Sequence of returns risk is a topic that has been getting a lot more prominence in the UK recently. We are living longer on average, and that means we will become more reliant on savings and pensions to fund retirement spending. Doubly so given the era of defined benefit pension schemes looks gone for good. Most readers of this site probably already know the basics of sequencing risk but it is good form to start from scratch. If you are familiar with it then just skip the first few paragraphs.

## Returns

A good place to start is with the calculation of returns. For some reason, some sections of the UK media use the arithmetic mean when stating how well a given market has done. This is the type of average that most people are familiar with in everyday life. For instance, imagine the stock market dropped by 10% over the course of a year. In the next year it increases by 20%, and then by another 20% in the year after that. Using the arithmetic mean would produce an annual average of 10%.

Now ask yourself the following question. If you invested £10,000 at the start of year one, how much would you have at the end of year three? The answer is £12,960. That is why the more common way of stating the average in this context is to take a geometric mean. Using our example, that produces average returns of just over 9% per annum. The maths behind that: £10,000 x 1.09 x 1.09 x 1.09 = £12,960 (rounding errors produce a slightly lower answer).

Another thing to note is that the *order* in which the individual yearly returns occur is irrelevant in our example. For instance, let’s assume the market increased by 20% in years one and two, then dropped 10% in year three. I’ve reversed the order, but the end result of £12,960 is unchanged. This is obvious when dealing with a couple of numbers (e.g. everybody knows that 5×10 and 10×5 both equal 50), but with a longer sequence it might be a bit less clear.

Of course, very few people in the real world save on the basis of a massive starting lump sum. Workers will contribute to a pension scheme on a regular basis, and maybe to an ISA or some other account on a regular or ad-hoc basis. This is where sequence of returns risk rears its head. Often, the discussion only takes place in terms of portfolio withdrawals, but it always strikes me as odd not to mention it first in the context of adding to your pot.

## Pound-Cost Averaging

Anyway, a regular saving scheme might better be referred to as pound-cost averaging. The obvious benefit of pound-cost averaging is that it removes any element of market timing. All you have to do is regularly contribute to your savings, which in the case of a workplace pension scheme is automatic anyway. Granted, you will end up investing in periods when valuations are very high, but the opposite is also true. All-in-all you might reasonably expect to capture the average market valuation.

(I should add that regular dividend reinvestment is also a form of pound-cost averaging. In some cases it has led to very stodgy stocks massively outperforming “growth” names, despite this being counterintuitive, because they have been undervalued for relatively long periods of time).

Pound-cost averaging has been a very good deal historically. For instance, the average historical earnings yield of the S&P 500 is around the 5.75% mark. The index has also posted average annual earnings growth well in excess of inflation over the same period. Overall, this combination has led to a total return of 10.8% per annum over the past thirty years. For the FTSE 250 – which is probably more relevant for the domestic audience – the figure is around the same I believe (I think it stands at around 11% per annum going back to the early 1990s).

## History Repeating Itself

Unfortunately (or not as it may turn out), the sequence in which these returns occur does matter for regular savers. Obviously the S&P 500 didn’t compound away at 10.8% every year like clockwork. It did better in some years and worse in others.

On that basis, it is entirely possible that the next three decades could produce the *same* headline outcome (i.e. 10.8% per annum for the S&P 500) but *different* returns for those who cost average compared to the last generation. It wouldn’t matter if they followed the *exact* same strategy with the *exact* same monetary amounts. Or put another way, history can kind of repeat itself and not repeat itself at the same time.

This throws up some interesting implications. The most interesting one from my point of view is the *optimal *scenario. In general, brutal bear markets at the beginning of your savings term are actually very good. (You can do the maths using very simple timeframes to convince yourself. Simply put bad years at the start and good years at the end. Then compare the returns with those you generate by using the reverse order).

In retirement, things typically work in reverse. You are no longer pound-cost averaging, but withdrawing a fixed amount every year (4% per annum, adjusting for inflation, is the figure that gets mentioned a lot). On that basis, hitting a bad run early on in retirement could see you deplete your portfolio if you are liquidating and withdrawing assets at a constant rate. Conversely, a good combination could see your portfolio actually *increase* in value substantially, despite regular withdrawals. Indeed due to the inherent nature of compound interest your upside is considerably more than your total downside.

## Solutions, ‘Natural Yield’

The big question that most people have: what can I do to remove this risk? A starting point for some is to focus on what has been termed ‘natural yield’. I dislike the expression, so instead will refer to its traditional name – dividends and interest. Essentially you just rely on whatever cash your assets pump out rather than liquidating and withdrawing them outright.

Obviously this is not a foolproof solution. Dividend income is incredibly volatile assuming you are looking at a broad index like the *FTSE All-Share Index*. In rough times your income would clearly take a big hit.

Okay, so what if your assets were not in an index tracker fund? The stuff I blog about on *The Compound Investor *should produce much more stable dividend income than the benchmark. Historically, that has undoubtedly been true. But will that continue into the future? It would be wrong to assert it is a fact, even though I think it will. That’s before getting into separate issues such as currency risk.

Other solutions also have their pros and cons. What if you diversify across asset classes? For instance, let’s say you own bonds in addition to stocks. When the latter heads south, you can focus on selling the former to avoid selling equities on the cheap. Obviously the reverse situation also applies.

That said, who would want to be accumulating bonds right now in the first place? The earnings yield on *Vanguard’s* *FTSE All-Share Index Fund* is around 6% right now. UK 10-year government debt yields 0.6% as I type. Give me the former with positive real terms growth over the latter any day of the week. A lot of people are understandably 100% equities right now.

## Sequence Of Returns Risk: My Own View

As far as I can see there are only two real solutions to sequence of returns risk. The first is to assume lower returns and subsequently save more. Okay this isn’t *really* a solution as such, but I have to mention it because it is the most obvious response to those worried about depleting their assets. Increasing your savings rate may not be possible, but again it needs to be mentioned.

This principle can also be applied if you want to diversify into lower returning assets. For instance, you might accept the outlook for bonds is currently poor, but you make up for that by saving more too. In the graph below I bump up the savings rate in the ‘bear market at end’ scenario by 20%. It *still* underperforms the ‘bear market at start’ scenario even though contributions in that one remained static.

As far as I can see the real problem with sequence of returns risk is twofold. Firstly, its impact is inherently random. Secondly, most ‘solutions’ are trying to square the circle of divorcing your lifestyle from the performance of your underlying assets.

That brings me to the second ‘solution’, which is to tie your withdrawals to the performance of your underlying assets. Actually this strikes me as the logical way of doing things. Relying on dividend and interest income is an obvious way of doing this, and lowering your withdrawal rate in bad times represents much the same principle albeit from a different angle. Obviously there are no easy answers to what may become a problem for a lot folks going forward.