The Butterfly Effect: How Chaos Theory Can Help With Retirement Income Planning

While accumulating wealth is a linear process, the act of taking withdrawals from a portfolio injects a significant degree of complexity. That fact in turn implies a far more messy process for advisors and their clients when it comes to making projections and shaping optimal decisions about sustainable spending in retirement.

In fact, according to research conducted by advisor and attorney James Sandidge, principle at the Sandidge Group, the situation facing retirees and their financial advisors in the income planning process is so messy that it is probably best viewed through the mathematical framework known as “chaos theory.”

As Sandidge stressed in comments recently shared with ThinkAdvisor, trying to solve retirement income using rules for accumulating wealth is downright dangerous. The potential negative outcomes range from clients going bankrupt late in life to clients without heirs or charitable-giving intentions leaving millions of dollars on the table out of simple fear of spending.

Sandidge, whose prior research on income planning and chaos theory has been featured by the Social Science Research Network, is currently hard at work extending the “chaos discussion” by examining the concepts of turbulence and seeking to identify patterns that are predictive of retirement income success or failure as early as the first year during life after work.

As he works on that project, Sandidge urges advisors to consider the paper he published in 2020, called “Chaos and Retirement Income,” which earned him the 2020 Investments and Wealth Institute Journal Research Award. According to Sandidge, the findings should help advisors who feel like they need a deeper understanding of the challenges of income planning.

As he writes in the paper’s opening section, chaos theory — which focuses on modeling nonlinear processes with complex and multiple variables — is key to understanding why and how the rules of portfolio management change from pre- to post-retirement.

“This understanding is the basis for creating safer portfolios for retirees,” Sandidge argues. “Chaos theory is also the basis for making retirement income simpler and more personalized because it allows us to see what to pay attention to and what to ignore.”

Basics of Chaos Theory

As Sandidge writes, in order to understand chaos theory and its potential application in the income planning process, it is useful to start by reviewing a more traditional analysis process, such as the one used to make projections in a simple linear system.

“In linear systems, inputs are proportional to outputs, so outcomes are easily and accurately predicted,” Sandidge explains. “For example, if every shelf holds 50 books, you can accurately forecast that 10 shelves will hold 500 books. The input (one shelf) is proportional to the output (50 books).”

Clearly, the relationship between books and shelves plots on a graph as a straight line, in this case sloping upward, and it can be accurately projected even very far into the future.

As Sandidge explains, wealth accumulation is more or less linear. As such, given the initial state of that process (i.e., an investment’s present value), an advisor and client can predict possible future states with a substantial degree of accuracy.

For example, one can project the value of a $100,000 investment after accumulating 25 years of returns, and can also glean insights by assuming different rates of return. As the return increases by 2%, for example, each total return figure projected jumps by about 64% from the previous assessment.

“Because the input is proportional to the output, it is a linear relationship, and as such is predictable,” Sandidge writes. “The linearity of these relationships is key to classical portfolio management and makes accumulation financial planning predictable.”

However, as Sandidge explores, taking withdrawals injects “significant nonlinearity” into portfolio management.

“In the nonlinear world of retirement income, inputs (returns) are not proportional to outputs (wealth), average returns are not predictors of success, neither higher returns nor lower fees guarantee better financial outcomes, and averages mask [highly diverse outcomes],” he warns.

How to Consider Chaos in Income Planning

While there are a number of ways for advisors to incorporate these insights into the planning process, Sandidge says one approachable method is to consider the oft-discussed but seldom fully understood “butterfly effect.”

As Sandidge recalls, the butterfly effect gets its name from “the idea that a butterfly flapping its wings in Brazil could trigger a sequence of events that culminate in the formation of a tornado in Texas.”

“In other words, small differences early in a nonlinear process potentially can result in big differences later,” he explains.

Using historical data, Sandidge shows how the year-by-year account values for investors who retired with $1 million one year apart while using the same retirement income strategy dramatically illustrates the butterfly effect.

As explored in the paper, if one person retired in 1966 and another in 1967, their retirement journeys would look very different. Despite the two investors sharing the same returns in the exact same sequence for 24 of their respective 25 years of retirement, the later retiree finishes the 25th year with $768,588 more, or $863,120 versus $94,532.

“That was the impact of the [single year] avoiding a negative 2.9% return,” Sandidge says. “Even if you extended the analysis for the earlier investor by one year so that it included all 25 years of the line, that investor would have finished the 26th year with $8,501. Incurring the small loss early almost depleted the portfolio after 25 years.”

Bottom Line

The underlying analysis here may be complex, Sandidge admits, but the takeaways for wealth managers are not.

“The sequence of returns is relevant to the essence of the problem when it includes negative returns, illustrating that negative returns are the simplifying axiom to focus on, and due to the butterfly effect, negative returns that happen early in retirement are particularly pernicious,” Sandidge warns. “Furthermore, because small losses can have big impact, large losses can have catastrophic impact.”

For this reason, Sandidge argues, retirees and their advisors should prepare for the worst case or black swan type of stock market as a baseline, then adapt to the actual circumstances as they unfold. Other retirement researchers have called this a ”guardrails approach,” likewise arguing it results in vastly superior outcomes over traditional fixed-withdrawal rules.

What’s at Stake in Income Planning

“The butterfly effect makes active management of [income] more important,” Sandidge writes, clarifying just how high the stakes are with a consideration of five more theoretical investors.

The first investor uses a 50-50 portfolio rebalanced annually, with a 5% initial withdrawal increased 3% annually. This passive, systematic or autopilot approach leaves $94,000 of the original $1 million investment at the end of the 25-year period.

The second investor did everything the same as the first, except he employed a 30% stock and 70% fixed income risk allocation the first year, then moved to the 50-50 mix in all remaining years. This small adjustment improved the first-year return from a negative 2.9% to a negative 0.04%, thereby increasing the ending account value to $232,000.

A third investor applies the same methodology as the second but does not increase cash flow in the fourth year, a year in which the portfolio had a negative return. This small difference increased the ending value to $401,000.

The fourth, in turn, did everything the same as the third, except she did not increase cash flow by the 3% starting assumption in the eighth, ninth or 12th years of retirement, pushing the ending value to $660,000.

Finally, the fifth investor followed the approach of the previous one but also had assumed access to an outside source of funds, from which he took withdrawals (rather than from the portfolio) in negative return years. This person then repaid that loan with 4% interest in the next positive return year. This “loan strategy” increased the ending value to $758,000.

As Sandidge warns, traditional Monte Carlo-style retirement income calculators that employ the same type of unbending approach as the first investor significantly overstate the risk of running out of money, because they understate the potential positive impact of actively managing risk and setting guardrails around cash flow out of the portfolio when times are tough.

“In [this example], actively managing risk and cash flow increased the ending value from $94,000 to $758,000,” Sandidge observes. “This illustrates the value of active management and how even small, seemingly insignificant changes to a retirement income portfolio can have significant impact long term.”

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