A time varying error correction model of price discovery implications for portfolio construction and hedging

A Time-Varying Error Correction Model of Price Discovery: Implications for Portfolio Construction and Hedging ABSTRACT We propose a model of time-varying price discovery based on a rolling-window error correction framework We show that price discovery in five commodities is dominated by the spot market, while, in only six commodities, price discovery is dominated by the futures market We consistently discover that for 14 commodities price discovery is time-varying, which has implications for portfolio construction and hedging Our findings, therefore, challenge the wellestablished view in commodity markets that it is the futures market which dominates the price discovery process Key words: Price Discovery; Time-varying; Error Correction Model; Spot and Futures Markets I Introduction 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 and Granger (GG, 1995) A feature of the empirical literature on price discovery is that the 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 popular in several strands of the literature There are studies on price discovery in commodity 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 price discovery in the equity or equity options markets (see, for instance, Muravyev et al (2013)); there are studies that examine the price discovery process in the stock and CDS spread markets; and there are studies based on the exchange rate market (see Chen and Gau (2010), Poskitt (2010), Cabrera et al (2009), and Tse et al (2006)) 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 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 co-variance, 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 in no fewer than 17 commodity markets (spot and futures) using monthly time series data that mostly span the period 1977 to 2012 This is not all We also utilise daily data to test the robustness of our results With an extensive empirical analysis, we discover strong evidence of price discovery in that, for 15 commodities, there is price discovery Of these 15 commodities, in five commodities (cocoa, corn, platinum, soybean yellow, and soybean oil) it is the spot market where discovery takes place, while the futures market dominates price discovery in only six commodities (canola, copper, crude oil, palladium, soybean meal, and wheat) 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 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 which price discovery is dominated by the futures market Finally, in an economic significance analysis, we show that time-varying price discovery has implications for portfolio construction and hedging in at least some of the commodity markets II Motivation: Why is price discovery time-varying? In this paper, our focus is on price discovery There are strong reasons to believe that price discovery can be time-varying Amongst the 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 discovery process to be time-varying Therefore, it is imperative to understand the factors that affect prices intermittently over time If one considers the literature on equity returns, there is no shortage of reasons why stock prices vary with time The main source of this time-varying nature of stock prices has been attributed to, among others, business cycles (Andersen et al (2007)) and monetary policy/macroeconomic news (Bernanke and Kuttner (2005), Garner (1989), Ederington and Lee (1993)) More specifically, let us consider the time-varying behaviour of commodity prices now 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 commodity price series, and document strong evidence that commodity prices are characterised 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 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 commodity prices are time-varying is the Prebisch and Singer (1950) hypothesis The Prebisch-Singer (PS) hypothesis states that relative commodity prices are steadily decreasing over time That commodity prices are negatively timevarying 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)) 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 policy news, for instance, commodity prices in the Frankel model react more than proportionately In other words, monetary policy shocks lead to an overshooting of commodity 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, 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 the nonlinearities in demand and supply schedules; and (b) for production and storage delays resulting from the market price In related empirical evidence, studies show that commodity prices are non-stationary, 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)) 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 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 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 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 not a continuous process, it is random; therefore, it should have a time-varying effect on the commodity spot and futures markets regardless of whether the speculation originates from the spot or futures markets What we learn from the literature? We learn that commodity prices are time-varying 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 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 markets are exposed to shocks (regardless of the type of shock), prices move to a new long-run 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 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 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 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 We then re-estimate the ECM over 120 months using a rolling window approach In other words, our next ECM is estimated over the period April 1983 to March 1993, then from May 1983 to April 1993, and so on This process of computing ECMs concludes when the last sample date (September 2012) is absorbed 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 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 is one other statistical consideration that needs to be entertained with our proposal, and we 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; 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 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 are not only unit root non-stationary but are cointegrated Against this background, our error correction model for each rolling window, say 𝑖𝑖, takes the following form: (1) 𝑞𝑞 Δ𝐹𝐹𝑡𝑡−𝑗𝑗 ⎤ ⎡� −𝐴𝐴11𝑗𝑗 Δ𝑆𝑆𝑡𝑡−𝑗𝑗 + 𝐴𝐴1𝑗𝑗 𝛼𝛼1 − 𝜆𝜆1 (𝑆𝑆𝑡𝑡−1 − 𝛽𝛽1𝑡𝑡 𝐹𝐹𝑡𝑡−1 ) Δ𝑆𝑆𝑡𝑡 𝑗𝑗=1 ⎢ ⎥ �+ � �=� 𝑞𝑞 Δ𝐹𝐹𝑡𝑡 𝛼𝛼2 + 𝜆𝜆2 (𝑆𝑆𝑡𝑡−1 − 𝛽𝛽2𝑡𝑡 𝐹𝐹𝑡𝑡−1 ) ⎢� −𝐴𝐴1 Δ𝑆𝑆 + 𝐴𝐴2 Δ𝐹𝐹 ⎥ 𝑡𝑡−𝑗𝑗 𝑡𝑡−𝑗𝑗 2𝑗𝑗 2𝑗𝑗 ⎣ 𝑗𝑗=1 ⎦ 𝑒𝑒𝑠𝑠,𝑡𝑡 + �𝑒𝑒 � 𝑓𝑓,𝑡𝑡 For simplicity, the constant term is dropped from the long-run cointegrating equation and as we will show later, both 𝑆𝑆𝑡𝑡 and 𝐹𝐹𝑡𝑡 follow a random walk process: (2) (3) 𝑆𝑆𝑡𝑡 = 𝑆𝑆𝑡𝑡−1 + 𝜂𝜂1𝑡𝑡 𝐹𝐹𝑡𝑡 = 𝐹𝐹𝑡𝑡−1 + 𝜂𝜂2𝑡𝑡 The error terms may be contemporaneously and serially correlated: (4) 𝑐𝑐𝑐𝑐𝑐𝑐(𝜂𝜂𝑡𝑡1 , 𝜂𝜂𝑡𝑡2 ) = 𝜔𝜔𝑡𝑡 (5) (6) 𝑣𝑣𝑣𝑣𝑣𝑣(𝜂𝜂𝑡𝑡1 ) = 𝜎𝜎𝜂𝜂21 𝑣𝑣𝑣𝑣𝑣𝑣(𝜂𝜂𝑡𝑡2 ) = 𝜎𝜎𝜂𝜂22 The evidence on price discovery is based on the error correction coefficients, 𝜆𝜆1 and 𝜆𝜆2 These coefficients measure the speed of adjustment When 𝜆𝜆1 ≤ and is statistically 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 𝜆𝜆2 > 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 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 (2005), one can simply utilise the coefficients of the error correction terms to measure price discovery This can be captured by the following expression: (7) 𝐺𝐺𝐺𝐺𝑆𝑆 = 𝜆𝜆2 , 𝜆𝜆2 − 𝜆𝜆1 Here 𝐺𝐺𝐺𝐺𝑆𝑆 represents the price discovery resulting from the spot market for rolling window 𝑖𝑖, where 𝑖𝑖 = 1, … , 𝑛𝑛 with 𝑛𝑛 representing the last window over which the ECM is estimated When in a twovariable ECM there is a cointegrating relationship, then GG must satisfy 𝐺𝐺𝐺𝐺𝑆𝑆 𝛼𝛼1 + 𝐺𝐺𝐺𝐺𝐹𝐹 𝛼𝛼2 = (orthogonality condition) and 𝐺𝐺𝐺𝐺𝑆𝑆 + 𝐺𝐺𝐺𝐺𝐹𝐹 = (equality condition), where 𝐺𝐺𝐺𝐺𝐹𝐹 is the price discovery resulting from the futures market Since the error correction term in the spot 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 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 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 IV Data and Results A Data We use monthly time series data on 17 commodity markets These commodities are noted in Table For each commodity, we consider two price series: the spot price and the futures price and compute their returns as the log difference All commodities not have the same start date although all data run up to September 2012 For 13 commodities the start date is January 1977, while for cotton, canola, 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 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 Commodity Research Bureau (CRB) data CD The futures price data are adjusted for contract rollovers Some preliminary observations of the data are presented in Table In panel A we 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 mean, coefficient of variation, skewness, kurtosis, and the Ljung-Box (1978) Q-statistic at the lag of 12, which examines the no autocorrelation hypothesis A brief account of these statistics is useful to demonstrate the difference among commodities The following observations, in particular, are noteworthy: • Mean spot returns of three commodities are negative and for the remaining 14 commodities mean returns fall in the range [0.02, 0.60] The commodities futures 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 • 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 • 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) 10 Friedman, M “The Case of Flexible Exchange Rates”, Essays in positive economics, Chicago: University of Chicago Press, (1953) Garbade, K D., and W L Silber “Price Movements and Price Discovery in Futures 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There Price Discovery in Equity Options?” Journal of Financial Economics, 107 (2013), 259-283 26 Narayan, P K., and S Sharma “New Evidence on Oil Price and Firm Returns.” Journal of Banking and Finance, 35 (2011), 3253-3262 Osterwald-Lenum, M “A Note on Quantiles of the Asymptotic Distribution of the Maximum Likelihood Cointegration Rank Test Statistic.” Oxford Bulletin of Economics and Statistics, 54 (1992), 461-472 Poskitt, R “Price Discovery in Electronic Foreign Exchange Markets: the Sterling/Dollar Market.” Journal of Futures Markets, 30 (2010), 590-606 Prebisch, R., (1950) The Economic Development of Latin America and Its Principal Problems, Economic Bulletin for Latin America 1962, 1-22 Schwarz T.V., and A.C Szakmary “Price Discovery in Petroleum Markets: Arbitrage, Cointegration, and the Time Interval of Analysis.” Journal of Futures Markets, 14 (1994), 147167 Singer, H “The Distribution of Gains between Investing and Borrowing Countries.” American Economic Review, 40 (1950), 473-485 Stephan, J A., and Whaley, R.E “Intraday price change and trading volume relationships in the stock and stock options markets.” Journal of Finance, 45 (1990), 191-220 27 Stoll, H., and Whaley, R.E “The dynamics of stock index and stock index futures returns.” Journal of Financial and Quantitative Analysis, 25 (1990), 441-468 Tse, Y.; J Xiang; and J K W Fung “Price Discovery in the Foreign Exchange Futures Market.” Journal of Futures Markets, 26 (2006), 1131–1143 Weller, P., and M Yano “Forward Exchange, Futures Trading, and Spot Price Variability: A General Equilibrium Approach.” Econometrica, 55 (1987), 1433-1450 Yang, J.; D.A Bessler; and D.J Leatham “Asset Storability and Price Discovery in Commodity Futures Markets: A New Look.” Journal of Futures Markets, 21 (2001), 279-300 Zanias, G.P “Testing for Trends in the Terms of Trade between Primary Commodities and Manufactured Goods.” Journal of Development Economics, 78 (2005), 49-59 28 Table 1: 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 Commodities Mean Soybean Oil Corn Cocoa Gold Copper Coffee Palladium Platinum Soybean Yellow Sugar Silver Soybean Meal Cotton Wheat Canola Crude Oil Natural Gas CV Skewness Kurtosis 0.1959 40.9607 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 6.8710 0.4109 19.1024 -0.4282 7.5417 -0.0335 278.3746 0.1342 5.5764 0.5712 16.7786 -0.8337 12.8707 0.5433 11.9461 -1.3910 16.8699 -0.0125 164.144 -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 CV Skewness Kurtosis 0.1914 41.4346 -0.07601 4.2603 0.2579 32.3410 -0.2420 6.6671 -0.1131 -79.8444 0.0304 3.4805 Panel B: Commodity futures return Commodities Mean Soybean Oil Corn Cocoa 29 ADF -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) ADF -21.2268[0] (0.0000) -13.1743[1] (0.0000) -25.1279[0] (0.0000) 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) LB Q-stat (12 lag) 13.2920 (0.3480) 18.5680 (0.099) 22.0950 (0.0360) Gold Copper Coffee Palladium Platinum Soybean Yellow Sugar Silver Soybean Meal Cotton Wheat Canola Crude Oil Natural Gas 0.6074 9.2753 0.2032 7.4270 0.408137 19.3660 -0.136460 5.347019 -0.0573 -191.7111 0.3266 4.1761 0.5729 18.2566 -0.5481 5.8628 0.5521 15.2789 -0.8210 12.0844 0.1800 43.0300 -0.8095 7.6004 0.2071 55.1651 0.2330 4.3913 0.4802 20.6351 -0.9977 15.3965 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 0.3729 25.8589 -0.2019 5.3498 0.3123 50.9686 -0.1140 3.6465 30 -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) Table 2: 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 𝑟𝑟 = and 𝑟𝑟 = Commodity Canola Cocoa Coffee Copper Corn Cotton Crude Oil Gold Natural Gas Palladium Platinum Silver Soybean Yellow Soybean Meal Soybean Oil Sugar Wheat Panel A: ADF results Spot price Futures price 1.6 14.1 5.2 4.5 4.2 12.9 6.1 4.2 3.5 13.5 24.8 45.5 26.5 26.5 5.5 4.5 82.8 93.4 3.9 7.7 16.1 16.8 24.2 25.2 8.1 5.8 2.9 8.4 2.3 4.8 5.2 6.8 1.6 3.5 31 Panel B: % of times trace test > 10% CV r=0 r=1 43.5 69.0 82.9 56.1 66.8 80.3 95.8 45.2 91.0 82.3 100.0 94.1 94.0 60.7 98.4 45.8 99.3 66.2 96.1 65.2 77.1 64.2 99.0 72.9 96.5 73.2 81.9 84.2 14.8 64.2 94.8 72.9 86.1 85.5 Table 3: 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< = against the alternative of r = Commodity Canola Cocoa Coffee Copper Corn Cotton Crude Oil Gold Natural Gas Palladium Platinum Silver Soybean Yellow Soybean Meal Soybean Oil Sugar Wheat Spot price [-2.7, 1.0] [-2.8, 0.1] [-2.7, 1.6] [-2.8, 6.3] [-2.8, 3.2] [-2.8, 4.6] [-2.8,2.7] [-2.6, 4.0] [-2.8, 2.9] [-2.8, 3.8] [-2.8, 3.9] [-2.8, 4.6] [-2.8, 1.0] [-2.8, 0.0] [-2.8, 3.2] [-2.8, 1.4] [-2.8, 3.6] ADF results Futures price [-2.7, 1.8] [-2.8, -0.0] [-2.8, 1.6] [-2.7, 5.2] [-2.8, 3.9] [-2.8, 4.3] [-2.8, 2.9] [-2.8, 3.3] [-2.8, -0.1] [-2.8, 4.7] [-2.8, 3.9] [-2.8, 2.9] [-2.8, 1.3] [-2.8, -0.1] [-2.8, 3.7] [-2.8, 1.3] [-2.7, 4.5] 32 Range when trace test > 10% CV 𝑟𝑟 = 𝑟𝑟 ≤ [13.5, 97.7] [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] [13.5, 74.7] [2.7, 13.4] [14.5, 48,8] [2.8, 10.8] [14.5, 52.6] [2.7, 16.8] [13.9, 55.0] [2.7, 22.1] [19.5, 36.2] [2.8, 12.8] [13.5, 89.2] [2.7, 30.1] [13.5, 260.3] [2.7, 8.7] [13.5, 69.1] [2.7, 23.3] [15.4, 50.5] [2.7, 10.9] [13.4, 38.4] [2.8, 13.8] [13.5, 18.8] [2.7, 8.5] [13.5, 116.0] [2.7, 10.4] [13.4, 43.3] [2.7, 10.5] Table 4: Summary of price discovery by commodity In this table, we report a summary of the price discovery results The second column contains the average (across the total number of rolling samples/regressions, which is noted in the last column) price discovery coefficient We also test the null hypothesis that the average GG coefficient is equal to zero; the resulting t-test statistic is reported in parenthesis in column Column notes the standard deviation of the mean price discovery coefficient while the 95% confidence interval for the mean price discovery coefficient is reported in column Columns and represent the minimum and maximum values of the price discovery coefficients from amongst the number of rolling regressions noted in the last column Finally, *** denotes statistical significant at the 1% level Commodities Canola Cocoa Coffee Copper Corn Cotton Crude Oil Gold Natural Gas Palladium Platinum Silver Soybean Yellow Soybean Meal Soybean Oil Sugar Wheat Mean 0.4838*** (164.79) 0.5163*** (180.39) 0.5061*** (146.19) 0.4855*** (253.11) 0.5103*** (309.579) 0.5169*** (201.41) 0.4555*** (337.21) 0.5062*** (611.97) 0.4033*** (361.17) 0.4287*** (57.391) 0.5118*** (209.59) 0.5055*** (485.435) 0.5602*** (41.032) 0.4894*** (322.93) 0.5322*** (276.19) 0.4944*** (158.34) 0.4528*** (132.51) SD 0.0468 0.0029 95% confidence interval [0.478, 0.489] [0.511, 0.522] Minimum 0.3389 Maximum 0.5579 No of rolling regressions 253 0.2734 0.5695 308 0.0609 [0.499, 0.513] 0.3648 1.0000 308 0.0337 [0.482, 0.489] 0.3645 0.5309 308 0.0016 [0.507, 0.514] 0.4097 0.5661 308 0.0433 [0.512, 0.522] 0.4447 0.5835 284 0.0206 [0.453, 0.458] 0.4257 0.5623 232 0.0145 [0.505, 0.508] 0.4641 0.5312 308 0.0137 [0.401, 0.405] 0.3689 0.4358 89 0.1313 [0.414, 0.443] 0.0604 0.6033 308 0.0429 [0.507, 0.517] 0.3678 0.6756 308 0.0183 [0.503, 0.508] 0.4468 0.5364 308 0.2399 [0.533, 0.587] 0.0000 1.0000 308 0.0266 [0.486, 0.492] 0.4381 0.5324 308 0.0339 [0.528, 0.536] 0.4521 0.5921 308 0.0549 [0.488, 0.501] 0.4108 0.6469 308 0.0034 [0.446, 0.459] 0.2982 0.6699 308 33 Table 5: 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 Phases when spot market dominated Events Canola 19982009; 2011-2012 19871996; 2007-2008 2007 to 2008 – Sharp increase in demand for canola and increase in oil prices Coffee 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 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 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 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 Copper 19901996; 1998-2005 Corn 1987-1995 1996-2012 Soybean Oil 19871994; 2004-2007 19952003; 2008-2010 34 1996 - Federal Agricultural Improvement and Reform Act 1990-1991 – Gulf War Sugar 1987-2003 2004-2012 Wheat 1987-2007 Palladium 2002-2012 1995-2001 Platinum 1999-2007 19871992; 2008-2012 Silver 1987-1994 2006 – Australian crops cut almost in half due to drought 2007 – late spring frost occurred in US that damaged the emerging crop 1985 – US Mint authorized to begin minting a silver bullion coin 35 2008-2012 1995-2011 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 2007- Australian crop cut in half for second year in row due to drought 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 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 emission standards 2011 China adopts Euro 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) Table 6: Robustness test results - Summary of price discovery by commodity based on daily data In this table, we report a summary of the price discovery results based on daily data In the last column, we report the number of rolling samples/regressions and in the second column we report the average (across the total number of samples) price discovery coefficients, its standard deviation appears in column 3, while in columns and we report the minimum and maximum price discovery coefficients, respectively No of rolling regressions Commodities Canola Cocoa Coffee Copper Corn Cotton Crude Oil Gold Palladium Platinum Silver Soybean Yellow Soybean Meal Soybean Oil Sugar Wheat Mean 0.2885 0.4738 0.3751 0.4547 0.4650 0.4371 0.5237 0.4914 0.4955 0.5164 0.4720 0.5086 0.4487 0.5418 0.5109 0.4894 SD 0.1880 0.0925 0.1839 0.0445 0.0434 0.1119 0.0389 0.0131 0.2214 0.1470 0.0399 0.0285 0.0466 0.0342 0.0450 0.0799 Minimum 0.0000 0.0000 0.0235 0.3303 0.3175 0.0000 0.4137 0.4591 0.0000 0.0000 0.3555 0.4398 0.3117 0.4753 0.4304 0.1814 36 Maximum 0.5299 0.6871 0.6585 0.5288 0.6491 0.6121 0.6208 0.5156 0.8626 0.9810 0.5212 0.5819 0.5637 0.6820 0.7115 0.7780 6833 8029 8029 8029 8029 7508 6369 8029 8029 8029 8029 8029 8029 8029 8029 8029 Table 7: An economic significance analysis 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 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% levels, respectively Soybean Oil Corn Cocoa Gold Copper Coffee Palladium Platinum Soybean Yellow Sugar Silver Soybean Meal Cotton Wheat Canola Crude oil Natural gas ADF test (GG series) -1.6329 [0] (0.4645) -3.4565 [0] (0.0098) -4.5210 [1] (0.0002) -2.4894 [1] (0.1190) -1.4585 [0] (0.5534) -2.1015 [3] (0.2444) -2.6416 [0] (0.0858) -2.2909 [0] (0.1756) -2.0746 [4] (0.2552) -0.3057 [1] (0.9210) -1.1636 (0.6908) -1.5938 [0] (0.4845) -1.8414 [0] (0.3600) -1.8508 [0] (0.3555) -1.3525 [0] (0.6053) -0.5279 [2] (0.8820) -2.8162 [0] (0.0584) Panel A: Portfolio analysis Mean 𝛽𝛽1 = portfolio weight -1.4748 0.5039 (0.1120) 1.5593* 0.5466 (0.0000) -0.1056 0.6679 (0.1757) 8.6344* 0.5571 (0.0000) -0.1556 0.5266 (0.8717) 0.0355 0.7040 (0.9215) -0.3056* 0.5628 (0.0000) 2.7328* 0.5514 (0.0000) -0.0071 0.5614 (0.8339) 0.3152 0.5627 (0.5903) 10.2669* 0.4835 (0.0000) 3.8543* 0.5413 (0.0036) 0.0241 0.5049 (0.8038) 0.1865 0.4218 (0.3691) -0.3554* 0.5612 (0.0045) -0.5617 0.4855 (0.7803) -0.7477 0.4205 (0.4796) 37 Panel B: Hedge ratios Mean hedge ratio 0.7575 0.6449 0.6022 0.7529 0.7125 0.5665 0.5120 0.6659 0.6750 0.7018 0.7561 0.6632 0.5967 0.6736 0.6342 0.8531 0.7595 ADF test (hedge ratio) ADF Test(hedge ratio) -4.5592* (0.0002) -3.4674* (0.0095) -3.8237* (0.0030) -4.8043* (0.0001) -4.2874* (0.0006) -4.8446* (0.0001) -3.9258* (0.0021) -4.9207* (0.0000) -5.0342* (0.0000) -3.8994* (0.0023) -5.3505* (0.0000) -4.0578* (0.0000) -2.1096 (0.2411) -3.4637* (0.0096) -2.8199*** (0.0568) -5.2914* (0.0000) 𝛽𝛽1 = Regression results 0.2728 (0.8607) -3.2879* (0.0000) 0.6146* (0.0000) -6.9470* (0.0000) 5.6793*** (0.0522) 0.0647 (0.7824) 0.4561* (0.0000) -0.0440 (0.9556) -0.0338 (0.5724) 0.2318 (0.8389) -0.9497 (0.7493) -4.7017* (0.0000) -1.0098 (0.2074) 0.1019 (0.8604) -0.3982 (0.4289) -0.5390** (0.0138) Figure 1: A plot of time-varying price discovery CANOLA COCOA 56 COFFEE 1.0 0.8 0.6 0.4 52 48 44 40 36 32 0.2 1990 1995 2000 2005 1990 2010 1995 COPPER 2000 2005 1990 2010 60 60 50 55 56 45 50 52 40 45 48 35 40 1995 2000 2005 1995 Crude Oil 2000 2005 1990 2010 1995 GOLD 60 56 2005 2010 2005 2010 2005 2010 2005 2010 44 1990 2010 2000 COTTON CORN 55 1990 1995 2000 Natural Gas 54 44 52 42 50 40 48 38 52 48 44 40 46 1990 1995 2000 2005 36 1990 2010 1995 PALLADIUM 2000 2005 1990 2010 1995 PLATINUM 6 2000 SILVER 54 52 50 48 46 1990 1995 2000 2005 44 1990 2010 1995 Soybean Meal 2000 2005 1990 2010 Soybean Oil 2000 Soybean Yellow 60 54 1995 1.0 52 0.8 55 50 0.6 48 0.4 50 46 0.2 44 42 45 1990 1995 2000 2005 0.0 1990 2010 1995 SUGAR 2000 2005 2010 2005 2010 WHEAT 65 60 55 50 45 40 1990 1995 2000 2005 2010 1990 1995 2000 38 1990 1995 2000 2005 2010 Figure 2: Robustness test - A plot of time-varying price discovery CANOLA COFFEE COCOA 8 6 4 2 0 1985 1990 1995 2000 2005 2010 1985 1990 COPPER 1995 2000 2005 2010 1985 1990 CORN 55 50 1995 2000 2005 2010 2005 2010 2005 2010 2005 2010 2005 2010 COTTON 6 4 45 40 35 30 1985 1990 1995 2000 2005 2010 1985 1990 1995 2000 2005 2010 1985 1990 GOLD CRUDEOIL 60 2000 PALLADIUM 52 65 1995 1.0 0.8 50 55 0.6 48 50 0.4 46 45 40 0.2 44 1985 1990 1995 2000 2005 2010 0.0 1985 1990 PLATINUM 1995 2000 2005 2010 1985 1990 SILVER 1.0 1995 2000 SOYBEANMEAL 60 55 55 0.8 50 50 0.6 45 45 0.4 40 40 0.2 35 0.0 35 1985 1990 1995 2000 2005 2010 30 1985 SOYBEANOIL 1990 1995 2000 2005 2010 1985 1990 SOYBEANYELLOW 70 60 65 56 60 52 55 48 50 44 1995 2000 SUGAR 45 40 1985 1990 1995 2000 2005 2010 2005 2010 1985 1990 1995 WHEAT 1985 1990 1995 2000 39 2000 2005 2010 1985 1990 1995 2000 ... spot and futures prices behave in a stationary manner 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, ... Development of Latin America and Its Principal Problems, Economic Bulletin for Latin America 1962, 1-22 Schwarz T.V., and A. C Szakmary ? ?Price Discovery in Petroleum Markets: Arbitrage, Cointegration, and. .. time- varying price discovery has implications for portfolio construction and hedging in at least some of the commodity markets II Motivation: Why is price discovery time- varying? In this paper,