Investing Isn’t Just Mathematics: Understanding Why A × B ≠ B × A

Investment returns seldom proceed in a linear fashion, just like family life. While I might forget specifics (like where we camped a decade ago, how we marked my son’s fifth birthday, or the debut book my daughter read aloud), it doesn’t negate the joy and challenges that come with raising a family, a point I sometimes try to express to my spouse.

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I once viewed investing similarly. My focus was on long-term averages, tolerating market volatility without concern for short-term fluctuations, believing that, akin to family memories, the details of returns held little significance.

As I grow older, I understand that in our personal lives, the precise details of past events—even a campsite, a birthday, or a first book—are less important than the experiences themselves. However, when it comes to investing, I have discovered that it’s not solely the long-term average return that matters; the timing of when we achieve above-average returns during our lives is crucial.

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This may seem evident, yet within an industry composed of individuals keen on fully funding their retirement, the significance of market cycle timing is only beginning to resonate. It resembles a lesson from mathematics: A x B equals B x A, where order is inconsequential.

But investing operates differently. Here, the sequence of returns can profoundly influence results.

This concept is termed sequence risk: the risk that the timing of gains or losses can significantly influence your overall outcome. Consider this scenario: Two investors begin saving in their mid-20s, contributing the same monthly amount and experiencing identical investment returns over 40 years, with one key difference in order: Investor A enjoys the best returns early on, while Investor B receives them later.

The results are remarkable. Investor A benefits from the best return on their initial contribution before their savings have substantially grown and faces the worst return at the end, impacting their entire portfolio. Conversely, Investor B compounds the best returns on a fully matured savings and encounters the worst returns only on their initial, smaller contributions.

It turns out that timing is often critical.

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Just as timing affects the growth of savings, it is equally important when those savings are withdrawn during retirement (the decumulation phase). In this phase, the order of returns holds significance for everyone because withdrawals reduce the portfolio size. Experiencing positive returns in the early stages means that each withdrawal constitutes a smaller portion of the total, prolonging the longevity of savings and facilitating greater growth over time.

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Of course, sequence risk is minimal if withdrawals are negligible compared to total assets. However, for individuals planning to deplete their savings during retirement, the opposite concern arises. They become particularly susceptible to adverse returns early in their retirement. For retirees, smoothing out returns might reduce the average expected return and diminish the advantages of strong early gains post-retirement.

Thus, for the majority of investors, sequence risk is a factor that cannot be overlooked. Just as timing shapes life experiences, it also influences investment outcomes. With fewer legacy assets and new savers starting small, strategies must account for the timing of returns to safeguard savings and maximize results.

David Crosoer is chief investment officer at PPS Investments.

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