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Divine proportion


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Divine proportion

You will be dismayed to hear that gold is heading for the next important Fibonacci level. As I write this week's blog, on Dec. 15, gold is at a new 11-month low of US$1,146 an ounce, and analysts are queuing up to note that the precious metal has broken through support levels and is heading toward US$1,120 an ounce. This price, you understand, is determined by a long-dead Italian mathematician.

Fibonacci is one of the most famous names in mathematics, but it is not the name of the mathematician. Leonardo Pisano, who was the son of a merchant in Pisa, Guglielmo Bonaccio, was born circa 1175 — the name Pisano simply indicated that he was from that city — and he died in 1250. When scholars were studying his work centuries later, they misinterpreted "filius Bonacci" — meaning "son of Bonaccio" — as his surname.

He has been immortalized by the famous sequence 0, 1, 1, 2, 3, 5, 8, 13, 21 et cetera, although his far greater mathematical achievement was helping to popularize our modern numbering system. Pisano's book, Liber Abaci, which means "The Book of Calculations," published in 1202, was one of the first Western books to describe a method of replacing the Roman numbering system (I, IV, X et cetera), which was eventually affected in the mid-13th century.

Pisano's book begins, "These are the nine figures of the Indians: 9 8 7 6 5 4 3 2 1. With these nine figures, and with this sign 0, which in Arabic is called zephirum, any number can be written, as will be demonstrated." The book was filled with practical problems and worked examples demonstrating how simply commercial and mathematical calculations could be done with this new number system compared with the unwieldy Roman numerals.

The Fibonacci sequence of numbers, which, ironically, appeared simply as an example in Liber Abaci, are such that each number, after the first two, is the sum of the two preceding ones. This sequence had already been described by the Indian mathematician Virahanka (circa 700 AD), whose own work is lost but was referenced by another Indian mathematician, Gopala, in the early 12th century.

The name "Fibonacci sequence" was first used by the 19th-century number theorist Edouard Lucas. The sequence appears unexpectedly often in nature and mathematics, and applications include computer algorithms, biology and graphs.

If we divide each number by the preceding value (giving 1.0, 2.0, 1.5, 1.67 etc), the values settled down to a particular value —1.618034 — called the golden mean, divine proportion or phi. The ratio is popular amongst chartists to define retracement levels, and so forecast the extent of a price correction. The most popular Fibonacci retracements are 61.8% and 38.2%, although some analysts looking at gold charts this week are warning of a bear market for gold if the price reaches the 78.6% Fibonacci retracement at US$1,120 an ounce.

The gold price started 2016 at just US$1,060 an ounce and enjoyed a strong first seven months, reaching a peak of US$1,370 an ounce in July. Confirmation of a bear market would be regrettable timing for a new quarterly publication being launched next week by S&P Global Market Intelligence. "Mined Supply: Gold" will draw on the SNL Metals & Mining database and, in the first issue, editor Chris Galbraith will report that six new gold mines completed commissioning in the June quarter and another completed an expansion. With collective new gold capacity of more than 800,000 ounces per year, the impact on gold production in the September quarter was sizable.

Among the top 10 gold mines worldwide, all but two posted production increases in the September quarter, relative to the previous year. All but one are on track to increase production this year.

Galbraith also notes that the falling gold prices of recent years has translated to rising head grades across the industry as companies reacted to the adverse market conditions. The weighted-average head grade at primary gold mines reached an 11-quarter high of 1.59 g/t Au in the September quarter.

Despite the higher ore grades, cash costs and all-in-sustaining costs have not fallen significantly, although operating profits in local currencies have benefited from falling exchange rates against the U.S. dollar.

In "Mined Supply: Gold," Galbraith notes that a number of smaller Chinese producers have posted shortfalls in production this year. Nevertheless, thanks to the number of Chinese mines, including many large operations, all indications point to China maintaining, and likely slightly exceeding, its 2015 benchmark.

Last year, Russia was the second-largest gold producer. However, Australia has shown growth in its gold mining sector and is set to match, or possibly exceed, Russian production in 2016. These rankings are expected to change again next year, and Galbraith expects Russia to maintain its gold production levels in 2017, while Australian output is likely to fall.

In North America, the U.S. has always surpassed Canadian gold output annually by a wide margin. However, the U.S. is now seeing a decline in production, while new mines are opening in Canada. If Canadian and American producers maintain their respective paths and mines open and deplete as forecast, Canada will surpass the U.S. in 2019 as the world's fourth-largest gold producer. Canada could even surpass Australia within the decade to become the third-largest producer.

The views and opinions expressed in this piece represent only those of the author and are not necessarily those of S&P Global Market Intelligence.