“Imagine a volatile share that sells for 50p in odd years and 100p in even years. If you invest £100 every year in this share, over a 10-year period you will have accumulated 1500 shares at an average price of 66,7p, well below the average market price, which is 75p. The system will, on average, outperform the market, and the more volatile the markets the greater the gains.

“The method is known as pound (or dollar) cost averaging. It works through its built-in mechanism for buying more when prices are relatively low and less when prices are relatively high. No judgment is required by the investor that prices are relatively low or relatively high.”

It sounds like a good idea, except for one thing: when it comes to selling, it would be wrong to assume you’re going to get either 75p or 66,7p. You have to assume you’re going to get the ruling price of either 50p (in the odd years) or 100p (in the even years). After all, if you’re buying at 50p there’s no reason to expect another buyer to pay more. Which means that if instead of buying you’re forced to sell in year five, for example, you’ll end up selling the 600 shares that have cost you £400 for £300, or at a 25% loss.

Therefore, the scheme only “really works” every second year (selling at 100p), and then only from year three. What’s more, in reality you’re just as likely to end up buying for several years at 100p before having to sell in a market languishing at 50p.

There is another, more traditional argument against dollar cost averaging, better explained by Michael Edesess, author of The Big Investment Lie, as follows:

“The myth floats on the fact that the average price of a share purchased by constant-dollar investments over time is less than the average share price over time. But this fact is irrelevant. To take a simple example, suppose the prices of a share of stock for three years are $20, $50 and $100.

“Purchasing $100 worth every year gives you eight shares at an average price of only $37,50, while the simple average price is a much greater $56,67: ($20 + $50 +$100)/3. You might think you got a bargain, but your eight shares will be worth only $800 in year three, while if you had invested your whole $300 in $20-priced shares at the beginning of the first year you would have had $1500. Historical simulations over extended time periods show that investing a lump sum in stocks right away nearly always produces a better result than dribbling it in slowly in equal annual amounts.”

As Edesess concludes: “Dollar cost averaging (or pound cost averaging) can be an effective subterfuge to impose an investing discipline on an otherwise recalcitrant investor. But it does not — as Mr Kay says it does — beat the market.”