Investing is not like maths: Why A × B ≠ B × A

Investment returns rarely follow a straight line, much like family life. I may forget the details (where we camped 10 years ago, how we celebrated my son’s fifth birthday, or the first book my daughter read aloud), yet as I sometimes try to convince my spouse, that does not mean I have not felt the joys and challenges of raising a family.

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I used to see investing the same way. I focused on long-term averages, taking on enough market risk and not worrying about short-term swings, thinking that, like family memories, the details of returns did not really matter.

The older I get, the more I realise that in our personal lives, the exact details of the past, whether a campsite, a birthday, or a first book, matter less than the experiences themselves. In investing, though, I have learnt that it is not just the long-term average return that counts; what really matters is when we experience above-average returns in our lifetimes.

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This may seem obvious, but in an industry shaped by a generation responsible for fully funding their retirements, recognising the impact of the timing of market cycles is only starting to sink in. It is a bit like what we learnt in school: A x B equals B x A. That works perfectly in mathematics, where order doesn’t matter.

But investing is different. Here, the sequence of returns can dramatically change your results.

This is known as sequence risk: the risk that the timing of gains or losses can significantly affect your outcome. Here is how one can explain this: Imagine two people start saving in their mid-20s, contributing the same amount every month and seeing the same set of investment returns over 40 years. The only difference is the order; investor A gets the best returns first, while investor B receives them at the end.

The effect is striking. Investor A earns the best return on their very first contribution before their savings have really grown, and faces their worst return at the end, when it hits their entire nest egg. Investor B, by contrast, compounds the best returns on their fully grown savings and only experiences the worst returns on their first, tiny contributions.

It turns out that timing often really matters.

But does the order of returns always matter? Not necessarily. It matters less when returns are steady, when you start with a big lump sum or when you have significant inherited wealth. For example, for wealthy households, the compounding of legacy assets is often so extensive that the timing of returns becomes less critical. For most other investors who rely on regular contributions to build their savings, avoiding sequence risk by smoothing returns can feel safer. However, such a strategy usually lowers average returns and reduces the chance of significant gains over time.

Just as timing affects how savings grow, it also plays a crucial role when those savings are withdrawn in retirement (the decumulation phase). In this phase, the order of returns matters for everyone because all withdrawals reduce the portfolio. Experiencing strong returns early means each withdrawal takes a smaller proportion of the total, helping savings last longer and grow more over time.

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Of course, sequence risk is minimal if withdrawals are tiny compared with total assets. But for investors planning to use up their savings during retirement, the reverse of the earlier example applies. They are especially vulnerable to negative returns early on. For retirees, smoothing out returns can lower the average expected return and the benefits of strong early gains after retirement.

So, for most investors, sequence risk cannot be ignored. Just as timing shapes life’s experiences, it shapes investment outcomes. With fewer legacy assets and new savers starting small, strategies must consider the timing of returns to protect savings and maximise results.

David Crosoer is chief investment officer at PPS Investments.

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