*Metals Price Analytics Limited’s (MPA’s) Adam Sotowicz has extensive experience in price modelling of currency pairs, equities, the precious metals and the LME base metals. He can create and maintain on a bespoke basis mathematical price models over a range of time-frames, from intra-day, to daily, to a few days ahead, to several years ahead (with the latter using monthly average figures). Over the past year MPA’s focus has been on daily price models for metal etfs , mining equities but more recently a new generation of Longer Term LME base metals is being developed in partnership with Bloomsbury Minerals Economics Ltd with an interactive Tin Model (Cash, M3 and Spread) already completed.*

*This work can also be extended to bespoke price modelling for non-metallic exchange traded industrial raw materials such as natural rubber and potentially non exchange-traded commodities (such as chemical raw materials and industrial gases), in the first instance most likely using monthly data and forecasting two to three years ahead, with clients providing assistance with data.*

**Long Term Models: LME base metals**

**Background History**

In traditional market analysis there is a persistent problem in linking circumstances in the market to price. There are two main, rival non-mathematical approaches to the price cycle, each of which has one strength and one weakness. Mathematical modelling brings the two approaches together, and also allows the cash price, the three-months (3M) price and the cash-3M spread (the contango or backwardation) rigorously to be dealt with.

The dominant non-modelling approach focuses on cycles of surplus and deficit which in turn drive cycles of stock change. Specific stock levels (or stock to consumption ratios) are then assumed to correspond to specific price levels. For some LME metals the stock to price relationship is poor, while for others it can be moderately good. The particular problem with this approach is that it is very poor at indicating peaks and troughs.

While the first approach is followed by many single-metal specialists, there is a second approach which tends to be favoured by multi-commodity analysts, who observe that the shift from bull to bear markets tends to coincide with the peak to global industrial production (IP) growth and the transition from bear to bull markets coincides with the trough to the IP growth cycle. This approach gives less guidance on price levels however.

Putting together the maths with some brain-storming led to unification of these approaches. A change in demand growth rates (IP growth serves as a good proxy) immediately triggers the primary price response, which only after a time lag triggers a supply response, and that lag initiates cycles of surpluses and deficits, which lead to secondary – or fine tuning – price adjustments.

Relatively simple price relationships of this sort were stable for a long period, from before 1990 to the middle of 2005, but then started to become unstable when pension fund money suddenly began flowing into the relatively small base metals markets in the tens of billions of dollars, and cash and forward prices of all of the LME metals began to turn upwards from modelled levels.

After the flood of pension money abated, the price relationships of the LME metals began to stabilize again (mostly from 2012, but a little later, from 2015, for tin stocks and prices) and mathematical modelling again became able once again to assist with analysis and forecasting of cash and 3M prices and the cash-3M spread.

**The price drivers used in the Tin Model**

Working from our unified view of price behaviour (as set out above), MPA developed a model of the cash and 3M prices of tin, with three drivers:

– Variation in the rate of demand growth is the initiator of the price cycle, but because monthly metals consumption figures tend to be contentious, MPA has used global IP growth as a proxy.

– The second driver is stocks. MPA is using LME stocks, because of the close causal link to contango and backwardation on the LME itself. Were MPA

– For the third driver, dollar strength or weakness, one could use the US$ major currencies index but in this instance MPA opted for the €/US$ rate, since that also has a forward curve and many potential customers prefer the latter for forecasting, rather than using forecast exchange rates.

Correlations of price drivers to cash and three months prices respectively are:

For year-on-year IP growth over 2012 to June 2019, 0.73 for the cash price, 0.73 for 3M price.

– For LME stocks just over 2015 through June 2019, -0.62 for the cash price and -0.61 for 3M.

– For the €/US$ exchange rate over 2012 through June 2019, 0.71 for cash and 0.72 for 3M.

Correlation of the actual and modelled cash prices are very good, at 0.87 over 2012 – June 2019 and for 3M prices the correlation is also 0.87. A separate model of the cash to three months spread has a correlation of 0.77 with the actual spread.

MPA’s interactive Tin price model run monthly to end 2020, so that clients can use them for their own forecasting and scenario analysis.

**Methodologies used**

MPA favours three modelling methods:

– LASSO (least absolute shrinkage and selection operator) and ‘Ridge Regression’ (also called Tikhonov Regularisation) which are favoured over multivariate linear regression as these techniques are more effective in reducing model complexity, reduce over-fitting and are also helpful with dealing with colinearity in the drivers.

– Multivariate Adaptive Regression Splines which help to deal with non-linear relationships and pinch points of the individual drivers

– Classification and Regression Trees which help to subset the data into different regions that may exhibit different behaviour (e.g. very low stocks or very high y-o-y IP).

**Deriving advantage from MPA price models**

Mining and metals companies, traders and brokers will, for different purposes, need to deal not just with cash prices (if their term contracts are on that basis) or three months prices (where the liquidity is for trading purposes) and the spread between them (and further forward quotes), where price exposure needs to be moved along the forward curve.

MPA’s mathematical price models allow analysis and forecasting of cash and 3M prices and the spread between them on a fully compatible basis, which is something that no non-mathematical approach can match.