The identification of the common factors that drivie commodity prices

International Journal of Financial Engineering and Risk Management, Vol. x, No. x, xxxx 1 The identification of the common factors that drivie commod...
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International Journal of Financial Engineering and Risk Management, Vol. x, No. x, xxxx 1

The identification of the common factors that drivie commodity prices Yusho KAGRAOKA Musashi University, 1-26-1, Toyotama-kami, Nerima-Ku, Tokyo 176-8534, Japan E-mail: [email protected] E-mail: [email protected] Abstract: This paper sheds light on recent fluctuations in commodity prices. In particular, the common factors in a generalized dynamic factor model are identified as price drivers or leaders of commodity prices. The empirical results of this study reveal four common factors that account for much of the variation in the commodity returns. These four common factors are the world industrial production, the inflation rate, the USD effective exchange rate (OITP), and the price of crude oil. Keywords: Co-movements among commodity prices; Spill-over effects of oil prices; Generalized dynamic factor models

1 Introduction Commodity prices have fluctuated violently since the 2000. The surge in commodity prices during the first half of 2008 marked the high point of the cyclical upswing in these prices. These prices collapsed, in the tumultuous environment that was created by the recent sub-prime mortgage crisis, which occurred in the fall of 2008; however, commodity prices have subsequently begun to increase once again. The boom that occurred the commodity markets.prior to 2008 ws pervasive. The commodities boom that ended in 2008 raised many issues, including questions about; whether commodity prices had been supported by real demand or were simply a bubble, which economic factors drive commodity prices, the number of factors that must be considered to achive an understanding commodity prices, and many other other considerations. Previous studies have proposed many factors that affected commodity prices; however, no study has quantitatively analyzed the contributions of these factors to commodity prices. Thus, no metric to evaluate the effects of economic indicators on commodity prices has previously been established. Traditional theories failed to explain the upward of commodity prices between 2000 and June 2008; instead, economists and researchers proclaimed that commodity prices were in a phase of a ‘super cycle’ (Radetzki, 2006; Jerrett and Cuddington, 2008; Humphreys, 2010). This ‘super cycle’ was primarily generated by the strong demand for raw materials that was produced by the explosive growth c 2009 Inderscience Enterprises Ltd. Copyright ⃝

2 of China and India. During the examined time period, these nations underwent relatively material-intensive growt. Radetzki et al. (2008) also observed supplyside causes for commodity price increases. In particular, mining capacities did not increase over the course of past two decades because of poor prices and low investor confidence during the period immediately before and after the year 2000. Traditionally, 3-5 years have typically been required before investments in minerals or energy result in new installations that are ready to contribute to the production of these resources. In general, the establishment of new capacity in minerals and enery to match the accelerated demand trends is a more time-consuming process than many individuals commonly assume; in fact, this process may require a decade or longer. Thus, a strong gap between demand and supply.existed with respect to commodities between 2000 and 2008. Several macroeconomic indicators are persuasive potential candidates for explaining variations in commodity prices. The dollar exchange rate may be a codriver of commodity prices in part because these prices are denominated in dollar currency (Sjaastad, 2008); thus a weaker dollar may lead to higher commodity prices. A second factor that may affect commodity prices is interest rates. Akram (2009) investigated not only whether a decline in real interest rates and in the US dollar contributed to higher commodity prices but also whether commodity prices displayed overshooting behaviors in response to changes in real interest rates. In particular, he analyzed the behaviors of the real prices of crude oil, food, metals and industrial raw materials by applying structural vector autoregressive (VAR) models. He concluded that commodity prices increased significantly in response to reductions in real interest rates and that a weaker dollar led to higher commodity prices. Sari et al. (2010) examined the co-movements among the US dollar/euro exchange rate., oil prices, and the spot prices of precious metals. These researchers found that the commodity prices that they examined responded significantly to a shock in the exchange rate. Inflation and interest rates are also important. considerations with respect to commodity prices. Inflation may influence commodity prices because investors move away from stocks and bonds and toward physical assets during the periods of expected inflation. Thus, real commodity prices are hypothesized to increase in response to interest rate shocks that lower interest rates. However, in contrary to this hypothesis, Blose (2010) empirically demonstrated that surprises in the CPI did not affect gold spot prices. To accurately model variations in commodity prices, we must account for spillover effects and high cross-correlations among the prices of different commodities. In fact, spill-over effects are one of the key characteristics for understanding commodity prices. High crude oil prices may increase the prices of other commodities through cost-push effects because the production of these other commodities may depend either directly or indirectly on the use of crude oil (Baffes, 2007). Zhang and Wei (2010) found that there was consistently a positive and significant correlation coefficient for the relationship between the crude oil price and the gold price during the period between 2000 and 2008. Hammoudeh et al. (2010) examined the conditional volatility for the prices of the four major precious metals. These researchers found significant short- and long-run interdependencies among these prices; these prices also demonstrated short- and long-run dependencies on news and on past volatility.

Common factors driving commodity prices

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During the past decade, funds for investment or speculation have moved easily among different markets. For instance, hedge funds invest not only in equity- and debt-based assets but also in real assets such as real estate and commodities. It is plausible that speculative money flows into the commodity markets cause commodities booms and volatile variations in commodity prices. The aim of this paper is to identify the common factors that affect commodity prices. A generalized dynamic factor model is employed in our analysis for two reasons: first, variations in commodity prices lead or lag changes in other commodity prices; and second, commodity prices have shown strong (inter)dependencies on other commodity prices. Our empirical analysis examines data from 2000 to 2012 and extends to a broad range of commodities, including (but not limited to) commodity indices, agricultural products, chemicals, energy, metals, and precious metals. Our empirical results indicate the existence of four common factors that explain more than 70% of the total variance in the examined commodity returns. This paper is organized as follows. In Section 2, we introduce our model and methodology. We focus on the generalized dynamic factor model and explain how the number of common factors affecting commodity prices is determined. Section 3 describes our dataset and documents our empirical results; in particular, we identify the common factors.that affect commodity prices and examine the proportion of the variance in these prices that is explained by the common factors that have been identified. Section 4 concludes our study.

2 The identification of the common factors that affect commodity prices 2.1 The generalized dynamic factor model The observed return of the examined commodities, xit , is expressed as the finite realization of a double array {Xi,t , i = 1, 2, . . . , n, t ∈ Z} of random variables, where n is the total number of commodities. Co-movements of commodity returns are well addressed by factor models. Principal component analysis and factor analysis are among the best known types of factor models. These two types of analyses are categorized as static factor models because they examine contemporaneous co-movements among the observations. The static factor model is not appropriate for our purposes because changes in certain factors might lead or lag changes in commodity returns that are examined Thus, dynamic factor models are better suited for our purposes. A dynamic factor model is represented as follows: xit =χit + ξit , χit := bij (L) :=

q ∑ j=1 ∞ ∑ k=1

(1)

bij (L)ujt ,

(2)

bijk Lk ,

(3)

4 where L stands for the lag operator. In the above equation, the variable ujt (j = 1, . . . , q) represents common shocks or factors that affect commodity returns, whereas the variables χit = xit − ξit and ξit are known as the common component and the idiosyncratic component of xit , respectively. The q-dimensional process {ut := (u1t , u2t , . . . , uqt )′ , t ∈ Z} represents orthogonal white noise. An exact dynamic factor model was first proposed by Geweke (1977); in this model, idiosyncratic components are assumed to be mutually orthogonal. A generalized dynamic factor model that was developed by Forni et al. (2000) and hereafter denoted as FHLR allows for weakly cross-correlated idiosyncratic components; in particular, the n-dimensional process {ξnt := (ξ1t , ξ2t , . . . , ξnt )′ , t ∈ Z} is zero-mean stationary for any n, and ξis ⊥ ujt for any i, j, s, and t. This feature is appealing to model commodity returns because it is not plausible to assume that idiosyncratic components of these return series will be orthogonal to each other. A key point of the FHLR approach is that common components are extracted through spectral analysis in a frequency domain rather than a time domain. We denote the spectral density matrix of xnt := (x1t , . . . , xnt )′ by Σn (θ) for θ ∈ [−π, π]. We denote eigenvalues of the spectral density matrix in descending order of magnitude by λn1 (θ), . . . , λnn (θ). Similarly, we allow λχnj (θ) and λξnj (θ) to be the eigenvalues that are associated with the spectral densities Σχn (θ) and Σξn (θ), respectively, that are obtained from χnt := (χ1t , . . . , χnt )′ and ξnt := (ξ1t , . . . , ξnt )′ , respectively. In an empirical study, the spectral density is unknown and must be estimated from n observed series that each has a finite length of T . Let ΣTn (θ) be the sample estimator of Σn (θ) that is calculated from T observations with a truncation parameter of MT . We use λTnj (θ) and pTnj (θ), respectively, to denote the ˜ to denote the adjoint eigenvalues and eigenvectors of the matrix ΣTn (θ). We use D (transposed, complex conjugate) of the matrix D. We define the two-sided filter KTni (L)

=

∞ ∑ k=−∞

KTni,k Lk

) ∞ (∫ π √ 1 ∑ − −1kθ T = Kni (θ)e dθ Lk , 2π −π

(4)

k=−∞

where KTni (θ) = p˜Tn1,i (θ)pTn1 (θ) + p˜Tn2,i (θ)pTn2 (θ) + · · · + p˜Tnq,i (θ)pTnq (θ).

(5)

Given the above conditions, the main results of FHLR may be stated in terms of the following propositions. Proposition 1 Under appropriate assumptions, the first q eigenvalues of Σn diverge as n → ∞, a.e. in [−π, π], whereas the (q + 1)th eigenvalues of Σn is uniformly bounded. In other words, there exists a real M such that λn,q+1 (θ) ≤ M for any θ ∈ [−π, π] and any n ∈ N. Proposition 2 For all ϵ > 0 and η > 0, there exists N0 (ϵ, η) such that [ ] Pr KTnit (L)xnt − χit > ϵ ≤ η

(6)

for a value of t that is located in a suitable central range of the observation period, all n ≥ N0 and all T that are larger than some T0 (n, ϵ, η).

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Thus, the two-sided filters, KTnit (L), that project xnt to the space that is spanned by the common factors are successfully estimated. The FHLR approach assumes that the number of common factors, q, is provided a priori. Hallin and Liska (2007) propose a criterion for selecting q, establish the consistency of this criterion as n and T approach infinity, and provide a complete procedure for determining the number of common factors in a dynamic factor model. We use qmax to denote a predefined upper bound. Proposition 3 Consider a logarithmic form of criterion ( ) MT n ∑ ∑ 1 1 ICnT (k) := log λTni (θl ) + kp(n, T ), n 2MT + 1 i=k+1

(7)

l=−MT

0 ≤ k ≤ qmax . where p(n, T ) is an adequate penalty such that ) )) ( ( ( √ √ MT 1 T −2 2 p(n, T ) = MT + + log min n, MT , , T n MT

(8)

and √ MT = 0.75 T .

(9)

Under the appropriate assumptions, Pr(qnT = q) → 1 provided that n and T both tend to infinity. T We use qc;n to denote the number of factors that result from applying criterion (7) with a penalty cp(n, T ), where c is a constant. We consider J-tuples of the form Tj qc;n j , j = 1, . . . , J, where 0 < n1 < · · · < nJ = n and 0 < T1 ≤ · · · ≤ TJ = T . The Tj variability among the J values of qc;n j , j = 1, . . . , J, is captured by the following expression:

2  J J ∑ ∑ 1 1 Tj qc,n Sc2 := − q Tj  . j J j=1 J j=1 c,nj

(10)

Thus, we consider the c 7→ Sc mapping and choose qˆ = qcˆT,n , where cˆ belongs to the second stable interval. We use Matlab to implement a program to determine the number of common factors in the dynamic factor model of this study and to estimate these common factors. 1

2.2 The creeping of explanatory variables into the commodity returns Previous studies have proposed many economic indicators as potential explanatory variables for commodity prices; however, no published investigation has evaluated the contribution of these indicators to variations in commodity prices. Thus, our approach marks the first attempt to quantitatively evaluate the contribution of

6 each examined economic indicator to variations in commodity prices. The common factors in the dynamic factor models are linear combinations of the lag operators. Therefore, it is not possible to directly link the common factors to economic indicators. Our methodology involves allowing economic indicators to sequentially creep into observations of commodity returns. To conduct further iterations of this approach, we interchangeably incorporate one of the explanatory variables into the examined commodity returns. We then we estimate common factors of the commodity returns including one time series of an economic indicator. Our approach is justified by the following two reasons. First, in our study, the number of cross-sections of the examined commodities is quite large (there are ninety examined commodity series); therefore, the inclusion of an economic indicator does not affect the observed spectral structure. Second, if an economic indicator were one of the common factors that affects commodity prices, the two-sided filter from eq.(4) should remain unchanged. We estimate proportion of the variance in an economic indicator that is explained by the examined common factors to evaluate the contribution of these common factors. This proportion would equal 1 if one of the common factors coincided with the economic indicator that was examined.

3 Empirical analysis 3.1 Commodity price data An extensive history of commodity prices is necessary for application of the generalized dynamic factor model. It is preferable to utilize commodity price data that are obtained as frequently as possible, and many economic indicators are calculated on a monthly basis. Thus, we construct monthly data for commodity prices. In particular, our dataset includes monthly commodity prices from December 1999 to April 2012. We use this dataset to calculate commodity return series from January 2000 to April 2012. We restrict our dataset to commodities with prices that are quoted in US dollars because this currency is used for the majority of the prices of commodities in the marketplace. The list of the examined commodities by category is summarized in Table 1. Broad categories of commodities are employed in this study. We consider nine series of commodity indices, fifteen series of agricultural product prices, fifteen series of chemical prices, twenty-three series of energy prices, fourteen series of metal prices, twelve series of precious metal prices, and two series that do not belong to the aforementioned categories. The trajectories of the examined commodity prices are depicted in Fig.1. Due to space considerations, we utilize the average of commodity prices for each category. The correlation coefficients between commodity returns are depicted in Fig.2.

3.2 Explanatory variables Industrial production is a candidate metric for measure the demand for commodities. The CPB Netherlands Bureau for Economic Policy Analysis

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constructs various industrial production indices. We adopt three industrial production indices as explanatory variables: world inductrial production,the industrial production of advanced countries, and the industrial production of emerging countries. For the purposes of these indices, the OECD member countries except for Turkey, Mexico, Korea, and the Central European OECD members are considered to be advanced countries. The emerging countries are regarded as the nations in the world that are not included in the definition of advanced countries. The world industrial production is an aggregate of the industrial productions of all of the countries of the world. GDP is often employed as a proxy for measuring economic activity; however, GDP is not an appropriate metric for our study because it includes added value from services and because it is calculated only at a frequent as quarterly at most. The commodities in our dataset are quoted in terms of US dollars, and the depreciation of the US dollar might therefore raise the prices of these commodities. Thus, we utilize effective exchange rates of the dollar as explanatory variables of this study. The Federal Reserve Board constructs three types of effective exchange rates; the nominal broad dollar index, the nominal major currencies dollar index, and the nominal other important trading partners (OITP) dollar index. The broad dollar index includes the twenty-six countries that featured bilateral shares of U.S. imports or exports that exceeded 0.5 percent in 1997. The major currencies dollar index utilizes of seven of the twenty-six currencies that are in the broad index (the euro, the Canadian dollar, the Japanese yen, the British pound, the Swiss franc, the Australian dollar, and the Swedish krona); these seven currencies are widely traded in currency markets outside of their respective home regions. The OITP index consists of the remaining nineteen currencies in the broad index. It is reasonable to expect that the inflation rate should affect commodity prices. We use the CPI in the United States (for the sample of all urban consumers and all items) as a proxy for the inflation rate. Interest rates have also been suggested as variables that influence commodity prices. Thus, we adopt both nominal and real interest rates in the United States as explanatory variables in the study because we are uncertain which of these two interest rates is more relevant to variations in commodity prices. There are various anecdotal metrics for assessing the amount of speculative money that exists in global markets. In this study, we use the M2 metric of money supply in the United States as a proxy for the quantity of speculative money in the markets. To summarize, we include five categories of explanatory variables; industrial production indices, effective exchange rates, a money supply metric, the inflation rate, and interest rates. Correlation coefficients between pairs of these economic explanatory variables are provided in Table 3. These correlation coefficients have low values for time series across different categories. To estimate the generalized dynamic factor model, we utilize two types of monthly differences in the explanatory variables. In particular, we use the log difference of the monthly observations for industrial production indices, exchange rates, and the money supply and the simple difference of the monthly observations for the inflation rate and interest rates. Before an economic variable is crept into the model for the examined commodity returns, the values of the variable are standardized to a mean of zero and a standard deviation of one.

8

3.3 Empirical results We calculate returns using the log differences of monthly commodity prices. We standardize each return series to mean of zero and a standard deviation of one. We first determine the number of common factors in the generalized dynamic factor models by following the procedure that was suggested by Hallin and Liska (2007). We set qmax = 10. Fig.3 illustrates the relationship between Sc and c. We find that the number of common factors for explaining commodity prices is equal to four (q = 4); this result is obtained by choosing a c that corresponds to the second interval in which Sc takes a value of zero. We estimate the common factors of the generalized dynamic factor model (Forni et al., 2000). The proportions of the variance that is explained by each common factor are presented in Fig.4. In particular, the four common factors individually explain 43.7%, 13.6%, 8.3%, and 6.3% of the total observed variance, and thus the combination of these factors explains 71.8% of the total variance. We examine the proportion of the variance that is explained by each of these four factors in detail. Fig.5 depicts this proportion for each of the examined commodities. For all of the indices except for the Baltic Exchange Dry Index, this proportion is close to one. This result implies that the the examined commodity indices are well constructed to reflect aggregated variations across individual commodities. For agricultural products, this proportion varies from 0.4444 for raw sugar to 0.9717 for soyabeans. The high proportion that is observed of soyabeans is highly impressive because prices of the agricultural products are affected by climate and demonstrate seasonal variations. For the chemicals, this proportion varies from 0.4617 for PVC to 0.9841 for naphtha. Remarkably, this proportion is very close to one for energy-related chemicals, particularly crude oils; this phenomenon appears to be reasonable because crude oils are used both directly and indirectly for industrial production. We infer that one of the common factors that determines commodity prices may be the price of the crude oil itself. The proportion of the price variance that is explained by the four common factors is also very high for all of the metals and precious metals that were examined except for palladium, rhodium, and ruthenium. This proportion is less high for the other commodities that were examined in this study, although it exceed 0.5 for these commodities. To summarize, the proportion of the variance in commodity prices that is explained by the four common factors are high for all of the commodity categories that are examined. We believe that the crude oil is one of the common factors for determining the variance in commodity prices because the proportion of the variance in crude oil prices that is explained by the common factors is nearly equal to one. We next investigate this proportion for the explanatory variables of this study. The results of this investigation are provided in Table 2 and Fig.6. A very high value of 0.776064 for this proportion is observed for world industrial production. Thus, the global demand for raw materials influences commodity prices. Among the examined USD effective exchange rates, this proportion is highest for the effective exchange rate of the UDS with the OITP nations. This phenomenon is reasonable because many raw materials are exported from the OITP nations. This proportion takes a high value of 0.735754 for the inflation rate and a comparably

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high value of 0.706307 for the real interest rate. These similar values are observed because the correlation coefficient between the inflation rate and the real interest rate has a high magnitude of −0.8995. The magnitudes of the pairwise correlation coefficients between the metrics of world industrial production, the inflation rate, and the effective exchange rate of the USD with OITP nations are small. Therefore, it is reasonable to regard these explanatory variables as independent factors. We conclude that candidates for the common factors that influence commodity prices include world industrial production, the inflation rate, and the effective exchange rate of USD with the OITP nations. In total, there are four common factors that determine commodity prices, and the remaining factor is the price of crude oil.

4 Conclusion We have applied the generalized dynamic factor model of Forni et al. (2000) (FHLR) to the examined commodity prices between 2000 and 2012. Based on the criterion proposed by Hallin and Liska (2007), we have determined that there are four common factors that determine these prices.. We have found that variations in the returns of the examined commodities are captured well by these four common factors. The four common factors have been identified as the world industrial production, the inflation rate, the effective exchange rate of the USD iwth respect to the OITP nations, and the prices of crude oil. The FHLR’ approach involves the extraction of common components in a frequency domain, and the resulting common factors are based on two-sided filters. Thus, FHLR is not appropriate for the forecasting of commodity returns. Forni et al. (2005) propose a one-sided version of the FHLR approach that could be utilized for forecasting. We will examine the forecasting ability of the generalized dynamic factor model in future studies.

References Akram, Q.F. (2009) ‘Commodity prices, interest rates and the dollar’, Energy Economics, vol. 31, pp.838–851. Baffes, J. (2007) ‘Oil spills on other commodities’, Resources Policy, vol. 32, pp.126–134. Blose, L.E. (2010) ‘Gold prices, cost of carry, and expected inflation’, Journal of Economics and Business, vol. 62, pp.35–47. Forni, M., Hallin, M., Lippi, M., and Reichlin, L. (2000) ‘The Generalized dynamic-factor model: Identification and estimation’, The Review of Economics and Statistics, vol. 82, pp.540–554. Forni, M., Hallin, M., Lippi, M., and Reichlin, L. (2005) ‘The generalized dynamic factor model: One-sided estimation and forecasting’, Journal of the American Statistical Association, vol. 100, pp.830–840.

10 Geweke, J. (1977) ‘The dynamic factor analysis of economic time-series models’, Latent Variables in Socio-Economic Models, North-Holland, edited by Aigner, D.J. and Goldberger, A.S., pp.365–383. Hallin, M. and Liska, R. (2007) ‘Determining the number of factors in the general dynamic factor model’, Journal of the American Statistical Association, vol. 102, pp.603–617. Hammoudeh, S.M., Yuan, Y., McAleer, M. and Thompson, M.A. (2010) ‘Precious metals – exchange rate volatility transmissions and hedging strategies’, International Review of Economics & Finance, vol. 19, pp.633–647. Humphreys, D. (2010) ‘The great metals boom: A retrospective’, Resources Policy, Vol. 35, pp.1–13. Jerrett, D. and Cuddington, J.T. (2008) ‘Broadening the statistical search for metal price super cycles to steel and related metals’, Resources Policy, Vol. 33, pp.188–195. Radetzki, M. (2006) ‘The anatomy of three commodity booms’, Resources Policy, Vol. 31, pp.56–64. Radetzki, M. (2006) ‘The boom in mineral markets: How long might it last?’, Resources Policy, Vol. 33, pp.125–128. Sari, R., Hammoudeh, S. and Soytas, U., (2010) ‘Dynamics of oil price, precious metal prices, and exchange rate’, Energy Economics, Vol. 32, pp.351–362. Sjaastad, L.A. (2008) ‘The price of gold and the exchange rates: Once again’, Resources Policy, Vol. 33, pp.118–124. Zhang, Y.-J. and Wei, Y.-M. (2010) ‘The crude oil market and the gold market: Evidence for cointegration, causality and price discovery’, Resources Policy, Vol. 35, pp.168–177.

Common factors driving commodity prices

Table 1

1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

11

List of commodities.

Incides Baltic Exchange Dry Index (BDI) CRB Spot Index (1967=100) DJ UBS- Commodity Ind TR Rogers International Commodity Ind TR LME-LMEX Index MLCX Total Return S&P GSCI Commodity Total Return TR Equal Weight CCI TR/Jefferies CRB Index TR Agriculturals Soya Oil, Crude Decatur Cents/lb Cotton, 1 1/16Str Low -Midl,Memph C/Lb Corn No.2 Yellow USC/Bushel Corn US No.2 South Central IL USD/BSH Wheat No.2, Soft Red Cts/Bu Wheat US HRS 14% Del Mineapolis/Dulut Wheat, No.2 Hard (Kansas) Cts/Bu HOG 51-52% US 3 AREA Ntnl MR USD/Cwt Soyabeans, No.1 Yellow C/Bushel Soymeal 48% FOB K.City USD/MT Yellow Soybn US NO.1 Sth Dvprt USD/Bsh Cocoa-ICCO Daily Price USD/MT Coffee-Brazilian (NY) Cents/lb Colombian Cofee ARAB Ex DC NY Cts/Lb Raw Sugar-ISA Daily Price c/lb Chemicals Acrylonitrile, CIF Import USD/MT Ammonia, Europe CFR NWE USD/MT Benzene, US Gulf Spot FOB Barges USD/GAL Butadiene, Spot FOB Rdam USD/MT Butadiene, US Gulf Spot CIF USC/LB MEG, USG Spot FOB USC/LB Naphtha Far East CFR Japan, 2Half, USD/MT Polye HDPE Bl/Mldg, NWE Spt FOB USD/MT PTA Contract Price USD/MT PTA,Contract USG Delivered USC/LB PVC, USG Domestic GP USC/LB Styrene, USG FOB Export Spot C/LB Toluene, Spot CFR NE Asia USD/MT VCM, USG Spot FOB USC/LB Xylenes, Spot FOB Rdam USD/MT

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 1 2

Energy S&P GSCI Energy Total Return Crude Oil North Sea BFO FOB USD/BBL Crude Oil WTI Cushing USD/BBL Crude Oil WTI FOB Cushing USD/BBL Crude Oil, Tapis FOB Malaysia USD/BBL Crude Oil-Brent Cur. Month FOB USD/BBL Crude Oil-Brent Dated FOB USD/BBL Crude Oil-WTI Spot Cushing USD/BBL Butane Mont Belvieu Del. Pipe USC/GAL Diesel Low Sulphur FOB NYH USC/GAL Fuel Oil, No.2, Spot NY Harbour C/GAL Gasoil, 0.2% Sulphur FOB ARA USD/MT Gasoline Reg. Unl. 10ppm NWE USD/MT Gasoline Reg. Unld. FOB NYH USC/GAL Gasoline, Unld. Prem. FOB NYH USC/Gal Gasoline, Unld. Reg. FOB NYH USC/Gal Jet Kerosene FOB Singapore USD/BBL Jet Kerosene FOB US Gulf USD/MT Jet Kerosene-Cargos CIF NWE USD/MT Naphtha Europe CIF USD/MT Naphtha, FOB Singapore USD/BBL Propane Mont Belvieu Del. Pipe USC/GAL Natural Gas, Henry Hub USD/MMBTU Metals LME-Aluminium 99.7% 3 Months USD/MT LME-Aluminium 99.7% Cash USD/MT LME-Aluminium Alloy 3 Months USD/MT LME-Aluminium Alloy Cash USD/MT LME-Copper, Grade A 3 Months USD/MT LME-Copper, Grade A Cash USD/MT LME-Lead 3 Months USD/MT LME-Lead Cash USD/MT LME-Nickel 3 Months USD/MT LME-Nickel Cash USD/MT LME-SHG Zinc 99.995% 3 Months USD/MT LME-SHG Zinc 99.995% Cash USD/MT LME-Tin 99.85% 3 Months USD/MT LME-Tin 99.85% Cash USD/MT Precious Metals Gold Bullion LBM USD/Troy Ounce Gold, Handy & Harman Base USD/Troy Oz London Platinum Free Market USD/Troy oz Palladium USD/Troy Ounce Rhodium CIF NWE USD/Ounce Ruthenium CIF NWE USD/Ounce S&P GSCI Gold Total Return S&P GSCI Platinum Total Return S&P GSCI Precious Metal Tot. Ret. S&P GSCI Silver Total Return Silver Fix LBM Cash USC/Troy ounce Silver, Handy&Harman (NY) USC/Troy OZ Other NBSK Pulp (CIF W. Europe) USD/MT RL-Western SPF #2& Btr 2X4 R/L Mill

12

Table 2

Explanatory variables and their proportions of variance explained by the common factors.

1 2 3 4 4 5 6 8 9 10 11 12

Industrial Production (World) Industrial Production (Advanced countries) Industrial Production: (Emerging countries) USD Effective Exchange Rate (Broad) USD Effective Exchange Rate (Major) USD Effective Exchange Rate (OITP) Money Supply (M2) Inflation Rate Nominal Interest Rate (3M) Nominal Interest Rate (5Y) Nominal Interest Rate (10Y) Real Interest Rate

0.776064 0.710425 0.727453 0.707872 0.612451 0.728258 0.576993 0.735754 0.604916 0.570764 0.624283 0.706307

Industrial Production (IP) World Advanced Emerging 1 0.9000 1 0.8334 0.5197 1 -0.3140 -0.2276 -0.3280 -0.2266 -0.1403 -0.2720 -0.3810 -0.3163 -0.3348 -0.3850 -0.3230 -0.3557 0.3539 0.2664 0.3631 0.1976 0.1880 0.1385 0.2018 0.1534 0.1787 0.1901 0.1338 0.1871 -0.2529 -0.1794 -0.2753 1 0.9490 0.8003 0.1447 -0.3126 -0.1023 -0.0074 -0.0139 0.3355 1 0.5737 0.0835 -0.2969 -0.0194 0.0662 0.0439 0.3557 1 0.2079 -0.2517 -0.2239 -0.1521 -0.1231 0.1989

Effective Exchange Rate Broad Major OITP

Correlation coefficients between the explanatory variables.

IP: World IP: Advanced IP: Emerging USD: Broad USD: Major USD: OITP MS Inflation NIR: 3M NIR: 5Y NIR: 10Y RIR

Table 3

1 -0.1509 -0.2656 -0.0928 -0.0694 0.0400

MS

1 0.1081 0.1786 0.2247 -0.8995

Inflation

1 0.3280 0.1842 0.0079

1 0.9278 0.1176

1 0.0864

Nominal Interest Rate (NIR) 3M 5Y 10Y

1

RIR

Common factors driving commodity prices 13

14 Averge price by category (Jan 2000 = 100) 550 Indices Agriculturals 500 Chemicals Energy 450 Metals Precious Metals 400 Other

350

300

250

200

150

100

50 01/01/00

Figure 1

07/02/02

01/01/05

07/02/07

01/01/10

07/02/12

Average prices of the commodities.

Average prices of commodities in each category are plotted. The prices at January 2000 are normalized to 100. List of the commodities by category is given in Table 1.

Common factors driving commodity prices

15

Correlationo coefficient between commodities

1.2

1

0.8

0.6

0.4

0.2

0

-0.2 Other Precious Metals Other Precious Metals

Metals Metals Energy Chemicals Agriculturals Indices

Figure 2

Energy Chemicals Agriculturals Indices

Correlation coefficients between commodities.

The correlation coefficients between commodity returns are depicted. List of the commodities by category is given in Table 1.

16 Estimated number of factors - log criterion

10 S c

qT c;n

8

6

4

2

0 0.05

0.1 c

Figure 3

Determining the number of factors.

0.15

0.2

Common factors driving commodity prices

17

Total variance explained by common factors 1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0 0

Figure 4

5

10

15

20

Proportion of variance explained by the common factors.

The bars represent proportion of variance explained by the common factors, and the line represents the accumulated proportion of variance explained by the common factors.

18

Indices

Agriculturals

Chemicals

1

1

1

0.5

0.5

0.5

0

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9101112131415

Energy

1 2 3 4 5 6 7 8 9101112131415

Metals

Precious Metals

1

1

1

0.5

0.5

0.5

0

0 0

20

40

0 1 2 3 4 5 6 7 8 91011121314

1 2 3 4 5 6 7 8 9101112

Other

1

0.5

0 1

Figure 5

2

Proportion of variance of the commodities explained by the common factors.

The proportion of variance explained by the common factors for the commodities is depicted by the commodities category. List of the commodities by category is given in Table 1. The number at the vertical axis corresponds to the number in Table 1.

Common factors driving commodity prices

19

Ratio of variance of economic variables explained by the common factors 0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0 1

Figure 6

2

3

4

5

6

7

8

9

10

11

12

Proportion of variance of the economic variables explained by the common factors.

The list of economic indicators is given as well as the proportion of variance explained by the common factors for the economic indicator. List of the economic indicators is given in Table 2. The number at the vertical axis corresponds to the number in Table 2.

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