"Pound Cost Averaging"

Another math-y post. I worried about offending those who have no taste for math. My readership is sufficiently small that I cannot reasonably run the chance of turning anyone away. But this did irk me.

The reading today is again taken from the Financial Times. I read a piece by a trader who advocated what he called 'pound cost averaging'. This was his term for buying the same value of, say, shares at regular intervals. He pointed out that this enables one to buy more shares when the price falls, and fewer when the price rises. All very well, I hear you say. But wait, there's more!

He followed this up with an example that made my heart sink. It ran something like this: "Suppose you buy £100 worth of shares in January at £1 per share, then £100 worth of shares in February at £1.50 a share. You end up with 100 shares in Jan and 67 shares in Feb, giving you 167 shares. If, on the other hand, you had spent all £200 at the average price of £1.25, you would only have 160 shares."

I wanted to weep. I have grown accustomed to meeting otherwise very bright people who have forgotten how to do basic arithmetic. But this was in the FT - the newspaper for people interested in money and numbers! The example proved nothing, as examples always don't; the final numbers came out so close that one might suppose the opposite result could be achieved in other circs; and most importantly, it missed a better point.

The point is about the arithmetic-geometric mean inequality. The point is that simple maths helps in simple finance problems, and interesting math helps in interesting finance problems. If the FT doesn't take every chance to illustrate this simple point, who will? (Apart from me.)