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Quantitative Finance

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Hedges or safe havens—revisit the role of gold andUSD against stock: a multivariate extended skew-tcopula approach

Chung-Shin Liu, Meng-Shiuh Chang, Ximing Wu & Chin Man Chui

To cite this article: Chung-Shin Liu, Meng-Shiuh Chang, Ximing Wu & Chin Man Chui (2016):Hedges or safe havens—revisit the role of gold and USD against stock: a multivariate extendedskew-t copula approach, Quantitative Finance

To link to this article: http://dx.doi.org/10.1080/14697688.2016.1176238

Published online: 24 May 2016.

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Hedges or safe havens—revisit the role of goldand USD against stock: a multivariate extended

skew-t copula approach

CHUNG-SHIN LIU†, MENG-SHIUH CHANG‡*, XIMING WU§,¶ and CHIN MAN CHUI‖

†School of Finance, Southwestern University of Finance and Economics, Sichuan 611130, China‡Institute of Poyang Lake Eco-economics, Jiangxi University of Finance and Economics, Nanchang 330013, China

§Department of Agricultural Economics, Texas A&M University, College Station, TX 77840, USA¶School of Economics, Xiamen University, Fujian 361005, China

‖Institute for Financial and Accounting Studies, Xiamen University, Fujian 361005, China

(Received 18 March 2015; accepted 31 March 2016; published online 24 May 2016)

Our paper concerns the question of whether there exist hedge assets during extreme marketconditions, which has become increasingly important since the recent financial crisis. This paperdevelops a novel extended skew-t copula model to examine the effectiveness of gold and USdollar (USD) as hedge or safe haven asset against stock prices for seven developed markets overthe 2000–2013 period. Our results indicate the existence of skewness and heavy/thin tails in thedistributions of all three types of assets in most of the developed markets, lending support to theemployment of flexible distributions to evaluate the tail dependences among assets. We find thatUSD is preferred to gold as a hedge asset during normal market conditions, while both assetscan serve as safe haven assets for most countries when stock markets crash. Our simultaneousanalysis of the three assets advises against a joint hedge strategy of gold and USD due to thehigh tail dependence between them during extreme market conditions. This result highlights theimportance of simultaneous modelling of multiple assets in financial risk analysis.

Keywords: Gold; USD; Extended skew-t copula; Hedge; Safe haven

JEL Classification: C13, G11, G14

1. Introduction

The past two decades have seen a tremendous growth infinancial markets and financial instruments in terms of theirvolume, value and scope. At the same time, many extrememarket conditions, such as the Internet bubble, the subprimecrisis and the European debt crisis, have reminded investorsof the importance of risk management. Traditionally, schol-ars in the asset-pricing or other finance areas tend to thinkof risk as systematic, given a well-diversified portfolio, dueto co-movement with the general market conditions. Thus,in practice, the most common tools to hedge for theseco-movements are derivatives, such as options and futures,and some Greek hedging strategies, such as delta andgamma hedging, have been widely applied to control formarket risk.

However, the recent relatively high frequency of extremeevents highlights the need for tools to hedge the risk underthese extremely severe market conditions. According toBaur and Lucey (2010), an asset is classified as a hedgeasset if it is unrelated or negatively related to another assetduring normal market movements, while it is called a safehaven if it is unrelated or negatively related to another assetin times of extreme market movements. Their definitions,which we follow throughout this paper, clearly distinguishthe hedging roles under normal market conditions and safehaven roles under extreme market conditions. Becauseregional and global financial crises have occurred more fre-quently in recent times, the search for safe haven assets hasbecome an important topic in international finance. Under-standing the value changes of the overall portfolios byincluding safe haven assets during extreme financial situa-tions is especially important for investors and financialinstitutions to protect their total investment values and for

*Corresponding author. Email: mslibretto@hotmail.com

© 2016 Informa UK Limited, trading as Taylor & Francis Group

Quantitative Finance, 2016http://dx.doi.org/10.1080/14697688.2016.1176238

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scholars to understand the comovement of asset returns dur-ing extreme market conditions.

To further investigate this problem, we develop a multi-variate extended skew-t (MEST) copula model to examinethe joint dependence and asymmetric tail dependenceamong different assets. We use the proposed model toexamine the effectiveness of gold and its competitor, USdollar (USD), as a hedge or safe haven against stock returnsfor seven developed markets over the 2000–2013 period,when Euros have been adopted as the unified currency inthe European Union (EU) and when many financial criseswere experienced. Although the commonly used normalityassumption of asset return distributions is simple, thisassumption has empirically been shown to be unrealisticbecause the skewness and excess kurtosis of return distribu-tions are usually non-zero (Campbell et al. 1997). Thisproblem will be especially crucial when we want to investi-gate asset performance during extreme market conditions.

Historically, many non-normal distributions have beenexamined to better describe the dynamics of asset returns.†Copula functions with non-normal distribution assumptionsare commonly used in finance, especially in the risk man-agement area.‡ However, so far, none of the previously pro-posed models can allow for a thin-tailed distribution orpreserve closed-form solutions under conditioning. Theadvantages of preserving a closed-form under conditioningare bifold. First, this property can facilitate theoreticaldevelopment of multivariate analysis such as the vine cop-ula and multivariate tail dependence functions. Second, thisproperty can mitigate the complexity of evaluation of condi-tional distributions. From our empirical analysis, we findthat the MEST copula is able to capture asymmetric depen-dence in a parsimonious way. Importantly, it accommodatesstrong asymmetric tail dependence among the assets. Thesignificant shape and extension parameters in the MESTcopula indicate the existence of skewness and heavy/thintails in most of the markets, justifying the merits of the pro-posed model. When estimated together with the skew-t (ST)copula model in terms of evaluating the lower tail depen-dence coefficients, our results demonstrate the advantagesof our proposed model over the ST model because thelower tail dependence coefficients by the ST copula modelare systematically overestimated. Moreover, we extend thebivariate copula analysis on the effectiveness of hedges andsafe havens to a multivariate case. Previous studies analysedtwo assets at a time without considering the structure of thejoint distribution and the influence of other assets, and wehave shown that without considering the effects of otherassets, the estimated tail dependences can be misinterpreted.To the best of our knowledge, this is the first study tomodel three assets jointly and investigate the hedge andsafe haven issue through non-normal distribution estima-tions at the same time.

Our empirical results demonstrate that the fundamentalfactors that drive hedging during normal times and those

that drive hedging during extreme market periods can bedifferent. Specifically, we find that gold serves, at best, as aweak hedge asset against stock market performance for allseven studied countries, but USD can possibly serve as astrong hedge asset for Canada and Australia under normalmarket conditions. This set of results is generally consistentwith the Pearson’s correlation commonly used in the litera-ture. During a stock market crisis, gold can serve as a weaksafe haven asset for all countries except Switzerland and asa strong safe haven asset for the USA, the UK andGermany. On the other hand, USD can serve as a weak safehaven asset for almost all countries, with the exception ofSwitzerland and Australia, and as a strong safe haven assetfor the UK, Germany, Japan and Australia. When an alter-native investment such as gold and USD serves as a hedgeasset for investors, it is not necessary that it also serve as asafe haven asset for the same group of investors, and viceversa. We attribute this finding to the theoretical foundationthat both assets can serve as a hedge against inflation fluc-tuations under normal market conditions, as suggested byJaffe (1989) and McCown and Zimmerman (2007), but theflight-to-quality hypothesis suggested by Caballero andKrishnamurthy (2008) may drive the safe haven effects ofthese investments under extreme market conditions.

To further test whether the safe haven roles of theseassets are jointly or independently determined, we use ourmultivariate model to analyse whether gold (USD) can actas a hedge or safe haven against stocks when USD (gold)returns are found under extreme market conditions. By test-ing the joint lower tail probability and conditional tail prob-ability, we conclude that USD can be a weak safe haven forthe UK and Germany conditional on large drops in goldprices, and gold can be a weak safe haven for the USA andAustralia conditional on the poor performance of USD.Generally, based on the analysis of both overall andextreme dependence measures, our results confirm that theUSD is a more likely hedge against stocks than gold, butthe safe haven effects of USD and gold will not increasewhen both assets are used as safe haven assets. We find thatneither of the assets dominates the other during stock mar-ket crashes, and this finding implies that the joint safehaven strategy does not outperform the single safe havenstrategy. Previous studies with no consideration of the jointproperties of USD and gold may lead to a naive conclusionabout the usefulness of gold and USD as safe haven assets.

Our work contributes to the rich literature on risk man-agement through alternative investments in the followingways. Regarding methodology, we generalize the extendedskew-t (EST) copula function to a multivariate case andprovide a new econometric framework to jointly analysethe hedge and safe haven effects of alternative investmentsto solve the problem that the traditional methodologies can-not allow for fat/thin tail generalization, and we apply thismodel to test multiple alternative investments at the sametime. In terms of the aspects of empirical results and eco-nomic interpretations, we reexamine the hedge and safehavens of stock–USD–gold from an investor’s point ofview, while most previous studies simply combine thesedata series without considering whether the implied invest-ment strategies can be obtained by domestic investors. Our

†A comprehensive review of the asymmetric distributions used infinance is provided in Adcock et al. (2012).‡See Demarta and McNeil (2005), Kollo and Pettere (2010), Azzaliniand Capitanio (2003), Christoffersen and Langlois (2013), etc.

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results indicate that the fundamental factors that drive thehedge and safe haven effects can be different and providesome indirect evidence supporting the inflation hedgehypothesis and the flight-to-quality safe haven hypothesis.Moreover, by simultaneously estimating stock, gold andUSD, we find that some of the findings that exist under thestock–USD and stock–gold unconditional analysis wouldnot hold when the third asset is added to investors’ portfo-lios. This finding questions whether gold and USD canserve as independent safe haven assets for investors’ riskmanagement strategies.

The paper proceeds as follows. In Section 2, we providea literature review on the relation between gold and theUSD on the stock market. Section 3 reviews the use ofnon-normal distribution and copula functions in the financeliterature, and Sections 4 and 5 derive our proposed MESTcopula model and the lower tail dependence coefficient ofthe MEST copula model. In Section 6, we present the data,model, estimation results and economic interpretations.Sections 7 and 8 provide some robustness checks and com-parisons between our proposed model and models used inprevious studies. Finally, Section 9 concludes. Some techni-cal details are gathered and presented in the Appendix.

2. Hedging the effectiveness of gold and the USD in theinternational capital market

Both gold and USD have been widely used by internationalinvestors for different purposes, such as hedging stock mar-ket movement and other macroeconomic variables. Accord-ing to a recent Gallup poll, some 30% of respondentsconsidered gold to be the best long-term investment, mak-ing it a more popular investment than real estate, stocksand bonds (Saad 2012). On the other hand, USD has beendeemed the most dominant currency worldwide for sometime, and it is not surprising that foreign investors holdsome assets in the form of US currencies. However, the rea-son for the popularity of these alternative investments isstill debated, and here, we focus our research on the hedg-ing role of these assets. The role of these alternative invest-ments in investors’ portfolios has been tested in differentforms and is sometimes modelled in the finance and eco-nomic literature. In this section, we will first review the cur-rent studies in the hedging effects of these two commonlydeemed safe assets. Later, we will develop the hypothesesthat will be tested under our empirical framework.

2.1. Literature review

Gold has been traditionally deemed as a good hedging toolagainst macroeconomic risk, including inflation and interestrate risk. In academia, there are some theoretical and empir-ical results regarding the hedging role of gold. Gorton andRouwenhorst (2006) document that commodities can offerpositive returns during financial downturns. Gold is gener-ally considered one of the most popular assets in the com-modity market. As shown by Batten et al. (2015), the

Over-the-counter (OTC) derivatives outstanding in goldaccount for one-fifth of all commodity derivatives in termsof the gross figure in 2013. According to Jaffe (1989), goldis a hedge against both stock losses and inflation; therefore,including gold in financial portfolios can reduce theirvariance and slightly improve returns. McCown andZimmerman (2007), based on the capital asset-pricingmodel, demonstrate that gold shows hedging ability onstock portfolios and inflation during the period from 1970to 2006. However, negative Capital-Asset-Pricing-Model(CAPM) betas are only observed during the 1970s, suggest-ing that stock-hedging ability may be attributed to inflation-hedging ability. Gold can hedge other macroeconomic statevariables as well. For example, Ruff and Childers (2013)show that the gold price and the Consumer Confidence Indexare negatively associated, implying that gold has characteris-tics of hedging against economic instability. However, not allstudies agree on the hedging role of gold against stock mar-ket movement. A recent paper by Erb and Harvey (2013) crit-ically examines the role of gold in asset allocations,including inflation hedging, currency hedging and disasterprotection against stock. Little evidence is found for gold tobe an effective hedge against inflation, and the gold-as-currency hedge argument does not seem to be supported bythe data. Other studies that examine the financial characteris-tics of gold include Faugere and Van Erlach (2006), Luceyet al. (2006) and Sherman (1982). While the majority of priorresearch agrees on the diversification benefits of gold undercertain conditions, there are also contradictory results. Forexample, Anderson et al. (2014) examine the so-called ‘per-manent portfolio’, which consists of stocks, bonds, gold andcash, and this permanent portfolio only outperforms buy-and-hold or stock and bond portfolios on a risk-adjusted basis.†

The USD is another candidate competing for hedgingagainst stock market fluctuations in foreign countries.Giovannini and Jorion (1989) show that the co-movementsand the dependence structure between equities and USDwould have important implications for their cross-market riskmanagement for global portfolio diversification. In the litera-ture, many theoretical models have been constructed toexplain the relationship and co-movements between thesetwo markets; see e.g. Dornbusch and Fischer (1980),Branson (1983) and Frankel (1983). All these models arguethat the stock market impacts the exchange rate and viceversa. Hau and Rey (2006) suggest that the relations betweenstock and USD can be either positive or negative due to thereturn-chasing, portfolio rebalancing and exposure effects.To sum up, empirical studies of the interaction or causal rela-tionship between these two assets report mixed results, andthus, the hedging effect of the USD is questionable.

Although these two assets are used to hedge risk in thestock market, there are few theoretical foundations for how

†There is also indirect evidence of the hedging effect of commodi-ties. The results are also mixed (Idzorek 2007, Woodard 2008,Cao et al. 2010, Conover et al. 2010, Daskalaki and Skiadopoulos2011, You and Daigler 2013). Recently, the financialization ofcommodities has been proposed and generally accepted as one rea-son why the correlation between stocks and commodities hasdeclined in recent years. See Kyle and Xiong (2001), Tang andXiong (2012) and Silvennoinen and Thorp (2013).

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these assets can hedge stock market risk during extremeeconomic conditions. There is some indirect evidence thatthese assets can theoretically serve as safe havens whenmarkets crash. For example, when the prices of risky finan-cial assets drop dramatically, investors may decide to sellrisky assets and rush into buying safe assets to alleviatelosses. Thus, under the flight-to-quality hypothesis ofCaballero and Krishnamurthy (2008), the prices of thesealternative assets may surge. However, to our knowledge,there is no theoretical model explaining why gold or theUSD is usually referred to as safe haven assets. McCauleyand McGuire (2009) suggest that the appreciation of USDduring the period can be attributed to the following fourreasons: safe haven, unwinding of carry trades, dollar short-age and overhedging by non-US investors. The main themeof the assertion is that because USD is generally deemed asa high-quality currency and used by local and foreign finan-cial market participators, the crisis increases the demand ofUSD, causing USD appreciation. This argument implies thatUSD will appreciate under financial crisis, which is consis-tent with our definition of safe haven.

Empirical studies provide mixed results regardingwhether gold is a safe haven asset. For example, Baur andLucey (2010) show that gold is a safe haven only in thevery short term: on average, gold holders earn a positivereturn on the day of an extreme negative stock return, butthe return on gold is likely to be negative on average in thefollowing two weeks. Ciner et al. (2013) employ thedynamic conditional correlation model to measure the corre-lation structure and find that gold consistently acts as a safehaven in times of market crashes. On the other hand, Baurand McDermott (2010) find that gold is a safe haven assetfor major European stock markets as well as the US stockmarket but not for Australia, Canada, Japan and largeemerging markets. In addition, Lucey and Li (2015) provideevidence of the strength of the safe haven, finding that, attimes, gold is not the strongest or the safest haven based onUS data. However, these studies (Baur and McDermott2010, Baur and Lucey 2010, Ciner et al. 2013) only exam-ine the marginal effects of stock prices on gold prices basedon the estimated coefficients from linear regressions.Threshold dummies are included and given by a specificquantile of the stock return distribution to capture extremestock market movements. The conventional correlationcoefficient may not be an appropriate measure of the depen-dence among financial assets when the bivariate normalityassumption on the joint distribution of stock and gold doesnot hold. Therefore, results obtained from linear regressionsmay not fully account for extreme market co-movements.

On the empirical investigation of the safe haven role ofdominant currencies on stock market crashes, Kaul andSapp (2006), Ranaldo and Soderlind (2010) analyse the safehaven status of various currencies. Beck and Rahbari(2008) find that dollar bonds act as ‘safe haven currencies’during sudden stops, and they are a better hedge for globalsudden stops and for regional sudden stops in Asia andLatin America. Ning (2010) uses copula models to examinethe extreme co-movements of USD and stock markets inG4 countries, finding significant symmetric tail dependencein all stock–USD return pairs for both pre- and post-Euro

periods. Wang et al. (2013) present a dependence-switchingcopula model to describe the dependence structure of thesetwo assets in six industrial countries between 1990 and2010. Their results demonstrate that the general dependenceand tail dependence are asymmetric for most countrieswhen the stock market and exchange rate market move inopposite directions, but they are symmetric for all countrieswhen these two markets move in the same direction.

To summarize the current studies in the field, there issome evidence that gold and USD can be used as hedgingtools through hedging inflation or other macroeconomicvariables, although the empirical results are somewhatmixed. Theoretically, few studies have examined why orwhether these assets can serve as safe havens except for theflight-to-quality hypothesis. There are some empirical stud-ies that investigate the roles of gold and USD as safehavens, but these studies often either examine two assets ata time without taking into account the possible effect of theexistence of other alternative assets, or investigate the aver-age dynamic correlation among multiple assets without con-sidering their extreme co-movements. For example, Ning(2010) and Wang et al. (2013) examine the extreme depen-dence between stocks and USD, but use only one alterna-tive investment, USD, as the safe haven. Zagaglia andMarzo (2013) investigate how the relation between goldand the USD has been affected by the financial turmoil.Other studies, such as Baur and McDermott (2010) andCiner et al. (2013), investigate the safe haven propertybetween stocks and gold or focus on pairwise correlationstructures for multiple assets, but do not consider extrememarket situations. Moreover, some studies analyse the rela-tionships between gold and exchange rate. An early workby Sjaastad and Scacciavillani (1996) show theoreticallyand empirically gold price can be linked to the exchangerate, and among different currencies, the European curren-cies, which possess high market power in the gold marketand inflations, cause the gold price fluctuating. On the otherhand, Capie et al. (2005) use Yen and Sterling as examplesto show that empirically, gold can serve as a hedge againstdollar only for some periods, and the relation is not guaran-teed. In a more recent work, Joy (2011) finds that gold canbe served as a hedge against exchange rates, but cannot beserved as a safe haven asset for exchange rates. Reboredoand Rivera-Castro (2014b) use a sample period similar toours (2000/01 to 2013/03) and find that the gold price ispositively correlated with the USD depreciation for mostcurrencies. Furthermore, they apply the Value-at-Risk (VaR)approach, which also can be used to measure the downwardrisk, and find that including gold into the portfolio of purecurrencies can provide some safe haven effects, especiallyin a shorter time horizon, such as days and weeks. Inanother work, Reboredo and Rivera-Castro (2014a) test thetail dependence between gold and currencies and find thatgold can serve as a hedge against USD, but it is a weaksafe haven asset against extreme USD price movements. Tothe best of our knowledge, none of the existing studiesinvestigates the joint relationship beyond two dimensionsand accounts for the joint extreme dependence at the sametime. This motivates our attempts to use innovative econo-metric tools to fill this gap in the literature by considering

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the effectiveness of gold and USD simultaneously as hedgesor safe havens on stock.

2.2. Hypothesis testing

In this section, we develop our hypothesis based on theprevious literature on a qualitative base. We defer themore detailed and quantitative descriptions of thesehypotheses to the Empirical Analysis section, after weintroduce our econometric model to help readers betterunderstand the economic reasons and econometric meth-ods in this paper.

From the previous literature, we can observe that bothGold and USD have been used and tested as hedging toolsor safe havens, but the reasons they can serve these roles arestill debated. Jaffe (1989) and McCown and Zimmerman(2007), among others, suggest that the inflation-hedgingability of gold is the reason gold can serve as a hedging toolagainst stock market movement. Gold, as one kind of pre-cious metal, is deemed to have a more stable real value dueto the limits of its supply, and the fluctuation of price levelscan be consistent with changes to the gold price. On theother hand, the change in USD can also be correlated withinflation or price level changes if imports or exports areimportant for domestic countries. For example, an apprecia-tion of USD (for residents in other countries) can increasethe price level of import goods and decrease local con-sumers’ real consumption but stimulate foreign consump-tions of export goods therefore increase the profitability ofproduction.

However, although both assets can theoretically be usedto hedge inflation changes, they may not be good hedgesagainst stock market movement. As argued by Boons et al.(2014), the performance of these inflation-hedged alterna-tive investments can be affected by the short-hedgeddemand by producers, the long-hedged demand by con-sumers and the speculative demand of investors.† Thus, ifthe forces from the two assets other than inflation hedgingby consumers are strong, the hedging ability of these alter-native assets can be largely weakened. For example, if thesetwo assets are used as pure speculation investment vehicles,the movement of the prices of these assets can deviate fromthe inflation; consequently, gold and USD cannot be usedas hedge assets. To test whether these alternative invest-ments can be used to hedge the risk in the stock market,we will test the following hypotheses:

Hypothesis 1A: Gold is a hedge asset against the domesticstock market movement.

Hypothesis 1B: USD is a hedge asset against the domesticstock market movement.

According to the definition used by Baur and Lucey (2010),if an asset can be used as a strong hedging tool against thestock market, it must have a significant, and often negative,co-movement with the stock market.‡ This is probably themost commonly seen measure of hedging. If the hedgeasset and the underlying assets are correlated significantly,we can easily find the degree of co-movement of these twoassets by finding the linear relation between these twovariables, which is similar to the concept of the commonlyused delta hedge. In the empirical testing, the generalco-movement of two assets can be measured by Pearson’scorrelation, Kendal’s s coefficients or by linear regressions,as commonly seen in the empirical literature.

When extreme market conditions are observed, theco-movements of stock markets and alternative investmentsmay not be solely caused by an inflation-hedging effect.Caballero and Krishnamurthy (2008) argue that the flight-to-quality hypothesis can explain the surge of the prices ofalternative investments under stock market crashes. Gold, asa store of value rather than as an earning asset, can main-tain the same real value when the prices of other assetsdrop and are thus traditionally deemed as a high-qualityasset under extreme market conditions.§ Alternatively, whenthe domestic stock market crashes, the local and foreigninvestors may decide to switch their investments from thelocal stock market to stock markets in other countries, andthis action can cause the depreciation of local currencies orthe appreciation of USD. In this sense, USD should serveas a safe asset during market crashes. Note that the explana-tion provided here cannot be explained solely by thechanges in inflation unless sudden changes in the inflationlevel constitute the main reason for stock market crashes.Thus, common significant co-movements between thesealternative investments and the domestic stock market donot guarantee a similarly significant relation observed inextreme market conditions. To test whether the hedging andsafe haven effects are consistent for gold and USD, we testthe following hypotheses:

Hypothesis 2A: Gold is a weak safe haven against domesticstock market crashes.

Hypothesis 2B: USD is a weak safe haven against domesticstock market crashes.

Hypothesis 3A: Gold is a strong safe haven against domes-tic stock market crashes.

Hypothesis 3B: USD is a strong safe haven against domes-tic stock market crashes.

Baur and Lucey (2010) call an asset a safe haven if it isunrelated or negatively related to another asset in times ofextreme market movements, and we follow their definitionthroughout this paper. Baur and McDermott (2010) further

†Strictly speaking, Boons et al.’s paper discusses the systematic riskassociated with commodity futures rather than the co-movement ofthese assets and stock markets. However, their model assumes thatthe commodity fully represents the consumption price level, whichis directly linked to inflation. Thus, their arguments can also be usedin the context here.

‡On the other hand, if the co-movement between the two assets isinsignificant, the chosen alternative asset can serve at best only asa weak safe haven asset. In the other words, investors can includethis asset in their portfolios for diversification purposes rather thanas the strong hedge, as it is commonly used.§The characteristics of gold as a financial asset are explained ingreater detail by Baur and McDermott (2010).

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investigate the difference between weak and strong safehaven assets. According to their definition, a strong (weak)safe haven is defined as an asset that is negatively corre-lated (uncorrelated) with another asset or portfolio in certainperiods only, e.g. in times of falling stock markets. Simplyspeaking, a weak safe haven would perform normallyregardless of whether the stock market crashes, but a strongsafe haven would perform extremely well during the marketdownturn. In econometrics tests, the tail dependences canbe used to test the co-movement of assets under extremesituations. Based on the tail dependence function developedin Section 5, we use the low (in stock)–low (in gold orUSD) tail dependence to test whether gold and USD areweak safe havens, and we use the low/up tail dependenceto test whether gold and USD are strong safe havens.†

Thus far, we have focused on the hedging or safe havenroles of gold and USD on the domestic stock market, butsome of the findings have already been presented in previ-ous studies, although usually for only one asset at a time.Under the flight-to-quality hypothesis, investors will chooseto withdraw funds from low-quality assets such as stocksduring domestic stock market crashes and switch tohigh-quality assets such as gold or USD. However, thesehigh-quality assets can be substitutes during market crashperiods, and which high-quality asset investors will chooseto flee to be unclear, surely presenting an interesting ques-tion. Hence, we later control for the performance of oneasset and test the hypotheses of whether safe haven effectsstill exist for the other asset.

Hypothesis 4A: Gold is a weak safe haven against domesticstock market crashes after controlling for the extreme poorperformance of USD.

Hypothesis 4B: USD is a weak safe haven against domesticstock market crashes after controlling for the extreme poorperformance of gold.

To understand the co-movements among these three assets(stocks, gold and USD), we need to estimate a multivariatedistribution with these three random variables. The econo-metric method used to estimate the multivariate distribu-tions will be discussed below, and the explicit form of thetail dependences, which are used to test the extreme condi-tions’ co-movements, will be derived in the next section.These newly developed econometric techniques shouldallow us to further understanding of the hedging and safehaven roles of alternative investments.

3. Non-normality distributions with copula functionmethodology reviews

In our later empirical studies, we model the entire jointdistribution of returns among these three assets without

assuming multivariate normality. Our newly developedMEST copula model allows for asymmetric dependence andtail dependence (fat-tailed as well as thin-tailed depen-dence), which cannot be obtained with previously proposedeconometric methods.

Theory that concerns multivariate joint distributionsthat are elliptically symmetric (Fang et al. 1990) hasemerged in the literature in the past two decades. How-ever, elliptically symmetric distributions cannot capturethe skewness of return distributions. In many cases,asymmetric distributions are more adequate to describeasset returns. For example, Campbell et al. (1997) pre-sent the moments of daily and monthly individual andaggregated stock from 1962 to1994 and find that excesskurtosis is seldom statistically insignificantly differentfrom zero and that the skewness of stock is also oftensignificantly different from zero, especially in the dailyreturn samples.

A number of recent papers consider skewness in multi-variate distributions. For example, Sahu et al. (2003) intro-duce skewness into multivariate elliptically symmetricdistributions. Azzalini and Capitanio (2003) study a generalprocedure to perturbate a multivariate density and to gener-ate a family of non-symmetric densities. Arellano-Valle andGenton (2010) propose a class of MEST distributions toallow for asymmetric and thin-tailed distributions. For theapplication of these distributions in asset pricing and portfo-lio selection, see Adcock (2010). A comprehensive reviewof asymmetric distributions used in finance is provided byAdcock et al. (2012).

The past two decades have seen the increased usage ofthe copula methods in the finance literature. Applicationsof copulas in finance are typically restricted to bivariate(either symmetric or asymmetric) or multivariate symmet-ric cases. Some recent studies have begun to employasymmetric distributions to construct multivariate asym-metric copulas to provide better flexibility. For instance,Demarta and McNeil (2005) propose a ST copula basedon a Gaussian mixture representation. Kollo and Pettere(2010) introduce a multivariate ST copula based on themultivariate ST distribution of Azzalini and Capitanio(2003). Smith et al. (2012) establish ST copulas impliedby Sahu et al. (2003). These methods have been adoptedin the finance literature. Christoffersen et al. (2012) pro-pose a new dynamic asymmetric copula model based onthe ST copula detailed by Demarta and McNeil (2005) tocapture long-run and short-run dynamic dependence,multivariate non-normality and asymmetries in large cross-sectional data. Christoffersen and Langlois (2013) applythe dynamic asymmetric copula on the four-factor CAPMmodel, and Christoffersen et al. (2013) use it to investi-gate the diversification in corporate credit. González-Pedraz et al. (2015) propose a conditional ST copula tocapture the impact on optimal portfolios. However, theseaforementioned copulas can only capture asymmetric andheavy-tailed dependence; they fail to allow for thin tailsof multivariate distributions and preserve the closed func-tional form under conditioning. All of these problems canbe mitigated in our proposed model, which will be derivedin detail in the next section.

†Note that if the joint distribution between alternative investmentsand the stock market is symmetric, there is no need to test bothweak and strong safe haven hypotheses. However, the significantskewness observed in later empirical results suggests that the sym-metric assumption is violated. This is another factor that motivatesus to apply a more complicated MEST in our empirical tests.

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4. MEST copula model

The copula function is a method to join or couple multivari-ate distribution functions to their one-dimensional marginaldistribution functions. Due to the separability of dependencestructures and marginal distributions, a copula-based estima-tor can accommodate rich dependence structures with just afew parameters. In addition, such an estimator facilitates themodelling of tail dependence to capture the stylized proper-ties of the tails. This section outlines the MEST copulamodel we develop to capture the dependence between vari-ables. Our model can be implemented by a two-stageprocess. We first fit each return series with a GARCHmodel and then calculate the implied standardized residuals.The empirical cumulative distribution functions of the stan-dardized residuals are used as inputs in the second-stagecopula density estimation, which features a MEST copula.

According to Sklar (1973), a multivariate distribution func-tion can be decomposed into marginal distributions and a cop-ula function that incorporates all marginal distributions. For acontinuous p-dimensional random vector X ¼ X 1; . . .; X p

� �with marginal densities f 1 x1ð Þ; . . .; f p xp

� �and marginal distri-

butions F1 x1ð Þ; . . .; Fp xp� �� �

, a unique copula functionexists that satisfies

f x1; . . .; xp; a1; . . .; ap; h� �¼Ypi¼1

f i xi; aið Þc F1 x1; a1ð Þ; . . .; Fp xp; ap� �

; h� �

;(1)

where cð�Þ is the copula density function. In practice, thedependence parameter h is often estimated by the maximumlikelihood method. Due to the non-i.i.d. nature of financialdata, a filtration is necessary to obtain i.i.d. series, which arerequired by the classical maximum likelihood theory. A com-mon practice of filtration is to fit a univariate GARCH-typemodel to each marginal series. Denote the resulting standard-ized residuals by li, i ¼ 1; . . .; p. Their corresponding ranksui, or empirical cumulative distributions, are used in the sub-sequent copula estimation. Below, we shall propose a MESTcopula model that will be used in our investigation of thedependence among the returns of assets.

4.1. Estimation of marginal distributions

The first stage of copula models consists of the estimationof individual marginal distributions. Because asset returnsmay exhibit autocorrelation and autoregressive conditionalheteroscedasticity (e.g. Patton 2004, 2006, Reboredo 2013),a filtration is necessary to obtain i.i.d. marginal series. In thisstudy, we consider an AR(p)-GJR(1,1) model (Glosten et al.1993), using the quasi-maximum likelihood estimation.

The error terms are assumed to follow the EST distribu-tion used by Arellano-Valle and Genton (2010) to allow forasymmetric and heavy/thin tails.

Denote the standardized error terms for the ith series by

li ¼ ei;1ffiffiffiffiffihi;1

p ; . . .;ei;Tffiffiffiffiffihi;T

p� �T

. Its density function is given by:

1

T1 s1=ffiffiffiffiffiffiffiffiffiffiffiffiffi1þ k2i

q; vi

� � t1 li;t; vi� �

T1

� kili;t þ si� � ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

vi þ 1

vi þ l2i;t

!vuut ; vi þ 1

8<:

9=;; t ¼ 1; . . .; T

(2)

where ki 2 R is a shape parameter and si 2 R is an exten-sion parameter. t1 �; við Þ is the density function of the uni-variate Student’s t distribution with a zero mean, unit scaleand degree of freedom vi and T1 �; vi þ 1ð Þ is the univariateStudent’s t distribution function with a degree of freedomvi þ 1.

We fit each marginal series to the EST distributions usingthe maximum likelihood estimator. The resulting standard-ized residuals are then transformed to ui;t ¼ ~F li;t

� �with

i ¼ 1; . . .; p and t ¼ 1; . . .; T , where~F lð Þ ¼ 1

Tþ1

PTt¼1 I l� li;t

� �is the rescaled empirical cumu-

lative distribution function.†

4.2. EST copula model

To capture the dependence structure among the variousasset returns that accommodates features of skewness andkurtosis, this study constructs a MEST copula based on theMEST distribution described by Arellano-Valle and Genton(2010).

Let Y ¼ Y 1; . . .; Yp

� �denote the filtered returns of p

assets. Suppose that Y has a MEST distribution, denoted byY�MESTp /; h; v; sð Þ. Its density function evaluated aty ¼ y1; . . .; yp

� � 2 Rp is given by:

1

T 1 s=ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ hTUh

p; v

tp y;U; vð ÞT 1

� hTyþ s� � vþ p

vþ yTU�1y

� �12

; vþ p

( ) (3)

where h ¼ h1; . . .; hp� �T2 R

p are the shape parameters,s 2 R is an extension parameter and v[ 0 is the degree offreedom. tp is a p-variate Student’s t density function with acorrelation matrix U, whose density is given by:

†There are two reasons for us to employ the empirical distributionof the standardized residual. First, Chen et al. (2006) note that thecanonical maximum likelihood estimator via the empirical cumula-tive distribution function (CDF) has the added benefit of that theasymptotic distribution of copula estimations in the second stage isnot affected by the sampling variations of first-stage estimation ofthe marginal distributions. In addition, we have conducted our esti-mation using either both inference functions for margins andcanonical maximum likelihood methods, and the results of multi-variate copula estimation from both methods are very similar.Therefore, we choose the more popular approach, which is thecanonical maximum likelihood, when computing the cumulativeprobability of the standardized residuals.

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tp y;U; vð Þ ¼ C vþp2

� �Uj j12 vpð Þ12C v

2

� � 1þ vþ yTU�1yv

� ��ðvþpÞ2

(4)

T1ð�; vÞ denotes a standard univariate Student’s t distributionfunction with degrees of freedom v.

The cumulative distribution function of Y is

F yð Þ ¼ P Y� yð Þ¼ 1

T1ð�s; vÞ Tpþ1y�s

�;

U �d�d 1

�; vþ 1

� �; y 2 R

p

(5)

where �s ¼ sffiffiffiffiffiffiffiffiffiffiffiffi1þhTUh

p , d ¼ Uhffiffiffiffiffiffiffiffiffiffiffiffi1þhTUh

p and Tpþ1ð�; vþ 1Þ denotesa p + 1 -variate Student’s t distribution function with adegree of freedom vþ 1.

Recall that the marginal density function of Y i takes theform

f i yið Þ ¼ 1

T1 s=ffiffiffiffiffiffiffiffiffiffiffiffiffi1þ k2i

q; v

� � t1 yi; vð ÞT1

� kiyi þ sð Þ vþ 1

vþ y2i

� �12

; vþ 1

( ); i ¼ 1; . . .; p

(6)

Let k ¼ k1; . . .; kp� �T

. The relation of the shape parametersbetween the joint and marginal distributions is given by

h ¼ D DUD�kkTð Þkffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þkT DUD�kkTð Þ�1

k

q , where

D ¼ diagffiffiffiffiffiffiffiffiffiffiffiffiffi1þ k21

q; . . .;

ffiffiffiffiffiffiffiffiffiffiffiffiffi1þ k2p

q� �.

As shown in (1), the joint density function can be inter-preted as the product of univariate marginal densities and acopula density function. It implies that the copula densityfunction is the joint density function divided by the productof univariate marginal densities. Therefore, the p-variateEST copula† is given by:

c u1; . . .; up;U; h kð Þ; k; s; v� �¼

f F�11 u1ð Þ; . . .; F�1

p up� �

;U; h kð Þ; k; s; vþ p

Qp1 f i F

�1i uið Þ; ki; s; vþ 1

� � :(7)

where F�1i ðuiÞ denotes the inverse distribution function of

univariate EST for the variable i. The copula function of(7) is then given by:

C u1; . . .; up;U; h kð Þ; k; s; v� �

¼ZF�11 u1ð Þ

�1� � � ;

ZF�1p upð Þ

�1c k1; . . .; kp;U; h kð Þ; k; s; v� �

dk1; . . .; dkp:

(8)

Subsequently, the MEST density function is expressed asfollows:

f y1;t; . . .; yp;t;U; h kð Þ; k; s; v ¼Ypi¼1

f yi;t; ki; s; v� �

c u1;t; . . .; up;t;U; h kð Þ; k; s; v� �: (9)

The log-likelihood function of (9) is:

L hð Þ ¼Xpi¼1

XTt¼1

Li;t W1;i

� �þXTi¼1

Lc;t W2ð Þ (10)

where H ¼ h kð Þ;Ut; k; s; vð Þ, W1;i ¼ ki; s; vð Þ andW2 ¼ U; h kð Þ; k; s; vð Þ. Li;t W1;i

� �and Lc;t W2ð Þ are the loga-

rithmic function of the marginal density of yi;t and the loga-rithmic function of the copula density, respectively.

The copula density can be estimated separately from themarginal densities using the method used by Li (2005). Inparticular, we can estimate the parametersW2 ¼ U; h kð Þ; k; s; vð Þ by maximizing

PTt¼1 Lc;t W2ð Þ, the

log-likelihood function of (10), based on a quasi-maximumlikelihood theory.

4.3. Interpretation of the coefficients of the EST model

Because the EST is more flexible than the general family ofelliptical distributions, such as Gaussian and Student’s t distri-butions, it is difficult to provide statistical meanings for a par-ticular coefficient of the EST. However, in some extremecases, the EST distribution can be transformed into some typesof simple distributions. For example, when the shape andextension parameters equal zero ki ¼ si ¼ 0ð Þ, the EST distri-bution degenerates to the conventional Student’s t distribution.When the degree of freedom goes to infinity and one (vi ! 1and vi ¼ 1), the EST distribution reduces to the skewed normaldistribution of Azzalini and Dalla Valle (1996) and the skewedCauchy distribution of Arnold and Beaver (2000), respectively.When the extension parameter equals zero (si ¼ 0), the ESTdistribution reduces to the ST distribution of Azzalini andCapitanio (2003). For detailed discussions of the EST, seeArellano-Valle and Genton (2010).

4.4. Application of the MEST model

To consider whether to apply the MEST model developedin this paper for research questions in finance, we can eval-uate the two main improvements of our MEST model com-pared to other more restricted distributions, such as

†As DCC models have been criticized in a number of papers, e.g.Füss et al. (2013), this study focuses on the static copula develop-ment. For the sake of completemenss, we report estimation resultswith the DCC in the Appendix.

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Gaussian and Student’s t distribution. At the same time, wewill provide some potential areas where we should use ourMEST model.

First, the MEST model allows the marginal distributionsto be with non-zero skewness and excess kurtosis, whichwill be especially useful in the content of risk managementbecause we care more about extreme situations. The prop-erty of the distribution on these distributions under theextreme value region will be especially important to help usset up the hedging strategies, In fact, one of the reasonswhy subprime mortgage crisis hurts the banking systemseverely is that the VaR calculation used in the banks pro-vides a presumably safe hurdle which in fact, providesmuch less safety than we thought. Thus, a distribution withflexible fat or thin tail definition will be much useful in thecontent of risk management. Other possible areas which wecould apply the MEST models may involve data with highfrequencies or non-linear payoff securities, such as somederivatives. In both cases, the normality assumptions willbe clearly violated and the MEST model will provide amore accurate estimations.

Second, the MEST model developed in this paper allowsfor multiple variables to be estimated at the same time. Inpractice, it is seldom that investors choose to hold onlysmall numbers of securities. Thus, when the research ques-tions we are interested in are with non-normal and unidenti-fied distributions, we will need our multivariate jointdistribution model to determine the expected return or riskof the portfolio held by investors, and apply the results tothe research questions.

In sum, our MEST model can be used for the scholars orpractitioners under the following situations (not mutuallyexclusive): high-frequency data, non-linear payoff securities,risk management and investing portfolios with multipleassets. Although it will be better to demonstrate the powerof this model by satisfying the four characteristics at thesame time, we believe it will be better to use this modelwith a straightforward and interesting research questionwith economic meaning.

In this paper, we choose to apply the MEST model onthe research question whether the USD and gold can beused as hedge or safe haven assets for domestic equity mar-ket investors. The empirical answer of this question requiresa joint distribution with USD, gold and domestic equitymarket index as three variables to be estimated at the sametime. Although the hedging ability of an asset, as definedpreviously, is usually not affected by the excess kurtosis ofthe marginal distribution, the safe haven ability should beaffected by the excess kurtosis because investors would liketo know what will be the risk deduction by including theUSD or gold in their portfolio under extreme situations inthe equity market. Hence, our research question is suitableto apply the MEST model.

Our research question can be further extended under thesame econometric framework. For example, we can furtherdiversify the domestic investors’ portfolio into a globalizedequity portfolio, which contains equity index from differentcountries. Our result can be easily extended into this settinggiven the multivariate assumption in our model. There aretwo main reasons why we choose not to apply this model

under the new setting. First, investors empirically showstrong home-bias when investing in equity market. A longlist of literatures starting from early 90’s, such as Frenchand Poterba (1991), shows that although it is possible forinvestors to diversify their portfolios worldwide, they maynot choose to do so, or at least to a lower extent. Second, ifinvestors decide to diversify their portfolios worldwide,they will need to invest in these indexes by the local cur-rencies. Thus, the exchange rate factors will be embeddedinto the equity index and, from our opinions, bring possiblymore confusions to the big picture.

The other possible extension of this question is to con-sider whether the crisis is regional or global. To achievethat, we can include the world equity index as the fourthassets into our joint distribution estimations. In this setting,the local crisis can be identified as the extreme bad scenariofor the domestic equity market, and the global crisis can beidentified as the intersection of the extreme bad scenariosfor both the domestic and world equity market. This will bealso an interesting application of the MEST model. Giventhat we are not even sure whether gold and USD can beused as safe haven assets, we choose not to investigate thispossibility in the current paper because we want to focuson our main research question. We believe distinguishinglocal and global market crisis is an interesting and separatedtopic to investigate in the future extension on this stream ofresearch.

4.5. Comparison of the MEST model with ST model

We conclude this section with a brief discussion on the dif-ference between the MEST and the ST distribution. TheEST copula derived from Arellano-Valle and Genton (2010)is more flexible than the ST copula from Demarta andMcNeil (2005).

First, for asymmetric distributions the concept of fat-tailness is not uniquely defined. It is entirely likely we haveone ‘fat’ tail and one ‘thin’ tail in the conventional sense.The merit of the EST distribution is that it introduces anextension parameter to the ST distribution to provide furtherflexibility.

Second, the EST copula has a more flexible third andfourth moments than the ST copula. Please refer to Proposi-tion 7 in Arellano-Valle and Genton (2010).

Third, it requires less restriction to retain a finite secondmoment in the EST copula than the ST copula. For exam-ple, the degree of freedom should be larger than four tohave a finite second moment in the ST copula, but it shouldbe larger than two in the EST copula. Please refer toSection 5.1 in Demarta and McNeil (2005) and Proposition7 in Arellano-Valle and Genton (2010).

5. Lower tail dependence coefficient for the MESTmodel

Since the global financial crisis of 2007, the extreme lowertail dependence has played an increasingly important role in

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measuring downside risk in finance. The lower tail depen-dence coefficient for the regular distribution has been welldeveloped; see Joe (1997) and Nelsen (1999). Several stud-ies provide approximations of lower tail dependence forsome irregular distributions, such as skewed elliptical distri-butions. For example, Fung and Seneta (2010) study thelower tail dependence of skewed normal and ST distribu-tions. Bortot (2010) finds that the ST is asymptoticallydependent in lower tails. In this study, we derive theasymptotic lower tail dependence of the bivariate EST dis-tribution.

The lower tail dependence coefficient for Y ¼ Y 1; Y 2½ �Tis defined as follows:

kL ¼ limu!0þ

P Y 1 �F�11 u1ð ÞjY 2 �F�1

2 uð Þ� �¼ lim

u!0þC u;uð Þ

u ¼ limu!0þ

dC u;uð Þdu

¼ limy!�1P Y 2 �F�1

2 F1ðyÞð ÞjY 1 ¼ y� �

þ limy!�1P Y 1 �F�1

1 F2ðyÞð ÞjY 2 ¼ y� �

:

(11)

Suppose that Y follows a bivariate EST ðU; h; s; vÞ with

mean zero. Define U ¼ 1 qq 1

�, h ¼ h1; h2½ �T ,

k1 ¼ h1þqh2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þh22 1�q2ð Þ

p , k2 ¼ h2þqh1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þh21 1�q2ð Þ

p , s1 ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þh22 1�q2ð Þ

p and

s2 ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þh21 1�q2ð Þ

p . The first term of (11) takes the form:

T1 s1=ffiffiffiffiffiffiffiffiffiffiffiffiffi1þ k21

q; v

� �

T 1 s=ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ hTUh

p; v

Z�a21

�1t1 z; vþ 1ð Þ

�T1 h2

ffiffiffiffiffiffiffiffi1�q2

vþ1

qz� qh2 þ h1ð Þ

� � ffiffiffiffiffiffiffiffiffivþ21þ z2

vþ1

q; vþ 2

� �T 1ð�k1

ffiffiffiffiffiffiffiffiffiffiffivþ 1

p; vþ 1Þ dz

(12)

where

a21 ¼T1 �k2

ffiffiffiffiffiffiffiffiffiffiffivþ 1

p; vþ 1

� �T1

s1ffiffiffiffiffiffiffiffi1þk21

p ; v

� �

T1 �k1ffiffiffiffiffiffiffiffiffiffiffivþ 1

p; vþ 1

� �T1

s2ffiffiffiffiffiffiffiffi1þk22

p ; v

� �0BB@

1CCA

1=v

�q

0BBB@

1CCCA

�ffiffiffiffiffiffiffiffiffiffiffiffiffivþ 1

1� q2

s:

Similarly, the second term of (11) is given by:

ðT 1 s2=

ffiffiffiffiffiffiffiffiffiffiffiffiffi1þ k22

q; v

� �

T 1 s=ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ hTUh

p; v

Z�a12

�1t1 z; vþ 1ð Þ

T 1 h1ffiffiffiffiffiffiffiffi1�q2

vþ1

qz� qh1 þ h2ð Þ

� � ffiffiffiffiffiffiffiffiffivþ21þ z2

vþ1

q; vþ 2

� �T 1 �k2

ffiffiffiffiffiffiffiffiffiffiffivþ 1

p; vþ 1

� � dz

(13)

where

a12 ¼T1 �k1

ffiffiffiffiffiffiffiffiffiffiffivþ 1

p; vþ 1

� �T1

s2ffiffiffiffiffiffiffiffi1þk22

p ; v

� �

T1 �k2ffiffiffiffiffiffiffiffiffiffiffivþ 1

p; vþ 1

� �T1

s1ffiffiffiffiffiffiffiffi1þk21

p ; v

� �0BB@

1CCA

1=v

�q

0BBB@

1CCCA

ffiffiffiffiffiffiffiffiffiffiffiffiffivþ 1

1� q2

s:

The detailed derivation of the lower tail dependence coeffi-cient is provided in the Appendix.† It processes nontrivialvalues of lower tail dependence. Whenh1 ¼ h2 ¼ k1 ¼ k2 ¼ s ¼ s1 ¼ s2 ¼ 0, kL reduces to thelower tail dependence coefficient of the Student’s t distribu-tion, which is symmetric in both tails.

6. Empirical analysis

6.1. Data

Weekly data of stock indices, nominal exchange rates andthe gold price are collected over the period 5 January2000–13 November 2013. The countries under considera-tion are the UK, Germany, Switzerland, the USA, Canada,Japan and Australia. Our sample period begins in 2000, asthe euro was launched as a currency in the financial marketin 1999. All data used in this paper are obtained fromDatastream.‡ Although we carefully select our samplecountries to include only one country, Germany, thatswitched local currency to Euro, we believe the existenceof Euro will affect the use of currencies, such foreign cur-rency reserves, and the exchange rate of Euro/USD whichis affected by the economy of countries other thanGermany. Because exchange rates are one of the chosenhedge assets in this study, we prefer to avoid the significantstructure change associated with the introduction of Euroand thus decide to use the observations only after 2000.Moreover, we use weekly data in our investigation and feelthat more than 700 observations per series suffice to ensureproper power of our econometric tests.§

The stock indices collected are the UK’s FTSE All-ShareIndex, Germany’s DAX composite index, Switzerland’s

†As the target of this study is to analyse the safe haven effect, wedo not address the details of upper tail dependence coefficient inthe context. Some applications of upper tail dependence coefficientare discussed in Appendix C.‡The same sample choice and the reasons behind the choice werealso given by Reboredo (2013). This choice of the sample periodthus facilitates comparison between our findings and existing stud-ies. Ning (2010) instead chooses the sample data from 1991 to2008 because 18 September 2008 is the last date that the data forGerman mark and French franc exchange rates are available fromDatastream. Due to the importance of European debt crisis, wedecide to focus on the post-Euro period to investigate the mostupdated situations.§Still, it will be interesting to include a longer time series of dataand test whether the pre-2000 and post-2000 periods the use ofhedge and safe haven assets change. This test would require amodification on the current model to allow for a structure break.Given the already complicated econometric model, we believe itwill be better to focus on the merit of allowing a more generalizeddistribution in this paper.

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SMI, the US S&P500 composite, Canada’s S&P/TSX 300composite, Japan’s Nikkei 225 Stock Average andAustralia’s S&P/ASX 300 composite. The price of gold ismeasured in domestic† currency per ounce (gold bullion indomestic currency $ per troy ounce). The nominal exchangerates are measured as the domestic currency per unit ofUSD (an exchange rate increase means appreciation ofUSD). Exchange rate data are collected for currencies asfollows: the British pound (GBP), the Euro, the Swiss franc(CHF), the Canadian dollar (CAD), the Japanese yen (JPY)and the Australian dollar (AUD). The set of countries usedfor this study includes the vast majority of market traders ininternational exchange. For the US data, we considered theBroad Trade-Weighted Exchange Index (TWEXB) of theUS Federal Reserve in order to examine the dependenceamong the US aggregate exchange rate, stock and goldprice. Thus, the interpretation of the results in the US is dif-ferent from that of other countries. The return series areconstructed from the log-difference of the correspondingstock index, USD and gold price.

Note that all three assets used in our analysis are quotedin domestic currencies. This specification ensures that ourtest can be applied in real risk management practicesbecause domestic investors can decide to invest in threealternative targets: the domestic stock index, USD and gold.Thus, the returns on these three investments need to bemeasured in the domestic currency, which is usuallyignored in previous studies regarding the hedge and safehaven roles of gold and/or USD.

Table 1 provides the summary statistics of the weeklyreturns of the three assets. All average returns (in absolutevalues) are smaller than their standard deviations, suggest-ing relatively high volatilities. The annualized averagereturns of gold measured in different currencies are between7.55% in Switzerland and 11.53% in the UK, while theannualized average returns of the stock market index in dif-ferent countries are between −1.72% in Japan and 4.11% inCanada. Given that stock and gold show relatively closedstandard deviations, this result suggests that during oursample period, gold seems to be a better investment targetthan stock according to their Sharpe ratios. One of the pos-sible explanations of this finding is the choice of our sam-ple period, which contains 2 years (2001 and 2008) or24 months of contraction periods. This observation seemsto suggest that gold is a relatively better investment targetduring economic downturns.

When adding the exchange rates into the analyses, stockand gold returns show higher standard deviations than theexchange rate returns. Stock and gold returns are skewed tothe left, and exchange returns show no clear skewness. Thenegative skewness of stock returns suggests the possibilityof extremely bad outcomes, which suggests the importanceof safe haven assets for pure stock market portfolios. Allthree return series show excessive kurtosis ranging from5.16 to 14.73. Of the three investments, stock returns usu-ally have the highest kurtosis, indicating considerable fat

tails relative to the normal distribution. Both the skewnessand kurtosis suggest that none of the return series are nor-mally distributed. The large Jarque–Bera test statisticsstrongly reject the normality of all the return distributions.This finding provides an important clue to support adoptinga distribution more flexible than the Gaussian distribution.

To take a first look at the hedging abilities of gold andUSD, we report the Pearson’s pairwise correlations and thepartial correlations between the stock–USD and stock–goldreturn pairs in the last two columns of Table 1.‡ From theresults, we observe the following patterns. First, except forthe UK, the Pearson’s pairwise correlations of stock–USDpairs are considerably larger than those of stock–gold pairsin absolute value, suggesting the stronger dependence ofstock–USD pairs than that of stock–gold pairs. However,the correlations range from −46.85% in Australia to33.40% in Japan, suggesting that the hedging effects ofUSD exist only for some countries and that the differencesin country characteristics may affect the co-movements ofstock market and USD. Second, except for Australia, thestock–gold pairs are positively related, indicating that theincrease (decrease) in returns of the local stock markets isassociated with the increase (decrease) in the gold returns.Although the observed close to zero correlation is consistentwith the hypothesis that gold can serve as a weak hedgingasset for stock market performances, the generally positivecorrelations between the two assets indeed place a questionmark on whether gold is a strong hedging asset against thedomestic stock index.

As argued in previous sections, there are reasons thatboth gold and USD can serve as hedge or safe haven assets,but which investment is preferred for risk management pur-poses is still an empirical question. To control for the effectof a third asset on the correlation, we also report the partialcorrelations in the last column of Table 1. The general pat-tern of the partial correlations is consistent with that of thePearson’s correlation for the stock–USD pairs, but the par-tial correlation of the stock–gold pairs seems to weakenwhen controlling for the USD fluctuations. When control-ling the USD changes, the largest positive correlation forthe stock–gold pairs drops from 21.71 to 11.96% (in Japan),and the largest negative correlation changes from −21.03 to−6.34% (in Australia.)

In general, the changes of USD, rather than the goldprices, are more correlated with the stock index changes,with or without controlling for the other alternative invest-ments. The low correlation between stock and gold returnssuggests that gold may be a weak but not a strong hedgeasset for stock market movements. The large magnitudewith undetermined signs of the correlations between thestock market and USD implies the possibility that USD canserve as a potential strong hedge asset for some countries,but so far, we do not have enough evidence to make a moreconfident conclusion about why and whether USD can be ahedge asset for some countries but not others. To providefurther evidence of the roles of USD and gold in risk

†The term ‘domestic’ means countries other than the US, such asthe UK and Germany. We will use this definition throughout thepaper.

‡The partial correlation between x and y after controlling for theeffect of z is defined as rxy;z ¼ rxy�rxz�ryzffiffiffiffiffiffiffiffi

1�r2xzp ffiffiffiffiffiffiffiffi

1�r2yzp , where rxy is the

Pearson’s correlation between x and y.

Hedges or safe havens role of gold and USD against stock 11

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management, we will estimate the joint distributions ofstock returns, USD returns and gold returns under ournewly developed econometric framework.

6.2. Estimation procedure

To test the hedging and safe haven hypotheses as men-tioned previously, one of the most important procedures isto measure the dependence structure among the three assets:stocks, gold and USD. This study applies the proposedMEST copula model to capture the possible skewness andfat-tailed properties and to allow for more flexibility in thejoint distribution of stocks, gold and USD returns. To esti-mate the parameters in the proposed MEST copula model,this paper applies the canonical maximum likelihood pro-posed by Genest et al. (1995). We present the procedures inthe following order.

(1) Model selection and estimation of parameters ofmarginal models for each return.

(2) Non-parametric transformation of filtered residuals.(3) Estimation of parameters of the MEST copula.

First, we fit each return series an AR(p)-GJR(1,1) model(Glosten et al. 1993), using the quasi-maximum likelihoodestimation. For the mean equation, the lag order (p) rangesfrom one to ten. The selection for the optimal order of lagof GJR(1,1) depends on the Bayesian information criterion.After selecting the lag length and model, the estimated

parameters ai; bi; /i; ci; di; xi

n oare given by:

arg maxai;bi;/i;ci;di;xi

XTt¼1

ln f i ri;t� �

(14)

where f iðri;tÞ follows a univariate EST distribution.After the parameters are estimated by the aforementioned

maximum likelihood process, we obtain the residuals ei andthe associated standardized residualsli ¼ ei;1ffiffiffiffiffi

hi;1p ; . . .;

ei;Tffiffiffiffiffihi;T

p� �T

for each return.

As noted in Section 4.1, this study uses a non-parametricestimation in the transformation of the standardized residu-als. The transformed residuals can be obtained by:ui;t ¼ ~F li;t

� �with i ¼ 1; 2; 3, where

Table 1. Descriptive statistics of stock, gold and exchange rate return series.

Mean (in %) Median (in %) SD Min Max Skewness Kurtosis J–B test Pearson Partial

UKStock 0.0020 0.2400 0.0251 −0.1273 0.1359 −0.3902 6.8983 476.1520***Exchange rate 0.0034 −0.0511 0.0133 −0.0530 0.0717 0.5149 5.8910 283.7203*** −0.0823 −0.0893Gold 0.2100 0.1600 0.0235 −0.1162 0.1029 −0.3359 5.7018 233.4951*** 0.0473 0.0587

GermanyStock 0.0458 0.4600 0.0342 −0.1680 0.1715 −0.7008 6.9215 522.4521***Exchange rate −0.0359 −0.0608 0.0145 −0.0981 0.0509 −0.2029 5.6925 223.3469*** −0.0814 −0.0839Gold 0.1700 0.1600 0.0229 −0.1189 0.0744 −0.3282 5.1625 153.8570*** 0.0136 0.0244

SwitzerlandStock 0.0189 0.1700 0.0265 −0.1399 0.1480 −0.3539 8.1612 817.5707***Exchange rate −0.0724 −0.0964 0.0153 −0.0999 0.0860 −0.0806 6.6219 395.9762*** 0.2299 0.2099Gold 0.1400 0.1800 0.0232 −0.1225 0.0889 −0.4057 5.7452 246.8637*** 0.1461 0.1106

USAStock 0.0331 0.1800 0.0252 −0.1645 0.1018 −0.5863 7.5667 669.6808***Exchange rate −0.0163 −0.0607 0.0059 −0.0299 0.0334 0.2750 5.8925 261.1503*** −0.3028 −0.3038Gold 0.1900 0.2200 0.0240 −0.1249 0.0909 −0.3639 5.7220 239.1635*** 0.0130 −0.0285

CanadaStock 0.0690 0.2000 0.0238 −0.1526 0.0783 −0.7508 6.4465 425.7637***Exchange rate −0.0452 −0.0376 0.0131 −0.0607 0.0602 0.2181 5.7730 237.3838*** −0.4168 −0.4255Gold 0.1600 0.2400 0.0233 −0.1089 0.0908 −0.1012 5.3595 168.9494*** 0.0530 0.1076

JapanStock −0.0334 0.2600 0.0322 −0.2113 0.1479 −0.5888 6.6063 433.5690***Exchange rate −0.0068 0.0363 0.0137 −0.0655 0.0693 −0.2720 5.2078 155.7591*** 0.3340 0.2845Gold 0.2000 0.3300 0.0265 −0.1432 0.0939 −0.6690 6.0055 326.0506*** 0.2171 0.1196

AustraliaStock 0.0775 0.2300 0.0210 −0.1145 0.1204 −0.5593 7.0513 532.1416***Exchange rate −0.0480 −0.1700 0.0182 −0.0636 0.1705 1.4700 14.7308 4405.9270*** −0.4685 −0.4320Gold 0.1600 0.0831 0.0250 −0.1105 0.2040 0.6358 11.1283 2039.0125*** −0.2103 −0.0634

Notes: ‘SD’ and ‘J–B test’ denote the standard deviation and the Jarqe–Beta normality test, respectively. ‘Pearson’ and ‘Partial’ denote the Pearson’scorrelation and the partial correlation, respectively. The number of observation is 723.***Denotes significance at 1%.

12 C.-S. Liu et al.

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~F lð Þ ¼ 1Tþ1

PTt¼1 I l� li;t

� �is the rescaled empirical cumu-

lative distribution function.Following Li (2005), the marginal densities and the cop-

ula density in our model can be individually estimated.Given the estimated marginal parameters and the rescaledempirical cumulative distribution function, u1, u2, u3 asinputs of the MEST copula function, we have the trivariateEST copula function:

c u1; u2; u3; U; h kð Þ; k; s; vð Þ

¼ f F�11 u1ð Þ; F�1

2 u2ð Þ; F�13 u3Þ; U; h kð Þ; k; s; ðvþ 3ð Þ� �

Q31 f i F

�1i uið Þ; ki; s; vþ 1

� �(15)

We can estimate the parameters W2 ¼ U; h kð Þ; k; s; vð Þ bymaximizing the log-likelihood function of the MEST copulafunction of (15) based on the quasi-maximum likelihoodtheory:

W2 ¼ U; h kð Þ; k; s; vð Þ (16)

6.3. Estimation results of marginal models

Table 2 reports the estimates of the marginal models forreturns of the stock price, USD and the gold price. Theslope parameters in the conditional variance function aregenerally significant at conventional levels.

To examine whether the selected models adequatelyremove the intertemporal dependence in the returns, weexamine the serial correlation and autoregressive conditionalheteroscedasticity in the residuals with the Q and ARCH-LMtests. The Q statistics fail to reject the hypothesis of no serialcorrelation at the 5% level. Meanwhile, the ARCH-LM statis-tics fail to reject the hypothesis of no autoregressive condi-tional heteroscedasticity in the residuals at the 5% level.

6.4. Estimation results of the EST copula model

After estimating the filtered residuals in the first stage, weestimate the MEST copula model for each country. Thecopula parameter estimates (v, k1, k2, k3 and s) are reportedin Table 3. The joint distribution of the markets in the UKhas heavier tails than those in other countries, as its esti-mated degrees of freedom v is relatively small, suggesting ahigher joint probability of extreme events in stock,exchange rates and gold markets. The estimated shapeparameters k1, k2 and k3 which control the skewness of themarginal and joint distributions, are significant in all exam-ined countries, indicating that the joint distributions of thethree markets for all countries are asymmetric. The esti-mated extension parameter s, which captures the heavy/thin-tailed property of joint distribution, is significant in allcountries except Canada, indicating that the EST copulamodel is more appropriate than the ST copula model basedon Azzalini and Capitanio (2003). Overall, the significanceof the shape and extension parameters indicates that

skewness and heavy/thin-tailed features exist in most of themarkets, demonstrating the suitability of our proposedmodel.

6.5. Unconditional analysis of hedging and the safehaven effect of gold and USD

Recall that the first aim of our investigation is to examinehypotheses H1a (gold is a hedge against stocks) and H1b(USD is a hedge against stocks). First, we analyse the over-all dependence of the stock–gold pair and stock–USDreturns separately without considering the interactionbetween gold and USD. The conventional way to examinethe dependence structure in the copula model is through thesingle copula parameter. In our study, the MEST copulamodel has multiple parameters, and the significance of theparameters in MEST copula is not appropriate for the analy-sis of the dependence of variables. We use the Kendal’s ss,which measures the association between two distributionsusing a non-parametric method of ordering as an index ofthe overall dependence measure, and we use the lower taildependence coefficient (kL), which measures the probabilityof extreme outcomes of one distribution conditional on theobservation of extreme outcomes on the other distribution,to measure tail dependence. These quantities are defined asfollows:

s ¼ 4

Z½0;1�2

C u1; u2ð ÞdC u1; u2ð Þ � 1 (17)

kL ¼ limu!0þ

Pr F1 y1ð Þ\ujF2 y2ð Þ\u½ �: (18)

6.5.1. Hedging analysis of gold and USD. Table 4reports the unconditional analysis for the Kendal’s τ and kLfor the pairs of stock and USD returns and of stock andgold returns for different countries. Panel A.1 presents theKendal’s τ for the stock–gold returns. The estimatedKendal’s τ varies from 0.0038 to 0.0148. The order ofKendal’s τ is qualitatively different from that of thePearson’s correlation in Table 1. Canada shows the stron-gest positive dependence, followed by Japan and the UK.On the other hand, Australia shows the weakest dependenceamong the countries in the sample. Due to the positivedependence between stock and gold returns, i.e. stock andgold prices move in the same direction, the hypothesis ofgold acting as a hedge against stocks in all the countriesconsidered in the sample should be rejected.

Panel B.1 of Table 4 presents the Kendal’s s for thestock–USD pair. Note that the measure of the exchange rateseries (USD) in the US is, by nature, different from othercurrencies and should be treated differently. The estimatedKendal’s s varies from −0.0142 to 0.0213. Approximatelyhalf of the sample countries—those other than the USA,

Hedges or safe havens role of gold and USD against stock 13

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Table

2.Estim

ationresults

ofmarginalfunctio

ns.

UK

Germany

Switzerland

Stock

Exchang

erate

Gold

Stock

Exchang

erate

Gold

Stock

Exchang

erate

Gold

AR(3)-GJR

AR(3)-GJR

AR(7)-GJR

AR(1)-GJR

AR(3)-GJR

AR(3)-GJR

AR(1)-GJR

AR(1)-GJR

AR(1)-GJR

α0.00

62**

*−0.00

060.00

21**

*0.0119

***

−0.00

470.00

14*

0.00

88**

*−0.00

10*

0.00

12*

(0.002

1)(0.001

4)(0.000

7)(0.002

2)(0.017

2)(0.000

8)(0.001

8)(0.000

5)(0.000

7)β 1

−0.10

86**

*0.02

000.01

95−0.15

22**

*0.00

340.00

87−0.15

46**

0.04

71−0.01

31(0.042

5)(0.0311)

(0.062

4)(0.042

1)(0.078

2)(0.081

4)(0.072

6)(0.029

1)(0.023

7)β p

−0.01

80−0.05

93*

−0.1117

**0.02

830.04

14(0.112

1)(0.034

2)(0.0311)

(0.050

3)(0.189

2)(0.037

9)(0.040

9)φ

3.21

e-05

*1.17

e-05

***

3.19

e-05

***

6.75

e-05

*1.33

e-05

***

2.76

e-05

***

5.30

e-05

*1.73

e-05

***

3.30

e-05

***

(1.79e-05)

(3.16e-07)

(1.01e-05)

(3.35e-05)

(2.33e-06)

(6.31e-06)

(2.84e-05)

(1.52e-07)

(3.28e-06)

γ0.26

31**

*0.09

17**

0.12

85**

*0.10

20**

0.08

40**

*0.15

78**

*0.22

03*

0.05

96*

0.18

87**

*(0.077

2)(0.038

3)(0.038

2)(0.043

1)(0.013

3)(0.050

5)(0.129

9)(0.030

8)(0.010

5)δ

0.79

38**

*0.84

13**

*0.81

73**

*0.75

30**

*0.87

40**

*0.79

94**

*0.72

35**

*0.84

86**

*0.76

42**

*(0.114

7)(0.025

4)(0.049

2)(0.071

9)(0.012

1)(0.062

7)(0.247

1)(0.030

4)(0.200

4)w

0.33

620.00

171.56

e-07

0.25

597.25

e-06

2.63

e-05

0.39

910.03

282.63

e-05

(0.853

1)(0.170

9)(4.16e-06)

(0.168

9)(5.69e-04)

(1.25e-04)

(0.383

2)(0.053

7)(5.71e-04)

Q22

.008

730

.426

5*23

.128

817

.2112

10.628

725

.659

517

.893

26.87

0222

.754

0[0.340

0][0.068

9][0.282

5][0.639

2][0.955

3][0.177

4][0.594

4][0.997

1][0.301

0]LM

0.51

800.00

280.59

900.33

510.06

020.00

400.88

400.39

970.02

37[0.471

7][0.958

1][0.439

0][0.562

7][0.806

2][0.949

8][0.347

1][0.527

3][0.877

7]

USA

Canada

Japan

Stock

Exchang

erate

Gold

Stock

Exchang

erate

Gold

Stock

Exchang

erate

Gold

AR(2)-GJR

AR(1)-GJR

AR(2)-GJR

AR(1)-GJR

AR(4)-GJR

AR(1)-GJR

AR(1)-GJR

AR(5)-GJR

AR(4)-GJR

α0.00

66**

*−0.00

020.00

030.00

82**

*−0.00

07−4.31

e-05

0.01

43**

0.00

050.00

23**

(0.002

1)(0.000

3)(0.007

7)(0.001

8)(0.000

6)(0.005

1)(0.005

8)(0.0011)

(0.000

8)β 1

−0.13

97**

*0.24

98**

*−0.06

11**

−0.10

39**

*−0.08

37**

0.04

07−0.01

220.02

55−0.07

02(0.045

2)(0.034

2)(0.029

7)(0.039

9)(0.036

1)(0.061

9)(0.100

8)(0.049

3)(0.063

8)β p

−0.05

26*

−0.04

790.00

910.04

65−0.05

55**

*(0.031

6)(0.033

1)(0.034

4)(0.030

6)(0.017

1)φ

2.69

e-05

**2.24

e-06

***

3.05

e-05

***

2.12

e-05

**5.86

e-06

***

3.11e-05

***

0.00

01**

1.26

e-05

**3.26

e-05

***

(1.26e-05)

(1.23e-07)

(1.39e-06)

(1.08e-05)

(3.66e-07)

(4.25e-06)

(5.09e-05)

(1.16e-06)

(3.39e-06)

γ0.23

90**

*0.12

62**

*0.08

77**

0.19

51**

0.13

10**

*0.08

63**

0.10

89*

0.07

12**

0.1111**

*(0.067

0)(0.042

2)(0.043

7)(0.096

0)(0.031

9)(0.035

1)(0.062

1)(0.030

4)(0.043

0)δ

0.80

44**

*0.81

06**

*0.85

40**

*0.82

53**

*0.84

39**

*0.85

43**

*0.80

23**

*0.85

75**

*0.84

22**

*(0.062

3)(0.016

9)(0.0411)

(0.049

9)(0.012

2)(0.030

7)(0.098

2)(0.075

1)(0.081

9)w

0.31

061.36

e-05

6.84

e-06

1.39

e-05

3.18

e-05

1.07

e-06

0.06

920.01

46(0.881

2)(0.050

9)(1.56e-05)

(0.090

6)(0.080

4)(9.21e-05)

(0.146

2)(0.014

1)Q

19.851

913

.291

725

.528

322

.021

423

.199

219

.999

719

.506

316

.064

118

.148

6[0.467

2][0.864

5][0.182

0][0.339

3][0.279

1][0.457

9][0.489

2][0.712

6][0.577

6]LM

0.43

400.22

100.13

430.46

641.57

480.07

900.00

670.32

240.83

76[0.510

0][0.638

3][0.714

0][0.494

6][0.209

5][0.778

7][0.935

0][0.570

2][0.360

1]

14 C.-S. Liu et al.

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Australia

Stock

Exchang

erate

Gold

AR(1)-GJR

AR(6)-GJR

AR(2)-GARCH

α0.00

52**

*−0.00

59**

*−0.00

33(0.001

2)(0.001

6)(0.004

0)β 1

−0.02

740.00

30−0.00

06(0.052

1)(0.036

1)(0.058

2)β p

0.05

98*

0.0117

(0.035

9)(0.069

5)φ

1.94

e-05

2.35

e-05

***

3.69

e-05

**(1.50e-05)

(5.17e-06)

(1.57e-05)

γ0.04

74**

0.15

32**

*0.15

63**

*(0.020

0)(0.033

1)(0.052

7)δ

0.81

92**

*0.82

78**

*0.80

98**

*(0.090

0)(0.025

4)(0.040

3)w

0.21

033.58

e-05

5.74

e-05

(0.978

0)(0.097

8)(0.019

4)Q

15.6110

31.197

834

.977

3[0.740

4][0.052

6][0.020

2]LM

0.09

220.75

310.08

53[0.761

4][0.385

5][0.770

2]

Notes:r ideno

teslogreturnsof

stockprice,

exchange

rate

andgo

ldprice.

Num

bers

inbrackets

arep-values

andnumbers

inparenthesesarestandard

deviations.Q

stands

forQ-statisticsfortestingthehy

pothesis

ofno

serial

correlation.

LM

stands

forARCH-LM

statisticsforthehypothesisof

noautoregressive

conditional

heteroscedasticity.

***D

enotesign

ificanceat

1%.

**Denotesign

ificanceat

5%.

*Denotesign

ificanceat

10%.

Hedges or safe havens role of gold and USD against stock 15

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Canada and Australia—show a positive dependence, withthe strongest dependence for Japan. For the countries withnegative dependences, Canada shows the strongest negativedependence, followed by Australia and the USA. From theestimation results in this table, we conclude that USD couldact as a strong hedge against stocks in Canada andAustralia, which is also consistent with our findings inTable 1. This partially supports our hypothesis H1b.

For the evaluation of the hedging role of gold and USD,the analysis given the MEST distribution assumption doesnot differ much from our previous results. Although theoverall dependences observed for stock–USD pairs here areall positive, they are relatively small in magnitude, which isconsistent with the corresponding Pearson’s correlationsreported in Table 1. On the other hand, USD could serve asa hedge asset for investors in Canada and Australia, whichis also consistent with the previous findings. Although itseems that our new econometric method does not providetoo many qualitatively different results, the goal here is toprovide a benchmark when we evaluate the safe haven rolesof gold and USD. Therefore, we can later judge whetherthese assets can be correlated (uncorrelated) with thedomestic stock performance in general but uncorrelated(correlated) when domestic stock markets crash.

6.5.2. Weak safe haven analysis of gold and USD.Panel A.2 of Table 4 shows the kL for the stock–goldreturns. For the observed tail dependences, we choose 0.01as the threshold for being a weak safe haven in our study.†Recall that the tail dependence measures the probability ofextreme outcomes of one distribution conditional on theobservation of extreme outcomes on the other distribution,and the choice of the 0.01‡ threshold means that when thestock is doing extremely poorly and passes the threshold,there is a 1% or higher chance that the alternative invest-ment, such as gold or USD, will also perform extremelypoorly. From our estimation, Switzerland has the largest kL(0.0563), followed by Germany (0.0045) and the UK(0.0003). Except for Switzerland, the kL for other countriesare less than 0.01 and are insignificant at 5% statisticallevel. Our results show that gold can act as a weak safe

Table 4. Unconditional dependence for hedge and weak safe haven investigations.

UK Germany Switzerland USA Canada Japan Australia

Panel A.1: Kendal’s τ between stocks and gold0.0131 0.0103 0.0124 0.0057 0.0148 0.0140 0.0038Panel A.2: kL between stocks and gold0.0003 0.0045* 0.0563*** 0.0000 0.0000 0.0000 0.0000

Panel B.1: Kendal’s τ between stocks and USD0.0059 0.0033 0.0157 −0.0133 −0.0142 0.0213 −0.0138Panel B.2: kL between stocks and USD0.0000 0.0000 0.0165*** 0.0000 0.0000 0.0000 0.0148**

Notes: We report the estimates of Kendal’s τ and lower tail dependence coefficient for stock–gold (Panel A) and stock–USD (Panel B)pairs using MEST copula model.***Denote significance at 1%.**Denote significance at 5%.*Denote significance at 10%.

Table 3. Estimated coefficient of EST copula functions.

UK Germany Switzerland USA Canada Japan Australia

v 6.6003* 7.2072*** 6.9101*** 25.1189*** 19.3183*** 9.9138*** 23.6333***(3.7855) (2.7930) (2.4363) (0.0850) (0.1199) (1.9648) (0.8971)

k1 0.1117 0.0379*** 0.0881*** −1.5834 0.2283*** 0.3050*** −0.3813***(0.0789) (0.0065) (0.0193) (1.0049) (0.0573) (0.0146) (0.0689)

k2 7.6448** 9.1369*** 9.2239*** 0.1906** 0.3038*** 0.3828*** 10.1732***(3.1728) (0.2884) (2.3009) (0.0783) (0.1029) (0.0296) (3.1518)

k3 0.0983 0.1042*** 0.2708*** 0.0124 3.9434*** 10.84447*** 0.3789***(0.0745) (0.0056) (0.0580) (0.0534) (0.8328) (1.3227) (0.0285)

τ 19.7331** 27.1675*** 27.6008*** −0.0723*** 20.0275 34.5608*** 31.7471***(10.0031) (2.4800) (8.2504) (0.0004) (13.1143) (3.6512) (1.0684)

Notes: Numbers in parentheses are standard deviations. ks are the shape parameters for marginal distribution, τ is an extension parameter and v is thedegree of freedom.***Denote significance at 1%.**Denote significance at 5%.*Denote significance at 10%.

†Although there is no closed-form solution for the distribution ofthe tail dependence, it is possible to use bootstrapping to obtainthe approximate significances.‡Under Basel Accord, financial institutions need to calculate10-day VaR with 99% confidence level for the financial assets onthe trading book. Because we use weekly data, which is somewhatclose to the 10-day interval as regulated, we believe a 1% thresh-old is reasonable also for the practice matters.

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haven against stock for the USA, Canada, Germany, theUK, Japan and Australia during the stock crisis.

Panel B.2 of Table 4 reports the kL for the stock–USDpair. Switzerland has the largest kL (0.0165), followed byAustralia (0.0148). Except for Switzerland and Australia,the kL for other countries are less than 0.01 and areinsignificant at 5% statistical level. Similar to the stock–gold pairs, the near-zero estimates of kL can explain the factthat USD acts as a weak safe haven against stock foralmost all countries except Switzerland and Australia duringthe crisis. Hypothesis H2b is supported in most countries,except Switzerland and Australia.

The hypotheses regarding the weak safe haven propertiesof USD and gold are justified using the tail dependencecoefficients. Gold and USD can serve as weak safe havenassets for most of the countries in our sample, which meansthe performances of these alternatives are not correlatedwith the stock market movement during stock marketcrashes. However, when holding portfolios with stocks andthese alternative assets, investors would like to see thesealternative assets perform better when the remaining part ofthe portfolio loses money. This property can be tested usingthe strong rather than weak safe haven definition, whichwill be tested next.

6.5.3. Strong safe haven effect of gold and USD. Thelower tail dependence coefficient with a range between zeroand one is used to detect whether two factors have positiveor zero correlations. Because a strong safe haven is definedas an asset that is negatively correlated with another assetunder extreme market conditions, the lower tail dependencecoefficient estimated in the previous section is not appropri-ate to verify whether gold/USD is a strong safe havenagainst a domestic stock market crash. According to thedefinition, a strong safe haven can nevertheless be deducedin another way: an asset that is positively correlated withanother asset with negative values. This implies thathypothesis H3a (H3b) can be identified by determiningwhether stock returns and negative gold returns (negativeUSD returns) are positively correlated. Table 5 reports theestimated kL with negative gold returns and negative USDreturns.

Panel A of Table 5 shows the kL for the stock andnegative gold returns. The estimated kL varies from 0.0002

in Switzerland to 0.1535 in Germany. In three of the sevencountries in our sample, the kL are above 0.1 and are signif-icant at 5% statistical level, which suggests there is agreater than 10% chance that the gold price is going tosurge when the stock market crashes. The results arebroadly consistent with H3a, supporting that gold is astrong safe haven against stocks in the USA, the UK,Germany and, probably, Australia. Panel B of Table 5shows the kL for the stock and negative USD returns. Theestimated kL are all greater than 0.01 and are significant at5% statistical level except for the USA and Switzerland,which have a near-zero value. Four of the seven countriesin our sample have a kL > 0.1. The results support hypothe-sis H3b that USD is a strong safe haven against stocks inthe UK, Germany, Japan, Australia and, probably, Canada.

6.5.4. Discussion. To conclude, we find the followingobservations from our estimated model. Gold serves as atthe best weak hedge asset against the stock market perfor-mances for all seven countries, but USD can possibly serveas strong hedge asset for Canada and Australia. During astock market crisis, gold can serve as a weak safe havenasset for all countries except Switzerland and as a strongsafe haven asset for the UK, and Germany and the USA.USD can serve as a weak safe haven asset for almost allcountries, with the exception of Switzerland and Australia,and as a strong safe haven asset for the UK, Germany,Japan and Australia.

The strong hedging effects of USD for Canadian andAustralian investors are consistent with the empirical resultsin Campbell et al. (2010). Without considering our general-ization on the return distributions, our empirical model isqualitatively similar to the first model presented in theirpaper, which examines the case of an investor who is fullyinvested in a single-country equity portfolio and is consider-ing whether exposure to one of the other currencies (USDonly, in our paper) would help reduce her portfolio volatili-ties. They find that only Canadian and Australian investorswould optimally choose to hold significant long position onthe USD, implying that the USD can help hedge their expo-sure to the domestic stock market risk. They attribute thesefindings to the observation that Australian and Canadiandollars tend to depreciate against all currencies when theirstock markets fall, which may be caused by the unusually

Table 5. Unconditional dependence for strong safe haven investigations.

UK Germany Switzerland USA Canada Japan Australia

Panel A: kL between stocks and gold0.1105*** 0.1535*** 0.0002 0.1120*** 0.0034* 0.0003 0.0440**

Panel B: kL between stocks and USD0.1009*** 0.1383*** 0.0001 0.0000 0.0243** 0.1384*** 0.1180***

Notes: We report the estimates of lower tail dependence coefficient for stock–gold (Panel A) and stock–USD (Panel B) pairs by negativeexchange rates and negative gold prices. The estimation is conducted using MEST copula model.***Denote significance at 1%.**Denote significance at 5%.*Denote significance at 10%.

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commodity-dependent economies in Canada and Australia,and thus foreign currency (USD) can serve as a hedgeagainst fluctuations in these stock markets.†

Our results regarding the (insignificant) safe haven prop-erty of gold and USD in Switzerland are consistent with thefindings in Ranaldo and Soderlind (2010). They find thatfor the US investors, Swiss franc shows the strongest safehaven patterns with the most significant coefficients and thelargest R-squares. They argue that their findings are consis-tent with the traditional view that Swiss franc provide onaverage safe haven or hedging benefits to the US investors.Their arguments imply that neither USD nor gold may benecessary for investors in Switzerland to hedge their risk innormal or extreme market time.‡ In contrast, we find theinvestors in the UK can enjoy the most benefits from hold-ing USD and gold as safe haven assets, consistent withRanaldo and Soderlind’s findings that British pound showsthe weakest safe haven pattern for the US investors.

From the summary of these results, we note the follow-ing patterns. First, although USD can serve as a hedge assetfor investors in some countries, it is positively correlatedwith the domestic stock market in others. This findingimplies that USD cannot serve as a hedge asset for eachcountry and thus the hedging ability of USD should be cor-related with some country-specific characteristics, such asimports and exports. Second, if an alternative investment isa strong safe haven asset against stock market crashes, it isalso a weak safe haven asset.§ Note that although this pat-tern seems to be guaranteed, it is not necessarily true in the-ory. For example, if the gold (or USD) returns becomeextremely volatile when stock markets crash, we mightobserve a very high tail dependence on both sides, as wedid in detecting the weak and strong safe haven assets.Third, if an alternative investment is a hedge asset againstnormal stock market movements, it is not necessarily agood safe haven asset against stock market crashes. We canillustrate this idea by comparing the results of the stock–USD pair in Canada and Japan. The general co-movementas measured by Kendal’s s is negative and large in magni-tude in Canada. However, USD can serve as only a weaksafe haven for Canadian investors. On the other hand, thePearson’s coefficient and Kendal’s s between USD andstock market returns are all positive in Japan, indicating thatUSD is not a good hedge asset for Japanese investors.However, USD serves not only as a weak safe haven, but

also a strong safe haven during Japanese stock marketcrashes.

These findings, combined with the discussions above,suggest that the fundamental factors driving the generalco-movement and the co-movement under extreme marketconditions might be different. The above findings are con-sistent with our hypotheses that the hedging ability of thesealternative assets may be related to the inflation hedgingability, as argued by Jaffe (1989) and McCown and Zim-merman (2007), while the safe haven ability of these assetsmay be caused by the flight-to-quality hypothesis suggestedby Caballero and Krishnamurthy (2008). A more detailedanalysis is beyond the scope of our current study andshould prove an interesting topic for further studies. How-ever, our methodologies provide a general framework forfuture researchers to analyse and distinguish the hedgingand safe haven roles of alternative investments.

Our finding of significant tail dependence in the stock–gold and stock–USD pairs has important implications inrisk management and asset pricing. A left tail dependenceindicates the potential of a simultaneous large loss in boththe stock and gold (or USD) markets. This joint downsiderisk has been well documented in the literature of stockmarket. Stock foreign exchange rate joint downside risk isimportant to global investors when investing in foreignstock markets. For example, an extreme market eventinvolving a 10% loss in the UK stock market would,under stock foreign exchange rate tail dependence, implythe potential of a large loss, for instance 5%, in theexchange rate. Consequently, a US investor who investedin the UK stock market would suffer from a loss which islarger than 10% in USD. Thus, the existence of lower taildependence implies a much higher downside risk in for-eign stock market investment than the case of no taildependence.

Although in this paper we do not suggest a portfoliochoice which can optimize the downward risk under theextreme market condition, our result does imply that thetraditional mean-variance efficient portfolio may not pro-tect investors under stock market crashes. The main rea-sons of this result come from two realistic assumptions:First, the asset returns are not distributed normally, andsecond, the dependence between two return series are notuniformly identical in different regions of their distribu-tions. Hence, a portfolio which is efficient given normalmarket conditions may not be efficient under extreme mar-ket conditions, and investors may need to make sometrade-off when deciding their asset allocations if theywould want to protect their investment from marketcrashes.

6.6. Conditional safe haven analysis based on the jointestimation of gold, USD and stock

In the existing literature, gold and USD are considered can-didates for hedge or safe haven assets against stocks. Fromour analysis above, gold and USD can serve as safe havenassets for most of the countries studied. An interestingquestion is whether investors in these countries should

†The consistent results between ours and Campbell et al. (2010)may ease the concern of our shorter sample period between 2000and 2013. The sample used in their paper is between 1975 and2005. However, we admit that we cannot fully assert that the dis-tributions of all series in our sample are identical to those before2000, which may have minor impacts on our analysis in safehaven properties.‡Campbell et al. (2010) presents a similar finding for global equityinvestors and makes the same argument. Both findings, along withour results, are consistent with the argument by Habib and Stracca(2012) that Switzerland is typically considered to be a safe havencountry.§The only exception is the stock–USD pair in Australia. However,the positive but small tail dependences (0.0148) observed inTable 4 can still be quite low, and USD can still be possibly aweak safe haven asset against stock market crashes in Australia.

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choose gold or USD for hedging against domestic stockmarket crashes. Moreover, we also want to know whetherthe safe haven effects exist when two alternative invest-ments are included in the portfolio. To answer these ques-tions, we need to consider stock market performance, goldand USD simultaneously. However, to our knowledge, thereis no literature discussing the joint behaviour of gold, USDand stocks. The econometric framework developed in ourpaper can help us easily analyse the joint behaviour of thesethree assets and choose the strongest one. Particularly, wetry to examine hypotheses H4a and H4b by studying theextreme dependence of two pairs: stock–gold conditional onthe USD market and stock–USD conditional on the goldmarket.

6.6.1. Conditional analysis of joint lower tail probabil-ity. As derived earlier, the conditional joint lower tailprobability can be used to test whether stock and one alter-native investment are correlated when the other alternativeinvestment is not performing well. In other words, we canuse the joint lower tail probability to test whether gold(USD) can serve as a strong safe haven asset when USD(gold) performs extremely poorly.

To estimate the joint lower tail probability, we first calcu-late the joint density of the y1 and y2 markets conditionalon the y3 markets:

f y1; y2jy3 2 Dð Þ; (19)

where Δ refers to a given region of either gold or USDreturns. The conditional joint tail probability is thenobtained as follows:

PL ¼ Pr y1\F�11 að Þ and y2\F�1

2 að Þjy3 2 D� �

¼ C a; ajy3 2 Dð Þ; a 2 ð0; 1Þ (20)

where C (·) refers to the MEST copula distribution function.In particular, we consider two extreme market scenarios:

DL ¼ y3 : F�13 ð0Þ� y3 �F�1

3 ð5%Þ� �(21)

DH ¼ y3 : F�13 ð95%Þ� y3 �F�1

3 ð100%Þ� �(22)

where F3 is the marginal distribution of either gold orUSD. We report the joint lower tail probability using theabove specifications in Table 6.

In Panel A of Table 6, the estimated joint probabilities ofstock and gold returns conditional on the USD marketunder the 5, 3 and 1% quantiles are reported. As shown inthe results, the estimates of the lower joint tail probabilityvary from 0.0268% (0.5020%) to 0.0301% (0.5630%) at the1% (5%) quantile, as USD returns fall between the 0 and5% quantiles. Note that countries with a higher joint lowerprobability with one specific α always have a higher jointlower probability with an alternative choice of α as well.

Thus, we will interpret the results only when α = 1%, andthe interpretations should be extended to different choicesof α.

If the gold and stock returns are perfectly correlatedgiven the conditional information set of the choices of USDchanges, the reported joint lower probability should equalα = 0.01, or 1%. On the other hand, if the two returns areuncorrelated, the reported joint lower probability shouldequal to 0.0001, or 0.01%. With greater than 0.01% jointlower probabilities across all countries or different condi-tional information sets, the results imply that when theUSD returns fall into the extreme cases on both tails, thegold and stock returns tend to fall into the lower tails moreoften than when these two asset returns are uncorrelated.

Although the above pattern exists across all countries,when compared with other countries, the estimated jointlower tail probabilities in Canada are smaller at variouslevels of quantiles. This indicates that in Canada, gold isrelatively uncorrelated with stocks in terms of extreme mar-ket movements when USD returns are between the 0 and5% quantiles. In contrast, the estimates of joint lower tailprobability vary from 0.0206% (0.3915%) to 0.0383%(0.7047%) at the 1% (5%) quantile, as USD returns arebetween the 95 and 100% quantiles, and the estimated jointlower tail probabilities in Japan are smaller than those inother countries. Thus, gold may act as a relatively weaksafe haven for Canadian investors when the USD stronglydepreciates and for Japanese investors when the USDstrongly appreciates. However, gold cannot be a strong safehaven for all the countries conditional on strong deprecia-tions of domestic currencies because the joint lower tailprobabilities for all countries are above 0.01%, which is thethreshold for conditional zero correlation.

Panel B of Table 6 presents the conditional joint proba-bility of stock–USD pairs under the 5, 3 and 1% quantiles.Because the gold returns fall between the 0 and 5% quan-tiles, the estimated joint lower tail probabilities vary from0.0275% (0.5154%) to 0.0363% (0.6737%) at the 1% (5%)quantiles. Of all the countries considered, the estimatedjoint lower tail probability in Japan is smaller than those inother countries at every quantile. This observation indicatesthat USD is relatively uncorrelated with Japanese stocks interms of extreme market movement when gold returns fallbetween the 0 and 5% quantiles. When gold is in the bullmarket, the estimated joint lower tail probabilities vary from0.0215% (0.4071%) to 0.0392% (0.57236%) at the 1%(5%) quantile. This indicates that there are 0.03% (0.50%)chances on average for the stock and USD to decreasetogether at the lowest 1% (5%) quantile. Among the mar-kets in the sample, the estimated lower joint tail probabilityof USD and Japanese stocks is the smallest given that thegold returns fall into either the top or bottom quantiles,indicating the probability of simultaneous large losses inUSD and Japanese stocks is smaller than the pairing ofUSD and other stocks. This indicates that USD is mostlikely a weak safe haven for Japanese investors. Again,similar to gold, USD cannot be a strong safe haven for allthe countries conditional on large drops in gold prices.Thus, neither USD nor gold can serve as strong safe havenassets when the other alternative asset performs poorly.

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6.6.2. Conditional independence analysis of lower tailprobability. The above empirical results indicate that thesafe haven effects of both gold and USD disappear whenthe other alternative investment is not doing well. This find-ing implies that the inclusions of both USD and gold indomestic stock portfolios will not provide stronger safehaven effects. However, it is still possible that the depen-dencies between stock and USD (gold) can be close to zerowhen gold (USD) prices drop suddenly. In this case, USD(gold) can still serve as a weak safe haven asset even if wehave already included the other alternative investment inour portfolios.

In statistics, we observe that x and y are independent condi-tional on z if and only if P (x|z) = P (x|y, z) when P (y, z) > 0.This principle implies that x and y are independent condi-tional on z if and only if P (x < a|z < a) = P (x < a|y < a,z < a). In this section, we attempt to test whether gold is aweak safe haven against a domestic stock market crash aftercontrolling for the extremely poor performance of USD andwhether USD is a weak safe haven against the domestic stockmarket crash after controlling for the extremely poor perfor-mance of gold. To test these hypotheses, we examine whetherstock and gold (USD) are independent conditional on thecrash of the USD (gold) market. For example, we can calcu-late the conditional density of the stock market conditional onthe USD and gold markets:

f y1jy2\F�12 að Þ; y3\F�1

3 að Þ; a 2 ð0; 1Þ� �(23)

where y1, y2 and y3 refer to stock, USD and gold returns,respectively. a refers to a given quantile. The correspondingconditional tail probability is then obtained byPr y1\F�1

1 ðaÞjy2\F�12 að Þ; y3\F�1

3 ðaÞ� �. In addition, we

calculate the conditional density of the y1 conditional onthe y3:

f y1jy3\F�13 ðaÞ� �

(24)

Similarly, the conditional tail probability on y3 isPr y1\F�1

1 að Þjy3\F�13 að Þ� �

. If two conditional probabili-ties are equivalent, then stock returns and USD returns areindependent conditional on a specific status of goldreturns.

From Panel A of Table 7, the difference of two condi-tional probabilities in absolute value vary from 0.3938%(Australia) to 3.8036% (Canada). The results indicate thatstock returns and gold returns are independent conditionalon gold returns in the USA and Australia. However, fromthe results in Panel B of Table 7, the differences of thetwo conditional probabilities in absolute value vary from0.0584% (the UK) to 6.9862% (the USA). This findingreveals that stock returns and USD returns are independentconditional on gold returns in the UK and Germany, asthe difference between the two probabilities is less than1%. Thus, we argue that USD can be a weak safe havenfor the UK and Germany conditional on large drops ingold prices, and gold can be a weak safe haven for theUSA and Australia conditional on the poor performanceof USD.

6.6.3. Discussion. In general, when stocks and two alter-native investments are considered within one framework,the results provide some evidence consistent with ourhypotheses regarding safe haven properties and some newinsights requiring our investigation. When one alternativeinvestment (gold or USD) is performing extremely well, thechances that stock and the other alternative investment willdrop together are often high. This finding can be consistentwith the flight-to-quality hypothesis. Suppose that domesticinvestors can invest in only these three assets.

Table 6. Joint safe haven effects: conditional joint lower tail probability.

Exchange rate UK Germany Switzerland USA Canada Japan Australia

Panel A: joint lower tail probability between stocks and gold conditional on USD (in %)0–5% α = 1% 0.0286 0.0286 0.0286 0.0301 0.0268 0.0280 0.0277

α = 3% 0.2032 0.2032 0.2033 0.2138 0.1904 0.1991 0.1971α = 5% 0.5358 0.5359 0.5362 0.5630 0.5020 0.5251 0.5197

95–100% α = 1% 0.0261 0.0264 0.0235 0.0383 0.0284 0.0206 0.0284α = 3% 0.1858 0.1882 0.1677 0.2695 0.2017 0.1474 0.2017α = 5% 0.4908 0.4967 0.4441 0.7047 0.5309 0.3915 0.5313

GoldPanel B: joint lower tail probability between stocks and USD conditional on gold (in %)0–5% α = 1% 0.0293 0.0293 0.0283 0.0363 0.0300 0.0275 0.0299

α = 3% 0.2081 0.2083 0.2014 0.2566 0.2134 0.1954 0.2127α = 5% 0.5488 0.5493 0.5312 0.6737 0.5628 0.5154 0.5610

95–100% α = 1% 0.0252 0.0256 0.0239 0.0392 0.0253 0.0215 0.0268α = 3% 0.1797 0.1825 0.1705 0.2764 0.1804 0.1535 0.1907α = 5% 0.4751 0.4824 0.4513 0.7236 0.4775 0.4071 0.5040

Notes:We report the estimates of the conditional joint tail probability for stock–gold and stock–USD pairs. The upper panel reports the estimated jointprobabilities of stock and gold returns, conditioning on USD market, under the 5, 3 and 1% quantiles. The lower panel reports the estimated joint proba-bilities of stock and USD returns, conditioning on gold market, under the 5, 3 and 1% quantiles.

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When very good news comes with one asset, investorsmay choose to withdraw their investments in the other twoassets and cause a sudden drop in the values of theseassets.

However, when we check the cases when the conditionalasset returns fall into the bottom quintile, the lower taildependencies are close to, or even larger than, their counter-party when the conditional asset returns fall into the topquintile. In other words, when USD (gold) prices drop sig-nificantly, the chances that stock and gold (USD) also dropsignificantly are higher than assuming that the latter two areuncorrelated. Thus, the strong safe haven effects as detectedin the two-variable model no longer exist when the thirdasset’s returns also fall into the bottom quintile. Althoughthe results under the conditional independence analysis stillshow that gold (USD) can still conditionally serve as aweak safe haven asset for a subset of the countries identi-fied in the unconditional analysis, the zero or positive con-ditional correlation implied in our model still brings intoquestion the joint safe haven effects of gold and USD.

The above findings may be a surprising result at firstglance, but they are in fact consistent with economic intu-ition. Sandoval and Franca (2012) show that the globalstock market tends to have a high correlation during greatcrashes, and this is also the time when global stock marketvolatilities are high (see e.g. Schwert 2011). Thus, the con-ditional distributions of all of the assets, including stocks,tend to have fatter tails than their unconditional distribu-tions, and the chances that the remaining assets also per-form extremely poor will be higher than those forunconditional cases. However, this observation does raisethe question of whether the safe haven properties of thesealternative investments may exist only under some circum-stances. The trivariable cases used here demonstrate the sit-uation when the prices of the assets used as safe havenassets also drop significantly, and we should be cautious inmaking quick conclusions about the safe haven roles ofthese assets before considering the other alternative invest-ment performances and other macroeconomic issues.

In short, our conditional analysis provides an importantanswer for a usually ignored question: Can investors usetwo or more alternative investments to prevent large lossesduring stock market crashes? Our results indicate that thesafe haven effects of USD and gold will decline when bothassets are used as safe haven assets. Neither asset will dom-inate the other during stock market crashes, and the joint

safe haven strategy does not outperform the single safehaven strategy. Previous studies with no consideration ofthe joint properties of USD and gold may lead to a naiveconclusion for risk management strategies.

7. Robustness test

In this section, we test whether the returns on the exchangerate influence the overall and tail correlations of stocks andgold returns using the gold returns evaluated in terms ofUSD. Although we believe the approach used in our paper,evaluating gold returns in terms of domestic currencies, ismore consistent with the portfolio choice problems faced bydomestic investors, it is common to see scholars use goldreturns in only one currency. The advantage of the latterapproach is that we can isolate the exchange rate fluctua-tions from the gold returns. To check whether our estima-tions are affected by the specifications of the data in thepaper, we reevaluate Kendal’s s and kL of stock–gold inTable 4 and present the revised results in Table 8.

The estimated Kendal’s s and kL between stocks andgold in Table 8 are broadly consistent with the results inTable 4, except probably for Switzerland. The correlationbetween stock and gold during the normal and extremetimes is slightly different for Switzerland, but it still pro-vides qualitatively similar conclusions.

8. Comparison of lower tail dependence coefficientswith the ST copula model

Another question to ask is whether our more generalizedMEST copula model can provide more accurate or differentresults from the more restricted approaches in previousstudies. We compare our proposed model with the ST cop-ula model discussed by Demarta and McNeil (2005) andChristoffersen et al. (2012) in the estimation of kL. Theresults are presented in Table 9. The estimated lower taildependence coefficients by the MEST copula model are sys-tematically lower than those by the ST copula model. Thisproperty strengthens the importance of controlling heavy/thin tails in the estimation of joint distributions.

The results reported in Table 9 are the estimates of thelower tail dependence coefficients for stock–gold and

Table 7. Joint safe haven effects: conditional independence test.

UK Germany Switzerland USA Canada Japan Australia

Panel A: joint lower tail probability between stocks and gold conditional on USD (in %)Pr y1\F�1

1 ðaÞjy2\F�12 ðaÞ� �

1.6715 1.6753 1.6738 1.8050 1.6169 1.6483 1.6762Pr y1\F�1

1 ðaÞjy2\F�12 ðaÞ; y3\F�1

3 ðaÞ� �1.7132 1.7042 1.7148 1.7934 1.6784 1.7011 1.6696

% difference between two probability 2.4948 1.7251 2.4495 −0.6427 3.8036 3.2033 −0.3938

Panel B: conditional lower tail probability between stocks and USD conditional on gold (in %)Pr y1\F�1

1 ðaÞjy2\F�12 ðaÞ� �

1.7122 1.7195 1.6515 1.9281 1.7967 1.6042 1.7840Pr y1\F�1

1 ðaÞjy2\F�12 ðaÞ; y3\F�1

3 ðaÞ� �1.7132 1.7142 1.7148 1.7934 1.6784 1.7011 1.6696

% difference between two probability 0.0584 −0.3082 3.8329 −6.9862 −6.5843 6.0404 −6.4126

Notes: We report the conditional lower tail probabilities of y1 on y2 and y3 and the conditional tail probabilities of y1 on y3, respectively. α = 0.01.

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stock–USD pairs in Panels A and B using the ST copulamodel. Compared with our model, the ST model assumesthe extension coefficient to be zero so that the fat-tailedproperty always comes with the distribution. If the real dis-tributions are not compatible with this specific type of fattail, the lower tail dependence coefficients may be overesti-mated. Compared with Panels A.2 and B.2 in Table 4, theresults generally confirm the overestimated lower taildependence by the ST model. The estimated lower taildependences for six of the seven countries are quite signifi-cant. Thus, the inappropriate restrictions placed on the STmodel can yield incorrect inferences about whether thesealternative investments can serve as safe haven assets dur-ing stock crises.

9. Concluding remarks

Since the recent financial crisis, risk management has beenan important issue in practice and in theory, and the devel-opment of alternative investment markets has acceleratedthe investigation of using these alternative investments tohedge the traditional stock portfolio returns under extrememarket conditions in this decade. In this paper, we try toanswer the questions of whether gold and USD can serveas hedge or safe haven assets for investors in seven differ-ent sample countries. We develop a MEST copula modeland derive the associated lower tail dependence coefficientto examine the overall dependence and tail dependence forstock, the exchange rate and gold markets. We find thatwhen gold and USD are used separately to hedge stock

market movements, USD is a better hedge asset under nor-mal market conditions. When the domestic stock marketcrashes, these two alternative investments can serve as weaksafe haven assets most of time and strong safe haven assetsfor a few countries in our sample. However, being a hedgeasset for investors from a certain country does not guaran-tee that this asset, whether USD or gold, can also be a safehaven asset in that country. This finding provides partialevidence of the fundamentally different drivers of hedgeand safe haven roles. When stock, USD, and gold arejointly estimated and analysed, we find that none of theassets will dominate the other during stock market crashes,which implies that the joint safe haven strategy does notoutperform the single safe haven strategy. While our generalconclusion complements recent studies on the hedge andsafe haven roles of alternative investments with non-normaldistributions, the joint estimation of stock, gold and USD,which can be obtained only in our model, addresses theimportance of using a multivariate distribution model todetermine the hedge and safe haven effects of these invest-ments.

In addition to the economic interpretations in our empiri-cal analysis, the empirical applications of gold and USDusing the proposed model illustrate how to apply oureconometric framework to portfolio allocation problemsgiven that the returns on assets in interest clearly violate thenormality assumptions. Although low-frequency stockreturns are generally considered close to the normal distri-bution, the distribution of high-frequency stock returns orthe returns of many newly developed alternative investmentmarkets, such as the exchange rate, commodities and inter-est rates, can severely violate normality assumptions. In this

Table 8. Unconditional estimation with traditional gold return definitions.

UK Germany Switzerland USA Canada Japan Australia

Panel A.1: Kendal’s τ between stocks and gold0.0104 0.0106 0.0553 0.0085 0.0162 0.0138 0.0084

Panel A.2: kL between stocks and gold0.0007 0.0000 0.0071* 0.0001 0.0002 0.0017 0.0247**

Notes:We report the estimates of Kendal’s τ and lower tail dependence coefficient for stock–gold in which the gold prices arecalculated in USD.**Denote significance at 5%.*Denote significance at 10%.

Table 9. Unconditional dependence estimation in ST copula model.

UK Germany Switzerland USA Canada Japan Australia

Panel A: kL between stocks and gold by ST0.2464 0.2318 0.2608 0.1965 0.0041 0.2900 0.0005

Panel B: kL between stocks and USD by ST0.2141 0.2039 0.2788 0.1146 0.0001 0.3089 0.0876

Note:We report the estimates of lower tail dependence coefficient for stock–gold and stock–USD pairs in Panel A.1 and PanelB.1 using ST copula model.

22 C.-S. Liu et al.

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case, our more generalized econometric model can providerelatively precise statistical inference regarding the eco-nomic questions we are interested in. Furthermore, thedevelopment of the lower tail dependence coefficient in ourstudy can help analyse the probability that two assets crashtogether when one of them is performing extremely poorly.However, this lower tail dependence coefficient is built onthe bivariate case, so we can only evaluate the extreme riskof a pairwise portfolio. Because a market portfolio usuallycontains more than two assets, extending the bivariate lowertail dependence coefficient to the multivariate one would bean important issue in future research.

Although our paper provides a comprehensive analysis ofthe joint behaviours of stock, USD and gold returns undernormal and extreme market conditions, we can only inferthat the economic forces driving the safe haven and hedgeeffects are different and that the alternative investments con-sidered in this paper, i.e. gold and USD, may not fulfil theirindependent safe haven roles on domestic investors’ portfo-lios from the current empirical evidence. It would be inter-esting to further examine the forces behind the riskmanagement roles of these alternative investments. Forexample, one hypothesis is that the balance of trade canaffect the imports of foreign products and the exports oflocal products and materials and, thus, may also adjust theconsumer or producer price level in a country. In that sense,USD may serve as a hedge asset for some countriesbecause it is correlated with domestic inflation. On the otherhand, the econometric framework with multivariate non-normal distributions introduced in this paper can help usfurther investigate whether other alternative investments,such as commodities, real estate and fixed-income products,can also serve as better hedge and safe haven assets. Inreality, it is unreasonable to assume that investors includeonly stocks and a few types of other financial assets in theirportfolios. The joint effects on the risk of investors’portfolios raise another interesting question and shouldattract further research.

Disclosure statement

No potential conflict of interest was reported by the authors.

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Appendix A: Derivation of lower tail dependencecoefficient

As presented in Demarta and McNeil (2005), the lower taildependence coefficient

kL ¼ limu!0þ

P Y1 �F�11 u1ð ÞjY2 �F�1

2 u2ð Þ� �¼ lim

u!0þ

C u; uð Þu

¼ limu!0þ

dC u; uð Þdu

¼ limu!0þ

P U2 � ujU1 ¼ uð Þ þ limu!0þ

P U1 � ujU2 ¼ uð Þ:

We also have

limu!0þ

P U2�ujU 1 ¼ uð Þ ¼ limu!0þ

P U 2�u;U 1 ¼ uð ÞP U 1 ¼ uð Þ

¼ limu!0þ

P F2 Y 2ð Þ�u;F1 Y 1ð Þ ¼ uð ÞP F1 Y 1ð Þ ¼ uð Þ

¼ limy!�1

P F2 Y 2ð Þ�F1 yð Þ;Y 1 ¼ yð ÞP Y 1 ¼ yð Þ

¼ limy!�1

P F2 Y 2ð Þ�F1 yð ÞjY 1 ¼ yð Þ¼ lim

y!�1P Y 2�F�12 F1ðyÞð ÞjY 1 ¼ y

� �

24 C.-S. Liu et al.

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Similarly,

limu!0þ

P U 1 � ujU 2 ¼ uð Þ ¼ limy!�1P Y 1 �F�1

1 F2ðyÞð ÞjY 2 ¼ y� �

:

Therefore,

kL ¼ limy!�1P Y2 �F�1

2 F1ðyÞð ÞjY1 ¼ y� �

þ limy!�1P Y1 �F�1

1 F2ðyÞð ÞjY2 ¼ y� �

:

Let us first derive the first term limy!�1 P Y2 �F�12 F1ðyÞð ÞjY1 ¼ y

� �.

Following Proposition 3 of Arellano-Valle and Genton (2010)and (5) and (8), the bivariate EST and the associated marginalEST are:

f Y ¼ xð Þ ¼ 1

T1 s=1þ hTUh; v� � C vþ2

2

� �pvC v

2

� �Uj j

� 1þ xTU�1xv

� ��vþ22

�T1 hTxþ s� � ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

vþ 2

xTU�1xþ x

r; vþ 2

� �(25)

and for Y 1

f Y 1 ¼ xð Þ

¼ 1

T1 s1=ffiffiffiffiffiffiffiffiffiffiffiffi1þk21

q;v

� � C vþ12

� �ffiffiffiffiffipv

pC v

2

� � 1þ x2

v

� ��ðvþ1Þ=2�

T1 k1xþ s1ð Þffiffiffiffiffiffiffiffiffiffiffiffivþ1

vþ x2

r;vþ1

( )

(26)

where k ¼ k1; k2; k3½ �T , h ¼ D DUD�kkTð Þkffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þkT DUD�kkTð Þ�1

k

q , and

D ¼ diagffiffiffiffiffiffiffiffiffiffiffiffiffi1þ k21

q;ffiffiffiffiffiffiffiffiffiffiffiffiffi1þ k22

q;ffiffiffiffiffiffiffiffiffiffiffiffiffi1þ k23

q;

� �.

Suppose that s; s1; s2f g[ �1 such that the bivariate and themarginal EST do not degenerate to zero. As x ! �1 the lowertail behaviour of Y 1:

P Y 1 � xð Þ� 1

T1 s1=ffiffiffiffiffiffiffiffiffiffiffiffiffi1þ k21

q; v

� � C vþ12

� �ffiffiffiffiffipv

pC v

2

� � xj j�vT 1

�k1ffiffiffiffiffiffiffiffiffiffiffivþ 1

p; vþ 1

� � (27)

Using (25), (26), the conditional density of Y 2j1 ¼ Y 2jY 1 ¼ yð Þ is

f Y 2j1ðxÞ ¼ N � t1 x; qy; s yð Þ; vþ 1ð Þ

T1 h1yþ h2xþ sð Þffiffiffiffiffiffiffiffiffiffiffiffiffi

vþ2

vþ x�qyð Þ21�q2

r; vþ 2

( )

T k1yþ s1ð Þffiffiffiffiffiffiffivþ1vþy2

q; vþ 1

n o (28)

where N T 1

s1ffiffiffiffiffiffi1þk2

1

p ;v

� �T 1

sffiffiffiffiffiffiffiffiffiffi1þhTUh

p ;v

and t1 x; qy; s yð Þ; vþ 1ð Þ is a Student’s t

density with location qy, scale s yð Þ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1�q2ð Þ y2þvð Þ

vþ1

qand the degree

of freedom vþ 1.Next, we derive the quantile function F�1

2 F1ðyÞð Þ as y ! �1.Suppose F�1

2 F1 yð Þð Þ ¼ cðyÞ. From (27), we observe that

c yð Þ�T1 �k2

ffiffiffiffiffiffiffiffiffiffiffivþ 1

p; vþ 1

� �T 1

s1ffiffiffiffiffiffiffiffi1þk21

p ; v

� �

T1 �k1ffiffiffiffiffiffiffiffiffiffiffivþ 1

p; vþ 1

� �T 1

s2ffiffiffiffiffiffiffiffi1þk22

p ; v

� �2664

37751=v

y as y

! 1(29)

Let z ¼ x�qysðyÞ , we have

P F2 �F�12 F1ðyÞð ÞjY 1 ¼ y

� �¼ N � c yð Þ�qy

sðyÞ�1 t1 z; 0; 1; vþ 1ð Þ

�T1 h1yþ h2 s yð Þzþ qyð Þ þ sð Þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffivþ2

vþ vþy2ð Þz21þv þy2

r; vþ 2

( )

T k1yþ s1ð Þffiffiffiffiffiffiffivþ1vþy2

q; vþ 1

n o dx

As y ! �1 and τ1 > −∞,

T1 k1yþ s1ð Þffiffiffiffiffiffiffiffiffiffiffiffivþ 1

vþ y2

s; vþ 1

( )

! T1 �k1ffiffiffiffiffiffiffiffiffiffiffivþ 1

p; vþ 1

� �[ 0 (30)

(30) implies

limy!�1 T1 k1yþ s1ð Þ

ffiffiffiffiffiffiffiffiffiffiffiffivþ 1

vþ y2

s; vþ 1

( ) !�1

\1

By the dominated convergence theorem,

limy!�1P Y 2 �F�1

2 F1ðyÞð ÞjY 1 ¼ y� �

¼T1 s1=

ffiffiffiffiffiffiffiffiffiffiffiffiffi1þ k21

q;

� �

T1 s=ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ hTUh

p; v

�a21�1 t1 z; 0; 1; vþ 1ð Þ

�T1 h2

ffiffiffiffiffiffiffiffi1�q2

vþ1

qz� qh2 þ h1ð Þ

� � ffiffiffiffiffiffiffiffiffivþ21þ z2

vþ1

q; vþ 2

� �T1 �k1

ffiffiffiffiffiffiffiffiffiffiffivþ 1

p; vþ 1

� � dz

where

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a21 ¼T1 �k2

ffiffiffiffiffiffiffiffiffiffiffivþ 1

p; vþ 1

� �T1

s1ffiffiffiffiffiffiffiffi1þk21

p ; v

� �

T1 �k1ffiffiffiffiffiffiffiffiffiffiffivþ 1

p; vþ 1

� �T1

s2ffiffiffiffiffiffiffiffi1þk22

p ; v

� �0BB@

1CCA

1=v

�q

0BBB@

1CCCA

ffiffiffiffiffiffiffiffiffiffiffiffiffivþ 1

1� q2

s:

Following the same process, the second term is given by

limy!�1P Y 2 �F�1

2 F1ðyÞð ÞjY 1 ¼ y� �

¼T 1 s1=

ffiffiffiffiffiffiffiffiffiffiffiffiffi1þ k21

q;

� �

T 1 s=ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ hTUh

p; v

�a21�1 t1 z; 0; 1; vþ 1ð Þ

�T1 h2

ffiffiffiffiffiffiffiffi1�q2

vþ1

qz� qh2 þ h1ð Þ

� � ffiffiffiffiffiffiffiffiffivþ21þ z2

vþ1

q; vþ 2

� �T 1 �k1

ffiffiffiffiffiffiffiffiffiffiffivþ 1

p; vþ 1

� � dz

where

a12 ¼T1 �k1

ffiffiffiffiffiffiffiffiffiffiffivþ 1

p; vþ 1

� �T1

s2ffiffiffiffiffiffiffiffi1þk22

p ; v

� �

T1 �k2ffiffiffiffiffiffiffiffiffiffiffivþ 1

p; vþ 1

� �T1

s1ffiffiffiffiffiffiffiffi1þk21

p ; v

� �0BB@

1CCA

1=v

�q

0BBB@

1CCCA

ffiffiffiffiffiffiffiffiffiffiffiffiffivþ 1

1� q2

s:

Appendix B: The EST copula with dynamic conditionalcorrelation

B.1: DCC-EST copula modelWe follow the dynamic conditional Ccrrelation (DCC) model of

Engel (2002). Let Qt be the auxiliary matrix driving the rank cor-relation dynamics and �Q ¼ E yty

Tt

� �with sample analogue

1T

PTt¼1 yty

Tt

� �. The dynamics of the process is modelled as fol-

lows:

Qt ¼ 1� c1 � c2ð Þ�Qþ c1yt�1yTt�1 þ c2Qt�1

where c1; c2 [ 0, c1 þ c2\1. The correlation matrix Ut is a matrixof rank correlation given by

Ut ¼ diag ðQtÞ�0:5 � Qt � diag ðQtÞ�0:5:

It follows that the dynamic EST copula density is given by:

c u1;t; . . .; up;t;Ut; h kð Þ; k; s; v� �¼

f F�11 u1;t� �

; . . .; F�1p up;t� �

;Ut; h kð Þ; k; s; vþ p

Qp1 f i F

�1i ui;t� �

; ki; s; vþ 1� �

B.2: Estimation resultsThe estimated coefficients c1 and c2 in the dynamic conditional

copula correlation Qt still can illustrate the dynamic nature of thecopula correlations. The estimated values of c1 and c2 are mainlyinsignificant in Table 10, with the estimated coefficients of c2 inthe ranges of 0.97 for the UK and 0.76 for the USA. This indi-cates that the time-varying feature in the copula correlation cannotwell capture the persistence of the dependence in our variablescomparing with the static copula correlation.

Table 10. Estimated coefficient of DCC model.

UK Germany Swiss USA Canada Japan Australia

c1 0.0189 0.0432** 0.0531 0.0659 0.0232 0.0301 0.0342(0.0742) (0.0198) (0.2018) (0.1266) (0.1069) (0.0520) (0.0726)

c2 0.9726*** 0.9371*** 0.8529 0.7601 0.6649* 0.9614*** 0.5560(0.0116) (0.0353) (0.8402) (0.9302) (0.5177) (0.0177) (0.4114)

Notes:Numbers in parentheses are standard deviations.***Denote significance at 1%.**Denote significance at 5%.*Denote significance at 10%.

Table 11. Upper tail dependence coefficients.

UK Germany Switzerland USA Canada Japan Australia

Panel A: kU between stocks and gold0.0001 0.0013 0.0118** 0.0011 0.0000 0.0000 0.0001

Panel B: kU between stocks and USD0.0053* 0.0096* 0.0253*** 0.0046* 0.0002 0.0345** 0.0026

***Denote significance at 1%.**Denote significance at 5%.*Denote significance at 10%.

26 C.-S. Liu et al.

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Appendix C: The upper tail dependence coefficient

As the difference between the upper and lower tail dependencefunctions is that the former function uses the survival function ofthe copula model. Therefore, this study only reports the estimatedresults of upper tail dependence coefficients for stock–gold andstock–USD pairs. Pane A in Table 11 shows the kU for stock–goldpair. From our estimation, Switzerland has the largest kU (0.0118),

followed by Germany (0.0013) and the UK (0.0011). Except forSwitzerland, the kU for other countries are less than 0.01 andstatistically insignificant at 5% level.

Panel B of Table 11 reports the for the stock–USD pair. Japanhas the largest kU (0.0345), followed by Switzerland (0.0253).Except for Switzerland and Japan, the kU for other countries areless than 0.01 and statistically insignificant at 5% level.

Hedges or safe havens role of gold and USD against stock 27

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