Tail dependence between gold and sectorial stocks in China: Insights for portfolio diversification

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1 Tail dependence beween gold and secorial socks in China: Insighs for porfolio diversificaion Joscha Beckmann, a Theo Berger, b Rober Czudaj c and Thi-Hong-Van Hoang d a Universiy of Duisburg-Essen, Deparmen of Economics, Chair for Macroeconomics, ermany b Universiy of Bremen, Deparmen of Business Adminisraion, Chair for Applied Saisics and Empirical Economics, ermany c Universiy of Duisburg-Essen, Deparmen of Economics, Chair for Economerics, ermany d Monpellier Business School, Monpellier Research in Managemen, France Augus 25, 2015 Absrac This aricle analyzes dynamics of relaionship beween gold quoed on he Shanghai old Exchange and Chinese secorial socks from 2009 o Using differen copulas, our resuls show ha here is weak symmeric ail dependence beween gold and secorial socks. Based on he efficien fronier, opimal weigh, hedge raio and hedging effeciveness, we find ha adding gold o Chinese sock porfolios can help o reduce heir risk. old appears o be he mos efficien wih socks of he Energy, Informaion, Telecommunicaion and Maerials secors and he less efficien wih he Uiliies secor. As a robusness check, gold is compared o oil and he resuls show ha gold is also more efficien han oil in he diversificaion of Chinese sock porfolios. JEL Classificaions: 11, C58 Keywords: Shanghai old Exchange, Chinese secorial socks, oil, copulas, porfolio implicaions addresses: J. Beckmann (joscha.beckmann@uni-due.de), T. Berger (hberger@uni-bremen.de), R. Czudaj (rober.czudaj@uni-due.de) and T.H.V. Hoang (hv.hoang@monpellier-bs.com) 1

2 1. Inroducion China has been he larges producer in gold in 2014, conribuing 45% of he world producion and is also he larges world consumer joinly wih India wih boh markes accouning for 54 percen of consumer gold demand according o he World ould Council. 1 However, since Chinese invesors canno rade gold abroad wihou resricions, he Shanghai old Exchange (SE) is he main rading plaform for heir gold invesmen (Cheng 2014). A he LBMA Bullion Marke Forum 2014 in Singapore, Mr. Luode, he curren Chairman of he SE, announced is opening o inernaional members for he firs ime and his acually happened on Sepember 18, The SE is sill a relaively novel marke which was opened on Ocober 30, 2002, and is developmen has been noiced in numerous analyses of specialiss (World old Council, 2014). Chinese insiuional and individual invesors have been able o inves in gold hrough he SE only since 2004 and 2007, respecively (Cheng, 2014). The FMS old Survey 2014 repored ha he urnover of he SE was jus behind London, New York (Comex) and Tokyo (Tocom) over he period. According o Wang (2011), he previous Chairman of he SE, from Ocober 2002 o April 2011, he ransacion volume of gold on he SE reached more han 20,000 ons. In 2013, i was 10,701 ons, of which 1,132 ons were privae demand (Cheng, 2014). Wang (2011) indicaed ha commercial banks accoun for 58% of he ransacion volume, individual invesors for 19% and insiuional members for 23% in Taking ino accoun he leading role of China in he global gold marke, he growing developmen and inernaionalizaion of he SE has araced ineres among researchers and invesors. However, he number of sudies on he SE remains quie small compared o he huge lieraure on he financial economics of gold. 3 To he bes of our knowledge, here are only hree sudies dealing wih he SE: Lucey e al. (2014) and Hoang e al. (2015a,b). Lucey e al. (2014) sudy he relaionship beween gold markes around he world and find ha he SE is an isolaed one and does no have significan ineracion wih oher inernaional gold markes. Hoang e al. (2015a) sudy he relaionship beween gold and inflaion in five counries from 2002 o 2013 and find ha gold is no a good hedge agains 1 According o he World old Council, he oal global demand for gold in 2014 was 3,924 onnes, wih India s consumer demand accouning for 843 onnes and China's for 814 onnes. See World old Council, old Demand Trends, February In 2015, he SE offers 13 producs (spo and fuures) covering gold, silver and plainum on he Main Board wih 167 domesic members, 8000 corporae cusomers and over seven individual invesors rading on he SE hrough heir carrying members. As for he Inernaional Board, here are 40 members, such as HSBC, oldman Sachs, Deusche Bank, ec., wih hree producs (iau100g, iau99.99 and iau99.95). 3 O Connor e al. (2015) presen a deailed survey of his lieraure srand and show ha he number of papers published on gold has increased significanly in he las years wih a peak in 2010 (almos 30 published papers). 2

3 Chinese inflaion in he long erm. Hoang e al. (2015b) find ha including gold quoed a he SE in Chinese sock and bond porfolios is more preferable o risk-seeking invesors han o risk-averse ones. Some oher sudies provide analysis on he relaionship beween Chinese socks and gold, such as Ziaei (2012), Anand and Madhogaria (2012), Thuraisamy e al. (2013), ürgün and Ünalmis (2014) and Arouri e al. (2015). However, hey do no ake ino accoun gold prices from he SE bu hose from London convered ino Chinese currency. 4 However, his choice can only be appropriae for foreign invesors bu no for Chinese who canno rade gold abroad as menioned above. Thus, using gold prices on he SE is more appropriae for Chinese invesors whose demand for gold invesmens has increased srongly and i is esimaed ha he privae demand would reach 1,350 ons in 2017 (Cheng 2014). In his wofold conex, he rapid developmen of he SE wih a lack of lieraure on i, he objecive of our aricle is o analyze he relaionship beween Chinese socks and gold quoed a he SE. We provide a new perspecive on gold invesmens in general and he Chinese marke in paricular for several reasons. Firs, we use gold prices quoed a he SE and no hose from London convered ino Chinese currency. As we menioned above, his is more suiable o Chinese invesors and may also bear some ineresing implicaions for inernaional invesors, which rade gold on he SE using he local currency, i.e. he Renminbi. Thus, he resuls ha we obain would provide raional informaion o boh Chinese and inernaional invesors on he SE. Second, we pay a paricular aenion o he exreme reurns of gold and socks in China hrough heir ail dependence calculaed by differen copulas (aussian,, umbel, Clayon and Frank) based on he generalized Pareo disribuion on JR-ARCH filered reurns. Third, we analyze he impac of he secor of Chinese socks on is relaionship wih gold. To he bes of our knowledge, his issue has no been analyzed before for he SE. However, i is of paricular imporance considering he specificiy of each secor. Fourh, we furher invesigae how he ail dependence of reurns beween gold on he SE and Chinese secorial socks would be profiable in he diversificaion of porfolios. Our porfolio analysis considers four ypes of porfolios for each sock secor: 100% socks, 50% socks+50% gold, weighs of each asse following he minimal-variance porfolio on he efficien fronier of Markowiz (1952) and following he opimal weigh of gold o minimize he condiional variance of reurns proposed by Kroner e al. (1998). We hen compare hese porfolios o analyze he benefi of gold in a porfolio using he hedging effeciveness raio proposed by Ku e al. (2007). Furhermore, as a robusness check, we also 4 Mr. Cheng noed his poin in an inerview in April 2015 a he Dubai Precious Meals Conference hps:// 3

4 perform he above-menioned analysis o invesigae he relaionship beween oil and secorial socks in China o verify he resuls of recen sudies on he similar behavior of gold and oil vis-à-vis socks. Our daily daase is composed of spo gold prices on he SE and values of secorial socks quoed on he Shanghai Sock Exchange (SSE) wih 1,314 observaions in oal. As for oil prices, we use hose provided by Wes Texas Inermediae (WTI) as a robusness check. Our findings show ha The res of he paper is organized as follows. The second secion deails he lieraure review relaed o he role of gold in he diversificaion of porfolios. Secion 3 presens our mehodology while Secion 4 focuses on he daa se. Secion 5 analyzes our resuls on he ail dependence and provides insighs for porfolio diversificaion. Secion 6 presens a robusness check including oil and Secion 7 concludes. 2. Lieraure review: old in he diversificaion of porfolios old invesmens and he link beween sock prices and gold has been analyzed by several auhors. The firs sudy invesigaing gold invesmens has been provided by McDonald and Solnik (1977), several years afer he aboliion of he Breon-Woods sysem. I is followed by Sherman (1982), Jaffe (1989), Chua e al. (1990), Blose (1996), Blose and Shieh (1995), Davidson e al. (2003) and Lucey e al. (2006). All hese sudies reveal he significan relaionship beween gold and socks, and he posiive role of gold in he diversificaion of porfolios. In 2010, Baur and Lucey (2010) and Baur and McDermo (2010) invesigae he role of gold as a safe haven asse. Following hese wo sudies, many ohers, for example, Hood and Malik (2013) or Beckmann e al. (2015a) examined he role of gold in sock and bond porfolios in differen counries, relying on differen frameworks wih he laer also accouning for nonlineariies. Following he ideas from Baur and Lucey (2010) and Baur and McDermo (2010) o invesigae he safe haven characerisic of gold, Baur (2011) uses US daa from 1979 o 2011 o conclude ha gold evolved as a safe haven only recenly. Ciner e al. (2013) show ha socks, bonds, gold, and oil in he US and UK can be used as a safe haven for each oher. Hood and Malik (2013) show ha unlike oher precious meals, gold can serve as a hedge and weak safe haven for he US sock marke. Soucek (2013) finds ha in unsable periods, he correlaion beween gold and equiy ends o be weak or negaive. old can hus serve as a safe haven as well as ges he benefi from he diversificaion. However, Beckmann e al. (2015a) find ha he role of gold as a hedge and safe haven may be marke-specific while 4

5 proposing a more flexible approach o es hese hypoheses compared o Baur and Lucey (2010). Sadorsy (2014) reveals ha gold and oil can also be used as a hedge and safe haven for socially responsible socks, in a similar way as for convenional socks. In comparing gold o bonds, Flavin e al. (2014) find ha boh gold and longer-daed bonds can be considered as safe haven asses. Applying he wavele approach on daily daa from 1980 o 2013, Bredin e al. (2015) conclude ha gold acs as a safe haven for socks and bonds only for horizons up o one year, bu his is no rue in he early 1980s. Overall, he above-menioned sudies show ha gold acs as a safe haven for socks and bonds. However, i is ime-varying and markespecific. Oher sudies go beyond analyzing he usual role of gold as a safe haven and focus on is impac in he diversificaion of porfolios. For example, Hammoudeh e al. (2013) find significan relaionship beween gold and socks and conclude ha gold can hus play an imporan role in he diversificaion of sock porfolios. Kumar (2014) shows ha sock and gold porfolios perform beer han porfolios only consising of socks. Based on a wavele analysis, Michis (2014) concludes ha gold provides he lowes conribuion o he porfolios risk a medium- and long-erm invesmen horizons. Baur and Löffler (2015), Choundhry e al. (2015), and Malliaris and Malliaris (2015) confirm he resuls of previous aricles abou he significan impac of gold in he diversificaion of porfolios. So far, he lieraure is silen on he relaionship beween gold prices from he SE and Chinese secorial socks. The exisen aricles dealing wih he Chinese marke only use gold prices from London convered ino Chinese currency. For example, Arouri e al. (2015) examine he relaionship beween world gold prices and Chinese socks using he VAR- ARCH framework for he period. Furhermore, Anand and Madhogaria (2012) assess he correlaion and causaliy beween gold prices and socks in six counries (including China) using daily daa from he London gold marke convered ino local currencies. Thuraisamy e al. (2013) sudy he relaionship beween 14 Asian (including Chinese) equiy and commodiy fuures markes based on gold prices from London. In he same vein, ürgün and Ünalmis (2014) use daily daa from MSCI and Bloomberg o analyze he safe haven characerisic of gold agains he equiy markes in emerging and developing counries, including China. However, as already discussed in he previous secion using gold prices in London convered ino he Chinese currency is no appropriae for Chinese invesors for whom invesmens in gold abroad are sill under he conrol of he governmen. 5

6 3. Mehodology Our mehodology can be divided ino wo differen pars. In he firs sep, we explore he ail dependence beween gold and secorial socks in China using several copula measures based on he generalized Pareo disribuion on JR-ARCH filered reurns. In he second par, we will invesigae he hedging efficiency of gold in Chinese secorial sock porfolios based on he four ypes of porfolios which have already been menioned in he Inroducion JR-ARCH Before applying differen copula measures o invesigae he ail dependence, we firs focus on he heeroscedasiciy and auocorrelaion of he second momen of he disribuion of reurns and as convenional in he lieraure (see for insance Beckmann e al. 2015b) we apply an ARCH filer since we deal wih daily reurn series ha are characerized by auocorrelaion and condiional heeroscedasiciy. Moreover, o accoun for he poenial ha shocks end o impac condiional volailiy asymmerically, we apply a JR-ARCH filer as defined by losen e al. (1993): where denoes he reurn series and represens he variance of is error erms. In his seup, Ω represens a consan, α measures he impac of shocks and β indicaes he persisence of he process. Moreover, o capure he asymmeric impac of shocks on he volailiy, γ akes a value of uniy if he shock is negaive and 0 oherwise eneralized Pareo disribuion As we deal wih differen asses and hus wih differen asse specific properies, we apply a flexible reurn disribuion ha adjuss o each asse individually. More precisely, according o Longin and Solnik (2001), we apply he generalized Pareo disribuion (PD), which models he ails of each disribuion individually whereas he inerior par of he disribuion is described by he empirical disribuion. In order o model boh ails of he marginal reurn disribuion individually, we need o define he amoun of observaions ha should be considered in he ails. Therefore, we se a predefined hreshold of, so ha he lowes 10% and highes 10% values of he ime series are modeled via he PD. Based on he JR-ARCH filered reurn series, le x be he exceedances of he predefined hreshold, hen he cumulaive disribuion funcion (CDF) of PD is given by 6

7 wih and. In his seup, deermines he shape and he scale of he respecive ail. The parameers are maximized via he log likelihood funcion as defined by Longin and Solnik (2001) Copulas The linear correlaion coefficien lacks in capuring non-linear ransformaions of he margins and i does no capure he ail dependence. Tha is why we use he copula approach o separae he modeling of he marginal disribuion from he modeling of he dependence. enerally, he copula approach goes back o Sklar s Theorem (1959). Based on he modeled margins, we apply differen copulas o assess differen paerns of he ail dependence. These copulas are briefly inroduced in he following. aussian Copula The aussian copula is direcly derived from he mulivariae normal disribuion: sands for he mulivariae normal disribuion. If all margins are normally disribued, his copula equals he mulivariae normal disribuion. The aussian copula does no capure ail dependence beween he analyzed ime series. Therefore, join exreme movemens canno be adequaely capured. To accoun for his feaure we also consider he copula. Copula Analogous o he aussian copula, he copula is direcly derived from he mulivariae disribuion and is given as follows: sands for he mulivariae disribuion. Due o is degrees of freedom, he copula capures join exreme movemens and is herefore characerized as symmeric ail dependence. For, he copula approximaes a aussian copula. Boh he aussian and he copula belong o he class of ellipical copulas. 7

8 umbel Copula In conras, he umbel copula belongs o he family of Archimedean copulas and is widely used as i capures asymmeric join movemens. The seup of he umbel copula is given as follows wih. Posiive ail dependence is described by. Clayon Copula Anoher Archimedean copula is given by he Clayon copula. In conradicion o he seup of he umbel copula, he Clayon copula capures join negaive shocks, so called negaive ail dependence: wih. Negaive ail dependence is characerized by. Frank Copula The Frank copula does also belong o he family of Archimedean copulas, whereas i accouns for symmeric ail dependence: For All parameers are esimaed via he log-likelihood in a wo-sep mechanism (see Joe 1996). This seup is ofen referred o as inference o he margins (IFM) and allows us o esimae he ARCH parameers in he firs sep and he copula parameers in a second sep Efficien fronier The classical mean-variance porfolio opimizaion (MVPO) model inroduced by Markowiz (1952) can be used o deermine he asse allocaion for a given amoun of capial hrough he efficien fronier. To presen he MVPO model formally, we assume ha here are n asses and le x i (i=1,,n) be he fracion of he capial invesed in asse i of porfolio P in 2 which he average reurn R p is maximized, subjec o a given level of is variance σ p. We denoe R i o be he expeced reurn of asse i and σ ij he covariance of reurns beween asses i and j, for any i, j =1,,n. The general MVPO model is presened as follows: Max R n p = Ri xi, subjec o: i= 1 n n i= 1 j= 1 σ x x = σ 2 ij i j p and n xi = 1. If shor sale is no used, we add i= 1 one more condiion: x 0, i = 1,..., n. i 8

9 3.5. Opimal weigh and hedging effeciveness To assess he hedging and diversificaion of porfolios wih gold, we deermine he opimal weigh of gold in Chinese secorial sock porfolios in referring o he mehod proposed by Kroner e al. (1998) as follows: w = h P h h 2h + h P P P wih P w as he opimal weigh of gold in he porfolio, h as he condiional variance of he sock-only porfolio P, P h as he condiional covariance beween he sock-only porfolio and gold, and h as he condiional variance of gold. The opimal weigh is hus calculaed for each dae under he condiion ha: w = 0 if w < 0 ; w = w if 0 w 1, and w = 1 if w > 1. We use he average over he sudy period which is he average opimal weigh of gold o minimize he condiional variance of reurns of he porfolio. In his sudy, we rely on he bivariae CCC-ARCH(1,1) model of Bollerslev (1990) o esimae he condiional variances and covariance. We use he CCC represenaion as i provides more economic significance in esimaing condiional correlaion raher han he condiional covariance (like in he BEKK-ARCH model of Engle and Kroner (1995) for example). In general, for each pair of sock-only porfolio and gold reurns, he bivariae VAR(1)-ARCH(1,1) has he following specificaion: R µ + ΦR 1/ 2 ε = H η = 1 P where R = ( R, R ) is he vecor of reurns of he sock-only porfolio and gold, + ε respecively. Φ refers o a (2 x 2) marix of coefficiens φ1 Φ = 0 0 φ2 P, ε ( ε, ε ) = is he vecor of he error erms of he condiional mean equaions for he sock-only porfolio and P gold, respecively. η ( η, η ) = refers o a sequence of independenly and idenically P P disribued (i.i.d) random errors wih E( η ) = 0 and Var (η ) = I ; and h h N Η = P h h marix of condiional variances of he sock-only porfolio and gold reurns. The CCC-ARCH(1,1) model specifies he Η marix as follows: is he Η = DKD, 9

10 P where D = diag( h, h ), and K = ρ ) is he (2 x 2) marix conaining he consan ( ij condiional correlaions ρ ij wih ρ ii = 1, i = P,. The condiional variances and covariance are given by h h h P P = C = C P = ρ h P + α ( ε ) P P h α ( ε ) β h P + β h To esimae his model, he maximum likelihood mehod is used. P 1 1 As for he opimal hedge raio o minimize he condiional variance of reurns of he porfolio, Kroner and Sulan (1993) consider a wo-asse porfolio, equivalen o a porfolio composed of secorial Chinese socks and gold (or oil) in our sudy. To minimize he risk of his hedged porfolio, a long-posiion of one Yuan on he sock segmen mus be hedged by a S shor posiion of β Yuan of gold. This opimal hedge raio is given by he following: S S h β =. h Furhermore, he hedging effeciveness can be evaluaed by examining he realized hedging errors which are deermined as follows (Ku e al. 2007): Var HE = where he variance of he hedged porfolios unhedged Var Var unhedged hedged Var is obained from he variance of he hedged reurns of he gold-sock porfolios, he variance of he unhedged porfolios Var is unhedged obained from he variance of he sock-only porfolios. A higher HE raio indicaes a greaer hedging effeciveness in erms of he porfolio s variance decrease. 4. Daa and preliminary analysis To invesigae he relaionship beween gold quoed a he SE and Chinese secorial socks, our daily daase running from January 9, 2009 o January 9, 2015 is colleced from he websies of he Shanghai old Exchange (SE) and he Shanghai Sock Exchange (SSE). The saring dae is condiioned by he availabiliy of he daa on Chinese secorial sock indexes on he SSE s websie. Therefore, our daase is composed of 1,314 daily observaions. More deails abou gold prices on he SE and secorial socks on he SSE are presened in he following. old prices from he Shanghai old Exchange (SE) Au99.99 and Au99.95 are wo principal gold spo asses raded on he SE since is opening (99.99 and indicae he puriy of gold over 100%). We choose he Au

11 asse in our analysis because i is considered o be he reference gold spo asse in annual repors of he SE. Is prices are in Chinese Yuan per gram and are available on he SE websie. Secorial sock indexes from he Shanghai Sock Exchange (SSE) Daily daa on secorial socks in China are available on he websie of he SSE saring from January 9, The secorial indexes ha are considered by he SSE are: Consumer Discreionary, Consumer Saples, Energy, Financials, Healh Care, Indusrials, Informaion Technology, Maerials, Telecommunicaion Services and Uiliies. We use he oal reurn index in order o ake ino accoun dividends paid on socks under consideraion. Following informaion abou he mehodology of secorial index consrucion given on he SSE websie, all socks in he A-shares lis, meaning socks ha are limied o domesic invesors, excluding socks ha are IPOs wihin 3 monhs and have anomalies (see he SSE websie for more deails). Furhermore, all socks a he boom 15% by rading value and a he boom 2% by cumulaive marke capializaion are deleed. For secors which have less han 30 socks, all he socks ener he index. If his is no he case, socks are ranked by daily average marke capializaion and only he op ranked socks are chosen ill he cumulaive marke capializaion coverage reaches 80% of he oal value or he number of socks reaches 50. The consiuens of each index are adjused semi-annually. Currenly, in 2015, he number of socks ha are considered in each secor is: 50, 30, 30, 30, 30, 50, 31, 50, 11 and 30, respecively o he lis of secors ha we presen above. Descripive saisics Figure 1 presens daily values of indexes on secorial socks and gold prices in China from January 2009 o January Figure 1: Daily values of indexes on secorial socks and gold in China from 2009 o 2015 Consumpion secors Indusrial secors 11

12 Service secors Technology secors Noe: For an easier comparison, we fix all values a he same basis of 100 on January 9, From Figure 1, we noice ha all gold and socks were very volaile in China from 2009 o I is hus necessary o sudy he ail dependence of hese wo asses. A he beginning of he sample period, secorial sock indexes seem o exhibi a high degree of co-movemens while his paern seems o become lower as ime evolves. Furhermore, he indusrial secors (Energy, Indusrials and Maerials) seem o behave differenly compared o oher secors in being in a decreasing endency from 2013 while i is an increasing endency for oher secors. More imporanly, in mos of he ime, gold prices evolve inversely wih hose of socks and wo sub-periods seem o appear. The firs period is from January 9, 2009, o Sepember 9, 2011, when gold prices were increasing and reached is peak on Sepember 9, This same period is also characerized by an increasing endency of sock prices in mos cases. The second period is from Sepember 10, 2011 o January 9, 2015 and is characerized by he increasing endency of socks and decreasing endency of gold. As a preliminary analysis, we assess he linear dependence beween all asses wih a simple correlaion measure (Table 1). Table 1: Linear correlaion Disc Sap Energy Finance Healh Indus Info Maeri Tele Uili old Discreionary Saples Energy Financials Healh Care Indusrials Informaion Maerials Telecom Uiliies OLD 1 Noe: All coefficiens are significan a 1%. 12

13 The correlaion beween differen secors is relaively high, ranging beween 0.5 and 0.9. We noice ha he correlaion of he consumpion (Discreionary and Saples) and energy secors wih he oher ones is he highes. The financial secor is he less correlaed o he oher secors. In all cases, he correlaion beween gold and secorial socks is low, around 0.1. The secor he less correlaed wih gold is Uiliies and he highes is Maerials. This may be explained by he fac ha gold is used more in he Maerials secor han in he Uiliies one. Table 2 gives he principal descripive saisics of our sample daa. Table 2: Descripive saisics Average SD Skewness Kurosis excess JB KS Discreionary 16.82% 26.83% *** 2.67 *** 412 *** 0.05 *** Saples 13.49% 24.83% *** 1.65 *** 194 *** 0.05 *** Energy 1.75% 30.63% *** 485 *** 0.06 *** Financials 13.03% 27.82% 0.52 *** 6.03 *** 2043 *** 0.07 *** Healh Care 19.46% * 26.74% *** 237 *** 0.05 *** Indusrials 5.32% 24.93% *** 2.10 *** 280 *** 0.06 *** Informaion 19.78% 31.17% *** 1.05 *** 107 *** 0.05 *** Maerials 7.52% 29.81% *** 2.69 *** 414 *** 0.06 *** Telecom 7.80% 28.63% *** 1.51 *** 139 *** 0.05 *** Uiliies 8.66% 22.38% *** 2.84 *** 529 *** 0.07 *** OLD 4.31% 19.17% *** *** *** 0.08 *** Noe: Mean and SD (sandard deviaion) are in annualized values, esimaed by muliplying he daily values by 252 and 252, respecively. *** means ha he value is significan a he 1% hreshold. No aserisk means ha he value is no significan a he 10% hreshold. JB (Jarque-Bera) and KS (Kolmogorov-Smirnov) are ess for he normaliy of he disribuion in which *** means ha i is no normal a he 1% hreshold. From Table 2, we noe ha gold is less profiable han secorial socks in mos cases, excep he Energy secor for which he annualized rae of reurn is only 1.75%, vs. over 4% for gold. The secors he mos profiable are Healh Care and Informaion Technology, almos 20% per year. The sandard deviaions are very high in all cases, from 20% o 34% per year. The highes ones are for he Informaion and Energy secors (over 30%) and he lowes one is for gold (abou 19%). The skewness coefficiens are negaive in mos cases (excep for he Energy and Financials secors). This means ha, in mos cases, he disribuion of reurns is skewed o he lef. The excess kurosis is he highes for gold (abou 15), meaning ha here are he mos exreme values for gold reurns. This is followed by he Financials secor (abou 6). As usually found, all he normaliy ess (JB and KS) show ha he disribuions of all reurn series are no normal. From his preliminary analysis, we find ha from 2009 o 2015, i is more profiable o inves in socks han in gold in China. The secors which are he mos profiable are Healh 13

14 Care and Informaion Technology. However, gold can provide profiable impac o secorial sock porfolios since gold has a lower variance and a low correlaion o socks. In he nex par of our sudy, we will invesigae he ail dependence of reurn disribuions and is implicaions in he porfolio diversificaion beween gold and secorial socks in China. 5. Empirical resuls and discussions 5.1. JR-ARCH esimaes and copula parameers Before assessing he ail dependence beween gold and differen Chinese secorial socks, we firs presen he resuls of he JR-ARCH model based on he univariae ime series. As menioned in Secion 3, we apply an ARCH filer o deal wih auocorrelaion and condiional heeroscedasiciy of our sample daily reurns. Table 3 repors he esimaed parameers for all invesigaed asses. Table 3: JR-ARCH Parameers old Discreionary Saples Energy Financials Healh Care Indusrials Informaion Maerials Telecom Uiliies Omega 3,85 2,09 2,64 0,00 2,35 2,37 1,97 0,00 1,81 34,65 0,00 -Value 536,30 447,20 406,30 0,00 465,70 48,03 244,10 0,00 416,60 0,00 0,00 Alpha 0,09 0,07 0,09 0,23 0,06 0,22 0,06 0,21 0,06 0,00 0,27 -Value 5,23 5,12 5,29 6,81 4,98 6,33 4,22 11,29 4,55 0,00 0,00 amma 0,02 0,01 0,00 0,00 0,01 0,00 0,02 0,00 0,01 0,25 0,00 -Value 1,17 1,07 0,11 0,00 0,62 0,00 0,93 0,00 0,70 4,36 0,00 Bea 0,88 0,92 0,89 0,40 0,93 0,22 0,92 0,42 0,94 0,00 0,73 -Value 37,89 53,62 34,56 0,00 61,91 0,86 39,58 0,00 62,85 0,00 0,00 LL Q-Sa 50,44 43,12 38,16 29,65 49,77 73,07 44,61 43,29 36,70 47,38 35,59 LM 15,86 16,26 18,59 8,78 15,49 44,86 11,45 14,50 10,92 10,60 11,91 Noes: Omega represens he consan. Alpha measures he ARCH effec. amma capures he asymmeric impac of shocks on he volailiy and Bea indicaes he persisence of he process. LL denoes he log likelihood, Q-sa represens he Ljung-Box es saisic for serial correlaion, and LM gives he Lagrange muliplier es saisic for serial correlaion up o order 20. The alpha coefficiens which measure he adjusmen o pas shocks are low bu significan for all secors, excep for Uiliies and he Telecommunicaion. Ineresingly, he reurns of he Telecommunicaion secor are characerized by an asymmeric negaive impac of shocks on heir volailiy due o he significance of he gamma coefficien. Moreover, he bea coefficiens which measure he persisence of he process (i.e he exen o which a volailiy shock oday feeds hrough ino nex period s volailiy) ake values beween 0.88 and 0.94 and are significan for mos secors, excep for Energy, Healh Care, Informaion, Telecommunicaion and Uiliies. Therefore, excep for he Uiliies secor, all oher secors under observaion are described by significan ARCH effecs. We hus accoun for hese secor-specific sylized facs by filering he reurns based on a JR-ARCH approach. On 14

15 he filered reurn series, we carry on by assessing differen copula measures and heir respecive parameers. Table 4: Copula parameers beween gold and secorial socks in China Discreionary Saples Energy Financials Healh Care Indusrials Informaion Maerials Telecom Uiliies auss 0,12 0,10 0,15 0,10 0,08 0,10 0,10 0,22 0,09 0,07 AIC -15,47-12,07-28,58-10,00-6,60-12,05-11,36-65,41-9,17-4,84 0,11 0,09 0,15 0,10 0,07 0,10 0,10 0,22 0,09 0,07 DoF 15,35 12,59 12,28 8,95 16,51 14,26 30,55 14,31 20,38 20,33 AIC -21,13-20,47-36,60-27,16-12,10-19,18-12,83-71,78-12,06-8,11 Frank 0,58 0,52 0,86 0,56 0,41 0,59 0,53 1,32 0,49 0,37 AIC -9,87-7,50-24,07-8,91-4,13-10,29-8,07-58,54-6,48-2,87 Clayon 0,11 0,08 0,17 0,12 0,06 0,12 0,09 0,26 0,09 0,07 AIC -10,53-5,71-25,64-13,62-2,08-13,64-6,96-59,24-7,83-4,33 umbel 1,07 1,07 1,09 1,06 1,05 1,06 1,06 1,14 1,05 1,04 AIC -23,67-23,61-26,24-15,34-18,58-9,72-13,30-55,10-9,09-6,69 Noes: DoF denoes he degree of freedom. AIC denoes he Akaike informaion crierion. The values in he cells presen he copulas esimaed by he aussian, Suden, Frank, Clayon and umbel approaches as described in Secion 3. Table 4 presens he ail dependence beween all asses and gold which is measured by differen copulas. In line wih he resuls from Table 1, he dependence beween gold and he invesigaed socks appears o be weak and he applied aussian and copulas lead o values ha are similar o he linear correlaion coefficiens repored in Table 1. According o he AIC informaion crierion, i is he copula ha adequaely describes he dependence beween all asses. Alhough he dependence per se is weak, he copula indicaes significan ail dependence. Moreover, he relaively small values for he degrees of freedom also underline he exisence of he ail dependence beween gold and secorial Chinese socks which could be inerpreed ha exreme evens end o occur joinly in gold and sock markes. Overall, our resuls on copulas show ha gold and secorial socks in China are characerized by ail dependence. This means ha exreme reurns of gold and secorial socks are correlaed. In oher words, exreme evens may have impac on gold and secorial socks joinly. The weak values of copulas sugges ha his dependence is no high. Thus, an exreme even can have impac on boh gold and socks joinly bu he way ha each asse responds o his exreme even is no similar. As for secorial differences, based on he -copulas, he highes value is for he Maerials secor (0.22) and he lowes value is for he Healh Care and Uiliies secors (0.07). This means ha he ail dependence of reurns is he highes beween gold and he Maerials secor. This may be explained by he fac ha gold may be used in he firms belonging o he Maerials secor, which is no he case for he Healh Care and Uiliies secors. The Energy secor has also a higher -copula value compared o oher secors (0.15). This may be explained by he close relaionship beween gold and energy firms such as firms involved in oil and gas aciviies. Indeed, i is well known ha gold and oil can have similar behavior regarding heir relaionship wih socks (e.g., Mensi e al. 2013, Ewing and Malik 15

16 2013, Sadorsy 2014). Thus, as a robusness check, we will invesigae he ail dependence beween oil and secorial socks in China and also is insighs in he diversificaion of porfolios in Secion 6 below. How can invesors profi from his ail dependence in heir asse allocaion? I is wha we would like o sudy in he nex secion Insighs for he diversificaion of porfolios As explained in he Inroducion and Secion 3, o invesigae he profi of he ail dependence beween gold and secorial socks in China, we base on he comparison of four ypes of porfolios: 100% socks, 50% socks+50% gold, and weighs of gold deermined in he minimal-variance porfolio (Markowiz, 1952) and by he opimal weigh proposed by Kroner and Ng (1998). The firs sub-secion will focus on he efficien fronier analysis while he second sub-secion will compare he four above-menioned porfolios using he hedging effeciveness measure (Ku e al., 2007) Efficien froniers We apply he classical Markowiz approach and minimize he porfolio variance wih respec o he expeced porfolio reurn. In his conex, we consider wo differen seups: (a) a porfolio in he absence of shor selling (only posiive weighs of asses), where he maximum weigh for each individual asse is se o 30% and o ensure a realisic risk diversificaion, (b) a porfolio in he presence of shor selling (wih also negaive weighs of asses), where he minimum and maximum weigh of each individual asse is se o beween -30% and 30%. For boh seups, we examine he following wo scenarios: 1.) The porfolio manager exclusively invess in Chinese socks. 2.) The porfolio manager invess in Chinese socks and gold. The relevan efficien froniers are illusraed in Figure 2. Figure 2: Mean-Variance efficien froniers A. Wihou shor sale B. Wih shor sale 16

17 Noe: The graphs show he mean-variance efficien froniers for hree differen porfolios: (1) including all secorial Chinese socks, (2) including all secorial Chinese socks + gold, and (3) including all secorial Chinese socks + oil. The laer porfolio serves as a robusness check and is discussed in Secion 6. Figure 2 plos he mean-variance efficien froniers for he wo above-menioned scenarios wihou shor sales (Panel A) and wih shor sales (Panel B). Obviously, adding gold leads o porfolios ha are characerized by lower risk for a given expeced reurn and a higher reurn for a given level of risk. This is because he efficien froniers wih gold are boh higher han he one wih only socks (wih all secors ogeher or each secor separaely). As can be seen in Panel B, including shor sales does no change he resul qualiaively. To sress his finding, we compare he porfolio allocaions ha lead o he minimum degree of risk for each scenario (i.e. he minimal-variance porfolio). For a given invesmen of 1,000,000 Yuan, he respecive amouns for he expeced reurn and risk of each porfolio are presened in Table 6. In addiion, Figure 3 shows he weighs of each asse included in hese porfolios presened in boxplo diagrams. Table 6: Minimal-variance porfolios in hree differen scenarios wih and wihou shor selling In Yuan Expeced reurn Expeced risk Wihou shor selling Only socks Socks + old Wih shor selling Only socks Socks + old Noe: Risk is given by he sandard deviaion. The figures in his able show he reurn and sandard deviaion based on 1,000,000 Yuan invesed in he minimalvariance porfolio. Obviously, adding gold o Chinese sock porfolios 5 lowers he risk. However, we noice ha he expeced reurn of he only-sock porfolio is higher han he ones wih gold. This is explained by he fac ha wihin he sudy period ( ), he raes of reurn for socks were higher han he ones for gold (see Table 2). 5 We refer o he porfolio composed of all sock secors, as shown in he efficien froniers in Figure 2. 17

18 Figure 3: The weigh of each asse in he minimal-variance porfolios Noe: The graph presens he porfolio weighs for each asse as a boxplo diagram. The cenral mark in he box indicaes he median, he edges of he box are he 25h and 75h perceniles and he whiskers limis describe he exreme daa poins. No considered ouliers are marked individually (in red). The asses are numbered on he horizonal axis according o heir appearance order in he ables. 1=Discreionary, 2=Saples, 3=Energy, 4=Financials, 5=Healh Care, 6=Indusrials, 7=Informaion, 8=Maerials, 9=Telecom, 10=Uiliies, 11=old or Oil. The graphs in he firs (second) line refer o he case wihou (wih) shor selling. The porfolio weighs including oil are discussed in Secion 6. In Figure 3, he weigh of each asse in he minimal-variance porfolios is shown (we refer o he porfolio composed of all sock secors). The sum of all he weighs presened in he graphs is always 100%, and he maximal weigh for one asse is 30% and he minimal one is - 30% when shor sales are used. The graphs in he firs line (wihou shor sales) show ha when gold is no included, he minimal-variance porfolio is composed of six secors essenially: Consumer Discreionary, Consumer Saples, Financials, Healh Care, Informaion and Uiliies. When gold is included, he weigh of he Financials, he Informaion, and he Uiliies secor becomes 0 and he weigh of he Energy, Indusrials and Maerials secors increased srongly. The weigh of gold is around 0 and 15% in 50% of he porfolios. As we showed in Table 6, including gold lowers he reurn bu also he sandard deviaion. Overall, he graphs in he firs line (wihou shor sales) show ha he composiion of asses can change significanly when including gold ino secorial sock porfolios. The graphs in he second line show ha he weigh of each secor also changes when using shor sales. Furhermore, he weigh of gold is very large in each porfolio, i.e. 30%. This finding suggess ha gold should be more efficien in he diversificaion of porfolios when allowing for shor sales. The resuls in Table 6 also show ha he sandard deviaion of he minimal-variance porfolio is even lower using shor sales. Overall, his analysis allows us o conclude ha including gold can change he weigh of each secor in he minimal-variance porfolio significanly. Furhermore, shor selling sraegies are less convenien wih he use of gold o diversify porfolios. For insance, if no gold ges added o he porfolio, in he absence of shor selling, he Consumer Saples and 18

19 Energy secors presen a relevan invesmen. However, if we allow for shor selling, Energy, Maerials and Telecom are characerized by larger weighs. Furhermore, in he absence of shor selling, adding gold leads o lower weighs on Financials, Informaion and Uiliies bu o larger weighs on Energy, Indusrials and Maerials. In he presence of shor selling, adding gold leads o larger weighs on Financial and Indusrials. To have a clearer view on he effec of gold in each sock secor, we coninue our analysis wih four differen ypes of porfolios for each secor diversified wih gold Hedging effeciveness of gold in Chinese secorial sock porfolios In his secion, we will compare only-sock porfolios (PF1) wih hree oher ones: PF2 is composed of 50% of sock and 50% of gold; PF3 is composed following he minimalvariance porfolio aken from he mean-variance efficien fronier; and PF4 is composed following he opimal weigh of gold calculaed using he CCC-ARCH model (Kroner and Ng, 1998). Table 7 presens he weigh of gold in PF3 and PF4 as well as he hedge raio (Kroner and Sulan, 1993) for each secor. Table 7: The weigh of gold in PF3, PF4 and he hedge raio Secors PF3 : Minimal-Variance PF4 : CCC-ARCH Hedge raio Discreionary 68.52% 68.00% 17.60% Saples 64.49% 64.17% 16.26% Energy 75.49% 74.64% 23.61% Financials 70.05% 69.16% 15.35% Healh Care 68.02% 67.91% 15.53% Indusrials 64.40% 64.64% 14.04% Informaion 74.95% 74.68% 17.29% Maerials 76.15% 74.93% 34.16% Telecommunicaion 71.19% 71.33% 15.85% Uiliies 58.50% 58.12% 9.99% Noe: The calculaions of hese values are explained in Secion 3. From Table 7, we find ha here is no significan difference beween he opimal weighs calculaed by Kroner and Ng (1998) and hose in he minimal-variance porfolio proposed by Markowiz (1952). In he firs case, he objecive is o minimize he risk which is measured by he condiional volailiy while in he second case; i is measured by he variance. On average, he difference beween he wo mehods is only 0.42%. In all cases, he weigh of gold o include in each secor sock porfolio is very high, ranging beween 58% and 74%. The secors for which he weighs of gold are he highes are Energy, Informaion and Maerials (from 74% o 76%) and he lowes is for he Uiliies secor (58%). Thus, once again, we find 19

20 ha he secors in which gold is involved in heir aciviies (such as Energy, Informaion and Maerials) are he mos suiable o be diversified wih gold invesmens. As for he hedge raio (or bea), i means ha a long posiion of 100 Yuan on he sock segmen mus be hedged by a shor posiion on gold whose value corresponds o he hedge raio. The las column of Table 7 shows ha invesors should ake a shor posiion on gold beween abou 10 and 34 Yuan using fuure conracs available on he Shanghai old Exchange. The highes value of he shor posiion on gold is wih he Maerials secor and he lowes one is for he Uiliies secor. Again, we find ha socks of he Maerials secor are he mos suiable o be diversified wih gold. Table 8 presens he hedging effeciveness (Ku e al., 2007) when gold is included in Chinese secorial sock porfolios. Table 8: Hedging effeciveness Secors PF2: 50% Socks PF3: Minimal-variance PF4: CCC-ARCH Discreionary 57.51% 62.04% 62.04% Saples 55.08% 58.01% 58.01% Energy 60.26% 68.01% 68.00% Financials 58.99% 64.26% 64.25% Healh Care 58.02% 62.41% 62.41% Indusrials 55.95% 58.89% 58.89% Informaion 62.24% 70.00% 70.00% Maerials 57.34% 65.01% 65.00% Telecommunicaion 60.11% 65.96% 65.96% Uiliies 52.55% 53.68% 53.68% Noe: This able presens he hedging effeciveness of PF2, PF3 and PF4 (including gold) compared o PF1 (only socks) as presened in Secion 3. The higher he value, he greaer he hedging effeciveness is. From Table 8, we noe ha in all cases, including gold helps o reduce he volailiy of reurns of Chinese secorial sock porfolios. The hedging effeciveness is beween 53% and 70%. We also noice ha he hedging effeciveness is greaer for minimal-variance porfolios and CCC-ARCH porfolios han for he equal-weighed one where he share of gold in he porfolio is lower. The Informaion secor has he highes hedging effeciveness (70%), followed by Energy (68%) and Maerials (65%). Again, he Uiliies secor has he lowes hedging effeciveness (53%). 6. Robusness check: Is oil a beer hedge han gold? As analyzed in Secion 5.1, he ail dependence is he highes beween gold and he Energy secor. We hus hypohesize ha his high dependence may be due o he close relaionship beween gold and energy firms, ofen srongly relaed o oil, as i is well known ha gold and 20

21 oil can have similar behavior regarding heir relaionship wih socks (e.g., Mensi e al., 2013; Ewing and Malik, 2013; Sadorsy, 2014). The objecive of his secion is hus o verify his conjecure in he Chinese conex. For ha, we will conduc he same calculaions as we have done for gold, meaning JR-ARCH filer, ail dependence wih differen copulas, efficien froniers, and he comparison beween four ypes of porfolios. We use oil prices provided by he Wes Texas Inermediae (WTI) which have been aken from he websie of he Federal Reserve Bank of Sain Louis. These are nominal prices expressed in he USD. Thus, o be consisen wih daa on socks and gold prices, we conver oil prices ino he Chinese Yuan using he exchange rae, also available on he websie of he Federal Reserve Bank of Sain Louis. In order o save space, he corresponding ables are presened in he Appendix and we will only briefly discuss he main findings in his secion. Our findings on copula parameers (Appendix 1) show ha he -copula also dominaes oher copulas for he ail dependence beween oil and secorial socks. We find ha he magniude of he ail dependence beween oil and secorial socks is also similar o he case of gold. However, he degrees of freedom for he -copula are a bi higher for oil han for gold. Consequenly, he ail dependence beween gold prices and Chinese socks is sronger han beween oil prices and Chinese socks. This means ha he likelihood of exreme join movemens wih socks ends o be higher for gold han for oil. This suggess ha Chinese socks end o reac more o exreme variaions of gold prices quoed on he Shanghai old Exchange han inernaional oil prices. Moreover, following he -copula resuls, he ail dependence beween oil and he Energy secor is he highes, followed by he Financials, Indusrials and Telecommunicaion secors. This is differen from gold for which he highes -copula value is wih he Maerials secor, followed by he Energy, Indusrials and Informaion secors. This difference may be explained by he fac ha gold can be used in he producion sysem of he Maerials secors while oil can be used in Energy firms. Our findings on efficien froniers (Figure 2) show ha adding eiher oil or gold leads o porfolios characerized by lower risk for a given expeced reurn and a higher reurn for a given level of risk. We also noice ha he efficien fronier wih gold ouperforms he one wih oil. This is explained by he fac ha he sandard deviaion of oil is much higher han he one of gold (34% vs. 19%). As for he rae of reurn and sandard deviaion of he minimal variance porfolio (Appendix 2), porfolios wih oil have higher raes of reurns bu also higher sandard deviaions ha hose wih gold. This is explained by he fac ha he reurn and sandard deviaion of oil are boh higher han ha of gold (7% vs. 4% for he reurn and 34% vs. 19% for he sandard deviaion). 21

22 As for he weigh of oil in PF3 and PF4 (Appendix 3), we noice ha, in all cases, he opimal weigh of gold is higher han he one of oil (abou 70% vs. 40%). This suggess ha gold is more efficien o reduce he risk of Chinese sock porfolios han oil. The secors for which he weighs of gold are he highes are Energy, Informaion and Maerials (ranging from 74% o 76%). For oil, he secors are also he same bu he weighs of oil are much lower han gold, ranging from 42% o 44%. As for he hedge raio (Appendix 3), he highes value of he shor posiion on gold is wih he Maerials secor and he lowes one is for he Uiliies secor. For oil, hese values are 5 and 15 Yuan for he Healh Care and Uiliies secors, respecively. Finally, referring o he hedging effeciveness (Appendix 4), in all cases, gold is more efficien han oil. The Informaion secor has he highes hedging effeciveness and he Uiliies secor has he lowes one, wih boh oil and gold. Overall, his robusness check shows ha gold and oil have effecively similar impacs on Chinese secorial socks wih similar copula coefficiens and similar impac on he efficien fronier of Chinese secorial sock porfolios. However, he principal difference is ha gold quoed on he Shanghai old Exchange ends o inerac more han oil wih Chinese socks. Furhermore, oil ends o be more correlaed wih he Energy secor while for gold, i is he Maerials secor. To our opinion, his resul is consisen wih he implicaion of oil in he Energy secor and gold in he Maerials secor. In general, oil offers higher rae of reurn bu also higher risk han gold. This implies ha he weigh of gold o include in Chinese secorial sock porfolios is higher han ha of oil o minimize he risk (measured by he variance or condiional variance). In all cases, socks of he Uiliies secor seem o be he less efficien in he diversificaion wih eiher gold or oil. Finally, gold has a higher hedging effeciveness han oil in Chinese secorial sock porfolios. 7. Conclusion We have analyzed he ail dependence beween gold quoed on he Shanghai old Exchange and Chinese secorial socks and he implicaion of his dependence on he hedging of hese porfolios wih daily daa from January 2009 o January Our resuls show ha he dependence beween gold and Chinese secorial socks is characerized by a weak bu significan symmeric ail dependence. This leads o a posiive role of gold in Chinese secorial sock porfolios in he sense ha i helps o reduce risk. The weigh of gold o be included in hese porfolios can be very high, over 60%. Following he hedging effeciveness measure, he secors for which gold is he mos efficien are Informaion, Telecommunicaion and Energy. The Uiliies secor is he less efficien when being diversified wih gold. As a 22