commodity prices and usd jan06

8/4/2019 Commodity Prices and USD Jan06

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Introduction

Recent years have seen the commodities

complex enjoy an impressive bull run.

With few exceptions, commodity prices

have experienced major increases and

have generally outperformed traditional

investments. This trend has brought the

asset class under the focus of the finan-

cial community. Indeed, the involvement

of speculators in the commodities mar-

kets has been on the increase, while a

limited number of longer-term strategic

players are also believed to have entered

the game.

As a general rule, commodities are

priced in US dollars. Recent years haveseen the US currency weaken. Other

things remaining equal, this weakness in

the currency in which an asset is denom-

inated would, by definition, result in an

increase in the assets price. The com-

modities bull run thus discussed above

is, at least in some part, expected to be

related to the decline in the US dollar

exchange rate.

The question arises: what is the extent to

which recent years rise in commodities

prices was a product of the depreciation

in the US dollar that has taken place over

the same period? Can fluctuations in the

said currency fully explain changes in

commodity prices, or is there only a par-

tial effect (if any at all)?

If the latter were true, a measure of the

partial impact of changes in the dollar on

commodity prices would by definition

indicate how effective commodities

would be as a hedge against fluctuations

in the US currency. The question

becomes ever more relevant in the light

of arguments for adding commoditiesand related derivatives to portfolios, in an

effort to diversify away from traditional

investments and assets linked in one way

or another to the dollar.

Furthermore, it would be interesting to

examine whether this ability to provide a

hedge against the dollar varies across

different commodities. This would in-

dicate which commodities, if any, are

more suitable than others as diversifying

investment instruments to protect against

changes in the US currency.

Finally, is any relationship between com-

modity prices and the US dollar unchanged

over time, or does it vary with changing

circumstances in the world economy and

the relevant markets? For instance, is the

link equally strong both during times

when the dollar is rising and falling, and

if not, when is it stronger, and why?

Methodology & Data

A simple look at the underlying funda-

mental markets is sufficient to show that

this recent rally in commodities pricescannot be purely explained by the weak-

ness of the greenback. There is little

doubt, for instance, of the fundamental

tightness in energy and metals markets

(one driven by either demand or supply

shocks), which would have boosted

related commodities prices regardless

of any changes in the strength of the

greenback.

1

J A N U A R Y 2 0 0 6

gold:report

Commodity Prices and the

Influence of the US DollarBy Nikos Kavalis, GFMS Limited1

1 This report was prepared by GFMS Limited on behalf of the World Gold Council. Please read the disclaimer on the final page.


2/12

To further illustrate this point, one can

look at the relative performance of differ-

ent commodities over time. Were the dol-

lar the only driver of changes in

commodity prices, one would expect

these to have moved in the same way

over time. Looking at the charts in

Appendix 3 at the end of the report,

which feature indexed mid-weekly prices

for a number of commodities over the

1994-2004 period, this has clearly not

been the case.

To evaluate the strength of the relation-

ship between the dollar and commodity

prices, there are a number of statistical

approaches that can be used. The most

simple and widely used approach is to

look at the correlation between the two,

measured by the correlation coefficient.

A brief explanation of the meaning of cor-

relation and some technical notes on the

calculation of the correlation coefficient

are provided in the technical appendix

(Appendix 2) at the end of this report.

More specifically, for this particular case,

we look at the correlations between the

dollar and the individual price of a num-

ber of commodities, a list of which can be

seen in Appendix 1 of this report. With

the exception of lead, all commodities in

the list are components of at least two of

the leading tradable commodity indices

(Goldman Sachs Commodity Index,Reuters/Jefferies CRB Total Return Index,

Dow-Jones AIG Commodity Index).

Two approaches are followed: we first look

at static correlations over a set period,

and then examine the evolution of rolling

annual correlations over the same period.

To reduce the noise inherent in daily

data, we use mid-week observations.2

It is important to note here that the analy-

sis in this report provides no information

whatsoever on the causality that drives

any correlations between the dollar and

commodity prices. The purpose of the

report is to simply examine whether the

two tend to move consistently in relation

to one another, so as to evaluate the

dollar-hedge property of different com-

modities, and not to develop a model of

how changes in one feed into the other.

In fact, the existence of strong correlation

between two assets could coincide with

a complete lack of causal relationship

between them.

To remove any non-stationarities inherent

in the variables (for instance, trend), which

could produce spurious results with a

bias to exaggerate the correlation coeffi-

cient, it is customary to look at the corre-

lation in changes or returns in the two

variables examined. To demonstrate this

point, an example of an extreme case

where use of returns rather than levels

generates a radically different correlation

coefficient is provided in the technical

appendix at the end of this report.

When discussing returns throughout this

report, we are referring to spot or net

returns, meaning ones related to the

change compared to the previous obser-

vation. Furthermore, rather than using

simple or arithmetic returns we have

decided to use log- or geometric returns.

A brief explanation of the differences

between the two is also provided in the

reports technical appendix.

With regards to the data series used, for

the US currency exchange rate we look

at the trade weighted dollar. For the com-

modities studied, we use the consensus

benchmark price in each market. Where

they are available, spot prices are used,

while the nearest month contract price is

used as a proxy where they are not. Spot

prices are used to strip out the effects of

changes in the contango or backward-

ation3 prevailing in each of the market,

gold:report www.gold.org

2J A N U A R Y 2 0 0 6

2 We decided not to use weekly averages, due to statistical problems inherent with temporal aggregation of data, as explained in Mills, T C (1990), Time Series

Techniques for Economists, Cambridge: Cambridge University Press, chapter 11.5, and the references contained therein.3 Detailed information on the notions of contango & backwardation, and how these can affect returns on investments on commodities, see Metals & Backwardation and

Investing in commodities: a risky business?, available in the research section of the World Gold Council Website (URL: http://www.gold.org/value/stats/research/index.html)

80

90

100

110

120

130

20032001199919971995

First PeriodJuly 1995 -June 1997

Second PeriodJanuary 2002 - December 2004

US$

Effective

Exchang

e

Rate

Index:1990=100

Figure 1: Trade Weighted Dollar

Source: Bank of England


3/12

which could bias the results in either

direction. Detailed information of the prices

used and the sources used is provided in

Appendix 1 at the end of this report.

Static Correlation Analysis

In this section we evaluate how strong

the correlation between log returns in the

trade-weighted dollar and the prices of

different commodities were over two dis-

tinct three-year periods. The first period

examined was the one commencing in

July 1995 and ending at end-June 1998,

while the second period was the one

commencing at the beginning of 2002

and finishing at end-2004. Note that while

throughout the former period the dollar

trended upwards, it was on a declining

trend over the latter. Thus, comparing the

results from the two would provide an

idea of how the strength of the implied

relationship in question might vary under

different circumstances.

Table 1 below features the list of com-

modities examined for the purposes of

this report, along with their correlation

coefficients with the trade weighted dollar

calculated over the two periods discussed.

Looking at the table, a number of inter-

esting points are immediately obvious.

First of all, the majority (although for the

earlier period a relatively close one) of

commodities examined demonstrate

negative correlation with the US dollar.

Secondly, the number of commodities

negatively correlated with the dollar is

larger for the later period. Furthermore,

for most commodities examined, this

correlation is stronger over the later

period that it is in the earlier one.

The differences observed between the

two periods seem to indicate that the

relationship between commodities and

the dollar becomes stronger during times

when the latter is weakening. One possi-

ble explanation why this could be the

case is that during times of dollar weak-

ness investors diversify part of their capi-

tal away from dollar-linked assets. This

move can benefit investments in com-

modities (and in fact has done so in the

past), boosting the negative relationship

between the two.

Moreover, during the 2002-2004 period,

the commodities complex received

exceptional attention from the financial

media, which certainly boosted the

sectors popularity with investors. The

unimpressive performance that equity

markets demonstrated over parts of

the period was another factor that

certainly gave commodities further rela-

tive appeal. The increased investor

involvement in the sector resulted in

commodity prices being in greater part

driven by speculative activity, boosting

the strength of the negative correlation of

prices with the US dollar, which was

declining at the same time for different

reasons.

Another interesting fact is that the co-

efficients calculated for the different

commodities vary greatly. The majorityof them seem too low to indicate a

significant link exists. Performing a statis-

tical test confirms this, and in fact

shows that only four commodities coeffi-

cients are significant for the first period

examined, while eight are significant for

the second. A description of the con-

struction and properties of the statistical

test used is provided in the technical

appendix at the end of this report, while

the results are presented in Table 1.

3

Table 1: Static Correlations Analysis

Correlation Correlation Correlation Correlation

Coefficient over Coefficient Coefficient over Coefficient

07/95 - 06/98 Significant 01/02 - 12/04 Significant

Period at 5% level* Period at 5% level*

Natural Gas -0.07 No -0.17 Yes

Oil, Light Crude -0.01 No -0.17 Yes

Unleaded Gasoline 0.10 No -0.20 Yes

Heating Oil 0.01 No -0.15 No

Live Cattle -0.03 No 0.11 No

Lean Hogs 0.00 No 0.06 No

Wheat -0.09 No -0.08 No

Corn 0.00 No -0.20 Yes

Soybeans -0.06 No -0.18 Yes

Sugar -0.12 No 0.01 No

Cotton 0.05 No -0.07 NoCoffee 0.13 No -0.16** No

Cocoa -0.21 Yes -0.01 No

Aluminium -0.18 Yes -0.16 No

Copper -0.11 No -0.09 No

Zinc -0.08 No -0.12 No

Nickel 0.03 No -0.14 No

Lead -0.18 Yes -0.08 No

Gold -0.19 Yes -0.51 Yes

Silver 0.01 No -0.37 Yes

Platinum -0.13 No -0.16** Yes

Palladium -0.03 No -0.01 No

*see technical appendix for explanation**Coffee and platinum showing the same correlation coefficient but only one being significant is due to

rounding to two decimal places. The coefficient for coffee is in fact 0.155, while that for platinum 0.160.


4/12

The commodities that demonstrated

significant correlation with the dollar over

the first period were cocoa, gold, aluminium

and lead. Over the second period, they

were gold, silver, unleaded gasoline,

corn, soybeans, crude oil natural gas

and platinum. Interestingly, none of the

coefficients that were found to be signifi-

cant were positive, in accordance to our

expectations (basis the conjecture that, if

anything, commodities are expected to

be negatively correlated with the dollar).

At -0.51, the correlation coefficient cal-

culated between gold and the dollar for

the latter period dwarfs all the other

statistics we calculated for this section.

The second strongest link in the list, the

one with silver, is significantly weaker, the

correlation coefficient being -0.37. All

other coefficients we calculated stood at

-0.21 or lower (in absolute terms). It is

worth a mention, furthermore, that gold

was the only commodity with a signifi-

cant correlation coefficient over both

periods examined.

It would thus seem to be the case that,

basis the sample examined, gold is a

better hedge against the dollar than other

commodities. This comes as no surprise,

as the yellow metal has always been con-

sidered to have an inverse relationship

with the greenback4. This relationship is

to a large extent self-fuelled, due toinvestors trading on the back of it.

Moreover, the correlation coefficient

between the yellow metal and the dollar

over the first period examined is a mere

0.19. The difference between the coeffi-

cients calculated over the two periods is

thus more pronounced for gold than for

the other commodities (with the excep-

tion of silver, which is discussed later in

this report). This fact is in accordance

with a known practice in the investment

world, that of the flight to quality. The

term refers to the action of investors mov-

ing their capital away from riskier or more

volatile assets and into ones considered

to be safer and less volatile. The move

tends to take place during times of

uncertainty in the financial markets and

world economy, and reflects some

investors risk aversion.

The second highest (in absolute terms)

correlation coefficient calculated was the

one between silver and the dollar over

the 2002-2004 period. It is our under-

standing that the link between the two is

indirect and primarily stems from the

relationship between gold and silver

prices, which GFMS have documented in

past publications5. This point is dis-

cussed further in later sections of this

report. Having examined changes in

the prices of the two metals, we have

concluded that these show significant

positive correlation.

As mentioned previously, the remaining

six commodities with significant correla-

tion coefficients showed much weaker

links to the US currency. Furthermore,

none of the six were significant over both

periods examined. We can thus deduce

that their ability to provide a hedge

against changes in the US dollar is very

limited compared to gold and, to an

extent, silver.

We finally repeated the exercise using

the three leading commodity indices,

Goldman Sachs Commodity Index, CRB

Index (the spot index related to the

Reuters/Jefferies CRB Total Return Index)

and Dow-Jones AIG Commodity Index.

The results are presented in Table 2

below, and come as no surprise given

our previous findings (namely that gold

and silver were the most strongly corre-

lated commodities from the group, and

that over the second period the links

between commodities and the dollar

were much stronger).

As expected, over the first period, log-

returns in all three indices demonstrated

very weak and statistically insignificant

negative correlation to log-returns in

the greenback, while over the second

period, the figures were higher (in

absolute terms). Looking at the differ-

ences between the coefficients and

focusing on the 2002-2004 period, the

AIG is the index with the strongest nega-

tive correlation to the dollar, while the

CRB the one with the lowest. Again, this

is not surprising, as the AIG is the index

with the highest weighting in gold and


4J A N U A R Y 2 0 0 6

4 For example, see Gold as a Hedge against the US Dollar by Forrest Capie, Terence C. Mills and Geoffrey Wood, available in the research section of the WorldGold Council Website (URL: http://www.gold.org/value/stats/research/index.html)5 For example, World Silver Survey 2005, Chapter 2

Table 2: Static Correlations Analysis Commodity Indices





GSCI -0.05 No -0.21 Yes

AIG -0.06 No -0.26 Yes

CRB Spot -0.11 No -0.15 No

*see technical appendix for explanation


5/12

silver and the CRB contains neither of the

two metals6.

Rolling Correlation Analysis

In this section, we look at how the 52-

week rolling correlation coefficients

evolved for each the commodities under

examination, over the same two periods

discussed in the static correlation analy-

sis section above (an explanation of what

is meant by 52-week rolling correlation

coefficients is provided in the technical

appendix at the end of this report).

Having compiled a series of 52-week

rolling correlation coefficients between

log-returns on the prices of each of the

commodities and the trade weighted

dollar, we looked at the averages over

the last two years of the two periods

examined above7 and performed the test

we used in the previous section to estab-

lish whether these were significant. The

results are presented in Table 3 below.

Interestingly, many of the commodities

that had demonstrated significant corre-

lation with the dollar under the static

analysis failed to do so when using this

approach. In fact, only gold and silver

were significant, and only for the second

period discussed.

Nevertheless, the principal findings of the

static analysis were in line with the ones

from this exercise. More specifically, the

rolling averages indicated that gold is the

commodity that demonstrates the

strongest link to the dollar, with silver

being the second best. Furthermore, the

averages calculated over the 2003-2004

period for these two commodities were

markedly higher (in absolute terms) than

the ones over the earlier period. More

specifically, the average 52-week cor-

relation coefficient between gold and

the trade weighted dollar stood at

-0.21 over the earlier period and at

-0.56 over the more recent one. The

respective averages for silver were 0.02

and -0.38.

Figures 2 and 3 provide an illustration

of the daily evolution of the rolling cor-

relation coefficient between the trade

weighted dollar and gold as well as silver

over the 1995-2004 period (thus includ-

ing both subsets discussed above). Two

interesting facts are immediately

obvious:

First of all, there is a clear upward trend

in the strength of the implied relationship

between the dollar and each of the two

commodities, over the period from the

turn of the millennium through to the end

of 2004.

Secondly, over much of the nine-yearperiod examined, the rolling coefficients

for the two commodities seem to have

moved in a similar manner. This is main-

ly due to the fact that, as we mentioned

in the previous section, there is a strong

positive correlation between gold and

5

6 For information on the weightings of individual commodities in each of the indices, see Indices Enticing Investors, available in the research section of the World

Gold Council Website (URL: http://www.gold.org/value/stats/research/index.html)

7 We decided to average the 52-week rolling correlations over the July 1996 June 1998 and January 2003 December 2004 periods, so that overall, all and nomore than the weekly observations used in our initial samples (July 1995 June 1998 and January 2002 December 2004) are used in the analysis. This way, when

comparing the results of the two analyses we can be certain that the same amount of information is used, and that only the methodology changes.

Table 3: Rolling Correlations Analysis Period Averages of 52-

Week Coefficients





Natural Gas -0.12 No -0.14 No

Oil, Light Crude -0.01 No -0.17 No

Unleaded Gasoline 0.13 No -0.19 No

Heating Oil 0.03 No -0.14 No

Live Cattle 0.00 No 0.19 No

Lean Hogs -0.02 No 0.04 No

Wheat -0.07 No -0.08 No

Corn 0.06 No -0.19 No

Soybeans -0.04 No -0.18 No

Sugar -0.03 No 0.08 No

Cotton -0.04 No -0.02 No

Coffee 0.16 No -0.14 No

Cocoa -0.22 No 0.02 No

Aluminium -0.21 No -0.16 No

Copper -0.14 No -0.02 No

Zinc -0.07 No -0.12 NoNickel 0.04 No -0.10 No

Lead -0.21 No -0.06 No

Gold -0.21 No -0.56 Yes

Silver -0.02 No -0.38 Yes

Platinum -0.14 No -0.12 No

Palladium -0.07 No 0.00 No

*see technical appendix for explanation


6/12

silver prices (the rolling correlation

coefficient averaged 0.58 over the 1995-

2004 period). This evidence provides

some empirical support to our under-

standing that the link between silver and

the US dollar is by and large driven by

the one between the white metal and

gold.

The remaining commodities that were

significantly correlated to the dollar had

average coefficients of -0.22 or less

(always in absolute terms). Furthermore,

similarly to the case under the static

analysis, gold was the only one from the

group with a significant average for both

periods we looked into. The conclusions

we can draw from this exercise are thus

similar to the ones we saw under static

analysis. Firstly, gold is by far the most

relevant commodity in hedging against

the US dollar. Secondly, it becomes par-

ticularly relevant during times of dollar

weakness.

We finally looked at the rolling correla-

tions between the three spot indices and

the trade weighted dollar. Figure 4 pro-

vides an illustration of these correlations

over the 1995-2004 period. Again the

conclusions are essentially identical to

those drawn from the previous section,

the correlations between the AIG index

and the dollar being stronger than the

ones between either of the other twoindices and the US currency.

It is worth noting that, despite average

correlations for the two periods in ques-

tion being unimpressive for the other

commodities, there were shorter periods

over which some of them were more than

adequately correlated to the greenback.

Nevertheless, we believe this evidence to

be circumstantial, and driven by specific

conditions that prevailed in the relevant

markets at certain times.


6J A N U A R Y 2 0 0 6

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

20032001199919971995

52-WeekCorrelationCoefficient

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

20032001199919971995


CRB

GSCIAIG

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

-0.0

0.1

0.2

20032001199919971995


Figure 2: Gold Rolling 52-Week Correlation Coefficients

Figure 3: Silver Rolling 52-Week Correlation Coefficients

Figure 4: Commodity Indices Rolling 52-Week Correlation Coefficients


7/12

The Theoretical Case for Gold

Providing a Hedge Against the

US Dollar

Having established the statistical case for

gold being superior to other commodi-

ties as a hedge against the dollar, it is

interesting to examine the theoretical

properties behind this attribute the metal

seems to possess. What are the reasons

gold is a suitable instrument for hedging

against the US dollar, and more specifi-

cally, what are the reasons it is a more

suitable instrument in this regard, com-

pared to other commodities?

First of all, like all physical commodities,

gold is an asset that bears no credit risk.

Holding assets in the metal involves no

counterparty and is no ones liability. This

of course does not apply to investments

in paper gold products, which by defini-

tion involve an issuing institution.

In addition to that, the physical properties

of the metal make it an excellent alterna-

tive to money. Gold is durable. Unlike

many of the other commodities exam-

ined, other things remaining equal (i.e.

assuming no changes in price), there is

no depreciation in the value of gold,

other than any storage costs that might

apply. Gold is fungible. It is, at least in

theory, infinitely divisible with virtually no

losses (other than any operational costs

the process might incur).

Furthermore, gold has a high value to vol-

ume ratio, which makes it easily transfer-

able, with low transport and storage costs.

Moreover, gold is one of the deepest

commodity markets with the highest liq-

uidity. At end-2004, above ground stocks

of gold, defined as cumulative mine pro-

duction, stood at roughly 153,000 tonnes

(source: GFMS, Gold Survey 2005),

translating to over $2.1 trillion (using the

end-2004 gold price). As a point of refer-

ence, the equivalent figure for silver, the

second most strongly correlated com-

modity to the dollar according to our

analysis above, is less than $0.2 trillion.

This liquidity of the gold market conveys

financial characteristics on the metal,

thus making it a suitable alternative to fiat

money.

The most important such property

though, is golds legacy as a monetary

commodity, and the fact that investors

treat and trade it as one. For a great part

of human history, large parts of the world

accepted the metal as the ultimate store

of value. In fact, it was not until the 1970s

that gold stopped being the benchmark

for the international currency market.

After the move to a system of floating fiat

currencies, and currency and inflation

risk developed, so did the need to hedge

against this risk, using some sort of hard,

value-retaining asset. The natural choice

for this was and has been the commodi-

ty that had in the past acted as such,

namely gold.

7

GFMS is the worlds foremost precious

metals consultancy, specialising in

research into the global gold, silver, plat-

inum and palladium markets.

GFMS is based in London, UK, but has

representation in Australia, India, China,

Spain, Germany and Russia, and a vast

range of contacts and associates across

the world.

Products & Services include: Publications,

Consultancy Services, Price Forecasts,

Seminars.

Nikos Kavalis

Metals Analyst, GFMS Limited

Nikos Kavalis joined GFMS on 1st

September 2003. He is primarily assist-

ing Philip Klapwik in investment as well

as official sector activity research. He is also

responsible for developing econometric

modeling, which is currently focused on

future gold and silver prices.

Nikos holds a first degree in Econometrics

and Economics from the University of

York, and a MSc in Econometrics and

Mathematical Economics from the

London School of Economics.

www.gfms.co.uk [email protected]


8/12

The list of commodities examined in the

report, as well as the price used as a

benchmark for each of these can be

seen in the table below. Note that all

prices used were denominated in US dol-

lars. The source used to retrieve the

series was the EcoWin database, and

where data was unavailable, the previous

or most recent observation was used.

As an indicator of US dollar performance,

the Bank of England Effective Exchange

Rate Index was used.


8J A N U A R Y 2 0 0 6

Commodity Price Used

Natural Gas Henry Hub, Spot, Close

Oil, Light Crude Spot (WTI), Nymex

Unleaded Gasoline New York, Spot, Close

Heating Oil No.2, New York, Spot, Close

Live Cattle Futures 1-Pos, CME, Close

Lean Hogs Futures 1-pos, CME, Close

Wheat Futures 1-Pos, CBT, Close

Corn Futures 1-Pos, CBT, CloseSoybeans Futures 1-Pos, CBT, Close

Sugar NYBOT World No. 11 Futures 1-Pos, Close

Cotton No. 2 Futures 1-Pos, NYBOT, Close

Coffee Arabica C Futures 1-Pos, NYBOT, Close

Cocoa Futures 1-Pos, NYBOT, Close

Aluminium Spot, LME, Close

Copper Spot, LME, Close

Zinc Spot, LME, Close

Nickel Spot, LME, Close

Lead Spot, LME, Close

Gold LBMA London PM, Fixing

Silver LBMA London, FixingPlatinum LPPM London PM, Fixing

Palladium LPPM London PM, Fixing

Appendix 1: The Data


9/12

N.B. The algebraic expressions below

are provided as a reference and are not

essential to understanding the rest of this

report and appendices.

i. Notes on Correlation

The notion of correlation between two

variables refers to the way in which either

of the two moves in relation to the other.

In the case of positive correlation, both

variables tend to move in the same direc-

tion (when one variable increases, so

does the other), while in the case of neg-

ative correlation they tend to move in

opposite directions (when one variable

increases, the other decreases).

Further to the question of whether corre-

lation exists between two variables is the

question of how strong this correlation is.

This idea of strength refers to the consis-

tency in the way in which changes in one

variable relate to changes in the other.

The more consistent the link, the

stronger we say the correlation between

the two variables is.

A different way to define this is by looking

at the ratio between absolute changes in

the two variables. The more consistent

this ratio is across the population (or

sample), the stronger the correlation

between the two variables.

It is important to note here that, when dis-cussing the idea of correlations, it is cus-

tomary to assume a linear relationship

between the two series. Furthermore, it is

essential to understand that the idea of

correlation only refers to how two series

move in relation to one another and is by

no means indicative of any causal rela-

tionship between them. Indeed there are

many examples of variable pairs that

show very strong correlation and are not

directly related to one another. This could

be due to the same (or similar) exoge-

nous factors driving both variables, the

two series being non-stationary1 or pure

chance.

Having discussed the notion of correla-

tion between two variables, the question

of how to measure such a property

immediately arises. The correlation coef-

ficient, known also as the Pearson

Product-Moment Correlation Coefficient,

is a number that summarises the

direction (positive or negative) and

degree (i.e. strength or closeness) of

linear relations between two variables.

This can take values from 1 through 0 to

1. In accordance to intuition, a positive

correlation coefficient indicates the two

series are positively correlated and vice

versa. Furthermore, the higher the

absolute value of the coefficient, the

more strongly the two series are said to

be correlated (the extreme case of per-

fect correlation being an absolute value

of 1).

It is important to distinguish here

between population correlation coeffi-

cients (normally denoted ), which

describe the theoretical correlation

across the whole spectrum of values two

variables can take, and sample correlationcoefficients (normally denoted r), which

provides an empirical measure of the

correlation between two variables, basis

a specific sample of values under exami-

nation. As it involves analysis of given

periods of data, our analysis and discus-

sion of results throughout this paper is,

by definition, strictly limited to the latter

measure.

The formula of the correlation coefficient

is the following:

(1)

where N is the sample size, x and y are

deviation scores:

(2)

Xand Yare sample means:

(3)

SX and SY are sample standard deviations:

(4)

Combining (1), (2), (3) and (4) above:

(5)

Finally, the distinction between static and

rolling correlation coefficients should be

made. The former refers to the correla-

tion coefficient calculated over a certain

period, while the latter covers a series of

correlation coefficients, each calculated

over a sub-sample of a certain length (in

the case of this report, this sample lengthwas one year or 52 weeks), ending

on each of the observations under

examination.

For example, in the Static Correlation

Analysis section we look at the correla-

tion coefficients of log-returns in weekly

prices over two set periods, while in the

Rolling Correlation Analysis section,

using the same two sub-samples, we

9

Appendix 2: Technical Appendix

1 For more on non-stationary variables see James D. Hamilton, 1994, Time Series Analysis, Princeton University Press, Chapters 15-20


10/12

generate two series of correlation co-

efficients, each calculated over a 52-

week period.

ii. Notes on the use of

Log-Returns

As mentioned in the Methodology &

Data section earlier in the report, in

order to avoid generating spurious

results, we decided to look at the correla-

tion between changes rather than levels

of weekly prices. The theoretical case

behind this argument is discussed in

much of the literature on non-stationary

time series2.


1 0J A N U A R Y 2 0 0 6

2 for example, William H. Greene, Econometric Analysis, Fifth Edition, 2003, Prentice, Hall, p. 631-636

Series 1 Series 2

1 1

2 1

3 1

4 1

5 1

6 1

7 1

8 1

9 1

10 1

11 1

12 113 1

14 1

15 1

16 100

17 100

18 100

19 100

20 100

21 100

22 100

23 100

24 10025 100

26 100

27 100

28 100

29 100

30 100

In order to test the null hypothesis that

the sample correlation coefficients esti-

mated are zero, against the two-sided

alternative that they are not, we used the

following test statistic:

Where rxy is the sample correlation coeffi-

cient between the two variables x and y,

and N the size of the sample used. The

above statistic follows a t-distribution,

with N-2 degrees of freedom.

To examine whether each of the correla-

tion coefficients are significant or not, we

simply generated the above statistic and

compared it to the relevant value of the

t-distribution.

In order to demonstrate the reasons for

using this approach, we can examine an

extreme case, for which the difference in

results using the two different approaches

(levels and differences) is particularly pro-

nounced. Consider the following series:

A simple look at the data is sufficient to

decide that the two series show essen-

tially no link to one another.

Using expression (5) above though

generates an impressive correlation

coefficient of 0.87, which indicates a

very high correlation exists between the

two series. Taken at face value, such

a result provides a very misleading

picture, implying that the two variables

move consistently in relation to each

other (despite this clearly not being the

case).

Looking at the same two series, and

repeating the exercise using changes in

the two series rather than levels gener-

ates radically different results. When

looking at percentage or log-returns

(more on that below), the correlation

coefficient is a mere -0.08, while when

using absolute returns, it is undefined (as

changes in Series 1 are fixed at 1 across

the sample, and the correlation coeffi-

cient is meaningless if there is no varia-

tion in the data).

Further to deciding to examine the corre-

lation in returns in our analysis of com-

modities and the US dollar, we decided

to use log-returns. The log-return

between two observations Xt and X(t-1) of

variable x, at time t and (t+1) is defined

as:

This approach is an alternative to using

simple returns (or percentage returns),

defined as:

One of the main differences between the

two lies in the formula used to compound

simple and log returns. More specifically,

whereas,

iii. Notes on testing of the correlation coefficient


11/12

1 1

Appendix 3: Reference Charts Indexed Price Charts

0

100

200

300

400

500

200420022000199819961994

Wheat

Live Cattle

Natural Gas

Indexed Prices

Aluminium

Index:5th

Jan

1994

=1

00

0

50

100

150

200

250

300

350

200420022000199819961994

Index:5th

Jan

1994

=1

00

Sugar

Soybeans

Unleaded Gasoline

Indexed Prices

Gold

0

100

200

300

400

500

200420022000199819961994

Index:5th

Jan

1994

=

100

Nickel

Platinum

Coffee

Indexed Prices

0

50

100

150

200

250

300

350

400

200420022000199819961994

Index:5th

Jan

1994

=

100

Corn

Lean Hogs

Oil

Indexed Prices

Copper

0

50

100

150

200

250

300

350

200420022000199819961994

Index:5th

Jan

1994

=1

00

Zinc

Cotton

Heating Oil

Indexed Prices

Silver

0

200

400

600

800

1000

200420022000199819961994

Index:5th

Jan

1994

=

100

Lead

Palladium

Cocoa

Indexed Prices


12/12

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J A N U A R Y 2 0 0 6 1 2

commodity prices and usd jan06

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