gold factor exposures in international asset pricing

Gold factor exposures in international assetpricing

Sinclair Davidson a,*, Robert Faff b,1, David Hillier c,2

a School of Economics and Finance, Royal Melbourne Institute of Technology, GPO Box 2476V, Melbourne,

Vic. 3001, Australiab Department of Accounting and Finance, PO Box 11 E, Monash University, Melbourne, Vic. 3800, Australia

c Department of Accounting and Finance, University of Strathclyde, 100 Cathedral Street,

GlasgowG4 0LN UK

Received 23 March 2002; accepted 17 July 2002

Abstract

The purpose of this paper is to examine the role of gold in modern international asset

pricing. We find that although the real premium on gold has been negative since the beginning

of the 1980s, many industries still have a significant exposure to the commodity. Moreover,

this exposure is stable and consistent over the 20 years of the study. Asset pricing tests reject

the null hypothesis that the market and gold factor exposure of the world’s industries are

jointly equal to 0, providing fresh evidence that gold still retains its importance in today’s

economy.

# 2002 Elsevier Science B.V. All rights reserved.

Keywords: Gold; International asset pricing; Multi-factor model; ICAPM

JEL classification: G12; G15

* Corresponding author. Tel.: �/61-3992-55869; fax: �/61-3992-55986.

E-mail addresses: [email protected] (S. Davidson), [email protected] (R.

Faff), [email protected] (D. Hillier).1 Tel.: �/61-3-9905-2387; fax: �/61-3-9905-2339.2 Tel.: �/44-141-548-3889; fax: �/44-141-552-3547.

Int. Fin. Markets, Inst. and Money 13 (2003) 271�/289

www.elsevier.com/locate/econbase

1042-4431/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved.

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1. Introduction

Over recent years, the importance of gold in the world economy has come under

increasing scrutiny. Whereas gold was historically perceived to be a hedging

mechanism against economic uncertainty, the current consensus is that gold has

lost much of its importance in the world’s financial markets. Indeed, several authors

(Salant and Henderson, 1978; Solt and Swanson, 1981) have suggested that the role

of gold has evolved over a period of time and is now viewed just like any other traded

commodity. This argument has, however, stuttered in the aftermath of the recent

Asian financial crisis as gold was once again returned to center stage amid strong

evidence that it was being used as a hedging device by investors.3

It is not improbable that gold is an important factor to corporate forms. Indeed,

there has been continuing interest in the role and impact that gold has had on

financial markets, investors and the modern day firm. To this end, we can identify a

range of related issues that have been the focus of past research. First, Tschoegl

(1980), Solt and Swanson (1981) and Aggarwal and Soenen (1988) have explored the

nature and efficiency of the gold market in the US. While these studies uncover

minor elements of returns dependence and non-normality, they generally conclude in

favor of market efficiency due to a belief that none of the distributional vagaries are

material enough to present exploitable opportunities. Using data from 1975 to 1977,

Tschoegl (1980) tests for weak-form efficiency and finds some short-term depen-

dence in gold price changes. Solt and Swanson (1981) investigate a sample of gold

and silver prices covering the period 1971�/1979. The return distributions do exhibit

some nonstationarity and non-normality in means and standard deviations, but

again this does not seem large enough for investors to exploit. Aggarwal and Soenen

(1988) examine a longer period from 1973 to 1982 and find in favor of gold price

efficiency. Similarly, Muradoglu et al. (1998) examine market efficiency on the

Istanbul gold exchange.

Second, McDonald and Solnik (1977), Blose and Shieh (1995) and Selvanathan

and Selvanathan (1999) examined the impact of gold prices on the value of gold

mining firms. For example, Blose and Shieh (1995) develop a model that estimates

the theoretical gold elasticity of a gold mining stock and predict that for companies

whose assets comprise primarily of operating gold mines, the elasticity should exceed

one. A test of their model using a sample of 23 gold mining stocks over the period

1981�/1990, supports their model.

3 In a cover story run by Fortune (1998), it was suggested that the financial crisis turned Asians to gold

sellers. For example, while the Indonesian ‘. . . rupiah lost 80% of its value against the US dollar. . .gold

declined only about 15% (and so gold jewelry shot up by 50% in rupiah)’. As the article so aptly summed

up: ‘. . . for Asians, at least, gold fulfilled its traditional role as asset of last resort, helping to protect its

holders from the disintegration of the currencies’.

S. Davidson et al. / Int. Fin. Markets, Inst. and Money 13 (2003) 271�/289272

Third, Booth et al. (1982) and Frank and Stengos (1989) both carried

out an econometric analysis of the distributional properties of gold prices.

Booth et al. found that over the period 1969�/1980, gold price returns

reveal persistent dependence over the long term and that cycles of unequal duration

occur. Frank and Stengos (1989) look at gold and silver prices over the period

from mid-1970 to mid-1980. They find that while standard linear tests do

not reveal anything untoward, more sophisticated tests suggest a degree ofnon-linear dependence exists. Related to this, Chan and Mountain (1988) explored

the pricing relationship between gold and other precious metals. Specifically,

using data from 1980 to 1983, they employed time series models to test causality

between gold and silver prices and found a ‘feedback causal’ relationship between

the two.

Fourth, Chua et al. (1990) and Jaffe (1989) analyzed the benefits of diversifying

investment portfolios with gold stocks. In the case of Jaffe (1989), (over the period

1971�/1987) it was generally found that gold presented diversification benefits.Johnson and Soenen (1997) extended this work by investigating the role of gold in

investment portfolios from a global perspective. They generally found that over the

period since 1984, the performance of gold as an investment has been dominated by

stocks and bonds.

Fifth, some studies have examined the link between the gold price and the macro

economy. Salant and Henderson (1978) analyzed the gold price as a manifestation of

the market’s anticipation of government policies in the US. Sjaastad and

Scacciavillani (1996) examined the relationship between the gold price and theexchange rate using data from 1982 to 1990. The major finding from this study is

that ‘. . .since the dissolution of the Bretton Woods International monetary system,

floating exchange rates among the major currencies have been a major source of

price instability in the world gold market . . .’ (p. 879). Taylor (1998) employs data

from 1914 to 1937 and 1968 to 1996, to explore the relationship between precious

metal prices and inflation (gold, silver and palladium). He finds that the precious

metals were successful short and long-term hedges for inflation pre-1939 and around

the OPEC oil shock of 1979. More recently, and using a set of intraday data,Christie-David et al. (2000) find that gold (and to some extent silver) futures prices

respond strongly to the release of capacity utilization; CPI; unemployment rate;

GDP and PPI news releases.

Finally, Tufano (1996) examined the risk management practices followed in the

North American gold mining industry, using data for 48 firms from 1990 to 1993.

Generally, he found little evidence in favour of wealth maximization, but rather that

managerial risk aversion was a more important factor underlying gold industry risk

management practices.It is surprising that as yet no study has examined the role of gold in an

international asset pricing context. Indeed, with its long distinguished and prominent

role in the financial markets, gold is an ideal candidate to be a factor in international

extensions to asset pricing models such as Merton (1973) intertemporal capital asset

pricing model (ICAPM). Indeed, Rubio (1989) included the return on gold as a

potential hedging variable, in his tests of the applicability of an ICAPM in the

S. Davidson et al. / Int. Fin. Markets, Inst. and Money 13 (2003) 271�/289 273

Spanish market.4 The ICAPM assumes that investors can construct portfolios to

hedge against uncertainties in state variables. Since the ICAPM fails to identify the

associated state variables, the choice of factors is essentially an empirical concern.

Although several other variables (such as interest rate and foreign exchange rate

uncertainty) have been put forward as potential ICAPM factors, it is perhaps

surprising that gold has not been included in any analysis.

While it has been shown that firms in the gold mining industry are affected by

movements in the gold price (Blose and Shieh, 1995; Tufano, 1998), it is less certain

whether companies in other industries will be affected to the same or lesser extent.

Tufano (1998) developed a theoretical model in which he posited several

determinants of gold factor exposures in gold mining firms. Specifically, he examined

a sample of 48 North American (US and Canadian) gold mining firms and suggested

that the factors which determine the exposure to gold price movements are related to

‘market conditions’ (gold price; volatility of gold prices; and interest rates);

‘exogenous firm factors’ (quantity of production; reserves; and variable and fixed

costs); financial policy (financial leverage); and risk management policy (percentage

of output hedged and hedge price). Although firms operating in businesses outside of

the mining industry should be less strongly linked with the gold price, it could also be

argued that they would be indirectly affected by movements in gold prices. The

mining sector is a major force in many world economies and as such, changes in the

gold price would have a subsidiary effect on other industries. This would especially

be applicable to those involved in the use, supply and production of gold and other

commodity metals or those industries whose customers or suppliers are affected by

gold. Some industries may have negative exposures to the gold price. For example, if

gold is used as a hedging device by investors, then decreases in the value of gold may

be associated with increases in the value of competing products such as tobacco,

tourism and airlines as these become more in demand.

This paper studies the exposure of world industry equity portfolios to fluctuations

in gold prices. Given the importance of the gold industry in many economies as well

as the long history of gold in the world’s financial markets, we argue that gold

should be included as an additional factor in international asset pricing models. We

first measure the magnitude and direction of the gold factor exposures of global

industry equity portfolios. The analysis is extended to investigate whether the

importance of the gold factor diminished in the early 1990s. Finally, we generate an

empirical specification that allows us to test whether the market and gold factor

exposures are jointly significant and different from 0.

We find that 22 of the 24 world industries examined had significant exposures to

the gold factor. As expected, industries with a positive exposure had strong links to

the gold industry whereas those with a negative exposure were in industries

commonly perceived to be substitutes for retail investors’ hedging activity. Using

4 Merton proposed that interest rates represent one such state variable and Rubio (1989), Shanken

(1990), Song (1994), Elyasiani and Mansur (1998), Scruggs (1998) and others have investigated this

possibility in tests of the ICAPM.


the traditional static methodology developed in earlier asset pricing studies5 we find

evidence that gold lost none of its importance in recent years. Finally, we use

generalized method of moments (GMM) estimation to determine the joint exposures

of the market and gold factor and find that both are jointly significant from 0 for our

combined sample. Thus we can firmly conclude that gold has had an important role

in international asset pricing models in the 1990s even though the real premium on

gold was negative during this time.The remainder of the paper is as follows. Section 2 outlines the data used in the

study. Hypotheses and results are presented in Section 3 and Section 4 concludes the

paper.

2. Description of data

The data employed are continuously compounded monthly returns on 34 global

industry indices, sourced from the Morgan Stanley database and from Datastream.

The proxy for the market portfolio is the value-weighted world index supplied by

Morgan Stanley, while the gold price data is the London price obtained from the

DRI database. The data covers 240 months from January 1975 to December 1994.All data are measured in US dollar terms.

3. Hypotheses tested and results

3.1. Extra-market gold price exposure of global industry portfolios

The initial focus of this study is to estimate the extra-market sensitivity (gi) of

global industry portfolio equity returns to gold price returns (Rgoldt). Thesesensitivities are estimated in the two-factor model given below:6

Rit�ai�biRwt�giRgoldt�eit (1)

where Rit is the return on the global industry portfolio i in month t , Rwt is the return

on the world market index in month t and all returns are expressed in US dollars.In this setting, the predicted signs of gamma are expected to be industry

dependent. Further, there is the collective prediction coming from Merton’s (1973)

ICAPM, namely, for a negative correlation between beta and gamma. That is,

gamma will tend to be negative (positive) when beta is high (low).7 Hence, industries

that have a high beta risk should also tend to have a negative exposure to gold

5 See for example He and Ng (1998) and Allayannis and Ofek (2001) for foreign exchange exposures;

Elyasiani and Mansur (1998) for interest rate exposures; French, Ruback and Schwert (1983) for inflation

exposures; Blose and Shieh (1995), and Tufano (1998) for gold price exposures.6 This equation has been employed in similar domestic research settings, such as McDonald and Solnik

(1977) and Tufano (1998).7 See Merton (1973, p.884).


returns whereas low beta risk industries will tend to have high exposures. One

obvious qualification needs to be made here, namely, the prediction on the global

gold industry portfolio itself. Given the strong direct positive gold price effect on this

portfolio, it is expected that this will dominate the Merton negative correlation

effect.

Table 1 presents results from estimating the two-factor model outlined in Eq. (1)

for the 34 MSCI industry portfolios over the full sample period from February 1975to December 1994. The results indicate that 16 industries (47%) have a statistically

significant exposure to the gold price factor, at the 5% level of significance. Of this

group of industries, 9 have positive exposures (namely Gold Mines; Metals and Non-

Ferrous; Miscellaneous Materials and Commodities; Real Estate; Wholesale and

International Trade; Energy; Finance; Materials; and Services). The remaining 7

global industry portfolios having significantly negative extra-market gold price

sensitivity are Automobiles; Beverages and Tobacco; Food and Household Products;

Health and Personal Care; Leisure and Tourism; Merchandise; and Transport(Airlines).

3.2. Tests for stability of gold factor exposures

Given the length of the full sample period, a further issue to be considered is howstable the gold factor estimates are over time. Apart from having a general concern

about the stability of the sensitivity coefficients, we wish to investigate the argument

that during the late 1980s and into the 1990s gold lost its prominence as a potential

hedging factor. Accordingly, three non-overlapping subperiods, together with the

entire time period, was used for analysis of the global industry portfolios.

Specifically, the subperiods chosen are: (1) January 1975�/December 1980; (2)

January 1981�/December 1987; and (3) January 1988�/December 1994.

To accommodate the subperiod analysis the main model of Eq. (1) is re-specifiedutilizing appropriately defined dummy variables as follows:

Rit�X3

j�1

ajiDj�X3

j�1

bji[DjRwt]�X3

j�1

gji[DjRgoldt]�eit (2)

where all variables are defined as earlier and the j subscript pertains to the respective

subperiod.

For a given global industry portfolio, the equality of the subperiod gold price

exposures can be tested in the following hypotheses:

H01:gi1�gi2�gi3

H02:gi1�gi2

H03:gi2�gi3 (2a)

From Table 2, in the case of the first subperiod (1975/80) it can be seen that 11

global industry portfolios display significant extra-market gold price sensitivity.


Table 1

Estimation of a gold price factor augmented market model for MSCI global industry portfolios: 1975: 2�/1994:12

Industry aia bI gi fi

b R2 DW

Automobiles �/0.0012 (�/0.52) 0.9555** (16.69) �/0.1023** (�/2.45) �/ 0.542 1.856

Banking �/0.0025 (�/1.18) 1.0604** (20.43) 0.0390 (1.03) �/ 0.645 1.785

Beverages and tobacco 0.0016 (0.76) 0.8670** (22.85) �/0.0802** (�/2.78) 0.2308** (3.58) 0.686 1.979

Building materials components �/0.0050** (�/3.01) 1.1196** (28.09) 0.0372 (1.28) �/ 0.774 1.945

Chemicals �/0.0046** (�/3.48) 1.0704** (33.41) 0.0001 (0.00) �/ 0.827 1.822

Electronic components �/0.0018 (�/0.55) 1.1130** (14.57) �/0.0667 (�/1.20) �/ 0.474 1.876

Energy sources �/0.0019 (�/0.75) 0.8752** (14.84) 0.0620 (1.44) �/ 0.493 1.809

Financial services �/0.0064** (�/2.20) 1.5174** (21.70) �/0.0502 (�/0.99) �/ 0.667 1.903

Food and household products 0.0007 (0.41) 0.8297** (25.03) �/0.0619** (�/2.50) 0.1798** (2.78) 0.724 1.972

Forest Products/Paper �/0.0067** (�/2.90) 1.1124** (20.15) 0.0130 (0.32) �/ 0.636 1.979

Gold mines �/0.0085 (�/1.26) 0.7834** (4.84) 0.7979** (6.77) �/ 0.247 2.327

Health and personal care �/0.0004 (�/0.20) 0.9234** (21.79) �/0.1067** (�/3.46) �/ 0.669 1.853

Industrial components �/0.0026* (�/1.72) 1.0474** (29.39) �/0.0342 (�/1.32) �/ 0.786 1.755

Insurance �/0.0012 (�/0.78) 0.9667** (25.28) �/0.0340 (�/1.22) �/ 0.731 1.664

Leisure and tourism 0.0000 (0.04) 1.0701** (19.11) �/0.1837** (�/4.50) �/ 0.611 1.639

Machinery and engineering �/0.0054** (�/3.18) 1.1514** (28.03) �/0.0171 (�/0.57) �/ 0.770 1.757

Merchandise �/0.0021 (�/1.20) 0.9300** (21.70) �/0.0951** (�/3.05) �/ 0.666 1.750

Metals and non-ferrous �/0.0080** (�/2.44) 1.1439** (14.39) 0.2874** (4.96) �/ 0.515 2.104

Metals and steel �/0.0078** (�/2.10) 1.2068** (13.54) 0.0712 (1.10) �/ 0.446 1.641

Miscellaneous materials and commodities �/0.0042** (�/2.38) 1.1451** (27.28) 0.0626** (2.05) �/ 0.765 2.328

1.0638** (25.49) �/0.0445 (�/1.46) �/ 0.734 2.033Multi industry �/0.0032 (�/1.84)*

Real estate �/0.0047 (�/1.41) 1.1825** (14.70) 0.1530** (2.61) �/ 0.498 1.954

Textiles and apparel �/0.0049** (�/2.33) 1.1394** (22.70) �/0.0487 (�/1.33) �/ 0.686 1.871

Transport airlines �/0.0012 (�/0.36) 0.9590** (11.97) �/0.1143** (�/1.96) �/ 0.378 1.992

Transport, road and rail 0.0036 (1.45) 1.1650** (19.75) 0.0350 (0.81) �/ 0.628 1.939

Transport shipping �/0.0069** (�/2.16) 1.0211** (13.38) �/0.0534 (�/0.96) �/ 0.432 1.871

Utilities electricity and gas �/0.0017 (�/0.87) 0.7242** (15.39) 0.0061 (0.18) �/ 0.505 1.855

Wholesale and international trade �/0.0056 (�/1.52) 1.3154** (14.77) 0.1444** (2.22) �/ 0.497 2.103

Capital equipment �/0.0068** (�/2.25) 1.0030** (12.00) 0.1101* (1.90) �/0.1690** (�/2.60) 0.392 1.938

Consumer goods �/0.0014 (�/0.73) 0.8417** (14.99) �/0.0138 (�/0.36) �/0.2701** (�/4.21) 0.483 2.022

Energy �/0.0062** (�/2.08) 0.8418** (10.32) 0.2206** (3.89) �/0.1578** (�/2.43) 0.356 2.030

S.

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Table 1 (Continued )

Industry aia bI gi fi

b R2 DW

Finance �/0.0048* (�/1.79) 1.0549** (13.41) 0.1173** (2.21) �/0.2257** (�/3.46) 0.442 1.982

Materials �/0.0082** (�/2.74) 1.1022** (12.92) 0.1422** (2.43) �/0.2060** (�/3.19) 0.434 1.994

Services �/0.0041 (�/1.01) 0.9025** (9.16) 0.2671** (3.72) �/ 0.311 2.199

Number of significant coefficients 5% (10%) level 13 (17) 34 (34) 16 (17) 7 (7) �/ �/

This table reports the outcome of estimating regression in the following equation:

Rit�ai�biRmt�giRgoldt�eit

where Rit is the return on the global industry portfolio i in month t , Rwt is the return on the world market index in month t , Rgoldt is the return on holding gold

bullion in month t and all returns are expressed in US dollars.Notes: ** (*) Coefficient estimate is significantly different from 0 at the 5% (10%) level.a Below each coefficient estimate is the associated t statistic in parentheses.b This coefficient is an estimate of the first-order autoregressive coefficient produced by the Cochrane and Orcutt (1949) procedure for those instances in

which significant autocorrelation is detected according to the Durbin-Watson test in the original, unadjusted regression.

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Only three of these industries (Beverages and Tobacco; Health and Personal Care;

and Leisure and Tourism) show a negative coefficient, in contrast to the seven

reported for the full sample period in the previous Table 1. Interestingly, the middle

period of our sample shows a drop to 5 industries for which a significant (5% level)

gold factor exposure is found. These industries are: Gold Mines; Metals (Non-

Ferrous) and Miscellaneous Materials and Commodities (all positive); and Leisure

and Tourism; and Merchandise (both negative). In the final period of our analysis(1988/94), there are 7 industries with significant gold price factors. Of these, 4

different industries are now involved, namely, Automobiles (negative); Banking

(negative); Metals and Steel (positive); and Multi Industry (negative).

To test whether the different subperiod gold price exposures reveal any evidence of

instability we carry out a Wald test for each hypothesis in Eq. (2a). The results

(provided in the final three columns of Table 2) provide little evidence. From the

table it can be seen that for each pairwise test, the null hypothesis of stability can

only be rejected in one or two cases.One further issue is introduced with this choice of data and subperiods, namely,

the potential effect of the stock market crash of October 1987 on the full sample

period results and the results of the middle subperiod. Some sensitivity analysis was

conducted to assess how robust the findings are to this extreme market occurrence.

Consistent with previous findings (see e.g., Roll (1988)), the estimates of beta risk

relative to the market were affected considerably, in some instances. However,

estimation of the gold price sensitivities were qualitatively unaffected and,

importantly, the conclusions drawn based upon them are robust to the treatmentof the crash. Given that the main focus of this paper are the gold factor exposures,

these latter results are not reported to conserve space.8

A final research design issue worthy of mention is that of multicollinearity. This

will be particularly acute if the correlation between the market and gold factor is

high. Accordingly, we calculated the correlation between the market return series

and gold price return series over our full sample period as well as the individual

subperiods identified above. In short, the correlations were low suggesting that

multicollinearity is not a problem.9

3.3. Test of Merton’s (1973) negative correlation prediction

Merton (1973) predicts that in the ICAPM, there will be a negative correlation

between the market and gold factor exposure. Cross-correlations for the results of

the previous analysis are presented in Table 3. First, with regard to the 34 industry

8 The sensitivity results are available from the authors upon request. We also conducted some

sensitivity analysis regarding the re-definition of the gold return in terms of an unanticipated return. Since

these findings are qualitatively similar they are not reported in this paper.9 The correlations were: (a) 0.110 in the overall sample period of 1975�/1994; (b) 0.223 in the subperiod

1975�/1980; (c) 0.099 in the subperiod 1981�/1987; and (d)�/0.032 in the subperiod 1988�/1994.


Table 2

Estimation of a gold price factor augmented market model across MSCI global industry portfolios over three subperiods

Industry bia gi

a Wald testsb

1975/

1980

1981/

1987

1988/1994 1975/

1980

1981/

1987

1988/

1994

Test H01:

gi 1�/gi 2�/gi 3

Test

H02:gi 1�/gi 2

Test

H03:gi 2�/gi 3

Automobiles 0.8266** 1.0060** 0.9567** �/0.0544 �/0.0987 �/0.2619** 2.33 0.221 1.284

(6.70) (11.19) (10.03) (�/0.94) (�/1.32) (�/2.13) (0.312) (0.639) (0.257)

Banking 0.7941** 1.0261** 1.2573** 0.043 0.0458 0.2285** 2.555 0.001 2.087

(7.33) (13.00) (15.01) (0.85) (0.7) (2.11) (0.279) (0.973) (0.149)

Beverages and tobacco 0.9147** 0.8917** 0.8088** �/0.0807** �/0.0503 �/0.1429* 0.951 0.222 0.942

(11.12) (14.66) (13.22) (�/2.01) (�/1.00) (�/1.74) (0.622) (0.637) (0.332)

Building materials components 0.9374** 1.1679** 1.1568** 0.0897** 0.0552 �/0.1536* 6.850** 0.286 4.492**

(11.11) (18.99) (17.72) (2.26) (1.08) (�/1.82) (0.033) (0.593) (0.034)

Chemicals 1.0494** 1.1102** 1.0351** 0.0047 0.0154 0.0034 0.046 0.041 0.022

(15.26) (22.15) (19.46) (0.15) (0.37) (0.05) (0.977) (0.84) (0.882)

Electronic components 1.3781** 1.1991** 0.8584** �/0.1116 �/0.0009 �/0.2278 1.62 0.79 1.428

(8.47) (10.11) (6.82) (�/1.46) (�/0.01) (�/1.40) (0.445) (0.374) (0.232

Energy sources 1.0123** 1.0283** 0.6446** 0.042 0.0134 0.0744 0.198 0.091 0.178

(8.18) (11.4) (6.73) (0.72) (0.18) (0.60) (0.906) (0.763) (0.673)

Financial services 1.1399** 1.5605** 1.6920** �/0.0746 0.0103 0.137 1.876 0.567 0.543

(7.74) (14.53) (14.85) (�/1.08) (0.12) (0.93) (0.391) (0.452) (0.461)

Food and household products 0.8509** 0.7989** 0.8329** �/0.0399 �/0.0709* �/0.0928 0.606 0.312 0.07

(11.85) (15.20) (15.59) (�/1.16) (�/1.64) (�/1.32) (0.739) (0.577) (0.791)

Forest products/paper 1.3004** 1.2605** 0.8376** 0.0075 �/0.009 0.0132 0.044 0.034 0.027

(11.22) (14.92) (9.34) (0.14) (�/0.13) (0.11) (0.978) (0.853) (0.870)

Gold mines 0.9088** 1.0421** 0.3406 0.8219** 0.8513** 1.3816** 2.377 0.014 1.873

(2.58) (4.38) (1.29) 5.41 4.08 4.01 (0.305 (0.907) (0.171)

Health and personal care 1.1138** 0.9551** 0.7791** �/0.1382** �/0.081 �/0.0613 1.033 0.696 0.035

(12.43) (14.63) (11.24) (�/3.29) (�/1.50) (�/0.69) (0.597) (0.404) (0.851)

Industrial components 0.9999** 1.0435** 1.0703** �/0.0228 0.0084 �/0.0623 0.659 0.27 0.613

(12.82) (18.35) (18.4) (�/0.61) 0.18 (�/0.81) (0.719) (0.603) (0.434)

Insurance 0.9928** 0.9555** 0.9486** �/0.0181 �/0.0267 �/0.0858 0.563 0.018 0.378

(11.99) (15.7) (15.41) (�/0.45) (�/0.53) (�/1.05) (0.755) (0.894) (0.539)

Leisure and tourism 1.2545** 0.9657** 0.9622** �/0.1891** �/0.1561** �/0.3092** 1.278 0.125 1.267

(10.48) (11.09) (10.92) (�/3.33) (�/2.14) (�/2.64) (0.528) (0.724) (0.26)

Machinery and engineering 0.9049** 1.1055** 1.3922** �/0.0053 0.0357 �/0.0439 0.773 0.398 0.667

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Industry bia gi

a Wald testsb

1975/

1980

1981/

1987

1988/1994 1975/

1980

1981/

1987

1988/

1994

Test H01:

gi 1�/gi 2�/gi 3

Test

H02:gi 1�/gi 2

Test

H03:gi 2�/gi 3

(10.65) (17.6) (22.03) (�/0.13) 0.7 (�/0.53) (0.679) (0.528) (0.414)

Merchandise 0.9519** 0.9796** 0.8568** �/0.0586 �/0.1112** �/0.1479 1.079 0.575 0.114

(10.4) (14.68) (12.1) (�/1.36) (�/2.02) (�/1.62) (0.583) (0.448) (0.736)

Metals nonferrous 1.3208** 1.3732** 0.7972** 0.2829** 0.2913** 0.1493 0.594 0.004 0.529

(7.9) (11.27) (6.17) (3.6) (2.88) (0.89) (0.743) (0.948) (0.467)

Metals and steel 0.9371** 0.9930** 1.6717** 0.0722 0.0955 0.4373** 3.402 0.027 2.5960

(5.15) (7.32) (12.3) (0.81) (0.86) (2.42) (0.183) (0.87) (107)

Miscellaneous materials and commodities 1.0299** 1.1514** 1.2208** 0.0504 0.1172** �/0.0142 1.925 1.032 1.639

(11.16) (18.37) (17.66) (1.27) (2.23) (�/0.16) (0.382) (0.31) (0.2)

Multi industry 1.3270** 1.1374** 0.8260** �/0.0637 �/0.0237 �/0.2040** 3.315 0.379 3.296*

(15.6) 18.34) (12.55) 1.60) (�/0.46 (�/2.40) (0.191) (0.538) (0.069)

Real estate 1.1581** 1.1311** 1.2675** 0.2174** �/0.0007 0.2344 3.003 2.714* 1.355

(6.7) (8.97) (9.47) (2.68) (�/0.01) (1.36) (0.223) (0.099) (0.244)

Textiles and apparel 0.9985** 1.0934** 1.2789** �/0.0733 �/0.0161 0.0244 0.926 0.484 0.104

(9.29) (13.96) (15.39 (�/1.45) (�/0.25) (0.23) (0.629) (0.486) (0.747)

Transport airlines 0.9377** 0.6620** 1.2854** �/0.047 �/0.1806* �/0.1561 1.175 1.068 0.015

(5.55) (5.38) (9.84) (�/0.59) (�/1.77) (�/0.93) (0.556) (0.301) (0.901)

Transport road and rail 1.0090** 1.0810** 1.3659** 0.0276 0.0016 0.2104* 2.147 0.073 2.0310

(8.04) (11.82) (14.07) (0.47) (0.02) (1.68) (0.342) (0.787) (0.154)

Transport shipping 0.7449** 0.7940** 1.4702** �/0.0286 �/0.0255 0.0065 0.041 0.001 0.03

(4.72) (6.9) (12.04) (�/0.39) (�/0.27) (0.04) (0.98) (0.979) (0.862)

Utilities, electricity and gas 0.6767** 0.5309** 0.9715** �/0.0244 0.0642 0.1001 2.166 1.401 0.099

(6.92) (7.45) (12.84) (�/0.53) (1.09) (1.02) (0.339) (0.237) (0.753)

Wholesale and international trade 0.7401** 1.2932** 1.7194** 0.1352 0.1593 0.4846** 3.01 0.029 2.268

(4) (9.59) (12.02) (1.56) (1.42) (2.62) (0.222) (0.865) (0.132)

Capital equipment 1.7214** 0.8947** 0.6972** 0.1139 0.1128 �/0.113 1.595 0 1.321

(9.62) (7.38) (4.99) (1.48) (1.12) (�/0.67) (0.451) (0.994) (0.250)

Consumer goods 1.1870** 0.8218** 0.6540** 0.011 �/0.0329 �/0.0918 0.812 0.277 0.208

(9.98) (10.34) (7) (0.22) (�/0.49) (�/0.82) (0.666) (0.599) (0.648)

Energy 1.8022** 0.7249** 0.4475** 0.2719** 0.0269 0.1712 4.442 4.437** (0.035)

(11.04) (6.51) (3.58) (3.87) (0.29) (1.11) (0.109) 0.644 (0.422)

Finance 1.4278** 0.9771** 0.9098** 0.1637** 0.0404 0.1153 1.074 1.074 0.165

(8.44) (8.58) (6.73) (2.3) (0.43) (�/0.73) (0.585) (0.3) (0.685)

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Industry bia gi

a Wald testsb

1975/

1980

1981/

1987

1988/1994 1975/

1980

1981/

1987

1988/

1994

Test H01:

gi 1�/gi 2�/gi 3

Test

H02:gi 1�/gi 2

Test

H03:gi 2�/gi 3

Materials 1.7710** 1.0424** 0.7681** 0.1536** 0.1302 �/0.0331 0.985 0.033 0.667

(9.71) (8.44) (5.37) (1.97) (1.26) (�/0.19) (0.611) (0.857) (0.414)

Services 1.6181** 0.7431** 0.6154** 0.4193** 0.0626 �/0.0357 7.668** 5.411** 0.176

(8.08) (5.09) (3.97) (4.46) (0.52) (�/0.18) (0.022) (0.02) (0.674)

Number of significant test statistics at 5 % (10 %) level 34 34 33 11 5 7 2 2 1

(34) (34) (33) (11) (7) (10) (2) (3) (2)

This table reports the outcome of estimating regression in the following equation:

Rit�X3

j�1

ajiDj�X3

j�1

bji[DjRwt]�X3

j�1

gji[DjRgoldt]�eit

where Rit is the return on the global industry portfolio i in mouth t , Rwt is the return on the world market index in month t , Rgoldt is the return on holding gold

bullion in month t and all returns are expressed in US dollars. D1, D2 and D3 are dummy variables representing subperiods 1975 to 1980; 1981 to 1987 and 1988

to 1994, respectively.** (*), Statistic is significantly different from 0 at the 5% (10%) level.a This is the subperiod estimate of gamma, with the associated t statistic in parentheses.b The Wald test statistics have a x2 distribution; H01 has 2 degrees of freedom, while H02 and H03 have 1 degrees of freedom. The P -value is given in

parentheses.

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portfolios over the full sample period (reported in Table 1) we find a cross-

correlation between beta and gamma of �/0.1464 which is consistent with the

Merton hypothesis. However, for the case of the subperiod analysis (reported in

Table 2), we find the following cross-correlations: (a) 0.2463 (1975/80); (b) 0.2138

(1981/87); (c) 0.0050 (1988/94); and (d) 0.1147 (1975/94-pooled subperiods). Giventhat none of these correlations are negative, the subperiod evidence is less

convincing. In summary, the evidence of a negative correlation between beta and

gamma, as predicted by Merton (1973) is weak. Consequently, this aspect of

Merton’s ICAPM using a gold price (hedging) factor in an international setting is

open to question.

3.4. Asset pricing tests of joint significance of market and gold factor exposures

In this section, GMM estimation is used to test for the joint significance of

the market and gold factor exposures. An important motivation for conducting

this type of analysis is the concern identified by Kan and Zhang (1999) about‘useless’ factors.

Specifically, they argue that if the hypothesis of joint equality to 0 cannot

be rejected then this should signal a serious concern regarding whether the

factor under scrutiny is indeed ‘useless’. In conducting asset-pricing tests of the

two factor international pricing model, we assume that the factor generating

process is adequately described by a market and gold price factor specification as

follows:

Rit�E(Ri)�bi[Rwt�E(Rw)]�di[Rgoldt�E(Rgold)]�eit (3)

where Rit is the return on the i th asset or portfolio in month t , Rwt is the return on

Table 3

Cross-correlations between beta and gamma

Subperiod

1975/1994 1975/1980 1981/1987 1988/1994 Pooled subperiods

MSCI industry portfolios Global �/0.1464* 0.2463* 0.2138 0.0050 0.1147

This table reports cross-sectional correlation between global industry beta and gamma estimates, where

the betas and gammas are obtained from a regression of the following general form:

Rit�ai�biRmt�giRgoldt�eit


on the world market index in month t , Rgoldt is the return on holding gold bullion in

month t and all returns are expressed in US dollars.* Significantly different from 0 at the 5% level.


the world market index in month t and Rgoldt is the return on the gold price in month

t , where all variables are expressed in common currency.

Assuming that a risk-free asset does not exist, a two-factor version of the Ross

(1976) Arbitrage Pricing Theory (APT) is:10

E(Ri)�g0�bi[E(Rw)�g0]�di[E(Rgold)�0] (4)

for i�/1,2,. . ...,N ; where E (.) is the expected value operator.

To aid testing, the risk premiums in Eq. (4) above can be parameterized as follows:

fw�E(Rw)�g0 (5)

fg�E(Rgold)�g0 (6)

By substituting Eqs. (5) and (6) into Eq. (4) we obtain:

E(Ri)�g0�bifw�difg (7)

The empirical application of the two-factor APT simply requires the substitution

of the economic model of Eq. (7) back into the assumed two-factor returns

generating process of Eq. (3):

Rit� [g0�bifw�difg]�bi[Rwt�E(Rw)]�di[Rgoldt�E(Rgold)]�eit (8)

Furthermore, by solving (Eq. (5)) and (Eq. (6)) in terms of E (Rw) and E (Rg)

respectively, and substituting into Eq. (8) we obtain:

Rit� [g0�bifw�difg]�bi[Rwt�(fw�g0)]�di[Rgoldt�(fg�g0)]�eit (9)

To complete the empirical specification, the mean of the market and gold price

return are modeled respectively as,

Rwt�(fw�g0)�jt (10)

Rgoldt�(fg�g0)�yt (11)

The null hypothesis imposed by the APT in Eq. (7) on the empirical system of

equations given by Eqs. (9)�/(11) is tested using the GMM approach of MacKinlay

and Richardson (1991).

Specifically, each equation takes on its own regressors as instrumental variables.

For this empirical system there are (3N�/2) sample moment equations. Thus GMM

involves an evaluation of the (3N�/2) sample moments, with (2N�/3) unknown

parameters (f) to be estimated (i.e. b1, b2,. . ., bN , d1, d2,. . ., dN , g0, fw, fg) Hence,

(N�/1) over-identifying restrictions exist and they are tested using:11

GMM�(T�N�1)+gT (f̂)?S�1T gT (f̂) (12)

where gT (f̂)�1=TaT

t�1ft(f̂); is the empirical moment condition vector.

10 This model could alternatively be interpreted as a version of the ICAPM, whereby the gold price

factor takes on the role of a hedging factor.11 This represents the small-sample adjusted version following MacKinlay and Richardson (1991).


The GMM estimator is (asymptotically) distributed as a x2 statistic with N�/1

degrees of freedom.

To ensure a measure of confidence in our results, we randomly sorted the global

industry portfolios into two groups. In the context of the system of Eqs. (9)�/(11),

Wald test statistics from the GMM estimation for the null hypothesis of joint

equality to 0 are reported in Table 4. As is starkly apparent, the null hypothesis is

strongly rejected at all levels of significance. These results are valid for all subperiods

tested*/thus providing evidence that gold is not a ‘useless’ factor.

Table 4

Multivariate tests of the joint significance of market and gold betas across global industry portfolios

H0: b1�/b2�/. . .�/

b17

H0: d1�/d2�/. . .�/

d17

H0: d1�/d2�/. . .�/

d17�/0

Panel A: group I global indus-

tries a

1975�/1980 441.31 591.27 968.50

(0.0000) (0.0000) (0.0000)

1981�/1987 547.13 199.76 200.43

(0.0000) (0.0000) (0.0000)

1988�/1994 788.89 520.24 593.19

(0.0000) (0.0000) (0.0000)

1975�/1994 311.31 304.82 387.82

(0.0000) (0.0000) (0.0000)

Panel B: group II global indus-

tries a

1975�/1980 924.30 695.02 695.91

(0.0000) (0.0000) (0.0000)

1981�/1987 1, 159.15 173.64 277.89

(0.0000) (0.0000) (0.0000)

1988�/1994 1, 037.41 357.42 363.97

(0.0000) (0.0000) (0.0000)

1975�/1994 300.79 182.75 199.85

(0.0000) (0.0000) (0.0000)

Degrees of Freedom 16 16 17

This table presents the results of testing the joint significance of market and gold betas within the two-

factor APT in the system of regressions equations:

Rit�[g0�bifw�difg]�bi[Rwt�(fw�g0)]�di[Rgoldt�(fg�g0)]�eit[i�1; 2; :::; N]

Rmt�(fw�g0)�jt

Rgoldt�(fg�g0)�nt



month t and all returns are expressed in US dollars.a World industries were randomly selected and allocated to either group I or II. The test statistics

reported are from Wald tests of each null hypothesis and follow x2 distributions with degrees of freedom

indicated in the final row of the table. The associated P -value is contained in parentheses below the

statistic.


The model specification given in Eqs. (8)�/(11) also allows for the estimation of the

real risk premium on the extra-market gold factor using GMM. It is clear that whilethe market factor has experienced significant gains over the sample period, the gold

factor has realized real losses. An analysis of the individual subperiods shows that

while the real gold premium was positive in the late 1970s, it experienced a sharp

decline and remained negative for the remainder of the period.

4. Summary and conclusions

An important thrust of the contemporary asset pricing literature is the applic-

ability of the pricing models in the international finance setting, particularly, at theaggregate country level, where risk is defined relative to a world or global market

factor and/or to other international or global factors. One approach to this problem

at the theoretical level is to refine the model in a way that introduces additional ‘risk’

variables. Merton (1973) proposed an intertemporal CAPM (ICAPM) in which

investors are assumed to be able to construct portfolios that protect against

Table 5

GMM tests of an international two-factor asset pricing model using a world market factor and a gold price

factor*/real gold premium

Group I Group II

fg GMMa fg GMMa

1975�/1980 0.02784b 10.048 0.02790b 9.117

(4.06) (0.864) (3.42) (0.909)

1981�/1987 �/0.02788 10.562 �/0.00544 11.830

(�/5.29) (0.836) (�/1.45) (0.756)

1988�/1994 �/0.01982 11.122 �/0.01420 10.915

(�/6.94) (0.802) (�/4.53) (0.815)

1975�/1994 �/0.00573 24.674 �/0.00885 20.563

(�/1.76) (0.076) (�/2.65) (0.196)

This table presents the results of testing the two-factor APT in the system of regressions in the following

equations:

Rit�[g0�bifm�difg]�bi[Rmt�(fm�g0)]�di[Rgoldt�(fg�g0)]�eit[i�1; 2; :::; N]

Rmt�(fm�g0)�jt

Rgoldt�(fg�g0)�nt



month t and all returns are expressed in US dollars.a The generalized method of moments test statistic (GMM) for the null hypothesis that the two-factor

International ICAPM holds is distributed as a x2 with (N�/1) degrees of freedom. The statistic has had the

small sample adjustment applied following MacKinlay and Richardson (1991). The associated P -value is

contained in parentheses below the statistic.b GMM systems estimate of given coefficient with associated t statistic given below in parentheses.


uncertainties in state variables. Historically, investors have sought financial shelter

from inflation and political instability through investing in gold. As such, a gold

price factor is a strong candidate to play a hedging role in the ICAPM. Accordingly,

the central objective of the current paper was to investigate the exposure of world

industry equity returns to a gold price factor, over and above the exposure to global

market returns. In addition, the analysis was extended to performing multivariate

asset pricing tests of the resulting international two-factor ICAPM.Our main results can be summarized as follows. First, we found that 22 global

industries display at least some evidence of extra-market sensitivity to the gold price.

Notable examples of significant positive exposure were the Gold Mines; Metals

(Non-Ferrous); Real Estate; and Wholesale and International Trade world industry

portfolios. Notable examples of significant negative exposure were the Food and

Household Products; Leisure and Tourism; and Merchandise global industry

portfolios. Second, there is little evidence of instability in the extra-market gold

sensitivity of the global industry portfolios. Third, we find strong evidence rejectingthe joint equality (equal to 0) of the gold factor exposures across the global industry

portfolios. This supports the view that the gold price factor is not ‘useless’ and

fourth, with regard to the formal asset pricing tests, we find strong evidence in favor

of the two-factor international asset pricing model. Finally, we show using

generalized method of moments estimation that the real returns on the gold factor

were negative during the 80s and early 90s.

It appears that although the real value of gold has declined over recent years,

corporate exposure to this historically prominent commodity is still as strong. Thefinding of negative and positive exposures is intriguing and indicative of different

and contrasting corporate forms within each industry. Exploring the determinants of

the exposure to a gold factor for industries other than the gold mining industries

(Tufano, 1996) is an area that is important for future research and could provide

further clarification of the role of gold in the current global economy.

Acknowledgements

The authors would like to thank Garry Hobbes and seminar participants at

Macquarie University, University of Lancaster, Jonkoping International Business

School and the 1999 Southern African Finance Association conference for their

helpful comments on an earlier version of this paper. We also thank Sveta Rismanfor her careful research assistance. Finally, we appreciate the helpful comments of an

anonymous referee.

References

Aggarwal, R., Soenen, L., 1988. The nature and efficiency of the gold market. Journal of Portfolio

Management 14, 18�/21.


Allayannis, G., Ofek, E., 2001. Exchange rate exposure, hedging, and the use of foreign currency

derivatives. Journal of International Money and Finance 20, 273�/296.

Blose, L., Shieh, J., 1995. The impact of gold price on the value of gold mining stock. Review of Financial

Economics 4, 125�/139.

Booth, G., Kaen, F., Koveos, P., 1982. Persistent dependence in gold prices. Journal of Financial Research

5, 85�/93.

Chan, M., Mountain, D., 1988. The interactive and causal relationships involving precious metal price

movements. Journal of Business and Economic Statistics 6, 69�/77.

Christie-David, R., Chaudhry, M., Koch, T., 2000. Do macroeconomic news releases affect gold and silver

prices? Journal of Economics and Business 52, 405�/421.

Chua, J., Sick, G., Woodward, R., 1990. Diversifying with gold stocks. Financial Analysts Journal 46, 76�/

79.

Cochrane, D., Orcutt, G., 1949. Application of least squares regressions to relationships containing

autocorrelated error terms. Journal of the American Statistical Association 44, 32�/61.

Elyasiani, E., Mansur, I., 1998. Sensitivity of the bank stock returns distribution to changes in the level

and volatility of interest rate: a GARCH-M model. Journal of Banking and Finance 22, 535�/563.

Fortune, 1998. Burned by gold, March 16, 34�/40.

Frank, M., Stengos, T., 1989. Measuring the strangeness of gold and silver rates of return. Review of

Economic Studies 56, 553�/567.

French, K., Ruback, R., Schwert, WG. 1983. Effects of Nominal Contracting on Stock Returns. The

Journal of Political Economy 91, 70�/96.

He, J., Ng, L., 1998. The foreign exchange exposure of Japanese multinational corporations. Journal of

Finance 53, 733�/753.

Jaffe, J., 1989. Gold and gold stocks as investments for institutional portfolios. Financial Analysts Journal

45, 53�/59.

Johnson, R., Soenen, L., 1997. Gold as an investment asset: perspectives from different countries. Journal

of Investing 6, 94�/99.

Kan, R., Zhang, C., 1999. Two-pass tests of asset pricing models with useless factors. Journal of Finance

54, 203�/235.

MacKinlay, A., Richardson, M., 1991. Using generalized method of moments to test mean-variance

efficiency. Journal of Finance 46, 511�/527.

McDonald, J., Solnik, B., 1977. Valuation and strategy for gold stocks. Journal of Portfolio Management

4, 29�/33.

Merton, R., 1973. An intertemporal capital asset pricing model. Econometrica 41, 867�/887.

Muradoglu, G., Akkaya, N., Chafra, J., 1998. The effect of the establishment of an organized exchange on

weak form efficiency: the case of Istanbul gold exchange. European Journal of Finance 4, 85�/92.

Roll, R., 1988. The international crash of October 1987. Financial Analysts Journal 44, 19�/35.

Ross, S., 1976. The arbitrage theory of capital asset pricing. Journal of Economic Theory 13, 341�/360.

Rubio, G., 1989. An empirical evaluation of the intertemporal capital asset pricing model: the stock

market in Spain. Journal of Business Finance and Accounting 16, 729�/743.

Salant, S., Henderson, D., 1978. Market anticipations of government policies and the price of gold.

Journal of Political Economy 86, 627�/648.

Scruggs, J.T., 1998. Resolving the puzzling intertemporal relation between the market risk premium and

conditional market variance: a two-factor approach. Journal of Finance 53, 575�/603.

Selvanathan, S., Selvanathan, E., 1999. The effect of the price of gold on its production: a time-series

analysis. Resources Policy 25, 265�/275.

Shanken, J., 1990. Intertemporal asset pricing: an empirical investigation. Journal of Econometrics 45,

99�/120.

Sjaastad, L., Scacciavillani, F., 1996. The price of gold and the exchange rate. Journal of International

Money and Finance 15, 879�/897.

Song, F., 1994. A two-factor ARCH model for deposit-institution stock returns. Journal of Money, Credit

and Banking 26, 323�/340.

Solt, M., Swanson, P., 1981. On the efficiency of the markets for gold and silver. Journal of Business 54,

453�/478.


Taylor, N., 1998. Precious metals and inflation. Applied Financial Economics 8, 201�/210.

Tschoegl, A., 1980. Efficiency in the gold market*/A note. Journal of Banking and Finance 4, 371�/379.

Tufano, P., 1996. Who manages risk? An empirical examination of risk management practices in the gold

mining industry. Journal of Finance 51, 1097�/1137.

Tufano, P., 1998. The determinants of stock price exposure: financial engineering and the gold mining

industry. Journal of Finance 53, 1015�/1052.


gold factor exposures in international asset pricing

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