# Difference between revisions of "Metal price forecasting"

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− | Introduction |
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− | Metal price is the key determining factor in project feasibility from a technical and valuation perspective. Therefore establishing a robust metal price forecast is of critical importance to mine planning. The goal of this article is to provide guidance in the development of robust metal price forecasts for base metals, suitable for a scoping level of study. The methodologies described below will generate stable bounds on metal prices which allows for high and low price cases to be considered in early project planning, where constant metal price assumptions are used. |
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− | The following steps will be outlined and followed to arrive at a reasonably robust base metal price forecast, suitable for a scoping level of study in mine design. |
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+ | Introduction <br>Metal price is the key determining factor in project feasibility from a technical and valuation perspective. Therefore establishing a robust metal price forecast is of critical importance to mine planning. The goal of this article is to provide guidance in the development of robust metal price forecasts for base metals, suitable for a scoping level of study. The methodologies described below will generate stable bounds on metal prices which allows for high and low price cases to be considered in early project planning, where constant metal price assumptions are used.<br>The following steps will be outlined and followed to arrive at a reasonably robust base metal price forecast, suitable for a scoping level of study in mine design.<br> Gather historical pricing data <br> Adjust pricing for inflation <br> Establish recent historical price variance<br> Establish recent historical price floor and ceiling <br> Bound the price forecast based on 3 and 4<br> Using forecast techniques and analyst predictions set price forecast<br> <br>Understanding historical pricing<br>Steps 1 & 2<br>The spot or current price of a metal is what the market currently values a unit of metal. As an example the daily spot price of Copper over the past one year, obtained from kitco [1], is shown in Figure 1 below. <br> [[Image:Figure1.png|center|600px|Figure 1 Copper spot price, 12 month period [1]]]<br><br>In the one year spot price seen in Figure 1 above, one can see that the current (as of January 22, 2014) spot price of $3.3252 USD/ lb, represents close to the yearly average Copper price for the last one year period. To better understand the historical market value of Copper it would be useful to look at data from a larger period. Fortunately the United States Geological Survey (USGS) maintains records of annual value for many commodities going back in some cases more than 100 years [2]. A plot of Copper prices in USD/ lb from 1850 – 2010, taken from the USGS, can be seen in Figure 2 below.<br> [[Image:Figure2.png|center|600px|Figure 2 Nominal Copper price per pound 1850-2010 [2]]]<br><br>The plot of historical prices in Figure 2 shows that Copper has exponentially increased in price, taking off aggressively after 2002. The issue with Figure 2 is that it represents the price of Copper in nominal dollars, put simply it represents the value of the metal in a given year, bought in the same year. As should be apparent, the purchasing power of a dollar in 1850 is significantly different from the purchasing power of a dollar today. To quantify the purchasing power of dollar in a given year we can use price indices. Price indices represent the value of a constant basket of goods, what is in the basket of goods depends on what index is being used. The consumer price index (CPI) is the most often used price index to quantify the purchasing power of a dollar in a given year, the CPI reports the value of a basket of items a consumer would buy like foods, housing, transport entertainment etc. Understanding how the price of the metal in question increases or decreases in relation to the price of a standard basket of goods will give better insight than looking at the nominal price in isolation. In Figure 3 below we can see the United States CPI by year, which is released by the Department of Labour, overlaid onto the long term Copper price from Figure 2. It is worth noting here that a number of other price indices exist, which use different baskets, for example the producer price index PPI uses a basket of goods relating to items producers would use, such as factory equipment. <br> [[Image:Figure3.png|center|600px| Figure 3 Nominal Copper price compared to consumer price index [2] [3] ]]<br>In Figure 3 above we see that the exponential rise in Copper prices since the mid-1950s follows the rise in price of a constant basket of goods, the CPI, so in effect the real value of Copper would not show the same rise. The real value of Copper, or any good, is the value of a constant good in a given year’s dollar. To calculate the real value of Copper we will use the CPI to adjust for inflation as seen in Equation 1 below.<br><br>Using the CPI deflator the inflation adjusted Copper price in 2010 dollars can be seen in Figure 4 below.<br> [[Image:Figure4.png|center|600px|Figure 4 Real Copper price per pound 1850 – 2010 [2] [3]]]<br><br>Comparing the effect of inflation adjustment seen comparing Figure 3 and Figure 4 it is clear that the real price changes seen in Figure 4 are not apparent when looking at nominal prices.<br> <br>Forecasting <br>Steps 3-6<br>Without knowledge of project length or start date the goal of metal price forecasting is to determine a stable long term price that will be representative of the average metal sale price ±50% over the best guess of project length. In the scoping phase of mine planning a constant metal price will be sufficient to determine whether a project should progress to the next stage of analysis, and as stated in the introduction the analysis is to provide a robust forecast that captures the upper and lower bounds of metal prices along with a reasonable base case metal price.<br>Establishing Variability <br>Step 3<br>It is impossible to predict future metal prices based exclusively on historical prices as there are major macroeconomic factors that influence the metal’s future price. What can be approximated by a metal’s pricing history is its variability over a given period. For each year calculate the maximum and minimum price in the previous period. Continuing the Copper example from above we will look at the time period from 1920 to 2010. To represent the variance within all ten year periods, a table of descriptive statistics of Copper variability within ten year periods can be seen in Table 1 below.<br> |
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− | 1. Gather historical pricing data |
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+ | {| width="200" cellspacing="1" cellpadding="1" border="1" align="center" |
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+ | |+ '''Table 1 Historical Copper price variability 1920-2010 [2]''' |
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+ | |- |
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+ | ! scope="col" | |
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+ | ! scope="col" | 10 Year Variance |
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+ | |- |
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+ | | Min |
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+ | | |
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+ | $0.50 |
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− | 2. Adjust pricing for inflation |
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+ | |- |
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+ | | 10th |
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+ | | $0.63 |
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+ | |- |
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+ | | 25th |
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+ | | $0.99 |
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+ | |- |
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+ | | Median |
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+ | | $1.22 |
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+ | |- |
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+ | | 75th |
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+ | | $1.42 |
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+ | |- |
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+ | | 90th |
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+ | | $2.30 |
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+ | |- |
||

+ | | Max |
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+ | | $2.72 |
||

+ | |- |
||

+ | | Mean |
||

+ | | $1.30 |
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+ | |} |
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− | 3. Establish recent historical price variance |
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− | 4. Establish recent historical price floor and ceiling |
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− | 5. Bound the price forecast based on 3 and 4 |
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+ | <br>The descriptive statistics on real Copper price variance in Table 1 above shows that in 50% of 10 year periods the Copper price has not changed by more than $1.25/lb in real 2010 USD, importantly it also shows the extreme and maximum variance expected over the course of recent history.<br> <br>Establishing Price Floors and Ceilings<br>Step 4<br>Looking at historical real Copper prices in Figure 4 it appears that there exists a maximum and minimum price that the market will tolerate before correcting to average conditions. The price floor and ceiling tolerated by the market is linked to technological innovations in (supply) and usage (demand). For the purposes of a scoping/ prefeasibility price forecast we will not consider changes to technological innovations and consider recent (current innovation period) historical data when establishing price floors and ceilings. Continuing the Copper example with the price history seen in Figure 4 above from 1920 – 2010 shows a price floor close to the $1/lb mark and ceiling around $3.50/lb (excluding the price spike driven by the first world war). For the analysis to be robust it is useful to quantify this floor and ceiling, again descriptive statistics are useful here. Seen in Table 2 below are descriptive statistics on the historical prices from current history (1920-2010). <br> |
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− | 6. Using forecast techniques and analyst predictions set price forecast |
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+ | {| width="200" cellspacing="1" cellpadding="1" border="1" align="center" |
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+ | |+ '''Table 2 Historical Copper price history 1920 – 2010 [2]''' |
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+ | |- |
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+ | ! scope="col" | |
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+ | ! scope="col" | 1920-2010 |
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+ | |- |
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+ | ! scope="row" | Min |
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+ | | $0.92 |
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+ | |- |
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+ | ! scope="row" | 10th |
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+ | | $1.27 |
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+ | |- |
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+ | ! scope="row" | 25th |
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+ | | $1.56 |
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+ | |- |
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+ | ! scope="row" | Median |
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+ | | $1.97 |
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+ | |- |
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+ | ! scope="row" | 75th |
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+ | | $2.43 |
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+ | |- |
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+ | ! scope="row" | 90th |
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+ | | $3.22 |
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+ | |- |
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+ | ! scope="row" | Max |
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+ | | $3.63 |
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+ | |- |
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+ | ! scope="row" | Mean |
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+ | | $2.05 |
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+ | |} |
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+ | <br>To exclude extremes in pricing we will define the price floor and ceiling as the minimum and maximum of recent pricing history. For our Copper pricing example the price floor and ceilings are taken to be $0.92/lb and $3.63/lb respectively. <br> <br>Bounding the Estimate <br>Step 5<br>From the introduction the goal of pricing is to determine a robust forecast that bounds a range of possibilities. Using the expected variance and price floors for a given base metal a robust forecast appropriate for a scoping study can be determined. <br>The upper bound of the price estimate can be defined as the price ceiling less half of the median variance. This definition of an upper bound captures the maximum expected price, within the expected variance of the given base metal.<br>The lower bound of the price estimate can be defined as the price floor plus half of the median variance. This definition of a lower bound captures the minimum expected price, within the expected variance of the given base metal.<br>The base case is defined as the average between the lower and upper price bounds and is adopted as the long term forecast for the metal.<br>An example of the bounding methodology applied to Copper prices can be seen in Figure 5 below.<br> [[Image:Figure5.png|center|600px| Figure 5 Historical Copper pricing with bounding overlaid [2] [3]]] |
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+ | <br>Other techniques and analyst forecasts <br>Step 6<br>The Trailing Average <br>The trailing average is another valuable technique for analyzing longer term trends in metal pricing. The trailing average is defined in Equation 2 below;<br>Equation 2 Trailing average<br>A_t=(X_t+X_(t-1)+⋯+X_(t-n+1) )/n [4]<br>Where Xt represents the observation made in period t, and At denotes the moving average calculated after making the observation in period n [4].<br>For base metal price forecasting it is useful to calculate trailing averages based periods relating to pricing cycles. From the Copper example, Copper has hit market bottom twice, once in the early 1930s and again in the early 2000s, indicating a 70 year pricing cycle, the distance between more localized peaks and troughs indicates relevance in the 20 year cycle. Both the 70 and 20 year trailing averages of historical price can be seen in the summary plot of Figure 6.<br>Analyst Forecasts <br>A number of groups and individuals publish forecasts for a range of metal prices as well as the larger economy. One of the most comprehensive forecasts is the Commodity Price Forecast published quarterly by the World Bank Development Prospects Group [5]. The forecast covers energy, agricultural, base metals precious metals and other categories out to 2025. The World Bank models its forecasts off of macroeconomic factors and historical performance of the commodity in question along with commodities in its category. The main advantages to the World Bank forecast is its reputability within the investment community and its consideration of overall market factors. Depending on the objectives of a forecast the disadvantage to the World Bank forecasts would be that compared to other analyst groups the World Bank forecasts tend to be conservative.<br>Other analyst forecasts can be obtained on publications by major banks, investment groups and news outlets. It is important to note that many analyst groups will have some bias to their forecast and to take a range of forecasts into account when deciding on a metal price to use in the scoping study. In the summary plot on Figure 6 we can see the World Bank forecast for Copper price overlaid onto the bounding analysis.<br> <br>Conclusion <br>To determine a robust base metal price forecast at a scoping level study the follows steps are advised<br> Gather historical pricing data <br> Adjust pricing for inflation <br> Establish recent historical price variance<br> Establish recent historical price floor and ceiling <br> Bound the price forecast based on 3 and 4<br> Using forecast techniques and analyst predictions set price forecast<br>The summary plot in Figure 6 below shows results of steps 1-6 being applied to Copper.<br> [[Image:Figure6.png|center|600px|Figure 6 Price forecast of Copper based on the described methodologies]]<br>As seen in Figure 6 above the convergence of the trailing averages, the World Bank forecast and the bounded estimate on $2.25/lb gives confidence that the base case value of Copper is a robust estimate and is suitable for a scoping level mine design study.<br>The same analysis method applied to Nickel pricing can be seen in Figure 7 below. It is of note that Nickel was greatly effect by the economic boom of the late 2000s so the price ceiling and floor were taken to be the 90th and 10th percentiles of historical pricing instead of the absolute maximum and minimums used in the Copper example.<br> [[Image:Figure7.png|center|600px| Figure 7 Price forecast of Nickel based on the described methodologies]] |
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− | |||

+ | Limitations of the Method and Assumptions <br>It is important to understand the assumptions made in the forecasting method described above. The major assumption in this method was that reasonably long periods of constant supply and demand exist for the metal in question, resulting in reasonably firm price floors and ceilings. This assumption can be seen to be valid for base metals in which supply is spread over many sources and their use in investment goods keeps demand relatively constant, within normal economic cycles. <br>The forecasting technique described above will not account for ‘step changes’ in supply or demand like those spurred by break through advances in technology or changes in intrinsic value. For the reliance on the assumption of price floors and ceilings the methodology described above is not appropriate for non-base metals, specifically precious metals, diamonds and metals with a small number of suppliers. |
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− | Understanding historical pricing |
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+ | = = |
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− | Steps 1 & 2 |
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− | The spot or current price of a metal is what the market currently values a unit of metal at. As an example the daily spot price of Copper over the past one year, obtained from kitco [1], is shown in Figure 1 below. |
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+ | References |
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+ | [1] K. Baker and S. Powell, "Chapter 9: Short- Term Forecasting," in Management Science The Art of Modeling with Spreadsheets, Wiley, 2008. <br>[2] World Bank, Development Prospects Group, "Commodity Price Forcast Update," 2013. [Online]. Available: http://siteresources.worldbank.org/INTPROSPECTS/Resources/334934-1304428586133/Price_Forecast.pdf. [Accessed 7 January 2014].<br>[3] US Geological Survey, "Metal Prices in the United States Through 2010," 2013. [Online]. Available: http://pubs.usgs.gov/sir/2012/5188/. [Accessed 5 January 2014].<br>[4] US Geological Survey, "Mineral Commodity Summaries," January 2013. [Online]. Available: http://minerals.usgs.gov/minerals/pubs/commodity/nickel/mcs-2013-nicke.pdf. [Accessed 5 January 2014].<br>[5] Kitco Inc., "Historical Charts - Copper," 15 January 2014. [Online]. Available: http://www.kitcometals.com/charts/copper_historical_large.html. [Accessed 15 January 2014].<br>[6] United States Department of Labor, "Historical Monthly Consumer Price Index All Urban Consumers (CPI-U)," Bureau of Labor Statistics , Washington , 2013.<br>[7] D. Humphreys, "Chapter 2.2 - Pricing and Trading in Metals and Minerals," in SME Handbook, 2011, pp. 49-56. |
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− | Figure 1 Copper spot price, 12 month period [1] |
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+ | = = |
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− | In the one year sport price seen in Figure 1 above, one can see that the current (as of January 22, 2014) spot price of $3.3252 USD/ lb, represents close to the yearly average Copper price for the last one year period. To better understand the historical market value of Copper it would be useful to look at data from a larger period. Fortunately the United States Geological Survey (USGS) maintains records of annual value for many commodities going back in some cases more than 100 years [2]. A plot of Copper prices in USD/ lb from 1850 – 2010, taken from the USGS, can be seen in Figure 2 below. |
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+ | = <br><br> = |
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− | |||

− | |||

− | Figure 2 Nominal Copper price per pound 1850-2010 [2] |
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− | |||

− | The plot of historical prices in Figure 2 shows that Copper has exponentially increased in price, taking off aggressively after 2002. The issue with Figure 2 is that it represents the price of Copper in nominal dollars, put simply it represents the value of the metal in a given year, bought in the same year. As should be apparent, the purchasing power of a dollar in 1850 is significantly different from the purchasing power of a dollar today. To quantify the purchasing power of dollar in a given year we can use price indices. Price indices represent the value of a constant basket of goods, what is in the basket of goods depends on what index is being used. The consumer price index (CPI) is the most often used price index to quantify the purchasing power of a dollar in a given year, the CPI reports the value of a basket of items a consumer would buy like foods, housing, transport entertainment etc. Understanding how the price of the metal in question increases or decreases in relation to the price of a standard basket of goods will give better insight than looking at the nominal price in isolation. In Figure 3 below we can see the United States CPI by year, which is released by the Department of Labour, overlaid onto the long term Copper price from Figure 2. It is worth noting here that a number of other price indices exist, which use different baskets, for example the producer price index PPI uses a basket of goods relating to items producers would use, like factory equipment. |
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− | |||

− | |||

− | Figure 3 Nominal Copper price compared to consumer price index [2] [3] |
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− | |||

− | In Figure 3 above we see that the exponential rise in Copper prices since the mid-1950s follows the rise in price of a constant basket of goods, the CPI, so in effect the real value of Copper would not show the same rise. The real value of Copper, or any good, is the value of a constant good in a given year’s dollar. To calculate the real value of Copper we will use the CPI to adjust for inflation as seen in Equation 1 below. |
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− | |||

− | Equation 1 CPI deflation |
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− | |||

− | |||

− | |||

− | As an example let us find the Copper price in 1992 in real 2010 dollars |
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− | |||

− | |||

− | |||

− | |||

− | Using the CPI deflator the inflation adjusted Copper price in 2010 dollars can be seen in Figure 4 below. |
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− | |||

− | |||

− | Figure 4 Real Copper price per pound 1850 – 2010 [2] [3] |
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− | |||

− | Comparing the effect of inflation adjustment seen comparing Figure 3 & Figure 4 it is clear that the real price changes seen in Figure 4 are not apparent when looking at nominal prices. |
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− | |||

− | |||

− | |||

− | |||

− | |||

− | Forecasting |
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− | Steps 3-6 |
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− | |||

− | Without knowledge of project length or start date the goal of metal price forecasting is to determine a stable long term price that will be representative of the average metal sale price ±50% over the best guess of project length. In the scoping phase of mine planning a constant metal price will be sufficient to determine wither a project should progress to the next stage of analysis, and as stated in the introduction the analysis is to provide a robust forecast that captures the upper and lower bounds of metal prices along with a reasonable base case metal price. |
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− | |||

− | Establishing Variability |
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− | Step 3 |
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− | |||

− | It is impossible to predict future metal prices based exclusively on historical prices as there are major macroeconomic factors that influence the metals future price. What can be approximated by a metal’s pricing history is its variability over a given period. For each year calculate the maximum and minimum price in the previous period. Continuing the Copper example from above we will look at the time period from 1920 to 2010. To represent the variance within all ten year period a table of descriptive statistics of Copper variability within ten year periods can be seen in Table 1 below. |
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− | |||

− | Table 1 Historical Copper price variability 1920-2010 [2] |
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− | |||

− | |||

− | The descriptive statistics on real Copper price variance in Table 1 above shows that in 50% of 10 year periods the Copper price has not changed by more than $1.25/lb in real 2010 USD, importantly it also shows the extreme and maximum variance expected over the course of recent history. |
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− | |||

− | |||

− | |||

− | |||

− | |||

− | Establishing Price Floors and Ceilings |
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− | Step 4 |
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− | |||

− | Looking at historical real Copper prices in Figure 4 it appears that there exists a maximum and minimum price that the market will tolerate before correcting to average conditions. The price floor and ceiling tolerated by the market is linked to technological innovations in (supply) and usage (demand). For the purposes of a scoping/ prefeasibility price forecast we will not consider changes to technological innovations and consider recent (current innovation period) historical data when establishing price floors and ceilings. Continuing the Copper example we the price history seen in Figure 4 above from 1910 – 2010 shows a price floor close to the $1/lb mark and ceiling around $3.50/lb (excluding the price spike driven by the first world war). For the analysis to be robust it is useful to quantify this floor and ceiling, again descriptive statistics are useful here. Seen in Table 2 below are descriptive statistics on the historical prices from current history (1920-2010). |
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− | |||

− | Table 2 Historical Copper price history 1920 – 2010 [2] |
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− | |||

− | |||

− | To exclude extremes in pricing we will define the price floor and ceiling as the minimum and maximum of recent pricing history. For our Copper pricing example the price floor and ceilings are taken to be $0.92/lb and $3.63/lb respectively. |
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− | |||

− | |||

− | |||

− | |||

− | |||

− | Bounding the Estimate |
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− | Step 5 |
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− | |||

− | From the introduction the goal of pricing is to determine a robust forecast that bounds a range of possibilities. Using the expected variance and price floors for a given base metal a robust forecast appropriate for a scoping study can be determined. |
||

− | |||

− | The upper bound of price estimate can be defined as the price ceiling less half of the median variance. This definition of an upper bound captures the maximum expected price, within the expected variance of the given base metal. |
||

− | |||

− | The lower bound of the price estimate can be defined as the price floor plus half of the median variance. This definition of a lower bound captures the minimum expected price, within the expected variance of the given base metal. |
||

− | |||

− | The base case is defined as the average between the lower and upper price bounds and is adopted as the long term forecast for the metal. |
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− | |||

− | An example of the bounding methodology applied to Copper prices can be seen in Figure 5 below. |
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− | |||

− | |||

− | Figure 5 Historical Copper pricing with bounding overlaid [2] [3] |
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− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | Other techniques and analyst forecasts |
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− | Step 6 |
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− | |||

− | The Trailing Average |
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− | The trailing average is another valuable technique for analyzing longer term trends in metal pricing. The trailing average is defined in Equation 2 below; |
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− | |||

− | Equation 2 Trailing average |
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− | |||

− | [4] |
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− | |||

− | Where Xt represents the observation made in period t, and At denotes the moving average calculated after making the observation in period n [4]. |
||

− | |||

− | For base metal price forecasting it is useful to calculate trailing averages based periods relating to pricing cycles. |
||

− | |||

− | From the Copper example, Copper has hit market bottom twice, once in the early 1930s and again in the early 2000s, indicating a 70 year pricing cycle, the distance between more localized peaks and troughs indicates relevance in the 20 year cycle. Both the 70 and 20 year trailing averages of historical price can be seen in the summary plot of Figure 6. |
||

− | |||

− | Analyst Forecasts |
||

− | A number of groups and individuals publish forecasts for a range of metal prices as well as the larger economy. One of the most comprehensive forecasts is the Commodity Price Forecast published quarterly by the World Bank Development Prospects Group [5]. The forecast covers energy, agricultural, base metals precious metals and other categories out to 2025. The World Bank models its forecasts off of macroeconomic factors and historical performance of the commodity in question along with commodities in its category. The main advantages to the World Bank forecast is its reputability within the investment community and its consideration of overall market factors. Depending on the objectives of a forecast the disadvantage to the World Bank forecasts would be that compared to other analyst groups the World Bank forecasts tend to be conservative. |
||

− | |||

− | Other analyst forecasts can be obtained on publications by major banks, investment groups and news outlets. It is important to note that many analyst groups will have some bias to their forecast and to take a range of forecasts into account when deciding on a metal price to use in the scoping study. In the summary plot on Figure 6 we can see the World Bank forecast for Copper price overlaid onto the bounding analysis. |
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− | |||

− | |||

− | |||

− | |||

− | |||

− | Conclusion |
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− | To determine a robust base metal price forecast at a scoping level study the follows steps are advised |
||

− | |||

− | 1. Gather historical pricing data |
||

− | |||

− | 2. Adjust pricing for inflation |
||

− | |||

− | 3. Establish recent historical price variance |
||

− | |||

− | 4. Establish recent historical price floor and ceiling |
||

− | |||

− | 5. Bound the price forecast based on 3 and 4 |
||

− | |||

− | 6. Using forecast techniques and analyst predictions set price forecast |
||

− | |||

− | The summary plot in Figure 6 below shows results of steps 1-6 being applied to Copper. |
||

− | |||

− | |||

− | Figure 6 Price forecast of Copper based on the described methodologies |
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− | |||

− | As seen in Figure 6 above the convergence of the trailing averages, the World Bank forecast and the bounded estimate on $2.25/lb gives confidence that the base case value of Copper is a robust estimate and is suitable for a scoping level mine design study. |
||

− | |||

− | The same analysis method applied to Nickel pricing can be seen in Figure 7 below. It is of note that Nickel was greatly effect by the economic boom of the late 2000s so the price ceiling and floor were taken to be the 90th and 10th percentiles of historical pricing instead of the absolute maximum and minimums used in the Copper example. |
||

− | |||

− | |||

− | Figure 7 Price forecast of Nickel based on the described methodologies |
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− | |||

− | |||

− | |||

− | Limitations of the Method and Assumptions |
||

− | It is important to understand the assumptions made in the forecasting method described above. The major assumption in this method was that reasonably long periods of constant supply and demand exist for the metal in question, resulting in reasonably firm price floors and ceilings. This assumption can be seen to be valid for base metals in which supply is spread over many sources and their use in investment goods keeps demand relatively constant, within normal economic cycles. |
||

− | |||

− | The forecasting technique described above will not account for ‘step changes’ in supply or demand like those spurred by break through advances in technology or changes in intrinsic value. For the reliance on the assumption of price floors and ceilings the methodology described above is not appropriate for non-base metals, specifically precious metals, diamonds and metals with a small number of suppliers. |
||

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | References |
||

− | [1] |
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+ | <br> |
||

− | K. Baker and S. Powell, "Chapter 9: Short- Term Forecasting," in Management Science The Art of Modeling with Spreadsheets, Wiley, 2008. |
||

− | |||

− | [2] |
||

− | World Bank, Development Prospects Group, "Commodity Price Forcast Update," 2013. [Online]. Available: http://siteresources.worldbank.org/INTPROSPECTS/Resources/334934-1304428586133/Price_Forecast.pdf. [Accessed 7 January 2014]. |
||

− | |||

− | [3] |
||

− | US Geological Survey, "Metal Prices in the United States Through 2010," 2013. [Online]. Available: http://pubs.usgs.gov/sir/2012/5188/. [Accessed 5 January 2014]. |
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− | |||

− | [4] |
||

− | US Geological Survey, "Mineral Commodity Summaries," January 2013. [Online]. Available: http://minerals.usgs.gov/minerals/pubs/commodity/nickel/mcs-2013-nicke.pdf. [Accessed 5 January 2014]. |
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− | |||

− | [5] |
||

− | Kitco Inc., "Historical Charts - Copper," 15 January 2014. [Online]. Available: http://www.kitcometals.com/charts/copper_historical_large.html. [Accessed 15 January 2014]. |
||

− | |||

− | [6] |
||

− | United States Department of Labor, "Historical Monthly Consumer Price Index All Urban Consumers (CPI-U)," Bureau of Labor Statistics , Washington , 2013. |
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− | |||

− | [7] |
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− | D. Humphreys, "Chapter 2.2 - Pricing and Trading in Metals and Minerals," in SME Handbook, 2011, pp. 49-56. |

## Revision as of 19:47, 4 February 2014

# Introduction

Metal price is the key determining factor in project feasibility from a technical and valuation perspective. Therefore establishing a robust metal price forecast is of critical importance to mine planning. The goal of this article is to provide guidance in the development of robust metal price forecasts for base metals, suitable for a scoping level of study. The methodologies described below will generate stable bounds on metal prices which allows for high and low price cases to be considered in early project planning, where constant metal price assumptions are used.

The following steps will be outlined and followed to arrive at a reasonably robust base metal price forecast, suitable for a scoping level of study in mine design.

Gather historical pricing data

Adjust pricing for inflation

Establish recent historical price variance

Establish recent historical price floor and ceiling

Bound the price forecast based on 3 and 4

Using forecast techniques and analyst predictions set price forecast

Understanding historical pricing

Steps 1 & 2

The spot or current price of a metal is what the market currently values a unit of metal. As an example the daily spot price of Copper over the past one year, obtained from kitco [1], is shown in Figure 1 below.

In the one year spot price seen in Figure 1 above, one can see that the current (as of January 22, 2014) spot price of $3.3252 USD/ lb, represents close to the yearly average Copper price for the last one year period. To better understand the historical market value of Copper it would be useful to look at data from a larger period. Fortunately the United States Geological Survey (USGS) maintains records of annual value for many commodities going back in some cases more than 100 years [2]. A plot of Copper prices in USD/ lb from 1850 – 2010, taken from the USGS, can be seen in Figure 2 below.

The plot of historical prices in Figure 2 shows that Copper has exponentially increased in price, taking off aggressively after 2002. The issue with Figure 2 is that it represents the price of Copper in nominal dollars, put simply it represents the value of the metal in a given year, bought in the same year. As should be apparent, the purchasing power of a dollar in 1850 is significantly different from the purchasing power of a dollar today. To quantify the purchasing power of dollar in a given year we can use price indices. Price indices represent the value of a constant basket of goods, what is in the basket of goods depends on what index is being used. The consumer price index (CPI) is the most often used price index to quantify the purchasing power of a dollar in a given year, the CPI reports the value of a basket of items a consumer would buy like foods, housing, transport entertainment etc. Understanding how the price of the metal in question increases or decreases in relation to the price of a standard basket of goods will give better insight than looking at the nominal price in isolation. In Figure 3 below we can see the United States CPI by year, which is released by the Department of Labour, overlaid onto the long term Copper price from Figure 2. It is worth noting here that a number of other price indices exist, which use different baskets, for example the producer price index PPI uses a basket of goods relating to items producers would use, such as factory equipment.

In Figure 3 above we see that the exponential rise in Copper prices since the mid-1950s follows the rise in price of a constant basket of goods, the CPI, so in effect the real value of Copper would not show the same rise. The real value of Copper, or any good, is the value of a constant good in a given year’s dollar. To calculate the real value of Copper we will use the CPI to adjust for inflation as seen in Equation 1 below.

Using the CPI deflator the inflation adjusted Copper price in 2010 dollars can be seen in Figure 4 below.

Comparing the effect of inflation adjustment seen comparing Figure 3 and Figure 4 it is clear that the real price changes seen in Figure 4 are not apparent when looking at nominal prices.

Forecasting

Steps 3-6

Without knowledge of project length or start date the goal of metal price forecasting is to determine a stable long term price that will be representative of the average metal sale price ±50% over the best guess of project length. In the scoping phase of mine planning a constant metal price will be sufficient to determine whether a project should progress to the next stage of analysis, and as stated in the introduction the analysis is to provide a robust forecast that captures the upper and lower bounds of metal prices along with a reasonable base case metal price.

Establishing Variability

Step 3

It is impossible to predict future metal prices based exclusively on historical prices as there are major macroeconomic factors that influence the metal’s future price. What can be approximated by a metal’s pricing history is its variability over a given period. For each year calculate the maximum and minimum price in the previous period. Continuing the Copper example from above we will look at the time period from 1920 to 2010. To represent the variance within all ten year periods, a table of descriptive statistics of Copper variability within ten year periods can be seen in Table 1 below.

10 Year Variance | |
---|---|

Min |
$0.50 |

10th | $0.63 |

25th | $0.99 |

Median | $1.22 |

75th | $1.42 |

90th | $2.30 |

Max | $2.72 |

Mean | $1.30 |

The descriptive statistics on real Copper price variance in Table 1 above shows that in 50% of 10 year periods the Copper price has not changed by more than $1.25/lb in real 2010 USD, importantly it also shows the extreme and maximum variance expected over the course of recent history.

Establishing Price Floors and Ceilings

Step 4

Looking at historical real Copper prices in Figure 4 it appears that there exists a maximum and minimum price that the market will tolerate before correcting to average conditions. The price floor and ceiling tolerated by the market is linked to technological innovations in (supply) and usage (demand). For the purposes of a scoping/ prefeasibility price forecast we will not consider changes to technological innovations and consider recent (current innovation period) historical data when establishing price floors and ceilings. Continuing the Copper example with the price history seen in Figure 4 above from 1920 – 2010 shows a price floor close to the $1/lb mark and ceiling around $3.50/lb (excluding the price spike driven by the first world war). For the analysis to be robust it is useful to quantify this floor and ceiling, again descriptive statistics are useful here. Seen in Table 2 below are descriptive statistics on the historical prices from current history (1920-2010).

1920-2010 | |
---|---|

Min | $0.92 |

10th | $1.27 |

25th | $1.56 |

Median | $1.97 |

75th | $2.43 |

90th | $3.22 |

Max | $3.63 |

Mean | $2.05 |

To exclude extremes in pricing we will define the price floor and ceiling as the minimum and maximum of recent pricing history. For our Copper pricing example the price floor and ceilings are taken to be $0.92/lb and $3.63/lb respectively.

Bounding the Estimate

Step 5

From the introduction the goal of pricing is to determine a robust forecast that bounds a range of possibilities. Using the expected variance and price floors for a given base metal a robust forecast appropriate for a scoping study can be determined.

The upper bound of the price estimate can be defined as the price ceiling less half of the median variance. This definition of an upper bound captures the maximum expected price, within the expected variance of the given base metal.

The lower bound of the price estimate can be defined as the price floor plus half of the median variance. This definition of a lower bound captures the minimum expected price, within the expected variance of the given base metal.

The base case is defined as the average between the lower and upper price bounds and is adopted as the long term forecast for the metal.

An example of the bounding methodology applied to Copper prices can be seen in Figure 5 below.

Other techniques and analyst forecasts

Step 6

The Trailing Average

The trailing average is another valuable technique for analyzing longer term trends in metal pricing. The trailing average is defined in Equation 2 below;

Equation 2 Trailing average

A_t=(X_t+X_(t-1)+⋯+X_(t-n+1) )/n [4]

Where Xt represents the observation made in period t, and At denotes the moving average calculated after making the observation in period n [4].

For base metal price forecasting it is useful to calculate trailing averages based periods relating to pricing cycles. From the Copper example, Copper has hit market bottom twice, once in the early 1930s and again in the early 2000s, indicating a 70 year pricing cycle, the distance between more localized peaks and troughs indicates relevance in the 20 year cycle. Both the 70 and 20 year trailing averages of historical price can be seen in the summary plot of Figure 6.

Analyst Forecasts

A number of groups and individuals publish forecasts for a range of metal prices as well as the larger economy. One of the most comprehensive forecasts is the Commodity Price Forecast published quarterly by the World Bank Development Prospects Group [5]. The forecast covers energy, agricultural, base metals precious metals and other categories out to 2025. The World Bank models its forecasts off of macroeconomic factors and historical performance of the commodity in question along with commodities in its category. The main advantages to the World Bank forecast is its reputability within the investment community and its consideration of overall market factors. Depending on the objectives of a forecast the disadvantage to the World Bank forecasts would be that compared to other analyst groups the World Bank forecasts tend to be conservative.

Other analyst forecasts can be obtained on publications by major banks, investment groups and news outlets. It is important to note that many analyst groups will have some bias to their forecast and to take a range of forecasts into account when deciding on a metal price to use in the scoping study. In the summary plot on Figure 6 we can see the World Bank forecast for Copper price overlaid onto the bounding analysis.

Conclusion

To determine a robust base metal price forecast at a scoping level study the follows steps are advised

Gather historical pricing data

Adjust pricing for inflation

Establish recent historical price variance

Establish recent historical price floor and ceiling

Bound the price forecast based on 3 and 4

Using forecast techniques and analyst predictions set price forecast

The summary plot in Figure 6 below shows results of steps 1-6 being applied to Copper.

As seen in Figure 6 above the convergence of the trailing averages, the World Bank forecast and the bounded estimate on $2.25/lb gives confidence that the base case value of Copper is a robust estimate and is suitable for a scoping level mine design study.

The same analysis method applied to Nickel pricing can be seen in Figure 7 below. It is of note that Nickel was greatly effect by the economic boom of the late 2000s so the price ceiling and floor were taken to be the 90th and 10th percentiles of historical pricing instead of the absolute maximum and minimums used in the Copper example.

Limitations of the Method and Assumptions

It is important to understand the assumptions made in the forecasting method described above. The major assumption in this method was that reasonably long periods of constant supply and demand exist for the metal in question, resulting in reasonably firm price floors and ceilings. This assumption can be seen to be valid for base metals in which supply is spread over many sources and their use in investment goods keeps demand relatively constant, within normal economic cycles.

The forecasting technique described above will not account for ‘step changes’ in supply or demand like those spurred by break through advances in technology or changes in intrinsic value. For the reliance on the assumption of price floors and ceilings the methodology described above is not appropriate for non-base metals, specifically precious metals, diamonds and metals with a small number of suppliers.

References

[1] K. Baker and S. Powell, "Chapter 9: Short- Term Forecasting," in Management Science The Art of Modeling with Spreadsheets, Wiley, 2008.

[2] World Bank, Development Prospects Group, "Commodity Price Forcast Update," 2013. [Online]. Available: http://siteresources.worldbank.org/INTPROSPECTS/Resources/334934-1304428586133/Price_Forecast.pdf. [Accessed 7 January 2014].

[3] US Geological Survey, "Metal Prices in the United States Through 2010," 2013. [Online]. Available: http://pubs.usgs.gov/sir/2012/5188/. [Accessed 5 January 2014].

[4] US Geological Survey, "Mineral Commodity Summaries," January 2013. [Online]. Available: http://minerals.usgs.gov/minerals/pubs/commodity/nickel/mcs-2013-nicke.pdf. [Accessed 5 January 2014].

[5] Kitco Inc., "Historical Charts - Copper," 15 January 2014. [Online]. Available: http://www.kitcometals.com/charts/copper_historical_large.html. [Accessed 15 January 2014].

[6] United States Department of Labor, "Historical Monthly Consumer Price Index All Urban Consumers (CPI-U)," Bureau of Labor Statistics , Washington , 2013.

[7] D. Humphreys, "Chapter 2.2 - Pricing and Trading in Metals and Minerals," in SME Handbook, 2011, pp. 49-56.