The View from England: Gold supported by the divine proportion

What a Leap Year it has been! Quite apart from Brexit in Europe, a chaotic Presidential election in the United States and Covid-19 everywhere, we have uncertainty over the price direction of gold as this horrid year draws to a close.

I am neither a chartist nor a particular exponent of gold, but I can’t see any concern about the precious metal’s price direction — at least not yet. The reason has much to do with a long dead Italian mathematician.

Gold has enjoyed a five-year bull market since falling to barely US$1,060 per oz. in December 2015. The price was particularly buoyant in 2019 and the first half of this year, with the precious metal reaching over US$2,070 per oz. in August. Gold has since faltered, and analysts have scuttled to explain the mechanism.

The explanation has been known for over 100 years, when stock-exchange brokers noticed that strong upward price movements tended to suffer intermittent corrections of one-third or two-thirds of the initial movement.

The precise ratios had actually been established 500 years earlier by one of the most famous names in mathematics, Fibonacci. This is not, however, the name of the mathematician. Born circa 1175, Leonardo Pisano was the son of Guglielmo Bonaccio (the name Pisano simply indicated he came from Pisa, where his father was a merchant). Pisano died in 1250, and, centuries later, when scholars were studying his work they misinterpreted ‘filius Bonacci’ (meaning ‘son of Bonaccio’) as his surname.

Pisano is immortalized by the famous sequence 0, 1, 1, 2, 3, 5, 8, 13, 21 etcetera, such that each number, after the first two, is the sum of the two preceding ones. However, this sequence had already been described by the Indian mathematician Virahanka in circa 700 AD, and Pisano’s real claim to fame is describing a method of replacing the unwieldy Roman numbering system (I, IV, X etc.). In his book, Liber Abaci (‘The Book of Calculations’), published in 1202, Pisano explained that commercial and mathematical calculations could be done using nine Indian numbers (1 to 9) and the Arabic sign ‘0’ (called zephirum).

The term ‘Fibonacci sequence’ was first used in the 19th century by number theorist Edouard Lucas. The sequence appears frequently in nature and mathematics, and is extremely popular amongst chartists to predict price retracements.

If each number in the sequence is divided by the preceding value (giving 1.0, 2.0, 1.5, 1.67 etc.), the values eventually settle down to a fixed irrational number (meaning its terms go on forever) of just over 1.618. Called the golden mean, divine proportion or phi, this value is related, through trigonometry, to Archimedes’ Constant (pi), which is another irrational number (almost 3.1416) that is the ratio of a circle’s circumference to its diameter.

For unknown reasons, these Fibonacci ratios seem to play a role in the stock market, just as they do in nature. For chartists, the most popular Fibonacci retracements are 61.8% and 38.2%, which are found by dividing one number in the series by the number that follows it (yielding 0.618) or by the number located two places to the right (0.382).

So how does this support gold?

Helped by a weakening U.S. dollar, the price of gold rose 36% in under five months following an interim low of US$1,490 per oz. in March. As the dollar recovered, the precious metal retreated, but has gained ground again following turmoil over the U.S. presidential election.

The gold price benefits from political and economic uncertainty, of course, and the latter threat has eased recently, not least following the announcement of effective coronavirus vaccines.

Nevertheless, low interest rates and high inflation are likely to benefit the precious metal for much of 2021 as investors tend to switch from the U.S. dollar to gold during times of monetary easing.

At the end-November interim low of US$1,770 per oz., gold had fallen US$300 per oz. from its peak of four months ago. At the time of writing (Dec. 14), the precious metal is trading at almost US$1,830 per ounce. An entirely normal Fibonacci retracement of 38.2% on the over US$1,000 per oz. price appreciation over the past five years would have taken gold to below US$1,700 per ounce.

That support level was not tested, and, even for a non-chartist, gold’s upward progress seems untroubled for now. Having said that, gold in the United Kingdom is trading today at an historically very heady £1,370 per oz., making the metal alone in my wedding ring worth over £400 (US$540); blimey.

— Dr. Chris Hinde is a mining engineer and the director of Pick and Pen Ltd., a U.K.-based consulting firm he set up in 2018 specializing in mining industry trends. He previously worked for S&P Global Market Intelligence’s Metals and Mining division.