Dependence Structures between Commodity Futures and Corresponding Producer Indices across Varying Market Conditions : A cross-quantilogram approach

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Linköping University | Department of Management and Engineering Master’s thesis, 30 credits | Master’s programme in Economics - Financial economics Spring 2020 | LIU-IEI-FIL-A--20/03399--SE

Dependence Structures

between Commodity

Futures and Corresponding

Producer Indices across

Varying Market Conditions

– A cross-quantilogram approach

Elin Borg

Ilya Kits

Supervisor: Gazi Salah Uddin

Linköpings universitet SE-581 83 Linköping, Sverige 013-28 10 00, www.liu.se

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Title:

Dependence Structures between Commodity Futures and

Corresponding Producer Indices across Varying Market Conditions - A cross-quantilogram approach Authors: Elin Borg elibo980@student.liu.se Ilya Kits iljki158@student.liu.se Supervisor:

Gazi Salah Uddin

Publication type:

Master’s Thesis in Economics

Master’s Programme in Economics at Linköping University Advanced level, 30 credits

Spring semester 2020

ISRN Number: LIU-IEI-FIL-A--20/03399--SE Linköping University

Department of Management and Engineering (IEI) www.liu.se

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Abstract

This thesis examines the dependence structures between commodity futures and corresponding commodity producer equity indices in bearish, bullish and normal market conditions. We study commodity futures and producer indices in the energy, precious metals, gold and agriculture commodity markets using daily return data that ranges from 16 December 2005 to 28 June 2019. We employ the cross-quantilogram approach developed by Han et al. (2016) to examine dependence structures in the full quantile range, which represents different market states. Furthermore, we control for different lag structures, uncertainties and time-varying dependence structures. From our results we conclude the following: 1) There are time-varying asymmetric and symmetric dependencies in different commodity markets. There is asymmetric dependence between commodity futures and producer indices in the precious metals, gold and agricultural markets. In the oil market, the relationship is symmetrical. No relationship is found in the natural gas market. 2) Heterogenous dependence structures are identified in the gold, precious metals and agricultural commodity markets. The oil market uncovers homogenous dependence structures. 3) The observed spillover in all markets occur in the very short run, at one day, and dissipates after a week and additionally after a month. Our results provide new information regarding commodity diversification attributes which can be useful to investors. Our results also provide important policy implications: Since volatility spillovers between commodity futures and producer indices may deter investors from including commodities in their portfolios, as they might lose their diversifier qualities, it is important to enforce policies that will prevent the spillovers between the assets. Further, regulations of the commodity futures markets could be an alternative to reduce the spillovers.

Key words: Commodity futures contracts, Commodity producer index, Cross-quantilogram,

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Acknowledgements

First, we would like to thank our supervisor Gazi Salah Uddin for his guidance and support during the writing of this thesis. We would also like thank David Stenvall and Samir Cedic for their help related to programming. Lastly, we thank our opponents, Sofia Holmberg and Johanna Näslund, for their valuable comments on earlier versions of this thesis.

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1. Introduction

In 2019, the amount of money invested in commodity futures and commodity options contracts accumulated to 7.22 billion dollars, where Brent crude oil was the most frequently traded commodity futures contract that year (Futures Industry Association, 2020). It is evident that the interest for investing in commodities has grown over recent years and commodities have become a common asset in many investor portfolios. Commodities have traditionally offered attractive diversification opportunities and risk hedging possibilities due to their sometimes low or negative correlations with other portfolio assets (Jensen et al., 2000). However, advancements in market trading technologies and improved information transmissions have led to increased global market integration, which may have challenged the commodities’ portfolio qualities.

The Global Financial Crisis (GFC) in 2008 was a result of increased global financial markets which emanated in increased volatility in not only stock markets but also in commodity markets (Silvennoinen and Thorp, 2013; Creti et al., 2013; Delatte and Lopez, 2013). The increased volatility in the commodity markets during the GFC made researchers question the validity of the diversification argument (Delatte and Lopez, 2013). The vast inflow of investments, also known as financialization, to commodity futures could potentially be a contributing factor to the increased integration among commodities and which may further challenge the commodities’ diversifier aspects (Tang and Xiong, 2010). This study therefore examines the dependence structures between commodity futures and corresponding producer equity indices, which can provide new information that can be useful to investors in regard to commodities’ diversification attributes. Commodity futures contracts are different from other financial assets such as stocks and bonds as they are derivative securities. While stocks involve liability claims on corporations and are used for raising resources for firms, a commodity futures contract on the other hand is an agreement to buy or sell a commodity in the future. The futures contract outlines the exact quantity that should be delivered at a predetermined date to the price that was initially agreed upon when entering the contract. The commodity futures provide insurance to producers by locking in future prices to which the producer is able to sell their commodity. In this way, the producers hedge against price risk and in turn, the investor obtains a risk premium for assuming the risk of future price fluctuations. The price of the commodity futures contract is essentially determined by future expectations of the commodity spot price. Although, there are other drivers that affect the commodity futures price, such as storability alternatives. (Gorton and Rouwenhorst, 2006). Commodities are different from each other as some commodities are storable and some are not, which also makes some commodities more affected by seasons than others (Gorton and Rouwenhorst, 2006). For instance, agricultural commodities are more affected by weather conditions than other commodities since it affects the supply. Metals are often used as intermediate goods and could therefore be more vulnerable to which production process it is needed for (Hull, 2018). The oil market is unique as its supply is mainly decided by the Organization of the Petroleum

Exporting Countries (OPEC) (Dées et al. 2007).

Figure 1 illustrates the yearly total volume of futures contracts in agriculture, energy and precious metals from 2009 to 2018. The figure depicts an increasing trend in total volume of futures contracts, where the energy market outperforms the other two markets. The energy futures market

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has a noteworthy price development with an increase by 350 percent during the years 2009-2018. The metals futures market indicates somewhat stable growth, whereas the agriculture futures market displays dips in investment levels after 2016. The agriculture market obtains the lowest growth rate during 2009-2018, indicating a total increase of only 57 percent.

Figure 1: Total volume of futures contracts in agriculture, energy and precious metals between

2009-2018

Source: Futures Industry Association (FIA).

Figure 2 displays the performance of the corresponding producer equity indices of the energy, agriculture, gold and precious metals commodity sectors. The figure depicts a distinct dip in all producer indices’ price levels after the GFC in 2008. The agriculture index obtains the highest price level and is the only producer index that displays an increasing growth rate. The agriculture producer index has increased by remarkably 260 percent, whereas the other producer indices have decreased in value since 2006. This is an interesting observation to compare to the previous figure which shows that investment in agriculture futures contracts have increased the least out of the commodity futures.

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3 Figure 2: Relative performance of commodities

Note: The figure displays price movements in producer indices in different commodity markets. Index values are represented on the vertical axis. The prices are expressed in USD. Time period is presented on the horizontal axis. Source: Thomson Reuters Datastream (2020).

The increased levels of volatility in both stock markets and commodity markets after the GFC raises suspicion whether the cross-market linkages between the two assets have changed and if there potentially could be signs of a financial contagion. Previous literature has mainly focused on examining the volatility spillover between commodity futures and stock markets, or cross-market linkages between different commodity markets. In general, studies that examine spillovers between commodity futures and stock markets typically apply aggregate stock market indices for measuring equity market performance, like S&P 500 (see Chiou and Lee, 2009; Chang et al., 2013; Delatte and Lopez, 2013; Mensi et al., 2013) and Dow Jones (See Chang et al., 2013; Kartsonakis-Mademlis and Dritsakis, 2018). Another branch of literature has focused on the GFC’s effects on co-movements between assets (Tang and Xiong, 2010; Creti et al., 2013; Delatte and Lopez, 2013; Silvennoinen and Thorp, 2013). Creti et al. (2013), find evidence for time-varying correlations between commodity markets and stock markets, where the GFC showed noticeable impact on the dependency structures.

There is limited literature that investigates the closer relationship between assets within the same commodity sector. Hammoudeh et al. (2004) examines the volatility spillover between crude oil prices and different sector stock indices of the U.S oil industry and find that oil futures transmit volatility to some oil sector stocks. A more recent study by Aurori et al. (2011a), examines the volatility spillovers between crude oil futures and stock markets in Europe and sector stock returns in the U.S. The authors find evidence of bidirectional volatility spillover between crude oil and the

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U.S sector stock returns. However, they find unidirectional spillover between crude oil and European stock markets. Tang and Xiong (2010), examines the price co-movements of indexed and off-indexed commodities by studying 28 commodities and two different commodity indices. The authors find evidence of increased correlation between oil and indexed non-energy commodity futures prices after 2004 and underline that this result can imply that commodity index trading transmits volatility to commodity markets.

The above brief review of literature distinguishes two important research gaps. First, there is no previous literature to our knowledge that specifically examines the dependence structures between commodity futures and corresponding producer equity indices. Neither is there any literature that examines these relationships within the energy, gold, precious metals and agriculture commodity sectors all at once. Second, the previous literature that examines the dependence structures in commodity sectors in different market conditions is scarce. The remaining literature mainly employs different types of dynamic GARCH models to examine the time-varying mean-to-mean dependency structures. However, these types of dynamic models disregard the complete correlation structures since they are unable to assess the tail dependencies. The purpose of this thesis is to examine the dependence structures between commodity futures and corresponding commodity producer equity indices in bearish, bullish and normal market conditions. We study commodity futures and producer indices in the energy, precious metals, gold and agriculture commodity markets.

We use the cross-quantilogram approach developed by Han et al. (2016) in order to accomplish the purpose of this study. This method allows for dependency and directionality analysis between commodity futures and their corresponding producer indices when they are in different quantiles, which essentially represents different market states. We examine the quantile dependencies at 1, 5 and 22 lags, which represents the time horizons of one day, one week and one month. To robustness test our results, we apply the partial cross-quantilogram which allows for the inclusion of economic policy and equity market uncertainty as control variables. We further estimate rolling window samples to examine if the dependence structures between the commodity futures and the producer indices are time varying.

The results generate three key findings. The first finding is that there are time-varying asymmetric and symmetric dependencies in different commodity markets. There is asymmetric dependence between commodity futures and producer indices in the precious metals, gold and agricultural markets. In the oil market, the relationship is symmetrical. No relationship is found in the natural gas market. The second finding is that heterogenous dependence structures are identified in the gold, precious metals and agricultural commodity markets. The oil market uncovers homogenous dependence structures. The last key finding is that the observed spillover in all markets occur in the very short run, at one day, and dissipates after a week and additionally after a month.

This thesis contributes in numerous aspects. First, it expands the literature that studies the commodity markets. By examining the dependence structures between commodity futures and corresponding producer indices, we are the first to our knowledge to study this relationship. We also contribute to the literature by applying cross-quantilograms to investigate this topic, which has not been observed in many previous studies regarding commodity markets. Second, this thesis

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offers new information regarding commodity markets’ diversifying attributes which can be beneficial to investors. At last, our thesis contributes to policy makers by providing useful information about volatility spillovers between commodity futures and producer indices which could distort price signals to producers. In this way, this new information can provide a framework for regulation of the commodity futures market which may prevent the transmission of risk between these assets.

The remaining part of this thesis is structured as following: section 2 reviews previous literature in the field and section 3 presents the theoretical framework. In section 4, we outline the methodology that is used in this thesis, section 5 discloses data and descriptive statistics. Section 6 presents empirical results and discussion and at last, section 7 presents the conclusions and policy implications.

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2. Literature Review

During the last decade researchers have examined spillovers in the commodity markets through multiple perspectives that can mainly be divided into three research strands. The first strand focuses on commodity index investors impact on integration between stock and commodity markets. The second strand concentrates on dependence structures between commodity markets and equity markets. The last research strand is directed to examining spillovers between different commodity markets. In the review below, we present advancements that have been made within each research strand. We focus on the commodity markets that are of interest namely the energy, gold, precious metals and agriculture markets.

2.1 Commodity index investors’ impact on spillovers between commodity

and equity markets

The financial contagion between commodity markets and equity markets has been researched in numerous aspects. One strand of literature has focused on commodity index investors’ impact on the increased spillovers between commodity markets and equity markets. In a study by Tang and Xiong (2010), the authors find increased integration between different commodities that are included in the two popular commodity indices SP-GSCI and DJ-UBS. They argue that the underlying reason to this result may involve the growing importance of index trading. Delatte and Lopez (2013), extends the analysis by investigating the dependence structures between commodity markets and equity markets using the same commodity indices, SP-GSCI and DJ-UBS, and also four major equity indices S&P500, FTSE100, CAC40, DAX. By using a coupla approach, the authors find time-varying and symmetric dependence structures between commodity markets and equity markets. They further show that these dependencies have increased since the GFC in 2008. Henderson et al. (2012) have found evidence showing return spillover from index investments to futures markets. More specifically, they show that index investments create positive price pressures to futures markets, when they examine trading of new commodity linked notes, which is a form of index investment.

Adams and Glück (2015) examine the underlying reasons behind financialization of commodities and co-movements between commodity markets and stock markets. Their empirical results suggest that the combination of the financial crisis and the behavior of commodity index traders may have amplified the occurrence of risk spillovers between commodity markets and equity markets. This is because in market distress, investors quickly sell off assets in both equity markets and commodity markets in order to rescue their portfolio values. Caporale et al. (2014) support that investor behavior during financial turmoil can cause higher interaction between markets.

2.2 Volatility spillovers between oil prices, natural gas prices and equity

markets

Out of the four commodity markets of interest, it is apparent that a substantial body of literature is directed towards examining the oil market. Yet, there is no consensus in the volatility spillover aspects between the energy market and stock markets. Hammoudeh et al. (2004) study the volatility spillover between five oil futures contracts and five S&P oil sector stock indices using a multivariate generalized autoregressive conditional heteroskedasticity (GARCH) model. Their

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main findings show that future movements in oil futures prices are not affected by oil industry stock indices. Further, the authors find evidence supporting that the oil futures market’s volatility yields volatility-echoing effects on oil exploration company stocks. On a different note, Chang et al. (2009) find no evidence of spillover between WTI future returns and oil company stock returns using a vector ARMA-asymmetric GARCH.

Previous literature also examines the volatility spillover between oil futures and aggregate stock indices. Sadorsky (1999) finds when utilizing an unrestricted vector autoregressive (VAR) model that oil prices movements impact broad-based stock returns. This result is further supported by Aurori et al. (2011b), who find that world oil prices affect stock returns in Gulf Cooperation Council (GCC) countries. They further observe an intensification in volatility spillover between the assets during the financial crisis in 2008. Contrarily, Kirithiga et al. (2018) find evidence of bidirectional risk spillover between crude oil and an Indian benchmarking equity futures index when employing a VAR model. This bidirectional volatility spillover is also discovered in a study by Aurori et al. (2011a) which examines the relationship between crude oil futures and stock markets in Europe and sector stock returns in the U.S. Aurori et al. (2011a) utilize a VAR-GARCH approach and document a bidirectional transmission of volatility between crude oil futures and the U.S sector stock returns and unidirectional spillover from crude oil futures to the European stock markets. Chiou and Lee (2009) find that high fluctuations in oil prices generate asymmetric impacts on S&P500 returns.

The literature that examines the risk spillovers in natural gas generates mixed results. Oberndorfer (2009) applies a GARCH model and find no connection between natural gas returns and energy companies’ stock returns in the Eurozone. Kirithiga et al. (2018) do not find any volatility spillover between natural gas returns an Indian benchmarking equity futures index. On a different note, Zhang et al. (2017) find closer dependence structures between natural gas returns and stock market returns.

Another strand of literature pertaining to the energy market focuses on the impact of speculator capital constraints and producer hedging demand on commodity futures prices. Acharya et al. (2013) use data for crude oil and natural gas futures prices and oil and natural gas producing firms. They construct their own mathematical model that tries to measure producers’ propensity to hedge and how it potentially affects commodity futures prices. Their results indicate that increased levels of hedging by producers could be detrimental to commodity futures prices.

2.3 Spillover effects between gold and equity markets

Thuraisamy et al. (2013) discover bidirectional volatility spillover between gold futures and equity markets in China and the Philippines, when applying a multivariate GARCH model. However, they further observe unidirectional transmission of risk from equity markets in Japan, Sri Lanka and Vietnam to gold futures markets. Mensi et al. (2013) also identify unidirectional volatility spillover from the equity market to the gold market. Their results indicate that the S&P500 explain price movements of the gold price index. In a study by Blose and Shieh (1995) the authors show that gold mining companies’ stocks have a high responsiveness to changes in the gold price. The gold market’s safe haven properties have been examined in a study by Baur and McDermott (2010). In this study, the authors find that gold can be used as a safe haven for equity markets in

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Europe and the U.S. This is further supported by Baur and Lucey (2010), who demonstrate that gold can offer hedging properties to a portfolio of stocks in extreme market conditions.

2.4 Spillover effects between precious metals and stock markets

In a study by Al-Yahyaee et al. (2019), the authors examine the transmitter/recipient of information relationship in the precious metals market and GCC stock markets. They infer from their findings that silver and platinum are net transmitters of return shocks to GCC markets. On a similar note, Creti et al. (2013) identify close correlations between silver, platinum, palladium and stock markets. Using a dynamic conditional correlation (DCC) GARCH framework, the authors find that precious metals and stock markets exhibit increasing correlation especially during the financial crisis 2007-2008.

Another research strand investigates the correlations between precious metals and other commodities. Kang et al. (2017) show that silver operates as an information transmitter to other commodity futures markets in the recent financial crisis. When examining risk spillover effects from energy, metals and food commodity markets, Algieri and Leccadito (2017) infer that oil and metals exhibit the largest contagious impacts on the whole economy.

In a study by Fernandez (2010), the author examines the validity of the efficient market hypothesis (EMH) by comparing commodity indices composed of futures contracts and their respective sub-indices. When using a weighted wavelet-based estimator, the author finds evidence of anti-persistence in the returns in the precious metals market. Based on these findings, the author argues that the EMH is invalidated and that economic actors are incapable of accurately pricing some commodity indices.

2.5 Volatility transmission between agricultural commodity markets and

other commodities

The empirical literature that investigates the dependence structures between agricultural commodities and equity markets is narrow. A study by Candila and Farace (2018) examines the volatility spillovers between agricultural commodities and Latin American stock markets. The authors employ a multivariate GARCH model and find no evidence of bidirectional spillover between corn and wheat and Latin American stock markets. Instead, they show that agricultural commodity markets unidirectionally transmit volatility to these stock markets.

The remaining part of the literature regarding agricultural commodity prices is mainly devoted to examining their response to fluctuations in oil prices. This could because agricultural commodities are dependent on different types of fuel in their production (Harri et al., 2009). Some previous literature finds no evidence of risk transmission between agriculture commodities and oil prices (Zhang et al., 2010; Nazlioglu et al., 2013). Contrarily, some research show that oil prices affect agricultural commodity prices (Harri et al., 2009; Du et al., 2011; Koirala et al., 2015). According to Kang et al. (2017), corn commodity futures are the largest recipients of volatility out of gold, silver, WTI, corn and wheat commodity futures. During the recent financial crisis, the same study shows that both corn and wheat were net recipients of risk spillovers.

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From the above review of literature, we can conclude that the relationship between commodity prices and equity market is complicated and it is well-known that these markets are characterized by more volatile dynamics in recent years. Further, we can conclude that there is a gap in the previous literature in regard to the dependence structures between commodity futures and corresponding producer indices. This calls for a deeper analysis of volatility spillover between commodity futures and producer indices within the same market in order to understand the complete dynamics.

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3. Theoretical framework

In this section we present relevant theories that will contribute to the understanding of commodity markets. First, we will distinguish the commodity markets’ characteristics. Second, we will review portfolio risk management and hedging properties of commodities. Third, we will introduce financialization, financial contagion and investor behavior in the commodity markets. Lastly, we will explore the efficient market hypothesis.

3.1 Differences in the commodity markets

It is important to distinguish the commodity markets from each other because they obtain characteristics that separates their behavior and their pricing mechanisms. As demonstrated by Hull (2018), the agriculture, metals and energy markets obtain distinctive sensitivities. As for agricultural products, the weather conditions play an instrumental role in determining the supply, which in turn affects its pricing mechanisms. The apparent seasonality among agricultural commodities also affects the prices since storage is expensive. It has been identified that agricultural commodities experience price volatilities at different harvest periods. At pre-harvest periods the price volatility is at its peak before the inventory level is identified.

Metals are on the contrary to agriculture commodities, not sensitive to weather conditions and are relatively easy to store. Metals are instead mainly sensitive to what production process it will be used for, its substitutability with new sources of metals, changes in exploration, geopolitics and changes in extraction methods. Metals sometimes experience price volatility caused by exchange rate volatility. This is because metals are usually quoted in other prices than the domestic currency from where the metals were first extracted. Certain metals, such as gold and silver, do not follow the same behavior as other metals, considering they are mainly held for investing purposes rather than consuming purposes. According to Black (1976), the gold spot price has random fluctuations.

Energy commodities, such as crude oil, are distinctly different from other commodity markets because the supply is determined by both independent producers (non-OPEC nations) and by the organization OPEC. Since OPEC exercises a lot of power in oil supply decisions, this makes oil prices sensitive to changes in OPEC behavior (Dées et al. (2007). In addition, the oil price could show vulnerability to geopolitics and changes in macroeconomic fundamentals (Caldara and Iacoviello, 2019).

3.2 Portfolio theory and hedging properties

Commodities have been considered, by many investors, an asset class with attractive hedging properties generating low or negative correlations with stocks and bonds and positive correlations with inflation (Cheng and Xiong, 2013). First formalized by Markowitz (1952), the portfolio optimization theory emphasizes the importance of low or negative correlations when constructing a portfolio. Markowitz (1952) stresses the importance of taking the whole portfolio into account when deciding on asset components, rather than looking at each asset separately. This way of thinking emphasizes the importance of diversification, which essentially can generate higher risk-adjusted-return in the portfolio. Markowitz portfolio optimization theory also involves assigning

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optimal weights to different assets in the portfolio, and these weights are determined by their return and correlation with other portfolio assets. This is where the low and negative correlations are introduced, which reap effective reductions in total risk of the portfolio through diversification benefits and hedging properties. The low or negative correlations function as hedges in a portfolio because it gives off the opposite response to the other portfolio assets. If for instance one asset increases in value, the hedging assets would decrease. On the contrary if one asset decreases, the hedging asset would instead increase. Hence, including hedges in a portfolio generates effective reductions in total risk of the portfolio. (Markowitz, 1952).

3.3 Financialization, financial contagion and investor behavior

There is little consensus regarding the significance of the term financialization. According to Epstein (2005), financialization broadly stipulates the growing importance of financial motives, financial markets, financial actors and financial institutions in domestic and international economies. Researchers have gained interest in the phenomenon because of its tendencies of generating co-movements between different assets. Commodities are frequently brought up in the context of financialization. Commercial hedgers and non-commercial traders have traditionally been regarded as the main market participants of commodity investing, however, over the last decade there has been a large inflow of commodity index investors (Cheng and Xiong, 2013). The large inflow of market participants has raised concerns that financialization has led to a dramatic increase in commodity prices through index speculation (Cheng and Xiong, 2013). Financialization may also distort price signals in commodities. This is because it might be difficult for producers to detect what causes the price changes in commodity futures, if it is because of changes in financial investor trading or changes in global economic fundamentals (Cheng and Xiong, 2013).

The recent phenomenon financial contagion has often been brought up in context with financialization and growing market integration. While there is no clear definition of what constitutes a financial contagion, Claessens and Forbes (2001) describe it as the transmission of financial market stress across countries. Kodres and Pritsker (2002) define it as the risk transmission across financial markets. The financial contagion challenges investors when optimizing their portfolios, since correlations between assets might vary in different market conditions, which makes it difficult for investors to find assets with steady negative correlations. Claessens and Forbes (2001) describe that increased co-movements in asset prices may transpire as a result of certain investor behavior and that financial markets may facilitate the spread of it.

Investor behavior, such as financial panic, herd behavior, confidence loss or increased levels of risk aversion might increase volatility and induce a financial contagion. An example of how this could emerge is if investors withdraw their investments from several markets due to a crisis occurring in one country, and this would then set off risk transmission. This type of investor behavior may emerge in financial turmoil due to reduced risk appetite among financial traders (Cheng et al., 2015). This type of behavior could further be triggered by liquidity constraints and is more likely to pressure leveraged institutional investors that are facing margin calls in the wake of a crisis. Leveraged institutional investors would then have to sell their assets in other markets and it could therefore lead to risk transmission (Claessens and Forbes, 2001).

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3.4 Efficient Market Hypothesis

Kendall (1953) and Fama (1970) were the first to introduce the concept of the efficient market hypothesis (EMH). They found that stock markets are efficient markets since stocks follow unpredictable and random processes. The key takeaway of the efficient market hypothesis (EMH) is that security prices should reflect all available information at any time. This entails that in situations where a stock is underpriced, its performance will later be reflected in its stock price, because investors will bid up its price to the level that commensurate its risk. Further, the hypothesis postulates that new information will reflect the movements of the stock in an unpredictable manner. This is the motivation behind the close relationship between the efficient market hypothesis and the random walk model (or more precisely a sub-martingale) since the stocks should follow unpredictable price movements (Bodie et al., 2014). Black (1976) explains that given commodity futures markets are efficient, futures prices can provide useful information to participants in the commodity market and can be incorporated in production, storage and processing decisions. This assumes that investors act quickly to new information which then will be reflected in the price.

The efficient market hypothesis is a widely discussed theory, where there is no consensus of its explanatory power today. The hypothesis has been even more so criticized after the recent financial crisis (Bodie et al., 2014). When studying the graphs of our chosen commodity futures and corresponding producer indices, it is difficult to determine if the markets are efficient or not. Assuming that the EMH entails new information should randomly be reflected in the price movements, one could expect that new information would be reflected in a similar way in the futures prices and corresponding producer index prices of the same commodity market.

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4. Methodology

This study examines the cross-quantile dependencies between commodity futures contracts and their corresponding producer indices. In this section, we will start off by presenting the unit-root tests. Thereafter, we will introduce the cross-quantilogram approach by Han et. al (2016) and the partial cross-quantilogram method. Lastly, we will perform rolling window estimations.

4.1 Unit-root tests

In order to assess the cross-quantile dependencies between our variables, we first have to control for stationarity among our series (Han et al., 2016). Non-stationarity makes statistical inference impossible due to its time-varying mean, variance and never-ending covariance (Sjö, 2019a). Non-stationary series, such as random walks, do not follow standard distributions and this is why misleading results could emanate when not taking this into account. Applying standard distributions on stochastic trend variables in estimation will thus lead to spurious regression, meaning that false evidence of significant relationships between two independent non-stationary variables will be uncovered (Verbeek, 2012).

We perform two unit-root tests to robustness test our stationary results (Sjö, 2019b). We perform the augmented test developed by Dickey-Fuller (1979) and the other test developed by Phillips Perron (1988). We also control graphically for stationarity by examining the integrated graphs. The Augmented Dickey-Fuller (ADF) test corrects for serial autocorrelation in the error term by including the difference operator estimator, Δ, which adds the lags of the dependent variable, xt

(Gujarati and Porter, 2009), The white noise term is denoted as,

ε

t

,

and the optimal number of

lags of the dependent variable is defined by, ρ. There are three different ADF-models that controls for stationarity while imposing varying restrictions. We will only present two ADF-models, since they are the ones that are relevant in this thesis. The least restricted model is specified in equation (1) and accommodates an intercept, α, and a deterministic time trend, t. The moderately restricted ADF-test is specified in equation (2) including an intercept but no time trend.

∆#_! = % + '_!+ (#_!"#+ ∑%_$&#*_$∆#_!"$+ +_! (1)

∆#_!= % + (#_!"#+ ∑%_$&#*_$∆#_!"$+ +_! (2)

The null hypothesis of all ADF tests is π= 0, which implies that there is a unit-root. The rejection of the null hypothesis thus implies that the time series variable is stationary. We perform the ADF-tests and then apply the Akaike Information Criteria (AIC) optimal lag length when choosing the model with lowest AIC-value and white noise residuals (Verbeek, 2012).

On the contrary to the ADF-tests, the Phillips Perron (PP) test employs a non-parametric statistical method to correct for non-white noise residuals instead of adding lagged difference terms. This test is similar to the non-augmented Dickey-Fuller test. However, the PP-test modifies its test

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statistic to better fit the Dickey-Fuller distribution. Any lag specification is not necessary when performing the PP-test (Sjö, 2019b). The following equations display the PP-test with only a trend and then with both a trend and an intercept:

,_! = '_'+ '_#!,_!"#+ -_! (3)

,! = '(+ '#!,!"#+ % ./ −#₎12 + -! (4)

The null hypothesis of the PP-test suggests that the series is integrated of order one. In rejection of the null hypothesis, the series might be non-stationary or contain a segmented deterministic trend (Sjö, 2019b).

4.2 Cross-quantilogram and recursive rolling sample estimations

We address the dependence structures and directional predictability between commodity futures, and their corresponding producer indices in their quantiles, by using the cross-quantilogram approach developed by Han et al. (2016). The quantilogram, developed by Linton and Whang (2007), is the predecessor of the cross-quantilogram model and it uses “quantile hits” in correlograms to measure the directional predictability of a stationary time series in different quantiles in a univariate setting. The quantilogram compares the correlations of the “quantile hits” to pointwise confidence intervals. The extended cross-quantilogram, on the other hand, employs a multivariate approach by examining the directional dependence of two time series using conditional quantiles. The cross-quantilogram distribution has asymptotic properties and is therefore uniformly applicable over a variety of quantiles.

The cross-quantilogram approach can be conducted after reassuring that the variables follow a stationary stochastic process. The cross-quantilogram approach first estimates the “quantile-hits” between two events {y1t ≤ q1 (τ1)} and {y2t-k ≤ q2 (τ2)}. This procedure is essentially the estimation

of the serial dependence and it incorporates any arbitrary pair of

τ

t . The cross-correlations between

different quantile-hits are later estimated, where the quantile-hit process for i=1,2 is defined as {1[yit ≤ qi,t (⋅)]}, where 1[⋅] is the indicator function. Equation (5) captures the cross-correlations

of the quantile-hit process for τ-quantile with k lead-lags periods to time t.

4_*(6) = +,-!"./"#"0",#(*")3-!%./%,#&'"0%,#&'(*%)34

5+,-_!"% _./

"#"0",#(*")345+,-!%% ./%,#&'"0%,#&'(*%)34

(5)

Where y1t , y2t ,..., yit are stochastic stationary processes with the quantiles qit (τt). The quantile, τt , is

either conditional or unconditional to yit , and τ ∈ α and 0 <

α

< 1. We use the lag length k=1, 5

and 22, which enables analysis of cross-correlations on a daily, weekly and monthly basis. The correlation of the quantile-hit process is denoted by ρτ(k) and its size is determined by the

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15

can be represented as 9!=1[:<0]–% (Han et.al, 2016). In the context of our paper, y1 could for

example represent gold futures contracts and y2 could represent the gold producer index, or any

other futures contract and their corresponding producer index. Let us take for example that we want to examine the dependence structures between the gold variables in the quantile 0,05. We therefore assume y1 has q1(0,05) at time t and y2 has q2(0,05) at time t-1. We examine if the

correlation of the quantile-hit process is ρτ(1)≠ 0, which would imply that there is tail dependence

between the gold futures and the gold producer index. This result would further indicate that there is a one event directional predictability between the two markets in the 0.05 quantiles. In the case of ρτ(1)= 0, this would entail no directional predictability between the two markets, hence no tail

dependence would be evident either. In equation (6) we introduce the sample counterpart of the cross-quantilogram and it is computed to generate the empirical estimations of our study.

4;_*(6) = ∑)#*'+"-!"./"#"07",#(*")3-!%./%,#&'"07%,#&'(*%)3 5∑)#*'+"-!"% ./"#"07",#(*")35∑)#*'+"-!%% ./%#"07%,#(*%)3

(6)

Where the unconditional sample quantile of

y

i,t is denoted as #$"(α8) (Han et. al, 2016). Thereafter,

the Box-Ljung test is computed with the objective of testing the validity of the null hypothesis through statistical inference. The null hypothesis is tested, H0= ρτ(1) = … = ρτ

(ρ) = 0, to examine

if the conditional correlations are not statistically different from zero for some k ∈ {0, …, ρ}. The null hypothesis is tested against the alternative hypothesis, H1= ρτ(k) ≠ 0, which entails evidence

of statistically significant conditional correlations. The Box-Ljung test is presented in following equation: =>*(?) = 1(1 + 2) ∑ 9: %_(;) <"; % ;&# (7)

We then apply the partial cross-correlogram (PCQ) model, which is an extension of the CQ method, and allows for the inclusion of control variables to the model to control for intermediate events. In our case, we introduce the EPU and VIX as control variables for economic policy and equity market uncertainties and examine their effect on the relationship between two events {y1t ≤

q1 (τ1)} and {y2t-k ≤ q2 (τ2)} between t and t-k. The partial cross-correlation is defined in equation

(9), where A̅ = [9(y#3 − q3t(C3)), ..., 9(y#n− qnt(C3))]⊺ is a vector of all control variables.

4_*=|? = − 9!,"%,,,,,,

@9!,,""9!,,%% (8)

ht(C̅) is a vector of quantile-hit processes and we let C̅ = (C1 ,...,C%)⊺ compose a single set of quantiles.

In this way, we re-define ht(C̅) = [9z1(y#3 − q3t(C3)), ..., 9z2(y#n− qnt(C3))]⊺. The partial cross-correlation can also be written as equation (10), where δ is a scalar parameter. The predictability between two quantile hits can be estimated by testing the null hypothesis ρ#̅τ = 0, while controlling for the

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16

4_*=|? = D*"(#"*")

*%(#"*%) (9)

Further, we re-estimate the CQCs using a recursive subsample estimation process in order to attain time-varying dependence structures and to identify potential changes of cross-quantile correlations over time (Uddin et. al, 2019). This method facilitates analysis of the possible integration between futures prices with producer index prices over time. We start off by estimating the first rolling window of the CQC period, using a window length of 252 days1_{. We subsequently add one day to}

the subsample and then perform new estimations using the same window length. Finally, this process is halted when the end of the subsample is reached.

The rolling window estimation process generates blue lines, which represents time-varying CQCs in the recursive subsamples, and can be observed in figure 7. The red lines are generated by a bootstrap procedure and illustrate 95% confidence intervals of no predictability between the variables. This means that the blue lines inside the red lines represent statistically significant result, and insignificant results are detected in cases where the blue lines are detected outside the confidence intervals. The bootstrapping procedure generates confidence intervals by taking our data sample as a proxy for the population and performs a range of iterations that provides broad information about the data. We choose to perform 500 bootstrap iterations in order to produce robust estimations and we select the five percent significance level, based on econometric standards.

The cross-quantilogram output generates heat maps consisting of 121 squares that unveils different quantile combinations of our chosen variables. The X-axis and Y-axis in the heat maps represent the following quantile distribution between two variables: [q = (0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.95)]. The cross-quantilogram approach enables analysis of cross-correlations in different market conditions, since the lower quantiles 0.05 represents “bad” market conditions and the upper quantiles 0.95 displays “good” market conditions. These extreme quantiles are often called the “tails” of the distributions. “Normal” market conditions are represented by the middle quantile, 0.5. These heatmaps provide an effective graphical illustration of the unconditional bivariate cross-quantile correlation between two distributions and offers a complete picture of their dependence structures. The level of correlation is designated by the color scale, where red color indicates strong positive correlation and blue color represents strong negative correlation. Statistically insignificant results are set to zero and are represented by the green color. The statistical insignificance implies that there is no directional predictability between the quantiles of the variables of interest. (Han et al., 2016).

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5. Data and preliminary analysis

In this section we will introduce the chosen variables of this thesis and present their historical price movements. We will further present their descriptive statistics and perform diagnostic tests in order to examine their characteristics.

This study analyzes the dependence structures between commodity futures contracts and corresponding commodity producer indices in different market conditions. Our data sample consists of daily return data that ranges from 16 December 2005 to 28 June 2019, which gives us 3397 observations in total. All data is expressed in USD and is retrieved from Thomson Reuters Datastream. The sample period is chosen as we wanted to include the financial crisis of 2008, since previous literature indicate that spillover between commodities and financial markets has increased after the crisis (see Ji and Fan, 2012; Nazlioglu et al., 2013; Silvennoinen and Thorp, 2013; Adams and Glück, 2015). We consider four different commodity markets in our study, namely energy, gold, precious metals and agriculture commodities. The chosen variables are presented in table 1. The selection of commodity markets is based on the motive of examining the commodity market in broad terms and to include commodities with idiosyncratic characteristics.

Table 1: Variable description

Note: The table displays all chosen variables and their abbreviations. Source: Thomson Reuters Datastream (2020).

To capture the production aspects of the commodity markets, we choose four commodity stock indices to respectively represent the stock performance of companies involved in production and exploration of each commodity sector. Our chosen indices constitute some of the largest publicly traded commodity producing companies and each index exercise market-capitalization requirements for inclusion. All indices employ a market-value weighting method. The S&P Commodity Producers Oil and Gas Exploration and Production Index is chosen to represent oil and gas producers’ stock returns. The index has 60 constituents and the countries with the largest index weights are USA, Canada and Russia, where American oil and gas producing companies compose 52,7 percent of the index.

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The S&P Commodity Producers Gold Index represents stock returns of companies involved in exploration and production of gold. This index comprises 51 gold producing companies where the top three gold producing countries are Canada, USA and Australia. Canada is assigned the largest index weight at 49,8 percent. The Dow Jones Precious Metals Index is chosen to represent the production in the precious metals market. The index measures the stock performance of 30 companies that are engaged in the production and exploration of gold, silver and platinum-group metals, which are listed on U.S stock exchanges. The S&P Commodity Producers Agribusiness Index consists of 67 companies engaged in the agriculture business. This index involves companies that devote their production to consumer staples (52,3%), materials (27,7%) and industrials (20%). More specifically, the included companies engage in business operations that involve breeding and production of livestock and animal feed and harvesting and production of commodities such as corn, wheat, coffee and more. The business operations further involve manufacturing and distribution of agricultural equipment.

We have selected commodity future contracts from the same commodity sectors as our chosen commodity producer indices. This is because it enables analysis of risk spillover between the two asset groups for each commodity sector. The selected commodity future contracts are NYM light crude oil, natural gas, gold, silver, platinum, copper, corn, wheat and coffee. All future contracts are continuous which means that at the start of a new month, the current finite future contract rolls over to extend the contract, without expiring it.

We control for a set of uncertainties by using the Economic Policy Uncertainty Index (EPU) and the Volatility Index (VIX). The EPU, which is developed by Baker et al. (2016), represents uncertainties associated with economic policy-related events and is measured through different indicators. More specifically, it is measured through the newspaper coverage frequencies of economic policy-related discussions. This index also draws on tax code expiration data and economic forecaster disagreement data at the individual level. As there are country-specific versions of this index, we chose the EPU index for the U.S. This selection is based on the fact that the majority of our assets are traded on American financial markets. The VIX index is established by the Chicago Board Options Exchange (CBOE) and it measures the market’s expectation of future volatility in financial markets. This index produces a 30-day expected volatility of the U.S stock market by taking the midpoints of bid/ask price quotations of S&P 500 index options.

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19 Table 2: Descriptive statistics

Note: Calculations based on series expressed in logarithmic returns. Time period covered is 16 December 2005 - 28 June 2019, with 3397 observations per series, retrieved from Thomson Reuters Datastream. Ljung–Box (Q and Q^2), ARCH–LM, Jarque–Bera (JB), Augmented Dickey–Fuller (ADF) and Phillips–Perron (PP) are test statistics to test the null hypotheses. ADF(a) represents the test with intercept only, ADF(b) with intercept and trend. Optimal lag length is determined based on Akaike Information Criterion (AIC) and is presented in parenthesis ( ). ***, **, * correspond to 1%, 5% and 10 % significance levels.

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The descriptive statistics for the logarithmic first difference of all indices and future contracts are presented in table 2. The mean values of each asset are close to zero which is expected considering our sample consists of daily data. While the majority of the assets display positive mean values, natural gas is the only asset that indicates a slightly negative value. This means that natural gas generates negative returns during the sample period. When examining the standard deviations, we can further observe that natural gas obtains the largest standard deviations out of our sample. This implies that natural gas has experienced more volatile market conditions during the sample period in comparison to the other future contracts and producer indices. However, both uncertainty indices display larger standard deviations than natural gas, which could indicate that natural gas does not experience higher volatility than the overall financial market.

The majority of the commodity producer indices obtain negative skewness, meaning that their probability distributions are skewed to the left. On the contrary, the Dow Jones Precious Metals Index has a positive skewness indicating a tail extended to the right. Both financial and economic uncertainty indices also have positively skewed distributions. We can observe that the producer indices with most skewed distributions are the S&P Commodity Producers Agribusiness Index and the S&P Commodity Producers Oil and Gas Exploration and Production Index. When further examining the skewness distributions for the future contracts we observe that gold, silver, platinum, copper and corn indicate negative skewness. In contrast, crude oil, natural gas, wheat and coffee have positive skewness values. Among the future contracts, silver, corn and natural gas have the most skewed distributions. Additionally, our variables exhibit higher probability for extreme events than in normal distribution, which is demonstrated by the high kurtosis values. The noticeably high kurtosis value in the S&P agribusiness index can be attributed to unpredictability of inventory levels at pre-harvest periods, due to agribusinesses’ exposedness to weather conditions, as mentioned in section 3.1. Contrastingly, the only assets with kurtosis values lower than three are the future contracts for wheat and coffee, which means that these assets have thinner tails and are thus normally distributed (Verbeek, 2012).

We further perform some diagnostic tests to examine the series’ characteristics. The Jarque-Bera test (1980) shows that the null hypothesis can be rejected at one percent significance level for all series, which confirms the non-normality of all indices and future contracts. We also test for heteroskedasticity using the ARCH-LM test (Engle, 1982). The null hypothesis is also rejected at one percent significance level for all series, meaning that the residuals of all variables may suffer from autoregressive conditional heteroskedasticity. Testing for residual autocorrelation using the Ljung-Box test (1978) strongly suggests autocorrelation as the Q^2-statistics for all time series are statistically insignificant.

Finally, to satisfy the main assumption required to employ the cross-quantilogram (CQ) method, the time-series must be stationary (Han et al., 2016). Stationarity of our series is therefore tested using the Augmented Dickey–Fuller test (1979) and Phillips-Perron test (1988), which tests for unit-roots. Both ADF-tests indicate evidence of stationarity among all indices and future contracts. The PP-test further confirms the stationarity among all variables, since the null hypothesis is rejected for all time series.

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21 Figure 3: All variable time series presented in logarithmic first difference

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22 Figure 3: All variable time series presented in logarithmic first difference (Continues)

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In figure 3, all time series are expressed in logarithmic first differences. The producer equity indices exhibit in general less volatility in comparison to the individual commodity futures. The global financial crisis (GFC) show predominant volatility effects on returns of all producer equity indices and all commodity futures markets. All assets exhibit large return variations at around year 2011-2012. In 2014-2015, there is another volatile period where the oil and gas producer index, gold producer index, precious metals producer index and the crude oil, natural gas, corn, coffee and gold futures experienced volatile returns. This increased volatility could be attributed to the OPEC oil glut taking place in 2014-2015. As for the increased volatility in coffee in year 2014, this could be explained by the climate shock taking place in Brazil in 2014. This climate shock could in turn have affected the supply of coffee beans, as Brazil is the largest coffee producing country in the world (worldatlas.com, 2019; ico.org, 2020).

Table 3: Unconditional correlation matrix

Note: Table 3 presents correlations between producer indices and commodity futures. Only correlations within one sector are presented as they are the focus of this study and cross-sectoral correlations do not contribute with noteworthy information. Correlations between producer indices and corresponding commodities within different sectors are not perfectly comparable as they are affected by the composition of the indices and weights of each commodity within them.

Table 3 displays the correlations between the chosen producer indices and the commodity futures. From the correlation matrix we observe the highest correlations between the crude oil futures and the oil and gas producer index, indicating close to perfect correlations. We can further observe from the table the lowest correlations between the gold futures and the gold producer index. The low correlation in the gold market is close to zero, which could suggest that the gold market obtains attractive diversification benefits. The platinum future obtains the highest correlations with the precious metals index out of the precious metals futures, whereas the silver future obtains the lowest correlation out of the precious metals. The correlations between the agriculture futures and the agribusiness producer index are almost on identical levels, indicating mild correlations with the producer index.

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24 Figure 4: Historical prices of commodity future contracts and commodity producer indices

Note: The figure gives an overview of co-movements between commodity futures and producer indices in each commodity market. All series are expressed in level. The prices are expressed in USD. Source: Thomson Reuters Datastream (2020).

Figure 4 depicts the historical price changes of each selected commodity sector. This figure gives an overview of the co-movements between the assets in separate sectors. In general, we can observe tendencies of co-movement between producer indices and future contracts in every sector. The co-movement between the producer indices and the futures contracts is prevalent around the GFC. The oil and gas producer index and the agribusiness producer index are more expensive compared to their respective commodity futures. Interestingly, the platinum future is more expensive than its corresponding producer index and the other precious metals futures. The gold producer index is more expensive than the gold future until around year 2012, thereafter, the gold future exceeds the gold producer index price. What is further interesting is that the agribusiness producer index depicts a price increasing trend since 2008, whereas the agriculture commodity futures have remained at almost constant price levels.

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25 Figure 5: Dynamic conditional correlations between silver future contracts and precious metals

producer index

Note: Graph portraying dynamic correlations between silver futures and precious metals producer index. Only one dynamic correlation is displayed to support that there is evidence for suspecting time-varying correlations between the assets. Source: Thomson Reuters Datastream (2020).

To further investigate the potential co-movements between producer indices and commodity futures, we estimate the dynamic conditional correlations generalized autoregressive model (DCC-GARCH), which is illustrated in figure 5. The figure portrays the potential co-movement between silver futures and the precious metals producer index. The multivariate DCC-model enables analysis between two variables in a time-varying autoregressive correlation setting (Sjö, 2019a). The DCC addresses the issue with volatility clustering by allowing the error variance to depend on its lagged value. The volatility clustering problem implies that shocks in financial time series data tend to persist to subsequent time periods, causing varying variance and heteroskedasticity. The DCC-GARCH model is a symmetric model which means that “good” and “bad” news impact future volatility in the same magnitude.

In figure 5, the result for our sample period shows that the silver market is mainly located in the positive correlation spectrum and that the correlation is time-varying. Further, we can observe that the correlation coefficient varies from -0.06 to 0.5 between the silver futures and the producer index, which confirms that our assets are time-varying and that quantile dependence may exist. These observations justify our study of examining the closer correlation structures in different market conditions using the cross-quantilogram approach.

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6. Empirical results and discussion

The following section presents the empirical results in three subsections. In the first subsection we present the results from our cross-quantilogram estimations for each commodity sector and analyze the results. The second subsection includes the partial cross-quantilogram estimations, when controlling for uncertainty. At last, in the third subsection we evaluate the results from the recursive window sample estimations.

6.1 Cross-quantile dependence between commodity futures’ contracts and

corresponding commodity producer indices

To assess the overall dependence structure within each commodity sector, we need to analyze the directionalities going both ways. This means that we are studying the directionality from the commodity future to the producer index, but also the directionality from the producer index to the commodity future. If there is spillover going both ways, the relationship is symmetric. However, if there is spillover from one asset to the other, the relationship is asymmetric.

We start by evaluating the results from our cross-quantilogram correlations (CQC) that depict spillover between oil and natural gas commodity futures and the oil and natural gas producer index. We then proceed to the other commodity markets. The interpretations of the CQCs differ depending on which direction is examined. Panel A of figure 6 shows the spillover from commodity futures to respective producer index. Panel B depicts spillover from producer indices to respective commodity futures. In panel A, the quantiles of the commodity future are presented on the horizontal axis and the quantiles of the producer index are represented on the vertical axis. In panel B, the quantiles of the producer index are presented on the horizontal axis and the quantiles of the commodity future are represented on the vertical axis. Each panel displays CQCs over varying time frequencies. We choose to examine the CQCs on a daily (1 lag), weekly (5 lags) and monthly (22 lags) basis.

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27 Figure 6: Cross-quantile correlations between commodity futures and producer stock indices

Panel A Panel B

Note: Figure 6 depicts heatmaps from CQ-estimation. The horizontal axis represents quantiles of the commodity futures and vertical axis represents quantiles of the producer indices in heatmaps illustrating spillover from futures to producer indices. In heatmaps depicting spillover from producer indices to commodity futures the horizontal axis represents quantiles of the indices and vertical axis represents the quantiles of the commodity futures. Panel A depicts spillover from commodity futures to producer indices. The upper left corner (0.05:0.95) represents low returns of commodity futures and low returns of the producer index. The upper right corner (0.95.0.95) represents high returns of both series, while the lower left corner (0.05:0.05) represents low returns in both series. The lower right corner (0.95:0.05) represents high returns of commodity futures and low returns of producer indices. In panel B, depicting spillover from producer indices to commodity futures, the relation is opposite. The abbreviations used in this model mean the following: OGPI - Oil and gas producer index, COF - Crude oil future, NGF - Natural gas future, GPI - Gold producer index, GF - Gold future, PMPI - Precious metals producer index, SF - silver future, PF - Platinum future.

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28 Figure 6: Cross-quantile correlations between commodity futures and producer stock indices (Continues)

Panel A Panel B

Note: The abbreviations used in this model mean the following: PMPI - Precious metals producer index, CopF - Copper future, ABPI - Agribusiness producer index, CrnF - Corn future, WF - Wheat future, CofF - Coffee future.

Dependence Structures between Commodity Futures and Corresponding Producer Indices across Varying Market Conditions : A cross-quantilogram approach