Is gold a safe haven or a hedge for the US dollar implications for risk management

Journal of Banking & Finance 37 (2013) 2665–2676

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Journal of Banking & Finance
journal homepage: www.elsevier.com/locate/jbf

Is gold a safe haven or a hedge for the US dollar? Implications for risk
management
Juan C. Reboredo ⇑
Universidade de Santiago de Compostela, Departmento de Fundamentos del Análisis Económico, Avda. Xoán XXIII, s/n, 15782 Santiago de Compostela, Spain

a r t i c l e

i n f o

Article history:
Received 5 December 2012
Accepted 23 March 2013
Available online 18 April 2013
JEL classification:
C52
C58
F3
G1

a b s t r a c t
We assess the role of gold as a safe haven or hedge against the US dollar (USD) using copulas to characterize average and extreme market dependence between gold and the USD. For a wide set of currencies,
our empirical evidence revealed (1) positive and significant average dependence between gold and USD
depreciation, consistent with the fact that gold can act as hedge against USD rate movements, and (2)
symmetric tail dependence between gold and USD exchange rates, indicating that gold can act as an

effective safe haven against extreme USD rate movements. We evaluate the implications for mixed
gold-currency portfolios, finding evidence of diversification benefits and downside risk reduction that
confirms the usefulness of gold in currency portfolio risk management.
Ó 2013 Elsevier B.V. All rights reserved.

Keywords:
Gold
Exchange rates
Hedge
Safe haven
Copulas

1. Introduction
For many years strengthened gold prices in combination with
US dollar (USD) depreciation has attracted the attention of investors, risk managers and the financial media. The fact that when
the USD goes down as gold goes up suggests the possibility of using
gold as a hedge against currency movements and as a safe-haven
asset against extreme currency movements.1
Some studies have examined the usefulness of gold as a hedge
against inflation (Chua and Woodward, 1982; Jaffe, 1989; Ghosh et al.,
2004; McCown and Zimmerman, 2006; Worthington and Pahlavani,
2007; Tully and Lucey, 2007; Blose, 2010; Wang et al., 2011 and references therein), whereas other studies have examined gold’s safe-haven
status with respect to stock market movements (Baur and McDermott,
2010; Baur and Lucey, 2010; Miyazaki et al., 2012) and oil price changes
(Reboredo, 2013a).2 However, few studies have considered the role of
⇑ Tel.: +34 881811675; fax: +34 981547134.
E-mail address:
Pukthuanthong and Roll (2011) showed that the price of gold is related with
currency depreciation in every country. O’Connor and Lucey (2012) analyse the
negative correlation between returns for gold and traded-weighted exchange returns

for the dollar, yen and euro.
2
Other studies analyse the relationship between gold, oil and exchange rates (see,
e.g., Sari et al., 2010; Kim and Dilts, 2011; Malliaris and Malliaris, 2013) and between
these variables and interest rates (Wang and Chueh, 2013).
1

0378-4266/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved.
/>
gold as hedge or investment safe haven against currency depreciation.
Beckers and Soenen (1984) studied gold’s attractiveness for investors
and its hedging properties, finding asymmetric risk diversification for
gold’s holding positions for US and non-US investors. Sjasstad and Scacciavillani (1996) and Sjasstad (2008) found that currency appreciations or
depreciations had strong effects on the price of gold. Capie et al. (2005)
confirmed the positive relationship between USD depreciation and the
price of gold, making gold an effective hedge against the USD. More recently, Joy (2011) analysed whether gold could serve as a hedge or an
investment safe haven, finding that gold has been an effective hedge
but a poor safe haven against the USD. This paper contributes in two ways
to the existing literature on gold as a hedge and/or safe haven against currency depreciation.
First, we study the dependence structure for gold and the USD by
using copula functions, which provide a measure of both average
dependence and upper and lower tail dependence (joint extreme
movements). This information is crucial in determining gold’s role
as a hedge or an investment safe haven, provided the distinction between a hedge and safe-haven asset is made in terms of dependence
under different market circumstances (see, e.g., Baur and McDermott,
2010; Joy, 2011). Previous studies have examined the behavior of the
correlation coefficient between gold and the USD exchange rate (Joy,
2011), but only provide an average measure of dependence. Other
studies have examined the marginal effects of stock prices on gold
prices using a threshold regression model, with the threshold given

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J.C. Reboredo / Journal of Banking & Finance 37 (2013) 2665–2676

by a specific quantile of the stock returns distribution (Baur and
McDermott, 2010; Baur and Lucey, 2010; Wang and Lee, 2011; Ciner
et al., 2012); however, the correlation coefficient is insufficient to describe the dependence structure (Embrechts et al., 2003)—especially
when the joint distribution of gold and exchange rates is far from
the elliptical distribution—and the marginal effects captured by the
threshold regression do not fully account for joint extreme market
movements. Therefore, we propose the use of copulas to test gold’s
hedge and safe-haven ability, as they fully describe the dependence
structure and allow more modeling flexibility than parametric bivariate distributions.
Second, since knowledge of gold and USD co-movement is useful for
portfolio managers who want portfolio diversification and investment
protection against downside risk, we investigated the implications of
gold-USD market average and tail dependence for risk management by
comparing the risk for gold-USD portfolio holdings to the risk for simple
currency portfolios. We also evaluated whether an investor could achieve
downside risk gains from a portfolio composed of gold and currency by
studying the value-at-risk (VaR) performance.
Our empirical study of the hedge and safe-haven properties of
gold against USD exchange rates covered the period January
2000–September 2012 and evaluated the USD exchange rate with
a wide set of currencies and a USD exchange rate index. We modeled marginal distributions with an autoregressive moving average
(ARMA) model with threshold generalized autoregressive conditional heteroskedasticity (TGARCH) errors and different copula
models with tail independence, symmetric and asymmetric tail
dependence. We provide empirical evidence of positive average

dependence and symmetric tail dependence between gold and
USD depreciation, with the Student-t copula as the best performing
dependence model. This evidence is consistent with the role of
gold as a hedge and safe-haven asset against currency movements.
We also address the risk management consequences of the links
between gold and USD depreciation, providing evidence for gold’s
usefulness in a currency portfolio—given that it shows evidence of
hedging effectiveness in reducing portfolio risk—and for a VaR
reduction and better performance in terms of the investor’s loss
function with respect to a portfolio composed only of currency.
The rest of the paper is laid out as follows: in Section 2 we outline the methodology and test our hypothesis. In Sections 3 and 4
we present data and results, respectively, and we discuss the implications in terms of portfolio risk management in Section 5. Finally,
Section 6 concludes the paper.

2. Methodology
The role of gold as a hedge or safe haven with respect to currency movements depends on how gold and currency price
changes are linked under different market circumstances. Following the definitional approach adopted in Kaul and Sapp (2006),
Baur and Lucey (2010) and Baur and McDermott (2010), the distinctive feature of an asset as a hedge or safe haven is as follows:
– Hedge: an asset is a hedge if it is uncorrelated or negatively correlated with another asset or portfolio on average.
– Safe haven: an asset is a safe haven if it is uncorrelated or negatively correlated with another asset or portfolio in times of
extreme market movements.
The crucial distinction between the two is whether dependence
holds on average or under extreme market movements.3 To distin3
Baur and McDermott (2010) draw a distinction between strong and weak hedges
and safe havens on the basis of the negative value or null value of the correlation,
respectively.

guish between hedge and safe-haven properties we need to measure
dependence between two or more random variables in terms of average movements across marginals and in terms of joint extreme market
movements.

We used copulas to flexibly model the joint distribution of gold
and the USD and then linked information on average and tail
dependence arising from copulas to the hedge and safe-haven
properties of gold against the USD. A copula4 is a multivariate
cumulative distribution function with uniform marginals U and V,
C(u, v) = Pr[U 6 u, V 6 v], that capture dependence between two random variables, X and Y, irrespective of their marginal distributions,
FX(x) and FY(y), respectively. Sklar’s (1959) theorem states that there
exists a copula such that

F XY ðx; yÞ ¼ CðF X ðxÞ; F Y ðyÞÞ;

ð1Þ

where FXY(x, y) is the joint distribution of X and Y, u = FX(x) and

v = FY(y). C is uniquely determined on RanFXx RanFY when the margins are continuous. Likewise, if C is a copula, then the function FXY
in Eq. (1) is a joint distribution function with margins FX and FY. The
conditional copula function (Patton, 2006) can be written as:

F XYjW ðx; yjwÞ ¼ CðF XjW ðxjwÞ; F YjW ðyjwÞjwÞ;

ð2Þ

where W is the conditioning variable, FXjW(xjw) is the conditional
distribution of XjW = w, FYjW(yjw) is the conditional distribution of
YjW = w and FXYjW(x, yjw) is the joint conditional distribution of
(X, Y)jW = w.
Consequently, the copula function relates the quantiles of the
marginal distributions rather than the original variables. This means
that the copula is unaffected by the monotonically increasing transformation of the variables. Copulas can also be used to connect margins to a multivariate distribution function, which, in turn, can be

decomposed into its univariate marginal distributions and a copula
that captures the dependence structure between the two random
variables. Thus, copulas allow the marginal behavior of the random
variables and the dependence structure to be modeled separately
and this offers greater flexibility than would be possible with parametric multivariate distributions. Moreover, modeling dependence
structure with copulas is useful when the joint distribution of two
variables is far from the elliptical distribution. In those cases, the traditional dependence measure given by the linear correlation coefficient is insufficient to describe the dependence structure (see
Embrechts et al., 2003). Furthermore, some measures of concordance (Nelsen, 2006) between random variables, like Spearman’s
rho and Kendall’s tau, are properties of the copula.
A remarkable feature of the copula is tail dependence, which
measures the probability that two variables are in the lower or upper
joint tails of their bivariate distribution. This is a measure of the propensity of two random variables to go up or down together. The coefficient of upper (right) and lower (left) tail dependence for two
random variables X and Y can be expressed in terms of the copula as:

h
i
1 À 2u þ Cðu; uÞ
À1
kU ¼ limPr X P F À1
;
X ðuÞjY P F Y ðuÞ ¼ lim
u!1
u!1
1Àu
h
i
Cðu; uÞ
À1
;
kL ¼ limPr X 6 F À1

X ðuÞjY 6 F Y ðuÞ ¼ lim
u!0
u!0
u

ð3Þ
ð4Þ

where F À1
and F À1
x
Y are the marginal quantile functions and where
kU, kL 2 [0, 1]. Two random variables exhibit lower (upper) tail
dependence if kL > 0 (kU > 0), which indicates a non-zero probability
of observing an extremely small (large) value for one series together
with an extremely small (large) value for another series.
The copula provides information on both dependence on average
and dependence in times of extreme market movements. Dependence on average (given by linear correlation, Spearman’s rho or
4
For an introduction to copulas, see Joe (1997) and Nelsen (2006). For an overview
of copula applications to finance, see Cherubini et al. (2004).


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J.C. Reboredo / Journal of Banking & Finance 37 (2013) 2665–2676

Kendall’s tau) can be obtained from the dependence parameter of the
copula; dependence in times of extreme market movements can be
obtained through the copula tail dependence parameters given by

Eqs. (3) and (4). On the basis of copula dependence information,
we can formulate two hypotheses in order to determine whether
gold can serve as a hedge or as a safe haven against USD depreciation:

Hypothesis 1 : qG;C P 0ðgold is a hedgeÞ;
Hypothesis 2 : kU > 0 ðgold is a safe havenÞ;
where qG,C is the measure of average dependence between the value
of gold and USD depreciation. Thus, gold can act as a hedge if we do
not find evidence against Hypothesis 1. Similarly, if Hypothesis 2 is
not rejected, gold can serve as a safe-haven asset against extreme
market movements in the USD depreciation; in other words, gold preserves its value when the USD depreciates (there is co-movement between gold and exchange rates at the upper tail of their joint
distribution). By considering kL instead of kU in Hypothesis 2, we
can test gold’s safe-haven property in the case of extreme downward
market movements, which is of interest for investors holding short
positions in the USD. In this case, gold can act as a safe-haven asset
against extreme downward market movements provided Hypothesis
2 is not rejected for kL.
The specification of the copula function is crucial to determining the role of gold as a hedge or safe haven against the USD. We
considered different copula function specifications in order to capture different patterns of dependence and tail dependence,
whether tail independence, tail dependence, asymmetric tail
dependence or time-varying dependence. The bivariate Gaussian
copula (N) is defined by CN(u, v; q) = U(UÀ1(u), UÀ1(v)), where U
is the bivariate standard normal cumulative distribution function
with correlation q between X and Y and where UÀ1(u) and
UÀ1(v) are standard normal quantile functions. The Gaussian copula has zero tail dependence, kU = kL = 0. The Student-t copula is giÀ
Á
À1
ven by C ST ðu; v ; q; tÞ ¼ T t À1
t ðuÞ; t t ðv Þ , with T as the bivariate
Student-t cumulative distribution function with a correlation coefÀ1

ficient q, and where tÀ1
t ðuÞ and t t ðv Þ are the quantile functions of
the univariate Student-t distribution with t as the degree-of-freedom parameter. The appealing feature of the Student-t copula is
that, since it allows for symmetric non-zero dependence in the tails
(see Embrechts et al., 2003), large joint positive or negative realizations
have
the
same
probability
of
occurrence,
À pffiffiffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiÁ
kU ¼ kL ¼ 2t tþ1 À t þ 1 1 À q= 1 þ q > 0, where tt+1(Á) is the
cumulative distribution function (CDF) of the Student-t distribution. Tail dependence relies on both the correlation coefficient
and the degree-of-freedom parameter. The Clayton copula is given
by C CL ðu; v ; aÞ ¼ maxfðuÀa þ v Àa À 1ÞÀ1=a ; 0g. It is asymmetric, as
dependence is greater in the lower tail than in the upper tail,
where it is zero: kL = 2À1/a (kU = 0). The Gumbel copula is also
asymmetric but has greater dependence in the upper tail than in
the lower tail, where it is zero: kU = 2 À 21/d(kL = 0). The Gumbel
copula is given by CG(u, v; d) = exp (À((Àlogu)d + (Àlogv)d)1/d). Note
that, when d = 1, the two variables are independent. The symmetrized Joe–Clayton copula (see Patton, 2006) allows upper and lower tail dependence and symmetric dependence as a special case
when kU = kL. This copula is defined as:

C SJC ðu; v ; kU ; kL Þ ¼ 0:5ðC JC ðu; v ; kU ; kL Þ þ C JC ð1 À u; 1 À v ; kU ; kL Þ
þ u þ v À 1Þ;

ð5Þ

where CJC(u, v; kU, kL) is the Joe–Clayton copula, defined as:

À
È
C JC ðu; v ; kU ; kL Þ ¼ 1 À 1 À ½1 À ð1 À uÞj ŠÀc
ÉÀ1=c 1=j
;
þ½1 À ð1 À v Þj ŠÀc À 1

ð6Þ

where j = 1/log2(2 À kU), c = À1/log2(kL), and kL 2 (0, 1), kU 2 (0, 1).
With a view to considering possible time variation in the conditional
copula—and thus in gold and exchange rate dependence—we will assume that the copula dependence parameters vary according to an
evolution equation. Following Patton (2006), for the Gaussian and
Student-t copulas, we specify the linear dependence parameter qt
so that it evolves according to an ARMA (1,q)-type process:

!
q
1 X À1
À1
qt ¼ K w0 þ w1 qtÀ1 þ w2
U ðutÀj Þ Á U ðv tÀj Þ ;
q j¼1

ð7Þ

where K(x) = (1 À eÀx)(1 + eÀx)À1 is the modified logistic transformation to keep the value of qt in (À1, 1). The dependence parameter is
explained by a constant, w0, by an autoregressive term, w1, and by
the average product over the last q observations of the transformed

variables, w2. For the Student-t copula, UÀ1(x) is substituted by t À1
t ðxÞ.
The above copula parameters are estimated by maximum likelihood (ML) using a two-step procedure called the inference function for margins (IFMs) method (Joe and Xu, 1996). The bivariate
density function is decomposed into the product of the marginal
densities and the copula density according to Eqs. (1) and (2).
We first estimate the parameters of the marginal distributions separately by ML and then estimate the parameters of a parametric
copula by solving the following problem:
T
X
^ t ; v^ t ; hÞ;
h ¼ arg max
ln cðu
h

ð8Þ

t¼1

^ x Þ and v^ t ¼ F Y ðyt ; a
^y Þ
^ t ¼ F X ðxt ; a
where h are the copula parameters, u
are pseudo-sample observations from the copula.5
For the marginal distribution, we considered an ARMA (p, q)
model with TGARCH as introduced by Zakoian (1994) and Glosten
et al. (1993) with the aim of accounting for the most important
stylized features of gold and exchange rate return marginal distributions, such as fat tails and the leverage effect.6 As a result, the
marginal model for the gold or exchange rate return, rt, can be specified as:

rt ¼ /0 þ

p
q
X
X
/j r tÀj þ et À
hi etÀi ;
j¼1

ð9Þ

i¼1

where p and q are non-negative integers and where / and h are the
AR and MA parameters, respectively. It is assumed that the white
noise process et follows a Student-t distribution:

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

t
e $ i:i:d: tt ;
r2t ðt À 2Þ t

ð10Þ

with t degrees of freedom, and where r2t is the conditional variance
of et evolving according to:

r2t ¼ x þ

r
m
m
X
X
X
bj r2tÀj þ
aj e2tÀi þ cj etÀj ItÀj ;
j¼1

i¼1

ð11Þ

j¼1

where x is a constant; r2tÀj is the previous period’s forecast error variance, the generalized autoregressive conditional heteroskedasticity
(GARCH) component; etÀj is news about volatility from previous
periods, the autoregressive conditional heteroskedasticity (ARCH)
component; ItÀj = 1 if etÀj < 0, otherwise 0; and where c captures
leverage effects. For c > 0, the future conditional variance will increase proportionally more following a negative shock than following a positive shock of the same magnitude. Leverage or inverse
5
Under standard regularity conditions, this two-step estimation is consistent and
the parameter estimates are asymptotically efficient and normal (see Joe, 1997).
6
We also modeled marginal distributions using a more general GARCH specification; namely, the general class of power ARCH models as proposed by Ding et al.
(1993) and Hentschel (1995). The empirical results were similar to those presented
here for the TGARCH model. These results are available on request.

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J.C. Reboredo / Journal of Banking & Finance 37 (2013) 2665–2676

leverage effects have been found in some commodity prices (see, e.g.,
Mohammadi and Su, 2010; Bowden and Payne, 2008; Reboredo,
2011; Reboredo, 2012b) and in some exchange rates (Reboredo,
2012a). The number of p, q, r and m lags for each series was selected
using the Akaike information criterion (AIC).
The performance of the different copula models was evaluated
using the AIC adjusted for small-sample bias, as in Breymann
et al. (2001) and Rodriguez (2007).

3. Data
We empirically investigated the hedge and safe-haven properties of gold against the USD using weekly data from 7 January
2000 to 21 September 2012. The starting sample period was determined by the introduction of the euro as a currency in financial
markets from 1999. Also, the use of weekly data is more appropriate for our purpose of characterizing the dependence structures
between gold and the USD; this is because daily or high-frequency
data may be affected by drifts and noise that could mask the
dependence relationship and complicate modeling of the marginal
distributions through non-stationary variances, sudden jumps or
long memory. Data for gold prices—measured in USD per ounce—
and the USD rate—measured as USD per unit of foreign currency
(an exchange rate increase means USD depreciation)—were downloaded from the website of the Bank of England (). Exchange rate data was collected for currencies
as follows: the Australian dollar (AUD), the Canadian dollar
(CAD), the euro (Germany, France, Italy, Netherlands, Belgium/Luxembourg, Ireland, Spain, Austria, Finland, Portugal, Greece, Slovenia, Cyprus, Slovakia and Malta), the British pound (GBP), the
Japanese yen (JPY), the Norwegian krone (NOK) and the Swiss franc
(CHF). The set of countries used for this study includes the vast
majority of market traders in international exchange. Additionally,
to examine the relationship between gold and the USD aggregate

exchange rate, we considered the Broad Trade Weighted Exchange
Index (TWEXB) of the US Federal Reserve (these data were downloaded from the Federal Reserve Bank of Saint Louis, http://
www.frbstlouis.com). Fig. 1 displays gold price-exchange rate
dynamics for the different currencies considered throughout the
sampling period. Consistent trends can be observed: gold prices
rose exponentially, whereas the USD depreciated against the main
currencies. With the intensification of the global financial crisis
after 2008, gold prices and USD depreciation with respect to most
currencies analysed also moved in lock-step.
Descriptive statistics and stochastic properties for the return
data for gold and USD rates are reported in Table 1. The mean returns were close to zero for all returns series and were small relative to their standard deviations, which would indicate no
significant trend in the data. The difference between the maximum
and minimum values shows that gold prices were more volatile
than the USD. Negative values for skewness were common for all
series and all returns show excess kurtosis—ranging from 4.1 to
14.5—confirming thus the presence of fat tails in the marginal distributions or relatively frequent extreme observations. The Jarque–
Bera test for normality of the unconditional distribution strongly
rejected the normality of the unconditional distribution for all
the series. Furthermore, the values of the Ljung-Box statistic for
uncorrelation up to 20th order in the squared returns suggested
the existence of serial correlation for all the series. Also, the Lagrange multiplier for ARCH (ARCH-LM) statistic for serially correlated squared returns indicated that ARCH effects were likely to
be found in all the return series with the exception of the Swiss
franc. The linear correlation coefficient indicates that gold and
USD exchange rates were positively dependent; hence, the value

of gold and the USD value move in opposite directions, opening
up the possibility of using gold as a hedge.
We firstly examined the dependence structure between gold
and the USD by obtaining the empirical copula table for the returns in the following way. For each pair of gold and USD returns,
we ranked each series in ascending order and separated observations uniformly into 10 bins in such a way that bin 1 included

observations with the lowest values and bin 10 included observations with the highest values. We then counted the number of
observations that shared each (i, j) bin for i, j = 1, . . . , 10 through
the sample period, for t = 1, . . . , T, and included this number in
a 10 Â 10 matrix in such a way that the matrix rows included
the bins of one series in ascending order from top to bottom
and the matrix columns included the bins of the other series in
ascending order from left to right. If the two series were perfectly
positively (negatively) correlated we would see most observations
lying on the diagonal connecting the upper-left corner with the
lower-right corner (the lower-left corner with the upper-right
corner) of the 10 Â 10 matrix; and if they were independent we
would expect the numbers in each cell to be about the same. In
addition, if there was lower tail dependence between the two series we would expect more observations in cell (1, 1); and if there
was upper tail dependence we would expect more observations
in cell (10, 10).
Table 2 displays the empirical copula table for all the gold-USD
exchange rate pairs. Evidence of positive dependence is indicated
by the fact that the number of observations along the upper-left/
lower-right diagonal is greater than the number of observations
in the other cells. Hence, the USD value and gold prices move in
opposite directions. Likewise, in comparing the lowest and highest
10th percentiles, there are no significant differences in the joint extreme frequencies, which is evidence of potential symmetric tail
dependence. Furthermore, frequencies at the upper and lower
quantiles are greater than for the remaining quantiles. Overall,
the results in Table 2 are fully consistent with the positive dependence shown by the unconditional correlation coefficient displayed
in Table 1.

4. Empirical results
4.1. Results for the marginal models
The marginal distribution model described in Eqs. (9)–(11) was

estimated for gold and all the exchange rates by considering different combinations of the parameters p, q, r and m for values ranging
from zero to a maximum lag of two. Table 3 reports the results. The
most suitable model was, according to the AIC values, an ARMA
(0,0)-TGARCH (1,1) specification with the exception of gold, where
lags 1 and 5 were included in the mean specification, and the yen,
where a TGARCH (2,2) volatility specification was preferred. Volatility was quite persistent in all the series and the leverage effect
was significant for gold and two exchange rates; this is consistent
with previous empirical results for gold and exchange rates (see,
e.g., McKenzie and Mitchell, 2002; Reboredo, 2012a). In addition,
the last two rows of Table 3 also show that neither autocorrelation
nor ARCH effects remained in the residuals.
The goodness-of-fit assessment of the marginal models is crucially important given that the copula is mis-specified when the
marginal distribution models are also mis-specified, that is, when
^ x Þ and v
^yÞ
^ t ¼ F X ðxt ; a
^ t ¼ F Y ðyt ; a
the probability transformations u
are not i.i.d. uniform (0, 1). Therefore, we tested the goodness-of^t
fit of the marginal models by testing the i.i.d. uniform (0, 1) of u
^ t in two steps (see Diebold et al., 1998).
and v
^t À u
 Þk and
First, we tested for the serial correlation of ðu
k
^t À v
 Þ on h = 20 lags for both variables for k = 1, 2, 3, 4 and used
ðv

J.C. Reboredo / Journal of Banking & Finance 37 (2013) 2665–2676

Fig. 1. Gold prices and USD exchange rates (7 January 2000–21 September 2012).

2669


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J.C. Reboredo / Journal of Banking & Finance 37 (2013) 2665–2676

Table 1
Descriptive statistics for gold and USD exchange rate returns.

Mean
Std. dev.
Max.
Min.
Skewness
Kurtosis
JB
Q(20)
ARCH-LM
Corr. gold

GOLD

AUD

CAD

EUR

GBP

JPY

NOK

CHF

TWEXB

0.003
0.027
0.147
À0.138
À0.351
6.268
308.63⁄
434.40⁄
10.93⁄
1

0.001
0.020
0.071
À0.174
À1.674

14.513
3971.2⁄
166.64⁄
5.70⁄
0.34

0.001
0.013
0.045
À0.091
À0.935
8.800
1025.7⁄
404.97⁄
12.27⁄
0.36

0.000
0.014
0.053
À0.056
À0.245
3.803
24.47⁄
95.44⁄
3.58⁄
0.43

0.000
0.014

0.053
À0.086
À0.817
7.819
715.4⁄
454.87⁄
13.81⁄
0.35

0.000
0.014
0.085
À0.054
0.491
5.196
159.7⁄
53.02⁄
2.71⁄
0.17

0.000
0.017
0.070
À0.064
À0.355
3.824
32.64⁄
112.30⁄
2.75⁄
0.47

0.001
0.016
0.061
À0.121
À0.627
8.245
803.40⁄
21.25⁄
0.89
0.43

0.000
0.010
0.039
À0.043
À0.368
4.172
52.89⁄
153.97⁄
4.81⁄
0.47

Notes. Weekly data for the period 7 January 2000–21 September 2012. JB is the v2 statistic for the test of normality. Q(k) is the Ljung–Box statistics for serial correlation in the
squared returns computed with k lags. ARCH-LM is Engle’s LM test for heteroskedasticity, computed using 20 lags. Corr. Gold is the Pearson correlation for each series with
gold.
⁄
Indicates rejection of the null hypothesis at the 5% level.

the LM statistic, defined as (T À h)R2 where R2 is the coefficient of

determination for the regression, to test the null of serial independence. The LM statistic is distributed as v2(h) under the null. Table 4 reports the results of this test for the marginal distribution
models; the i.i.d. assumption could not be rejected at the 5% level.
^ t and v
^ t were uniform (0, 1) using the KolSecond, we tested if u
mogorov–Smirnov, Cramer–von Mises and Anderson–Darling tests,
which compare the empirical distribution and the specified theoretical distribution function. P values for all these tests are reported in
the last three rows of Table 4; for all the marginal models we were
unable to reject the null of correct specification of the distribution
function at the 5% significance level. To sum up, the goodness-offit tests for our marginal distribution models indicated that these
were not mis-specified; as a result, the copula model can correctly
capture co-movement between gold and exchange rate markets.
4.2. Copula estimates of dependence
Before providing estimates for the parametric copulas described
above, we first obtained a non-parametric estimate of the 
copula.
This estimate, proposed by Deheuvels (1978), at points Ti ; Tj , is given by



T
X
b i;j ¼1
C
1fu 6u ;v 6v g ;
T T
T k¼1 k ðiÞ k ðjÞ

ð12Þ

where u(1) 6 u(2) 6 Á Á Á 6 u(T) and v(1) 6 v(2) 6 Á Á Á 6 v(T) are the order

statistics of the univariate samples and where 1 is the usual indicator function. Fig. 2, which depicts non-parametric density estimates
for bivariate density for gold and USD depreciation, indicates (a) positive dependence between gold and the USD depreciation against a
wide set of currencies; (b) upper and lower tail dependence, meaning that gold and USD exchange rate markets boom and crash together; and (c) a low probability of disjoint extreme market
movements, so extreme upward (downward) gold price movements
are not in lock-step with extreme downward (upward) USD depreciation movements. This graphical evidence is consistent with the
empirical copula results shown in Table 2 and has, obviously, implications for the role of gold as a safe-haven asset (discussed below).
Table 5 reports results for the parametric copula models described above. Examining the elliptical copulas, for all exchange
rates the dependence parameter in the Gaussian and Student-t
copulas (i.e., the correlation coefficient) was positive, strongly significant and consistently close to the linear correlation coefficient
for the data. The strength of dependence was very similar across
currencies, for correlation coefficients ranging between 0.37 and
0.51. The degrees of freedom for the Student-t copula were not
very low (ranging from 9 to 18), indicating the existence of tail
dependence for all the currencies. By considering asymmetric tail

dependence, parameter estimates for the Clayton and Gumbel copulas were significant and reflected positive dependence between
gold and exchange rates. Tail dependence was also different from
zero and the lower and upper tail dependence parameters of the
Clayton and Gumbel copulas had similar values. Additionally, the
estimated values of kL and kU for the symmetrized Joe–Clayton copula were significant in most of the cases, indicating similar dependence in the lower and upper tails (with the exception of CAD and
JPY). Finally, time-varying dependence results for the normal and
Student-t copulas also indicated positive dependence, as the correlation coefficients had positive values throughout the sample period, displaying good results in terms of the AIC for the time-varying
Gaussian copula for the yen.
The comparison of the estimated copula models is essential to
test the two hypotheses regarding gold’s hedge or safe-haven status against the USD; different copula models have different average and tail dependence characteristics, so we need to choose
the copula that most adequately represents the dependence structure of gold and the USD exchange rate. For the AIC adjusted for
small-sample bias, the Student-t copula offered the best performance for all the exchange rates, except for CAD and JPY where
the symmetrized Joe-Clayton copula and the time-varying Gaussian copula, respectively, performed better.7 Hence: (a) Hypothesis
1 cannot be rejected since the correlation coefficient is significant
and positive for the whole sample period, meaning that gold is a

hedge against the USD (when the USD value falls/the USD exchange
rate rises, the gold price rises and vice versa); (b) Hypothesis 2 cannot be rejected for both kL and kU because the Student-t copula
exhibits upper and lower tail dependence, so gold is a safe haven
against USD movements.
However, the results for Hypothesis 2 were slightly different for
the CAD and the JPY. For the CAD, lower tail dependence was significant, although not upper tail dependence, indicating gold as a
strong safe haven against the USD-CAD exchange rate in market
downturns, but not in market upturns. For the JPY, there was tail
independence since the Gaussian copula was preferred, meaning
that market movements between gold and the JPY were independent under extreme market circumstances.
5. Implications for risk management
Evidence regarding strengthened gold prices and USD depreciation presented above through copulas is crucially relevant for currency investors hedging their exposure to currency price
movements and downside risk. The portfolio implications were
7
Similar results were obtained using the goodness of fit test proposed by Genest
et al. (2009). They are available on request.


2671

J.C. Reboredo / Journal of Banking & Finance 37 (2013) 2665–2676
Table 2
Empirical copula for gold and USD exchange rate returns.
Gold-AUD

Gold-CAD

Gold-EUR

Gold-GBP

Gold-JPY

Gold-NOK

Gold-CHF

Gold-TWEXB

22
16
10
4
4
2
0
2
1
6
23
11
6
5
3
6
1
3
3
6
22

12
9
7
2
4
2
2
3
4
20
11
8
4
4
4
3
5
5
3
15
16
6
7
7
4
4
2
4
2
30

9
7
6
3
4
1
1
3
3
27
12
10
7
3
1
0
2
2
3
21
12
7
8
4
4

14
10
10
10

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

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

4
4
9
2
5
3
19
10
8
8
8
1

8
8
11
9
5
5
7
5
6
2
6
11
10
8
10
5
4

5
4
3
9
9
12
10
9
0
7
2
6
2
9
11
12
9
3
3
8
1
5
5
9
4
10
7
9
6
8

5
3
5
8
8
8
9
7
6
7
2
7
4
7
13
6
12
6
5
3
5
5
4
5
9
17
9
6
4

6
12
5
12
9
2
6
3
5
6
6
10
4
8
9
7
8
7
4
3
4
9
5
12
9
6
6
5
7
3

7
9
9
5
5
11
7
4
2
7
1
6
10
11
9
6
5
5
6
7
10
11
6
11
5
7
6
4
2
4

9
6
11
6
8
4
7
7
4
4
5
12
7
8
4
11

6
6
9
4
6
11
5
7
8
4
5
7
6

10
11
9
4
1
7
6
8
9
9
4
4
12
6
5
4
5
5
5
4
10
8
9
10
3
8
4
6
8
8

5
5
5
9
7
8
5
1
6
6
8
10
7
7
5
11
5
3
6
8
10
6
11
10
2
7
3
9
6
6

12
9
6

3
2
7
11
6
7
8
9
6
8
4
6
9
11
6
5
7
8
6
5
2
5
8
7
9
10

7
7
6
6
4
5
7
9
9
7
6
8
6
6
6
7
5
5
7
10
9
3
6
9
4
5
7
7
10
6

9
12
3
4
2
7
7
5
7
13
6
8
4
8
2
6
9
5
11
7

3
4
3
4
7
10
11
8
8

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

7
2
6
6
5
3
5
9
11
9
10
4
5
8
6
5
6
5
11
10
6
1
6
4
7
16
4
7
8
5

8
1
4
6
7
7
10

3
4
5
5
14
6
6
9
7
7
4
6
6
4
4
7
10
7
11
7
2
2

3
5
6
9
6
11
12
10
2
5
2
6
10
11
7
10
6
7
6
1
5
4
10
11
8
8
8
5
0
8

4
3
8
9
8
11
5
10
5
3
5
8
5
11
9
9
7
4
2
4
3
4
7
7

1
0
4
3
4

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

7
8
12
10
6
3
5
5
7
5
11
7
10
4
9
0
0
3
8
9
10
7
7
8
14
0
3
4
2
4

7
7
12
13
14
1
0
3
3
3
14

1
4
2
4
7
8
5
9
13
14
1
5
2
3
1
11
5
11

14
14
1
2
2
2
9
9
8
8
11
15
1
3
3
3
7
5
5
11
11
18
11
5
3
3
6
2
3
10

13
11
0
3
2
2
6
7
8
8
15
16
1
0
0
3
7
7
8
11
14
16
2
3
0
2
7
3

2

4
0
5

5
2
2
3

7
2
4
3

6
2
7
4

6
3
6
3

9
6
6
6

4

13
9
5

12
8
13
6

8
16
4
14

7
10
15
18

Notes: For each series there are 663 observations. Gold returns are ranked along the
horizontal axis and in ascending order (from top to bottom) and oil returns are
ranked along the vertical axis and in ascending order (from left to right). Each box
includes the number of observations that belongs to the respective quantiles of the
gold and oil series.

considered in order to determine whether the use of gold could reduce currency-related risks and losses. Hence, to evaluate the
attractiveness of gold in terms of currency risk management, we
considered different kind of portfolios against a benchmark portfolio, called portfolio 1, composed only of currency.
First, we considered a portfolio, called portfolio 2, obtained by
minimizing the risk of a currency-gold portfolio without reducing

the expected return. According to Kroner and Ng (1998), the optimal weight of gold in portfolio 2 at time t is given by:
C

xGt ¼

GÀC

ht À ht
G

GÀC

ht À 2ht

C

þ ht

;

ð13Þ

under the restriction that xGt ¼ 1 if xGt > 1 and xGt ¼ 0 if xGt < 0
G
C
GÀC
and where ht , ht , and ht
are the conditional volatility of gold,
the conditional volatility of currency and the conditional covariance
between gold and currency at time t, respectively. By construction,

À
Á
the weight of the currency in the portfolio is equal to 1 À xGt . The
optimal portfolio at each time t resulted from using the relevant
information in Eq. (13) from the ARMA-TGARCH model and the best
copula model fit (the Student-t copula for most of the exchange
rates). Second, we considered an equally weighted portfolio called
portfolio 3, with good out-of-sample performance according to
DeMiguel et al. (2009). Third, we considered a hedged portfolio
called portfolio 4, obtained from a variance minimization hedging
strategy consisting of holding a short position of an amount of b futures and a long position in the spot market (see Hull, 2011). We
considered a long position of one USD on the currency market
hedged by a short position of b USD on the gold market, given by:
GÀC

bt ¼

ht

G

ht

ð14Þ

:

The risk reduction effectiveness of each portfolio was evaluated
by comparing the percentage reduction in the variance of a portfolio with respect to portfolio 1:

REv ariance ¼ 1 À

VariancePortfolio j
;
VariancePortfolio 1

ð15Þ

where j = 2, 3, 4 and variancePortfolio j and variancePortfolio 1 are variances in the returns for the portfolio j and portfolio 1, respectively.
A higher risk reduction effectiveness ratio means greater variance
reduction. Table 6 reports the risk reduction effectiveness results
for gold and currency portfolios 2–4 by considering different currencies with respect to the USD. The results indicate consistent risk
reduction effectiveness for gold in portfolios 2 and 4, where weights
were obtained optimally. However, when the weights were not derived optimally (i.e., they were determined exogenously and maintained constant over time), as happened with portfolio 3, there were
no gains from including gold in the portfolio. This evidence was
common to the different currencies, with generally better results
for portfolio 4 than for portfolio 2 (with the exception of the CAD
and the JPY). These results confirm the usefulness of gold in reducing risk in a currency portfolio.


2672

J.C. Reboredo / Journal of Banking & Finance 37 (2013) 2665–2676

Table 3
Estimates of the marginal distribution models for gold and exchange rate returns.

Mean
/0

GOLD

AUD

CAD

EUR

GBP

JPY

NOK

CHF

TWEXB

0.003
(3.99)⁄

0.002
(2.77)⁄

0.001
(1.88)

0.001
(1.21)

0.000
(0.678)

0.000
(0.42)

0.001
(1.12)

0.001
(1.80)

0.001
(1.453)

0.000
(1.97)⁄
0.192
(3.22)⁄
0.852
(20.14)⁄
À0.145
(À2.46)⁄
12.369
(2.45)⁄
1531.8
17.20
[0.64]
0.88
[0.61]

0.000
(2.45)⁄
0.083
(1.28)
0.782
(11.77)⁄
0.062
(0.97)
7.102
(3.88)⁄
1763.9
24.89
[0.21]
0.74
[0.78]

0.000
(2.11)⁄
0.121
(2.71)⁄
0.882
(28.84)⁄
0.036
(0.49)
12.468
(2.29)⁄
2028.6
17.68
[0.34]

1.37
[0.23]

0.000
(1.46)
0.037
(1.28)
0.921
(29.94)⁄
0.030
(0.96)
26.780
(1.18)
1885.8
20.85
[0.41]
1.08
[0.36]

0.000
(2.36)⁄
0.082
(1.66)
0.835
(12.19)⁄
0.030
(0.61)
19.993
(1.48)
1967.6

10.30
[0.96]
1.12
[0.32]

0.000
(2.45)⁄
0.009
(0.22)
1.017
(3.19)⁄
À0.113
(À2.80)⁄
18.977
(1.85)
1900.5
26.74
[0.14]
1.25
[0.23]

0.000
(1.75)
0.001
(0.02)
0.927
(24.16)⁄
0.057
(1.97)⁄
16.901

(1.73)
1792.2
20.25
[0.44]
0.19
[0.99]

0.000
(1.63)
0.119
(2.40)⁄
0.846
(11.91)⁄
À0.090
(À1.76)
16.134
(2.48)⁄
1843.3
21.67
[0.35]
0.59
[0.92]

0.000
(1.64)
0.065
(1.69)
0.897
(21.92)⁄
À0.006

(À0.17)
22.094
(1.24)
2116.1
16.70
[0.67]
1.20
[0.24]

Variance

x

a1
b1
k
Tail
LogLik
LJ
ARCH

Notes: This table reports the ML estimates and z statistic (in brackets) for the parameters of the marginal distribution model defined in Eqs. (9)–(11). The lags p, q, r and m
were selected using the AIC for different combinations of values ranging from 0 to 2. For the JPY series a TGARCH (2,2) specification was selected (reported values are for the
first lag). LogLik is the log-likelihood value. LJ is the Ljung–Box statistic for serial correlation in the model residuals computed with 20 lags. ARCH is Engle’s LM test for the
ARCH effect in the residuals up to 10th order. P values (in square brackets) below 0.05 indicate rejection of the null hypothesis.
⁄
Indicates significance at the 5% level.

Table 4
Goodness-of-fit test for the marginal distribution models.

First moment
Second moment
Third moment
Fourth moment
K–S test
C–vM test
A–D test

GOLD

AUD

CAD

EUR

GBP

JPY

NOK

CHF

TWEXB

0.290
0.441
0.407

0.165
0.750
0.679
0.735

0.182
0.627
0.325
0.592
0.399
0.302
0.123

0.193
0.635
0.393
0.115
0.383
0.416
0.438

0.600
0.600
0.443
0.715
0.837
0.719
0.664

0.990

0.255
0.944
0.164
0.444
0.511
0.360

0.231
0.586
0.130
0.601
0.974
0.941
0.791

0.584
0.979
0.521
0.994
0.174
0.144
0.081

0.766
0.303
0.487
0.496
0.655
0.450
0.498

0.540
0.138
0.790
0.163
0.266
0.252
0.204

Notes: This table reports the p values for the LM statistic for the null of no serial correlation for the first four moments of the variables ut and vt from the marginal models
^t À u
 Þk and ðv
^t À v
 Þk are regressed on 20 lags for both variables for k = 1, 2, 3, 4 and the LM statistic is distributed as v2(20) under the null. P
presented in Table 4, where ðu
values below 0.05 indicate rejection of the null hypothesis that the model is correctly specified. K–S, C–vM and A–D denote the Kolmogorov–Smirnov, Cramer–von Mises and
Anderson–Darling tests (for which p values are reported) for the adequacy of the distribution model.

In addition, we evaluated the usefulness of gold in providing
protection against downside risk and possibly dangerous tail-risk
events, by estimating the VaR of a portfolio composed of gold
and currencies. The VaR is defined as the maximum loss in portfolio value for a given time period and a given confidence level. The
VaR at time t for an asset or a portfolio with a return rt is characterized, for a (1 À p) confidence level, as:

Prðr t 6 VaRt jwtÀ1 Þ ¼ p;

ð16Þ

where wtÀ1 is the information set at t À 1. So, the VaR is simply the
loss associated with the pth percentile of the returns distribution for

a given period. It can be computed as:

pffiffiffiffiffi
VaRt ðpÞ ¼ lt À t À1
t ðpÞ ht ;

ð17Þ

ES ¼ E½r t jr t < VaRt ðpފ:

ð18Þ

pffiffiffiffiffi
where lt and ht are the conditional mean and standard deviation
for the asset returns and where t À1
t ðpÞ denotes the p quantile of the
Student-t distribution with t degrees of freedom, since gold and exchange rate returns followed this distribution.
A risk measure related to VaR is the expected shortfall (ES), defined as the expected size of the loss if the VaR is exceeded, that is:

Given a portfolio composed of gold and currencies, we compute
the single-period log returns as:


À
Á C
G
rt ¼ log xGt ert þ 1 À xGt ert ;

ð19Þ

where r Gt ; r Ct and xGt are the continuously compounded log-returns
for gold, for the currencies and for the fraction of the portfolio invested in gold, respectively. We used Monte Carlo simulation to calculate the portfolio VaR and ES from the marginal distribution
functions and the copula function information as follows: (1) from
estimated copula functions we simulated two innovations for each
time t; (2) we transformed these simulated values into standardized
residuals by inverting the marginal cumulated distribution function
for each index; and (3) we used the simulated standardized residuals to compute gold and currency returns from the estimated marginal models and, for given portfolio weights, computed the
portfolio returns in Eq. (19). We repeated this process 1000 times
for t = 1, . . . , T. The VaR was obtained as the value of the pth percentile in the distribution of the portfolio returns. The ES was measured
as the mean value for situations in which portfolio returns exceeded
the VaR.
We evaluated downside risk gains as follows. First, the accuracy
of the VaR for each portfolio was tested using the likelihood ratio
test of correct conditional coverage proposed by Christoffersen
(1998), which takes independence and unconditional coverage into
account (see, e.g., Jorion, 2007). Second, we considered the VaR and
ES reductions for portfolios 2–4 compared to those for portfolio 1.


2673

J.C. Reboredo / Journal of Banking & Finance 37 (2013) 2665–2676

1.5

Density

Density

1.5

1.0

1.0

0.5

0.5

0.8

0.4
0.2

0.2

0.8

0.6

0.6

0.4

AUD

0.8

0.8

0.6

CAD

Gold

0.6

0.4

0.4
0.2

Gold

0.2

1.4
1.2

Density

Density

1.5
1.0

1.0
0.8
0.6
0.4

0.5

0.2
0.8

0.8

y

0.6

0.4

0.4
0.2

0.2

0.8

0.6

0.8

0.6

y

0.6

0.4
0.2

x

0.4
0.2

x

1.4

1.5

Density

Density

1.2
1.0
0.8
0.6

1.0
0.5

0.4

0.8

0.8

JPY

NOK

0.6

0.4
0.2

0.4
0.2

0.8

0.6

0.8

0.6

0.6

0.4
0.2

Gold

0.4
0.2

Gold

2.0
1.5

Density

Density

1.5
1.0

1.0
0.5

0.5

0.8

0.8
0.8

0.6

CHF

0.6

0.4
0.2

0.4
0.2

Gold

0.8

0.6

TWEXB

0.6

0.4

0.4
0.2

0.2

Fig. 2. Empirical non-parametric density estimates for gold and the USD exchange rates.

Gold


2674

J.C. Reboredo / Journal of Banking & Finance 37 (2013) 2665–2676

Table 5
Estimates for the copula models.

Gaussian

q
AIC

Student-t

q
t
AIC

Clayton

a

Gumbel

AIC
d

SJC

AIC
kU

kL
AIC

TVP
Gaussian

w0
w2
w1
AIC

TVP
Student-t

w0
w2
w1
AIC

AUS

CAD

EUR

GBP

JPY

NOK

CHF

TWEXB

0.455
(0.028)⁄
À150.04
0.475
(0.030)⁄
9.433
(3.515)⁄
À158.91
0.6187
(0.063)⁄
À137.748
1.423
(0.043)⁄
À133.83
0.200
(0.067)⁄
0.308
(0.041)⁄
À147.92
2.041
(0.191)⁄
0.386
(0.097)⁄
À2.564
(0.082)⁄

À148.78
1.796
(1.069)
0.107
(0.148)
À1.821
(2.284)
À150.28

0.375
(0.031)⁄
À97.95
0.382
(0.032)⁄
11.701
(4.783)⁄
À101.21
0.5072
(0.061)⁄
À96.744
1.295
(0.039)⁄
À77.39
0.091
(0.064)
0.263
(0.043)⁄
À102.29
À0.015
(0.116)

À0.016
(0.031)
2.166
(0.296)⁄
À94.35
0.305
(0.960)
À0.023
(0.071)
1.318
(2.511)
À91.16

0.446
(0.028)⁄
À143.73
0.477
(0.029)⁄
10.268
(3.169)⁄
À155.94
0.5575
(0.062)⁄
À121.133
1.430
(0.045)⁄
À131.95
0.229
(0.059)⁄
0.264

(0.046)⁄
À136.82
À0.037
(0.043)
À0.063
(0.024)⁄
2.321
(0.077)⁄
À144.16
1.841
(0.919)⁄
0.080
(0.121)
À1.849
(1.912)
À144.52

0.402
(0.030)⁄
À114.13
0.415
(0.031)⁄
11.352
(4.612)⁄
À117.39
0.5126
(0.061)⁄
À97.914
1.345
(0.041)⁄

À100.67
0.184
(0.062)⁄
0.240
(0.046)⁄
À110.72
0.512
(0.759)
À0.079
(0.136)
0.944
(1.777)
À110.69
0.244
(0.678)
À0.045
(0.080)
1.611
(1.541)
À108.97

0.225
(0.036)⁄
À32.15
0.248
(0.036)⁄
11.000
(4.672)⁄
À36.40
0.3263

(0.058)⁄
À38.048
0.144
(0.032)⁄
À21.99
0.000
(0.004)
0.177
(0.054)⁄
À34.75
0.752
(0.157)⁄
0.853
(0.159)⁄
À2.142
(0.037)⁄
À40.75
0.596
(0.283)⁄
0.336
(0.156)⁄
À0.884
(1.114)
À30.29

0.484
(0.026)⁄
À173.22
0.489
(0.028)⁄

18.841
(13.751)
À173.43
0.6416
(0.063)⁄
À149.244
1.448
(0.044)⁄
À152.11
0.258
(0.058)⁄
0.301
(0.044)⁄
À166.54
0.033
(0.343)
0.032
(0.062)
2.085
(0.743)⁄
À169.70
1.023
(0.440)⁄
0.014
(0.108)
À0.028
(0.902)
À159.59

0.480

(0.027)⁄
À170.60
0.490
(0.024)⁄
15.082
(6.974)⁄
À171.74
0.6887
(0.067)⁄
À143.576
1.424
(0.043)⁄
À146.77
0.219
(0.059)⁄
0.331
(0.043)⁄
À160.10
0.132
(0.230)
0.113
(0.084)⁄
1.799
(0.527)⁄
À169.18
0.086
(0.268)
0.043
(0.049)
1.933

(0.594)⁄
À160.26

0.505
(0.025)⁄
À191.69
0.519
(0.027)⁄
9.989
(1.068)⁄
À197.53
0.7007
(0.066)⁄
À160.461
1.491
(0.046)⁄
À173.57
0.296
(0.056)⁄
0.311
(0.047)⁄
À182.20
2.295
(0.212)⁄
0.356
(0.195)
À2.647
(0.105)⁄
À189.68
0.319

(1.278)
À0.031
(0.069)
1.635
(2.421)
À188.92

Notes: The table shows the ML estimates for the different copula models for gold and the USD. Standard error values (in brackets) and the AIC values adjusted for smallsample bias are provided for the different copula models. The minimum AIC value (for gold) indicates the best copula fit. For the TVP Gaussian and Student-t copulas, q in Eq.
(7) was set to 10.
⁄
Indicates significance at the 5% level.

Table 6
Risk reduction effectiveness for gold and currency portfolios.

Portfolio 2
Portfolio 3
Portfolio 4

AUD

CAD

EUR

GBP

JPY

NOK

CHF

TWEXB

0.113
À0.071
0.226

0.152
À0.006
0.146

0.112
À0.073
0.228

0.137
À0.029
0.172

0.217
0.087
0.062

0.108
À0.081
0.239

0.108

À0.082
0.240

0.098
À0.102
0.269

Notes: This table reports the results of risk reduction effectiveness for portfolios composed of gold and currencies with respect to a portfolio composed only of currencies
according to the risk effectiveness ratio in Eq. (15). Portfolio 2 weights are given by Eq. (13), portfolio 3 has equal weights and portfolio 4 weights are given by Eq. (14).

Third, we considered a VaR-based investor loss function (see Sarma
et al., 2003; Reboredo, 2013b; Reboredo et al., 2012) given by:

lt ¼ E½r t À VaRt ðpފ2 1frt ÀVaRt ðpÞg ;

ð20Þ

where 1 is the usual indicator function and where the quadratic term
takes into account the magnitude of the failure, penalizing large
deviations more than small deviations. We compared portfolios 2–
1

4 with portfolio 1 considering the loss differential, zt ¼ lt À lt . We
tested the null of a zero median loss differential against the alternative of a negative median loss differential by employing the oneP

T
À0:5
. This
sided sign test defined as: S ¼
t¼1 1fzt P0g À 0:5T ð0:25TÞ

test was asymptotically distributed as a standard normal and the null
could be rejected when S < À1.645.
Table 7 reports the risk evaluation results for a 99% confidence
level using the best fitting copula, the Student-t copula (with the
exception of the CAD and the JPY).8 The conditional coverage test
8
For reasons of brevity, we do not report the results for 95% and 99.9%. They are,
however, available on request.

indicated that portfolios composed of gold and currencies performed
equally well in terms of the VaR, since the null of correct conditional
coverage was not rejected at the 5% significance level, except for
portfolio 2 with the JPY and portfolio 3 with the AUD. Conditional
coverage results for portfolio 1 were less positive, since half of the
currency portfolios did not have correct conditional coverage at
the 5% significance level, although they did at 10% (with the exception of the EUR). By examining the effect of the VaR reduction of
including gold in the currency portfolio, we found evidence of VaR
reduction only in the portfolios configured for optimal weights.
Hence, the expected maximum loss in portfolio value was greater
in the currency portfolios than in the mixed gold and currency portfolios. Consistent with the increase in average risk reported above,
there was no reduction in VaR for the equally weighted portfolio.
The ES was also reduced for portfolios 2 and 3, and was, in general,
slightly larger for portfolio 4. Finally, evidence provided by the onesided sign test indicated that the optimal weight and equally
weighted portfolios outperformed the currency portfolio. These results support the usefulness of including gold in a currency portfolio
for risk management purposes.


2675

J.C. Reboredo / Journal of Banking & Finance 37 (2013) 2665–2676

Table 7
Downside risk evaluation for gold and currency portfolios.
AUD

CAD

EUR

GBP

JPY

NOK

CHF

TWEXB

Portfolio 1
Cond. cov.
ES
Portfolio 2
Cond. cov.
VaR reduc.
ES
Sign Test

0.909
À0.018

0.593
À0.019

0.045
À0.017

0.075
À0.017

0.077
À0.017

0.114
À0.018

0.113
À0.018

0.075
À0.017

0.921
0.004
À0.014
À25.50

0.395
0.004
À0.012
À25.34

0.112
0.003
À0.015
À25.34

0.112
0.004
À0.013
À25.34

0.064
0.006
À0.011
À25.11

0.395
0.003
À0.015
À25.42

0.398
0.003
À0.015
À25.42

0.112
0.003
À0.015
À25.50

Portfolio 3
Cond. Cov.
VaR Reduc.
ES
Sign Test

0.024
À0.002
À0.006
À25.57

0.781
0.000
À0.007
À25.42

0.915
À0.001
À0.007
À25.34

0.921
À0.001
À0.008
À25.34

0.186
0.002
À0.008

À25.26

0.781
À0.002
À0.007
À25.42

0.781
À0.002
À0.007
À25.42

0.921
À0.002
À0.007
À25.34

Portfolio 4
Cond. Cov.
VaR Reduc.
ES
Sign Test

0.915
0.006
À0.026
À25.18

0.238
0.004

À0.018
À25.11

0.238
0.005
À0.024
À25.11

0.238
0.004
À0.022
À25.11

0.238
0.001
À0.018
À25.18

0.238
0.006
À0.023
À25.11

0.238
0.006
À0.023
À25.11

0.131
0.007

À0.023
À25.03

Notes: This table reports the results for downside risk gains for portfolios composed of gold and currencies with respect to a portfolio composed only of currencies (portfolio
1). Portfolio 2 weights are given by Eq. (13), portfolio 3 has equal weights and portfolio 4 weights are given by Eq. (14). Cond. Cov. indicates the p values for the conditional
coverage test. VaR Reduc. is the reduction in the VaR portfolio with respect to portfolio 1 (positive values indicate VaR reduction). ES is the expected shortfall. The sign test is
the one-sided sign test for differences in the loss function for portfolios 2–4 compared to portfolio 1.

6. Conclusions
The combination of strengthened gold prices and USD depreciation opens up the possibility of using gold as a hedge against currency movements and as a safe haven asset. In this paper, we
contribute to research into gold-USD exchange rate dependence
by studying the role of gold as a hedge or safe-haven asset against
USD depreciation using copulas to analyse the dependence structure in terms of average and tail dependence information.
Using a wide set of currencies, we applied different copula functions to weekly data for the period January 2000–September 2012.
Empirical evidence revealed positive and significant dependence between gold and USD depreciation against different currencies, implying that gold can hedge against USD movements. Moreover,
symmetric tail dependence obtained from the Student-t copula indicated that gold can act as an effective safe haven in periods of extreme USD market movements. We considered the practical
implications of this result regarding gold-USD depreciation interdependence for risk hedging and downside risk. Our results for different portfolios composed of gold and currencies indicated the risk
reduction effectiveness of gold for portfolios where weights were obtained optimally (by a risk minimization or variance minimization
hedging strategy), which was common across different currencies.
Likewise, we showed that a portfolio composed of both gold and currencies experienced VaR and ES reductions and performed better on
the basis of a VaR investor’s loss function. These results confirm the
usefulness of gold in the risk-management of a currency portfolio.
Acknowledgements
We would like to thank an anonymous reviewer for their constructive and helpful comments. Any remaining errors are entirely
our own responsibility. Financial support provided by the Xunta de
Galicia under research Grant INCITE09201042PR and by the Spanish Ministry of Education under research Grant MTM2008-03010 is
gratefully acknowledged.
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