Lacking better insights, financial planners cling to rules of thumb, such as allocating a percentage of assets to fixed income based on a client’s age. More recently, those rules have been institutionalized through products like target-date funds, which maintain a fixed glide path for all investors. But new research has led to the development of software products that allow advisors to easily improve on the suboptimal outcomes to which clients were previously destined.
Retirement income planning is a growth industry for advisors and a popular subject for academic research. Unfortunately, there is little communication between the academic community and those providing advice for clients. Planning can be improved if we can bridge this gap. I'll discuss advantages of the approach advocated by academic economists and highlight new software that demonstrates its value.
Life-cycle planning
Academic research on retirement income can be traced to the work of economist Frank Ramsey more than 80 years ago. Many prominent economists have been involved since, including Nobel Prize winners Paul Samuelson, Edmund Phelps, Franco Modigliani, Robert Merton, and William Sharpe. Their work has focused on the full life cycle — not just retirement, but accumulation as well – hence the term "life-cycle planning" that describes their recommended approach.
Unfortunately, this research has had little impact on the practice of financial planning. Much of the work makes heavy use of mathematics and uses concepts familiar only to economists, making it inaccessible to many advisors, who continue to rely on inferior rules-of-thumb.
Financial planners have produced their own less technical retirement income research, beginning with Bill Bengen and the "4% Rule" in the early 1990s, with later refinements by Bengen and other planners. Most of the financial planning software in use today is tied to this "practitioner approach" – the sole exception being ESPlanner, which is based on life-cycle planning and was developed by Boston University economics Professor Laurence Kotlikoff and colleagues. Robert Huebscher provided a summary of key features in this 2011 Advisor Perspectivesarticle, and more details are available at the ESPlanner website.
Others have attempted to bridge the gulf between academics and practitioners. Boston University Professor Zvi Bodie has produced several articles and papers in which he presents life-cycle planning in user-friendly terms. An example is a paper with Jonathan Treussard and Paul Willen contained in the CFA publication, The Future of Life-Cycle Saving and Investing, which contains the papers from a 2006 conference that Bodie organized. York University Professor Moshe Milevsky has also been involved in bridging the divide, including his 2010 paper with Huaxiong Huang, Spending Retirement on Planet Vulcan, in which they offer practical advice for retirement income planning based on academic research. From the practitioner side, financial planner Paula Hogan discussed life-cycle finance in a 2007 paper in the Journal of Financial Planning.
But there is much more that needs to be done to connect the academic and practitioner worlds. About a year ago, I launched my own investigation of the academic literature to find practical applications for retirement planning. My research initially produced more confusion than enlightenment, but took a major leap forward a few months ago when I connected with Gordon Irlam, the developer of AACalc – software that applies the life-cycle approach to financial planning. Irlam is not an academic economist. He has had a very successful career as a Silicon Valley software developer, but he has the requisite training in math and economics needed to develop AACalc. I have communicated with him as he continued to refine and test the software. For those who wish to try AAcalc, it is available for free here.
Irlam has run experiments to test some of the theoretical work produced by academic economists. His experiments deal with the two most fundamental questions in retirement income planning: how much to spend each year, and how to allocate savings between stocks and bonds. I'll report the results of this research, but first I'll highlight two key building blocks of the life-cycle approach: risk aversion and utility and stochastic dynamic programming (SDP).
Risk aversion and utility
The life-cycle approach focuses on consumption-based spending and relies on a risk-aversion measure of the willingness to trade variable consumption for fixed consumption. For example, an individual might be asked what fixed annual consumption amount he or she would accept in trade for a 50/50 chance of being able to spend $30,000 or $50,000. Most individuals would pick an amount less than $40,000, and a person who picked $35,000 would be described as more risk averse than an individual picking $38,000. With the life-cycle approach, assumptions about risk aversion feed into what economists refer to as a "utility function," a measure of the satisfaction gained from varying levels of consumption spending. Optimization involves maximizing lifetime utility.
Stochastic dynamic programming (SDP)
Under the life-cycle approach, building a retirement plan involves choosing year-by-year asset allocations and consumption spending in order to maximize expected lifetime utility. If we consider that retirement may last 30 or 40 years, and that choices made each year will affect all subsequent years, determining the best retirement plan quickly becomes overwhelming. We need a way to reduce the number of calculations, and that’s where SDP comes into the picture.
This optimization technique was invented by Richard Bellman in the 1950s for solving complicated engineering problems. The genius of the method is that it works backwards. For example, think about the problem of landing a man on the moon. This technique would find a solution by beginning with the moon landing and then working back through the steps to the rocket launch.
The retirement planning analog begins with the last year of retirement and works back to the beginning of retirement. Although SDP may seem to be mysterious and complex, the key point is that it is nothing more than a technique to streamline computations.
Samuelson and Merton
An early application of the life-cycle approach can be found in companion papers produced by Paul Samuelson and Robert Mertonin 1969. Samuelson's motivation for the research was to examine the popular planning strategy that stock allocations should decline with age. Samuelson applied utility theory and SDP to demonstrate that maximizing lifetime utility required level, rather than decreasing, year-by-year stock allocations, with the optimum level determined by the degree of risk aversion. Merton achieved the same result, but with a continuous-time model instead of Samuelson's year-by-year analysis.
Samuelson and Merton’s theoretical research also produced findings about consumption over the life cycle. They demonstrated that optimum consumption each year could be determined as a function of current wealth and age. Under one particular set of reasonable assumptions, Samuelson showed optimal spending to be current wealth divided by life expectancy. Milevsky and Huang produced similar findings in the "Planet Vulcan" paper mentioned earlier. The required minimum distribution (RMD) rules, which the government applies to savings in retirement accounts, follow a similar pattern – all quite different from the inflation-adjusted withdrawals often used in practitioner research.
AACalc
AACalc provides a more empirical and less theoretical way of determining optimal allocations and consumption. As shown in the chart below, Irlam compared the results from full optimization using SDP to outcomes from various rule-of-thumb strategies. The dollar measure he used for comparison is "certainty equivalent" – the program calculates lifetime utility for each allocation and withdrawal scheme, and then converts the utilities to level annual consumption amounts in today's dollars. A more detailed description of the analysis and additional comparisons can be found here.
The inflation-adjusted withdrawal scheme uses an approach similar to the 4% rule: The first year withdrawal is a percentage of initial savings, and the dollar amount of withdrawals is increased at the inflation rate each year (unless savings are depleted). "1/Life" refers to a withdrawal scheme where the withdrawal each year equals savings divided by remaining life expectancy. The first year percentages shown were chosen by the AACalc optimization to produce the highest dollar amounts for each of the three asset allocation alternatives. For the fixed asset allocation, a 40/60 mix of stocks and bonds produced a higher amount than other fixed allocations. The "SDP" column takes away restrictions on the withdrawal scheme and allows the program to determine the year-by-year withdrawals that maximize lifetime utility. For fixed allocations, both 1/Life and SDP optimized with an 80/20 stock/bond allocation.
The table has three columns for withdrawal schemes (inflation-adjusted, 1/life and SDP) and three rows that depict the asset allocation over the retirement horizon (fixed, age in bonds and SDP). The values in each cell are the “certainty equivalents” – the level annual consumption that can be supported by each of combination of withdrawal scheme and asset allocation.
Lifetime utility of consumption comparison
|
Withdrawal Scheme
|
|
Inflation-Adjusted
|
1/Life
|
SDP
|
|
|
Asset Allocation
|
Fixed
|
$40,101 (40/60 4.8%)
|
$45,284 (80/20)
|
$45,597 (80/20)
|
|
Age in bonds
|
$39,643 (4.6%)
|
$42,534
|
$42,716
|
|
SDP
|
$40,757 (5.0%)
|
$45,493
|
$45,743
|
|
Source: Gordon Irlam and AACalc
The bottom right SDP/SDP cell produces the greatest certainty equivalent because both the asset allocation and the withdrawal scheme are unrestricted and the program is free to optimize both. The approaches based on popular rules-of-thumb, such as the "4% rule" and "age in bonds," do poorly compared to the SDP/SDP approach.
The most revealing insight is that a fixed allocation with 1/Life withdrawals does almost as well as SDP/SDP. This is the combination that Samuelson's and Merton's theoretical work uncovered more than 40 years ago. This result reinforces the practical value that economic research provides over commonplace rules-of-thumb.
Planning applications
Best practices for advisors include frequent plan updates, and this applies regardless of the planning approach. Although a plan based on SDP can provide recommended asset allocations and withdrawal amounts for the remainder of a client’s life, its greatest value is the optimal beginning strategy. Then, depending on what happens with investment returns and other spending considerations each year, advisors can adjust the plan. If recommended adjustments generated by SDP are too disruptive, changes can be dialed back, but at least there is an indication of the optimal moves. This strategy challenges approaches such as target-date fund "set-it-and-forget-it" glide paths.
The life-cycle approach may fit best with floor-and-upside planning, which separates basic and discretionary spending. For example, one could first compare basic spending needs to lifetime income sources such as Social Security or pensions, and fill any gap with some type of annuity or guaranteed income source. Then, SDP can optimize discretionary spending.
Some might argue that SDP optimization requires too many guesswork assumptions to be of practical value. The counterargument is that the only additional assumption needed, compared to the approaches used by most planners today, is the utility function, and there are feasible ways to build utility functions based on risk-aversion characteristics. However, it is important to consider reasonableness and not just pick utility function parameters without examining the implied tradeoffs.
Looking ahead
Despite decades of economic research, we are at the beginning stage in bringing the life-cycle approach into the work being done by practitioners. Most financial planning is done with software that does not use dynamic programming. My own game plan is to continue to use the AllocationMaster planning software I have been using for years to do projections, and to test the results against AACalc optimizations. I also plan to learn more about ESPlanner. Advisors can improve retirement income planning, and financial planning in general, by developing and applying a better understanding of the life-cycle approach.
Joe Tomlinson, an actuary and financial planner, is managing director of Tomlinson Financial Planning, LLC in Greenville, Maine. His practice focuses on retirement planning. He also does research and writing on financial planning and investment topics.
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