Three things the arithmetic gets right and intuition does not

A 0.9% charge costs a fifth of the outcome. The advertised average is not the return you received. And the order of returns matters enormously — but only once you start taking money out.

Three things worth understanding, and none of them is a forecast

Investment arithmetic is not hard. What makes it worth doing carefully is that intuition is reliably wrong about three specific things, and all three cost real money.

None of what follows is a prediction. A return figure is an assumption, and no amount of compounding turns an assumption into knowledge about next year.

A 0.9% charge does not cost 0.9%

It costs a fifth of the outcome, or more, over a working life.

The reason is that the fee compounds against you exactly as returns compound for you. A pound taken in year three is not just a pound; it is also everything that pound would have earned in the thirty years after. The charge and the growth are the same mechanism pointed in opposite directions.

Two details make it worse than the headline suggests. The fee is levied on the balance, not on the return, so it is charged in bad years as well as good — a fund that loses 10% still takes its 0.9%. And it is charged on the largest balance you ever have, at the end, when the pounds are worth most to you.

Work an example: £10,000 to start, £500 a month, thirty years, 7% assumed. At 0.05% you finish with about £657,000. At 0.9% you finish with about £552,000. The difference — £105,000, sixteen per cent of the outcome — comes from a gap of 0.85 percentage points a year.

This matters more than most investment decisions because it is one of the very few things an ordinary investor actually controls. Nobody can choose next year's return. Anybody can read two fact sheets.

The average return nobody receives

Almost every published “average annual return” is the arithmetic mean of the yearly figures, and it is not what any investor got.

The clearest demonstration takes two years. A fund rises 50%, then falls 50%. The arithmetic mean is exactly zero. Your £100 is now £75.

What you receive is the geometric mean — in that case about −13.4% a year. It is always lower than the arithmetic mean, never higher, and the gap widens with volatility. That is a mathematical certainty rather than a tendency.

The practical consequence: a wildly volatile fund can advertise a higher average annual return than a steady one and still leave its holders with less money. When comparing two funds, the figure that matters is what a pound invested at the start became at the end.

When the order of returns matters, and when it cannot

This one is genuinely counter-intuitive, because the answer changes completely depending on what you are doing.

While you are contributing, the order makes no difference at all. Not a small difference — none. The same set of yearly returns in any sequence produces the same final multiple, because multiplication does not care about order. A terrible first decade followed by a wonderful second gets you to exactly the same place as the reverse.

Once you are taking money out, the order matters enormously. A bad first year forces you to sell units at a low price to fund that year's income, and those units are gone. When the recovery arrives it happens on a smaller holding. The loss is locked in by the act of spending.

Two people can retire with the same balance, experience the same fifteen years of returns and the same average, and end up hundreds of thousands apart — on nothing but which years came first. That risk has a name, sequence risk, and it is the reason retirement planning uses sequences rather than averages.

It is also why a careful calculation takes the withdrawal at the start of each year, before that year's return. You spend in January; you do not wait to see how the year goes. Taking it at the end flatters every result by the return on money you had already spent.

The index number in the news is not the return

When a headline says an index rose four per cent, that is almost always the price index, which excludes dividends.

Over a single year the difference is a couple of percentage points and easy to ignore. Over thirty years, with dividends reinvested, it can be a third or more of the entire total return. Comparing a fund's performance against a price index is comparing two different things and reaching a flattering conclusion about neither.

Lump sum or spread it out?

The arithmetic cannot answer this, and any tool that claims to is overreaching.

Which comes out ahead is decided entirely by what the market does during the period you are spreading the money in. If it rises, investing everything at once wins, because the money was in for longer. If it falls, spreading wins, because later instalments bought more. Nobody knows which in advance — that is what “market” means.

What a calculation can honestly do is show what each would have produced under an assumption you chose. That is useful for understanding the mechanism. It is not a recommendation, and the difference between those two things is the whole point.

What none of this can do

It cannot predict anything. Every return figure is an assumption typed in by a person.

It models a constant return compounded smoothly, which no market does. Real sequences are lumpy, and the lumpiness is exactly what matters in drawdown.

It does not know your tax position, your account type, your country, your other income, your obligations or your plans. Which means it cannot tell you what to buy, sell or hold — that is a conversation for a licensed adviser who knows all of those things.

Frequently asked questions

Why does a 0.9% fee cost so much more than 0.9%?

Because it compounds against you exactly as returns compound for you: a pound taken in year three is also everything that pound would have earned in the thirty years after. It is charged on the balance rather than the return, so it is levied in bad years too, and it is charged on the largest balance you ever have. Over thirty years an 0.85 point gap commonly costs sixteen per cent of the outcome.

Why is my actual return lower than the average return quoted?

Because the quoted figure is the arithmetic mean and what you receive is the geometric mean. Up 50% then down 50% averages zero and leaves you with 75% of your money. The geometric mean is always lower and the gap widens with volatility — which is why a volatile fund can advertise a higher average than a steady one and leave holders with less.

Does the order of good and bad years affect my outcome?

Only if you are taking money out. While contributing it makes no difference whatsoever — multiplication does not care about order. In drawdown it matters enormously: a bad first year sells units at a low price to fund that year's income, and the recovery happens on a smaller holding.

What is sequence risk?

The risk that the order of returns, not their average, determines your outcome. Two people can retire with the same balance, see the same fifteen years of returns, and end up hundreds of thousands apart depending only on which years came first.

Should I invest a lump sum or drip-feed it?

The arithmetic cannot tell you. If the market rises during the spreading period the lump sum wins because the money was in longer; if it falls, spreading wins. Nobody knows which in advance. A calculator can show what each would have produced under an assumption you chose — that is not a recommendation.

Why does the index in the news differ from a fund's total return?

Because the headline number is usually the price index, which excludes dividends. Over a year that is a couple of per cent; over thirty years with dividends reinvested it can be a third or more of the total return.

When should a withdrawal be modelled as happening?

At the start of the year, before that year's return. It is the conservative convention and the conventional one for planning — you spend in January rather than waiting to see how the year goes. Modelling it at the end flatters every result by the return on money already spent.

Is any of this investment advice?

No. These are calculators. They do not know your circumstances, tax position, country or obligations, and nothing in them predicts what a market will do. What to buy, sell or hold is a conversation for a licensed adviser.