The Spot-Futures Relationship In Commodities Industrial Metals

Marius Oddvar Malde MSc Finance Aarhus University Department of Economics & Business May 2016

Academic Advisor: Niels Strange Grønborg Department of Economics and Business Economics

Abstract The aim of this paper is to examine the relationship between spot and futures prices. Futures contracts on commodities have become more and more popular in recent years. Can this growth in futures contracts affect the price of a commodity, meaning that speculation can have an effect on the current spot price. To examine this, daily spot and futures prices of three commodities ranging from the 18th of January 2006 until the 18th of January 2016 are obtained. The three commodities are all industrial metals; aluminium, copper and nickel. By using the standard Granger-causality test and a modified Granger-causality test by Toda and Yamamoto (1995), we examine whether past values of the spot can help predict the current value of futures and whether futures can help predict the current spot price. Some of the findings confirms that futures can help predict the current spot price, thereby concluding that speculation can have its effect. The causality that is found is dependent on the metal type and the maturity of the futures.

Table of Contents Introduction................................................................................................................................ 3 Problem Statement .................................................................................................................... 4 Method ....................................................................................................................................... 5 Delimitation ................................................................................................................................ 6 Chapter 1 – The Commodity Market.......................................................................................... 7 Are Commodities An Asset Class? .......................................................................................... 7 Market Participation .............................................................................................................. 8 Market Participants ................................................................................................................ 8 Sectors of the Commodity Market ......................................................................................... 9 Aluminium ............................................................................................................................ 10 Copper .................................................................................................................................. 12 Nickel .................................................................................................................................... 14 Chapter 3: Spot-Futures Relationship ...................................................................................... 16 Backwardation and Contango .............................................................................................. 16 Aluminium ............................................................................................................................ 17 Copper .................................................................................................................................. 19 Nickel .................................................................................................................................... 20 Chapter 4: Methodology .......................................................................................................... 22 Stationarity ........................................................................................................................... 22 Cointegration ........................................................................................................................ 25 The Optimal Lag Length.................................................................................................... 25 Deterministic Terms ......................................................................................................... 26 Johansen Cointegration Test ............................................................................................ 27 Granger Causality Test ......................................................................................................... 32 Modified Granger Causality Test .......................................................................................... 34 Chapter 5: Granger Causality & Modified Granger Causality Test ........................................... 36 Full Sample ........................................................................................................................... 36 Pre-crisis Sample .................................................................................................................. 38 Crisis Sample......................................................................................................................... 39 Conclusion ................................................................................................................................ 41 References ................................................................................................................................ 43 Appendix................................................................................... Feil! Bokmerke er ikke definert. Side 1 av 45

Figures Figure 1: Aluminium Spot Price Vs. Consumption & Production

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Figure 2: Copper Spot Prices Vs. Consumption & Production

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Figure 3: Nickel Spot Prices Vs. Consumption & Production

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Figure 4: Aluminium Spot Price Vs. 3-, 15- & 27-month Futures

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Figure 5: Copper Spot Price Vs. 3-, 15- & 27-month Futures

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Figure 6: Nickel Spot Price Vs. 3-, 15- & 27-month Futures

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Figure 7: Unit Root Test

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Figure 8: Unit root test in the first difference

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Figure 9: Aluminium Cointegration Test

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Figure 10: Copper Cointegration Test

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Figure 11: Nickel Cointegration Test

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Figure 12: Full Sample Analysis

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Figure 13: Pre-Crisis Sample Analysis

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Figure 14: Crisis Sample Analysis

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Introduction The trading of commodities and commodity futures has been around for a relatively long time. But compared to the equity market, the commodity market hasn’t been that active, especially for the average investor. Since 1994 there has been a constant growth in the trading of commodities and commodity futures. In 1994 only about 500 million futures contracts were traded and by the year 2000 the number of futures had doubled. The real growth in commodities futures can after the millennium. Since 2000 there has been a continuous growth year by year on the trading of commodity futures and in 2009 about 5,5 billion futures contracts were traded. In the six years before the millennium, we saw a growth of around 500 million contracts, over the whole period. Compared to the ten years after the millennium, which had an average growth of almost one billion more contracts per year. Eight billion futures were traded in the year of 2010 and this amount to a growth of about 1600% over the last 16 years. In the most recent years, the trading of commodities has stagnated, but still this growth in futures should have made a huge impact on the commodity market (CRB Yearbook 2015). This huge increase in commodities futures should depict a huge increase in speculation on the commodity market. This kind of an increase in speculation could affect the price fluctuations of a given commodity. It is this effect this paper is going to examine and to investigate this effect some commodities are chosen. The effect of speculation on the commodity spot prices will be examined through three different industrial metals. These metals are aluminium, copper and nickel. These are some of the most common and most traded industrial metals in the world. Generally industrial metals are mostly driven by the global supply and demand, and are strongly correlated to the current economic situation in the world. An increase in speculation in these metals could distort this picture. From 2009 until 2013 London Metal Exchange (LME) had a growth of 55% in futures traded. Aluminium saw a 36% growth in futures traded, while copper saw a 62% growth and nickel futures grew a massive 104% over this five year period (CRB Yearbook 2015). In 2013 there were 65 million futures contracts traded on aluminium only at the LME, and about 50 million metric tons of aluminium was produced worldwide. Since a aluminium futures contract at the LME has a lot size of 25 tonnes, the aluminium production was traded 32 times on the futures market at LME (LME aluminium, CRB Yearbook 2015, Aluminiumleader.com) A futures contract on copper has also a lot size of 25 tonnes. In 2013 the production of copper was 21 million tonnes and 40,5 million futures contracts on copper was traded. This means that the production of copper was traded 48 times on the futures market only at the LME (LME copper, CRB Yearbook 2015, ICSG). Nickel production in 2013 was almost two million metric tons worldwide and 13,7 million futures contracts were traded on nickel at the LME. Since nickel futures contracts calls for a delivery of six metric tons, the nickel production was traded 41 times on the futures market at LME (LME nickel, CRB Yearbook 2015, INSG).

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Since only one percent of futures are settled by delivery (Fabozzi), the majority of this increase in futures has to be due to speculation. But speculation in a commodity doesn’t necessarily mean that speculation affects the price of the commodity, at least not in the long-run. This paper won’t research if the speculation is normal or excessive, neither if the speculation is positive or negative. The main focus of this paper is to see whether speculation can have an effect on the current price of the given commodity.

Problem Statement The objective of this paper is to get a better understanding of commodities and how commodities are used as financial instruments. A commodity is generally driven by the simple rules of supply and demand, but in the recent years the futures market on commodities has exploded. Futures are often used as a hedging tool, and where there are hedgers, there has to be speculators. The financial crisis has made the last ten years a very interesting period of time to analyze. This crisis should have incentivized both producers and consumers to hedge, and thereby incentivizing speculating. This paper's goal is to research the effect speculation can have on a commodity. Since the volume of futures contracts on commodities have increased a lot since the 2000s, could speculation on the commodity market have an effect on the price of a commodity? The aim of this analysis is to research the dynamic connection between spot and futures in commodities, specifically in industrial metals. To examine this, the direction of causality is analyzed. The conventional “cost-of-carry” model says that futures are mostly driven by the spot price and generally the spot price is driven by the supply and demand. But what if futures prices drive the spot price? A direction of causality from futures to spot, will give necessary evidence that speculation can be a main driver of the commodity price. Without this direction of causality, speculation has no special role. That’s why it is necessary, but not perhaps sufficient evidence. The futures market can drive the spot market based on forecasts and expectations of the future, but if there is causality from futures to spot, there is at least some evidence that speculation has an effect.

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Method The first part of this paper will be a detailed description of the commodity market. It will describe how the commodity works and who participates on this market. The paper will then move on to describe the commodities that have been picked for this analysis. A thorough description of Aluminium, Copper and Nickel as commodities will be given to the reader. Then we have come to the core of the paper, the relationship between spot and futures. A basic understanding of the theoretical relationship between spot and futures will be provided. The second part of this paper is the empirical one. It starts with explaining the methodology for the tests that are being performed later in the paper. The first step of this testing procedure is stationarity. A description of what stationarity is and what it entails, will give the reader a better understanding of why it is important. Stationarity will be tested through four different kinds of tests. The augmented Dickey-Fuller, Phillips & Perron, Dickey-Fuller (GLS) and the KPSS test will be applied to test the notion of stationarity/non-stationarity. If the variables are found to be stationary, an augmented Dickey-fuller test in the first-order difference will be applied to see if the variables are stationary in the first-order difference. The next step in the testing procedure is cointegration. Since the cointegration test in this paper is dependent on optimal lag length and deterministic terms, a selection of this has to be performed before starting the cointegration test. Why this is important and how an optimal lag length and deterministic term can be selected, is then described. When this is done, the Johansen Cointegration test can be performed. The spot is paired with their respective three different maturity futures and tested whether there exist cointegration between them. Now the actual Granger causality test can be performed. The standard Granger causality test is presented and the drawbacks of this model are illustrated. Models that can correct for these drawbacks are then presented and discussed. Then the modified Granger causality test proposed by Toda and Yamamoto (1995) can be presented. This is a model that should be superior to the standard Granger causality test, since it circumvents the drawbacks associated with the standard Granger causality test. Then the empirical analysis can start. First the full sample is analyzed by both the standard Granger causality test and the modified Granger causality test. Nine different bivariate VAR’s are tested through a test which is called “Block Exogeneity Wald Test”. Both tests will then estimate two different chi-squared (Wald) statistics for their respective bivariate VAR. The first statistic is whether futures “Granger cause” spot, and the second statistic is whether spot “Granger causes” futures. When the past values of a variable helps predict the value of another variable, the first variable is said to “Granger cause” the second variable. These chisquared statistics are compared to the critical values of the standard χ2-distribution with n degrees of freedom. The null hypothesis of no Granger causality can’t be rejected when the test-statistic is below the critical values. If the test-statistic is higher than the critical values, the null of no Granger causality can be rejected.

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The test statistics are compared to critical values at the 10%, 5% and 1% significance level. This is to see how strong the evidence of causality is. Only if the null hypothesis is rejected at the 5% significance level, a conclusion about the causality can be done. The same procedure will be followed for the sub-samples.

Delimitation The main focus of this paper will be the last 10 years, from 2006 until 2016. The LME spot and futures prices obtained from “Thomson Reuters Datastream” is dated from 18th of January 2006 until 18th of January 2016. This will of course be the full sample of our analysis. In addition to the full sample, two sub-samples will be created. The first sub-sample is called “pre-crisis”. This is limited to 18th of January 2006 until 15th of September 2008. The Lehman Brothers collapse on 15th of September 2008 started a new phase in the financial crisis (CRB Encyclopedia 2014). People started investing more in commodities, bonds and currency at this point, so this was thought of a good place to end the pre-financial crisis sample in this analysis. The second sub-sample is of course the eight years after the Lehman Brothers collapse until 18th of January 2016. This could depict an effect on the commodities from the global financial crisis. Hopefully the increased investing in commodities can be depicted by comparing the two sub-samples. While the first chapter of this paper is generally for the commodity market, the rest of the paper is limited to the industrial metals: Aluminium, copper and nickel.

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Chapter 1 – The Commodity Market The commodity market is the oldest financial market we have. A commodity is defined as an undifferentiated physical item that satisfies an economic want or need. Commodities, like livestock, agriculture, and metals, have been traded for ages (Clark). Within the last 200 years, the commodity market has been institutionalized by the Americans. There is evidence of a commodity exchange from the 18th century in Osaka, Japan, where they traded on rice futures, but the first institution was founded in the US. The Chicago Board of Trade was founded in 1848 and became the first of its kind. Not far behind, The London Metal Exchange was founded in 1877. Commodities traded on these exchanges were primarily agricultural and metal commodities. The trading of futures on energy first started in 1980, which makes that market fairly recent compared to the trading of metals and agricultural commodities (Fabozzi). In recent years, the commodity market has been through a renaissance. This is due to an increase in commodities as investment objects. Over the last few decades, pension funds and traditional portfolio managers have found it more beneficial to invest in commodities, which have increased the demand for commodities. A second drive for the increase is the “BRIC” countries. Brazil and Russia have two of the fastest growing economies in the world, and China and India have an increasing demand for consumer goods. This has led to a large growth in the short-term price of commodities at the start of the millennium. One example of this trend was China’s expansion of investments in infrastructure. From 2001 to 2005, China’s demand for aluminium, copper and iron increased by 85%, 78% and 92% respectively (Fabozzi). One of the factors that make the commodity market so different from the equity market, and the foreign exchange market, is the inability for someone to intervene in that market. Since producers of commodities reacts slowly to distortions on the market, shocks in demand and short-term supply are compensated by only price movements (Fabozzi).

Are Commodities An Asset Class? The definition of an asset class is a class of similar assets that show a homogenous riskreturn and have a low external correlation toward other asset classes. Assets on the market today can be put into three main classes; capital assets, consumable or transferable assets (C/T) and store of value assets. Commodities fit well into the second class, C/T assets. A main difference between commodities as an asset, in contrast to bonds and stocks, is that most commodities don’t have a continuous cash flow. Commodities are unique in this regard. They have a value because they can be consumed or used as input goods. Since there isn’t a continuous cash flow, you can’t determine the price on a commodity by methods like the net present value or by discounting the future cash flows. These two methods are largely influenced by interest rates, and since they can’t be used to price commodities, the interest rates don’t have a great impact on the value of commodities. Another difference between capital assets and commodities is how their progress can reflect economic development in a country or a region. Equity markets can largely reflect the economic development in a Side 7 av 45

country or a region, but that isn’t the case with commodities. Firstly, commodities are denominated in US Dollars worldwide and the supply and demand of a specific commodity isn’t determined by a regional supply and demand. The value of a commodity is actually determined by the global supply and demand of that commodity, so the markets can reflect the economic development on a global level instead of a regional (Fabozzi).

Market Participation To participate on the commodity market, there are generally five different ways to do so. The first, and the most obvious, is to actually invest directly in the physical goods. The second opportunity is to make an indirect investment into the commodity market. By an indirect investment, it is understood that you invest in companies that largely base their business around commodities. Not only companies that sell or buy commodities, but also companies that explore, mine, refine, manufacture, trade or supply them to other companies. But when investing indirectly, there are many other variables to take into account. Since the correlation between the commodity price and a company’s stocks are low, there are many more variables that determine the stocks. Variables like capital structure, expectations, information about the company, management quality, profit growth, risk sensitivity, and strategic position, must now be taken into account. As a result,an increase in the oil price doesn’t necessarily mean the same increase in Exxon’s stock price, or even an increase at all (Fabozzi). A third way to participate in the market is by investing in commodity funds. This will give the investor a beneficial diversification factor. The fourth way is to invest in commodity futures. This is a contract which obligates the buyer or seller to buy or sell an asset at a specific date and price. Futures can be settled in two ways, either by a delivery of the commodity or by closing the futures position. By closing the futures position, the investor buys or sells the same amount of contracts before maturity so that the investor doesn’t have to receive the physical good, but still can make a profit from it. Only in one percent of futures contracts, the settlement has been by delivery at maturity. Since a future position doesn’t have high capital requirements, it can be very advantageous for an investor, but it requires a lot of time and effort to manage these positions. The last and fifth way to participate on the commodity markets is to invest in structured products on commodity futures indexes. Here the investor will get reasonable exposure to commodities or a commodity sector, and the products are easily traded and not that expensive. But still there is a high exposure to the US dollar, since indexes are denominated in this currency just like commodities are (Fabozzi).

Market Participants In the commodity market there are several participants. When talking about physical commodity, we almost exclusively talk about producers and consumers. But when talking about the participants in the commodity market, we must take into account the participants on the futures market. Normally the participants on the futures market are arbitrageurs, hedgers and speculators. Arbitrageurs play the smallest part of this market. They will try to take advantage of market differences, which can provide them a riskless profit. This can be Side 8 av 45

differences between the spot and futures market, or time- or location-based differences in the futures market. Arbitrageurs are looking for a market imbalance to make a profit, so after they have made their riskless profit, the price relationship will be restored and the market will be balanced again. Hedgers are often participants in the commodity market with a high exposure to one or more commodities. To minimize risk they will hedge against a price increase or decrease. A producer of aluminium will often hedge against a price decrease, while a consumer, like a manufacturer of cars, will often hedge against a price increase (Fabozzi). Speculators are the largest group on the futures market, and the main focus in this paper. Because of a volatile market which is difficult to forecast, the producers of a commodity want to get rid of price risk. They do this by paying a premium and passing the risk along to the speculators. To make a profit, speculators are betting on falling and rising prices. Contrary to hedging, they are increasing their risk. By taking on this risk they provide liquidity and balance the long and short hedges. You can say that speculators are the opposite of hedgers, since they are betting on price changes and increase their risk to make a profit (Fabozzi).

Sectors of the Commodity Market Commodities can be categorized in many different ways. One way is to categorize them by their demand. An upstream commodity is a commodity which satisfies an industrial demand, like oil and aluminium. A downstream commodity is a commodity which satisfies the end users, like gasoline and gold (Clark). But the easiest way to categorize them is by their physical characteristics. For example we can categorize commodities into hard and soft. Within hard commodities, we find commodities from the energy and the metals market. In the energy column, we count commodities like oil, coal, natural gas and electricity. While in the metal column, there is again a division into two subcategories, industrial and precious metals. The industrial, or base metal category, contains metals which are mostly used in the building and manufacturing industries, such as aluminium, copper, nickel and lead. Actually, the base metal category can be divided into two more subcategories; non-ferrous and ferrous metals. Non-ferrous metals are metals that don’t contain any iron, like aluminium, nickel and copper. Ferrous metals contain iron, like for example iron and steel (Clark). The precious metal category contains rare and expensive metals like gold, silver and platinum. Soft commodities are commodities that are more weather dependent than hard commodities, like corn and sugar (Fabozzi). We also distinguish between commodities when it comes to availability, renewability and storability. A commodity that has a low cost of storage, compared to its value, and isn’t perishable, have a high degree of storability. Livestock has a low degree of storability, since they need to be fed and housed, and they are only profitable at a certain time of their life. On the other hand, aluminium and copper are good examples of commodities with a high degree of storability.

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Another way of distinguishing commodities is by renewability. Commodities like gold, oil and aluminium are not renewable, so the supply of them is dependent on discovery and exploration of new reserves. The price of renewable commodities is more dependent on the expected production costs in the future, while the price of non-renewable commodities is largely dependent on investors demand.

Chapter 2: Aluminium, Copper & Nickel Aluminium Aluminium is the most significant raw base metal on earth, and it is found in the earth’s crust. It was only first isolated in the 1820s by the Danish chemist Hans Christian Oersted. Since then, many different methods for producing aluminium have been created. But in 1886, the first practical method for producing aluminium was discovered. The method of producing aluminium through electrolytic reduction is still the primary method used today (CRB Yearbook 2015). Because of its expensive extracting process, aluminium was more expensive than gold for a period of time. When found in nature, aluminium isn’t of the highest quality, but it is improved by using chemical connections. The most common way of extracting aluminium, is from a bauxite which is mostly found around the equator. The production of aluminium is a costly one because of the high amount of energy that goes into the production. To produce one pound of aluminium, the operation requires six to eight kilowatts of electrical energy (Clark). About 50% of the production costs come from the energy released during the production, and therefore aluminium is highly correlated to energy prices, especially oil prices. Attributes like its light weight, corrosion resistance and very good malleability, makes aluminium essential for the manufacturing of vehicles, airplanes and construction in general (Fabozzi). In 2014 the production of aluminium was 54 million tons (Aluminiumleader.com). The largest supplier was Asia with 67,90% of the worldwide supply. China (47%) and Russia (7%) are the two main contributors to the Asian supply. Canada (6%), the U.S. (3,5%) and Australia (3,4%) are some main suppliers outside of Asia. The largest supplier of aluminium in Europe is Norway (not counting Russia). In 2014 Norway produced about 2% of the worldwide supply of aluminium (CRB Yearbook 2015). The automotive and transport industry is the largest demander of aluminium, taking 27% of the supply. The building industry follows closely with a demand of 25%, while packaging has a demand of 16% (Aluminiumleader.com). In 2012, China alone was the largest demander of aluminium in the world, with a demand of 45%. Europe had a demand of 17%, the rest of Asia and Oceania 16%, while North America had 13% (Clark). In figure 1 you can see the aluminium spot price from 18 th of January 2006 until 18th of January 2016. You can also see how the consumption and production has moved in the same time period. From 2006 until 2008, the aluminium market, along with the other commodity Side 10 av 45

markets, was in a bull market. Bull market refers to a state in the market where it is trending upwards. This was mainly due to a weak dollar and a strong commodity demand from the BRIC-countries and other emerging markets. In the middle of 2008 we can clearly see the financial crisis hit. Consumption and production decreases, and the aluminium price plunges. In the aftermath of the financial crisis in 2009-2011, aluminium prices started to rise again. This was brought on by the extra liquidity from the unusually easy monetary policy from the U.S. The price was also driven up by many people who bought commodities as protection. They did this because they thought the monetary policy from the U.S. would cause hyperinflation and a massive depreciation of the U.S. dollar (CRB Yearbook 2015). In the crisis years of 2008-2009, many smelters were shut down due to declining prices as the demand declined. But in the years of 2010-2011 most of these smelters were restarted and the production of aluminium grew (USGS Aluminium, 2011). As seen in figure 1, the aluminium price topped in mid-2011, and afterwards has been on a downward track. This is because of the low economic growth worldwide and the unlikely arrival of the aforementioned hyperinflation. China, and other emerging countries, had a slowed growth in 2013-2014, which didn’t help the aluminium price. In the mid- and late2014, the U.S. dollar appreciated, and together with a plummeting oil price, gave a downward pressure on the aluminium price (CRB Yearbook 2015)

Figure 1: Aluminium Spot Price Vs. Consumption & Production

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(Own adaption. Sources: Datastream, Aluminiumleader.com, world-aluminium.org) From 2011 until 2014, countries like China, India and Saudi Arabia have tried to increase production by making new smelters and expanding existing smelters. This has partly been offset by difficult situations in other countries. High power prices, low aluminium prices, a weak domestic currency, and financial challenges have forced many countries to close their smelters. The demand in 2015 increased because of Europe, which continues to recover Side 11 av 45

from the debt-crisis and has an automobile industry using more and more aluminium in each car (USGS Aluminium, 2014). Both consumption and production has seen an annual growth rate of 7% over this 10-year period. In the crisis years, from 2007 until 2009, the consumption had a declining growth of 9% and the production had a declining growth of 1%.

Copper Copper is one of the oldest metals and its use can be traced back 10 000 years. The name copper actually comes from the name of the island Cyprus, which was a primary source of copper (CRB Yearbook 2015). Copper is found as a heavy metal in nature and naturally has high quality. The key attribute that makes copper one of the most used industrial metals, is its excellent ability to transport heat and electricity. It is also easy to transform and is corrosion resistant. Because of these key attributes, copper is mostly used to make roofs, installation conduits and electric cables. Silver and copper are actually the next best metals for conducting electricity after gold, but the relatively low price of copper compared to silver and gold, makes it beneficial for industrial use (Clark). Bacteria don’t grow on copper, making it perfect for air-conditioning systems, doorknobs, and food appliances (CRB Yearbook 2015). Copper is also used to make brass (copper/zinc alloy) and bronze (copper/tin alloy). The end product is made up of 60% concentrates and 40% of copper scrap, and it has to be 99,99% pure to be traded (Fabozzi). The mine production of copper in 2014 was about 18.7 million tonnes. By far the largest contributor to the worldwide supply of copper is Chile. Chile produces 31% of the global copper supply, while China (8,7%) Peru (7,5%) , the U.S. (7,3%) and Australia (5,4%) followed (CRB Yearbook 2015). In the consumption and production graph in figure 2, refined copper is used. In the production of refined copper in 2014, China had over a third of the production, while Chile (12%), Japan (7%) and the U.S. (5%) followed. China is ahead of Chile at this point because of their dominance in copper smelter production (ICSG). The largest demanders of copper are building construction with 30%, and the equipment industry with 31%. Around 75% of the copper that is produced is used for electrical purposes. Since an average house in the U.S. contains about 200 kg of copper, the price movements in copper can largely reflect economic growth and housing constructions (Clark). The U.S. has previously been the largest consumer of copper, but in 2003 they were surpassed for the first time, by China (Fabozzi). 62% of the copper demand comes from Asia, while 19% derives from the European market and 14% from North and South American market (ICSG). In the time before the financial crisis, the copper price was in a bull market. From 2001 the price had increased every year until 2006. This was also because of the high commodity demand from BRIC-countries, which affected the whole commodity market. As with aluminium, the copper price plummeted in mid-2008 when the financial crisis hit. The interesting part is that both consumption and production wasn’t greatly affected by the financial crisis. On average the refined copper production has grown 3,2% per year over the last 10 years, but in 2009 it had only grown by 0,23%. The refined copper consumption grew Side 12 av 45

only 0,04% from 2008 until 2009, which is a lot less than the yearly average of 3,5% growth. Compared to most commodities, which saw a decrease in both consumption and production in this period, copper didn’t. From 2009 until 2011, the copper price saw the same bullish market as aluminium. The upward trend in copper prices in this period was mostly due to China’s high levels of imported copper, and that the general demand for copper exceeded the production. In 2009, China’s demand for refined copper increased by 38% (USGS Copper, 2009 &10). Even with rising inventories, the high copper price continued in 2011, still due to China and a shortage in the supply of copper. The growing uncertainty over the European debt crisis and a slowdown in China’s growth, made the copper price fall at the end of 2011 (USGS Copper, 2011).

Figure 2: Copper Spot Prices Vs. Consumption & Production

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(Own adaption. Sources: Datastream, International Copper Study Group) The copper price continued its decline from 2011 into 2012. As seen in figure 2, the market balance for copper was relatively tight. This made industry news the main reason for the decline in the price. News about a change in China’s demand made the copper price trending downward (USGS Copper, 2012). At the end of 2013, the copper price continued to decline. This was due to an expected appreciation of the U.S. dollar. News about U.S. Federal Reserve’s plan to reduce the stimulus of the economy by reducing bond purchases, could appreciate the U.S. dollar and thereby making copper more expensive for international consumers. The U.S. Federal Reserve’s plan began in January 2014. The slowdown of China’s economic growth (the world’s largest copper consumer), and the strong U.S. dollar, continued the downward pressure on the copper price through 2014 and 2015 (USGS Copper, 2013).

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Nickel Nickel, like copper, is a very old metal. It was discovered by a mistake 5000 years ago. It was found as an unmeltable component of the copper ore. Independently, nickel first came into the industry in the 18th century, around 1751 (Clark). Nickel is a magnetic metal, and you can find it in over 300 000 different products. It is a very hard and conductive metal, which makes it essential to the production of high-grade steel. It makes steel firmer and corrosion resistant. Around 60% of the produced nickel goes to the production of high-grade steel and other unoxidizable alloys (Fabozzi). One fun fact about nickel is that the 5 cent US coin contains 1,25 grams of nickel and 3,75 grams of copper. With favourable metal prices, the value of this coin could actually be greater than its 5 cent face value. Because of this, the US has made it illegal to melt or export a significant amount of 5 cent coins (Clark). Almost 2 million tons of nickel was produced in 2014. The main producer is the Philippines with 18% of the global supply, while Russia, Canada and Indonesia follows with about 10% each (CRB Yearbook 2015, INSG). 20% of the worldwide supply of nickel actually comes from scrap, so recycling of nickel becomes more and more important. The building industry is the largest consumer, same as copper, followed by the automotive industry. These two industries are large consumer because of the suitability of high-grade steel in construction (Fabozzi). Asia has the highest demand of nickel with 67%, and Europe follows with 21%. The nickel market is facing a challenging time. In Europe, India and North America, primary nickel is substituted with nickel scrap in stainless steel and other alloys. In China, there is Nickel Pig Iron (NPI) that substitutes both primary nickel and nickel scrap because of their low cost and easy availability (INSG). The price of nickel, over the last 10 years, has the same characteristics as aluminium and copper.. A high demand that exceeded the production in 2006, gave the nickel price an upward trend. China’s demand for stainless steel has been strong since 2000, and since twothirds of the nickel consumption goes to making stainless steel, the nickel price was driven by this strong demand (USGS Nickel, 2007). This trend continued into 2007, and the nickel price reached an extraordinary level in the first half of 2007. Because of high gasoline prices, and the introduction of hybrid motor vehicles, there was a higher demand for nickel-metal hydride batteries (NiMH), which are often used in hybrid motors (USGS Nickel, 2008). Like copper, the nickel consumption and production didn’t take that much of a hit when the global financial crisis was a fact in 2008, but the price plummeted. The price started to trend upwards after 23 governments started programs to stimulate the economy, but a high unemployment rate, and tight credit in many countries, weakened the nickel demand at the end of 2009 (USGS Nickel, 2010). An increasing consumption and production from 2009, made the price trend upward, but it is far from recovered. The nickel price peaked in the start of 2012 after a 12-month decline, but was put on a downward trend because of the European debt situation and the slowing down of the Chinese economy (USGS Nickel, 2013).

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Figure 3: Nickel Spot Prices Vs. Consumption & Production

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$60 000 $50 000 $40 000 $30 000 $20 000 $10 000 $0

2 000 1 500 1 000 500 0 20062007200820092010201120122013201420152016

Spot Prices in US Dollar

Thousand Metric Tonnes Nickel

Dates For Spot Prices

Production Consumption Nickel Spot Prices

Years For Consumption & Production

(Own adaption. Sources: Datastream, International Nickel Study Group, metal.com) From the price peak in 2012, until 2015, there has been a clear surplus of supply in the nickel market, which has caused a downward pressure on the price. The increase of nickel pig iron production has weakened the demand. The economic challenges in Europe have helped the continuing downward trend in the nickel price together with the oversupply (USGS Nickel, 2014). The nickel price saw a peak in the mid-2014, but was declining at the end of the year because of the European situation and a strong U.S. Dollar (USGS Nickel, 2015). Declining production of stainless steel, and increasing production of ferronickel, together with Europe, the dollar, and a slow growth in China, has kept the price declining in 2015 (USGS Nickel, 2016). During the sample period, the nickel consumption has had an annual growth rate of about 4%, and the nickel production has had a slightly higher growth rate at 4,44%.

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Chapter 3: Spot-Futures Relationship A futures contract is a contract between two parties where each party is obligated to buy or sell an underlying asset at a specific price, at a specific time in the future. The seller of the asset has a short position in the futures contract, while the buyer has a long position. If the buyer or seller doesn’t want to buy or sell the asset, they have to buy or sell a new futures contract, which offsets the current futures contract. Only about 1% of futures contracts are settled by the delivery of the physical asset. Because commodities are not financial assets, they do not have an identical pricing dynamic, in contrast to financial futures. The types of futures are very similar, but there are some key differences. Firstly, a commodity futures contract has storage costs. This is a negative income associated with holding the physical commodity. The second difference between them is the convenience yield. This is a benefit the investor could have from holding the physical commodity. The investor can profit from holding the commodity by creating a brief or local demand and supply imbalance, or try to keep the production of the commodity at a certain level. Certain precious metals, like gold and silver, can be loaned to electronic and jewellery manufacturers. The rate of this loan will then be the convenience yield. The convenience yield should reflect the benefits an investor can have from holding the physical commodity (Fabozzi). Thus the price of a commodity futures contract can be stated as such: F = S𝑒 (𝑟+𝑐−𝑦)(𝑇−𝑡) Where the risk-free rate is denoted by r, the storage cost is denoted by c, and the convenience yield is denoted by y. It is subtracted because it reduces the cost of owning the commodity. The term structure of a commodity futures contract is similar to the term structure of interest rates. It can be downward sloping or upward sloping, and this depends on the behaviour of hedgers and speculators on the market. When there is evidence of a term structure that is downward sloping, it is in backwardation. And when the opposite is true, it is called contango (Fabozzi).

Backwardation and Contango By backwardation we understand that there is a negative trend in the term structure curve. This implies that the futures’ prices, with longer maturity, have a lower price than the current spot price of that commodity. On the opposite side, if the term structure curve has a positive trend, it is called contango. When in contango, the price of futures with longer maturity is higher than the current spot prices of that commodity (Fabozzi). Commodities that are exposed to strong stock price fluctuations, because of a shock in demand or supply, can experience change or actually a reversion in their term structure. The trend of the term structure can therefore illustrate the stock of a commodity and how the market is forecasting the availability of that commodity in the future. Backwardation and contango has a high correlation with the demand and the supply situation on the global commodity market. If there is evidence of backwardation, it means that the demand for short hedges is much larger than the demand for long hedges. In backwardation, the most Side 16 av 45

profitable position for an investor is to be long in the futures contracts. And of course, the opposite is true for contango (Fabozzi). Backwardation is not a sign of an abnormal market situation, it is relatively common because commodity producers are more likely to hedge against price risk than commodity consumers (Keynes). When the hedger is naturally short in the commodity, a contango situation will occur (Fabozzi). A commodity company is exposed to the risk of a declining commodity price when it is exploring, developing, marketing and refining its commodity. To reduce their exposure to this price risk, they sell futures contracts on the commodity, thereby separating the price risk from the business risk. By hedging this price risk, they don’t need to be as protected against a potentially declining commodity price, and can allocate the reserved capital to protect against the business risk. But when someone reduces their risk, another party has to increase their risk, and get compensated for doing so. This other party is often a speculator (Fabozzi). When the market is in backwardation, the speculator is compensated by a futures price that is lower than the expected future spot price. The greater the maturity, the greater the discount. In a contango market, it isn’t the producer who wants to reduce the risk, it is the consumer. In this situation, the speculator sells a futures contract to the consumer at a price which is higher than the expected spot price, and the speculator will thus be compensated by a premium return. For the speculators, it doesn’t matter which way the curve goes, they can make a profit regardless. Since a backwardated market encourages producers to produce their commodity, the commodity markets are mostly in a backwardated situation (Fabozzi). Observations of the different commodity sectors from 1970-2006 have shown that nonstorable commodities, or commodities with high storage costs, tend to be more in backwardation than commodities with low storage costs. Energy and livestock are typical commodities that are non-storable, or have high costs associated with their storage. These kinds of commodities stay in backwardation more often than industrial and precious metals. They mostly stay in contango. Industrial metals were in backwardation 18,33% of the time in this observation period (Fabozzi).

Aluminium After a close examination of the aluminium futures prices at 3-months, 15-months and 27months, the results were in favor of contango. From the 18th of January 2006 until 18th of January 2016, 3-month aluminium futures were in backwardation only 5,86% of the time. 15-month futures were in backwardation 13,45% of the time, while 27-month futures were 15,41% of the time in backwardation. This is clear from figure 4. The blue line in figure 4 represents the spot prices, and lies below the other lines most of the time period. This is clear evidence of the contango situation in aluminium, and in line with the observation that industrial metals are mostly in contango.

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This means that consumers have been the hedgers of aluminium over the last 10 years, and that speculators have been compensated by those with a premium. The automotive and transport, building and packaging industry are the world’s leading consumers of aluminium. In this situation they are naturally short in aluminium, and hedge against the aluminium price.

Figure 4: Aluminium Spot Prices Vs. 3-, 15- & 27-month Futures 4000 Aluminium Spot Prices 3 Month Future 3000

2000

1000

0

(Own adaption. Source: Datastream) At the start of the sample period, 15-month and 27-month futures are in backwardation. This was probably due to the high demand for aluminium during this period. To meet the strong demand, producers had to be encouraged to produce more and thereby creating backwardation. By mid-2006, 3-month futures were also in backwardation, but this only lasted until the end of March 2007. 15-month and 27-month futures were first in contango in June 2007 and august 2007 respectively. At this point in time, the consumption of aluminium was declining, and the financial crisis in the U.S. had started. Since the early signs of the financial crisis in 2007, all aluminium futures have mostly been in contango. Since 2009, the consumption of aluminium has increased at a greater rate than the production, and was almost level in the year 2015. When there are high or increasing prices, like in 2006-2007, producers are more concerned about a price dip, and hedge themselves against this. This puts the aluminium market in a backwardated state. When the prices are low or declining, like the ones during and after the financial crisis, consumers are more concerned about a price upturn and hedge themselves against this. Thereby putting the market in contango.

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Copper While copper is an industrial metal, it doesn’t fit the normal characteristics when it comes to contango and backwardation, at least not in this time frame. 3-month copper futures were in contango in a slight majority of the time. 47% of the time, 3-month futures were priced lower than the current spot price, in other words in backwardation. This percentage of backwardation only increased with the higher maturity futures. 15-month futures were actually backwardated most of the time, having been set at a lower price compared to the spot price in 57% of the cases. 27-month futures were in backwardation 71% of the time. Compared to the average industrial metal that is in backwardation 18% of the time, copper experienced a high amount of backwardation during this sample period. Copper futures started like aluminium futures. The spot price was relatively high and increasing, while there was a strong demand for copper. This made the futures mostly stay in backwardation until the middle of the financial crisis in October 2008. Demand fell together with the spot price, making the consumers naturally concerned, which brought on a period of contango. For 3-month futures, this period of contango lasted until November 2010, when prices peaked again. 27-month futures were mostly in backwardation by the summer of 2009, while 15-month futures went back and forth, until September 2010 when they experienced a relatively long period in backwardation.

Figure 5: Copper Spot Prices Vs. 3-, 15- & 27-Month Futures 12000 10000 8000 6000

Copper Spot Prices 3 Month Future

4000

15 Month Future 27 Month Future

2000 0

(Own adaption. Source: Datastream)

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This period of backwardation didn’t last for long. Prices started to drop at the start of 2011, and 3-month futures went into contango again. The other futures weren’t far behind, and in April of 2011, 15-month futures followed 3-month futures into contango. 27-month futures experienced some contango after the summer of 2011, but stayed, for most of the time, in backwardation. The declining copper prices made 3-month and 15-month futures stay mostly in contango all the way until December 2013. From 2010 through 2013, the demand had surpassed the production of copper. This need for more production put the futures in backwardation most of the time until the sample time period ended in 2016. After 2015, the demand for copper were still higher than the production, but considerably less so than in the years of 2010 until 2014. On average the demand had been 1,16% higher than production during this time, and in 2015 the demand surplus was only 0,25%.

Nickel Both 3-month and 15-month nickel futures were, for most of the time, in contango. 14,6% and 37,3% in backwardation respectively. Nickel stayed more in backwardation than aluminium, but a lot less than copper. 27-month nickel futures did fit the pattern of more backwardation with higher maturities. This could probably be due to the fact that producers of commodities more often hedge their risk in longer maturity futures. With 51% in backwardation, 27-month futures were slightly more in backwardation than in contango.

Figure 6: Nickel Spot Prices Vs. 3-, 15- & 27-month Futures 60000 50000 40000 30000

Nickel Spot Prices 3 Month Future

20000

15 Month Future 27 Month Future

10000 0

(Own adaption. Source: Datastream, International Nickel Study Group)

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The nickel price had the same characteristics at the start of the sample period as both aluminium and copper. Increasing, and reaching a peak, in the middle of 2007. In contrast to aluminium and copper, where 3-month futures were in backwardation because of an increasing spot price, 3-month nickel futures had some time in contango. But at the end of April 2006, it followed the pattern of being in backwardation when prices are increasing. This period in backwardation lasted until the middle of 2007, when nickel prices started to drop. Both 15- and 27-month nickel futures started the sample period with a long period in backwardation due to the increasing nickel price. Another factor that could have played a part is that in 2006 the demand for nickel was higher than the production. The period with backwardation increased production, and it had surpassed the demand by 2007. At the end of 2007, prices, together with demand and production, were declining, making both 3-month futures and 15-month futures to go into a contango state. When the nickel price neared its bottom at the end of 2008, 27-month futures also went into contango. The contango state ended for 15- and 27-month futures when prices, production and demand were increasing at the end of the financial crisis, in the middle of 2009. 3-month futures stayed in contango from 2007 all the way through the sample period. Even with increasing prices and growing demand and supply, there was enough uncertainty with consumers to keep the 3-month futures in contango. After the nickel price reached its peak in mid-2011, the price started to decline, together with a slower growth rate in consumption compared to production. This made the 15-month future go into contango in the summer of 2011, and 27-month futures followed at the start of 2012. As prices declined through the sample period, and the production was in a surplus, all the three futures contracts stayed most of the time in contango. One exception was in the middle of 2014. There was a slower growth in production than in consumption in this period, and an increasing nickel price. This made 27-month futures go into a backwardated state for about three months in the middle of 2014. After the small peak in nickel prices at the start of 2015, prices started to decline again, and the consumption surpassed the production during 2015. All the three futures contracts were in a contango state at the end of the sample period.

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Chapter 4: Methodology To analyze the relationship between spot and futures prices, the standard Granger causality test (Granger, 1969) will be applied. This is a test that examines if past values of one variable can help predict another variable. In this case, the paper examines if past spot prices can help predict futures prices, and if past futures prices can help predict spot prices. The null hypothesis in this test is that variable one “does not Granger cause” variable two (Verbeek). But there are some drawbacks with the standard Granger causality test, especially when testing the relationship between spot and futures. Since spot and futures prices are generally suspected of being integrated or cointegrated, this can make the standard Granger causality test invalid. When time series are integrated, or cointegrated, the standard Granger causality test does not have a standard distribution (Toda & Yamamoto, 1995). The standard Granger causality test will still be performed, but will be compared to a modified Granger causality test proposed by Toda & Yamamoto (1995). This modified Granger causality test will not be affected by either stationarity or integration/cointegration. Before these two tests are performed, stationarity and integration/cointegration needs to be tested.

Stationarity Firstly, the test for non-stationarity is necessary, this is because non-stationary and stationary series should be treated differently. A stationary series is a series with a constant mean, constant variance and constant autocovariance at each lag. A non-stationary series does not have these properties, and is said to contain a unit root. A non-stationary series is a time series that has different means, and different variances, at different lags. A shock in the spot or futures prices will affect a stationary series at the time t, but the effect will be less in time t+1, and even less in time t+2. The effect of a shock in a non-stationary series will be permanent, not temporary as with stationary series (Brooks, 2008). To understand the difference between stationarity and non-stationarity, this simple autoregressive process can be of assistance: 𝑦𝑡 = µ + 𝜌𝑦𝑡−1 + 𝑢𝑡 Here the variable y is dependent on the constant term µ, the lagged value of y and the error term ut. But it is the ρ value that is interesting in terms of whether the time series is stationary or non-stationary. The value of ρ can have three different outcomes. ρ can be smaller than 1, and if this is the case, the time series is stationary, i.e. mean reversion. If the ρ is equal to 1, the time series is non-stationary, and variable y contains a unit root. The third and last outcome is that ρ is larger than 1. This is also regarded as a non-stationary time series, but is not found in many economic and financial time series (Brooks, 2008).

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To test for non-stationarity, or a unit root, four different tests will be applied. The ADF (Dickey and Fuller, 1979), the PP (Phillips and Perron, 1988), the DF-GLS test (Elliott, Rothenberg and Stock, 1996), and the KPSS test (Kwiatkowski, Phillips, Schmidt and Shin, 1992). The null hypothesis of the three first tests says that there is a unit root in the time series, i.e. a non-stationary series. While the last test, the KPSS test has a null hypothesis of stationarity. Looking at the results in Figure 7, we can see that in the ADF, PP and DF-GLS tests, the values are not larger than the critical values at the 5% significance level. This means that we cannot reject the null hypothesis of a unit root, i.e. the time series are nonstationary. In the KPSS test, we can see that the values are larger than the critical values at the 5% significance level, but this null hypothesis says that the series is stationary. The rejections of all the null hypothesis in the KPSS test is a confirmation of non-stationarity in the time series. After testing for stationarity with and without trend, there is clear evidence that the time series in this analysis are non-stationary time series and contains a unit root. Figure 7: Unit Root Test Full Sample

Without

Trend

(2609 Obs)

ADF

PP

With KPSS

DFGL S -1,13

ADF

Tren d PP

KPSS

DFGL S 0,19* -2,35

Aluminium -1,65 -1,67 2,83* -2,72 -2,60 Spot Aluminium F3 -1,55 -1,58 2,87* -1,07 -2,53 -2,56 0,19* Aluminium -1,44 -1,51 2,63* -1,33 -2,48 -2,56 0,17* F15 Aluminium -1,46 -1,58 2,09* -1,52 -2,36 -2,48 0,24* F27 Copper Spot -2,05 -2,13 0,47* -1,14 -2,12 -2,19 0,48* Copper F3 -2,07 -2,15 0,49* -1,09 -2,12 -2,19 0,5* Copper F15 -2,16 -2,19 0,7* -0,87 -2,02 -2,05 0,6* Copper F27 -2,25 -2,27 1,14* -0,74 -1,88 -1,9 0,73* Nickel Spot -1,48 -1,53 2,41* -1,36 -2,64 -2,68 0,2* Nickel F3 -1,46 -1,42 2,39* -1,34 -2,62 -2,6 0,19* Nickel F15 -1,62 -1,55 2,11* -1,44 -2,68 -2,61 0,18* Nickel F27 -1,84 -1,69 1,74* -1,55 -2,73 -2,59 0,21* CV (5%) -2,86 -2,86 0,46 -1,94 -3,41 -3,41 0,14* * Rejection of null hypothesis of no stationarity (KPSS: H0 = stationarity) at the 5% significance level

-2,27 -1,94 -1,70 -1,22 -1,17 -0,92 -0,79 -1,35 -1,33 -1,43 -1,54 -2,89

The conclusion is that the spot and futures prices in the analysis are non-stationary, but the order of integration is still unknown. Since cointegration tests are being performed later in this analysis, the order of integration for spot and futures prices need to be determined. Financial variables, like spot and futures prices, tend to be non-stationary, but develop together over time. From figure 4-6, there is evidence of a relationship between the spot and futures prices. Financial variables that contain a unit root, can be integrated by the Side 23 av 45

order of one, I(1). But rather than just assuming it, we will do a quick ADF test in the firstorder difference to get evidence that the time series are integrated by the order of one (Brooks, 2008). In figure 8, all variables clearly reject the null hypothesis of non-stationarity (unit root) in the first-order difference at the 5% significance level. This means that we have made the nonstationary series into stationary series by differencing them one time. By differencing a series d times to make it stationary, the series is integrated by the order of d. In this case the series are made stationary by differencing them one time, i.e. the series are integrated by the order of one, I(1) (Brooks, 2008).

Figure 8: Unit root test in the first-order difference With Constant

First-order Difference ADF

Full Sample Aluminium Spot -45,25* Aluminium F3 -45,44* Aluminium F15 -45,45* Aluminium F27 -45,38* Copper Spot -54,76* Copper F3 -54,65* Copper F15 -55,09* Copper F27 -55,15* Nickel Spot -42,74* Nickel F3 -42,69* Nickel F15 -43,00* Nickel F27 -43,43* CV (5%) -2,86 * Rejection of the null hypothesis of non-stationarity at the 5% significance level The results for the unit root tests of the two sub-samples can be seen in Appendix A and B. In the sample period, from 2008-2016, the result from the tests gave the same conclusions as in the full sample period. The variables are non-stationary time series and contain a unit root. The pre-crisis sample period, from 2006 to 2008, has some irregularities compared to the full sample. The ADF test without trend rejects the null hypothesis of a unit root in aluminium spot price, aluminium 3-month future and copper 15-month future. On the other hand, the Phillips-Perron test without trend rejects the null hypothesis of a unit root in copper 3-month futures and copper 15-month futures. Also the KPSS test with trend can’t reject the null hypothesis of stationarity in all of the copper futures. This could mean that these series are stationary, but because four tests are performed, and 50% or more of those tests say they are non-stationary, the conclusion is that they are non-stationary time series in this sample period also. All of the ADF tests in the first-order difference reject the null hypothesis, so they are integrated by the order of one, I(1). Side 24 av 45

Cointegration The concept of cointegration comes from the work of Engle and Granger (1987). Cointegration between variables means that the variables share the same long-term stochastic trend. If the variables are both integrated by the order of one I(1),in most cases the combination will also be integrated by one I(1). If the variables are both integrated by the same order, the linear combination is also integrated by this order. If the variables differ in integration order, the linear combination will take the highest order of integration. Cointegration appears first when the linear combination of I(1) variables is I(0), i.e. the linear combination is stationary. The residuals can be seen as a linear combination between the variables, and when the variables are cointegrated, residuals are stationary and constant over time. Cointegration cannot exist if variables are integrated by different orders (Brooks, 2008). Variables, like spot and future prices, are series that often are non-stationary, but can be cointegrated. This is because they are dependent on the same factors in the long run, like the supply and demand of a commodity. Since every variable in this analysis is integrated by the same order, cointegration between variables is possible (Brooks, 2008). For testing the cointegration between spot and futures prices, the Johansen test (Johansen, 1991) will be applied. Since this test is very dependent on the selected lag length, and which deterministic terms you include, pre-tests have to be performed. Before the cointegration test can be performed, the optimal lag length, and which deterministic term to include, has to be found. The Optimal Lag Length For determining the optimal lag length for the Johansen cointegration test, the method of information criterion, and the likelihood ratio (LR) test, will be applied. When looking at the information criterion, the object is to choose a lag length that minimizes the value of the information criteria. Because the commodity market is open five days a week, it seems reasonable to choose a maximum lag length of 5. Where the information criteria are at its lowest, from lag length 1-5, is the optimal lag length for that information criterion. The information criterion that will be used is the Akaike’s (1974) information criterion (AIC), and final prediction error (FPE), Schwarz’s (1978) Bayesian information criterion (BIC/SIC) and the Hannan-Quinn criterion (HQC). The information criteria is build up by two factors, one that is the function of the residual sum of squares, and the other is a penalty for losing a degree of freedom when adding an extra lag (Brooks, 2008) The likelihood ratio test involves estimating two models, an unrestricted model and a restricted model. Then combine the maximized value of the unrestricted model with the maximized value of the restricted model in the formula: 𝐿𝑅 = −2(𝐿𝑟 − 𝐿𝑢 ) ~ 𝜒 2 (𝑚) The restricted model is denoted by Lr the unrestricted model is denoted by Lu, and m is the number of restrictions. The LR test statistic follows a chi-squared distribution, and where the null hypothesis is rejected, the optimal lag length is found (Brooks, 2008). Side 25 av 45

When choosing the optimal lag length, there are now five different criteria to choose from. AIC and FPE can overestimate the true lag order, but this overestimation can also be preferable. The BIC/SIC criteria can produce very small estimates in finite samples, but is strongly consistent (Clark & Mirza, 2006). If the majority of information criterion prefers a certain lag length, this lag length is optimal. When there are five different information criteria, this should prevent a tie between lag lengths, but three different information criteria don’t necessarily pick the same lag length. In three of the cases, two information criteria choose one lag length, while two other information criteria choose another lag length. In these cases, the author took a judgement call on what seemed to be the best fit for the model. The optimal lag lengths can be seen together with the Granger causality analysis in figure 12-14. Deterministic Terms After finding the optimal lag length for every pair being tested for cointegration, the next step is to find which deterministic terms that should be included in the VAR, or in the cointegration relation. This can be a constant term and/or a trend. These five different models are suggested by Juselius (2005): Model 1: This is a model without any deterministic terms in the data, i.e. no intercept or trend in the cointegration relation or VAR. This model should only be used when measurements start at zero, or when measurements cancel out the cointegration relations. This model won’t be considered because there is need for an intercept as our model needs to account for the initial data (Juselius, 2005). Model 2: The second model has a constant term that is restricted in the cointegration relations. This means that there are no linear trends in the data and that the equilibrium mean is different from zero (Juselius, 2005). Model 3: In the third model, the constant term is unrestricted, which means that there aren’t linear trends in the VAR model. There are linear trends in the data, but not in the cointegration relations. Since the constant term is unrestricted, this model could be of good use if the trend seems to be stochastic (Juselius, 2005). Model 4: The trend term is included in the fourth model, but restricted to the cointegration relations. The constant is unrestricted in the model. The trend will allow linear trend in the data, but not quadratic. The difference from model 3, is that there is a trend in the cointegration relations. If it is believed that some variables are “trend-stationary”, this model should be used (Juselius, 2005). Model 5: The last model has no restrictions on either trend or constant, meaning quadratic trends. Like model 1, this won’t be considered because they do not occur often in practice (Juselius, 2005).

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When doing the cointegration test, only models 2, 3 and 4 will be considered. Model 1 and 5 seem too unlikely to be the correct specifications to our analysis, so these aren’t to be tested. Choosing which of the three models best suited for this purpose is a bit difficult. To arrive at a conclusion, the “Pantula Principle”, suggested by Johansen (1992), was applied. This principle follows a structure where you estimate all the three models and order them according to restrictiveness. Meaning that model 2 (the most restrictive model) is first and model 4 (the least restrictive model) is last. The process of picking a model starts with comparing the test statistics (max Eigenvalue) to the critical value for the most restrictive model. If we fail to reject the null hypothesis, the process of picking a model can stop here. If the null hypothesis of no cointegration vectors is rejected, we move on to the next most restrictive model. When the null hypothesis cannot be rejected for the first time, the appropriate model is found. Johansen Cointegration Test The optimal lag length is selected for each VAR, and the appropriate deterministic terms are found, so the Johansen cointegration test can be performed. When wanting to test for cointegration between two variables, there are several different methods to use. The best, and most accurate method, seems to be the Johansen test. Unlike the Engle-Granger 2-step method, it doesn’t suffer from problems like a lack of power in the cointegration test, simultaneous equations bias, and the inability to perform hypothesis tests. The Johansen test is an excellent tool for testing cointegration in a multivariate case, but also in this case where there are only two variables (Brooks, 2008). The Johansen technique is built up by a VAR model that includes more than one dependent variable. The VAR model could be set up like this:

𝑦𝑡= 𝛽1 𝑦𝑡−1+

𝛽2 𝑦𝑡−2 +⋯+ 𝛽𝑘 𝑦𝑡−𝑘 +𝑢𝑡

In order to use this VAR model in the Johansen test, it needs to be a vector error correction model (VECM) like this:

∆𝑦𝑡 = Π𝑦𝑡−𝑘 + Γ1 ∆𝑦𝑡−1 + Γ2 ∆𝑦𝑡−2 + ⋯ + Γ𝑘−1 ∆𝑦𝑡−(𝑘−1) + 𝑢𝑡 Where the variables are in first difference, and have k-1 lags of the dependent variables. The Γ is the coefficient matrix for every lagged variable, and the Π is a long-run coefficient matrix. This test calculates the cointegration between variables by testing the rank of the long-run coefficient matrix Π. The rank of the Π matrix is the eigenvalues that are different from zero. The rank of this matrix will then be equal to the number of cointegration vectors between the variables.

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When performing the cointegration test with the Johansen method, the trace test, and the maximum eigenvalue test, is estimated. The latter will be the focus of this cointegration test, and is formulated as such (Brooks, 2008):

𝜆𝑚𝑎𝑥 (𝑟, 𝑟 + 1) = −𝑇 ln(1 − 𝜆̂𝑟+1 ) The number of cointegration vectors are denoted by r and the 𝜆̂ is the estimated eigenvalue from the Π matrix. The difference between the two tests is that the maximum eigenvalue test performs separate tests on each eigenvalue, and its null hypothesis is that of r cointegration vectors against r+1 cointegration vectors. While the trace test is a joint test with a null hypothesis of less or equal to r cointegration vectors, against more than r cointegration vectors. Both tests were conducted, but since the same conclusions could be drawn from both tests, only the max eigenvalue results are provided. From the VAR model it is apparent that the optimal lag length is critical for this test. The critical values of this test are strongly dependent on which deterministic term we use. The null hypothesis is that there are no cointegration vectors. If this test statistic (max. eigenvalue) is higher than the critical value, the null of no cointegration vectors is rejected, and the test with a null hypothesis of one cointegration vector is performed (Brooks, 2008). There are three outcomes of this cointegration test. The first is that of full rank (g), which actually means that the original variables are stationary, i.e. cointegration is not possible. The second one is that of a zero rank. This means no long-run relationship between the variables, i.e. no cointegration. The last outcome is a reduced rank, where there is evidence of cointegration with r cointegrating vectors (Brooks, 2008). In figure 9, we find the results from the Johansen cointegration test for aluminium. The optimal lag length for the cointegration test is shown in the parenthesis. This lag length is actually (k-1) lags because the Johansen cointegration test estimates in the first-order difference. The testing started with the most restrictive model and, according to the Pantula principle, the correct model to use should be where you cannot reject the null hypothesis of no cointegration for the first time. In the first cointegration test between aluminium spot prices and 3-month aluminium futures prices, cointegration vectors were detected with each of the three models. First when testing the spot price against 15-month futures prices, the null hypothesis could be rejected for the first time. On that basis, the model with restricted constant and no trend seems to be the best fit for aluminium. With this model applied, there is cointegration between the aluminium spot price and 3-month futures, but no cointegration between the spot price and 15- and 27-month futures.

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Figure 9: Aluminium Cointegration Test Full Sample (18.01.06 - 18.01.16) 2609 Obs

Cointe- None gration

Aluminium Cointegration Test

rank

MaxEigen Stat

At most 1 Critical PValue Value

MaxEigen Stat

Critical PValue Valu e

Spot Vs. F3 (2 lags)

Restricted constant, 1 No trend 24,13* 15,89 0,00 4,06 9,16 Unrestricted constant, 2 No trend 23,97* 14,26 0,00 3,84* 3,84 Unrestricted constant, 1 Restricted trend 24,57* 19,39 0,01 8,70 12,52 Spot Restricted constant, 0 Vs. F15 No trend 12,72 15,89 0,15 6,17 9,16 (1 lag) Unrestricted constant, 0 No trend 12,72 14,26 0,09 5,87 3,84 Unrestricted constant, 0 Restricted trend 13,12 19,39 0,32 9,46 12,52 Spot Restricted constant, 0 Vs. F27 No trend 10,13 15,89 0,32 7,57 9,16 (2 lags Unrestricted constant, 0 No trend 10,10 14,26 0,21 7,30 3,84 Unrestricted constant, 0 Restricted trend 12,32 19,39 0,39 8,83 12,52 *Rejection of the null hypothesis of no cointegration vectors, or at most one cointegration vector at the 5% significance level

0,40 0,05 0,20 0,18 0,02 0,15 0,10 0,01 0,19

The cointegration tests for the sub-samples can be found in Appendix C. In the pre-crisis sample, there was no sign of cointegration between the variables. The cointegration results from the full sample were replicated in the crisis sample period. The cointegration between spot prices and 3-month futures prices in both the full sample and the crisis sample should mean that there has to be some sort of causality between them. It could either be causality both ways, or just from one variable to the other (Granger, 1988). In the cointegration test for copper, as seen in figure 10, the results are a bit different from aluminium. The null of no cointegration can be rejected in model 2 and model 3, but can’t be rejected in the last model. Model 4 is the least restrictive model, and by choosing this model there is no cointegration between the copper spot and copper futures in the full sample. The absence of cointegration in our test doesn’t say a lot about the causality between the variables. If causality is detected between the variables, the effect would probably only be short-term.

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Figure 10: Copper Cointegration Test Full Sample (18.01.06 - 18.01.16) 2609 Obs Copper Cointegration Test

Cointegration rank

Spot Vs. F3

Restricted constant, No trend

1

(4 lags)

Unrestricted constant, No trend

2

None MaxEigen Stat

Critical Value

PValue

16,57 *

15,89

0,04

16,46 *

14,26

0,02

At most 1 MaxEigen Stat

Critical Value

PValue

4,54

9,16

0,34

4,53*

3,84

0,03

Unrestricted constant, 0 Restricted trend 16,64 19,38 0,12 7,12 12,51 Spot Restricted constant, No 0 Vs. F15 trend 13,74 15,89 0,11 4,89 9,16 (1 lag) Unrestricted constant, No 0 trend 13,41 14,26 0,07 4,85 3,84 Unrestricted constant, 0 Restricted trend 13,91 19,38 0,26 6,38 12,52 Spot Restricted constant, No 0 Vs. F27 trend 11,09 15,89 0,25 5,56 9,16 (1 lag) Unrestricted constant, No 0 trend 10,73 14,26 0,17 5,52 3,84 Unrestricted constant, 0 Restricted trend 11,28 19,38 0,48 6,52 12,51 *Rejection of the null hypothesis of no cointegration vectors, or at most one cointegration vector at the 5% significance level

0,33 0,30 0,03 0,41 0,23 0,02 0,40

In Appendix D, the cointegration results for the pre-crisis, and crisis sample, are provided. In the pre-crisis sample, there is no evidence of cointegration when looking at the results with the last deterministic model. When looking at the crisis sample, there seems to be more cointegration. This could be due to the beginning of the sample period. In figure 5, there appears to be less of a relationship between the variables from 2006-2008 than from 2008 until the end of the sample period. The results from the cointegration test, with the last deterministic model, shows evidence of cointegration between the copper spot price and 3month copper futures. Between the copper spot price and the other futures, the null hypothesis of no cointegration cannot be rejected. This should be evidence that spot prices and 3-month futures prices have some sort of causality in this sample period. When looking at figure 11, there are a lot of signs in favour of cointegration. Between spot price and 3-month futures, there seems to be cointegration in each of the models, meaning that there should be some causality between these two variables. As with copper, the null of no cointegration cannot be rejected before model 4, and according to the Pantula principle, this model should be chosen for nickel. The model with unrestricted constant and restricted Side 30 av 45

trend estimates cointegration between the spot price and 3-month futures prices, but no cointegration between the spot price and the two other futures prices

Figure 11: Nickel Cointegration Test Full Sample (18.01.06 - 18.01.16) 2609 Obs

Cointegration

None

Nickel Cointgration Test

rank

MaxEigen Stat

Critical Value

PValue

At most 1 MaxEigen Stat

Critical Value

Spot Vs. F3 (4 lags)

Restricted constant, No 1 0,00 trend 35,15* 15,89 3,09 9,16 Unrestricted constant, No 1 0,00 trend 35,12* 14,26 3,05 3,84 Unrestricted constant, 1 0,00 Restricted trend 35,14* 19,38 9,14 12,51 Spot Restricted constant, No 1 Vs. F15 trend 16,78* 15,89 0,04 6,39 9,16 (4 lags) Unrestricted constant, No 2 trend 16,73* 14,26 0,02 6,38* 3,84 Unrestricted constant, 0 Restricted trend 17,65 19,38 0,09 11,70 12,52 Spot Restricted constant, No 0 Vs. F27 trend 14,47 15,89 0,08 5,72 9,16 (4 lags) Unrestricted constant, No 2 trend 14,43* 14,26 0,05 5,72* 3,84 Unrestricted constant, 0 Restricted trend 16,02 19,38 0,14 9,67 12,51 *Rejection of the null hypothesis of no cointegration vectors, or at most one cointegration vector at the 5% significance level The results from the cointegration tests of the subsamples of nickel can be seen in Appendix E. In the pre-crisis sample, the result is no cointegration between the variables, as with aluminium and copper. In the start of the sample period, from 2006 until 2008, there seems to be a lower relationship between the spot prices and the futures prices. This is the same for aluminium, copper and nickel, so this could be the source of no cointegration in the precrisis sample. It could also be due to the fact that the pre-crisis samples are relatively small, and only amount to about 27% of the full sample period. In the crisis sample, cointegration can be detected between the spot price and 3-month futures, whilst the other futures don’t seem cointegrated with the spot price. This is more or less the same result that was estimated in the full sample period for nickel. After the cointegration test, there is now five different bivariate VAR-models that has evidence of cointegration. Cointegrating relations were detected between aluminium spot prices and 3-month futures prices both in the full sample and in the crisis sample. A restricted constant, and no trend, will be included when testing causality between these two Side 31 av 45

PValue

0,56 0,08 0,18 0,16 0,01 0,07 0,21 0,02 0,14

variables. In the same samples, there was also cointegration between the nickel spot price and 3-month futures prices. This cointegration could first be rejected at the deterministic term, which included an unrestricted constant and a restricted term. The last deterministic model will be applied when the causality between these variables are to be tested. Model 4 was also the same model where the cointegration first could be rejected in the copper cointegration test. Copper spot prices, and 3-month futures prices in the crisis sample, were the only pair of variables that had detection of cointegration with this deterministic model. This means that there should be causality in two bivariate VAR’s in the full sample, and causality in three bivariate VAR’s in the crisis sample. Which way the causality goes, or if its bidirectional, is still unknown and should be uncovered by the Granger causality analysis later (Granger, 1988). It is not surprising that cointegration was found between spot price and the lowest maturity futures rather than higher maturity futures. This is because lower maturity futures seem to have a stronger relationship with the spot than higher maturity futures. It seems that for cointegration to be between spot and higher maturity futures there has to be cointegration between spot and lower maturity futures. Since the other variables are not cointegrated, it is difficult to say anything about their direction of causality. There could be evidence of no causality, unidirectional causality or bidirectional. The only thing that can be said is that the causality effect is in the short-run when there is no cointegration.

Granger Causality Test After testing for stationarity, finding the optimal lag length and deterministic terms, and testing for cointegration, the Granger causality test can be performed. The purpose of this test is to examine if lagged values of one variable can predict another variable (Verbeek, 2012). In this case to see if spot prices can help predict futures prices, and if futures prices can help predict spot prices. The null hypothesis of this test is that spot/futures “does not Granger cause” futures/spot. If this null hypothesis is rejected, it can be said that the past values of one variable can help predict the value of the other variable. The standard Granger causality test can be represented as such: 𝑛

𝑞

𝑋𝑡 = 𝛼0 + ∑ 𝛼𝑖 𝑋𝑡−𝑖 + ∑ 𝛽𝑗 𝑌𝑡−𝑗 + 𝜀𝑋,𝑡 𝑖=1

𝑗=1

𝑛

𝑞

𝑌𝑡 = 𝛽0 + ∑ 𝛼𝑖 𝑋𝑡−𝑖 + ∑ 𝛽𝑗 𝑌𝑡−𝑗 + 𝜀𝑦,𝑡 𝑖=1

𝑗=1

Where X and Y are stationary variables, in our case the spot prices and futures prices. m and n are the lag lengths for the variables. The null hypothesis can be represented by H 0: β1= …βj = 0 and the alternative hypothesis H1 : βj ≠ 0. If all the β-coefficients are insignificant, then “Y does not Granger cause X”, and if one β-coefficient is significant the null hypothesis is rejected, and “Y Granger causes X”. When testing for whether “X Granger causes Y”, the null hypothesis and the alternative hypothesis focuses on the αi rather than the βi. This test follows a standard F-distribution with (n, T-n-q-1) degrees of freedom. Side 32 av 45

The standard Granger causality model assumes stationarity in the variables. All the variables in this analysis are non-stationary variables. To make the variables stationary, they are to be used in the first-order difference. This is to avoid spurious regressions which can lead to results that shouldn’t be taken seriously. When X and Y are non-stationary I(1) variables, the εt also becomes a non-stationary I(1) variable. This makes the residuals highly autocorrelated, and can make the results useless. But because lagged values of the dependent and independent variable are used in this regression, the problem of spurious regressions disappears (Verbeek, 2012). On that basis, the variables in the regression will be used in levels, since past values of both variables are included. Now that the problem with stationarity is resolved, a discussion about the cointegration is appropriate. According to Granger (1988), if X and Y are both I(1) but cointegrated, an “error-correction” model (VECM) should be applied. Since there is cointegration between the variables, there is a long-run relationship between them and a unidirectional causality should at least be present. Five of the bivariate VAR’s have cointegration, while the rest don’t have cointegration, and therein lies the problem. To estimate the cointegrated model correctly, Granger (1988) suggest using a VECM model, but what about the other bivariate VAR’s that are not cointegrated? If the unrestricted VAR is used on those who are not cointegrated, and the VECM model is used on those who are cointegrated, there seems to be a “pretesting bias” in our analysis. The VECM test is performed conditional on the outcome of the cointegration test. In an optimal situation, every bivariate VAR should be cointegrated or not cointegrated to avoid the notion of pretesting bias. But since there are some bivariate VAR’s with cointegration and some without cointegration in this case, the situation is a bit difficult. The author decided to test the five cointegrated bivariate VAR’s with the VECM, and the not cointegrated bivariate VAR’s with the unrestricted VAR model. Since cointegration is concerned with the long-run, and the causality is concerned with the short-run forecastability, the author finds it important to include an error correction term so that the model isn’t misspecified. Failure to include an error correction term in a cointegrated bivariate VAR, could lead to loss of forecastability and make the tester reach incorrect conclusions about the causality (Granger, 1988). The use of both VECM and unrestricted VAR can also illustrate some of the pre-testing drawbacks with the standard Granger causality test. The VECM can be represented by these equations: 𝑛

𝑛

𝑛

𝛥𝑋𝑡 = 𝛼0 + ∑ 𝛼1𝑖 𝛥𝑋𝑡−𝑖 + ∑ 𝛼2𝑖 𝛥𝑌𝑡−𝑖 + ∑ 𝛼3 𝐸𝐶𝑡−𝑛 + 𝜀𝑖 𝑖=1 𝑛

𝑖=1

𝑖=1

𝑛

𝑛

𝛥𝑌𝑡 = 𝛼0 + ∑ 𝛼1𝑗 𝛥𝑋𝑡−𝑗 + ∑ 𝛼2𝑗 𝛥𝑌𝑡−𝑗 + ∑ 𝛼3 𝐸𝐶𝑡−𝑛 + 𝜀𝑗 𝑗=1

𝑗=1

𝑗=1

The error correction term takes account for the cointegration, and if this term is significant, there is evidence of a long-run effect. Since there is cointegration and no need for the VECM if the error correction term is insignificant, the long-run effect is evident. The focus of this Side 33 av 45

paper is the causality, i.e. the short-run forecastability. The null hypothesis is now that H0: α21….α2i = 0 and H0: α11 …..α1j = 0. Whilst the alternative hypothesis is H1: α2i ≠0 and H1: α1j ≠ 0. The deterministic term is also included in the VECM for the respective bivariate VAR’s. When testing the aluminium variables, a restricted constant is included, while an unrestricted constant and a restricted trend is included when testing the copper and nickel variables. Both the VECM and the unrestricted VAR model, is tested through a block exogeneity test. This test makes spot/futures the dependent variable, and tests whether the lags of the excluded variable; futures/spot, have an effect on the dependent variable. This test is a Wald test and therefore follows a standard chi-squared distribution with n degrees of freedom.

Modified Granger Causality Test If economic variables, like spot prices and futures, are integrated or cointegrated, they may not be applicable in test for VAR’s in levels. As previously discussed, we can estimate the VAR in first-order differences, so that the asymptotic theory is valid for the VAR testing. And when it comes to cointegration, it is the aforementioned specification of an error correction model. Because it is difficult to know in advance whether variables are integrated, cointegrated or stationary, tests for this is required before estimation of the VAR model can start (Toda & Yamamoto 1995). But since there can be drawbacks with these pre-tests, a different approach has been proposed by Toda and Yamamoto (1995). As seen in the start of this chapter, unit root/stationarity tests were performed. A clear indication of non-stationarity in the variables was found, but according to Toda and Yamamoto (1995), these tests can lack power against the hypothesis of stationarity. Also when moving onto the cointegration test, there can be some drawbacks. The Johansen cointegration test can be very sensitive to nuisance parameters in finite samples, and therefore sample sizes, which are often used with economic time series, can make the test unreliable. Again the notion of pre-test biases enters. We perform a test conditioned on whether our variables are non-stationary or/and cointegrated, like in first-order difference when non-stationarity exists, and VECM when cointegration exists. This modified Granger causality test, proposed by Toda and Yamamoto (1995) ,circumvents the notion of pre-test biases and has a more robust approach to the integration and cointegration “problems” of the standard Granger causality test (Toda & Yamamoto, 1995). The idea behind this approach is to first choose a maximum order of integration, dmax. If one time series is believed to be I(1), dmax = 1. If one time series is believed to be I(2), dmax = 2. Economic time series, like spot and futures prices, are often I(1) processes, but this can be cross-checked by applying unit root/stationarity tests, like the one in the start of this chapter. Then the optimal lag length has to be found. This is done as described earlier in this chapter, and denoted by n. When specifying the VAR model, additional lags of dmax should be added to both of the variables in the equations. In the testing procedure, these additional lags should be put as exogenous variables, and thereby ignored in the Wald-test. This is done to ensure that the model is asymptotically distributed as chi-squared with the normal degrees of freedom (Toda & Yamamoto, 1995). Side 34 av 45

The VAR models proposed by Toda and Yamamoto (1995), can be represented as such: 𝑛

𝑑𝑚𝑎𝑥

𝑛

𝑑𝑚𝑎𝑥

𝑋𝑡 = 𝛼0 + ∑ 𝛼1𝑖 𝑋𝑡−𝑖 + ∑ 𝛼2𝑗 𝑋𝑡−𝑗 + ∑ 𝜙1𝑖 𝑌𝑡−𝑖 + ∑ 𝜙2𝑗 𝑌𝑡−𝑗 + 𝜀1𝑡 𝑖=1

𝑗=𝑘+1

𝑖=1

𝑗=𝑘+1

𝑛

𝑑𝑚𝑎𝑥

𝑛

𝑑𝑚𝑎𝑥

𝑌𝑡 = 𝛽0 + ∑ 𝛽1𝑖 𝑋𝑡−𝑖 + ∑ 𝛽2𝑗 𝑋𝑡−𝑗 + ∑ 𝛿1𝑖 𝑌𝑡−𝑖 + ∑ 𝛿2𝑗 𝑌𝑡−𝑗 + 𝜀2𝑡 𝑖=1

𝑗=𝑘+1

𝑖=1

𝑗=𝑘+1

The null hypothesis of no Granger causality from futures (Y) on spot (X) is that φ11….φ1i = 0, and the alternative hypothesis of Granger causality is φ1i ≠ 0. While from spot (X) on futures (Y), the null is that β11….β1i = 0, and the alternative that β1i ≠ 0. This is a modified Wald test, so it follows the chi-squared distribution with n degrees of freedom. The Wald statistics from every test will then be compared to the critical values of the standard χ2-distribution with n degrees of freedom. Every Granger causality test is done through a Block Exogeneity Wald test. This test will estimate a chi-squared statistic (Waldstatistic), which will be compared to the critical values at the 10%, 5% and 1% significance level. The null hypothesis is rejected when the Wald statistic is higher than the critical value, and then it can be concluded that spot/futures “Granger causes” futures/spot.

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Chapter 5: Granger Causality & Modified Granger Causality Test First, the standard Granger causality analysis is performed. The bivariate VAR’s with cointegration is tested with a VECM, and with their respective deterministic terms. The bivariate VAR’s without cointegration is tested in levels and with an unrestricted VAR model. Testing them in first-order difference was considered, but since lagged values of both variables are included in the regression, the error term εt is I(0), and thus there are no spurious regression problems. Subsequently, the modified Granger causality analysis, proposed by Toda and Yamamoto (1995), is performed. This is also done through an unrestricted VAR, but an extra lagged value for both variables are included as exogenous variables. These chi-squared statistics (Wald-statistics) are then compared to the critical values at the 10%, 5% and 1% significance level. This is done to see how strong the rejection of null is. A rejection of the null at the 10% significance level will not make the conclusion of Granger causality, because it is too weak. If the chi-squared statistic exceeds the critical values, the null hypothesis of “No Granger causality” is rejected. If the chi-squared statistic is lower than the critical values, the null hypothesis of “No Granger Causality” can’t be rejected.

Full Sample As seen in figure 12, the first bivariate VAR between the aluminium spot price and 3-month futures price, there is cointegration. This should mean that there at least should be unidirectional causality between them (Granger, 1988). “On some occasions, causation could be present, but would not be detected by the testing procedures used. This problem only arises when the series are I(1) and cointegrated, but this could be a common situation when causality questions are asked”. This quote from Granger (1988) depicts this situation. When cross-checking with the modified Granger causality test, there doesn’t seem to be any causation between them, i.e. no cointegration. This evidence of cointegration and no causation can be due to the drawbacks of the Johansen cointegration test stated by Toda and Yamamoto (1995). On the basis of the statistics that are provided, the conclusion has to be that there is no causality between aluminium spot prices and 3-month futures prices.

Figure 12: Full Sample Analysis

(If some numbers are difficult to read, it is referred to in Appendix F)

* H0 is rejected at the 10% significance level ** H0 is rejected at the 5% significance level *** H0 is rejected at the 1% significance level Side 36 av 45

Between aluminium spot prices, and 15-month futures prices, there is no cointegration. This means that the causality can be unidirectional, bidirectional, or no causation at all. In this case, there is no causation detected by the standard Granger causality test, but a unidirectional causality in the modified Granger causality test. Both on the 10% and 5% significance level, the null hypothesis that futures prices do not “Granger cause” spot prices is rejected. This is evidence that past values of 15-month futures have a short-run relationship with the spot price, and could help predict the price of the spot (Verbeek, 2012). In the last bivariate VAR of aluminium, there is some causation between the variables. The standard Granger causality analysis shows that there is bidirectional causality between the variables. This implies that the spot “Granger causes” futures, while the futures also “Granger causes” the spot. Past values of spot/futures can help predict the current value of futures/spot. The modified Granger causality test only replicates the causality from futures on spot price. Since the modified Granger causality is preferred, it can only be concluded that there is causality from futures to the spot price. When looking at the bivariate VARs concerning the copper variables, there is no cointegration. The standard Granger causality test replicates every result that the modified Granger causality estimates. Between copper spot prices and 3-month futures, there is bidirectional causality at the 10% significance level. But only a unidirectional causality from futures on spot at the 5% significance level. It is worth noting that the null hypothesis of spot “does not Granger cause” futures would have been rejected at the 5% significance level if the p-value approach was used. Still the conclusion is that there is only a unidirectional causality from futures on spot. At 15-month copper futures and 27-month copper futures there is the same relationship as at 3-month futures. The null of no Granger causality is strongly rejected from futures to spot. The conclusion can then be that every copper futures can help predict the value of the spot. All the nickel bivariate VARs had an optimal lag length that was at the maximum lag length. Part of the reason for this is that the majority of information criteria included the AIC and the FPE. These two information criterion from Akaike tends to favour an overestimation of the true lag order (Clarke & Mirza, 2004). Between the spot price and 3-month futures, there was cointegration, so a VECM was applied, which included an unrestricted constant and a restricted term. The results were nearly identical to the ones produced by the modified Granger causality test. The null hypothesis was rejected on every significance level, so there is strong evidence of bidirectional causality between the nickel spot prices and 3-month nickel futures. In this case, the notion that cointegration is equal to causation was confirmed. In the next two bivariate VAR’s, the results are somewhat contradicting. The results from the modified test are that there are no causality between the spot price and the futures, while the standard test gave evidence of bidirectional causality. Because there is no cointegration between the two pairs, it seems like the large number of lags made the statistics relatively high. Still the modified Granger causality test is preferred, so no causation between spot prices and 15- and 27-month futures prices exists.

Side 37 av 45

Pre-crisis Sample The pre-crisis sample was created to see if the financial crisis had made a difference in our results. One of the most apparent differences from the full sample test is that there weren’t a single bivariate VAR with cointegration. Another difference in the pre-crisis sample is that the optimal lag lengths are low compared to the full sample. This is most likely due to the relatively small sample size. In the test for causality between the aluminium spot price and the futures, there wasn’t any sign of causation. Every null hypothesis couldn’t be rejected, and therefore past futures/spot prices couldn’t help predict spot/futures prices in this sample period. The years of financial crisis made a difference when looking at the causality between aluminium spot prices and aluminium futures prices.

Figure 13: Pre-Crisis Sample (18.01.06 – 15.09.08) 18.01.06-15.09.08 Observations: 694 Information Commodity: Bivariate VAR Lags Criteria Aluminium Spot-F3 1 FPE, AIC, BIC, HQC Aluminium Spot-F15 1 LR, FPE, AIC, BIC, HQC Aluminium Spot-F27 1 LR, FPE, AIC, BIC, HQC Copper Spot-F3 2 LR, FPE, AIC, HQC Copper Spot-F15 2 FPE, AIC, BIC, HQC Copper Spot-F27 2 LR, FPE, AIC, BIC, HQC Nickel Spot-F3 2 LR, BIC, HQC Nickel Spot-F15 2 LR, FPE, AIC Nickel Spot-F27 5 LR, FPE, AIC

Standard Wald Test Modified Wald Test Critical Value Cointegration Futures GC Spot Spot GC Futures Futures GC Spot Spot GC Futures χ2-distribution rank Test Stat P-value Test Stat P-value Test Stat P-value Test Stat P-value 10 % 5% 0 0,580 0,446 0,241 0,624 0,291 0,590 0,037 0,848 0,00 3,84 0,00 5,02 0 0,142 0,706 0,668 0,414 1,178 0,278 0,048 0,827 0,00 3,84 0,00 5,02 0 0,026 0,873 1,179 0,278 1,972 0,160 0,266 0,606 0,00 3,84 0,00 5,02 0 4,443 0,108 3,007 0,222 7,298* 0,026 5,786 0,055 0,10 5,99 0,05 7,38 0 8,165** 0,017 1,172 0,557 10,446** 0,005 2,845 0,241 0,10 5,99 0,05 7,38 0 12,569*** 0,002 0,019 0,991 13,564*** 0,001 0,225 0,894 0,10 5,99 0,05 7,38 0 7,433** 0,024 4,692 0,096 8,501** 0,014 3,270 0,195 0,10 5,99 0,05 7,38 0 5,925 0,052 5,665 0,059 1,981 0,371 2,887 0,236 0,10 5,99 0,05 7,38 0 4,681 0,456 6,508 0,260 0,350 0,997 3,274 0,658 1,15 11,07 0,83 12,83

1% 0,00 0,00 0,00 0,01 0,01 0,01 0,01 0,01 0,41

(If some numbers are difficult to read, it is referred to in Appendix G)

* H0 is rejected at the 10% significance level ** H0 is rejected at the 5% significance level *** H0 is rejected at the 1% significance level In the copper part of the test, there is more similarity to the full sample test. Between the spot price and 3-month futures, there was some causality detected at the 10% significance level. The causation was detected from futures to spot in the modified Granger causality test. This was also one of those cases where the null is not rejected at the 5% significance level with the critical value approach, but would have been rejected with the p-value approach. Ultimately, causality between the copper spot price and 3-month copper futures is rejected. Between the spot price and 15-month copper futures, there is stronger evidence of causality. This is a causality that says “futures Granger causes spot”. Here the null hypothesis is rejected at the 5% significance level, and the conclusion of causality from futures to spot could be made. In the last bivariate VAR for copper, there is strong evidence for the same causality. The null hypothesis was rejected at the 1% significance level, both in the standard and the modified Granger causality test. In other words, there is strong evidence that 15- and 27-month futures prices “Granger cause” spot prices before the financial crisis. Between the nickel variables in the pre-crisis sample, causality was only detected in the first bivariate VAR. Again the direction of causality was from futures to spot. Side 38 av 45

7,88 7,88 7,88 10,60 10,60 10,60 10,60 10,60 16,75

Crisis Sample Since the test is performed with a sample before the financial crisis, the test with the sample during the financial crisis, until the sample end, had to be performed. This was a much larger sample size, thus it was expected that the results from the full sample would be replicated in this sample period. The optimal lag lengths are very similar to the ones in the full sample, with the exception of the nickel bivariate VAR’s. In the crisis sample, the optimal lag lengths for nickel spot 15-month futures, and nickel spot-27-month futures, were considerably lower than in the full sample test. The cointegration between aluminium and nickel spot prices and 3-month futures was also replicated in the crisis sample. In addition to these two cointegrated bivariate VAR’s, the copper spot and 3-month futures are also cointegrated. In the other copper samples, there were signs of cointegration in models 2 and 3, but it was rejected in model 4. In the crisis sample, the null of no cointegration could be rejected for copper with the fourth deterministic model.

Figure 14: Crisis Sample (16.09.08 – 01.18.16) 16.09.08-18.01.16 Observations: 1915 Information Commodity: Bivariate VAR Lags Criteria Aluminium Spot-F3 3 LR, FPE, AIC, HQC Aluminium Spot-F15 3 LR, FPE, AIC, HQC Aluminium Spot-F27 2 LR, FPE, AIC, BIC, HQC Copper Spot-F3 5 LR, FPE, AIC Copper Spot-F15 3 LR, FPE, AIC Copper Spot-F27 2 LR, FPE, AIC, BIC, HQC Nickel Spot-F3 5 FPE, AIC Nickel Spot-F15 1 FPE, AIC, BIC, HQC Nickel Spot-F27 2 LR, FPE, AIC

Standard Wald Test Modified Wald Test Critical Value Cointegration Futures GC Spot Spot GC Futures Futures GC Spot Spot GC Futures χ2-distribution rank Test Stat P-value Test Stat P-value Test Stat P-value Test Stat P-value 10 % 5% 1% 1 1,433 0,698 1,872 0,600 3,367 0,339 4,542 0,209 0,35 7,82 0,22 9,35 0,07 12,84 0 5,603 0,133 6,250 0,100 2,592 0,459 2,415 0,491 0,35 7,82 0,22 9,35 0,07 12,84 0 5,250 0,072 4,487 0,106 2,649 0,266 0,189 0,910 0,10 5,99 0,05 7,38 0,01 10,60 1 10,219 0,069 9,896 0,078 8,053 0,153 7,798 0,168 1,15 11,07 0,83 12,83 0,41 16,75 0 8,767* 0,033 6,970 0,073 11,072** 0,011 8,836* 0,032 0,35 7,82 0,22 9,35 0,07 12,84 0 9,633** 0,008 7,149* 0,028 8,081** 0,018 4,156 0,125 0,10 5,99 0,05 7,38 0,01 10,60 1 11,592* 0,041 11,633* 0,040 13,467** 0,019 13,376** 0,020 1,15 11,07 0,83 12,83 0,41 16,75 0 9,374*** 0,002 10,126*** 0,002 4,326* 0,038 4,710* 0,030 0,00 3,84 0,00 5,02 0,00 7,88 0 11,136*** 0,004 12,029*** 0,002 7,556** 0,023 7,862** 0,020 0,10 5,99 0,05 7,38 0,41 16,75

(If some numbers are difficult to read, it is referred to in Appendix H)

* H0 is rejected at the 10% significance level ** H0 is rejected at the 5% significance level *** H0 is rejected at the 1% significance level Even with more lags and a cointegrated bivariate VAR, the causality results for aluminium gives actually the same conclusions as in the pre-crisis sample. There is no evidence of Granger causality between any of the spot prices and the futures, even in the cointegrated VAR that should imply causation. This problem was also encountered in the full sample, so at least it is a consistent problem. On the basis of the results in the modified Granger causality test, which also couldn’t reject the null hypothesis, aluminium spot prices and 3-month futures shouldn’t be cointegrated. This could be due to the problem with Johansen’s cointegration test and economic series as stated in the full sample analysis. Moving on to the copper variables, the first bivariate VAR, which is cointegrated, should have some causality. But, as with aluminium, there is no sign of causality either in the direction between copper spot prices and 3-month futures in the crisis sample. The fact that only three out of five cointegrated bivariate VAR’s doesn’t show any causality should be evidence of some of the drawbacks with using the standard Granger causality method. In the other VARs for copper, there is evidence of causality. Between the spot and 15-month futures, there is evidence at the 5% significance level that 15-month futures “Granger causes” spot. There is also some evidence that spot “Granger causes” 15-month futures at the 10% significance level, but this is rejected due to the weakness. Side 39 av 45

Still it is worth noting that the null hypothesis of spot “does not Granger cause” 15-month futures, would have been rejected at the 5% significance level if the p-value approach was applied. As in every sample period for copper, there is evidence that 27-month futures “Granger causes” spot. The nickel bivariate of spot and 3-month futures is the only cointegrated VAR in the crisis sample that follows Granger (1988) statement that cointegration should imply causality. Not only is there causality, but it is actually bidirectional. Therefore it can be concluded that the past values of the nickel spot prices helps predict the value of 3-month nickel futures, and that past values of 3-month nickel futures help predict the value of the nickel spot prices. In the last two bivariate VAR’s of nickel, there is less lags compared to the pre-crisis sample and the full sample. In the standard Granger causality test, a bidirectional causality is evident at the 1% significance level for both 15-month and 27-month nickel futures. In the modified Granger causality test, there isn’t any sign of causality between spot prices and 15- and 27month futures in the previous samples. But in the crisis-sample there are. At the 10% significance level, bidirectional causality is evident between the spot price and 15-month futures. As earlier stated, a rejection of the null at the 10% significance level can’t be concluded on, but is worth noting. It is also worth noting that these could have been concluded at the 5% significance level if the p-value approach was used. The last bivariate VAR between the nickel spot price and 27-month futures also has a bidirectional causality. The standard Granger causality test shows very strong evidence of this bidirectional causality, while the modified Granger causality test only rejects the null of no causality at the 5% significance level. Then the conclusion is that nickel spot “Granger causes” 27-month futures, and the 27-month nickel futures “Granger causes” the nickel spot, in the crisis sample.

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Conclusion In this paper, spot prices and 3-, 15- and 27-month futures prices for three industrial metals are used to examine whether speculation can have an effect on the spot prices. The time frame for this analysis is from the 18th of January 2006 until 18th of January 2016, and includes 2609 observations. To investigate whether speculation can have its effect on the spot price, the Granger causality test was applied. Because there are some drawbacks to the standard Granger causality, a modified Granger causality test was also applied. Both tests estimate Wald-statistics, which can determine the direction of the causality. There can be no causality, unidirectional causality or bidirectional causality. For speculation to have its effect on spot prices there has to be causality from futures to spot. No causality or causality in both directions is not sufficient evidence that speculation can have its effect on the spot. In addition to our full sample analysis, two sub-samples were created. The first sub-sample examined if there was any effect from speculation before the financial crisis in the years from 2006 until 2008. The second sub-sample examined the effects during the financial crisis in the years 2008 until 2016. The results from the analysis were in favour of an effect from speculation on the industrial metals market. In the aluminium market, there was only evidence that futures prices “Granger causes” spot price. There was no evidence of this causality in the sample period before the financial crisis or in the sample during the financial crisis. The full sample period estimated evidence for a Granger causality that went from futures to spot prices. Both 15month and 27-month aluminium futures showed evidence that they “Granger cause” the spot price. This means that 15- and 27-month aluminium futures can help predict the current aluminium spot price. It is difficult to say whether this is because of speculation, or just expectations about the future of aluminium. Still it can be concluded that speculation in 15- and 27-month aluminium futures can be one of the main causes of the fluctuations in aluminium price. Since causality is mostly concerned with the short-run, the effect of speculation can only be concluded in the short-run. With copper, there was causality from 15- and 27-month futures to spot prices in all of the samples. In the full sample, the evidence was so strong that the null hypothesis of no causality could be rejected at the 1% significance level. The weak evidence of causality from 3-month copper futures to copper spot prices only became stronger in the full sample, even when it had disappeared during the financial crisis. On that basis, it can be concluded that copper futures help predict the current copper spot prices independently of the contract's maturity. Like aluminium, it can also be concluded that speculation can be a main cause of the copper price fluctuations in the short-run. The only difference here is that every future, independent of maturity, “Granger causes” the spot.

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Before the financial crisis, there was evidence that speculation in 3-month futures could be a main cause for the fluctuations in nickel prices. This unidirectional causality became bidirectional causality during the financial crisis. In the full sample, there was only causality between spot prices and 3-month nickel futures. Since the causality in the full sample is bidirectional, speculation cannot be concluded as a main reason for the nickel price fluctuations. Because nickel spot “Granger causes” 3-month nickel futures, and 3-month nickel futures “Granger causes” spot, speculation can only be said to affect the nickel price like any other fundamental factor. Therefore, the conclusion can’t be that speculation is a main cause for the nickel price fluctuations. Speculation can only affect the nickel price like any other fundamental factor. When comparing the two tests against one another, they seem to produce many identical results. Many of the same conclusions can be drawn from both the standard Granger causality test, and the modified Granger causality test. The main concern with the standard Granger causality test is whether the results are trustworthy. The modified Granger causality test is easier, more efficient, and circumvents all the notions of pre-test bias. When time series are suspected of being non-stationary, and/or cointegrated, the modified Granger causality test, proposed by Toda and Yamamoto (1995), is superior to the standard Granger causality test. The lack of cointegration between many of the variables was something that was very surprising. It was expected that there should have been cointegration in every bivariate VAR since spot prices and futures develop together over time. It was also surprising that only two of the five cointegrated bivariate VAR’s had evidence of causality. Cointegration should imply some causality, and the lack of causality should be evidence of the drawbacks with the Johansen cointegration test. It is also evidence of the advantages with the modified Granger causality test, where a cointegration test doesn’t need to be applied. An extension of this analysis could be to do it recursively. That approach could give more cointegration between the variables, and stronger results in the Granger causality test. Then a stronger conclusion of the long-run effect from speculation could be drawn.

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References Books: Brooks, C. (2008): Introductory econometrics for finance. 2 ed., Cambridge University Press, New York Clark, Iain J.(2004): Commodity Option Pricing; A Practitioner’s Guide. Somerset, GB: Wiley. CRB Encyclopedia 2015 CRB 2015 Yearbook Fabozzi, F.J., Füss, R., Kaiser D.G. (2008): The Handbook of Commodity Investing, Wiley & Sons. Verbeek, M. (2012): A Guide to Modern Econometrics. 4th edition, Wiley & Sons

Articles: Clarke, J.A. and Mirza, S. (2004): “A comparison of some common methods for detecting Granger noncausality”, Journal of Statistical Computation and Simulation Vol. 76, No. 3, March 2006, 207–231. Dickey, D. A. and W. A. Fuller (1979): “Distribution of the estimators for autoregressive time series with a unit root”, Journal of the American statistical association, 74(366a), 427-431. Elliott G., Rothenberg T. and Stock J. (1996): Efficient tests for an autoregressive unit root", Econometrica 64, pp. 813-836. Engle, R. F. and C. W. Granger (1987): “Co-integration and error correction: representation, estimation, and testing” Econometrica: Journal of the Econometric Society, 251-276. Granger, C.W. (1969): “Investigating Causal Relations by Econometric Models and Crossspectral Methods”, Econometrica, Vol. 37, No. 3. pp. 424-438. Granger, C. W. (1988): “Some recent development in a concept of causality”, Journal of econometrics, 39(1), 199-211. Juselius, K. (2005): The cointegrated VAR model: methodology and applications, Advanced Texts in Econometrics, Oxford University Press Inc., New York. Johansen, S. (1991): “Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models”, Econometrica: Journal of the Econometric Society, 15511580. Johansen, S. (1992). Determination of cointegration rank in the presence of a linear trend, Oxford Bulletin of Economics and Statistics 54: 383–397 Side 43 av 45

John M. Keynes, A Treatise on Money (London: Macmillan, 1930). Kwiatkowski D., Phillips P.C.B., Schmidt P. and Shin Y. (1992),: “Testing the null hypothesis of stationarity against the alternative of a unit root.", Journal of Econometrics 54, pp. 159-178. Phillips P.C.B. and Perron P. (1988): “Testing for a unit root in time series regression", Biometrika 75, pp. 335{346. Toda H.Y. and Yamamoto T. (1995), “Statistical inferences in vector autoregressions with possibly integrated processes", Journal of Econometrics 66(1-2), pp. 225-250.

Web-pages: Alumniumleader.com: http://www.aluminiumleader.com/economics/world_market/ World-aluminium.org: http://www.world-aluminium.org/statistics/ International Copper Study Group, The World Copper Factbook 2015: http://www.icsg.org/index.php/component/jdownloads/viewdownload/170/2092 INSG: International Nickel Study Group: http://www.insg.org/stats.aspx http://www.insg.org/docs/INSG_Sample_World_Ni_Stats_Yearbook.pdf http://unctad.org/meetings/en/Presentation/SUC_MYEM2013_20032013_Don%20SMALE.p df LME Aluminium: https://www.lme.com/en-gb/metals/non-ferrous/aluminium/contractspecifications/futures/ LME Copper: https://www.lme.com/en-gb/metals/non-ferrous/copper/contract-specifications/futures/ LME Nickel: https://www.lme.com/en-gb/metals/non-ferrous/nickel/contract-specifications/futures/ Metal.com: http://www.metal.com/newscontent/65860_world-nickel-output-and-utilization-toincrease-in-2015-says-insg

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USGS Aluminium, 2011, 2014: http://minerals.usgs.gov/minerals/pubs/commodity/aluminum/myb1-2011-alumi.pdf http://minerals.usgs.gov/minerals/pubs/commodity/aluminum/myb1-2014-alumi.pdf USGS Copper, 2009, 2010, 2011, 2013: http://minerals.usgs.gov/minerals/pubs/commodity/copper/myb1-2009-coppe.pdf http://minerals.usgs.gov/minerals/pubs/commodity/copper/myb1-2010-coppe.pdf http://minerals.usgs.gov/minerals/pubs/commodity/copper/myb1-2011-coppe.pdf http://minerals.usgs.gov/minerals/pubs/commodity/copper/myb1-2013-coppe.pdf USGS Nickel, 2007, 2008, 2010, 2013, 2014, 2015, 2016: http://minerals.usgs.gov/minerals/pubs/commodity/nickel/nickemcs07.pdf http://minerals.usgs.gov/minerals/pubs/commodity/nickel/mcs-2008-nicke.pdf http://minerals.usgs.gov/minerals/pubs/commodity/nickel/mcs-2010-nicke.pdf http://minerals.usgs.gov/minerals/pubs/commodity/nickel/mcs-2013-nicke.pdf http://minerals.usgs.gov/minerals/pubs/commodity/nickel/mcs-2014-nicke.pdf http://minerals.usgs.gov/minerals/pubs/commodity/nickel/mcs-2015-nicke.pdf http://minerals.usgs.gov/minerals/pubs/commodity/nickel/mcs-2016-nicke.pdf

Data: Datastream, Thompson Reuters Eviews

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