the trials are generated, in this paper, I will call historical sequence-based analysis a Monte Carlo simulation using historical scenario paths.
  2. Because most planners and clients prefer an income plan with at least 80 percent–85 percent confidence, observing at worst the 2nd percentile provides a good measure of tail risk for such a plan.
  3. The plan is based on the assumption of both Peter and Linda living for another 50 years. It is likely that will not happen. When one of them dies, one stream of Social Security will disappear. To handle that possibility, the adviser may explore buying life annuities or building a bond ladder once the couple reaches their late 70s or early 80s.


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Pfau, Wade D. 2012. “Capital Market Expectations, Asset Allocation, and Safe Withdrawal Rates.” Journal of Financial Planning (January): 36–43.

Shankar, S. Gowri. 2009. “A New Strategy to Guarantee Retirement Income Using TIPS and Longevity Insurance.” Financial Services Review 18, 1: 53–68.

Tomlinson, Joe. 2012. “Income Annuities Versus GLWBs: A Product Comparison.” Advisor Perspectives (January 17). 

Appendix: Capital Market Assumptions

Capital market assumptions of low returns and high inflation, and low returns and moderate inflation, are outlined in Table 6. The geometric mean of the actual real return provided as input is converted to the arithmetic mean of the logarithmic real return before scenario generation. Standard deviation and correlation specified are among logarithmic real returns and logarithmic inflation.
The capital market assumptions have been built based on review of multiple sources of capital market assumptions: Ibbotson forward-looking assumptions and the Yale Endowment’s assumptions as available in the book Pioneering Portfolio Management by David F. Swensen. Most planners believe forward-looking returns will be lower than past expectations, while the volatility will be the same or higher. That belief led to return expectations that are around 1.5 percent to 2 percent lower than past expectations and standard deviations at the same level as other historically observed values. See Tables 6–8.

Although the scenario sets generated had absolute return and private equity asset classes, these asset classes are not part of the model allocations used in the case studies.

AUG12 Malhotra Table 6

AUG12 Malhotra Table 7

AUG12 Malhotra Table 8

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