Journal of Banking & Finance 37 (2013) 2665–2676 Contents lists available at SciVerse ScienceDirect 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 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 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: juancarlos.reboredo@usc.es 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 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) 0378-4266/$ - see front matter Ó 2013 Elsevier B.V All rights reserved http://dx.doi.org/10.1016/j.jbankfin.2013.03.020 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 2666 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 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 we outline the methodology and test our hypothesis In Sections and we present data and results, respectively, and we discuss the implications in terms of portfolio risk management in Section Finally, Section concludes the paper 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 u, V 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 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 F À1 X ðuÞjY 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 [0, 1] Two random variables exhibit lower (upper) tail dependence if kL > (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 For an introduction to copulas, see Joe (1997) and Nelsen (2006) For an overview of copula applications to finance, see Cherubini et al (2004) 2667 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 : qG;C P 0ðgold is a hedgeÞ; Hypothesis : kU > 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 not find evidence against Hypothesis Similarly, if Hypothesis 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 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 = 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 À q= 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 = 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; 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 À À ½1 À ð1 À uÞj ŠÀc ÉÀ1=c 1=j ; þ½1 À ð1 À v Þj ŠÀc À ð6Þ where j = 1/log2(2 À kU), c = À1/log2(kL), and kL (0, 1), kU (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 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 = 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 Under standard regularity conditions, this two-step estimation is consistent and the parameter estimates are asymptotically efficient and normal (see Joe, 1997) 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 2668 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) Data We empirically investigated the hedge and safe-haven properties of gold against the USD using weekly data from 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 (http://www.bankofengland.co.uk) 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 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 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 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  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  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 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 are fully consistent with the positive dependence shown by the unconditional correlation coefficient displayed in Table 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 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 and 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 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, and used ðv J.C Reboredo / Journal of Banking & Finance 37 (2013) 2665–2676 Fig Gold prices and USD exchange rates (7 January 2000–21 September 2012) 2669 2670 J.C Reboredo / Journal of Banking & Finance 37 (2013) 2665–2676 Table 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⁄ 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 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 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) u(2) Á Á Á u(T) and v(1) v(2) Á Á Á v(T) are the order statistics of the univariate samples and where 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 and has, obviously, implications for the role of gold as a safe-haven asset (discussed below) Table 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 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 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 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 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 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 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 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 2 23 11 6 3 22 12 2 20 11 4 5 15 16 7 4 30 1 3 27 12 10 2 21 12 4 14 10 10 10 4 14 10 6 2 15 10 12 6 2 13 10 13 6 8 12 5 10 11 15 12 10 11 4 19 10 8 8 11 5 6 11 10 10 5 9 12 10 9 11 12 3 5 10 5 8 7 7 13 12 5 5 17 6 12 12 6 10 4 12 6 7 9 5 11 7 10 11 5 10 11 11 4 11 7 4 12 11 6 11 10 11 9 4 12 5 5 10 10 8 5 6 10 7 11 10 11 10 6 12 11 9 11 5 10 7 6 9 6 5 10 9 7 10 12 7 13 8 11 4 10 11 8 9 10 12 9 11 11 7 11 7 6 5 11 10 6 11 10 6 16 8 7 10 5 14 6 7 6 4 10 11 2 11 12 10 10 11 10 10 11 8 8 11 10 5 11 9 4 7 4 11 14 10 11 10 10 10 11 4 13 15 5 7 12 10 5 11 10 0 10 7 14 4 7 12 13 14 3 14 4 13 14 11 11 14 14 2 9 8 11 15 3 5 11 11 18 11 3 10 13 11 2 8 15 16 0 7 11 14 16 5 2 7 6 6 13 12 13 16 14 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 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 if xGt > and xGt ¼ if xGt < 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 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 À VariancePortfolio j ; VariancePortfolio ð15Þ where j = 2, 3, and variancePortfolio j and variancePortfolio are variances in the returns for the portfolio j and portfolio 1, respectively A higher risk reduction effectiveness ratio means greater variance reduction Table 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 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 than for portfolio (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 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 to 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 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, 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 VaRt jwtÀ1 Þ ¼ p; ð16Þ where wtÀ1 is the information set at t À 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 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 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 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 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 Risk reduction effectiveness for gold and currency portfolios Portfolio Portfolio Portfolio 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 weights are given by Eq (13), portfolio has equal weights and portfolio 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 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– with portfolio 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 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 For reasons of brevity, we 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 with the JPY and portfolio with the AUD Conditional coverage results for portfolio 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 and 3, and was, in general, slightly larger for portfolio 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 Downside risk evaluation for gold and currency portfolios AUD CAD EUR GBP JPY NOK CHF TWEXB Portfolio Cond cov ES Portfolio 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 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 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 weights are given by Eq (13), portfolio has equal weights and portfolio 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 (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 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 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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... whether gold can serve as a hedge or as a safe haven against USD depreciation: Hypothesis : qG;C P 0 gold is a hedge ; Hypothesis : kU > gold is a safe haven ; where qG,C is the measure of average... 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