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

What You Need to Know

Trying to solve retirement income using rules for accumulating wealth is downright dangerous, advisor and attorney James Sandidge says.
One of the most powerful insights in his research is that actively managing income can result in profoundly superior outcomes.
By recognizing the power of small changes at key moments, advisors can help retired clients spend with confidence.

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 Awards. 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.”