What Drives Commodity Returns? Market, Sector or Idiosyncratic Factors?

Jun Ma Department of Economics, Finance and Legal Studies

Culverhouse College of Commerce and Business Administration University of Alabama

Box 870224 Tuscaloosa, AL 35487 Phone: 205-348-8985

E-mail: jma@cba.ua.edu

Andrew Vivian School of Business and Economics

Loughborough University Leicestershire LE11 3TU

England, UK Phone: 011-44-150-922-3242

E-mail: a.j.vivian@lboro.ac.uk

Mark E. Wohar Department of Economics

University of Nebraska at Omaha RH-512K

Omaha, NE 68182-0286 Phone: 402-554-3712 Fax: 402-554-2853

E-mail: mwohar@unomaha.edu

Preliminary Do note cite without author’s permission

February 2015

What Drives Commodity Returns? Market, Sector or Idiosyncratic Factors?

Abstract

This paper examines the relationship between commodity returns using a dynamic factor model. The factor model decomposes each commodity return into a market, sector-specific and commodity-specific component. We find the return variation explained by the common factor has increased substantially for the recent period. This phenomenon is strongest for non-agricultural products. We link the amount of variation explained by the common factor to economic variables. (JEL C12, C32, E20, G12, G15) Keywords: dynamic factor model; commodity markets; common variation; financialization

3

1. Introduction

Economic shocks have an impact that often go far beyond the immediate asset, product or

country from which they emanate. For example, the impact of economic shocks will be greater

if commodity markets are integrated and share a common component. The extent to which

commodity returns are globally determined has received relatively little attention and little

rigorous analysis has been conducted. This topic is of great importance though, given that strong

links between markets could result in global shocks having a dramatic impact upon commodities

as witnessed during the recent financial crisis of 2008-2010. Market-wide transmission of shocks

also have policy implications for commodity producers and extractors who could find that

diversification benefits are not as large as anticipated.

There is a large literature examining international co-movements of commodity prices

that builds on the seminal paper of Pindyck and Rotemburg (1990). This area of inquiry tends to

focus upon the economic determinants of co-movement and tries to resolve the puzzle that

commodity price co-movement is much greater than can be explained by economic fundamentals.

This literature also tends to focus on monthly, quarterly or even annual returns (see Pindyck and

Rotemberg,1990 for monthly data; Lombardi et al., 2010 for quarterly data; and Byrne, Fazio,

and Fiess, 2013 for annual data).1

A second and much smaller body of literature has examined commodity returns and

whether these are correlated with each other. In stark contrast to the literature on commodity

price co-movement, studies using commodity returns generally suggest that the market is highly

segmented and any common component is very small (see for example Erb and Harvey, 2006).

Even at the sector level there is limited evidence of a substantial common determinant of

commodity returns. However, since the turn of the millenium there have been dramatic

1 See Phylaktis and Xia (2006) who investigate a large number of markets with differing characteristics.

4

developments within commodity markets. In particular, there has been an influx of speculative

investors who view commodities purely as financial assets; there has been rapid growth in the

money under management in commodity investment funds. Hence, it is plausible that the nature

of co-movement has changed substantially over the last 10 years.

The main objective of this paper is to model the dynamic behaviour of commodity returns

in the context of a sample of 51 commodities drawn from six sectors over the period January

1984-December 2013. To meet this main objective a dynamic factor model is employed, which

extends those implemented in other contexts (e.g. Stock and Watson, 2002; Neely and Rapach,

2011) by allowing for time varying parameters and stochastic volatility. The stochastic volatility

dynamic factor model decomposes commodity returns into three components: a common (or

market) factor, a sectoral factor and a commodity-specific factor. Note that the common factor

and sectoral factor are orthogonal (in the population). Importantly, the common factor is not

based on value-weighted commodity indices, such as S&P GSCI, and hence is not driven by the

largest market(s); this is in contrast to much literature where the commodity market factor is

based on a value-weighted index (see e.g. Tang and Xiong, 2012).

Our sample includes a wide cross-section of 51 commodities, which covers sectors from

Industrial Metals to Cereals and from Energy to Raw Materials. This enables us to examine the

role of market-wide and sectoral factors across a wide spectrum of different commodities. Prior

literature generally tends to either ignore market-wide factors or focus upon the individual factor.

While the perceived wisdom has been that the supply (and to an extent the demand) for

individual commodities primarily determine their prices and returns, this position can now be

questioned given the changing market dynamics. There has been an increase of speculative

investors, most importantly large investment funds and high frequency traders, who respond to

5

factors other than those facing the commodity producer or commodity consumer (Gorton and

Rouwenhorst, 2006; Tang and Xiong, 2012). These investors include active traders and hedge

funds as well as investment funds which may follow more passive diversification strategy

through holding a commodity index tracker.

An important contribution of this paper is to demonstrate that the common component of

commodity returns can explain a statistically significant amount of the variance for the vast

majority of commodities since 2004. Further, we find that the importance of the market

component is generally substantially larger for non-agricultural products. For durable

commodities (for example metal and energy commodities) the market-wide component of

returns is generally more important than the commodity-specific component over recent years.

The outline of the paper is as follows. Section 2 provides a short review of previous

literature. In sections 3 and 4 the econometric techniques used are presented. A description of the

data is presented in section 5. The empirical results from the factor model and the cross-

commodity analysis is presented in section 6. Section 7 concludes.

2. Review of the empirical literature

Introduction

The factors underlying the determinants of commodity price fluctuations have resulted in

a large amount of investigation in both academic as well as policy circles. Since the beginning

of 2000, there were dramatic increases in commodity prices that continued until mid-2008. None

of the proposed theories brought forth in the literature thus far have been able to fully explain

this phenomenon. It is thought that one major factor that contributes to this increase in

commodity prices has been global economic growth, especially for such commodities as energy

6

and metals.

One theme that is receiving strong recent attention is "financialization" of commodity

markets (see for example Irwin and Sanders, 2011; Tang and Xiong, 2012). That is, the idea that

financial investors now consider commodities as a distinct asset class. The financialization of

commodity markets can be beneficial. For example, in the crude oil market, if investors are

willing to take long forward exposures then they can increase their potential for risk sharing and

hedging. It is argued that price stability and the process of price discovery may also be improved

with these developments. However, financialization may also bring about the possibility for

noise trading and momentum strategies (Miffre and Rallis, 2007) to increasingly affect prices

especially if there are a large proportion of active speculative investors in the market. It is still a

matter of debate as to whether such trading played a role in the acceleration of commodity prices

between 2000 and 2008.

Co-movement of Commodity Returns

Since the early 2000s, commodities have emerged as an asset class alongside stocks and

bonds. Studies, using data starting prior to 2000s, find that return correlations between

commodity and stock returns have been increasing (Greer, 2000; Gorton and Rouwenhorst, 2006)

as have the return correlations between crude oil and other commodities (Tang and Xiong, 2012;

Silvennoinen and Thorp, 2013). However, generally return correlations among commodities in

different sectors are small (Erb and Harvey, 2006). A number of studies have reported decreasing

or non-increasing trends in return correlations between commodities and stocks before the recent

financial crisis (Chong and Miffre, 2010; Buyuksahin, Haigh, and Robe, 2010).

The above mentioned characteristics of commodity returns suggest an opportunity for

7

diversification. Institutional investors and hedge funds have started allocating funds in

commodities intensively through trading commodity indices such as Standard & Poor's Goldman

Sachs Commodity Index (S&P GSCI) and the Dow-Jones UBS Commodity Index (DJUBS), and

commodity derivatives. As a result, time-varying correlations in commodity markets became

increasingly of interest for empirical work (Silvennoinen and Thorp, 2013; Olson et al., 2014).

Commodity Returns also exhibit time-varying volatility (Vivian and Wohar, 2012;

Silvennoinen and Thorp, 2013). Vivian and Wohar (2012) provide evidence of structural breaks

in unconditional volatility of commodity returns. Structural breaks are largely idiosyncratic and

occur throughout the 1985-2011 sample period; structural breaks are not concentrated in the

financial crisis period or when financialisation occurred. Silvennoinen and Thorp (2013) model

conditional volatility of commodity returns in a GARCH framework. They find factors such as

Bond spread, T-Bill and Open Interest are determinants of conditional volatility for some

commodities.

Poncela, Senra and Sierra (2014) extend the empirical evidence on commodity

comovement in two dimensions. First, they attempt to determine the extent of comovements in

44 monthly nonfuel commodity return series over the period 1992-2012, while previous

literature focuses upon commodity prices. They provide evidence that the links among

commodity returns, or co-movement, have increased since the end of 2003, as suggested by

those who have discussed the financialization hypothesis (Masters, 2008; Tang and Xiong, 2012;

among others). Second, they highlight the role of uncertainty (VIX) and macroeconomic

fundamentals as potential drivers of non-energy comovement in the short term. (This paper will

be discussed in more detail in a later section on Factor Models).

8

Co-movement and Determinants of Commodity Prices

While the focus of this paper is on common movement in Commodity returns, we briefly

highlight key research from the extensive literature on co-movement in Commodity prices,

which has also gathered a great deal of attention in the literature in recent years.2 One of the

important stylized facts concerning commodity prices is the puzzling nature of their co-

movements.3 Prices that should apparently not be correlated (that have very different demand

and supply characteristics) actually share a common factor over time.

In a seminal paper, Pindyck and Rotemberg (1990) report that there is excess

comovement among commodity prices after accounting for macroeconomic and market

conditions. This evidence casts doubt on the idea that prices are formed competitively in the

commodity market and offers the possibility of studying what role speculation plays in this

market. The large literature that followed, examines and questions the extent of this excess

comovement. For example, Deb, Trivedi, and Varangis (1996) argue that once

heteroscedasticity and dynamics of commodity prices are modelled then the excess comovement

decreases dramatically. 4 Later work by Cashin, McDermott and Scott (1999) report strong

evidence of price co-movement within agricultural and metal commodities, but not between

them. This suggests there are sectoral effects but not market-wide effects.

The evidence that there is some comovement amongst commodities raises the issue of the

source of this comovement. Interest has been ignited in this issue by the upsurge in many

commodity prices in the 2000s. The first main determinant of commodity price co-movement

2 See, for example, Deaton (1999), Beck (2001), Cashin, McDermott and Scott (2002), Enders and Holt (2012) and Karali and Power (2013). 3 See Saadi (2011) for a review of commodity price co-movement in international markets. 4 Ai, Chatrath and Song (2006) do not find excess co-movement in agricultural commodities prices.

9

that has been suggested is real interest rates (Frankel, 2008; Calvo, 2008; Vansteenkiste, 2009).5

Although, Akram (2009), finds that the response to interest rates varies depending upon the type

of commodity.6 Second, global demand, especially from emerging markets such as China and

India is noted to purportedly be a determinant of commodity price movements (for example,

Wolf, 2008; Svensson, 2008; Vansteenkiste, 2009; Lombardi et al., 2010). Third, aggregate

supply shifts have been explored (for example, Svensson, 2008; Radetzki et al., 2008;

Vansteenkiste, 2009).

Fourth, the dollar exchange rate influences commodities prices in part because

commodity prices are denominated in the US dollar (Sjaastad, 2008; Sari et al., 2010; Lombardi

et al., 2010; Vansteenkiste, 2009). Fifth, (macroeconomic) uncertainty may play a role (Beck,

1993, 2001; Dixit and Pindyck, 1994). Sixth, inflation can have an influence on commodity

prices as investors alter their portfolio of stocks and bonds to a portfolio of physical assets, as

expected inflation rises (see Blose, 2010). 7 Seventh, the role of asset managers using

commodities for diversification or speculation may play a role. Calvo (2008) finds that the

growth of sovereign wealth funds are important factors in the short-term contributing to co-

movements of commodity prices. Finally, Baffes (2007), Krugman (2008) and Zhang and Wei

(2010) investigate the impact of oil prices; Krugman (2008) argues that a high oil price provides

an incentive for biofuel prices to rise, which has been argued to be a cause of a general rise in

5 Frankel (2008) argues that a increase in the real interest rate results in an incentive to increase mining activity so that profits may be invested. Following this, the supply of natural resources should increase, resulting in a fall in commodity prices. It is argued that, at the same time, higher rates of return on bonds will decrease the speculative demand for commodities and, leading to a decline in their price. Finally, it is argued that higher real interest rates will decrease inventory demand and commodity prices. 6 Akram (2009) finds that oil prices and prices of industrial raw materials exhibit overshooting behavior in response to interest rate shocks, while metal prices only respond gradually. 7 Ohashi and Okimoto (2013) investigate the recent time period employing real co-movements in an attempt to determine whether co-movements are excessive. Gospodinov and Ng (2013)) examine if commodity price movements can help forecast inflation.

10

food prices. Zhang and Wei (2010) find a significant positive correlation between oil price and

the gold prices over the period 2000-2008. Despite all of the above studies the empirical

evidence has not reached a consensus on the important variables in determining commodity co-

movements. Not surprisingly, each variable influences the movement of commodity prices,

some more in one period than other periods.8

Factor Models

Factor models have been used for the last 40 years in econometrics. Static factor models

assume that all factors are given contemporaneously (See Stock and Watson (2002a,b)). The

approximate factor model of Chamberlain (1983) and Chamberlain and Rothschild (1983) allows

for idiosyncratic components which are cross-sectionally weakly correlated (approximate factor

model), but are static. The dynamic factor models were first employed by Sargent and Sims

(1977) and Geweke (1977), and the original version has mutually orthogonal idiosyncratic

components. An intermediate model allowing for some dynamics is the restricted factor model

where q dynamic factor are expressed with r static factors, q<r (Forni et al., 2005; Forni et al.,

2009; Bai and Ng, 2007). A dynamic version of the approximate factor model, called the

generalized dynamic factor model, has weekly cross-correlated idiosyncratic components (Forni

and Lippi, 2001; Forni et al., 2000; Forni et al., 2004)

Byrne, Fazio, and Fiess (2013), Chen, Jackson, Kim, and Resiandini (2013), West and

Wong (2013), and Poncela, Senra and Sierra (2014) have applied factor models to a panel of

commodity prices. Byrne, Fazio, and Fiess (2013) base their empirical work on a stylized

theoretical model that investigates the role of the real interest rate, as suggested by Frankel (2008)

8 Commodity prices are also important for the welfare of both developing and developed countries (see, among the others, Daude et al., 2010; Frankel, 2008; Neftci and Lu, 2008).

11

and Calvo (2008), and uncertainty, as indicated by Beck (1993, 2001). They report empirical

evidence on 24 primary commodity prices using the Panel Analysis of Nonstationarity in

Idiosyncratic and Common Components (PANIC) method developed by Bai and Ng, 2004. and a

factor augmented vector autoregression (FAVAR). Byrne, Fazio, and Fiess (2013) find that after

deflating by CPI, the deflated factor responds as expected to shocks to interest rates as well as to

risk. They report a significant amount of price co-movement across 24 commodities; they also

argue that this co-movement may be the result of a common factor related to macroeconomic

fundamentals, such as the real interest rate and stock market uncertainty.

Chen, Jackson, Kim, and Resiandini (2013) conduct a factor analysis on a panel of 51

commodity prices over the 1980-2009 period. Similar to Byrne, Fazio, and Fiess (2013), they

also employ the PANIC procedure. Based on this analysis, they identify two common factors

driving relative commodity prices. The results suggest that the first (and most important)

common factor is nonstationary; they present graphical evidence suggesting that the first

common factor is a mirror image of the US nominal trade-weighted exchange rate.9

West and Wong (2013) also estimate a factor model for a panel of commodity prices

deflated by lagged US CPI. They investigate the extent to which a simple static factor model

captures co-movements of commodity prices.10 They provide evidence (both in-sample and out-

of-sample) that supports “reversion towards the factor”. West and Wong (2013) find that the first

principal component from each panel is correlated positively with a measure of real activity

(global industrial production) and negatively with the US dollar exchange rate. However, the

correlation is also low, suggesting that the factor either provides useful information not in those

9 They find that the second common factor and the idiosyncratic components are both stationary; this provides evidence in favor of market stability (Wang and Tomek, 2007; Kellard and Wohar, 2006). 10 By "static" they mean that they do not use lags or attempt to model dynamics in the factor. They state that they focus on static models for simplicity and also on the idea that the simpler models work relatively well in forecasting.

12

two macro variables or it omits useful information found in those variables.

Poncela, Senra and Sierra (2014) employ monthly nonfuel commodity price data over the

period January 1992 to December 2012 and proceed in two steps. First, they employ a dynamic

factor model approach, and conduct estimation through a principal components approach. They

find one latent factor-driving commodity prices (by using information criteria suggested in Bai

and Ng, 2002). They also investigate a sub-period analysis. They find that the common factor

can explain 9% of the variance of nonfuel commodity prices over the period February 1992 to

November 2003, however, this percentage increases to 23% for the period December 2003 to

December 2012. Second, they also employ a FAVAR approach (similar to that used in Bernanke

et al. 2005), to study if the co-movement of commodity prices are affected in the same way by

macroeconomic and speculative variables, in addition to an uncertainty variable over the two

sub-periods. Poncela, Senra and Sierra (2014) find greater synchronization among raw materials

since December 2003. Since then uncertainty has played an important role in determining short-

run fluctuations in non-energy raw material prices.

3. A Dynamic Factor Model with Time-Varying Parameter and Stochastic Volatility

We extend the typical constant parameter Dynamic Factor Model (DFM) to a DFM with

time-varying loading parameters and stochastic volatility (denoted by DFM-TV-SV), following

closely the recent paper by Del Negro and Otrok (2008). The DFM-TV-SV decomposes the

variations of each commodity return into three components: common market movement, sector-

specific movement, and each individual commodity’s idiosyncratic movement. Specifically the

model is set up as below:

titjtittiti esgy ,,,,, +⋅+⋅= gλ (1)

13

Here tiy , is the monthly return of commodity i ( ni ,,2,1 2= , and n is the total number of

commodities); tg is the common market factor that affects all commodities markets and the

economic forces behind this factor may be global economic activity that tends to affect all

commodities markets. The loading parameter for the common factor tg is ti,λ for commodity i

at time t. The sector-specific factor tjs , captures the movement specific to sector j ( mj ,,2,1 2=

and m is the number of sectors) and its loading parameter ti,g is also time-varying. Here tie , is

the idiosyncratic commodity-specific factor.

All of these time-varying loading parameters are assumed to follow random walk

processes for the sake of parsimony:

),0(...~, ,,1,,βηη ititititi Ndii Σ+= −ββ (2)

Where, [ ]',,, tititi gλ=β is a vector containing the time-varying loading parameters for both the

common market factor and the sector factor for commodity return tiy , . Following Del Negro and

Otrok (2008) we assume that the shocks to loading parameters are independent across i,

essentially ruling out the possibility of any common movement among these time-varying

loadings. This at first appears a quite restrictive assumption, and in principle it seems

straightforward to introduce common factors in s'β to capture any potential common movement

among them. However, as we will discuss next, the introduction of the stochastic volatility of

factors can capture potential common movements in the time-varying contributions of the market

and sector factors. This point is rightly made in Del Negro and Otrok (2008). In this sense, it

may be very difficult to separately identify the volatility component and any common factor in

the loading parameters s'β should it be introduced to the model.

As typical in the DFM, for identification purpose we assume that the common market

14

factor, sector factors, and the commodity factors are orthogonal to each other. The time

variations in these loading parameters permit timing varying contributions of various factors to

commodities returns. As a result, the variance decomposition of each commodity return is:

( ) ( ) ( ) ( )titjtjttiti eVarrVargVaryVar ,,2,

2,, +⋅+⋅= gλ (3)

In order to identify these factors we further assume certain time series dynamics for these

factors. The market factor follows a stationary AR(p) process with a stochastic volatility:

gt

gtpt

gpt

gt

gt hgggg εφφφ ⋅++++= −−− )exp(2211 2 (4)

Where ),0(...~ 2g

gt Ndii σε . The stochastic volatility follows a simple random walk process:

)1,0(...~,1 Ndiivvhh gt

gt

hg

gt

gt ⋅+= − σ (5)

Similarly, each sector factor also follows a stationary AR(l) process:

stj

stjltj

sljtj

sjtj

sjtj hssss ,,,,2,2,1,1,, )exp( εφφφ ⋅++++= −−− 2 (6)

Where ),0(...~ 2,, sj

stj Ndii σε . Its stochastic volatility follows a random walk process:

)1,0(...~, ,,,1,, Ndiivvhh stj

stj

hsj

stj

stj ⋅+= − σ (7)

Finally, each idiosyncratic commodity factor also follows a stationary AR(q) process:

titiqtiqitiitiiti heeee ,,,,2,2,1,1,, )exp( εφφφ ⋅++++= −−− 2 (8)

Where ),0(...~ 2, iti Ndii σε . The stochastic volatility follows a random walk process:

)1,0(...~, ,,1,, Ndiivvhh titihititi ⋅+= − σ (9)

The volatility shocks are assumed to be orthogonal to each other. Note that the loading

parameters and their corresponding factors shock variances are not separately identifiable. To

normalize we first restrict the shocks to market and sector factors so that

12,

2,1

2 ==== smsg σσσ . Also because in this model the factors volatilities are time varying, we

15

follow the approach in Del Negro and Otrok (2008) and impose the restriction that the time-

varying volatility h’s in eq. (5), (7) and (9) all start from zero as their initial values, i.e.,

0,0,0 isj

g vvh == for mj ,,2,1 2= and ni ,,2,1 2= . Finally, because the means of factors are not

separately identifiable, we demeaned all returns data before estimating the model.

4. Bayesian MCMC Estimation Algorithm

The above DFM-TV-SV is estimated using the Monte Carlo Markov Chain (MCMC)

Bayesian estimation method by breaking the whole model into several blocks and making

random draws from the conditional densities. Since most part of the model is linear and Gaussian

the standard Gibbs-Sampling algorithm as outlined in Kim and Nelson (1999) readily applies.

However, the time-varying stochastic volatility introduces nonlinear/non-Gaussian feature to the

model and the standard Kalman Filter is no longer applicable. Therefore we employ the

procedure developed by Kim, Shephard, and Chib (1998) that has been widely applied in the

literature to make draws of the stochastic volatility. Their approach is based on a mixture of

normal densities to approximate the underlying non-Gaussian density in making draws of the

stochastic volatility. As a result, such an estimation algorithm allows us to conveniently make

random draws of the parameters and state variables from conditional densities. When the

algorithm converges numerical integrations are easily taken given the Law of Large Numbers to

yield the marginal distributions of model parameters as well as the states.

The MCMC Gibbs-Sampling algorithm is outlined below:

(1) Make a random draw of the market and sectoral factors from the conditional distribution

{ } { }{ } { }{ } { } { } { } { } { }{ } { }{ }

=============

n

i

T

tti

m

j

T

ts

tjTt

gt

nii

nii,e

mjj,sg

n

iTti,t

m

j

T

ttjTtt hhhσsgf

11,11,112

111111,1 ,,,,,,,|, φφφβ ,

16

where i,tβ is the vector containing time-varying parameters as defined in eq. (2),

( )',, 21gp

ggg φφφ 2=φ , ( )',, ,2,1,,

slj

sj

sjsj φφφ 2=φ for mj ,,2,1 2= , ( )',, ,2,1,, qiiiei φφφ 2=φ for

ni ,,2,1 2= .

(2) Make a random draw of the AR parameters and variance parameters for the commodity

factor from the conditional distribution { } { } { } { }( )T

ttiTti,t

T

ttjTttiei hsgσf

1,11,12

, ,,,|,==== βφ . Note

that due to the orthogonality property, these draws can be made one by one without loss

of generality for each ni ,,2,1 2= and its corresponding mj ,,2,1 2= . To ensure a

stationary process any draw of parameters that implies nonstationarity is discarded.

(3) Make a random draw of the time-varying loading parameters and the shock variance

matrix from the conditional distribution { } { } { } { }( )T

ttiieiT

ttjTtti

Tti,t hσsgf

1,2

,1,11 ,,,,|,====

Σ φβ β for

ni ,,2,1 2= . Again due to the orthogonality property, these draws can be made one by

one for each series.

(4) Make a random draw of the AR parameters of the market and sector factors from the

conditional distributions { } { }( )Tt

gt

Tttg hgf 11 ,| ==φ and { } { }( )T

ts

tjT

ttjj,s hsf1,1, ,|

==φ for

mj ,,2,1 2= . To ensure a stationary process any draw of parameters that implies

nonstationarity is discarded.

(5) Make a random draw of the stochastic volatility for the market factor from the

conditional distribution { } { }( )gTtt

hg

Tt

gt ghf φ,|, 11 == σ , for the sector factors from the

conditional distribution { } { }( )sjT

ttjh

sjT

ts

tj shf ,1,,1, ,|, φ==

σ , for commodity factors from the

conditional distribution { } { } { } { }( )eiTti,t

T

ttjTtt

hi

T

tti sghf ,11,11, ,,,|, φβ====

σ

17

(6) Repeat step (1) through (5) for (D+S) number of times. Here D is the initial burn-in draws

needed to be discarded and the results are based on the saved S number of draws once the

convergence is achieved.

We follow recent literature such as Neely and Rapach (2011) and use 2 lags for all factors,

i.e., p=l=q=2. Given initial parameters the above procedure can be started and iterated for (D+S)

number of times, and we set D to 2000 and S to 8000. Below we explain further details of each

of the above steps along with the priors employed in the estimation.

4.1. Draws of the market and sector factors

To reduce dimension of the state vector so as to facilitate the estimation, we follow Kim

and Nelson (1999) and plug eq. (1) into (8) and this results in the following state-space

representation of the above factor model:

Measurement Equation:

titittti hy ,,*, )exp( ε⋅+⋅= ZH (10)

Transition Equation:

ttt ζZFZ +⋅= −1 (11)

Where, ( ) tiiiti yLLy ,2

2,1,*, 1 φφ −−= , ( )',,,',,, 2,2,1,1,,,2,2,1,1,, 00H itiititiitiititit φgφggφλφλλ −−−− −−−−=

and 0 is the zero vector with an appropriate dimension, and the state vector

( )',,,,,,,,,,,, 2,1,,2,1,,2,11,1,121 −−−−−−−−= tmtmtmtjtjtjttttttt sssssssssggg 22Z and here the i-th

commodity belongs to its corresponding j-th sector. The matrix in the transition equation is

18

=

0100010

0100010

0100010

0100010

2,1,

2,1,

2,11,1

21

rm

rm

rj

rj

rr

gg

φφ

φφ

φφ

φφ

F , where the blank areas

are all zeros, and the shock vector is

( )'0,0,)exp(,,0,0,)exp(,,0,0,)exp(,0,0,)exp( ,,,,,1,1s

tms

tms

tjs

tjst

st

gt

gtt hhhh εεεε ⋅⋅⋅⋅= 22ζ with

its variance matrix tQ .

Given the above state-space representation and the corresponding parameter values, we

implement the Kalman Filter and Carter and Kohn (1994) algorithm “filter forward, sample

backwards” to draw the latent factors tZ . See Kim and Nelson (1999) for details of the

algorithm.

4.2. Draws of the model parameters in factors dynamics

Given the market and sector factors obtained from the last step and the loading

parameters we compute the commodity factors tie , from (1). Given factors the model parameters

in factors dynamics such as the AR parameters and variance parameters in eq. (4), (6), and (8)

can simply be obtained through linear regressions. The only complication is that in all these

19

cases since the volatilities are time varying and hence the regression errors have a

heteroskedasticity structure we need to first re-scale the variables in these equations to make the

errors homoscedastic. In particular, divide both sides of eq. (4) by )exp( gth , eq. (6) by

)exp( ,s

tjh , and eq. (8) by )exp( ,tih . After the transformation we make draws of the AR

parameters from their posterior distributions based on (4), (6), and (8). For all these cases we use

the conjugate priors and set the priors as the following:

( ) ),(~', 22,1, I0Nii φφ , where 2I is the identify matrix and this is the same prior for all sets of the

AR(2) parameters of all factors; )0,0(~2 IGiσ , where IG denotes the Inverted-Gamma

distribution, and this setting-up ensures a diffuse prior for the variance parameters.

4.3. Draws of the loading parameters

To remove the serial auto-correlations in the error variables in eq. (1) we again subtract

lagged variables from both sides of eq. (1) and end up with the state-space representation for

each commodity i:

Measurement Equation

titittti hy ,,*, )exp( ε⋅+⋅= ΒΚ (12)

Transition Equation:

ttt ξΒGΒ +⋅= −1 (13)

Where, ( ) tiiiti yLLy ,2

2,1,*, 1 φφ −−= , ( )2,21,1,2211 ,,,,, −−−− ⋅−⋅−⋅−⋅−= tjitjitjtititt sssggg φφφφΚ ,

( )',,,,, 2,1,,2,1,, −−−−= titititititit gggλλλΒ , ( )0,0,,0,0, ,2,1 titit ηη=ξ and the matrix G is given by:

20

=

010000001000001000000010000001000001

G .

Since given factors and the corresponding parameters the loading parameters are

independent across commodity i, this step can be carried out for each commodity i. Again we

utilize Kalman Filter and Carter and Kohn (1994) algorithm “filter forward, sample backwards”

to draw the latent factors tΒ . For parameter matrix ),var()var( ,2,1, tititii ηηηβ ==Σ we employ

the conjugate prior: )3,0003.0(~ IWiβΣ . Here W denotes the Inverse-Wishart distribution, and

the parameter values ensures relatively diffuse prior. Random draws can then be taken from the

posterior distributions. Refer to Primiceri (2005) for further details.

4.4. Draws of time-varying stochastic volatility

Since conditional on factors and corresponding parameters the time-varying volatilities

for factors are independent from each other, we will first discuss the sampling algorithm for the

market factor, and the same procedure applies to the sector and commodity factors volatilities.

First given a draw of the market factor and corresponding parameters, it is

straightforward to compute the error variable in eq. (4):

gt

gtt

gt

gtt hgggg εφφ ⋅=−−= −− )exp(2211

* (14)

Squaring and taking a natural logarithm of both sides of the above equation gives:

gt

gtt hg ς+=** (15)

Where, ( )2*** ln tt gg = , ( )( )2ln gt

gt ες = , and the time-varying volatility g

th follows a simple

21

random walk process as stated in eq. (5), which is repeated here for reference:

)1,0(...~,1 Ndiivvhh gt

gt

hg

gt

gt ⋅+= − σ (5)

First note that the shocks gtς and g

tv are independent. However, the shock gtς in the

measurement equation is not normally distributed, and in fact its distribution is )1(ln 2χ . Kim,

Shephard, and Chib (1998) provides an approach based on a mixture of normal densities to

approximate the underlying non-normal distribution when utilizing the Kalman Filter to draw the

stochastic volatility. Specifically, they suggest using seven normal densities with means

2704.1−km and variances 2kτ , for 7,,12=k , and the component probabilities are kθ . They

carefully choose these values to closely replicate the exact density of )1(ln 2χ . Table 1 below is

replicated from Kim, Shephard, and Chib (1998) and reports these values.

[INSERT TABLE 1 AROUND HERE:]

Conditional on knowing **tg and the component probabilities the above state space model

is approximately linear and Gaussian, and as a result we can apply the standard Carter and Kohn

(1994) algorithm to sample the volatility. Given a sample of volatility, the component

probabilities can then by updated using the Bayesian rule. The general procedure here follows

Primiceri (2005), Koop and Korobilis (2010), and a correction procedure made by Del Negro and

Primiceri (2013).

5. Data

Our empirical analysis is based upon a broad cross-section of 51 commodities over the January

1984 to December 2013 sample period. There are three main reasons for selecting this data.

Firstly, an important consideration is to ensure that there is a broad cross-section of commodities

22

included in the sample. Our sample includes commodities from a range of different sectors from

Energy to Cereals and Vegetable Oils, from Industrial Raw Materials to Precious Metals and

from Other Food and Beverages to Industrial Metals. Secondly, our data sources are the widely

used IMF and Thomson Datastream datasets. Thirdly, we wanted to include a reasonably sized

comparator period to examine against the post-2000 period during which the Financialisation of

commodities occurred; this will help to identify more clearly if and when a change in commodity

market dynamics occurred.

In the empirical analysis we use commodity return defined as the natural log difference of

commodity prices which are denoted by lower case italics. i.e. pt - pt-1 = ln (Pt / Pt-1). Note all raw

data is de-meaned prior to estimation since the means of factors are not separately identifiable;

consequently by construction all estimated factors have an expected mean of zero. The expected

correlation between factors is also zero.

Descriptive statistics are provided in table 2. The mean of all factors is close to its

expected value of zero. However, there are substantial differences in the standard deviations of

the factors. This reflects the fact that the variances of the factor estimates are dynamic and

depend upon the persistence of the factors themselves.11 There are also substantial differences in

the percentiles of the factor distributions for the same reason. For example the Energy sector

lower quartile is -4.336 and upper quartile is 4.631; in contrast there is much less variation for

the Industrial Raw Materials sector where the lower quartile is -0.144 and upper quartile is 0.114.

These results suggest that there is substantial differences in the time-series properties of the

sectoral factors.

[INSERT TABLE 2:]

11 Hence despite the market and sectoral factors being subject to shocks of unit variance, the variance of the factors themselves can differ substantially.

23

6. Econometric results

6.1 Variance decompositions on average – constant loading and constant volatility model

Table 3 presents initial estimates from the static model for the variance decomposition

grouped by sectors. This table points to the individual factor being the most important source of

variation in commodity returns in general and for almost all sectors on average, except for

Cereals & Vegetable Oils. The common factor on average only plays a small role accounting for

less than 10% of the overall variation and less than 6% in all sectors on average apart from Other

Food & Beverages. This suggests that commodity returns are primarily driven by the individual

factors and secondly by the sector factors, which together account for more than 90% of total

variation in commodity returns. Overall, the effect of the common factor is small.

[INSERT TABLE 3:]

6.2 Common and sectoral factor estimates – stochastic volatility model

First, we present the estimates of the common and sectoral factors. These are shown in

Figure 1. Recall that by construction the common factors and sectoral factors are orthogonal. The

common factor identifies the one common component amongst all commodities, while the

sectoral factors captures variation within a sector that is not attributable to the common factor.

Please note that the common factor we estimate is not based on value-weighting and hence is not

driven by the largest commodities (energy). This is in contrast to much empirical finance

literature which uses the world market factor is based on a value-weighted index (see e.g. S&P

GSCI indices).

The common factor displays substantial time-variation and passes through its mean (zero)

24

numerous times. In fact, as expected, the common factor of returns is not very persistent. It also

appears there are a number of substantial shocks to the common factor which seem to be

especially prevalent since the Financialisation of financial markets and during the Financial

Crisis period.

The sectoral factor captures the comovement within a sector once the common factor is

accounted for; i.e. the sectoral factor is obtained once the common factor is subtracted out. The

sectoral factors are also not very persistent and cross their mean of zero multiple times. In

contrast to the common factor, the sectoral factors do not tend to have a general increase in the

magnitude (or number) of shocks after Financialisation occurred or during the Financial Crisis

period. In fact, for some sectors, such as Other Food and Beverages, and Industrial Raw

Materials, the largest shocks clearly occur prior to 2000.

[INSERT FIGURE 1:]

6.3 Variance decompositions on average – stochastic volatility model

Table 4 presents estimates from the stochastic volatility model for the variance

decomposition grouped by sector. Panel A presents the full sample results which are broadly

similar to those from the static model. However, there are a few differences. Firstly, the

contribution of the common factor is now greater than 5% on average for all sectors apart from

Other Food & Beverages. Secondly, the contribution of the common factor is much smaller for

Cereals and Vegetable Oils, but the impact of the sectoral factor here has increased substantially.

Thirdly, the importance of the individual factor is lowest on average at less than 50% for Energy

and Precious Metals, the two sectors which are arguably the most liquid markets, the greatest

interest from the financial press and the largest content of macroeconomic news.

25

We now consider results from three sub-sample periods of equal length: January 1984 –

December 1993, January 1994 – December 2003 and January 2004 – December 2013. The final

period is of special interest since the impact of speculative investors really gained impetus since

2003. Commodity-index related instruments are estimated to have increased to $200 billion by

mid-2008 from $15 billion in 2003 (CFTC, 2008; Tang and Xiong, 2012). Hence the 2004-2013

sub-period will potentially reflect the “Financialisation” of commodities, whereas the earliest

sub-period 1984-1993 will not.

Table 4 Panel B gives results for the 1984-1993 sub-sample period. The results here

indicate that the common factor in general explains about 40% less of the variance in the 1984-

1993 sub-sample compared to the full sample period (e.g. for all commodities it is 4.26% vs

7.95%). The sectoral factor has a similar impact while the individual factor in general explains

more of the variance overall. The common factor explains more than 70% of the variations on

average for four of the six sectors. Panel C reports results for the 1994-2003 sub-sample. The

main differences seem to be: i) the sector contribution has declined markedly for Industrial Raw

Materials and Precious Metals, ii) the sector contribution increases substantially for Industrial

Metals and iii) the individual contribution increases substantially for Industrial Metals but

decreases substantially for Industrial Raw Materials and Precious Metals.

Finally, the results for the 2004-2013 period are substantively different to the earlier sub-

periods. The contribution of the common factor increases dramatically from around 4% on

average to over 15%, while there are decreases in the sector factor and especially the individual

factor from around 73% to about 63%. For industrial metals the common factor can now explain

more than 25% of the variation. For Energy and for Precious metals the common and sectoral

factors can explain about 60% of variation, while the individual factor accounts for the

26

remaining 40%.

[INSERT TABLE 4:]

Overall, this suggests that commodity returns are still primarily driven by the individual

factors, the sectoral factor and the common factor now contribute substantially to their variation.

The sector and common factors now seem to be sufficiently large that they should not be

overlooked in subsequent analysis of commodity returns.

6.4 Cross-sectional variation in Variance decompositions – stochastic volatility model

We next examine the proportion of the commodity-level return variance that can be

explained by the common factor, sectoral factor and the individual factor respectively. These are

displayed in Figure 2 for the common factor, Figure 3 for the sector-specific component and

Figure 4 for the commodity-specific component.

6.4.1 Common Factor

Figure 2 interestingly shows that for the vast majority of commodities (44 out of 51) we

cannot reject the hypothesis that the common factor explains none of the variance in returns prior

to about 1995. However, there is a substantial increase in point estimates for the proportion of

variance explained by the common factor after 2000. For the majority of commodities the

contribution of the common factor is statistically significant from 0 for the last 10 years. There is

variation in the influence of the common factor even for commodities based in the same sector.

For example, for the industrial metals the common factor typically contributes less than

10% of total variation prior to 1995. However, since 2005 this has approached 50% for Copper,

Lead, Nickel and Zinc, however, for Uranium and Tin there has been much less of an increase.

27

For Energy commodities there has also been an increase in the influence of the common

factor over time. However, this is most apparent for the crude oil commodities and less apparent

for the refined oil commodities (such as Fuel Oil and Propane). Nevertheless all commodities

display significance of the common factor from 0 for much of the last 10 years.

For Cereal and Vegetable oil commodities, the increase in the importance of common

factor is most pronounced for Vegetable oils such as (Palm Oil and Soybean Oil) than for

Cereals (such as Barley and Wheat). The increase usage of vegetable oils as biofuels likely is a

determinant in the substantial increase in the explanatory power of the common factor for

variance in the post 2000-period.

With respect to Other Food and Beverage commodities, Figure 2 Panel B indicates the

common factor is typically not significantly different from 0 throughout the sample period. For

some there is a spike in the contribution of the common factor around the Financial Crisis period,

however, this appears to be short-lived and imprecisely estimated, since the confidence bounds

appear to increase.

For many industrial raw materials, especially animal products (such as Hides and Pork),

there is not typically a substantial increase in the mean point estimate of the common factor.

However, for a few raw materials such as Wool-based, Rubber and Hard Timber there is a

substantial increase from around 2005. Finally for precious metals there is an increase around the

time of the Financial Crisis in the importance of the common factor, however, this tends to

dissipate back towards previous levels at the end of our sample.

Overall there seems to be an upward trend in variance contribution of the common factor

for many durable commodities. These commodities such as industrial metals, oil and vegetable

oils can be easily stored for long periods with substantial storage capacity available. Such

28

commodities are much more demand-driven. In contrast a trend is barely apparent for Livestock

or most Food commodities. This may reflect that these commodities are typically more difficult

to store and therefore prices are much more supply inelastic and supply-driven.

[INSERT FIGURE 2:]

6.4.2 Sectoral Factor

Figure 3 interestingly shows results for the importance of the sectoral factor in explaining

commodity return variance. In general there is not a strong trend in the sectoral effect over time.

However, there are a few patterns that differ across commodities.

Perhaps the most striking result from Figure 3 is that for most commodities in the

Industrial Metals, Energy and Precious Metals groups that the sector factor contributes positively

and statistically different from 0 (and typically also from 1) for almost all of the sample period.

While there is some variation over time in the proportion of variance that can be explained, there

is no clear trend in this. In contrast for Other Food and Beverage commodities and for Industrial

Raw Materials the sector contributions are typically very weak; in fact the sector factor for Other

Food and Beverage primarily seems to capture variation in Coffee commodities, whereas the

Industrial Raw Materials sector factor seems to capture variation in Hard Logs / Hard Timber. It

is also worth noting that there is very little evidence that the importance of the sector factor

increases during the Financial crisis or since the Financialisation of commodities occurred.

[INSERT FIGURE 3:]

6.4.3 Individual Factor

We can also reject the hypothesis that the individual factor explains all (100%) of the

29

variance in commodity returns for many commodities in our sample. These results indicate that

our analysis is not plagued by the weak identification issue documented by Balke, Ma and

Wohar (2013a, 2013b), which can impact variance decompositions of various types. The likely

reason here is that by construction each factor is uncorrelated with the other factors, whereas in

other applications the components are correlated with each other.

In Figure 4 there is substantial variation in the point estimates, however, there are also

some noticeable trends. In particular there is generally a downward trend in the individual

contribution for industrial metals over the sample period. In contrast, there is only a downward

trend for precious metals and for some vegetable oils after about 2000. For the other

commodities there is little clearly apparent trend in the point estimates for the individual factor.

However, there is some evidence of a downward spike in the contribution of the individual factor

around the financial crisis period (see for example, Salmon, Fishmeal and Wool). Typically for

Other Food and Beverage as well as the Industrial Raw Material commodities the individual

factor contributes a majority of the variation in the return variation. For some commodities this

could reflect that it takes considerable time for supply to adjust to market factors and thus returns

in the short term will depend heavily on current crop yields, which are largely idiosyncratic

(commodity-specific); this is especially true for coffee and cocoa trees where a crop is not

produced until three years after planting (Josephs, 2014). In contrast for Precious Metals, Crude

Oil and for most Industrial Metals the individual factor contributes less than half of the variation.

This suggests that for a number of commodities the individual component is not the only

important factor determining its movements.

[INSERT FIGURE 4:]

30

6.5 Relationship of the Common Factor to other Variables

Table 5 reports results investigating the relationship of the common factor of commodity

returns from the stochastic volatility model with other variables. Candidate fundamental

variables include measures of the main determinants of variation in commodities suggested in

prior literature. These include the exchange rate, global economic activity, inflation, T-Bill rate

and the long-term bond rate. We also include two measures of uncertainty; first a measure of

economic uncertainty from Bloom (2012) and second a measure of financial market uncertainty,

the VIX index. We also examine the lag of the common factor since it could exhibit some

persistence.

Table 5 Panel A.1 provides evidence from bivariate regressions that many of the

fundamentals are statistically significantly related to the common factor of commodity returns.12

In fact there is a statistically significant relation between all determinants investigated apart from

the economic uncertainty measure. The signs on the relationships are also generally intuitively

acceptable. For example there is a positive relationship between the common factor and inflation

and global economic activity. This is consistent with demand pull inflation emanating from

increased economic activity that leads to an increase in commodity prices. The most striking

results from Panel 1 is the strong relationship between the change in the exchange rate and the

common factor. The change in the exchange rate can explain 32% of all the variation in the

common factor by itself. The exchange rate is a source of common variation across all

commodities since everything is priced is US dollars.

Table 5 Panel A.2 reports results from a multivariate regression, which can explain 57%

of the variation in the common factor. The main variables related to the common factor in this

12 Prior to estimation, the variables of these regressions were standardized by subtracting the mean and dividing by the standard deviation of the variable.

31

setting are the change in the exchange rate and the lag of the common factor. Both variables are

significant at the 5% level. The only other variable that is now even marginally significant at the

10% level is Inflation, but the sign on this variable has also changed from the bivariate model.

Hence, these results point to the change in the exchange rate being the most important

determinant of the common factor (apart from the lag of the common factor itself). Overall, there

is limited support for the other macro-financial determinants of commodity movements.

[INSERT TABLE 5 AND FIGURE XXX AROUND HERE:]

Panels B through D of Table 5 provide sub-sample analysis of which fundamentals are

related to the common factor. Table 5 Panel B indicates that over the 1984:1 – 1993:12 sub-

sample somewhat less of the total variation in the common factor is explained than for the full

sample period. In bivariate regressions only the change in exchange rate, real T-Bill, real Long

term Bond and the lagged common factor are statistically significant. However, in a multivariate

setting only the lagged common factor is statistically significant and the model goodness of fit is

less than 0.5. Panel C considers the 1994:1 – 2003:12 sub-period. In the bivariate regression all

variables except the change in economic uncertainty, change in VIX and real Long-term bond

are significant. In the multivariate setting in addition to the change in the exchange rate and

lagged common factor, the real T-Bill and real long-term bond are statistically significant. The

coefficients on real T-Bill and real long-term bond are of similar magnitude but of opposing

signs; this suggests the term spread could be an important factor for explaining the common

factor during this period.

Table 5 Panel D reports results for the 2004:1 – 2013:12 sample period. In the bivariate

setting most of the explanatory variables are statistically significant. However, it is the lagged

common factor and especially the change in the exchange rate which can explain more than half

32

the variation in the common factor by itself. In the multivariate setting only change in exchange

rate and the lagged common factor are significant. The adjusted r-squared is almost 0.75 which

indicates a very good fit from the model.

Overall, the results suggest that the common factor is quite persistent and that apart from

its first lag, the change in the exchange rate is its most important determinant. It is not surprising

that the exchange rate has an important common effect on the return to commodities. Although

all commodities are denominated in a common currency, US $’s, the variation in the exchange

rate reflects contemporaneous economic developments and future economic expectations. Hence

at least part of the common exchange rate fluctuation reflects fundamentals for the rest of the

world relative to the US. Engel and West (2005) demonstrate that exchange rate predict

fundamentals and are therefore forward-looking; Chen, Rogoff and Rossi (2009) provide further

evidence that exchange rates are forward looking, in particular for future commodity prices.

7. Conclusion

A large body of literature treats commodities as being largely idiosyncratic and especially

overlooks the importance of common movements in commodities. Prior work has focused on

commodity prices. However, the dynamics of realized commodity returns have received

relatively little attention until recently (notable exceptions include Poncela, Senra and Sierra

2014). In this paper the focus is on commodity returns and examining the extent to which these

are driven by common factors and the extent to which they are driven by individual factors. We

estimate a dynamic factor model which generates a common factor and sectoral factors that i)

capture common comovement and ii) are orthogonal. We apply the model to data for 51

commodities over the 1984M4 – 2013M12 sample period.

33

Firstly, this paper provides a dynamic factor model of 51 commodity returns which

allows for stochastic volatility. The common factor of commodity returns is relatively precisely

estimated (and has much narrower confidence intervals than the sectoral factors). The stochastic

volatility of the common factor of commodity returns varies over time and is especially high

from 2005 onwards. In contrast the stochastic volatility of sector factors generally do not show a

clear trend over time.

Secondly, this paper examines the drivers of movements in commodities. The paper

finds that the common factor and the local factor have a statistically significant role to play in

explaining movements in returns. Hence our analysis does not appear to be subject to the weak

identification issue outlined in Balke, Ma and Wohar (2013a, 2013b) which has plagued much

prior work examining variance decompositions. Crucially we find the importance of the

common factor for driving returns increases sharply after 2000. We find the common factor

contributes positively and statistically significantly to the variance of commodity returns for 43

out of 51 commodities over the January 1984 to December 2013 sample period. Consequently,

we add to a growing literature that emphasises that the financialization of commodities is having

an impact on the way in which these markets operate (Silvennoinen and Thorp, 2013);

specifically our contribution is to demonstrate that the common factor of commodity returns

drives an increasing proportion of the variance in many commodities after 2000. Hence

commodities have become a less effective tool for diversification over recent years; this insight

applies both to investment managers seeking to diversify portfolios of financial asset and also to

commodity producers considering diversifying their production.

34

References

Ai, C., Chatrath, A., and Song, F. (2006), “On the comovement of commodity prices,” American Journal of Agricultural Economics, 88(3): 574-588.

Akram, Q.F. (2009), “Commodity prices, interest rates and the dollar,” Energy Economics, 31: 838-851.

Baffes, J. (2007), “Oil spills on other commodities,” Resource Policy, 32: 126-134. Bai, J., and Ng, S. (2002), “Determining the number of factors in approximate factor models,”

Econometrica, 70: 191–221. Bai, J., and Ng, S. (2004), “A panic attack on unit roots and cointegration,” Econometrics, 72:

1127-1177. Bai, J., and Ng, S. (2007), “Determining the Number of Primitive Shocks in Factor Models,”

Journal of Business and Economic Statistics, 25: 52–60. Balke, N., Ma, J., Wohar, M. (2013a), “The contribution of economic fundamentals to

movements in exchange rates,” Journal of International Economics, 90: 1-16 Balke, N., Ma, J., Wohar, M. (2013b), “A bayesian analysis of weak identification in stock

price decomposition,” Macroeconomic Dynamics, forthcoming. Beck, S. (1993), “A rational expectations model of time varying risk premia in commodities

futures markets: theory and evidence,” International Economic Review, 34: 149-168, Beck, S. (2001), “Autoregressive conditional heteroscedasticity in commodity spot prices,”

Journal of Applied Econometrics, 16: 115-132. Bekaert, G., Hodrick, R., and Zhang, X. (2009), “International Stock Return Comovements,”

Journal of Finance, 64: 2591-2626. Bernanke, B.S., Boivin, J., and Eliasz, P. (2005), “Measuring the effects of monetary policy: a

factor-augmented vector autoregressive (FAVAR) approach,” Quarterly Journal of Economics, 120: 387-422,

Blose, L.E. (2010), “Gold prices, cost of carry, and expected inflation,” Journal of Economics and Business, 62: 35-47.

Buyuksahin, B., Haigh, M. S., and Robe, M. A. (2010), “Commodities and equities: Ever a ‘market of one’?” Journal of Alternative Investments, 12: 76-95.

Byrne, J.P., Fazio, G, and Fiess, N. (2011)," Primary Commodity Prices: Co-movements, Common Factors and Fundamentals,” Policy Research Working Paper Series 5578, The World Bank.

Byrne, J.P., Fazio, G, and Fiess, N. (2013), “Primary commodity prices: Co-movements, common factors and fundamentals,” Journal of Development Economics, 101: 16-26.

Calvo, G. (2008), “Exploding commodity prices, lax monetary policy and sovereign wealth funds.” Vox EU, June 20, http://www.voxeu.org/index.php?q=node/12441.

Carter, C.K., Kohn, R. (1994), “On Gibbs Sampling for State Space Models,” Biometrika, 81, 541-553.

Cashin, P., McDermott, J.C., and Scott, A. (1999), “The myth of co-moving commodity prices,” IMF Working Papers, 99/169.

Cashin, P., McDermott, J.C., Scott, A. (2002), “Booms and slumps in world commodity prices,” Journal of Development Economics 69: 277-296.

CFTC. (2008), “Staff Report on Commodity Swap Dealers & Index Traders with Commission Recommendations.” Commodity Futures Trading Commission (September).

35

Chamberlain, G. (1983), “Funds, Factors, and Diversification in Arbitrage Pricing Models,” Econometrica, 51: 1305–1323.

Chamberlain, G., Rothschild, M. (1983), “Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets,” Econometrica, 51: 1281–1304.

Chen, S., Jackson, J.D., Kim, H., and Resiandini, P. (2013), “What drives commodity prices?” working paper, AUWP 2013-03.

Chong, J., Miffre, J. (2010), “Conditional correlation and Volatility in Commodity Futures and Traditional Asset Markets,” Journal of Alternative Investments, 12: 61-75.

Daude, C., Melguizo, A., and Neut, A. (2010), “Fiscal policy in Latin America: Countercyclical and sustainable at last?” OECD Development Centre Working Papers, 291.

Deaton, A. (1999), “Commodity prices and growth in Africa,” The Journal of Economic Perspectives, 13(3): 23-40.

Deb, P., Trivedi, P. K., and Varangis, P. (1996), “The excess comovement of commodity prices reconsidered,” Journal of Applied Econometrics, 11(3): 275-291.

Del Negro, M., Otrok, C. (2008), “Dynamic Factor Models with Time-Varying Parameters: Measuring Changes in International Business Cycles,” Federal Reserve Bank of New York Staff Report, 326.

Del Negro, M, Primiceri, G. (2013), “Time Varying Structural Vector Autoregressions and Monetary Policy: A Corrigendum,” working paper, Department of Economics, Northwestern University.

Dixit, A.K., Pindyck, R.S. (1994), Investment Under Uncertainty, Princeton University Press, Princeton.

Enders, W., Holt, M.T. (2012), “Sharp breaks or smooth shifts? An investigation of the evolution of primary commodity prices,” American Journal of Agricultural Economics 94(3): 659-673.

Engel, C. and West, K.D. (2005), “Exchange rates and fundamentals”, Journal of Political Economy 113(3): 485-517.

Erb, C. B., Harvey, C. R. (2006), “The strategic and tactical value of commodity futures”, Financial Analysts Journal, 62: 69-97.

Forni, M., Giannone, D., Lippi, M., and Reichlin, L. (2009), “Opening the Black Box: Structural Factor Models with Large Cross Sections,” Econometric Theory, 25: 1319–1347.

Forni, M., Hallin, M., Lippi, M., and Reichlin, L. (2000), “The generalized dynamic-factor model: identification and estimation,” The Review of Economics and Statistics, 82: 540–554.

Forni, M., Hallin, M., Lippi, M., and Reichlin, L. (2004), “The generalized dynamic factor model consistency and rates,” Journal of Econometrics, 119: 231–255.

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, 100: 830–840.

Forni, M., Lippi, M. (2001), “The Generalized Dynamic Factor Model:Representation Theory,” Econometric Theory, 17: 1113–1141.

Frankel, J.A. (2008), “The effect of monetary policy on real commodity prices.” In: Campbell, J.Y. (Ed.), Asset Prices and Monetary Policy. NBER, University of Chicago, Chicago: 291-333.

36

Geweke, J. (1977), “The dynamic factor analysis of economic time-series models,” in D.J. Aigner and A.S. Goldberger (Eds.), Latent Variables in Socio- Economic Models, (North-Holland, Amsterdam), Chapter 16: 365–383.

Gorton, G. B., Rouwenhorst, G. K., (2006), “Facts and fantasies about commodity futures,” Financial Analysts Journal, 62: 47-68.

Gospodinov, N., Ng, S. (2013), “Commodity prices, convenience yields and inflation,” Review of Economics and Statistics, 95: 206-219.

Greer, R. (2000), “The nature of commodity index returns,” Journal of Alternative Investments, 3(1): 45-53.

Irwin, S. H., Sanders, D. R. and Merrin, R. (2009), “Devil or angel? The role of speculation in the recent commodity price boom (and bust)”, Journal of Agricultural and Applied Economics, 41(2): 377-391.

Irwin, S. H. and Sanders, D. R. (2011), “Index Funds, Financialization, and Commodity Futures Markets”, Applied Economic Perspectives and Policy, 33(1): 1-31.

Josephs, L. (2014), “Commodity Outliers Attract Investors” Wall Street Journal, 25 September 2014. http://online.wsj.com/articles/commodity-outliers-attract-investors-1411686300

Karali, B., Power, G.J. (2013), “Short- and long-run determinants of commodity price volatility,” American Journal of Agricultural Economics, 95(3): 724-738.

Kellard, N.M., Wohar, M.E. (2005), “On the prevalence of trends in primary commodity prices,” Journal of Development Economics, 79: 146-167.

Kim, S., Shephard, N., and Chib, S. (1998), “Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models,” Review of Economic Studies, 65: 361-393.

Kim, C., Nelson, C.R. (1999), State-Space Models with Regime Switching, The MIT Press, Cambridge, MA.

Koop, G., Korobilis, D. (2010), “Bayesian Multivariate Time Series Methods for Empirical Macroeconomics,” Foundations and Trends in Econometrics, 3: 267-358.

Krugman, P. (2008), “Running Out of Planet to Exploit,” New York Times Op-Ed Column, April 21, 2008. [http://www.nytimes.com/2008/04/21 /opinion/21/krugman.html].

Lombardi, M.J., Osbat, C., and Schnatz, B. (2010), "Global Commodity Cycles and Linkages: A FAVAR Approach", European Central Bank Working Papers, No. 1170.

Masters, M. (2008), Testimony before the committee on homeland security and governmental affairs, United States Senate, May 20.

Miffre, J., Rallis, G. (2007), Momentum strategies in commodity futures markets, Journal of Banking & Finance, 31(6): 1863-1886.

Neely, C., Rapach, D. (2011), “International Comovements in Inflation Rates and Country Characteristics,” Journal of International Money and Finance, 30: 1471-1490.

Neftci, S.N., Lu, Y. (2008), “Financial instruments to hedge commodity price risk for developing countries,” IMF Working Papers, 08/6.

Ohashi, K., Okimoto, T. (2013), “Increasing Trends in the Excess Comovement of Commodity Prices,” Research Institute of Economy, Trade and Industry Discussion Paper.

Olson, E., Vivian, A., and Wohar, M.E. (2014) “The Relationship Between Energy and Equity Markets: Evidence From Volatility Impulse Response Functions,”Energy Economics, 41: 95-109.

Pindyck, R.S., Rotemberg, J.J. (1990), “The excess co-movement of commodity prices,” The Economic Journal, 100: 1173-1187.

37

Phylaktis, K. and Xia L. (2006), “The Changing Roles of Industry and Country Effects in the Global Equity Markets,” European Journal of Finance, 12: 627-648.

Primiceri, G. (2005), “Time Varying Structural Vector Autoregressions and Monetary Policy,” Review of Economic Studies, 72: 821-852.

Poncela, P., Senra, E, and Sierra, L.P. (2014), “Common dynamics of nonenergy commodity prices and their relation to uncertainty,” Applied Economics, 46(30): 3724-3735.

Quinn, D. (1997), “The Correlates of Change in International Financial Regulation,” American Political Science Review, 91: 531-551.

Quinn, D. P., Toyoda, A. M. (2008), “Does Capital Account Liberalization Lead to Economic Growth?” Review of Financial Studies, 21: 1403-1449.

Radetzki, M., Eggert, R.G., Lagos, G., Lima, M., and Tilton, J.E (2008), “The boom in mineral markets: How long might it last?” Resources Policy, 33: 125-128.

Rajan R., (2005), “Has Financial Development Made the World Riskier?” NBER Working Papers, No. 11728.

Saadi, H. (2011), “Price comovements in international markets and their impacts on price dynamics,” In Methods to Analyze Agricultural Commodity Price, ed. Isabelle Piot-Lepetit and Robert M’Barek. Springer, New York.

Sargent, T.J., Sims, C.A. (1977), “Business cycle modeling without pretending to have too much a priori economic theory, in New Methods in Business Research, Christopher A. Sims (Ed.), Federal Reserve Bank of Minneapolis, Minneapolis.

Sari, R., Hammoudeh, S., and Soytas, U. (2010), “Dynamics of oil price, precious metal prices, and exchange rate,” Energy Economics, 32: 351-362.

Silvennoinen, A., Thorp. S. (2013), “Financialization, crisis and commodity correlation dynamics,” Journal of International Financial Markets, Institutions and Money, 24: 42-65.

Sjaastad, L.A. (2008), “The price of gold and the exchange rates: Once again,” Resources Policy, 33: 118-124.

Stiglitz J. (2010), “Risk and Global Economic Architecture: Why Full Financial Integration May Be Undesirable,” American Economic Review Papers & Proceedings, 100: 388-392.

Stock, J.H., Watson, M.W. (2002a), “Macroeconomic Forecasting Using Diffusion Indexes,” Journal of Business & Economic Statistics, 20: 147–162.

Stock, J.H., Watson, M.W. (2002b),” Forecasting Using Principal Components from a Large Number of Predictors,” Journal of the American Statistical Association, 97: 1167–1179.

Svensson, L. (2008). “The effect of monetary policy on real commodity prices: comment.” In: Campbell, J.Y. (Ed.), Asset Prices and Monetary Policy. NBER, University of Chicago, Chicago.

Tang, K., Xiong, W. (2012), “Index investment and the financialization of commodities,” Financial Analysts Journal, 68: 54-74.

Vansteenkiste, I. (2009), “How important are common factors in driving non-fuel commodity prices? A dynamic factor analysis,” European Central Bank Working Papers, No. 1072.

Vivian, A., Wohar, M. (2012) “Commodity Breaks in Volatility,” Journal of Financial Markets, Institutions and Money, 22(2): 395-422.

Wacziarg, R., Welch, K. (2008), “Trade Liberalization and Growth: New Evidence,” World Bank Economic Review, 22: 187–231.

Wang, D., Tomel, W.G. (2007), “Commodity prices and unit root tests,” American Journal

38

of Agricultural Economics, 89(4): 873-889. West, K.D., Wong, (2003), “A factor model for co-movements of commodity prices,” Journal of

International Money and Finance, 42(C): 289-309. Wolf. M. (2008), “Life in a tough world of high commodity prices,” Financial Times, March 4,

[http://blogs.ft.comieconomistsforum/2008/03/life-in-a-tough-world-of-high-commodity-prices/].

Zhang, Y.-J., Wei, Y.-M. (2010), “The crude oil market and the gold market: Evidence for cointegration, causality and price discovery,” Resources Policy, 35: 168-177.

39

TABLE 1: Selection of the mixing distribution to be )1(ln 2χ ω Pr( k=ω ) km 2

kτ

1 0.00730 -10.12999 5.79596

2 0.10556 -3.97281 2.61369

3 0.00002 -8.56686 5.17950

4 0.04395 2.77786 0.16735

5 0.34001 0.61942 0.64009

6 0.24566 1.79518 0.34023

7 0.25750 -1.08819 1.26261

40

TABLE 2. Descriptive Statistics for the Stochastic Volatility Dynamic Factor Model

Monthly Data: 1984M1 – 2013M12

Mean StDev Min 0.10 0.25 0.50 0.75 0.90 Max

MARKET FACTOR -0.055 1.614 -14.498 -1.294 -0.688 -0.062 0.611 1.534 5.376

SECTORAL FACTORS

1. INDUSTRIAL METALS -0.047 2.604 -9.920 -2.887 -1.445 0.000 1.464 2.858 10.236

2. ENERGY 0.112 9.102 -31.080 -10.189 -4.336 0.366 4.631 9.358 53.602 3. CEREALS & VEGETABLE OILS 0.015 0.939 -4.667 -0.952 -0.513 0.033 0.474 1.076 4.468

4. OTHER FOOD & BEVERAGES 0.045 3.114 -15.295 -3.023 -1.385 -0.025 1.109 3.225 20.895

5. INDUSTRIAL RAW MATERIALS -0.003 0.559 -3.691 -0.419 -0.144 -0.032 0.144 0.319 4.698

6. PRECIOUS METALS -0.008 0.975 -3.874 -1.095 -0.574 -0.001 0.569 1.189 3.574

INDIVIDUAL FACTORS

INDUSTRIAL METALS

ALUMINUM 0.110 4.297 -29.214 -3.846 -1.757 -0.107 1.969 4.902 16.314 COPPER 0.136 4.107 -15.970 -3.825 -1.573 0.071 1.887 4.050 21.059 LEAD 0.141 5.263 -22.497 -5.053 -2.591 -0.059 3.339 5.733 20.519 NICKEL 0.156 6.606 -24.569 -6.737 -2.972 -0.334 2.796 7.410 54.996 TIN 0.094 4.695 -24.563 -4.634 -2.035 -0.112 2.417 5.727 17.674 URANIUM 0.012 6.843 -31.471 -5.955 -2.240 -0.219 2.102 6.734 37.221 ZINC 0.134 4.333 -22.627 -4.446 -2.426 0.063 2.378 5.623 12.615 ENERGY

FUEL OIL 0.005 9.434 -69.328 -9.782 -4.110 0.497 4.785 9.040 55.068 PROPANE 0.020 12.446 -81.552 -11.228 -4.491 -0.264 5.115 11.557 113.465 HEATING OIL -0.013 6.957 -31.055 -9.147 -4.083 0.303 4.400 7.739 22.176 GASOLINE 0.025 9.901 -34.170 -11.765 -5.619 0.149 5.511 11.805 46.983 OIL – BRENT -0.015 1.476 -6.657 -1.612 -0.920 -0.067 0.863 1.693 5.922 OIL - DUBAI -0.011 2.204 -9.799 -2.048 -0.851 0.069 0.808 1.903 8.606 OIL - WTI -0.009 2.415 -15.141 -2.291 -1.028 -0.063 0.927 2.234 13.814 CEREALS & VEGETABLE OILS BARLEY 0.015 5.912 -18.355 -6.712 -3.085 0.134 3.297 5.982 28.497 MAIZE 0.000 4.624 -25.185 -4.837 -2.424 -0.133 2.583 5.537 14.309 OLIVE OIL 0.039 4.293 -20.786 -4.297 -1.967 -0.128 2.115 4.222 24.793 RAPESEED OIL 0.057 7.630 -45.365 -6.894 -2.665 -0.039 2.957 6.074 58.306 PALM OIL 0.072 6.567 -19.608 -7.941 -3.731 0.043 4.233 7.649 27.127 RICE 0.018 6.185 -28.522 -7.058 -2.535 -0.105 2.262 6.045 41.057 SOYBEAN MEAL -0.059 2.785 -13.589 -3.412 -1.673 0.111 1.857 3.079 9.382 SOYBEAN OIL 0.032 3.462 -12.921 -4.598 -2.154 -0.068 2.220 4.523 13.609 SOYBEANS -0.028 0.381 -5.277 -0.154 -0.065 0.006 0.071 0.129 0.312 SUNFLOWER OIL 0.024 7.407 -43.352 -5.722 -2.959 -0.388 2.601 5.767 65.333 WHEAT 0.008 5.320 -18.459 -6.174 -3.485 -0.025 3.056 6.198 20.849

41

OTHER FOOD & BEVERAGES

BANANAS COCOA -0.007 17.235 -45.510 -20.816 -8.312 -0.514 8.905 19.249 61.570 COFFEE – ARABICA 0.038 5.550 -20.702 -6.298 -3.704 -0.087 3.259 6.881 19.482

COFFEE – ROBUSTA -0.027 3.200 -13.092 -3.829 -1.788 0.080 1.902 3.758 10.638

TEA -0.024 2.860 -8.084 -3.400 -1.854 -0.268 1.699 3.866 9.681 FISHMEAL 0.023 7.563 -27.541 -8.428 -4.788 0.484 4.738 8.989 20.951 ORANGES 0.035 4.656 -23.890 -4.600 -2.006 -0.107 2.345 4.555 25.829 SALMON 0.013 12.811 -43.779 -15.548 -6.723 0.698 7.626 15.166 40.478 SUGAR – CSCE 0.060 5.737 -19.358 -7.423 -2.622 0.275 2.813 6.571 20.754 SUGAR - ISA 0.051 8.392 -26.338 -9.647 -5.609 0.233 5.726 10.170 33.217 INDUSTRIAL RAW MATERIALS

BEEF 0.014 3.680 -18.827 -3.968 -1.995 0.003 1.986 3.873 17.858 HIDES -0.002 6.467 -54.852 -5.706 -2.134 -0.114 2.387 6.145 25.621 LAMB 0.038 3.590 -14.695 -3.806 -2.120 -0.269 2.124 4.346 12.427 PORK 0.010 10.843 -48.983 -12.210 -5.876 -0.096 6.403 14.037 60.368 POULTRY -0.001 2.157 -5.917 -2.731 -1.323 -0.038 1.092 2.201 10.170 COTTON 0.050 5.376 -25.256 -5.942 -2.918 -0.144 2.830 5.746 17.573 LOGS – SOFT -0.007 6.695 -34.843 -7.351 -3.741 -0.245 3.787 7.404 28.451 LOGS – HARD 0.049 4.126 -16.746 -3.900 -1.828 0.061 1.279 4.030 25.684 RUBBER 0.093 5.753 -25.549 -6.290 -2.717 0.166 3.105 6.779 19.755 TIMBER – HARD 0.051 2.200 -12.011 -0.959 -0.200 -0.018 0.240 1.006 18.004 TIMBER – SOFT -0.007 6.521 -31.452 -7.012 -3.577 -0.008 3.369 6.988 31.266 WOOL – COARSE 0.075 4.407 -15.930 -5.322 -2.411 -0.024 2.379 5.205 15.719 WOOL - FINE 0.079 6.058 -38.669 -6.148 -3.110 -0.276 2.731 7.097 24.712 PRECIOUS METALS

GOLD 0.064 1.984 -5.681 -2.356 -1.113 -0.081 1.372 2.514 7.858 SILVER 0.130 3.989 -18.097 -4.196 -1.987 -0.205 1.999 5.125 15.700 PLATINUM 0.101 4.644 -33.948 -3.848 -1.767 0.039 2.228 4.641 29.254

Notes: This table provides descriptive statistics for all the factors. Please note mean is the sample average of the variable. SD is the standard deviation, MIN is the minimum value, then the 10th percentile (0.10), lower quartile (0.25), median (0.5), upper quartile (0.75) and 90th percentile (0.9). Finally the maximum is reported.

42

TABLE 3. Variance decompositions – Constant Loading and Constant Volatility Model –

Averages across sectoral groups, 1984:1-2013:12 Sector Common

factor Sectoral

Factor Individual

factor All 9.09% 22.97% 67.94% Industrial Metals 5.38% 31.51% 63.10% Energy 0.60% 58.77% 40.63% Cereals & Veg. Oils 33.39% 8.36% 58.24% Other Food & Beverages 1.47% 10.78% 87.75% Industrial Raw Materials 3.03% 13.92% 83.05% Precious Metals 2.73% 58.16% 39.11% Notes: This table reports results from commodity-level variance decompositions into components due to the Common factor, the Sectoral factor and the Individual factor. These are then averaged across commodities in each sector and for all commodities.

43

TABLE 4. Variance decompositions – Time Varying Volatility Model – Averages across sectoral groups, 1984:1-2013:12 Panel A: Full Sample Sector Common

factor Sectoral

factor Individual

factor All 7.95% 21.08% 69.76% Industrial Metals 15.36% 19.27% 62.81% Energy 8.25% 46.12% 43.80% Cereals & Veg. Oils 8.43% 25.00% 65.35% Other Food & Beverages 3.27% 8.35% 87.94% Industrial Raw Materials 8.62% 12.45% 77.98% Precious Metals 9.87% 39.21% 49.87% Panel B: 1984-1993 Sample Sector Common

factor Sectoral

factor Individual

factor All 4.26% 21.39% 73.58% Industrial Metals 8.40% 13.59% 76.44% Energy 4.65% 46.27% 47.91% Cereals & Veg. Oils 3.23% 22.35% 73.63% Other Food & Beverages 1.70% 10.15% 87.83% Industrial Raw Materials 5.85% 17.96% 75.74% Precious Metals 6.08% 43.43% 49.59% Panel C: 1994-2003 Sample Sector Common

factor Sectoral

factor Individual

factor All 3.94% 22.77% 72.33% Industrial Metals 11.29% 24.42% 61.58% Energy 2.25% 53.47% 43.26% Cereals & Veg. Oils 3.81% 26.77% 68.39% Other Food & Beverages 1.42% 9.33% 88.97% Industrial Raw Materials 3.65% 9.76% 85.94% Precious Metals 4.56% 34.42% 60.20% Panel D: 2004-2013 Sample Sector Common

factor Sectoral

factor Individual

factor All 15.66% 19.09% 63.36% Industrial Metals 26.38% 19.80% 50.42% Energy 17.85% 38.62% 40.24% Cereals & Veg. Oils 18.24% 25.88% 54.02% Other Food & Beverages 6.71% 5.58% 87.01% Industrial Raw Materials 16.36% 9.62% 72.26% Precious Metals 18.97% 39.79% 39.82% Notes: This table reports results from commodity-level variance decompositions into components due to the Common factor, the Sectoral factor and the Individual factor. These are then averaged across sectors and for all

44

commodities.

TABLE 5. The Determinants of the Common Factor – from Stochastic Volatility Model

Panel A.1: Bivariate

Panel A.2: Multivariate

1984:1-2013:12 Common Factor

Common Factor

β t r-sq β t r-sq

D_EX_RATE -0.560 -13.00*** 0.32

-0.473 -9.94*** D_ECON_UNCERT -0.057 -1.06 0.00

-0.014 -0.31

D_VIX -0.136 -2.14** 0.01

-0.065 -1.40 MARKET ECON ACTIVITY 0.221 4.31*** 0.05

-0.020 -0.39

INFLATION 0.181 3.28*** 0.03

-0.082 -1.73* REAL T-BILL -0.244 -4.49*** 0.06

0.025 0.23

REAL LTB -0.232 -4.26*** 0.05

-0.010 -0.11 CF(-1) 0.622 14.99*** 0.38

0.539 10.94*** 0.57

Panel B.1: Bivariate

Panel B.2: Multivariate

1984:1-1993:12 Common Factor

Common Factor

β t r-sq β t r-sq

D_EX_RATE -0.195 -5.45*** 0.19

0.007 0.18 D_ECON_UNCERT 0.014 0.33 -0.01

-0.045 -1.23

D_VIX 0.025 0.44 -0.02

0.018 0.40 MARKET ECON ACTIVITY 0.006 0.07 0.00

-0.003 -0.02

INFLATION 0.067 1.08 0.00

-0.099 -1.35 REAL T-BILL -0.147 -2.66*** 0.05

0.069 0.56

REAL LTB -0.126 -2.10** 0.03

-0.087 -0.11 CF(-1) 0.624 8.32*** 0.38

0.938 6.14*** 0.45

Panel C.1: Bivariate

Panel C.2: Multivariate

1994:1-2003:12 Common Factor

Common Factor

β t r-sq β t r-sq

D_EX_RATE -0.202 -4.22*** 0.12

-0.134 -3.90*** D_ECON_UNCERT -0.057 -1.19 0.00

-0.022 -0.67

D_VIX -0.025 -0.54 -0.01

0.005 0.17 MARKET ECON ACTIVITY 0.221 3.33*** 0.08

0.067 1.45

INFLATION 0.234 3.25*** 0.04

-0.086 -1.71* REAL T-BILL -0.147 -2.66*** 0.05

-0.302 -3.55***

REAL LTB -0.050 -0.56 0.00

0.299 2.99*** CF(-1) 0.706 10.69*** 0.49

0.458 5.65*** 0.61

45

Panel D.1: Bivariate

Panel D.2: Multivariate

2004:1-2013:12 Common Factor

Common Factor

β t r-sq β t r-sq

D_EX_RATE -1.247 -14.47*** 0.64

-1.025 -10.65*** D_ECON_UNCERT -0.105 -0.80 0.00

0.008 0.09

D_VIX -0.274 -2.03** 0.03

-0.020 -0.22 MARKET ECON ACTIVITY 0.286 2.44** 0.04

-0.040 -0.31

INFLATION 0.291 2.60** 0.06

-0.238 -1.62 REAL T-BILL -0.199 -0.99 0.00

0.315 1.43

REAL LTB -0.879 -2.91*** 0.08

-0.859 -1.55 CF(-1) 0.608 8.35*** 0.37

0.381 5.43*** 0.74

Notes: Table 5 Panel 1 reports results from simple bivariate time-series regressions and Panel 2 reports results from multivariate regressions. The column β reports the slope coefficient, t is the t-statistic value for the slope coefficient. R-sq is the coefficient of determination. * is significant at 10% level, ** is significant at 5% level and *** is significant at the 1% level. R-sq is the adjusted coefficient of determination. D_EX_RATE is the change in the (Broad) Trade-weighted US exchange Rate from the St Louis Fed series TWEXBMTH (available over … only) D_ECON_UNCERT is the change in economic uncertainty from the work of Bloom and downloaded from http://www.policyuncertainty.com/ D_VIX is the change in the VIX Index. VIX Index taken from http://www.cboe.com/micro/vix/historical.aspx from January 1990 to December 2013. MARKET_ECON_ACTIVITY is from Kilian (2009) and downloaded from his website: http://www-personal.umich.edu/~lkilian/ INFLATION is from IMF series I64…F. T-BILL is from IMF series I60B LTB is the Long-term Bond from IMF series I61. CF(-1) is the one period lag of the Common Factor.

46

Figure 1. Plots of Common and Sector factors

47

Figure 2: Panel A: Plots Variance Contribution of the Common Factor

48

Figure 2: Panel B: Plots Variance Contribution of the Common Factor (cont.)

49

Figure 3: Panel A: Plots Variance Contribution of the Sector Factor

50

Figure 3: Panel B: Plots Variance Contribution of the Sector Factor (cont.)

51

Figure 4: Panel A: Plots Variance Contribution of the Individual Factor

52

Figure 4: Panel B: Plots Variance Contribution of the Individual Factor (cont.)

53

Figure X: Plot of Stochastic Volatility – Common and Sector Factors

54

Figure XX Panel A: Plot of Stochastic Volatility – Individual Factors

55

Figure XX Panel B: Plot of Stochastic Volatility – Individual Factors (cont.)

56