Interesting ways to a million

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The Independent Online
AS FAR as I am aware, history has no record of the investment performance achieved by the great Albert Einstein. Yet if you were to ask a computer to analyse which names occur most frequently in books on the subject of investment, his name would appear high on the list. The reason is that when a pundit wants to extol the virtues of long-term investment, they invariably call in Einstein's observation that "compound interest is one of the greatest discoveries of the 20th century".

As so often with remarks of this sort, there is more than one version of what Einstein said, and it may well be the remark was, strictly speaking, apo-cryphal. No matter: there is no doubt that the underlying truth was real and profound. It crops up at almost every point in the investment spectrum, from day trading to pensions planning. Yet the paradox is, it remains an insight which continues to be widely ignored in practice, even by those who profess to have been influenced by it the most.

What Einstein was referring to was not a discovery, simply a mathematical truism. While seemingly trite, it has profound implications when applied to many day-to-day situations, of which investment performance is one of the most striking. All that compound interest says is that small differences in rates of interest today can make a huge difference over longer periods.

Suppose you invest pounds 5,000 in a fund that achieves an average total return of 7 per cent per annum and you keep reinvesting income you receive in the same fund. After one year, and ignoring all other factors (tax, transaction costs, inflation and so on), your fund will be worth pounds 5,000 x 1.07=pounds 5,350. You will be pounds 350 better off. But how much better off will you be if you stick with this fund for 30 years, reinvesting any income all the while? The naive answer is pounds 10,500 (30 x pounds 350=pounds 10,500). Most people know the real answer will be a lot more, but are still surprised at exactly how much greater the final figure proves to be. The correct answer is pounds 33,061.

A fund in which you invest pounds 5,000 today will be worth pounds 9,836 after 10 years, pounds 19,348 after 20 years, pounds 38,061 after 30 years, and pounds 74,872 after 40 years. Readers with more than basic maths knowledge will see the value of your fund roughly doubles every 10 years. Some may even recognise this as an example of the so-called Rule of 72, which says if you divide a percentage growth rate into 72, it will give you a rough guide to how many years it will take to double your starting number. (In this case 72 divided by 7 per cent=10).

Now suppose you invest the same amount of money in a fund that achieves an annual rate of return that is half as much again - 10.5 per cent as opposed to 7 per cent per annum. The magic of compounding means the value of your fund is a lot more than 50 per cent greater. The comparable figures are: after 10 years the fund is worth pounds 13,570; after 20 years pounds 36,831; after 30 years pounds 99,963 and after 40 years pounds 271,307. By the time you reach the 40-year horizon, your fund is worth three to four times as much as it would be if your rate of return was 7 per cent, instead of 10.5 per cent. (The Rule of 72 correctly predicts your money will double every seven years or so). The longer you hold the investment, the larger the gap between the two lines.

That is the wonder of compounding. As Jack Bogle, the chairman of Vanguard, likes to point out, what compound interest really tells us is that time is the fourth dimension of investing, after returns, risks and costs. The argument for shares in an investor's portfolio has always been that shares allow you to capture the higher returns the stock market consistently provides over time in a way that allows you to enjoy the benefits of compound interest and the risk reduction given by longer holding periods.

There is an interesting illustration from Bogle's new book, Common Sense on Mutual Funds, which shows how time reduces the risk in holding shares. Most people know the range of returns you can normally expect from a diversified portfolio of shares reduces the longer you hold them, but not everyone realises how it also reduces the risk of loss.

There is an inverse compounding effect that reduces the risk most sharply in the first five to ten years after purchase before tapering off into a narrow long-term range of between 4 per cent and 8 per cent. But the reach of compounding does not stop with returns and risks.

Another insight an Einstein-like perspective provides is on the many costs of investing in shares or any other investment class. For anyone who invests mainly through funds, the same logic that applies to returns applies with equal force to anything that reduces your annual rate of return, whether it is inflation (which reduces the buying power of your money),fees charged by fund management or the hidden costs (such as transaction costs if your fund turns over its portfoliorapidly, or tax inefficiency).

Individually, these may not add up to much each year. But the law of compounding is as inexorable on the negative side as on the plus. My chart demonstrates the dramatic impactfund management fees and other expenses can have on the long-term value of a fund.

It shows the difference between the value of a notional fund that achieves a 12 per cent per annum return over 40 years (a) before and (b) after you include 2 per cent per annum for management expenses (2 per cent is the average total expense ratio of an American mutual fund). That 2 per cent charge reduces the size of the final fund by more than half. On an initial investment of pounds 10,000, that is the the difference between a fund worth roughly pounds 930,000 and one worth pounds 450,000. If you add a similar proportion for high portfolio turnover and other wasteful practices, the impact can be enormous.

So what if you want to retire a millionaire? Assume you buy a tax-free index fund with 0.75 per cent annual expenses each year that stands to grow long-term at 8 per cent a year. Inflation is 1 per cent. You start at 25 and aim to retire at 65. How much will you need to invest to retire with a fund worth pounds 1m?

The answer is just under pounds 400 a month, which happens to be within the annual ISA limit for shares. If you buy an actively managed fund and pay 2 per cent a year, you will need an extra pounds 125 a month to achieve the same result. You don't need to be an Einstein to work out which is the bargain.