Why gold is different from other assets

Why is gold different from other assets?
An empirical investigation.

by

Colin Lawrence

March 2003

The author is Honorary Visiting Professor of Risk Management, Faculty of Finance, Cass Business
School, London and Managing Partner, LA Risk and Financial Ltd., a consulting firm. Professor
Lawrence was assisted in this research by Jinhui Luo, London School of Economics.

The findings, interpretations, and conclusions expressed in this report are those of the author and do not necessarily reflect the views of the World
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Executive Summary

The lack of correlation between returns on gold and those on financial assets such as equities has
become widely established. This research tested the argument that the fundamental reason for this
lack of correlation is that returns on gold are not correlated to economic activity whereas returns on
mainstream financial assets are. Other commodities, which are generally thought to be correlated with
economic activity, were also tested.

A number of different relationships were examined to show that returns on gold are independent of the
business cycle. Using both static and dynamic analysis this study examined to what extent there is a
relationship between economic variables and (i) financial indices (ii) commodities and (iii) gold.

Using the gold price and US macroeconomic and financial market quarterly data from January 1975 to
December 2001, the following conclusions were reached:

• There is no statistically significant correlation between returns on gold and changes in
macroeconomic variables such as GDP, inflation and interest rates;
• Returns on financial assets such as the Dow Jones Industrial Average Index, Standard &
Poor’s 500 index and 10-year US government bonds are correlated with changes in
macroeconomic variables;
• Changes in macroeconomic variables have a much stronger impact on other commodities
(such as aluminium, oil and zinc) than they do on gold; and
• Returns on gold are less correlated with returns on equity and bond indices than are returns on
other commodities.

These results support the notion that gold may be an effective portfolio diversifier.

It is thought that the reasons which set gold apart from other commodities stem from three crucial
attributes of gold: it is fungible, indestructible and, most importantly, the inventory of above-ground
stocks of gold is enormous relative to the supply flow. This last attribute means that a sudden surge in
gold demand can be quickly and easily met through sales of existing holdings of gold jewellery or other
products (either to fund new purchases or for cash), in this way increasing the amount of gold
recovered from scrap. It may also be met through the mechanism of the gold leasing market allied to
the trading of gold bullion Over-the-Counter. The potential for gold to be highly liquid and responsive
to price changes is seen as its critical difference from other commodities.

Although returns on gold may be correlated with those on other commodities, it is thought that the
strength of this relationship depends on the extent to which each commodity shares the crucial
attributes of gold, particularly that of high liquidity. Further study is, however, required to isolate the
effect of liquidity variation of different commodities.

2

1. Introduction

The flow demand of commodities is driven primarily by exogenous variables that are subject to

the business cycle, such as GDP or absorption. Consequently, one would expect that a sudden

unanticipated increase in the demand for a given commodity that is not met by an immediate increase

in supply should, all else being equal, drive the price of the commodity upwards. However, it is our

contention that, in the case of gold, buffer stocks can be supplied with perfect elasticity. If this

argument holds true, no such upward price pressure will be observed in the gold market in the

presence of a positive demand shock.

Gold Fields Mineral Services Ltd estimate the above-ground stocks of gold to have been some

145,200 tonnes at the end of 2001, a figure that dwarfs annual new mined supply of around 2,600

tonnes. Much of this is held in a form that can readily come back to the market under the right

conditions. This is obviously true for investment forms of gold but it is also true for much jewellery in

Asia and the Middle East. In these regions jewellery traditionally fulfills a dual role, both as a means of

adornment and as a means of savings. Notably, it is particularly important for women in Muslim and

Hindu cultures where traditionally a woman’s jewellery was often in practice her only financial asset.

Such jewellery is of high caratage (21 or 22 carats), and is traded by weight and sold at the current

gold price plus a moderate mark-up to allow for dealing and making costs. It is also fairly common for

jewellery to be bought or part-bought by the trading in of another piece of equivalent weight; the

traded-in piece will either be resold by the jeweller or melted down to create a new piece.

In Asia and the Middle East both gold investments and gold jewellery are considered as financial or

semi-financial assets. It is not known how much of the total stocks of gold lie in these regions but in

recent years they have accounted for approximately 60% of total demand; while the long-held cultural

affinity to gold would suggest that the majority of stocks in private hands lie in this area. Consumers

are very aware of price movements and very sensitive to them. Gold will be sold in times of financial

need but holders will frequently take profits and sell gold back to the market if the price rises. Thus the

supply of scrap gold will normally automatically rise if the gold price rises. Even gold used for industrial

purposes such as electrical contacts in electronic equipment is frequently recovered as scrap and a

rise in the gold price will increase the incentive for such recovery.

3

The existence of a sophisticated liquid market in gold leasing1 has, over the past 15 years, provided a

mechanism for gold held by central banks and other major institutions to come back to the market.

Although the demand for gold as an industrial input or as a final product (jewelry) differs across

regions, we argue that the core driver of the real price of gold is stock equilibrium rather than flow

equilibrium. This is not to say that exogenous shifts in flow demand will have no influence at all on the

price of gold, but rather that the large supply of inventory is likely to dampen any resultant spikes in

price. The extent of this dampening effect depends on the gestation lag within which liquid inventories

can be converted in industrial inputs.2 In the gold industry such time lags are typically very short.

Gold has three crucial attributes that, combined, set it apart from other commodities: firstly, assayed

gold is homogeneous; secondly, gold is indestructible and fungible; and thirdly, the inventory of above-

ground stocks is astronomically large relative to changes in flow demand. One consequence of these

attributes is a dramatic reduction in gestation lags, given low search costs and the well-developed

leasing market. One would expect that the time required to convert bullion into producer inventory is

short, relative to other commodities which may be less liquid and less homogenous than gold and may

require longer time scales to extract and be converted into usable producer inventory, making them

more vulnerable to cyclical price volatility. Of course, because of the variability of demand, the price

responsiveness of each commodity will depend in part on precautionary inventory holdings.

Finally, there is low to negative correlation between returns on gold and those on stock markets,

whereas it is well known that stock and bond market returns are highly correlated with GDP.3 This is

because, generally speaking, GDP is a leading indicator of productivity: during a boom, dividends can

be expected to rise. On the other hand, the increased demand for credit, counter-cyclical monetary

policy and higher expected inflation that characterize booms typically depress bond prices.4

The fundamental differences between gold and other financial assets and commodities give rise to the

following “hard line” hypothesis: the impact of cyclical demand  using as proxies GDP, inflation,

1
See, for example, Cross (2000) and Neuberger (2001).
2
See Kydland and Prescott (1982) and Lawrence and Siow (1985A) on Time To Build and the Aggregate Fluctuations).
3
Returns on bonds are defined as the value of coupons plus changes in the bond price. All variables used in this paper are real.
4
See Litterman and Weiss (1985).

4

nominal and real interest rates, and the term structure of interest rates  on returns on gold, is

negligible, in contrast to the impact of cyclical demand on other commodities and financial assets.

Using the gold price and US macroeconomic and financial market quarterly data from January 1975 to

December 2001, the following conclusions may be drawn:

(1) There is no statistically significant correlation between returns on gold and changes in

macroeconomic variables, such as GDP, inflation and interest rates; whereas returns on other

financial assets, such as the Dow Jones Industrial Average, Standard & Poor’s 500 index and 10-

year government bonds, are highly correlated with changes in macroeconomic variables.

(2) Macroeconomic variables have a much stronger impact on other commodities (such as aluminium,

oil and zinc) than they do on gold.

(3) Returns on gold are less correlated with equity and bond indices than are returns on other

commodities.

Assets that are not correlated with mainstream financial assets are valuable when it comes to

managing portfolio risk. This research establishes a theoretical underpinning for the absence of a

relationship that has been demonstrated empirically for a number of years; namely, that between

returns on gold and those on other financial assets.

The remainder of the paper is organized as follows. In Section 2 we formally state the hypotheses to

be tested. In Section 3 we describe the data and methodology used in this study. Sections 4 and 5

present the empirical findings based on the analysis of static correlations and a dynamic VAR system,

respectively. Section 6 contains a discussion of the conclusions that may be drawn from the results

and suggests avenues for further research.

5

2. Statement of hypotheses

The purpose of this study is to explore certain attributes of gold, which distinguish it from other

commodities. More specifically, we are concerned with testing a theory as to why gold is so little

correlated with financial assets.

Generally, the flow demand of any commodity is driven primarily by exogenous variables such as GDP

or absorption. To the extent that gold behaves like other commodities, one would expect that a

sudden unanticipated rise in the demand for gold which cannot be matched by an immediate increase

in supply should, all things being equal, drive the price of gold up. However, it is argued here that the

supply of gold is perfectly elastic, given the existence of large, homogeneous and liquid above-ground

stocks.

The term “contango” is used to describe a market situation where the spot price is lower than the

forward price, the difference between them representing carrying costs (e.g. storage) and the time

value of money (interest rates). The gold futures and forwards market is typically in contango; this is a

reflection of the ready availability of gold for leasing. The gold lease rate is the difference between the

US$ LIBOR rate nominal borrowing rate and the convenience yield or “the demand for immediacy”.5

The lease rate is the rate at which a lender is willing to lend gold (measured in real units of gold). The

convenience yield is the rate the borrower is willing to pay for borrowing gold. In equilibrium, the

convenience yield equals the lease rate. If, however, a demand surge occurs in the presence of

restricted supply and illiquid borrowing, the borrower (or the purchaser of the commodity) will be willing

to pay a higher rate to obtain the commodity immediately. In this case, the lease rate might exceed

US$ LIBOR, or, equivalently, the spot price might exceed the forward price – a situation described as

backwardation. The fact that backwardation in the gold market is extremely rare indicates that there is

less “urgency” to borrow gold. Backwardation typically occurs in markets that experience sudden

unexpected shocks where firms desperately need to replenish inventory as soon as possible.

5
The “demand for immediacy” refers to the “urgent time” demand for a commodity as an input in production, where producers’
opportunity costs are so high if they fail to deliver a finished product, they are willing to lend money at very cheap rates (even
negative in a backwardation mode (see Miller (1988) and Economides and Schwartz (1995)). This approach emphasises
demand for immediacy, which is the willingness to buy or sell now rather than wait. This demand depends on the volatility of the
underlying price and the extent to which the underlying price affects the wealth of the buyer or seller.
6
Backwardation is the opposite of contango, i.e. describes a market situation where the spot price exceeds the forward price.

6

This difference between gold and other commodities can be attributed to three crucial attributes of the

yellow metal: (1) assayed gold is homogenous, (2) gold is indestructible and fungible and (3) the

inventory of above-ground stocks is extremely large relative to changes in flow demand. These

attributes set gold apart from other commodities and financial assets and tend to make its returns

insensitive to business cycle fluctuations.

The above argument can be stated formally as a set of inter-related hypotheses as follows:

(1) Changes in real7 GDP, short term interest rates and the money supply are not correlated with the

real rate of return of gold.

(2) Changes in real GDP, short term interest rates and the money supply are correlated with real

returns on equities and bonds.

(3) Real rates of return on durable commodities other than gold such as oil, zinc, lead, silver and

aluminium are correlated with real changes in GDP, short term interest rates and the money

supply.

(4) Given that hypotheses 1, 2 and 3 hold, one may hypothesize further that:

(a) Returns on gold are not correlated with those on equities and bonds. This is tantamount to

suggesting that whilst core macroeconomic variables are the critical determinants of financial

index performance, they have no impact on the real price of gold.

(b) Returns on other commodities are correlated with returns on equities and bonds.

(c) Whilst returns on gold may be correlated with returns on other commodities, this correlation

tends to be small, and is a function of the extent to which the other commodities share the

crucial attributes of gold that set it at the extreme end of the continuum ranging from highly

liquid to very illiquid supply.

7
The deflator used throughout is the U.S. Producer Price Index.

7

3. Data and Methodology

The time series used in this study consisted of quarterly data from January 1975 to December

2001.8 The analysis was conducted using real data, obtained by deflating nominal series using the

percentage (logarithmic) change in United States producer price index as a proxy for inflation, with the

exception of the US GDP growth rate, which was based on constant GDP at 1990 prices. Quarterly

returns have been annualized. Table 1 below describes the data used in more detail.

The hypotheses listed in Section 2 are tested using two methods: firstly, by calculating simple pair-

wise correlations between the variables. The advantage of this approach is that it is widely used and

the results are therefore easier to understand. The Pearson product moment correlation coefficients

associated with each hypothesis are reported along with the relevant p-values, used to evaluate

whether each coefficient is significantly different from zero.9 A short-coming of pair-wise correlation

analysis is that it provides a static view of relationships, i.e. a snapshot in time. In this study, only

contemporaneous correlation coefficients were calculated. However, changes in a given economic

variable affect other economic variables over time, and these lags are long and variable. Therefore, to

gain insight into the dynamics of the relationships between the variables, the four hypotheses are then

tested using a Vector Auto Regressive (VAR) system.10 The advantage of the second approach,

although it is more difficult to apprehend, is that it becomes possible to identify relationships between

several variables across different time periods. For example, VAR analysis enables one to identify

whether the change in the interest rate in the previous period affects returns on gold in the current

period.

A VAR system usually takes the following form:

T
X t = ψ 0 + ∑ X t −i *ψ i + ε t
i =1

where X t = [ x1t , x 2t , L x kt ]' is a vector of variables; ψ i = [φ 2 , φ 2 , L, φ ki ]' is the coefficient vector for
i i

lag i; ε t = [ε 1t , ε 2t ,Lε kt ]' is a vector of error terms, E[ε t ] = 0 and E[ε t ε t ] = Ω
'

8
Data source: EcoWin

8

Variable Short code Description

Inflation INFL Log change of United States Producer Price Index (PPI).

GDP growth rate RGDP Real growth rate of United States GDP, defined as log change of GDP measured
at 1990 prices. DGDP is used as a proxy for real growth in “aggregate
11
absorption”.

Cyclical GDP CGDP Real growth rate of seasonally adjusted GDP defined as the difference between
the growth rate in the current period (DGDPt) and the three-year quarterly moving
12
average of DGDP.

Interest rate R3M Annualized 3 month United States Certificate of Deposit (CD) real rate of return,
defined as 3 month United States CD nominal return, deflated using the US PPI.
This is used as a proxy of the short-term US interest rate.

Money supply NRM2 Growth rate of nominal monetary expansion of M2 defined as log change of
nominal M2.

13
S&P 500 RSP Real percentage returns on the S&P 500 index (see Note 1).

Dow RDJ Real percentage returns on the Dow Jones Industrial Index (Dow) (see Note 1).

Bonds RBOND Real rate for return on 10-year United States government bonds, constructed
from ten year bond yield, deflated using the US (PPI).14

Gold RGOLD Real percentage returns on the London PM gold price fix (USD) (see Note 1).

Commodities RCRB Real percentage returns on the CRB index (see Note 1).15

Aluminium RALUM Real percentage returns on aluminium (see Note 1).

Copper RCOPPER Real percentage returns on copper (see Note 1).

Lead RLEAD Real percentage returns on commodity lead (see Note 1).

Zinc RZINC Real percentage returns on zinc (see Note 1).

Oil RWTI Real percentage returns on Western Texas Intermediate oil spot price (see Note
1).

Silver RSILVER Real percentage returns on silver (see Note 1).
Notes: (1) Defined as the log change in the index or price, deflated using the US PPI.

Table 1: Description of time series

In the present context, since we are investigating the dynamic relationship between returns on gold

(and other assets) and a set of macroeconomic variables, we incorporate the gold return and relevant

9
See, for example, Conover(1980), which compares the Pearson tests with Kendall’s tau rank correlation test and Spearman’s
rank test.
10
Simms(1980), Litterman and Weiss(1985), Lawrence and Siow(1986).
11
We also experimented with Industrial Production Index but found it too narrow to represent aggregate spending.
12
Because economic growth has been shown to exhibit significant changes in regimes, we have defined the long term trend as a
12 quarter moving average to avoid misspecification .
13
This does not take account of returns on reinvested dividends, i.e. is not a total return index. The same applies to the Dow.
14
The bond is sold at the end of each quarter and the total rate of return (in log form) is calculated, including coupons and capital
gains but excluding transaction costs. A new 10-year bond is purchased with the proceeds at the end of each period. This
provides a true theoretical measure of the real returns on 10-year US government bonds with a duration proxying the current 10-
year benchmark security.

9

macro economic variables into the VAR system. The VAR system for returns on gold (GOLDt), cyclical

GDP (CGDPt), short term interest rates (R3Mt) and inflation (INFLt) can be written as:

'
GOLD t  φ 1  φ 1i  GOLD t − i  ε 1 
0 t

CGDP   0  i CGDP   t
φ  φ  ε 
T
 t   t −i 

 R3M t 
= 2+
φ0
∑ φ 2i   R3M t − i 
+  2
εt
  2  2   2
i =1
 
 INFL t  φ 4 
0
  φ 4 
 
i
 INFL t − i  ε 4 
t
 

In the above dynamic system, the value of each variable depends on not only its own lags but also on

the lags of the other variables in the system. This model therefore enables us to explore how the

variables interact over time. The VAR system specified above consists of four equations, each of

which is estimated separately using ordinary least squares. The key reason for estimating them jointly

as a system of equations is that one can explore the impact of a shock, encapsulated in the error term

of the period in which the shock occurred (for example, εit), on the dynamic path of all four variables

(GOLDt, CGDPt, R3Mt and INFLt). In other words, we can identify how a shift in a given

macroeconomic variable affects all the other variables in the system over time. This makes it possible

to evaluate whether or not unexpected money growth, for example, affects the price of gold in the

current period and in the future. The partial cross correlations play a critical role. For example, an

unanticipated change in the short-term interest rate will affect the long-term rate and could also

conceivably affect CGDP. The changes in these variables could in turn affect the real rate of return on

gold. In addition to providing a dynamic view of the interaction between variables, the VAR system

also sheds light on indirect and spill over effects. Although each equation in the system is estimated

separately, the method allows for some interesting analysis, providing a richer framework than is

possible within the constraints of static correlation or univariate regression techniques.

All time series were tested for unit roots using Dickey Fuller tests. Level variables in log form were

found to be non-stationary, suggested that variable pairs might be cointegrated. Return series proved

to be stationary (see the final column of Table A1, Appendix A). In the event that series are

cointegrated, it is not appropriate to analyse them using a VAR system (cointegrated non-stationary

15
For more information on this index, visit http://www.crbtrader.com/crbindex/nfutures_current.asp .

10

data should be analysed using a Vector Error Correction Model (VECM)).18 Therefore, the Engle

Granger approach was used to test for cointegration of the variables. The results showed that the log

of real prices of gold and other commodities (using the Producer Price Index as a deflator) are not co-

integrated with the log of real GDP. Therefore, real rates of return were selected as the underlying

variables both for the static correlation analysis and the dynamic VAR analysis

18
See the seminal paper by Simms (1980) and later papers by Engle and Granger (1987) on unbiased and
efficient estimation.

11

4. Analysis of static correlations

The tables reported in this section contain correlation coefficients between variable pairs and

the p-value associated with each correlation coefficient19. The p-value indicates the significance level

at which the null hypothesis, defined as a zero correlation coefficient between the pair of variables can

be rejected. We have performed significance tests at the 1% and weaker 5% levels. For example, if a

p-value is less than 0.05, the null hypothesis (that there is no correlation between the variables) can be

rejected at a 5% level of significance; the probability of erroneously rejecting the null hypothesis

(whereas it is true) is less than 5%. In other words, the correlation between the variables is

significantly different from zero (they may be positively or negatively correlated). Conversely, if a p-

value is greater than 0.05, it is not possible to reject the null hypothesis of no correlation between the

variables at the 5% level of significance. In this case, it is reasonable to conclude that the variables

are not correlated. The lower the p-value, the less likely it is that the variables are not correlated.20

Table B2 in Appendix B consists of a correlation matrix covering all the variables tested. In the

discussion below, results are broken down into subsets of this table as applicable to each of the four

main hypotheses that were tested.

The first hypothesis was that changes in real GDP, short-term interest rates and the money supply are

not correlated with the real rate of return on gold. Table 2 reports the results of the statistical analysis,

along with the p-value associated with each correlation coefficient. Based on the results obtained, it is

concluded that the null hypothesis holds and that there is no correlation between changes in the

macro-economic variables covered and returns on gold for the period covered.

19
Pearson’s correlation coefficient is the covariance of a pair of variables, X and Y, divided by the product of the standard
σ X ,Y
2

deviations of X and Y, i.e. .
σ Xσ Y
20
We thus wish to perform a two tailed test in which we can reject the null hypothesis Ηο: ρ =0 at the 1% and 5% levels of
significance. The correlation coefficient (see Canover 1980) follows a Student’s t distribution, where the test statistic, t = ρ sqrt
(n –2)/(1-ρ**2) where n - 2 is the number of degrees of freedom and ρ is the correlation coefficient. Note that the t distribution is
symmetric if ρ =0, but is skewed for ρ not equal to 0. In the tests performed above, we assume the null and hence a symmetric
distribution.

12

RGDP R3M INFL NRM2 RBOND
RGOLD -0.13 -0.17 0.11 0.03 0.01
P-val (0.18) (0.08) (0.25) (0.78) (0.94)

Table 2: Return Correlation between gold and macro variables

The second hypothesis tested was that the key macro economic variables, real GDP growth, changes

in short term real interest rates and the rate of growth of money supply are correlated with real returns

on equities and bonds. The correlation coefficients and their corresponding p-values are reported in

Table 3 below. In this case, a low P-value is required to support the hypothesis being tested. The p-

value in the table measures the level of significance that the hypothesis of zero correlation can be

rejected. Thus the lower the value, the greater the likelihood that the null hypothesis can be rejected.

Any p-value less than 5% suggests the null is rejected at 5% and the stronger rejection of the null for a

p-value less than 1%.

RGDP R3M INFL NRM2 RBOND

RSP -0.01 0.27 -0.34 -0.01 0.34
P-val (0.90) (0.01) (0.00) (0.91) (0.00)

RDJ -0.02 0.27 -0.37 -0.04 0.33
P-val (0.87) (0.01) (0.00) (0.68) (0.00)

RBOND -0.33 0.42 -0.54 0.06 1.00
P-val (0.00) (0.00) (0.00) (0.55) (0.00)

Table 3: Return Correlations between financial indices and macro variables

Real returns on both the Dow Jones Industrial Average and the S&P 500 indices are found to be

significantly positively correlated with changes in real short-term interest rates and with the returns on

10-year government bonds, and are negatively correlated with inflation. Note that returns on bonds

are calculated as described in footnote 3 on page 3. However, there appears to be no

contemporaneous correlation between returns on equity indices and the growth rates of real GDP and

the money supply.

13

Whilst it may seem surprising that the real GDP growth rate does not directly affect returns on the

stock market indices, the simple correlations suggest that the mechanism of transmission is through

interest rates. This is consistent with the findings of Litterman and Weiss. Moreover, the apparent lack

of relationship may mask the dynamics of lagged effects.

We reach one key conclusion: financial assets tend to be significantly correlated with underlying

macroeconomic variables in contrast to gold prices. This provides support for our second key

hypothesis, that while gold returns tend to be independent from macroeconomic shocks, fixed income

and equity prices are driven by common macroeconomic factors. However, the mechanism of

transmission, while suggestive, needs to be more fully explored in a dynamic system where partial

correlations and autocorrelations are estimated. This is analysed in section 5 using VARs.

The third hypothesis tested was that, in contrast to gold, the real rates of return on durable

commodities such as oil, zinc, lead, silver and aluminium are correlated with real changes in GDP,

short-term interest rates and the money supply.

RGOLD RCRB RALUM RCOPPER RLEAD RZINC RWTI RSILVER
RGDP -0.13 0.07 0.15 0.19 0.20 0.26 0.03 0.04
0.18 0.45 0.11 0.05 0.04 0.01 0.74 0.71
INFL 0.11 0.08 0.04 0.06 0.00 0.06 0.49 0.14
0.25 0.42 0.68 0.54 0.96 0.57 0.00 0.15
NRM2 0.03 -0.04 0.11 -0.11 0.02 -0.05 -0.04 0.03
0.78 0.67 0.27 0.28 0.85 0.63 0.71 0.76
R3M -0.08 -0.21 -0.19 -0.04 -0.12 0.05 0.09 -0.12
0.42 0.03 0.04 0.70 0.21 0.58 0.34 0.21
RBOND 0.01 -0.14 -0.15 -0.14 -0.21 -0.26 -0.32 -0.24
0.94 0.14 0.12 0.14 0.03 0.01 0.00 0.01

Table 4: Return correlation between assets and macroeconomic variables.

The test results are found in Table 4. Price changes in copper, lead and zinc are positively correlated

with the growth rate of real GDP, while returns on oil, represented by the WTI index, are strongly

correlated with inflation. The test results suggest that there is no contemporaneous correlation

14

between the rate of growth of the money supply and returns on any of the commodities, nor on the

CRB Index, which covers a wider basket of commodities. Returns on the CRB Index and on

aluminium appear to be negatively correlated with short-term interest rates at the 5% level of

significance. The correlation coefficients between returns on 10-year government bonds, on the one

hand, and those on lead, zinc, oil and silver, on the other hand, were found to be negative. Out of all

the commodity returns that were analysed, only those on gold were not correlated with changes in any

of the macro-economic variables.

Again we can conclude that the nature of the commodity is important in determining the

responsiveness of price action to macro disturbances. Gold appears to be different from all other

commodities. The dynamics need further exploration.

The fourth hypothesis supporting our argument consisted of three sub-hypotheses, the first of which

(hypothesis 4a) was that returns on gold are not correlated with those on equities and bonds; in other

words, it should not be possible to reject the null hypothesis of no correlation (the corresponding p-

value would exceed 0.05). The results presented in Table 5 below indicate that there was no

significant contemporaneous correlation between returns on gold, on the one hand, and those on the

S&P 500, Dow Jones Industrial Average, bonds and short-term interest rates over the period covered.

RSP RDJ RBOND R3M
RGOLD -0.07 -0.09 0.01 -0.17
P-val 0.45 0.38 0.94 0.08

Table 5: Return correlation between gold and other financial assets

The second sub-hypothesis (hypothesis 4b) was that returns on other commodities, which are driven

by macroeconomic factors, tend to be correlated with returns on equities and bonds, which are

themselves correlated with changes in macroeconomic variables. In this case, a p-value less than

0.05 is needed to reject the null hypothesis (no correlation), in support of our argument.

15

The results reported in Table 6 indicate that returns on all commodities, with the exception of gold,

aluminium and copper yields, are correlated with financial assets. Lead, zinc, WTI (oil), and silver

returns are inversely correlated with bond yields. Returns on the CRB, WTI (oil) and silver are

negatively correlated with short-term interest rates, implying that higher bond yields (falling bond

prices) would tend to be associated with lower returns on commodities. Gold, aluminium and copper23

are the only commodities that appear to have no correlation with returns on any of the financial assets

considered. The same argument can be drawn from the correlation between de-trended shifts in these

variables. Oil, as proxied by the WTI index, is significantly negatively correlated with each of the

financial assets considered. Gold is, once again, shown to be independent of returns on financial

assets, as is copper, despite its strong correlation with GDP.

RGOLD RCRB RALUM RCOPPER RLEAD RZINC RWTI RSILVER
R3M -0.17 -0.22 -0.17 -0.09 -0.07 -0.03 -0.48 -0.23
P-val 0.08 0.03 0.09 0.36 0.46 0.79 0.00 0.02
RSP -0.07 -0.04 -0.01 -0.12 -0.18 -0.03 -0.29 0.03
P-val 0.45 0.71 0.94 0.22 0.07 0.78 0.00 0.77
RDJ -0.09 -0.01 0.02 -0.08 -0.12 -0.01 -0.31 0.02
P-val 0.38 0.90 0.81 0.42 0.23 0.95 0.00 0.80
RBOND 0.01 -0.14 -0.15 -0.14 -0.21 -0.26 -0.32 -0.24
P-val 0.94 0.14 0.12 0.14 0.03 0.01 0.00 0.01

Table 6: Return correlation between financial assets and commodities

The third, and final, sub-hypothesis (hypothesis 4b) was that, whilst returns on gold may be correlated

with returns on other commodities, this correlation tends to be small, and depends on the extent to

which the other commodities share the crucial attributes of gold that set it at the extreme end of the

continuum ranging from highly liquid to very illiquid supply. Defining this in rather starker terms for the

purposes of evaluation, the hypothesis to be tested is that there is no significant correlation between

returns on gold and those on the other commodities (in which case the p-value will exceed 0.05).

23
In section 5 we show that in contrast to gold, copper is a leading indicator of the PPI. In this sense, copper prices are not
insulated from business cycles.

16

RCRB RALUM RCOPPER RLEAD RZINC RWTI RSILVER
RGOLD 0.20 0.23 0.21 0.20 0.10 0.14 0.63
P-val 0.04 0.02 0.03 0.04 0.31 0.14 0.00

Table 7: Return correlation between gold and other commodities

The results reported in Table 7 show that this hypothesis is not supported. Specifically, there is a

positive correlation between returns on gold and those on the CRB index, aluminium, copper, lead and

silver. The only returns not correlated with those on gold were zinc and oil (as proxied by the WTI

index). Taking the CRB as the general or reference commodity market index, a significant “beta”

coefficient exists between all commodities (excluding zinc and WTI) and the CRB index. Gold has a

significant correlation of 0.20**, whilst all the others lie between 0.10** and 0.63*. Thus commodities

as a group with the exception of oil and zinc tends to move around “together” despite the differences in

the influence of macro economic variables. Gold returns are significantly correlated with aluminium,

copper, lead and silver.

This suggests that commodity prices in a given time period are influenced by common factors other

than the macro-economic environment in the same time period.

17

5. Dynamic analysis of gold and other asset returns over the business cycle

a) Vector Auto Regressions

We continue our investigation of the relationship between gold and macroeconomic variables

in a dynamic context using Vector Auto Regressions (VAR).25 We then contrast our findings with the

behaviour of other financial and commodity assets. Our key finding, using simple correlation analysis

as reported in Section 4, was that, while gold returns are independent of the business cycle, returns on

other assets, including a range of commodities, are profoundly dependent on the business cycle;

although there is a significant relationship between contemporaneous returns on gold and those on a

number of other commodities.

The advantage of the VAR technique is that it enables us to explore the interrelationship between

asset returns and all the macro variables in a multivariate setting and, furthermore, to explore some of

the dynamics.

The VAR system is a system of simple regression equations (estimated using ordinary least squares)

in which each dependent variable is regressed on lags of all the other variables and lags of itself. The

dataset as described in Table 1 contains quarterly data over the period 1978-Q3 to 2001-Q4.

b) Estimation and significance tests.

In tables C1 to C10 (see Appendix C), we estimate a VAR system which includes the (real)
26
rate of return of the asset and five core macro economic variables including cyclical GDP (CGDP) ;

the long term real rate of return, RBOND; the short-term three month real rate of return, R3M; the rate

of nominal monetary expansion, NRM2; and the rate of inflation, INFL. Each VAR system includes the

real rates of return on assets - these are RGOLD, RSP, RBOND, RSILVER, RCOPPER, RCRB,

RZINC, RLEAD, RWTI, and RALUM. We have included two lags of each of the five independent

variables.

18

In each ordinary least square regression equation we perform the standard F-statistic test. The null

hypothesis is that the joint impact of the lags of the independent variables on the dependent variable is

zero. The greater the F-statistic, the more likely it is that we can reject the null hypothesis of no impact

and confirm that the lagged variables do have a dynamic impact. We also report the significance level

at which we can reject the null hypothesis. The lower the significance level the greater the likelihood

that the null can be rejected. We assume the null is rejected at the 5% (and hence the stronger 1 %)

significance level.

c) Results: commodity yields over the business cycle

The F-statistics that result from each VAR system estimated for commodities and

macroeconomic variables (reported in detail in Appendix C, tables C1 to C10) are summarised in Table

8 below. Statistically significant relationships are highlighted in grey in this table.

The key empirical finding is that while the real rate of return of gold is independent of all

macroeconomic variables, the other commodities in the sample are all affected by at least one of the

macro-economic variables, with the exception of zinc.

Gold CRB WTI Silver Copper Alum Zinc Lead
CGDP ** ** **
NRM2
R3M ** ** ** **
RBOND ** **
INFL ** ** ** ** ** **
Note: A **-relation between return of commodity and macroeconomic variables implies either the F-test is significant at 5% level
or one can explain more than 10% of the other’s variance. For detailed results, please refer to Tables C1-C10 in Appendix C.

Table 8: Summary of VAR results

Only gold and zinc have no dynamic relationship with any of the core macroeconomic variables, i.e.,

based on the F-statistics, the null cannot be rejected at the 5% level of confidence. This implies that

the real rate of return of gold follows a random walk and cannot be predicted using lagged

25
See section 3, page 8 for an explanation of the Vector Autoregression analysis.
26
CGDP is estimated as the difference between actual real GDP growth and a twelve quarter moving average of real GDP
growth. We select this method to allow for secular changes in the economic growth rather than using the deviation from trend
proxy for cyclical GDP.

19

macroeconomic data. In other words, the dynamic path (or history) of macro variables has no impact

whatsoever on the real rate of return of gold.

Tables C1 through C10 demonstrate that real rates of return of commodities other than gold and (zinc)

have a significant relationship with core macroeconomic variables, although the mechanism differs

from one commodity to another. Silver returns are significantly influenced by long-term real bond

yields (F = 3.23**). By estimating the decomposition of variance we find that 52% of the variability of

RSILVER three quarters out is explained by macro economic variables. The real rate of return of

copper is a significant leading indicator of the producer price index and thus correlated with economic

activity. The F-statistic on the lagged impact of RCOPPER on INFL is significant at the 5% level of

significance (F = 2.98**). After one year the macroeconomic variables explain 36% of the variability

and after 2 years 40%, far higher levels than those achieved by gold.27

The remaining commodity yields, including the CRB index, aluminium, lead and oil, are all correlated

with the business cycle, with varying mechanisms and causalities. The CRB index is, not surprisingly,

a strong leading indicator of economic activity - the F-statistics are 5.5** on cyclical GDP, 7.19* on

inflation, 3.83* on long-term real bond yields and 3.57** on short-term yields, all significant at the 5%

confidence level. Thus investments in CRB components provide little insulation from the business

cycle. Lead is similar in behaviour to the CRB index, being a significant leading indicator of business

activity.

Oil is significantly correlated with lags of long-term bond yields at the 6% significance level and the

lagged response of oil on short-term rates is significant at the 5% level.

Only zinc and, to a lesser extent, aluminium have significant cross correlations with the

macroeconomic variables. In the case of aluminium however, inflation explains about 12% of its

volatility within one year. In this sense it is weakly correlated with the business cycle.

27
There is no “causality” running from any of the macro variables to RCOPPER. The correlation between economic activity and
RCOPPER in section 4 results from the value of copper as a leading indicator of economic activity.

20

With the exception of zinc, we can conclude that the evidence presented here suggests that returns on

investments in non-gold commodities will be affected by the business cycle.

d) Stock and bond yields over the business cycle

In tables C2 and C3 we show how real returns of the S&P 500 Index and bond yields are

affected by macroeconomic variables in strong contrast to the behaviour of the gold yield. Returns on

the S&P 500 are significantly affected by cyclical GDP and long-term bond yields at the 5% critical

level. Furthermore, the S&P 500 is a strong leading indicator of the business cycle. The F-statistic of

lagged S&P 500 on CGDP is 4.11*, significant at the 1% critical level. The decomposition of variance

suggests that the macro variables explain about 42% of the variation of the S&P 500 index within a

year.

Real long-term bond yields, whilst not affected directly through cyclical GDP, are strongly affected by

short-term real yields (F=5.14*, significant at the 1% level). The combined impact of all the macro

variables explains over 60% of the variation in long-term yields.

The above results should be contrasted to gold yields where no macroeconomic variable has any

notable lagged effect.

e) The relationship between financial yields and commodity yields

Whilst we have demonstrated that gold yields are independent of the business cycle and other

commodities (except zinc) and financial assets are not, this does not necessarily imply that gold is a

good diversifier.28 To investigate this question further, we estimate Vector Autoregressions (VAR) for

each commodity yield with short-term real rates, bond yields and equity returns. The gold yield VAR is

found in table C1 and the others are found in C11 thru C18 (see Appendix C). The results are further

summarised in table 9 below.

28
Much depends upon the magnitude of the impact of the business cycle on the yields described above. If the business cycle
explains the bulk of the variation, then we are likely to find that gold is a good diversifier due to its independence. In essence this
section indirectly tests how important the business cycle is in explaining both the volatility and correlation across assets.

21

CRB WTI Silver Copper Alum Zinc Lead Gold
RSP - ** ** - - - ** -
RBOND ** ** ** - - - ** -
R3M ** ** ** - - - ** -
** indicates a lead-or-lag causality at 10% significance level of F-test in VAR system. For detailed statistics, please refer to
Tables C11 to C18 in Appendix C.
Table 9: The relationship between returns of commodities and financial indices

Table C11 describes the VAR of RGOLD, RSP, RBOND and R3M. All the F-statistics rule out the

possibility that gold yields are determined by lagged returns of RSP, RBOND and R3M. Indeed as the

decomposition of variance suggests – within one year lags of RGOLD explain 95% of the variation.

This is consistent with the random walk equation described in C1. This clearly demonstrates that the

lack of correlation between gold yields and equity returns found by Smith (2001, 2002) can be

attributed to the properties of gold that immunize it from business cycle fluctuations.

Tables C12 through C18 describe significance tests for the VAR of the other commodities with equity

returns, the long-term bond yield and the short term real rate. The results here are mixed. We find

that the CRB index, WTI, silver and lead yields are significantly related to the financial market yields,

whereas copper, aluminium and zinc are not. We find that the CRB index yield has a lagged effect on

both money market and long term bond yields with no effect on the equity market, whereas oil, silver

and lead all have significant (cross) correlations with the three financial assets. The dynamics of the
29
relationship differ from commodity to commodity.

29
. When RCRB is the dependent variable, the F statistics appear to suggest that RCRB is invariant to lagged shifts in real
yields of alternative assets. However, the data is suggestive in that lagged RCRB does have an impact (9% level of significance)
on RBOND and R3M (F= 2.7524 0.068). In table C13 RBOND does have a significant impact on RSILVER (F= 2.87, 0.0917) as
well as the RSP (F=2.4348, .092). However, RSILVER has an impact on short-term interest rates (2.9744**). After a period of a
year, the yields on financial assets explain (directly and indirectly) 29% of the variation of silver. This confirms the importance of
the business cycle in explaining the real yield on silver.
The F statistics rule out that copper (Table C14), zinc (Table C16) and aluminium (Table C18) real returns are correlated with
lags of the returns of RSP, RBOND or R3M. Finally, WTI (Table C15) has a significant effect on predicting short-term real rates
(F= 3.50**) and RBOND has significant effect on RWTI (F=3.07**) at the 5% significance level. This confirms the linkage of oil to
financial market yields. In Table C17 we note that RBOND has a significant impact RLEAD (F=4.6343*) at the 1% significance
level and RLEAD is a leading indicator of short-term real rates (F= 4.1224*) at 1% level of significance.

22

6. Conclusions

The purpose of this research was to investigate whether or not the gold price is “insulated”

from the business cycle, in contrast to other financial assets and commodities. The “insulation”

hypothesis hinges on the fact that the supply and potential supply of inventory used in manufacturing is

huge in contrast to the flow demand of gold as an input. As aggregate demand rises through the cycle,

the increased demand is easily met through the incipient increase in supply without pressure on the

gold price. Commodities which exhibit all or most of the characteristics of gold such as homogeneity,

indestructibility, liquidity, identifiability and short inventory gestation lags would also tend to exhibit

price behaviour which is insulated in part from the business cycle. By examining simple correlations

and using dynamic VAR analysis we cannot reject our four core hypotheses:

(a) GDP and other core macro economic variables are uncorrelated with the real rate of return of

gold.

(b) Core macro economic variables are correlated with the S&P index, the Dow Jones Industrial

Index, a money market index and a bond index (all variables are defined as real rates of

return).

(c) Real rates of return of other commodities other than gold such as oil, zinc, lead, silver,

aluminium, copper and the CRB index are correlated with macro-economic variables.

(d) Gold and the financial indices are uncorrelated (this is tantamount to suggesting that the above

macro-economic variables are the critical determinants of financial index performance).

(e) Other commodities and financial indices are correlated since the core risk factors are driven by

the business cycle.

This study represents an initial exploration and necessarily leaves many stones unturned. Firstly, we

have not explicitly tested any theoretical paradigm and thus we can only state that the results are

consistent with our inventory hypothesis. Secondly, we have narrowly focused on only a few financial

assets. The range of assets should be expanded to include credit-based products and international

stock indices. Thirdly, we have focused on the US business cycle. Since cycles are not always

synchronized it is important to examine the hypotheses in a global setting. Fourthly, we believe that a

key portfolio aspect of gold is that it has “option” based attributes-that is, it is a store of value in times

23

of crisis. To examine this hypothesis the data will have to be decomposed with respect to frequency.

We believe that the gold price would exhibit highly correlated behavior when extreme outliers, such as

a breakdown of governance, war, or disaster, occur. For example, over the period 1982-1983, the gold

price rose by about 67% at a time when the economy, equity markets and inflation were all in bad

shape. Our findings do not at all support any relationship between booms and busts and gold prices.

Over the period, 1999-2000, during the dotcom frenzy, gold rose by 24% between June and

December. This rise, in particular, can be attributed at least in part to the announcement of the Central

Bank Agreement on Gold in September of the same year, an event that had little direct relationship, if

any at all, with the economic cycle.

Our findings confirm that gold appears to be independent of cycles in contrast to other commodities,

making it worth considering as a good portfolio diversifier.

.

24

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Cross Jessica , Gold Derivatives: The Market View, World Gold Council,August 2000.

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Dickey, D and Wayne A Fuller, “Likelihood Ration Statistics for Autoregressive Time Series
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Economides, Nicholas and Robert A. Schwartz (1995), “Equity Trading Practices and Market
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Enders Walter, Rats Handbook for Economic Time Series,John Wiley and Son, 1996.

Engle, Robert F and Clive W.J. Granger,”Cointegration and Error Correction: Representation,
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Frye J(1997), Principals of Risk, Finding VAR through factor based interest rate scenarios in
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Granger C.W.J, Investigating Causal relations by econometric models and cross spectral
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Grossman, S.J. and M. Miller (1988), Liquidity and Market Structure, 43 (3).

Kydland F.E and Prescott E.C, Time to Build and Aggregate Fluctuations, Econometrica
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Lawrence Colin and A. Siow (1995a), Interest rates and Investment Spending: Some
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Lawrence Colin and Siow (1985b), Investment variable interest rates and gestation periods,
First Boston Series, Columbia Graduate School of Business.

Litterman R and Weiss L 1985, Money, real interest rates and output: A reinterpretation of
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Litterman R and Sheinkman J, (1988), Common Factors affecting Bonds Returns, Journal of
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Neuburger Anthony , Gold Derivatives:The Market Impact, World Gold Council Report, May
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Simms Christopher(1980), Macroeconomics and Reality,Econometrica,48,no.1, 1-48.

Smith Graham, “The Price of Gold and Stock market Indices for the USA”, unpublished paper,
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Smith Graham, “London Gold Prices and Stock Prices in Europe and Japan”, unpublished
paper, February 2002

25

Appendix A

Table A1: Summary statistics and unit root test statistics

Asset Obs Mean Median SD Low High Skewness Kurtosis UnitRoot
RGDP 107 3.16 3.12 3.24 -8.24 15.12 -0.23 2.75 -7.448
R3M 107 4.38 4.13 5.16 -6.53 19.95 0.39 0.21 -6.054
INFL 107 3.03 2.24 5.60 -16.23 19.08 -0.04 1.43 -5.282
NRM2 107 6.64 6.59 3.83 -1.33 22.12 0.62 1.77 -5.388
RSP 107 6.78 10.41 32.21 -107.65 79.38 -0.54 0.95 -10.534
RDJ 107 6.57 7.44 32.73 -118.72 77.74 -0.65 1.49 -10.461
RBOND 107 5.50 4.54 21.32 -65.26 70.72 0.12 1.18 -9.399
RGOLD 107 -1.36 -6.54 34.49 -98.67 131.25 0.70 2.14 -8.497
RCRB 107 -3.03 -1.30 19.95 -55.30 42.92 -0.14 0.09 -12.128
RALUM 107 -1.63 -8.56 45.59 -165.16 130.52 0.11 2.10 -9.595
RCOPPE 107 -2.71 -2.92 46.07 -110.68 181.91 0.67 2.22 -10.6353
R
RLEAD 107 -3.30 -6.79 56.89 -179.74 155.47 -0.09 1.23 -12.057
RZINC 107 -3.21 -6.75 44.71 -119.43 123.34 0.03 0.19 -10.22
RWTI 107 -0.98 -4.95 59.76 -294.70 262.85 -0.24 7.91 -10.402
RSILVER 107 -2.80 -6.72 53.91 -176.37 182.33 0.56 2.95 -8.778
CGDP 96 -0.16 3.08 -10.86 9.66 -0.60 0.05 -7.148

26

APPENDIX B: TABLE B1 - Correlation and significance tests
RGDP R3M INFL NRM2 RSP RDJ RBOND RGOLD RCRB RALUM RCOPPER RLEAD RZINC RWTI RSILVER
RGDP 1.00
0.00
R3M -0.12 1.00
0.20 0.00
INFL 0.05 -0.82 1.00
0.61 0.00 0.00
NRM2 0.03 0.10 0.03 1.00
0.76 0.30 0.76 0.00
RSP -0.01 0.27 -0.34 -0.01 1.00
0.90 0.01 0.00 0.91 0.00
RDJ -0.02 0.27 -0.37 -0.04 0.95 1.00
0.87 0.01 0.00 0.68 0.00 0.00
RBOND -0.33 0.42 -0.54 0.06 0.34 0.33 1.00
0.00 0.00 0.00 0.55 0.00 0.00 0.00
RGOLD -0.13 -0.17 0.11 0.03 -0.07 -0.09 0.01 1.00
0.18 0.08 0.25 0.78 0.45 0.38 0.94 0.00
RCRB 0.07 -0.22 0.08 -0.04 -0.04 -0.01 -0.14 0.20 1.00
0.45 0.03 0.42 0.67 0.71 0.90 0.14 0.04 0.00
RALUM 0.15 -0.17 0.04 0.11 -0.01 0.02 -0.15 0.23 0.29 1.00
0.11 0.09 0.68 0.27 0.94 0.81 0.12 0.02 0.00 0.00
RCOPPER 0.19 -0.09 0.06 -0.11 -0.12 -0.08 -0.14 0.21 0.30 0.39 1.00
0.05 0.36 0.54 0.28 0.22 0.42 0.14 0.03 0.00 0.00 0.00
RLEAD 0.20 -0.07 0.00 0.02 -0.18 -0.12 -0.21 0.20 0.29 0.24 0.42 1.00
0.04 0.46 0.96 0.85 0.07 0.23 0.03 0.04 0.00 0.01 0.00 0.00
RZINC 0.26 -0.03 0.06 -0.05 -0.03 -0.01 -0.26 0.10 0.35 0.27 0.48 0.43 1.00
0.01 0.79 0.57 0.63 0.78 0.95 0.01 0.31 0.00 0.01 0.00 0.00 0.00
RWTI 0.03 -0.48 0.49 -0.04 -0.29 -0.31 -0.32 0.14 0.07 0.11 0.10 0.03 0.03 1.00
0.74 0.00 0.00 0.71 0.00 0.00 0.00 0.14 0.49 0.27 0.31 0.80 0.76 0.00
RSILVER 0.04 -0.23 0.14 0.03 0.03 0.02 -0.24 0.63 0.27 0.31 0.23 0.26 0.16 0.10 1.00

27

APPENDIX C

Explanatory notes:
1. Dependent variable fields have a gray background with text in italics, for ease of reference
2. F-statistics that are significantly different from zero at the 5% level of significance are reported in
bold.

Table C1: VAR of Gold and Macroeconomic Variables

Equation 1

Dependent Independent Variables
Variable
RGOLD CGDP INFL RBOND R3M NRM2
F-statistic 0.7170 1.7990 0.2660 0.6545 0.4636 0.0768
Significance 0.4912868 0.1720182 0.7671034 0.5224257 0.6306431 0.9261651
Equation 2

CGDP RGOLD INFL RBOND R3M NRM2
F-statistic 8.0658 0.6269 1.9923 3.8306 3.5977 0.6572
Significance 0.000639 0.536805 0.143004 0.025729 0.031848 0.521049
Equation 3

INFL RGOLD CGDP RBOND R3M NRM2
F-statistic 8.7798 2.0125 0.9911 3.5369 2.5715 1.0671
Significance 0.000354 0.140276 0.375637 0.033678 0.082649 0.348803
Equation 4

RBOND RGOLD CGDP INFL R3M NRM2
F-statistic 1.0475 0.461 0.9297 1.4334 4.6656 2.2651
Significance 0.355514 0.632304 0.398831 0.244473 0.012085 0.110353
Equation 5

R3M RGOLD CGDP INFL RBOND NRM2
F-statistic 4.4194 2.3157 0.2909 2.362 2.8043 1.4488
Significance 0.015078 0.105197 0.748392 0.100695 0.066439 0.240875
Equation 6

NRM2 RGOLD CGDP INFL RBOND R3M
F-statistic 8.0948 1.0312 0.1402 6.0656 4.0401 3.8605
Significance 0.000624 0.361214 0.869436 0.00351 0.021257 0.025038

28

Table C2: VAR of RSP (S&P 500) and Macroeconomic Variables

Equation 1

Variable
RSP CGDP INFL RBOND R3M NRM2
F-statistic 0.7221 4.025 0.025 3.1694 0.0871 0.06
Significance 0.48883 0.02155 0.975322 0.04729 0.916638 0.941853
Equation 2

CGDP RSP INFL RBOND R3M NRM2
F-statistic 8.6367 4.1138 2.3518 3.4191 4.2816 0.5661
Significance 0.0004 0.01988 0.101664 0.03754 0.017076 0.569969
Equation 3

INFL RSP CGDP RBOND R3M NRM2
F-statistic 8.1313 2.0328 0.5204 3.3735 1.7751 0.6175
Significance 0.00061 0.137603 0.59626 0.03915 0.175991 0.541784
Equation 4

RBOND RSP CGDP INFL R3M NRM2
F-statistic 0.6158 2.2537 0.8334 1.1371 4.8076 2.235
Significance 0.542693 0.111557 0.438259 0.325812 0.010642 0.113551
Equation 5

R3M RSP CGDP INFL RBOND NRM2
F-statistic 5.4798 1.4357 0.106 2.0668 3.0876 0.8702
Significance 0.005861 0.243946 0.899539 0.133209 0.051021 0.422755
Equation 6

NRM2 RSP CGDP INFL RBOND R3M
F-statistic 8.9633 0.0299 0.1927 5.618 4.0847 3.2655
Significance 0.000304 0.970601 0.825134 0.00519 0.020413 0.043261

29

Table C3: VAR of Macroeconomic Variables: Bonds, Short-term interest rates, M2 growth, GDP

Equation 1

Variable
RBOND CGDP INFL R3M NRM2
F-statistic 0.9525 0.9305 1.2336 5.1441 2.5105
Significance 0.389952 0.398434 0.296519 0.00783 0.087382
Equation 2

CGDP RBOND INFL R3M NRM2
F-statistic 8.8971 4.0156 2.5796 4.2529 0.6473
Significance 0.000316 0.021644 0.081869 0.017443 0.526077
Equation 3

INFL RBOND CGDP R3M NRM2
F-statistic 7.8624 3.3044 0.7055 1.7538 0.9321
Significance 0.000747 0.04161 0.496781 0.17947 0.397801
Equation 4

R3M RBOND CGDP INFL NRM2
F-statistic 5.8013 2.5979 0.1423 2.2933 1.1061
Significance 0.004383 0.080477 0.867561 0.107298 0.335669
Equation 5

NRM2 RBOND CGDP INFL R3M
F-statistic 9.2348 4.2344 0.2004 5.7607 3.3421
Significance 0.000239 0.017738 0.818824 0.004542 0.040184

30

Table C4: VAR of Silver and Macroeconomic Variables

F-Tests, Dependent Variable RSILVER

Equation 1
Dependent
Independent Variables
Variable
RSILVER CGDP INFL RBOND R3M NRM2
F-statistic 0.6423 0.8306 0.9503 3.2028 2.2231 0.9866
Significance 0.528719 0.439447 0.390912 0.045845 0.114833 0.377263

31

Table C5: VAR of Copper and Macroeconomic Variables

Equation 1
Dependent
Variable
RCOPPER CGDP INFL RBOND R3M NRM2
F-statistic 0.1123 0.1774 1.5172 1.6062 1.1681 0.2465
Significance 0.893944 0.837738 0.225492 0.206971 0.316136 0.782154
Equation 2

CGDP RCOPPER INFL RBOND R3M NRM2
F-statistic 8.7046 0.0404 2.54 3.8887 4.1573 0.5872
Significance 0.000376 0.960419 0.08513 0.024401 0.019112 0.558212
Equation 3

INFL RCOPPER CGDP RBOND R3M NRM2
F-statistic 8.2827 2.9772 0.6496 3.8567 2.1926 1.0252
Significance 0.000534 0.056537 0.524969 0.025123 0.118205 0.363319
Equation 4

RBOND RCOPPER CGDP INFL R3M NRM2
F-statistic 0.9567 0.1256 0.9451 1.236 5.0116 2.5577
Significance 0.388459 0.882167 0.392901 0.295954 0.008871 0.083725
Equation 5

R3M RCOPPER CGDP INFL RBOND NRM2
F-statistic 5.9492 2.8157 0.1532 2.8758 3.0501 1.0547
Significance 0.003884 0.065736 0.85819 0.062148 0.052826 0.353034
Equation 6

NRM2 RCOPPER CGDP INFL RBOND R3M
F-statistic 8.9694 0.1537 0.2494 5.5341 3.96 3.3382
Significance 0.000303 0.857791 0.779868 0.005587 0.022865 0.040447

32

Table C6: VAR of RCRB and Macroeconomic Variables

Equation 1
Dependent
Variable
RCRB CGDP INFL RBOND R3M NRM2
F-statistic 1.0876 0.0238 1.218 0.2435 2.9631 0.8415
Significance 0.34188 0.976455 0.301175 0.784433 0.057284 0.4348
Equation 2

CGDP RCRB INFL RBOND R3M NRM2
F-statistic 6.8279 5.503 2.9264 4.5013 3.5704 0.372
Significance 0.001818 0.005743 0.059279 0.014006 0.032656 0.690535
Equation 3

INFL RCRB CGDP RBOND R3M NRM2
F-statistic 10.3485 7.1931 1.164 2.3308 3.7313 0.8237
Significance 9.95E-05 0.001332 0.317414 0.103702 0.028177 0.442426
Equation 4

RBOND RCRB CGDP INFL R3M NRM2
F-statistic 0.4678 3.8319 1.5633 0.8376 1.9035 1.667
Significance 0.628043 0.025698 0.215699 0.43644 0.155661 0.195221
Equation 5

R3M RCRB CGDP INFL RBOND NRM2
F-statistic 2.3578 3.5703 0.4108 1.3827 2.1137 1.1672
Significance 0.101097 0.032661 0.664497 0.256768 0.1274 0.316404
Equation 6

NRM2 RCRB CGDP INFL RBOND R3M
F-statistic 9.7034 0.8048 0.248 5.0261 4.1591 1.7099
Significance 0.000167 0.450742 0.78096 0.008758 0.019079 0.187353

33

Table C7: VAR of Zinc and Macroeconomic Variables

Equation 1
Dependent
Variable
RZINC CGDP INFL RBOND R3M NRM2
F-statistic 0.068 0.8011 0.1475 0.8946 0.2048 0.1237
Significance 0.934354 0.452376 0.863096 0.412783 0.815197 0.883801
Equation 2

CGDP RZINC INFL RBOND R3M NRM2
F-statistic 6.5498 0.6816 2.6544 4.3485 4.3846 0.666
Significance 0.002309 0.508688 0.076456 0.016074 0.015559 0.516547
Equation 3

INFL RZINC CGDP RBOND R3M NRM2
F-statistic 7.8194 2.3643 0.3655 2.6696 1.7067 1.0483
Significance 0.000785 0.100476 0.69501 0.075377 0.187927 0.355253
Equation 4

RBOND RZINC CGDP INFL R3M NRM2
F-statistic 0.4869 1.682 1.0576 1.0953 5.2925 2.7685
Significance 0.616327 0.192432 0.352021 0.339343 0.006914 0.068704
Equation 5

R3M RZINC CGDP INFL RBOND NRM2
F-statistic 6.0919 1.7906 0.1605 2.4773 2.0258 1.1985
Significance 0.003431 0.173405 0.851966 0.090313 0.138512 0.306928
Equation 6

NRM2 RZINC CGDP INFL RBOND R3M
F-statistic 8.9615 0.0821 0.2468 5.6007 4.1269 3.2488
Significance 0.000305 0.921249 0.781908 0.00527 0.019646 0.043934

34

Table C8: VAR of Lead and Macroeconomic Variables

Equation 1
Dependent
Variable
RLEAD CGDP INFL RBOND R3M NRM2
F-statistic 1.8806 0.2893 1.5228 2.422 2.8971 2.6011
Significance 0.159093 0.749594 0.224281 0.095147 0.06092 0.08038
Equation 2

CGDP RLEAD INFL RBOND R3M NRM2
F-statistic 8.7712 0.5254 2.8206 3.2181 4.5243 0.6938
Significance 0.000356 0.593318 0.065433 0.045201 0.013719 0.502629
Equation 3

INFL RLEAD CGDP RBOND R3M NRM2
F-statistic 9.7861 2.8634 0.4193 3.2204 2.3502 0.6466
Significance 0.000156 0.06287 0.658937 0.045105 0.101822 0.52651
Equation 4

RBOND RLEAD CGDP INFL R3M NRM2
F-statistic 0.5597 0.8722 0.7933 1.1948 4.6679 2.7976
Significance 0.573601 0.421936 0.455853 0.308029 0.01206 0.066854
Equation 5

R3M RLEAD CGDP INFL RBOND NRM2
F-statistic 5.7957 4.1963 0.0283 2.2286 2.339 0.9017
Significance 0.004442 0.018447 0.972066 0.114246 0.102907 0.409931
Equation 6

NRM2 RLEAD CGDP INFL RBOND R3M
F-statistic 9.0787 0.2075 0.1693 5.4466 3.8615 3.1259
Significance 0.000277 0.813012 0.84458 0.006035 0.025014 0.049235

35

Table C9: VAR of Oil (WTI) and Macroeconomic Variables

Equation 1
Dependent
Variable
RWTI CGDP INFL RBOND R3M NRM2
F-statistic 2.2388 0.6243 1.5597 2.7928 1.6443 1.5749
Significance 0.113146 0.538195 0.216446 0.067158 0.199535 0.213294
Equation 2

CGDP RWTI INFL RBOND R3M NRM2
F-statistic 8.6547 0.0158 0.1313 3.7916 4.1066 0.5899
Significance 0.000392 0.984354 0.877131 0.026663 0.02001 0.556747
Equation 3

INFL RWTI CGDP RBOND R3M NRM2
F-statistic 1.5954 2.265 0.6054 2.825 1.5935 1.5302
Significance 0.20913 0.110368 0.548329 0.065167 0.209527 0.22269
Equation 4

RBOND RWTI CGDP INFL R3M NRM2
F-statistic 0.862 1.0167 0.9889 1.2388 5.907 2.9762
Significance 0.426158 0.366356 0.376431 0.295148 0.00403 0.056589
Equation 5

R3M RWTI CGDP INFL RBOND NRM2
F-statistic 6.7635 3.0232 0.0967 2.3752 1.9629 1.8163
Significance 0.001921 0.054169 0.90792 0.099445 0.147077 0.169192
Equation 6

NRM2 RWTI CGDP INFL RBOND R3M
F-statistic 9.981 1.4075 0.2454 1.2263 3.5684 2.2512
Significance 0.000133 0.250668 0.782989 0.298765 0.032718 0.111826

36

Table C10: VAR of Aluminium and Macroeconomic Variables

Equation 1
Dependent
Variable
RALUM CGDP INFL RBOND R3M NRM2
F-statistic 1.073 0.5225 1.3487 2.6785 0.9713 0.0562
Significance 0.346801 0.594993 0.265332 0.074748 0.382946 0.945425
Equation 2

CGDP RALUM INFL RBOND R3M NRM2
F-statistic 0.4729 2.4202 7.5585 2.1002 1.2576 1.8529
Significance 0.624886 0.095306 0.000978 0.129044 0.289814 0.163364
Equation 3

RBOND RALUM CGDP INFL R3M NRM2
F-statistic 0.4786 1.6858 0.9209 0.9007 4.9907 3.407
Significance 0.621381 0.19174 0.40228 0.410332 0.009038 0.037959
Equation 4

R3M RALUM CGDP INFL RBOND NRM2
F-statistic 4.2799 2.0005 0.0927 1.6635 1.7978 1.8439
Significance 0.017103 0.141901 0.911578 0.195874 0.172211 0.164776
Equation 5

NRM2 RALUM CGDP INFL RBOND R3M
F-statistic 8.6231 0.6922 0.1689 5.7232 3.777 3.2854
Significance 0.000403 0.50339 0.844889 0.004733 0.027021 0.042473

37

Table C11: VAR of Gold and Financial Assets

Equation 1
Dependent
Variable
RGOLD RSP RBOND R3M
F-statistic 1.7195 1.5864 0.0526 0.3462
Significance 0.184625 0.209978 0.948787 0.708249
Equation 2

RSP RGOLD RBOND R3M
F-statistic 0.8582 0.3188 3.4461 0.2728
Significance 0.427166 0.727801 0.03586 0.761866
Equation 3

RBOND RGOLD RSP R3M
F-statistic 0.0516 0.8386 2.2785 4.3489
Significance 0.949743 0.435467 0.107956 0.01556
Equation 4

R3M RGOLD RSP RBOND
F-statistic 7.9262 0.8379 1.6763 0.7758
Significance 0.000652 0.435746 0.192494 0.463217

38

Table C12: VAR of CRB index (RCRB) and Financial Assets

Equation 1
Dependent
Variable
RCRB RSP RBOND R3M
F-statistic 1.6039 1.6 0.9769 1.7435
Significance 0.206455 0.207228 0.380194 0.180406
Equation 2

RSP RCRB RBOND R3M
F-statistic 0.7075 0.0531 3.2754 0.3808
Significance 0.495405 0.948284 0.04207 0.684375
Equation 3

RBOND RCRB RSP R3M
F-statistic 0.1501 2.4496 1.6813 3.7228
Significance 0.860804 0.09171 0.191558 0.02772
Equation 4

R3M RCRB RSP RBOND
F-statistic 6.4009 2.7524 1.7142 0.8239
Significance 0.002457 0.06881 0.18557 0.441803

39

Table C13: VAR of Silver and Financial Assets

Equation 1
Dependent
Variable
RSILVER RSP RBOND R3M
F-statistic 8.503 2.4358 2.8729 1.0758
Significance 0.000398 0.09292 0.06141 0.345106
Equation 2

RSP RSILVER RBOND R3M
F-statistic 0.7683 0.0201 2.4233 0.0358
Significance 0.466654 0.98013 0.09403 0.964837

Equation 3

RBOND RSILVER RSP R3M
F-statistic 0.3652 1.3796 2.6676 2.8699
Significance 0.694993 0.256623 0.074562 0.06158
Equation 4

R3M RSILVER RSP RBOND
F-statistic 12.5342 2.9744 1.5299 2.7462
Significance 1.5E-05 0.0558 0.221784 0.06922

40

Table C14: VAR of Copper and Financial Assets

Equation 1
Dependent
Variable
RCOPPER RSP RBOND R3M
F-statistic 0.0413 1.1587 1.6154 0.4338
Significance 0.959599 0.318242 0.204172 0.649302
Equation 2

RSP RCOPPER RBOND R3M
F-statistic 0.7811 0.0258 3.467 0.3487
Significance 0.460801 0.974537 0.03517 0.706497
Equation 3

RBOND RCOPPER RSP R3M
F-statistic 0.0173 0.0059 2.2616 5.5464
Significance 0.982844 0.994071 0.109704 0.00525

Equation 4

R3M RCOPPER RSP RBOND
F-statistic 8.9726 2.0307 1.8919 0.709
Significance 0.00027 0.136846 0.156369 0.494672

41

Table C15: VAR of Oil (RWTI) and Financial Assets

Equation 1
Dependent
Variable
RWTI RSP RBOND R3M
F-statistic 9.3254 2.5471 3.0703 1.5168
Significance 0.0002 0.083591 0.05099 0.224621
Equation 2

RSP RWTI RBOND R3M
F-statistic 0.7654 0.049 2.4205 0.0537
Significance 0.467982 0.952222 0.09429 0.947713
Equation 3

RBOND RWTI RSP R3M
F-statistic 0.2374 1.0435 2.6504 2.5472
Significance 0.789108 0.35618 0.07579 0.083581
Equation 4

R3M RWTI RSP RBOND
F-statistic 13.1289 3.5039 1.648 3.3286
Significance 9.1E-06 0.03398 0.197832 0.04003

42

Table C16: VAR of Zinc and Financial Assets

Equation 1
Dependent
Variable
RZINC RSP RBOND R3M
F-statistic 0.1154 0.435 1.1486 0.2036
Significance 0.891115 0.648518 0.321403 0.816143
Equation 2

RSP RZINC RBOND R3M
F-statistic 0.6772 0.4995 2.7085 0.2911
Significance 0.510471 0.608418 0.07173 0.748131
Equation 3

RBOND RZINC RSP R3M
F-statistic 0.1875 1.4599 2.1844 6.0927
Significance 0.829351 0.237359 0.118112 0.00323
Equation 4

R3M RZINC RSP RBOND
F-statistic 10.4638 0.8963 1.4534 0.3204
Significance 7.7E-05 0.411468 0.238878 0.726645

43

Table C17: VAR of Lead and Financial Assets

Equation 1
Dependent
Variable
RLEAD RSP RBOND R3M
F-statistic 2.1636 1.4628 4.6343 0.917
Significance 0.120479 0.236711 0.01199 0.40319
Equation 2

RSP RLEAD RBOND R3M
F-statistic 0.7011 2.5105 2.5249 0.3522
Significance 0.498583 0.08655 0.08537 0.70406
Equation 3

RBOND RLEAD RSP R3M
F-statistic 0.1361 0.654 2.4359 5.1348
Significance 0.87296 0.522238 0.092916 0.00761
Equation 4

R3M RLEAD RSP RBOND
F-statistic 10.4177 4.1224 1.5741 0.3951
Significance 8E-05 0.01916 0.2125 0.674686

44

Table C18: VAR of Aluminium and Financial Assets

Equation 1
Dependent
Variable
RALUM RSP RBOND R3M
F-statistic 1.8457 0.0331 2.1832 0.1513
Significance 0.163475 0.967487 0.11824 0.859809
Equation 2

RSP RALUM RBOND R3M
F-statistic 0.7734 0.3819 3.6463 0.3552
Significance 0.464279 0.68361 0.02976 0.701962
Equation 3

RBOND RALUM RSP R3M
F-statistic 0.1075 0.7236 2.3087 5.2826
Significance 0.898214 0.487652 0.104889 0.00666
Equation 4

R3M RALUM RSP RBOND
F-statistic 8.1248 1.9137 1.7143 0.7094
Significance 0.00055 0.153125 0.185561 0.494521

45

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