How the maths can help you understand the price behaviour of base metals

Refined nickel. Credit: Glencore.

Studying the maths of base metals’ price behaviour is not done to compete with conventional market analysis, rather it helps all analysts to better quantify relationships between market circumstances and price, as well as to check whether their thinking on price behaviour is up-to-date, as price behaviour changes over time.

We have worked together to study and quantify base metal price behaviour for many years. The price drivers that we have come to study most closely have been selected for: (i) a close causal relationship to prices; (ii) having high correlations with prices; (iii) having uncontentious historical data; and (iv) themselves being forecastable.

That currencies turned out to have a key role in price behaviour is unsurprising. Early on in economics, one learns that price sits at the intersection of supply and demand curves. And when such global curves are expressed in any one currency, such as the US dollar, those curves shift every minute of every day as currencies get traded round the clock. Equilibrium prices shift continuously with exchange rates.

Correlation indicates the extent to which two data sets are related: 0.0 indicates no fit; +1.0 indicates a perfect direct fit; while -1.0 indicates a perfect but inverse fit.

The price driver that had the highest correlation with LME cash prices in US dollars (USD) for all the base metals used to be the US dollar index DXY. More recently — in the period studied from January 2017 to now — for aluminium, zinc, lead and tin, the highest correlation has switched to the exchange rate with Chinese currency (CNY), that is, USD/CNY. For copper prices, correlations are effectively the same with DXY and the USD/CNY exchange rate.

LME cash prices have correlations with the USD/CNY exchange rate of -0.84 for zinc; -0.83 for aluminium; -0.80 for copper; and -0.77 for tin. Such very high correlations between LME prices in US dollars and the USD/CNY exchange rate mean that one can model prices for these metals simultaneously in USD and in CNY, which is becoming of steadily greater significance. Not only is China the world’s largest consumer of base metals, but it has started the transition from being a price taker in USD towards becoming a price setter in CNY on its own increasingly important exchanges.

After exchange rates, the next best correlations of dollar prices are with changes in the rate of demand growth for base metals. Because monthly metals consumption data are contentious, Bloomsbury Minerals Economics (BME) and Metal Price Analytics (MPA) use global industrial production growth (Source: Global IP Watch, a monthly publication put out by independent zinc and lead market experts CHR) as a proxy. Correlations between IP growth and prices are 0.67 for zinc and aluminium; 0.65 for lead; and 0.42 for copper. BME and MPA believe that variations in demand growth are the fundamental drivers of price cycles for the industrial metals.

Because there are only partial census data for total stocks, BME and MPA have looked just at LME stocks and total global exchange stocks, on whose historical data all analysts can agree. LME metal prices have better correlations with LME stocks than with global total exchange stocks. Correlations between LME prices and LME stocks are generally still only moderate, however. For copper, the correlation is only -0.24 and for aluminium only -0.15. It is higher for nickel (-0.56). For both zinc and lead, stock are negatively correlated with price in the short term, but both those metals’ price to stock relationships saw a step change in mid-2018.

What are BME’s and MPA’s conclusions from all of this? First, that there is a clear hierarchy amongst price drivers, with exchange rates the most important, followed by changes in demand growth rates, followed by stocks (and thus market balances).

Concerning currencies, it is becoming more important to analyse prices in CNY as well as USD, because China, the principal user of base metals, is beginning the transition from being a price taker in USD to a price setter in CNY, on its own increasingly important exchanges.

After exchange rates, BME and MPA think of cyclical changes in the rate of demand growth as the main ‘fundamental’ in a medium term price cycle. Following a demand growth change, supply responds only after a time lag, and this sets off cycles both of stock change and price.

Regarding market balances and stock change, within a business cycle, BME reckons that these are more fine-tuners of prices than ‘fundamental’ drivers: production-consumption differences and stock change are part of prices’ over-shoot and correction process.

Since LME prices relate more closely to LME stocks than to global exchange stocks, BME reckons that analysts will need to calculate and forecast market balances separately for: (a) China; and (b) the rest of the world, rather than just (c) globally.

The above conclusions mainly refer to prices within a single business cycle. Over the longer term, other forces come into play as well: substitution, the price responsiveness of scrap supply, mine costs and incentive prices for mining projects.

For more information on mathematical modelling of cash and three month LME prices, please e-mail the authors, Peter Hollands ( and Adam Sotowicz (

Peter Hollands is the head of Bloomsbury Minerals Economics. He has a B.Sc. in geology from University College London (UCL) and is a conventional market analyst, having worked for 11 years at Commodities Research Unit, followed by 27 years at Bloomsbury Minerals Economics (BME). Adam Sotowicz is the founder and managing director of Metal Price Analytics. He has a Ph.D. in organic chemistry from UCL, and was head of I.T. and price modelling at BME for 26 years before joining Metal Price Analytics.


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