x Abu Dhabi, UAESaturday 20 January 2018

Can a long-dead mathematician help reverse my losses?

It's official. I am a loser. For the first time since I began fantasy trading 25 weeks ago, I have less money in shares than I started out with.

It's official. I am a loser. For the first time since I began fantasy trading 25 weeks ago, I have less money in shares than I started out with.

Outstanding, Gornall, go to the bottom of the day-trading class. Oh, wait. You're already there.

How did this happen? How did I manage to convert a one-time profit of more than £2,000 (Dh11,435) into a loss of £8.14?

Well, it wasn't easy, let me tell you. It took a massive and sustained application of ignorance and stupidity, garnished with lashings of guesswork, unfounded optimism and self-delusion.

BG, the former British Gas, looked good when I dipped my toe in the water on October 26, to the modest tune of 165 shares at 1,197.5 pence each. The following week, it looked even better - so much so that I started to sell off my other holdings to wade in chest deep and finance the purchase of even more shares: 661 at 1,246.5p on November 2.

After that, striking out for what appeared to be the nearby island of Easy Money, I was in over my head, grabbing a further 158 shares at 1,249p later that same day and, following a clear out of all remaining holdings, 629 at 1,278.5p on November 9.

That's when the sinking started.

Now, take a look at those prices. See what I did? That's right, I went buying on a rising tide - not even all at once, but gradually, hesitantly, as though deliberately holding out for less and less favourable terms.

And for the past couple of weeks, the tide has been going out; as I write, the price is down to 1,168.5p. Again, according to the rules, I should have sold the moment the tide turned. Instead, I decided to ride it out, based on ... well, see "ignorance, stupidity" above.

But it's not yet time to retire to the library with a revolver.

At the back of my mind throughout all of this has been a 13th-century Italian mathematician, Leonardo Fibonacci, who gave the world one of those deceptively simple mathematical observations that appear to echo some kind of universal truth of the type that has Dan Brown reaching for his publisher's number.

Fibonacci identified a sequence of numbers, starting with 0 and 1, in which each subsequent number is the sum of the two that precede it, so giving us 0, 1, 1, 2, 3, 5, 8, 13, and so on - and, to save you draining the battery on your calculator or brain, by the time we get to 50 Fibonacci numbers, we are at 7,778,742,049 (add together and divide by your age at your peril: I did and guess what? One. Spooky, huh?).

It turns out that manifestations of this sequence can be found throughout nature - in the designs of pine cones, sunflower heads and shells, the shapes of waves and the breeding patterns of rabbits, to name but a few examples.

Perhaps even more oddly, though certainly less romantically, Fibonacci's discovery also has an application in the interpretation and prediction of share-price movements. That much I half knew. But now, before scuttling my stake in BG only to discover a week later that I had sold just before a sharp rise in value, I have to learn how to apply the theory of what in the trading trade is known as Fibonacci retracement patterns.

There is, of course, a wild world of advice on this issue on the internet. There are also thousands of sites offering downloads of free software that claim to do the maths for you and spew out an educated guess at the other end but, as we all know, there is no such thing as a free hunch.

In the end, I put my faith in Swing-trade-stock.com, a site with some of the simplest explanations of some of the most complex features of trading.

"Stocks," begins its brilliantly clear section on Fibonacci retracements, "will often pull back or retrace a percentage of the previous move before reversing." Thanks to some mysterious numerical key to human behaviour - in this case, the urge to buy or sell stocks, as susceptible to the inevitability of mathematical certainty, it seems, as the growth patterns of tree branches - these retracements are usually seen at three points: at 38.2 per cent, 50 per cent and 61.8 per cent of a stock's share price, whether upward or downward-bound.

As I said, spooky.

The theory is that a rising (or falling) share price will stutter - or retrace - at or about these percentages of its lowest (or highest) value over a given swing range. The trick is to see these retracements coming and to sell or buy accordingly.

Such patterns, says Swing Trade Stocks' guide, can be calculated manually. The first task is to work out the range of any swing, up or down, from its high point to its low. In the case of BG, over the past month this is from a high of 1,296p to a low of 1,168p - a range of 128p.

Next, we multiply that range by each of the three Fibonacci ratios - so 128 multiplied by 0.382, 0.5 and 0.618 - which gives us 48.8, 64 and 79.1.

All that remains is to subtract those numbers from the swing high point to establish the three magic Fibonacci levels: so for BG's downward swing over the past month that's 1,247.2p, 1,232p and 1,216.9p.

True to form, a glance at the chart shows that, while the numbers are slightly out of sync, the pattern itself holds true. The price picked up briefly at about the first two of those points and any buyer watching the bouncing ball of the price line could have stepped in profitably each time. Any seller, on the other hand, could have waited for either of the bounces to peak before cashing in their chips.

So what to do now? Well, the current continuing fall-off in share price appears to be conforming to the pattern and, if human behaviour is all it's cracked up to be, then we should next expect a sell-off - which will in turn provoke a buying spree, raising the price once again.

Fibonacci's theory dictates this price rise will go only so far - probably to about 1,200p at best - not as good as the aggregated price of 1,242.7p I have paid overall, but at least better than the share's current value of 1,168.5p and a good time to bail out.

Which means that to see this experiment through to the end, there is nothing left to do but await developments, as predicted by a chap who died 760 years ago.

Maths, it seems, really can be fun - and even useful. Who knew?