An analysis of time-varying commodity market price discovery

Accepted Manuscript An analysis of time-varying commodity market price discovery

Paresh Kumar Narayan, Susan Sharma PII: DOI: Reference:

S1057-5219(18)30177-7 doi:10.1016/j.irfa.2018.03.008 FINANA 1205

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International Review of Financial Analysis

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20 August 2017 9 March 2018 14 March 2018

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ACCEPTED MANUSCRIPT An Analysis of Time-Varying Commodity Market Price Discovery Paresh Kumar Narayan (Deakin University) and Susan Sharma (Deakin University)

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Paresh K Narayan Deakin Business School Faculty of Business and Law Deakin University 221 Burwood Highway, Burwood Victoria 3125, Australia Telephone: +61 3 9244 6180 Fax: +61 3 9244 6034 Email: [email protected]

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Mailing Address

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ACCEPTED MANUSCRIPT An Analysis of Time-Varying Commodity Market Price Discovery

ABSTRACT We propose a model of time-varying price discovery based on a rolling-window error correction framework. We show that price discovery in nine commodities is dominated by the

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spot market, while, in only six commodities, price discovery is dominated by the futures

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market. Our findings, therefore, challenge the well-established view in commodity markets that it is the futures market which dominates the price discovery process. We also show the

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economic significance of price discovery through a portfolio construction and hedging strategy.

Key words: Price Discovery; Time-varying; Error Correction Model; Spot and Futures

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Markets.

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ACCEPTED MANUSCRIPT I.

Introduction

The goal of this paper is to examine whether price discovery in commodity markets is timevarying. In other words, we search for phases over which one market dominates the other market in an oscillatory manner. The interest in price discovery, or the lead and lag relationship between any two markets, has been motivated by the work of Hasbrouck (1995) and Gonzalo

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and Granger (GG, 1995). A feature of the empirical literature on price discovery is that the

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Hasbrouck and GG measures provide very consistent results on price discovery; see extensive comparative results in Blanco et al. (2005), for example. These methodologies have become

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popular in several strands of the literature. There are studies on price discovery in commodity

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spot and futures markets (see, inter alia, Schwarz and Szakmary (1994), Yang et al (2001), Garbade and Silber (1983), and F-Ferretti and Gonzalo (2010)); there are studies that test for

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price discovery in the equity or equity options markets (see, for instance, Muravyev et al. (2013), and Rourke (2013)); there are studies that examine the price discovery process in the

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stock and CDS spread markets; and there are studies that test for price discovery in the

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exchange rate market (see Narayan et al. (2014), Chen and Gau (2010), Poskitt (2010), Cabrera et al. (2009), and Tse et al. (2006)).

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A factor that is common across these different strands of the literature is that limited attempts have been made to explore the potential time-varying nature of the price discovery.

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On closer inspection of the literature, we find that with respect to the Hasbrouck measure while some attempt has been made, particularly by allowing for time-varying correlation and or covariance, nothing of this sort has been attempted when it comes to the GG measure. In this paper we propose a rolling-window-based error correction model to extract timevarying price discovery coefficients. We test for time-varying price discovery for a large number of commodities (spot and futures) using monthly time series data that mostly span the period 1977 to 2012. We discover strong evidence of price discovery in that for all commodities

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ACCEPTED MANUSCRIPT there is price discovery—that is, either in over 50% percentage of regressions the price discovery coefficient is greater than 0.5 or in over 50% of the regressions the coefficient is less than 0.5. In nine commodities (canola, cocoa, coffee, corn, gold, platinum, silver, soybean oil, and soybean yellow) it is the spot market where price discovery takes place, while the futures market dominates price discovery in only six commodities (copper, crude oil, palladium,

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soybean meal, sugar, and wheat). More strictly when we apply a 60% rule—that is, 60% of

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regressions in which price discovery coefficient is greater (less) than 0.5, we find this to be the

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case for seven (four) commodities, suggesting that there are more commodities in which price discovery is dominated by the spot market than the futures market.

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Moreover, for 14 commodities (canola, cocoa, coffee, copper, corn, gold, soybean oil, soybean yellow, sugar, wheat, palladium, platinum, silver, and soybean meal) there is clear

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evidence of time-varying price discovery. In other words, for these commodities there are cyclical patterns: phases over which spot market dominates price discovery and phases over

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which price discovery is dominated by the futures market. Finally, in an economic significance

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analysis, we show that time-varying price discovery has implications for portfolio construction and hedging in at least some of the commodity markets. Our results identifying changing

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dominance of markets in price discovery is consistent with theoretical work and empirical observations in the literature. Futures markets, for instance, tend to dominate price discovery

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process because they have more time to absorb information and therefore incorporate information since futures products are not for immediate delivery. This view is consistent with the information diffusion hypothesis. By comparison, spot market is for immediate delivery and traders do not have time to adjust to information (see Crain and Lee, 1996). The trading volume hypothesis has also been used to explain why price discovery oscillates. The trading volume based idea is consistent with the work of Lo and MacKinlay (1990) and Hou (2007). Karabiyik et al. (2017) show that indeed trading volume matters to price discovery. In their

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ACCEPTED MANUSCRIPT analysis of individual stocks and futures at the country level, they show that average trading volume of price discovery cash market is almost twice more than the corresponding futures. Dolatabadi et al. (2017) complement earlier studies by arguing that spot market tends to dominate price discovery when trading volume declines. They show this to be the case with respect to commodity markets. Finally, commodity markets differ in terms institutional forces,

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market demand and supply, price volatilities and exogenous shocks. These factors can delay

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the process of information incorporation particularly for less traded markets (Karabiyik et al.

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2017).

Our findings contribute to two specific branches of the literature. First, as pointed out

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earlier, there is a large and growing literature on price discovery. Our proposal of a timevarying price discovery framework adds to these studies, particularly by showing that it is

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possible to identify phases over which price discovery between two markets oscillates. This type of changing price discovery from one market to another is akin to the literature on

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nonlinear effects in financial markets. Therefore, our findings here can be interpreted as

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showing some sort of nonlinear relationship between commodity spot and futures markets. A time-varying approach allows us to extract this type of nonlinear behaviour in commodity

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markets.

Our finding that price discovery is not completely dominated by the futures market is

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not new, but our approach taken to show oscillating price discovery is. Our findings that price discovery is not exclusively in the futures market corroborates the results documented in Dolatabadi et al. (2015). Although a key difference between our study and Dolatabadi et al. (2015) should be noted: (a) their study uses a fractionally cointegrated autoregressive model; and (b) they use only four commodities. In this regard, our empirical analysis represents a more extensive treatment of price discovery in commodity markets.

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ACCEPTED MANUSCRIPT Our third contribution relates to the economic significance of price discovery. As noted earlier, there is a substantial body of literature on price discovery. The more recent literature focuses on establishing price discovery in commodity markets; see Dolatabadi et al. (2015) and Figuerola-Ferretti and Gonzalo (2010). One gap in this literature is that none of these studies identify the economic implications of the evidence on price discovery. We do. Our economic

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significance analysis masks two interesting outcomes. Our first main finding is that for seven

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commodities, as price discovery becomes more and more spot market dominant, optimal

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portfolio holding favours the spot market. Our second main finding is that as price discovery becomes more prevalent, less shorting of commodity futures is required to minimise risks.

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We organise the balance of the paper as follows. In Section II, we provide a motivation for the reasons behind time-varying price discovery in commodity markets. Section III

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discusses the empirical framework for estimating time-varying price discovery. Section IV

Motivation: Why is price discovery time-varying?

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II.

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discusses the results. The final section concludes.

There are strong reasons to believe that price discovery can be time-varying. Amongst the

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simplest of reasons, because price discovery is based on time-series price data, which naturally experience not one but many shocks over their historical time period, one can expect the price

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discovery process to be time-varying. This is because price discovery is a function of prices. If prices change over time so will price discovery. The formula for price discovery is based on moments (mean and variance) of prices (both its fundamental value and noise component), and the relation between the true price and the fundamental price (the long-run relation). So what is the implication? The implication is that if the price itself is time-varying so will be the moments of the fundamental price and noise of price. Similarly, the long-run relationship will also be different with time. Given these, it is natural that the resulting price discovery will also

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ACCEPTED MANUSCRIPT be time-varying. So, in order to understand time-varying price discovery, we need to understand time-varying prices. That is, under what conditions are prices time-varying? The objective of this section is precisely this: to understand what dictates time varying prices and, once understood, to infer what dictates time-varying price discovery. Therefore, it is imperative to understand the factors that affect prices intermittently over

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time. If one considers the literature on equity returns, there is no shortage of reasons why stock

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prices vary with time. The main source of this time-varying nature of stock prices has been

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attributed to, among others, business cycles (Andersen et al. (2007)) and monetary policy/macroeconomic news (Bernanke and Kuttner (2005), Garner (1989), Ederington and

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Lee (1993)).

More specifically, let us consider the time-varying behaviour of commodity prices now.

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Amongst empirical evidence, a number of studies document that commodity prices are characterised by boom and slump phases. Cashin et al. (2002) consider as many as 36

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commodity price series, and document strong evidence that commodity prices are characterised

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by booms and slumps. They show that price slumps last longer than price booms. Moreover, using data that span the period from 1957 to 1999, they find that there are, on average, six

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cycles in the 36 commodity prices. This empirical evidence points to the fact that commodity prices are time-varying. Perhaps the most famous hypothesis that reinforces the belief that

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commodity prices are time-varying is the Prebisch and Singer (1950) hypothesis. The PrebischSinger hypothesis states that commodity prices relative to manufactures are steadily decreasing over time. That commodity prices are negatively time-varying has been motivated by a number of factors, such as high income elasticity of demand for manufactured goods vis-à-vis primary commodities, productivity differentials between countries, and asymmetric market structures where the industrial sector is characterised by an oligopolistic structure, while primary commodities are generally perfectly competitive (see Kellard and Wohar (2006)).

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ACCEPTED MANUSCRIPT Commodity prices are also strongly dependent on business cycle phases and monetary policy news (see, inter alia, Hong and Sarkar (2008)). As an example, consider Frankel’s (1986) overshooting theory of commodity prices. The main idea of this theory is that commodities are exchanged on fast-moving auction markets. Commodity prices, therefore, respond instantaneously to any shocks that affect commodity markets. In response to monetary

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policy news, for instance, commodity prices in the Frankel model react more than

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proportionately. In other words, monetary policy shocks lead to an overshooting of commodity

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prices in that they move to new long-run equilibrium. Commodity cycles also result from the lag between the initiation of production decisions and the delivery of goods. Motivated by this,

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Mackey (1989) developed a continuous time model for the price dynamics of a single commodity market. The two key features of this model are that it accounts: (a) explicitly for

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the nonlinearities in demand and supply schedules; and (b) for production and storage delays resulting from the market price.

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In related empirical evidence, studies show that commodity prices are non-stationary,

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suggesting that shocks, such as those resulting from real interest rates, are responsible for the changing behaviour of the mean and variance of commodity prices (see Byrne et al. (2013)).

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The trend behaviour of commodity prices has occupied enough interest to be classified as a strand of the literature on commodity markets. Some examples are Zanias (2005), Kellard and

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Wohar (2006), Cuddington (1992), Ghoshray (2011), and Kim et al. (2003). Zanias (2005) claims that structural breaks in the data, which effectively contribute to the time-varying nature of prices, are due to productivity growth driven by the rise in commodity prices following the first World War. Kellard and Wohar (2006) show that commodity prices do not have a single downward trend; rather, they are best characterised by a shifting trend that also changes sign over time. Therefore, what is clear from Kellard and Wohar’s analysis is that while commodity prices are time-varying, this variability comes with an oscillating sign.

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ACCEPTED MANUSCRIPT Specific activities in the spot and futures markets could also affect markets differently and with time. Consider the role of speculative trading, for instance. Speculative trading in futures markets stabilizes the cash market (Lee and Ohk (1992)). From Friedman (1953), we know that speculation that results from the creation of stock index futures is inversely related to stock return volatility; for a related discussion, see Weller and Yano (1987). Speculation is

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not a continuous process, it is random; therefore, it should have a time-varying effect on the

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commodity spot and futures markets regardless of whether the speculation originates from the

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spot or futures markets.

What do we learn from the literature? We learn that commodity prices are time-varying.

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We also now know that there are multiple sources of time-variation in commodity prices. These include consumer income, labour productivity, market structure, monetary policy news, and

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business cycles in general. An associated branch of the literature shows that shocks to commodity prices have a permanent effect on prices, suggesting that every time commodity

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markets are exposed to shocks (regardless of the type of shock), prices move to a new long-run

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equilibrium. What are the implications for price discovery? The main implication here is that, because commodity prices are time-varying, the variance should be reflected in a test of price

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discovery. The path of price discovery may change depending not only on the existence of a shock but also on the magnitude of a shock. Shocks in our proposed model are based on error

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correction terms, as we explain in the next section. Therefore, both the shock(s) and their magnitude are reflected in the error correction terms. Therefore, an error correction model of time varying price discovery is ideal to address our proposed research question. III.

An error correction model of time-varying price discovery

In this section, we propose a rolling window-based error correction model (RW-ECM) of the price discovery process. Choosing a sufficiently large initial sample size then using rolling window samples allows us to extract time-varying error correction coefficients from the ECM.

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ACCEPTED MANUSCRIPT Therefore, a RW-ECM allows us to compute price discovery at every point in time beginning from the end of the chosen initial sample window. For example, consider the crude oil market. We have monthly data on spot and futures prices beginning in March 1983 and ending September 2012. We choose the initial window of 120 months (10 years), which implies that we first estimate the ECM over the period March 1983 to February 1993.1 We then re-estimate

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the ECM over 120 months using a rolling window approach. In other words, our next ECM is

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estimated over the period April 1983 to March 1993, then from May 1983 to April 1993, and

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so on. This process of computing ECMs concludes when the last sample date (September 2012) is absorbed.

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It should be kept in mind that while there is no statistical criterion to choose the rollingwindow size, the choice matters in practice: too small a window can lead to very erratic patterns

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in the coefficients of the model, while too large a window can potentially lead to little variations in coefficients over time. Our choice of 120 months is motivated by these costs. However, there

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is one other statistical consideration that needs to be entertained with our proposal, and we do.

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The ECM is predicated on two statistical conditions: (1) the two variables, which in our case are spot price and futures price, should be unit root non-stationary over the chosen windows;

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and (2) the two variables should be cointegrated—that is, they should share a long-run relationship over the chosen windows. Therefore, our choice of the rolling window is motivated

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by these two features of the data. After having selected the rolling window, we pre-test for unit roots and cointegration over the rolling samples to ensure that these conditions are met. The main implication here is that in the absence of any selection criteria, our proposal of a ECM requires as a prerequisite that we choose rolling window samples that ensure the two variables

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In additional trials, we used a short window (7 years) and a long window (13 years) and find no major differences in our results.

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ACCEPTED MANUSCRIPT are not only unit root non-stationary but are cointegrated. Against this background, our error correction model for each rolling window, say 𝑖, takes the following form: 𝑞

(1)

∑

Δ𝑆 𝛼 − 𝜆1 (𝑆𝑡−1 − 𝛽1𝑡 𝐹𝑡−1 ) [ 𝑡] = [ 1 ]+ Δ𝐹𝑡 𝛼2 + 𝜆2 (𝑆𝑡−1 − 𝛽2𝑡 𝐹𝑡−1 )

𝑗=1 𝑞

∑

[

𝑗=1

2 −𝐴11𝑗 Δ𝑆𝑡−𝑗 + 𝐴1𝑗 Δ𝐹𝑡−𝑗

−𝐴12𝑗 Δ𝑆𝑡−𝑗 + 𝐴22𝑗 Δ𝐹𝑡−𝑗

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𝑒𝑠,𝑡 + [𝑒 ]

]

𝑓,𝑡

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For simplicity, the constant term is dropped from the long-run cointegrating equation and as

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we will show later, both 𝑆𝑡 and 𝐹𝑡 follow a random walk process: 𝑆𝑡 = 𝑆𝑡−1 + 𝜂1𝑡

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𝐹𝑡 = 𝐹𝑡−1 + 𝜂2𝑡

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(2)

The error terms may be contemporaneously and serially correlated: 𝑐𝑜𝑣(𝜂𝑡1 , 𝜂𝑡2 ) = 𝜔𝑡

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𝑣𝑎𝑟(𝜂𝑡1 ) = 𝜎𝜂21

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𝑣𝑎𝑟(𝜂𝑡2 ) = 𝜎𝜂22

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(4)

The evidence on price discovery is based on the error correction coefficients, 𝜆1 and

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𝜆2 . These coefficients measure the speed of adjustment. When 𝜆1 ≤ 0 and is statistically

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significant, it implies that the futures market is contributing to any disequilibrium in spot returns. In other words, the spot market adjusts to information contained in the futures market. On the other hand, if 𝜆2 > 0 and is statistically significant, it implies that the spot market contributes to any disequilibrium in futures returns. In this case, the spot market will contribute to price discovery as the futures market will adjust to information contained in the spot market. Indeed, if both coefficients are statistically significant then both markets are contributing to price discovery (Blanco et al. (2005)). The inclusion of the error correction terms in the model is based on the assumption that both variables are cointegrated. Cointegration implies that at 11

ACCEPTED MANUSCRIPT least one market will adjust, in which case this market is inefficient because its price reacts to information contained in another price. The concept of cointegration and adjustment of the kind discussed here has been motivated by the Granger representation theorem (Engle and Granger (1987)). Following Gonzalo and Granger (GG, 1995), and see applications in Blanco et al.

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𝜆2 , 𝜆2 − 𝜆1

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𝐺𝐺𝑆 =

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discovery. This can be captured by the following expression:

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(2005), one can simply utilise the coefficients of the error correction terms to measure price

Here 𝐺𝐺𝑆 represents the price discovery resulting from the spot market for rolling window 𝑖,

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where 𝑖 = 1, … , 𝑛 with 𝑛 representing the last window over which the ECM is estimated. When

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in a two-variable ECM there is a cointegrating relationship, then GG must satisfy 𝐺𝐺𝑆 𝛼1 + 𝐺𝐺𝐹 𝛼2 = 0 (orthogonality condition) and 𝐺𝐺𝑆 + 𝐺𝐺𝐹 = 1 (equality condition), where 𝐺𝐺𝐹 is

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the price discovery resulting from the futures market. Since the error correction term in the spot

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market equation is expected to be negative, and positive in the futures market equation, the GG measure is expected to be in the [0,1] range. This will not be the case, however, if the error

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correction coefficients appear with incorrect (unexpected) signs. In this case, there is no evidence of price discovery; therefore, GG can be outside the [0,1] range. Because, as we

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explained earlier, we use a fixed window of 120 observations to estimate the ECM and then apply a rolling regression approach, we end up with a GG measure every month from the end of the fixed window estimation period. In this way we are able to extract a time-varying GG coefficient.

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ACCEPTED MANUSCRIPT IV. A.

Data and Results

Data

We use monthly time series data on 17 commodity markets. These commodities are noted in Table 1. For each commodity, we consider two price series: the spot price (closing price) and the futures price (nearest contract maturity price) and compute their returns as the log

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difference. All commodities do not have the same start date although all data run up to

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September 2012.2 For 13 commodities the start date is January 1977, while for cotton, canola,

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crude oil, and natural gas the start dates are January 1979, August 1981, May 1983, and April 1990, respectively. It follows that for 13 commodities there are no fewer than 429 monthly

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observations, while for the remaining four commodities the sample size ranges from 270 observations (natural gas) to 405 observations (cotton). All data were obtained from the

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Commodity Research Bureau (CRB) data CD. The contract rollover prices are only used in computing returns. Here is an example. 𝑅𝑒𝑡𝑢𝑟𝑛 = log[𝑃𝑟𝑖𝑐𝑒(𝑡)/𝑃𝑟𝑖𝑐𝑒(𝑡 − 1)] ∗ 100. So if

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the nearby contract for two successive periods 𝑡 − 1 are not the same the rolling return is

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computed using the same formula but the numerator is the closing price of the nearby contract at period (𝑡, 𝑡 − 1) and the denominator contains the closing price of the deferred contract at

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period 𝑡 − 1. So effectively what this is saying is that deferred prices instead of closing prices are used to compute returns when the nearby contracts are not same or else it’s computed using

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closing prices.

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Ideally, search for price discovery with high frequency data will be perfect. However, commodities data are not available in high frequency format to undertake a time-varying analysis. Indeed, given this data limitations the price discovery analysis in commodity markets have been based on monthly data; see, inter alia, Dolatabadi, Nielsen and Xu (2015), Dolatabadi et al. (2017), Yang et al. (2001), and Barkoulas et al. (1997). This aside, in additional tests, we did use daily data. There were only trivial changes in results and overall results were consistent with those from monthly data. We have, therefore, not reported daily data results here but they are available upon request. In future, as sufficient intraday time-series data becomes available researchers should extend the model in our paper by testing it using such high frequency data.

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ACCEPTED MANUSCRIPT To provide additional information on the commodities data on hand, in Table 1 we report the daily time-series average of volume (column 4) and open interest (column 5) which reflect, respectively, the number of futures contracts traded and the total number of outstanding futures contracts held by market participants. Based on volume, we find that the most popular commodity is crude oil followed by corn and gold. The least popular commodity is palladium,

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oats, lumber, and orange juice. The data on open interest suggest that crude oil is the most

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INSERT TABLE 1

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liquid commodity followed by corn and gold.

Some preliminary observations of the data are presented in Table 2. In panel A, we

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report commonly used descriptive statistics for commodity spot returns, while in panel B the corresponding statistics are reported for commodity futures returns. In particular, we report the

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mean, coefficient of variation, skewness, kurtosis, and the Ljung-Box (1978) Q-statistic at the lag of 12, which examines the no autocorrelation hypothesis.

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A brief account of these statistics is useful to demonstrate the difference among

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commodities. The following observations, in particular, are noteworthy: Mean spot returns of three commodities are negative and for the remaining 14

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commodities mean returns fall in the range [0.02, 0.60]. The commodities futures

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returns follow a very similar pattern, although, in only two commodities returns appear to be less than zero. 

The most volatile commodities are coffee, soybean yellow, and cotton. Most commodities appear to have a leptokurtic distribution with a negative skew. Only a small number (five) of commodities have a positive skewness.

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The ADF test applied to the returns of spot and futures series suggests that the null hypothesis of a unit root is comfortably rejected for all commodities at the 1% level. Therefore, as expected, returns are stationary. 14

ACCEPTED MANUSCRIPT 

When we consider the null hypothesis of no autocorrelation, we find that the null is only rejected (at the 5% level) for six commodities, namely, corn, copper, coffee, crude oil, gold, and natural gas, while in the futures market it is rejected for eight commodities (cocoa, gold, copper, soybean yellow, soybean meal, cotton, crude oil, and natural gas).

B.

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INSERT TABLE 2 Preliminary evidence

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In order to estimate rolling window ECMs, we need to first establish that spot and futures prices

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are unit root non-stationary and both price variables are cointegrated. With our data set, for 13 commodities we have 309 rolling regressions, while for cotton, canola, crude oil and natural

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gas we have 285, 254, 233, and 150 rolling regressions, respectively. As a next step, for each

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of the samples for rolling regressions, we have to ascertain that prices are not only unit root non-stationary but are also cointegrated.

We begin with an application of the unit root non-stationarity test. Our approach is to

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apply a rolling Augmented Dickey and Fuller (ADF, 1979) test to both the spot price and futures price. The ADF test examines the null hypothesis that there is a unit root while the alternative hypothesis is that the price variable is stationary. The model includes an intercept

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and a time trend. Lags of the dependent variable are used to control for any serial correlation

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in the model. The optimal lag length is chosen by applying the Schwarz Information Criterion (SIC). We set the maximum lag length to eight and then obtain the optimal lag length based on the SIC. For each commodity’s price series, we extract the ADF t-statistic for each sample of rolling regression. For most of the commodity price series, there is strong evidence that the price series in each rolling regression model is characterised by a unit root. At this point, we should emphasise the observation that, with the ADF test-statistic, there is clear evidence of variations over time. This is implying nothing but the randomness of shocks that impact these commodity price series. In other words, for some commodity prices the test statistics at some 15

ACCEPTED MANUSCRIPT points in time are too far away from the 5% critical value, while at other times they are very close to the 5% critical value. The plots of time-varying ADF test-statistics are available upon request. Similarly, we notice that at some times, evidence suggests that prices are more stationary than non-stationary. Consider some examples. Of the 308 rolling samples used for

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corn, at around the 235th sample, both spot and futures prices behave in a stationary manner.

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For cocoa, notice that spot and futures prices behave in a stationary manner during some of the early rolling samples. For the cocoa spot price, around the 148th rolling sample, some evidence

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of stationarity is noticed, while for the futures prices around the 125th to 130th samples some

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evidence of stationary prices are found. With copper spot and futures prices stationary prices are found around the 125th to 130th samples. With the rest of the commodity prices, similar

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evidence of random stationary prices are found at some point in time. In Table 3, we also provide a summary of the ADF test results. In particular, we report

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the percentage of times (out of the total number of rolling windows) the null hypothesis is

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rejected at the 5% level of significance. We find that natural gas is the only commodity for which the majority of the rolling windows reject the null; around 83% of rolling windows for

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spot prices and around 93% of the rolling windows for futures prices are found to be stationary. Cotton is another commodity for which greater evidence of stationary prices are found; with

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respect to the spot price, the null is rejected for 25% of rolling windows while with respect to the futures price the null is rejected for around 45% of rolling windows. For silver and crude oil, around 25-26% of the rolling windows suggest stationary prices. For nine commodities the rejection rate is less than 10% and for another three commodities the rejection rate is less than 15%. In Table 4, we summarise the findings further. We report the range of the t-test statistics across all rolling regressions per commodity. The test statistics are only for regressions where the null is not rejected.

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ACCEPTED MANUSCRIPT INSERT TABLES 3&4 The main implication here is that while, generally, there is extremely strong evidence that commodity prices are non-stationary, some (albeit limited) cases of stationary samples of prices cannot be ruled out. Even amongst the evidence of non-stationary prices, the ADF test statistics that are less than the CV, the variation is very much time-dependent. However, in

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terms of progressing to the next stage of testing for cointegration, it is best to drop natural gas,

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and entertain caution when considering results obtained from cotton in particular.

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To test for cointegration, we propose a rolling window-based Johansen (1991) trace test. The trace test examines the hypothesis that the system of equations contains, at most, 𝑟

NU

cointegrating vectors. The trace test is calculated as 𝜆(𝑟) = −𝑇 ∑𝑛𝑖=𝑟+1 𝑙𝑜𝑔(1 − 𝜆𝑖 ), where 𝜆𝑖 is the 𝑖th largest eigenvalue. The results are based on a model with a constant but no time trend.

MA

Critical values are obtained from Osterwald-Lenum (1992). In Table 3 (panel B) and in Table 4 (panel B) we report, respectively, the percentage of

D

times the trace test is greater than the 10% critical value (CV), and the range of the trace test.

PT E

The range of the trace test is extracted out of all rolling regressions, for which the null hypothesis of no cointegration (𝑟 = 0) is rejected against the alternative of 𝑟 = 1, and the null

CE

hypothesis of 𝑟 ≤ 1 against the alternative of 𝑟 = 2. These time-varying plots are available upon request. The results are as follows. Except for cotton and natural gas, where at least one

AC

of the price series is mostly stationary (that is, stationary in most of the rolling samples), the null hypothesis of a zero cointegrating vector is rejected in most rolling samples for most of the commodities. Take some examples. For eight commodities the null is rejected in over 90% of the rolling samples, while for another three commodities the null is rejected in over 80% of the rolling samples. Soybean oil and canola are the only two commodities for which the null is rejected in less than 50% of the rolling samples, suggesting weak evidence for cointegration. Although when we test the null hypothesis of, at most, one cointegrating vector against the

17

ACCEPTED MANUSCRIPT alternative of two vectors, except for two commodities (copper and gold), the null is rejected in favour of two cointegrating vectors in more than 50% of the rolling samples. On the whole, then, we find reasonable evidence that the spot and futures price series for most commodities contain at least one cointegrating vector.

Results on price discovery

PT

C.

RI

We now turn to results on price discovery. From our preceding analysis of unit roots and

SC

cointegration for rolling samples, it seems clear that natural gas is the only commodity that departs from the prerequisite that spot and futures prices should be non-stationary. In the case

NU

of cotton, prices seem to violate the non-stationarity condition in around 25-46% of rolling samples, therefore, while we do report the price discovery results for cotton.

MA

In Table 5 we report a summary of the price discovery results. In columns 2 and 3 we report the percentage of regressions (out of total) in which GG>0.5 and GG<0.5, respectively.

D

In the last column, we report the number of rolling samples/regressions. Before we read

PT E

evidence from this table, it is important to state that the mean price discovery falls in the range [0.4287, 0.5602]; the coefficient is lowest for palladium and highest for soybean yellow. The

CE

null hypothesis that the GG coefficient is equal to zero is rejected at the 1% level for all commodities. Now to evidence reported in the table. The percentage of times (regressions in

AC

which) the GG coefficient is greater than 0.5 (implying price discovery in the spot market) and the percentage of times the GG coefficient is less than 0.5 (implying price discovery in the futures market) is remarkable. For example for seven commodities (cocoa (80%), coffee (61%), corn (74%), gold (64%), platinum (83%), silver (69%), and soybean oil (78%)) GG>0.5 at least 61% of the time. On the other hand the GG<0.5 at least 66% of the time for four commodities— crude oil (94%), wheat (84%), palladium (73%), and sugar (66%).

18

ACCEPTED MANUSCRIPT Finally, we notice that the rolling samples reveal volatile price discovery coefficients when price discovery is compared across markets, suggesting nothing but the fact that commodity markets are heterogeneous with respect to price discovery.3 A limitation of averaging the price discovery coefficients across the various rolling samples is that we end up losing quite a bit of information on price discovery. In other words,

PT

if there are indeed time periods over which price discovery is dominated by one market over

RI

another, and vice versa, we have simply ignored this. The cost of doing so can be substantial

SC

because evidence of price discovery seems to be time-varying, as can be observed from Figure 1. There are some commodities for which time-varying price discovery is obvious. In Table 6

NU

we identify those commodities where there are clear phases of alternating price discovery processes between spot and futures markets. For crude oil, evidence is clear that it is the futures

MA

market that dominates price discovery. So now we consider selected commodities for which there is clear evidence that price discovery is time-varying and alternates between spot and

D

futures markets. For cocoa, corn, sugar, wheat, palladium, soybean yellow, and silver there is

PT E

evidence of one phase where the spot market dominates price discovery, and one phase where the futures market dominates price discovery. For coffee and soybean oil there is evidence of

CE

two phases of spot market and two phases of futures market dominance of price discovery. For canola, copper, and soybean meal there is evidence of two phases over which spot market

AC

dominates price discovery, and one phase over which the futures market is dominant, while for platinum evidence suggests one phase of spot market and two phases of futures market dominance of price discovery.

3

This is not entirely surprising as in a recent paper, although in a different context, Narayan and Sharma (2011) show that oil prices have a heterogeneous effect on stock returns.

19

ACCEPTED MANUSCRIPT D.

Are different phases of price discovery related to specific events?

In this section, we attempt to examine whether different phases of price discovery dominated by either the spot or futures market are related to any specific events. A summary of events relating to these phases of a market’s dominance for selected commodities are contained in Table 6. Generally, we find that for most of the phases some events can be associated with the

PT

dominance of price discovery. Consider some examples to demonstrate this point. The

RI

dominance of the canola spot market is associated with a sharp rise in demand for canola and

SC

the persistent rise in energy prices, while the dominance of the futures market coincides with the Agricultural Improvement and Reform Act (US) and the Gulf War. With regard to coffee,

NU

the dominance of the spot market coincides with agreements and disagreement on coffee export quotas, while the dominance of the futures market coincides with a 35% decline in yield in

MA

Ethiopia, the seventh largest producer of coffee in the world. With respect to activities on the copper market, we find that the dominance of the spot market coincides with stagnant world

D

demand and rising inventories, while the futures market dominance is associated with the

PT E

Chilean mine strike. To wheat, in this market while the spot market dominance is associated with the prolonged drought in Australia and the late spring frost in the US which damaged

drought.

CE

emerging crops, the futures market dominance only associates itself with the Australian

AC

As an overall general pattern, we see that spot markets dominance in price discovery starts in the late 1980s and early 1990s, which is a period of global recessions triggered by the United States. Price discovery and business cycles are related, as it appears for instance in the work of Andersen et al. (2007). While in our paper the objective is not to test the business cycle—price discovery nexus, the work of Andersen et al. (2007) allows us to infer that possibly there is also an association between price discovery and business cycles in the commodity markets.

20

ACCEPTED MANUSCRIPT V.

An Economic Significance Analysis of Price Discovery

We do not know anything about the relationship between price discovery, portfolio construction and hedging in commodity markets. Therefore, the goal of this section is two-fold. First, we want to examine optimal portfolio weights and test the effectiveness of hedging in the commodity markets. Second, we want to establish any potential relationship between time-

PT

varying price discovery and the corresponding time-varying portfolio weights and hedging

RI

ratios. These objectives stand out as they have not been investigated before. In the previous

SC

section, we established that in some commodities price discovery takes place in the spot market, while in others it takes place in the futures market, and, regardless of the source, price

NU

discovery is time-varying. Therefore, the question is: does time-varying price discovery have implications for portfolio allocation and hedging in commodity markets?

MA

Our approach is as follows. We begin with a portfolio analysis. From this analysis, following Kroner and Ng (1998), we obtain a portfolio that minimizes risk without reducing

D

expected returns. The weight (𝑤𝑠𝑓,𝑡 ) of the spot (s) market in a one dollar portfolio of spot and

PT E

futures (f) commodities at time t is given by: 𝑤𝑠𝑓,𝑡 =

ℎ𝑓,𝑡 − ℎ𝑠𝑓,𝑡 ℎ𝑠,𝑡 − 2ℎ𝑠𝑓,𝑡 + ℎ𝑓,𝑡

CE

(8)

The time-varying conditional variance of commodity spot (ℎ𝑠,𝑡 ) and commodity futures (ℎ𝑓,𝑡 ),

AC

and the conditional covariance (ℎ𝑠𝑓,𝑡 ) are extracted from estimating a bivariate GARCH model similar to the one proposed by Baillie and Myers (1991). The only difference is that because we find that for all commodities (over the full sample period) spot and futures prices are cointegrated, the mean equation of the bivariate GARCH model includes an error correction term, as in Kroner and Sultan (1993). Therefore, we have a bivariate error correction GARCH 𝑇

model, whose innovations, say {𝑒𝑡 }𝑇𝑡=1 = {𝑒𝑠,𝑡 }𝑡=1 + {𝑒𝑓,𝑡 }

21

𝑇 𝑡=1

where subscript 𝑠 and 𝑓

ACCEPTED MANUSCRIPT represent innovations resulting from the spot and futures error correction equations, respectively, are modelled as: 𝑒𝑡 |Ω𝑡−1 ~𝑁(0, ℎ𝑡 ), ℎ𝑡 = [

(9)

ℎ𝑠,𝑡 ℎ𝑓,𝑡

ℎ𝑓,𝑡 ] ℎ𝑠𝑓,𝑡

′ ) vec(ℎ𝑡 ) = 𝐶 + 𝐴 vec(𝑒𝑡−1 𝑒𝑡−1 + 𝐵 vec(ℎ𝑡−1 )

(10)

PT

From here, the conditional minimum variance hedge ratio, say 𝐻𝑅, at time 𝑡 is simply ℎ𝑠𝑓,𝑡 ⁄ℎ𝑓,𝑡 .

RI

Our key results are contained in Table 7. A range of results are reported here. We begin

SC

with a note on the unit root properties of time-varying price discovery (reported in column 2)

NU

and of the portfolio weight (unreported). This information is important as the mean equation of the GARCH model requires variables to be stationary. We find that the unit root null is

MA

strongly rejected for the portfolio weight series with regard to all commodities. However, for the price discovery series, the null is only rejected at the 1% level for corn and cocoa, and at

D

the 10% for palladium. Therefore, for those commodities where price discovery is non-

PT E

stationary, the variable enters the regression model in first difference form. Now, we consider the statistic of most importance, the portfolio weight, which is simply averaged over time and

CE

reported in the table. The optimal holding of spot and futures differs from commodity to commodity. For wheat the optimal holding of spot in a one dollar portfolio of spot and futures

AC

is around 42 cents. The corresponding optimal portfolio holdings for crude oil and silver are around 48 cents and 52 cents in spot and futures, respectively. For most commodities (corn, gold, palladium, platinum, soybean yellow, soybean meal, sugar, and canola) the optimal portfolio is between 54-56 cents in favour of the spot market. For cocoa and coffee, on the other hand, the optimal portfolio holding of spot is around 67 cents and 70 cents, respectively. The next issue is whether or not the optimal portfolio weights are related to price discovery. We test this. Specifically, we examine whether the dominance in price discovery

22

ACCEPTED MANUSCRIPT resulting from the spot market (𝑃𝐷𝑠,𝑡 ) increases the optimal holding of the spot commodity. To test this, we run the following GARCH (𝑝, 𝑞) model, where the mean equation is: (11)

𝑤𝑠𝑓,𝑡 = 𝛼0 + 𝛽1 𝑃𝐷𝑠,𝑡 + 𝜀𝑡

and the conditional variance, say 𝜎𝑡2 , is represented as a linear function of its past values and

𝑞

𝑝

PT

lagged squared innovations resulting from the mean equation. This can be specified as: 2 2 𝜎𝑡2 = 𝛼0 + ∑ 𝛼𝑖 𝜀𝑡−𝑖 + ∑ 𝛽𝑗 𝜎𝑡−1

(12)

𝑗=1

RI

𝑖=1

SC

where 𝛼0 > 0, 𝛼𝑖 ≥ 0 ∀𝑖, 𝛽𝑗 ≥ 0 ∀𝑗, and the characteristic roots of (1 − ∑ 𝛼𝑖 − ∑ 𝛽𝑗 ) lie outside the unit circle. We use the SIC to select the optimal lag orders of the GARCH model

NU

and find a GARCH (1,1) model to be the most relevant.

MA

Our finding suggests that there is a strong relationship between price discovery and optimal portfolio weight in some commodities but not all. The null that 𝛽1 = 0 is rejected in seven commodities, and, except for canola, the sign is positive, suggesting that as price

PT E

D

discovery becomes more and more spot market dominant, optimal portfolio holding favours the spot market.

We now turn to the results on the hedge ratio reported in panel B of Table 7. Three

CE

results are presented here: (i) the average of the hedge ratio, (ii) the ADF test of the hedge ratio

AC

measuring its degree of persistence, and (iii) the coefficient on 𝛽1 and, in parenthesis, the pvalue relating to the null hypothesis that 𝛽1 = 0. The regression model is the same as that used earlier with portfolio weight replaced by the time-varying hedge ratio as the dependent variable. The main messages emerging from the results can be summarised as follows. First, the hedge ratio varies from commodity to commodity, reflecting nothing other than the fact that commodities are heterogeneous in terms of the long (in spot) and short (in futures) positions. The hedge ratios fall in the range of 0.51 (palladium) to 0.85 (crude oil). This implies that in order to minimise risk for short hedgers, a one dollar long (buy) in the crude oil spot is 23

ACCEPTED MANUSCRIPT shorted (sold) by 85 cents of crude oil futures. By comparison, with palladium significantly less shorting of the futures is required to minimise risk when a one dollar long position is taken in the palladium spot market. Second, does a spot market dominated price discovery process affect hedging? We find that it does, not for all but for some commodities. Generally, the findings imply that as the dominance of the spot market in price discovery becomes more

VI.

Conclusion

RI

PT

prevalent, less shorting of commodity futures is required to minimise risk.

SC

While the subject of this paper is the familiar price discovery process, our contribution is

NU

different from the literature. We recognise the importance of the time-varying price discovery process in commodity markets. In order to progress our idea of understanding time-varying

MA

price discovery in commodity markets, we propose a rolling window error correction model. We test for time-varying price discovery in 17 commodity markets. Two commodities, namely,

D

natural gas and cotton, drop out after failing the unit root null hypothesis test for price variables.

PT E

We, therefore, analyse the remaining 15 commodities and find strong evidence of price discovery. More specifically, we discover that it is the spot market which dominates the price

CE

discovery process in nine commodities, and in six commodities it is the futures market that dominates price discovery. The evidence that in nine commodities the spot market dominates

AC

price discovery actually challenges the widely-held view that price discovery is generally dominated by the futures market. Moreover, for 14 commodities we consistently discover strong evidence of time-varying price discovery. In other words, for canola, cocoa, coffee, copper, corn, gold, soybean oil, soybean yellow, sugar, wheat, palladium, platinum, silver, and soybean meal, price discovery is oscillatory: over some time periods, it is the spot market where price discovery takes place, while during other periods discovery is dominant in the futures market. We are able to link these different phases of price discovery to specific commodity

24

ACCEPTED MANUSCRIPT market events. Finally, we test the relationship between price discovery and portfolio weights, and between price discovery and hedge ratios. We find that, in some commodities, price

AC

CE

PT E

D

MA

NU

SC

RI

PT

discovery helps explain portfolio construction (between spot and futures markets) and hedging.

25

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PT

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ACCEPTED MANUSCRIPT Table 1: Data Information In this table we report the daily time-series average of volume (column 4) and open interest (column 5) which reflect, respectively, the number of futures contracts traded and the total number of outstanding futures contracts held by market participants. Commodities

Futures Exchange

Average volume

Average open interest

ICE

5441

53443

Chicago

CBOT

61239

320828

Central Illinois

CBOT

50882

165613

Decatur, Illinois

CBOT

20198

91680

Wheat

St. Louis

CBOT

21605

102263

Cotton

Memphis

ICE

7232

52101

Decatur, Illinois

CBOT

18142

75344

New York

ICE

23694

166924

20017

101307

2697

14869

8337

47609

Soybean Meal Sugar

NYMEX NYMEX

Coffee

New York

ICE

Copper

New York

NYMEX

12627

68929

Canola

Vancouver

WCE

6255

53266

Gold

Composite

NYMEX

52332

198512

Palladium

New York

NYMEX

899

7531

Crude Oil

ICE

ICE

202147

573095

Natural gas

DOE

NYMEX

43308

116930

CE

PT E

D

MA

NU

Composite indust (Engelhard)

Platinum

AC

Silver

RI

Soybean Oil

PT

New York

Corn Soybean yellow

SC

Cocoa

Source of SPOT

33

ACCEPTED MANUSCRIPT Table 2: Summary statistics of the data In this table we report some commonly-used descriptive statistics, namely, the mean returns, the coefficient of variation, skewness, kurtosis, integration property in the form of ADF test which examines the null hypothesis of a unit root, and the Ljung-Box (1978) Q-statistic at lag 12, which examines the null hypothesis of no autocorrelation. For the ADF and the LB tests, the p-values used to take a decision on the null hypothesis are reported in parenthesis below the test statistic. Results are organised into two panels: panel A contains results for the spot return series, while panel B contains results for the futures return series. Panel A: Commodity spot return

Copper Coffee Palladium Platinum Soybean Yellow Sugar Silver Soybean Meal

Wheat Canola

0.0087

4.7913

0.2542

29.3757

-0.315631

4.368461

-0.0885

-89.2578

-0.1200

4.9757

0.6063

9.1259

0.0798

0.4109

19.1024

-0.4282

7.5417

-0.0335

278.3746

0.1342

5.5764

0.5712

16.7786

0.5433

11.9461

-0.0125

164.144

Crude Oil Natural Gas

ADF

PT

40.9607

SC

RI

-19.9100[0] (0.0000) -12.3152[1] (0.0000) -22.42076[0] (0.0000) -22.0050 [0] (0.0000) -19.0594[0] (0.0000) -20.6580[0] (0.0000) -20.2765[0] (0.0000) -20.4758[0] (0.0000) -18.948[0] (0.0000) -18.7009[0] (0.0000) -20.5762[0] (0.0000) -21.4571[0] (0.0000) -21.2042[0] (0.0000) -20.5204[0] (0.0000) -17.9588[0] (0.0000) -17.9441[0] (0.0000) -14.5468[1] (0.0000)

6.8710

-0.8337

12.8707

-1.3910

16.8699

-0.3097

3.3721

0.1855

59.0965

0.6615

5.2838

0.4771

20.6954

-1.5427

20.6564

0.2049

41.5405

-0.4718

5.5264

0.0227

436.2630

-2.0540

23.7876

0.2731

30.4686

-0.3434

4.5727

0.1699

39.5593

0.0116

5.9794

0.3778

28.8231

-0.2074

6.1722

0.2664

69.6189

-0.1950

5.0266

Mean

CV

Skewness

Kurtosis

ADF

0.1914

41.4346

-0.07601

4.2603

-21.2268[0] (0.0000)

AC

Cotton

0.1959

NU

Gold

Kurtosis

MA

Cocoa

Skewness

D

Corn

CV

PT E

Soybean Oil

Mean

CE

Commodities

LB Q-stat (12 lag) 13.5170 (0.3330) 25.6330 (0.0120) 14.0500 (0.2980) 24.1040 (0.0200) 24.6270 (0.0170) 26.8950 (0.0080) 7.7252 (0.8060) 13.0830 (0.3630) 19.444 (0.078) 8.6266 (0.7340) 9.8742 (0.6270) 11.6230 (0.4760) 15.0090 (0.2410) 14.8020 (0.2520) 18.4330 (0.1030) 22.1510 (0.0360) 35.0610 (0.0000)

Panel B: Commodity futures return Commodities Soybean Oil

34

LB Q-stat (12 lag) 13.2920 (0.3480)

ACCEPTED MANUSCRIPT Corn

0.2579

32.3410

-0.2420

6.6671

-13.1743[1] (0.0000)

18.5680 (0.099)

-0.1131

-79.8444

0.0304

3.4805

-25.1279[0] (0.0000)

22.0950 (0.0360)

0.6074

9.2753

0.2032

7.4270

0.408137

19.3660

-0.136460

5.347019

0.3266

4.1761

-16.2440[1] (0.0000) -19.2903[0] (0.0000) -23.2241[0] (0.0000) -20.3986[0] (0.0000) -21.7910[0] (0.0000) -21.6413[0] (0.0000) -19.0026[0] (0.0000) -19.9843[0] (0.0000) -22.4586[0] (0.0000) -21.3624[0] (0.0000) -23.1375[0] (0.0000) -20.8955[0] (0.0000) -15.7700[0] (0.0000) -13.8897[1] (0.0000)

24.759 (0.016) 22.0680 (0.0370) 17.7760 (0.1230) 9.64070 (0.6470) 10.3480 (0.5850) 31.5310 (0.0020) 9.6427 (0.6470) 11.2690 (0.5060) 38.1360 (0.0000) 27.5910 (0.0060) 16.9470 (0.1520) 9.8514 (0.6290) 30.3780 (0.0020) 37.3260 (0.0000)

Platinum Soybean Yellow Sugar Silver

Canola Crude Oil Natural Gas

5.8628

0.5521

15.2789

-0.8210

12.0844

0.1800

43.0300

-0.8095

7.6004

0.2071

55.1651

0.2330

0.4802

20.6351

-0.9977

0.1918

45.4078

-0.8094

8.3495

0.0275

348.8431

-1.7031

16.4660

0.2708

29.2123

0.2674

4.7304

0.1660

45.1120

-1.2692

13.3103

4.3913

15.3965

0.3729

25.8589

-0.2019

5.3498

0.3123

50.9686

-0.1140

3.6465

CE

Wheat

-0.5481

AC

Cotton

18.2566

PT E

Soybean Meal

0.5729

SC

Palladium

-191.7111

MA

-0.0573

RI

Coffee

NU

Copper

D

Gold

PT

Cocoa

35

ACCEPTED MANUSCRIPT Table 3: Summary, % of times the ADF t-statistic is smaller than the 5% CV This table contains summarised results on the ADF t-test (panel A) and the trace test (panel B). With regard to the ADF test, we report the percentage of times the t-statistic is smaller than the 5% critical value (CV) for each of the two price series. In other words, these percentages tell us the times the unit root null hypothesis is rejected at the 5% level. With regard to the trace test, we report the percentage of times the trace test exceeds the 10% CV (obtained from Osterwald-Lenum, 1992) when 𝑟 = 0 and 𝑟 = 1. Commodity

Panel A: ADF results

Panel B: % of times trace test > 10% CV

Futures price

r=0

Canola

1.6

14.1

43.5

69.0

Cocoa

5.2

4.5

82.9

56.1

Coffee

4.2

12.9

Copper

6.1

4.2

Corn

3.5

13.5

Cotton

24.8

Crude Oil

26.5

Gold

5.5

Natural Gas

82.8

Palladium

3.9

Platinum

16.1

RI

45.2

91.0

82.3

45.5

NU

100.0

94.1

26.5

94.0

60.7

4.5

98.4

45.8

93.4

99.3

66.2

7.7

96.1

65.2

16.8

77.1

64.2

24.2

25.2

99.0

72.9

8.1

5.8

96.5

73.2

2.9

CE

8.4

81.9

84.2

2.3

4.8

14.8

64.2

5.2

6.8

94.8

72.9

Wheat

1.6

3.5

86.1

85.5

D

PT E

AC

Sugar

MA

95.8

Soybean Yellow

Soybean Oil

r=1

80.3

Silver

Soybean Meal

PT

Spot price

36

SC

66.8

ACCEPTED MANUSCRIPT Table 4: Range of test statistics for rolling regressions when the null is not rejected for ADF test and when the null is rejected for trace test In this table we summarise the findings further. It should be appreciated that our empirical analysis involves many thousands of rolling regressions, and presenting detailed results is impossible, due to space constraints. A summarised form of results is an appropriate surrogate. For the ADF test, we report the range of the t-test statistics across all rolling regressions per commodity. The test statistics are only for regressions where the null is not rejected. Similarly, for the trace test, we report the range of trace test, extracted out of all rolling regressions, for which the null hypothesis of no cointegration (r=0) is rejected against the alternative of r = 1, and the null hypothesis of r< = 1 against the alternative of r = 2. Range when trace test > 10% CV

Spot price

Futures price

Canola

[-2.7, 1.0]

[-2.7, 1.8]

Cocoa

[-2.8, 0.1]

[-2.8, -0.0]

Coffee

[-2.7, 1.6]

[-2.8, 1.6]

Copper

[-2.8, 6.3]

[-2.7, 5.2]

Corn

[-2.8, 3.2]

Cotton

[-2.8, 4.6]

Crude Oil

[-2.8,2.7]

Gold

[-2.6, 4.0]

Natural Gas

[-2.8, 2.9]

Palladium

PT

ADF results

𝑟=0

RI

Commodity

𝑟≤1 [2.7, 12.4]

[13.5, 91.8]

[2.7, 8.8]

[13.5, 58.8]

[2.9, 9.2]

[13.5, 41.5]

[2.7, 9.4]

[-2.8, 3.9]

[13.5, 74.7]

[2.7, 13.4]

[-2.8, 4.3]

[14.5, 48,8]

[2.8, 10.8]

[-2.8, 2.9]

[14.5, 52.6]

[2.7, 16.8]

[-2.8, 3.3]

[13.9, 55.0]

[2.7, 22.1]

[-2.8, -0.1]

[19.5, 36.2]

[2.8, 12.8]

[-2.8, 3.8]

[-2.8, 4.7]

[13.5, 89.2]

[2.7, 30.1]

Platinum

[-2.8, 3.9]

[-2.8, 3.9]

[13.5, 260.3]

[2.7, 8.7]

Silver

[-2.8, 4.6]

[-2.8, 2.9]

[13.5, 69.1]

[2.7, 23.3]

[-2.8, 1.0]

[-2.8, 1.3]

[15.4, 50.5]

[2.7, 10.9]

[-2.8, 0.0]

[-2.8, -0.1]

[13.4, 38.4]

[2.8, 13.8]

Soybean Oil

[-2.8, 3.2]

[-2.8, 3.7]

[13.5, 18.8]

[2.7, 8.5]

Sugar

[-2.8, 1.4]

[-2.8, 1.3]

[13.5, 116.0]

[2.7, 10.4]

Wheat

[-2.8, 3.6]

[-2.7, 4.5]

[13.4, 43.3]

[2.7, 10.5]

NU

MA D

PT E

AC

Soybean Meal

CE

Soybean Yellow

SC

[13.5, 97.7]

37

ACCEPTED MANUSCRIPT Table 5: Summary of price discovery by commodity In this table, we report a summary of price discovery results. The second column contains the percent of times the GG coefficient is greater than 0.5. In the third column, we report the percent of times the GG coefficient is less than 0.5. Column 4 notes the standard deviation of the time-varying price discovery coefficients. The last column reports the number of rolling regressions for each commodity. GG<0.5 (%)

Canola

53

47

No. of rolling regressions 254

Cocoa

80

20

309

Coffee

61

39

309

Copper

48

52

Corn

74

26

Crude Oil

6

94

Gold

64

36

Palladium

27

73

Platinum

83

Silver

69

Soybean Meal

42

Soybean Oil

78

Soybean Yellow

56

Sugar

34

Wheat

16

SC

RI

PT

GG>0.5 (%)

309 233 309 309

17

309

31

309

58

309

22

309

44

309

66

309

84

309

NU MA

D PT E CE AC

38

309

ACCEPTED MANUSCRIPT Table 6: Summary of events relating to phases of price discovery between spot and futures markets This table provides a summary of events most closely related to phases over which the spot and futures markets dominated the price discovery process for selected commodities. Commodities

Canola

Coffee

Copper

Corn

Phases when spot market dominated

Events

19982009; 2011-2012 19871996; 2007-2008

2007 to 2008 – Sharp increase in demand for canola and increase in oil prices.

19901996; 1998-2005

Until 1986 the International Coffee Council (ICA), the decisionmaking body of the International Coffee Organisation (ICO), approved export quotas. In 1988 and 1989, ICO failed to reach an agreement on new export quotas, causing the 1983 ICA to break down. The ICA 2007, was adopted by the Council in September 2007. 1993 - Stagnant world demand and rising inventories; London Metal Exchange (LME) intervention in market causes sharp price drop in September. 1994 to 1995 - Strong global demand growth, sharp inventory decline, record high annual price, LME opens U.S. warehouses. 1996 - Sumitomo Corp. reveals huge trading losses and prices plummet at midyear despite global inventory decline.

Phases when futures market dominated 1992-1997

D E

T P

I R

1996 - Federal Agricultural Improvement and Reform Act 1990-1991 – Gulf War

C S U

N A

M

Events

19972006; 2009-2012

From 2002 to 2009, Ethiopian coffee yields declined by nearly 35%. Ethiopia is 7th largest coffee producer in 2006.

2006-2012

2011, 2012 – Chilean mine strike

1996-2012

2012 US drought 2005 – US energy policy act signed into law. Encouraged bio-fuel development in the US. Eventually as much as 23% of US corn crop went to ethanol. 2005: Hurricanes Katrina, Rita, Wilma hit the Gulf Coast. Katrina total loss of $120 B, insured losses of half that. Disruption to Gulf Oil production. 2008 - Flooding occurs throughout the US Midwest that could decrease yield and overall production.

T P E

C C

1987-1995

A

39

ACCEPTED MANUSCRIPT Soybean Oil

19871994; 2004-2007

19952003; 2008-2010

Sugar

1987-2003

2004-2012

Wheat

1987-2007

Palladium

2002-2012

2006 – Australian crops cut almost in half due to drought. 2007 – late spring frost occurred in US that damaged the emerging crop.

2008-2012

N A

Platinum

M

PT

1999-2007

19871992; 2008-2012

E C

C A Silver

1987-1994

1985 – US Mint authorized to begin minting a silver bullion coin.

40

T P

I R

2008 – Floods occur throughout US Midwest that could decrease production. 2007- Australian crop cut in half for second year in row due to drought.

C S U 1995-2001

D E

2006 – Concerns that many acres would be shifted to corn to meet the new renewable fuel mandates. 2008 – Floods occur throughout US Midwest that could decrease production. 2006 – Concerns that many acres would be shifted to corn to meet the new renewable fuel mandates.

1995-2011

1996 California emission standards require cold start emission control. Palladium determined as well-suited for that application. 2000 Catalytic substrate technology reaches capability of 900 cpsi in production models. Euro 3 regulations begin effect. Palladium supply from Russia enters difficulty, price spikes. 2004 US Tier II emissions standards begin phase-in period. Further large NOx emission reduction mandated. 2008 The EU mandates Euro 4 emission standards. 2011 China adopts Euro 4 emission standards. 1983 Rustenburg Platinum Holdings Ltd. in South Africa suspends its producer price quotations for PGM, increased trading of futures contracts on the New York Mercantile Exchange (NYMEX). 1984 Price increase for rhodium because of higher demand for rhodium in automobile three-way catalytic converters. 1986 Platinum price increases after a work stoppage at Impala Platinum Holdings Ltd. in South Africa 2006 – launch of Barclays’ Global Investors iShares Silver Trust Exchange Traded Fund (ETF)

ACCEPTED MANUSCRIPT Table 7: An economic significance analysis

RI

PT

This table reports results on an economic significance analysis of price discovery, portfolio construction between commodity spot and futures (Panel A), and hedging ratios (Panel B). The order of the results is as follows. In column 2 we report the ADF test, which examines the null hypothesis of a unit root in the price discovery series. The ADF regression model is estimated with an intercept term but no time trend. The optimal lag length, reported in square brackets, is chosen using the Schwarz Information Criterion beginning with a maximum of eight lags. The probability value used to decide on the null hypothesis is reported in parenthesis. In column 3, we report two statistics relating to the portfolio construction. First, we have the mean portfolio weight, which is simply an average of the time-varying optimum portfolio weight, while the second statistic examines the null hypothesis that the coefficient on the price discovery is zero in a regression where the dependent variable is the optimum portfolio weight. The p-value used to take a decision on the null hypothesis is reported in parenthesis. In the last three columns, we report results from the hedge ratio. This is divided into three parts. First, we report the mean hedge ratio which is simply the average of the time-varying hedge ratio, followed by a ADF test implemented on the hedge ratio. In the final column we report the outcome of the null hypothesis that the coefficient on price discovery is zero in a regression where the dependent variable is hedge ratio. The p-value used to take a decision on the null hypothesis is reported in parenthesis. *, ** and *** indicate significance at the 1%, 5% and 10% Panel A: Portfolio analysis

-1.4748

0.5039 (0.4645) -3.4565 [0]

1.5593*

D

0.5466

PT E

(0.0098) -4.5210 [1] Cocoa

CE

-2.4894 [1]

AC

8.6344*

0.0355

-0.3056* 0.5628

2.7328* 0.5514

(0.1756)

-3.4674[0]

-3.2879***

(0.0095)

(0.0000)

-3.8237 [2]

0.6146***

(0.0030)

(0.0000)

-4.8043 [1]

-6.9470***

(0.0001)

(0.0000)

-4.2874 [1]

5.6793*

(0.0006)

(0.0522)

-4.8446 [0]

0.0647

(0.0001)

(0.7824)

-3.9258 [0]

0.4561***

(0.0021)

(0.0000)

-4.9207 [0]

-0.0440

(0.0000)

(0.9556)

0.6565 (0.0000)

-2.2909 [0]

(0.8607)

0.6447 (0.9215)

(0.0858)

(0.0002)

0.7232

0.7040

-2.6416 [0]

0.2728

0.7609

(0.8717)

(0.2444)

Platinum

(0.1757)

-0.1556

-2.1015 [3]

Coffee

-4.5592 [1]

0.6244

0.5266

(0.5534)

Palladium

-0.1056

(0.0000)

-1.4585 [0]

Copper

(0.0000)

0.5571

(0.1190)

ADF test

0.6518

0.6679

(0.0002)

𝛽1 = 0

0.7555

(0.1120)

Corn

Gold

NU

-1.6329 [0]

Panel B: Hedge ratios

Mean hedge ratio

MA

ADF test

Soybean Oil

𝛽1 = 0

Mean portfolio weight

SC

levels, respectively.

0.6996 (0.0000)

41

ACCEPTED MANUSCRIPT -2.0746 [4]

-0.0071 0.5614

(0.2552)

(0.8339)

-0.3057 [1]

0.3152 0.5627

(0.9210)

(0.5903) 10.2669*

(0.6908)

(0.0000) 3.8543* 0.5413

0.6733

(0.4845)

(0.0036) 0.1865 0.4218

(0.3555)

(0.3691) -0.3554* 0.5612 (0.0045)

NU

(0.6053)

-0.5617 0.4855

(0.8389)

-5.3505 [0]

-0.9497

(0.0000)

(0.7493)

-4.0578 [1]

-4.7017***

(0.0000)

(0.0000)

-3.4637 [0]

0.1019

(0.0096)

(0.8604)

-2.8199 [0]

-0.3982

(0.0568)

(0.4289)

-5.2914 [0]

-0.5390**

(0.0000)

(0.0138)

0.8547

(0.7803)

AC

CE

PT E

D

MA

(0.8820)

(0.0023)

0.5904

-0.5279 [2] Crude oil

0.2318

0.6667

-1.3525 [0] Canola

-3.8994 [1]

0.7693

-1.8508 [0] Wheat

(0.5724)

PT

0.4835

-1.5938 [0] Soybean Meal

(0.0000)

0.6857

-1.1636 Silver

-0.0338

RI

Sugar

-5.0342 [0] 0.6736

SC

Soybean Yellow

42

ACCEPTED MANUSCRIPT Figure 1: A plot of time-varying price discovery CANOLA

COCOA

.56

COFFEE

.6

1.0

.5

0.8

.4

0.6

.3

0.4

.52 .48 .44 .40 .36 .2 88 90 92 94 96 98 00 02 04 06 08 10 12

0.2 88 90 92 94 96 98 00 02 04 06 08 10 12

COPPER

CORN

.52

.56

.48

.52

.44

.48

.40

.44

.56

.40 88 90 92 94 96 98 00 02 04 06 08 10 12

.52

.6

.50

.4

.48

.2

.48 .46 .44

CE

.50

88 90 92 94 96 98 00 02 04 06 08 10 12

AC

PLATINUM .7

.6

.4

.3 88 90 92 94 96 98 00 02 04 06 08 10 12

SOYBEAN MEAL

SOYBEAN OIL

.54

.600

.52

.575

.50

.550

.48

.525

.46

.500

.44

.475

.42

88 90 92 94 96 98 00 02 04 06 08 10 12

.450 88 90 92 94 96 98 00 02 04 06 08 10 12

SOYBEAN YELLOW

1.0

.40

88 90 92 94 96 98 00 02 04 06 08 10 12

PT E

.52

.44

.5

.0

88 90 92 94 96 98 00 02 04 06 08 10 12

D

.46

SILVER

.48

PALLADIUM

.8

MA

GOLD .54

.54

.52

88 90 92 94 96 98 00 02 04 06 08 10 12

NU

.36

88 90 92 94 96 98 00 02 04 06 08 10 12

SUGAR

WHEAT

.65

.7

.60

.6

0.6

.55

.5

0.4

.50

.4

0.2

.45

.3

0.8

0.0

.40 88 90 92 94 96 98 00 02 04 06 08 10 12

CRUDE OIL

.60

RI

.60

SC

.56

88 90 92 94 96 98 00 02 04 06 08 10 12

PT

.32

.2 88 90 92 94 96 98 00 02 04 06 08 10 12

43

88 90 92 94 96 98 00 02 04 06 08 10 12

ACCEPTED MANUSCRIPT An Analysis of Time-Varying Commodity Market Price Discovery

HIGHLIGHTS We propose a model of time-varying price discovery (PD).



A rolling-window error correction framework is proposed.



For nine commodities, PD dominated by the spot market



For six commodities PD is dominated by the futures market.



PD is useful in portfolio construction and hedging strategy.

AC

CE

PT E

D

MA

NU

SC

RI

PT



44