Dynamic co-movement and correlations in fixed income markets: Evidence from selected emerging market bond yields

Transcription

1 P Thupayagale* and I Molalapaa Dynamic co-movemen and correlaions in fixed income markes: Evidence from seleced emerging marke bond yield Dynamic co-movemen and correlaions in fixed income markes: Evidence from seleced emerging marke bond yields Received: 15 November 2011 Acceped: 20 March 2012 ABSTRACT This paper exends research concerned wih he evaluaion of co-movemen and correlaions in inernaional fixed income markes by examining dynamic linkages in hree emerging bond marke yields along wih he US. The empirical resuls sugges ha daily bond yields for hese markes are no linked, which implies significan long-run risk diversificaion. In addiion, dynamic correlaions beween emerging marke bond yields appear o be more sensiive o negaive news raher han o posiive news, albei a low magniudes. Furhermore, accouning for ime-variaion is mosly beneficial and leads in mos cases o an improvemen in he risk-reward raio relaive o measures which do no consider ime-variaion. 1. INTRODUCTION * Porfolio inflows o emerging fixed income markes have grown significanly in size as invesors argeing higher reurns and diversificaion benefis have direced capial ino hese markes. Local-currency deb issued by emerging marke economies has emerged as an imporan asse class, paricularly in a conex of low yields in advanced economies. In paricular, over he las 10 years, local currency bonds in he emerging markes generaed a cumulaive reurn of 142,4%; over he same period, US Treasuries have only reurned 71,6%. Addiionally, he Sharpe raio 1 for local currency deb was 2,58, much higher han ha for US-denominaed deb (1,36) and US Treasuries (0,53) (Bank of America Merrill Lynch, 2011). Emerging marke bonds are also benefiing from a rack record of srong risk-adjused reurns and low correlaions wih oher asse classes. Such characerisics are aracive from a porfolio opimisaion perspecive. Recen empirical lieraure has focused on he examinaion of he dynamic linkages among sovereign bond markes; and increasing aenion has been devoed o he analysis of linkages beween bond yields in emerging markes and developed economies (e.g., Benelli and Ganguly, 2007 and references herein). Exan research indicaes ha correlaions in inernaional bond markes have increased over ime (e.g., Blommesein and Saniso, 2007; IMF, 2008; Laopodis, 2010). Invesors are ineresed in assessing * Respecively Chief Dealer, Financial Markes Deparmen and Economis, Research Deparmen, Bank of Boswana, Privae Bag 154.Gaborone, Boswana. hupayagalep@bob.bw 1 The Sharpe raio is used o characerize how well he reurn of an asse compensaes he invesor for he risk aken, he higher he Sharpe raio numbers he beer. he level of bond marke linkages and he implicaions relaed o increased volailiy and correlaions, in order o design well-diversified porfolio sraegies. The purpose of his paper is o invesigae he exen of inerdependence among hree large emerging bond markes (Mexico, Souh Africa and Souh Korea) and he Unied Saes. An evaluaion of he emporal naure of fixed income marke correlaions is carried ou in ligh of recen ime series approaches and invesor ineres in emerging marke local currency deb, given is aracive reurn enhancemen poenial, along wih on-going improvemens in credi raings, he ne credi posiion of many issuers and he coninued economic growh ouperformance of hese markes relaive o hose of he advanced economies. Furhermore, i is imporan o characerize he dynamic linkages among hese markes and assess he implicaions relaed o increased volailiy and correlaions, in order o design well-diversified porfolio sraegies. 2 The exen of emerging bond marke linkages will be addressed wihin bivariae and mulivariae seings. Firs, we esimae a vecor auo regression (VAR) model and apply co-inegraion ess o deermine wheher here are any long-run relaionships among he bond yield changes. In paricular, co-inegraion implies ha sysemaic risk in hese markes canno be diversified away, as movemens in he yields of hese markes are linked in a predicable direcion. Second, we use he VAR model o generae insighs on how a shock o he yield in one counry affecs he yield in 2 The inclusion of he US reflecs he dominan posiion of he US in he global bond marke. Almos wo-hirds of all privae bonds are raded in US markes. Bond markes are hus a poenially imporan condui for spillovers from he US o he res of he world. Indeed, episodes of financial marke volailiy from he US are ofen hough o have a major impac on emerging marke economies (IMF s Fall 2006, Global Financial Sabiliy Repor). Invesmen Analyss Journal No

2 anoher counry. In paricular, igh marke linkages would also indicae ha a domesic capial marke may no be efficienly insulaed from exernal shocks and inernaional porfolio diversificaion benefis can be limied. Third, we consider bivariae GARCH models o examine rending behaviour in he dynamics of correlaions beween hese bond yields. Fourh, dynamic condiional correlaions are invesigaed, in order o quanify he magniude of he ime-varying coefficiens and evaluae he dynamic ineracions among hese bond reurns. We also es for asymmeric effecs in condiional bond yield correlaions in order o ascerain if downside shocks in hese bond yields amplify correlaions among hese markes. Finally, we evaluae he benefis from aking ime-variaion ino accoun in porfolio consrucion. The res of he paper is organized as follows. Secion II briefly reviews some relaed findings on dynamic linkages in inernaional fixed income markes. Secion III presens he empirical mehodology. In paricular, he models o be esed are oulined. Secion IV provides a descripion of he daa and discusses our main empirical resuls. Secion V compares porfolio performance afer adjusing for ime-variaion in volailiies and correlaions, while Secion VI concludes. 2. LITERATURE REVIEW Recen research has focused on he analysis of linkages in inernaional bond yields. Much of his research has aken place in he conex of eiher greaer financial and economic inegraion (e.g., he convergence of cenral and easern Europe wih he European Moneary Union) or episodes of financial conagion (e.g., he financial crisis ha began wih he US sub-prime morgage marke during he second half of 2007 and is ransmission o he res of he world). These evens apparenly provided evidence of srong linkages in he price movemens of he world s major fixed income markes. Ineres in he opic has also been enhanced by he globalisaion of financial markes and he increasing imporance of cross-border bond marke flows. More generally, i is well-known ha inernaional diversificaion benefis are associaed wih he correlaion of asse classes in a given porfolio. While much of recen empirical lieraure has focused on developed counry bond markes, surprisingly lile aenion has been devoed o he analysis of dynamic linkages among some of he major sovereign bond yields in emerging markes. The quesion of wheher emerging economy bond markes are inegraed wih each oher is also imporan from a porfolio diversificaion poin of view, bu also wih respec o poenial conagion from developmens in oher bond markes. The empirical lieraure on inernaional bond marke linkages can be raced o Clare e al. (1995), who examined he degree of co-movemen in he bond markes of he US, Japan, Germany and he UK from 1978 o 1990, using co-inegraion echniques. They found ha sysemaic risk can be diversified away as movemens in he yields of hese markes are no linked in a predicable direcion. Smih (2002) updaed Clare e al. s sudy by enlarging he sample (o include boh Canada and France) and employing more robus esimaion echniques and found evidence of co-inegraion among hese markes. He inerpres increased correlaions and co-movemens beween inernaional bond markes as suggesing reducions in he benefis of porfolio diversificaion, such ha porfolio managers would need o acively adjus heir porfolios in search of asses wih lower correlaions. A furher sudy by Clare and Lekkos (2000) invesigaed dynamic linkages among he American, Briish and German bond markes using vecor auo regression (VAR) mehods. They found ha global facors primarily explained variaions in dynamic behaviour among hese markes during periods of financial insabiliy. Davies (2007) idenified a common long-run rend in he sovereign fixed income markes of he major indusrialised economies from 1994 o 2006 using non-linear co-inegraion echniques. In general, hese resuls sugges ha if markes become more closely linked in he sense ha here are sronger co-movemens of prices across markes, hen his may resul in changes o opimal inernaional porfolio diversificaion sraegies. The issue of bond marke linkages is also relevan from a policy perspecive in an environmen where moves owards greaer regional economic inegraion are being promoed. Agains his background, recen sudies have concenraed on governmen bond marke inegraion, specifically in view of he European Moneary Union. Yang (2005) examined six European counries (Belgium, France, Germany, Ialy, Neherlands and he UK) and found evidence ha hese bond markes were no co-inegraed during he period, suggesing ha here had been limied financial and economic convergence beween hese counries. Laopodis (2008) re-examined governmen bond marke inegraion among a wide selecion of eurozone economies for he period 1994 o He found ha hese markes were no linked in a saisically and economically meaningful way in he period prior o he inroducion of he single European currency (i.e., he euro); however, in he pos-euro period, evidence of dynamic linkages among hese markes are found. In a more recen paper, Laopodis (2010) examines dynamic linkages among four inernaional bond markes (German, Japanese, UK and US) and finds evidence of significan shor-run relaionships among 26 Invesmen Analyss Journal No

3 hese bond marke yields, bu no evidence of long-run rending behaviour is revealed. Previous sudies on emerging markes have generally analysed wheher here has been volailiy conagion (e.g., Edwards, 1998 and Andrizkya, e al., 2007). Nowak. (2009) found ha he process of informaion absorpion in emerging economy bond markes ends o be more drawn ou han in maure bond markes and ha macroeconomic surprise in emerging bond markes are found o affec boh condiional reurns and volailiy, wih he effecs on volailiy being more pronounced and longer lasing han hose on prices. In relaion o emerging markes, Benelli and Ganguly (2007) found ha bond yields in Lain America are marked by weakening linkages wih U.S corporae bonds, while hey increased heir sensiiviy o movemens in oher emerging marke bond markes. An exensive srand of his lieraure, paricularly relevan o our paper, has documened how he Unied Saes is a major source of spill overs o financial markes around he globe (Ng (2000), and Chan-Lau and Ivaschenko (2002)). I is for his reason ha we include he US in our sudy for reference purposes. 3. METHODOLOGY 3.1 Co-inegraion In order o es for co-inegraion, we use he wellknown mehodology developed by Johansen (1996). In his framework, he co-inegraing equaion may be inerpreed as a long-run equilibrium relaionship among he respecive bond markes. If, in a sysem of k inegraed and non-saionary ime series (e.g., bond yield changes) here exis r co-inegraing relaionships, ha link he k bond yields ogeher (linearly), hen he non-saionary behaviour of he k bond markes is driven by a reduced number of n common sochasic rends. 3 The analysis is based on an auo regression model of he form: k 1 i i k i1 Y Y Y (1) which defines he p-dimensional vecor auoregressive process of kh order where is he firs-difference operaor, Y is a (p x 1) random vecor of ime series (of bond yields) inegraed of order one or less, is a (p x 1) vecor of conesans, i are (p x p) marices of parameers, is a vecor of independen and idenically disribued errors wih a mean of zero and variance of one, is a (p x p) marix of parameers, 3 The number of r co-inegraing relaionships has o be smaller han he number of non-saionary variables k: (0<r<k); moreover, he number of n common sochasic rends is given by n=k-r, which is he number of non-saionary variables minus r co-inegraing relaionships. he rank of which conains informaion abou long-run relaionships among he bond yields, and k is he lag lengh of he model. The vecor error correcion model (VECM) in equaion (1) reduces o an orhodox vecor auoregressive (VAR) model in firs differences if he rank (r) of is zero, while if has a full rank, r = p, all elemens in Y are saionary. We es for he exisence of a coinegraing relaionship beween he respecive bond yield changes by analysing he rank of he marix. If he coefficien marix has reduced rank r < p, hen here exis p x r marices and each wih rank r, such ha ' ' and y is saionary. In his framework, r, is he number of co-inegraing relaionships, he elemens of are known as he adjusmen (or loading) parameers in he VECM and each column of is a co-inegraing vecor. Johansen proposes wo differen likelihood raio ess of he significance of hese canonical correlaions and hereby he reduced rank of he marix: he race es and maximum eigenvalue es, respecively. 3 Bivariae VAR models Our nex exercise is o invesigae he dynamic inerdependence of financial markes using a bivariae vecor auo regression (VAR) model. This model esimaes he impac of bond yield changes in one marke on hose in anoher marke by joinly modelling changes in he respecive bond yields. Provided ha srucural shocks can be idenified, impulse responses based on hese bivariae VARs provide an insigh on he dynamic linkages beween he markes under sudy. This echnique, herefore, permis he idenificaion of relaionships beween any pair of yields, such ha we can es, wheher yield changes in one counry Granger cause yield changes in anoher counry. The bivariae VAR model is specified below: N N i i j i i i j i1 j1 r r r (2) N N j j i j j j i j1 i1 r r r (3) where r and r j are he yield changes of counry i and j a i ime, respecively. The opimal lag lengh, N, is deermined using he Schwarz informaion crieria (SIC). If our es resuls show ha j (in Equaion (3)) is no saisically differen from zero, his would sugges ha he yield of counry j is Granger-caused by he yield in counry i. In oher words, changes in counry j s yield drive changes in counry i s yield. Invesmen Analyss Journal No

4 3.3 Dynamic condiional correlaion-garch model We use a mulivariae generalised auoregressive condiional heeroskedasiciy (GARCH) framework for he esimaion, which allows for heeroskedasiciy of he daa and a ime-varying correlaion in he condiional variance. Specifically, he Dynamic Condiional Correlaion (DCC) specificaion by Engle (2002) is employed. This economeric echnique allows us o analyse he co-movemen of bond yields by inferring he correlaions of he changes in he yields discussed above, which, in urn, is essenial in undersanding wheher here are linkages among hese emerging bond markes. The DCC specificaion of he mulivariae condiional variance H, can be expressed as: H DRD (4) where D diag h is a diagonal marix wih he square i, roos of he condiional variances in he diagonal and R is he ime-varying condiional correlaions marix. The elemens of D are given by he firs order univariae GARCH (p, q) process: h h (5) 2 i, i i i, 1 i, 1 where h is he volailiy process o be esimaed, is a consan long-run or average variance, 2 capures 1 pas volailiy, reflecing squared news abou he reurn, and h is he previous esimae of he 1 condiional variance, i capures he shor-run persisence of a shock o bond yield i and i represens he conribuion of a shock o yield i o he long-run persisence. The condiional correlaion in he DCC model is specified as: ' Q 1 Q a b Q (6) where Q is he ime-varying covariance marix of, and he parameers 1 and 1 represen he effecs of previous shocks and lagged dynamic condiional correlaions on curren dynamic condiional correlaions. In oher words, 1 and 1 are he DCC Q E ' and represens he parameers. uncondiional correlaion beween he respecive bond marke yields (expressed in erms of sandardised residuals). We perform a hree sep procedure in he esimaion of Equaion (6). Firs, we fi univariae GARCH models for each of he four bond yields in he specificaion. Second, he long-run correlaions are compued from he uncondiional sample correlaions. In paricular, he inercep parameers are derived from he ransformed bond yields. Finally, he hird sage akes advanage of he esimaed parameers (in paricular Q ) o esimae he scalar parameers 1 and 1, which correspond o he dynamic correlaion parameers. In he case of sandard DCC (1,1), boh 1 and 1 are posiive and heir sum is less han uniy, implying ha Q is posiive and mean revering. This, in urn, suggess ha (afer a shock) he correlaion beween bond yields will reurn o he long-run uncondiional level. Furhermore, when 1 1 0, he DCC model converges o he consan correlaion model. The DCC model is esimaed by maximisaion of he following log-likelihood funcion (L): T 2 ' 2 L 0.5 k log 2 log D r D r i1 T 0.5 log R R where ' 1 ' (7) i1 he firs and second (brackeed) erms represen he volailiy and correlaion componens, respecively. 3 Asymmeric DCC (ADCC)-GARCH model A major limiaion of he DCC model concerns is inabiliy o capure asymmeric effecs in condiional bond yield correlaions. Specifically, he DCC model accouns for he magniude of pas yield (change) shocks on volailiy and correlaions, and i ignores he sign of his effec. I has been widely documened ha volailiy and correlaion dynamics respond asymmerically o pas negaive and posiive reurn shocks, wih negaive bond yield changes resuling in larger fuure volailiies (e.g., Loeys and Panigirzoglou, 2005). This feaure has led o he developmen of DCC models wih asymmeric or leverage effecs and, hence, he developmen of he asymmeric DCC (ADCC) model, which has been proposed by Cappiello e al. (2006) o capure asymmeric effecs in condiional asse correlaions. The ADCC model ness he DCC model. More specifically, equaion (6) can be modified o allow for asymmery in condiional correlaion as: ' ' Q 1 Q a b Q (8) , 1 where 28 Invesmen Analyss Journal No

5 he parameer inroduces a leverage or asymmery parameer ino he DCC model and I 0, where I is a funcion indicaor, which assumes he value of uniy if he error erms are negaive and 0 oherwise and is he Hadamard produc. ' 1 is he sample covariance marix of. The ADCC model, herefore, considers increases in condiional correlaions when bond yield changes are declining raher han rising. 4. EMPIRICAL RESULTS 4.1 Preliminary observaions Our analysis is based on daily daa for 10-year governmen bond yields for hree major emerging markes: Mexico, Souh Africa and Souh Korea. The US marke is also included for comparaive and reference purposes, given he imporance of he US bond marke in inernaional capial markes. The daa used in his sudy was sourced from Bloomberg and encompasses he period April 01, 2002 o April 29, 2011, resuling in observaions. Figure 1 shows he yields of he four bond markes over he sample period. As is eviden from he graph, emerging marke yields have followed a downward rend over he review period. For insance, Souh African 10-year yields have fallen from 13,24 per cen a he sar of he sample o a 8,50 per cen a he end of he sample. Mexican 10- year yields have fallen from 11,02 o 7,24 per cen over he sample period. Similarly, Souh Korean and US 10-year yields, have fallen o 4,47 per cen and 3,28 per cen from 6,14 per cen and 5,43 per cen, respecively. Prior o formal analysis, Table 1 examines he ime series properies of he individual daa using sandard diagnosic mehods. The resuls of he Augmened Dickey-Fuller (ADF) uni roo es offer evidence in favour of saionary bond yield changes for he four counries, which in urn provide a basis for robus saisical inference. This resul is furher subsaniaed by applicaion of he Kwiakowski-Phillips-Schmid- Shin (KPSS) es, which evaluaes he saionariy hypohesis (compared o he uni roo hypohesis esed by he ADF). In paricular, Table 1 repors summary saisics on each yield difference. These summary saisics reveal he usual characerisics of daily bond yield changes, ha is, a small mean value and a larger sandard deviaion. Evidence of non-normaliy and, in paricular, excess kurosis is also eviden, which is generally more pronounced for he emerging markes, suggesing hey are subjec o more large shocks han he US. Souh Africa is he excepion in his regard and his may reflec he srucural characerisics of his bond marke, paricularly, he dominaion of bond holdings by large insiuional invesors. Furhermore, evidence of Auoregressive Condiional Heeroskedasiciy (ARCH) effecs and non-normaliy provide evidence agains marke efficiency specified in he random walk version of he efficien marke hypohesis (EMH). Table 2 presens he cross correlaion beween he yield changes for emerging bond markes. Uncondiional correlaion coefficiens in bond yield changes indicae mosly low (o slighly negaive) pairwise correlaions. Indeed, porfolio diversificaion seeks o minimise risk by invesing in fixed income producs whose reurns are no correlaed. The larges correlaion coefficien is for he 10-year Mexican and Souh Korean bonds, a 0,0388 per cen. The lowes correlaion is beween changes in he yield of he 10- year US Treasury bond and he corresponding Mexican bond, which have a correlaion of -0,0173. Boh among hemselves and in relaion o he US 10- year yield changes, emerging marke bond yield changes show low and/or negaive pair-wise correlaions and hus appear o provide a diversificaion benefi o invesors. However, hese measures are saic correlaions and do no reveal he dynamic srucure and inerdependence among hese yields. 4 GARCH (1,1) model The non-whie noise properies of our daa moivaes he esimaion of he GARCH model developed by Engle (1982) and Bollerslev (1986). Table 3 confirms our previous findings on he imporance of he nonnormaliy and (G)ARCH effecs by showing ha he degree of freedom, as well as he GARCH and ARCH erms are all saisically significan. The parameers of he condiional variance equaions are all posiive and saisically significan. In addiion, hey saisfy he posiiviy consrain for he GARCH(1,1). This confirms he exisence of he ime-varying condiional variance, which can be inerpreed as ime-varying uncerainy among invesors abou bond yield flucuaions. The summaion of he coefficiens α and β in he GARCH models enables he measuremen of persisence in variance. The magniude of volailiy persisence is 0,9991, 0,9840, 0,9817 and 0,8567 for he US, Souh Africa, Souh Korea and Mexico, respecively, suggesing ha shocks o volailiy are very persisen. In addiion, he parameers of he condiional variance equaions for all hese markes (see Table 3) are all posiive and saisically significan a he 1 per cen significance level. Invesmen Analyss Journal No

6 Yield Dynamic co-movemen and correlaions in fixed income markes: Evidence from seleced emerging marke bond yield Year Mexico Souh Africa Souh Africa US Figure 1: Sovereign 10-Year Governmen Bond Yields Table 1: Descripive saisics of long-erm bond yield changes Mexico Souh Africa Souh Korea US Mean -0,0126-0,0159-0,0068-0,0045 Sandard deviaion 1,0004 0,7546 1,1504 1,8269 Skewness -1,6514 0,1300 0,6900-0,0811 Kurosis 36,834 5,3034 8,8809 7,6638 Normaliy ,33 ** 530,3719 ** 3601,830 ** 2149,589 ** ARCH (5) es 86,3275 ** 119,1607 ** 106,1162 ** 135,8944 ** ARCH (10) es 88,6779 ** 136,5420 ** 115,8585 ** 185,2340 ADF es (consan) -40,3785 ** -42,1790 ** -47,5809 ** -38,4222 ** ADF es (consan and rend) -40,3703 ** -42,2144 ** -47,5708 ** -38,4177 ** KPSS es (consan) 0,0222 ** 0,2739 ** 0,0409 ** 0,0441 ** KPSS es (consan and rend) 0,0198 ** 0,0607 ** 0,0410 ** 0,0361 ** Noes: 1/ All yields are in changes; ** indicaes saisical significance a he 1% significance. ADF and KPSS are he Augmened Dickey-Fuller and Kwiakowski-Phillips-Schmi-Shin ess, respecively. 2/ The non-normaliy es is based on he Jarque-Bera (1987) saisic. 3/ The ARCH es is derived from Engle s Lagrange Muliplier ARCH (1982) es. Table 2: Uncondiional correlaion marix (of long-erm bond yield changes) Mexico Souh Africa Souh Korea US Mexico 1,0000 Souh Africa 0,0093 1,0000 Souh Korea 0,0388 0,0282 1,0000 US -0,0173 0,0320 0,0012 1,0000 Noes: All yields are in changes Table 3: GARCH esimaes Souh Africa Souh Korea Mexico US Consan (ω) 0,0090 0,2814 (0,0117) ** 0,0063 (0,0025) ** (0,0023) ** 0,0275 (0,0027) α 0,0452 (0,0057) ** 0,0737 (0,0049) ** 0,5346 (0,0334) ** 0,0428 (0,0053) ** β 0,9388 (0,0082) ** 0,9080 (0,0052) ** 0,3221 (0,0208) ** 0,9563 (0,0050) ** df 8,9271 (0,0612) ** 5,6086 (0,7720) ** 5,9232 (1, 2087) ** 7,3664 (0,6439) ** α+β 0,9840 0,9817 (0,0000) ** 0,8567 0,9991 (0,5762) ** (0,0005) ** (0,0000) ** Numbers in parenheses are sandard errors, excep under column α+β, where enries are p-values from a Wald es ha α+β=1, 30 Invesmen Analyss Journal No

7 4.3 Bivariae co-inegraion Since co-inegraion can only be found wih nonsaionary variables we es his proposiion using sandard diagnosic mehods. Table 4 presens our resuls. In paricular, i shows ha he bond yields for he four counries are no saionary in levels. We herefore have a sound premise o conduc coinegraion analysis. Since each of he four series were found o be nonsaionary, we performed wo ess o deec he coinegraing relaion: he race and he maximumeigenvalue ess, respecively. We rejeced he null hypohesis of no co-inegraion only if boh ess rejec he null, which is a more sringen crierion han normally applied. The resuls for bilaeral co-inegraion are repored in Table 5, and broadly show no evidence of coinegraion among emerging marke bond yield changes. In addiion, he resuls show ha, generally, emerging markes are no co-inegraed wih he US bond marke. 4 Since he exisence of co-inegraion implies ha sysemaic risk canno be diversified away (given ha movemens in he bond yields are linked in a predicable direcion), our findings sugges he opposie, i.e., emerging markes provide scope for porfolio diversificaion, wih respec o hemselves and also in relaion o he US. Table 6 repors he bivariae VAR esimaes for he bond markes under sudy. In paricular, wo key observaions are made. Firs, changes in emerging marke yields (i.e., DSA, DSK and DMEX) do no appear o have a saisically significan impac on each oher s yields. This, in urn, suggess ha hese markes are insulaed from each oher. Second, changes in US yields have a saisically significan impac (or influence) on Souh African yields, while for he oher markes (i.e., Mexico and Souh Korea) he impacs of changes in US yields are no saisically differen from zero. Figure 2 plos he impulse responses of a shock o one counry s yield change by anoher counry s yield change (own yield responses were omied in he ineres of breviy). Souh African yields respond o shocks from he U.S yields. Meanwhile, he Souh Korean yield only responds posiively afer hree days while, for Mexico, here is no response. On he oher hand, he U.S yield s responses o shocks from he emerging markes are no saisically significan. The Souh African yield responds posiively o shocks from he Souh Korean yields. However, he response by he Souh African yield due o he Souh Korean 4 Similar resuls are obained using 1,2, or 3 lags. Thus, he resuls are robus o he use of differen lag lenghs. yield is no saisically significan. Meanwhile, he Souh Africa yield does no respond o shocks from he Mexican yield. The Mexican yield responds posiively o shocks from he Souh African and Souh Korean yields. However, he responses are no saisically significan. The Souh Korean yield responds posiively o Mexican yields (responses are no saisically significan), while here is no response from he Souh African yield. In oal, hese resuls highligh he segmenaion ha exiss among emerging markes and he US bond marke and he diversificaion benefis herein derived. 4 DCC-GARCH model resuls and discussion Table 7 presens he esimaes of he DCC-GARCH model. Several observaions are in order. The coefficiens (α and β, respecively) are shown o be saisically significan in many/mos cases. This resul aess o he ime-varying naure of bond marke volailiy in hese emerging markes. The sum α + β measures volailiy persisence (i.e., he exen o which shocks o curren volailiy remain imporan for long periods ino he fuure). As he sum α + β approaches uniy, he persisence of shocks o volailiy becomes greaer. Our resuls indicae ha volailiy is generally persisen across all marke pairs. However, he magniude of volailiy persisence for changes in Souh African yields are comparaively high for example, persisence in variance is 0,7630 (sum of 0,4116 and 0,3514), when relaed o he US yields over he sample period. In conras, he volailiy persisence for Souh African yields relaive o Mexican and Souh Korean yields is 0,3880 and 0,4970, respecively. This, in urn, reflecs he low financial linkages exising wih respec o hese bond marke yield changes. The esimaed dynamic condiional correlaions (DCC) are generally found o be saisically insignifican, in he case where he correlaion dynamic involves wo emerging markes. The excepion relaes o where he correlaion involves he US. In shor, i would appear ha correlaions wihin emerging markes are saisically insignifican, while hose involving he US are generally saisically imporan (wih he excepion of he US and Souh Korea). To furher evaluae he dynamic behaviour of bond yield correlaions among emerging marke yields and wih respec o he US, we plo he bivariae dynamic condiional correlaions. Figure 3 illusraes he imevarying naure of correlaions in he bond yields of Mexico, Souh Africa, Souh Korea and he US. Indeed, all yield pairs exhibi evidence of ime-variaion in heir evoluion over he sample period. The bivariae dynamic correlaions reveal a number of characerisics. Firs, all he bivariae dynamic correlaions display a volaile profile. In paricular, he dynamic correlaions flucuae sharply around zero. Invesmen Analyss Journal No

8 Table 4: Uni roo es on long-erm bond yields Mexico Souh Africa Souh Korea US ADF es (consan) -2,1020-3,8102 ** -2,1162-2,4283 ADF es (consan and rend) -3,9567 ** -3,4043-2,3307-2,6954 KPSS es (consan) 4,6708 2,2086 1,2303 2,4443 KPSS es (consan and rend) 0,2992 0,9463 0,5308 0,7042 Noes: 1/ ** indicaes saisical significance a he 5% significance, ADF and KPSS are he Augmened Dickey-Fuller and Kwiakowski- Phillips-Schmi-Shin ess, respecively, Table 5: Bilaeral co-inegraion resuls Emerging markes and he US Trace saisic Max eigenvalue saisic Souh Africa Mexico 0,23 0,04 Souh Korea 0,06 0,31 Unied Saes 0,05 0,07 Souh Korea Mexico 0,25 0,11 Souh Africa 0,14 0,22 Unied Saes 0,09 0,03 Mexico Souh Korea 0,29 0,26 Souh Africa 0,04 0,07 Unied Saes 0,09 0,21 Unied Saes Mexico 0,39 0,51 Souh Africa 0,07 0,07 Souh Korea 0,11 0,08 Source: Auhors calculaions 1/We performed wo lag lengh ess he Akaike informaion crierion (AIC) and he Schwarz informaion crierion (SIC) - o selec he appropriae number of lags o be used in he VAR, The ess suggesed ha only a small number of lags ranging from one o four are necessary in he VAR, Thereafer, we use four lags in he VARs, 1/ Sofware used for esimaion was E-Views 6,0, 2/ The able repors MacKinnon-Haug-Michelis (1999) p-values, The null hypohesis is ha here is no co-inegraion relaionship agains he alernaive of one co-inegraion equaion, The es equaion uses four lags, Table 6: Bivariae VAR esimaes DSA DSK DSA DMEX DSA DUS DMEX DUS DSA -1-0,0647 (0,0581) 0,1083 (0,0785) 0,3979 (0,2973) 0,1652 (0,1070) 0,05792 (0,4912) 0,0164 * (0,0093) DSA -2 0,1319 (0,1203) 0,0468 (0,0319) 0,1632 (0,1072) 0,0236 (0,0157) 0,2434 (0,172) 0,0038 * (0,0012) DSK -1 0,0155 (0,0147) 0,3377 (0,1674) DSK -2 0,0296 (0,0118) 0,0449 (0,0351) DMX -1 0,0276 (0,0235) 0,0562 (0,0367) 0,4093 (0,1433) -0,0871 (0,0032) DMX -2 0,4301 (0,3122) 0,2349 (0,1873) 0,0116 * (0,0038) -0,4462 (0,0634) DUS -1 0,0973 (0,0717) 0,1422 (0,0825) 0,3744 (0,2178) 0,4752 * (0,3152) DUS -2 0,2834 (0,0283) 0,2512 (0,1336) 0,1151 (0, 1022) 0,2163 * (0,1279) 2 R 0,0765 0,1233 0,2318 0,1404 0,1262 0,0921 0,3186 0, Invesmen Analyss Journal No

9 Table 6: Coninued DMEX DSK DUS DMEX DMX -1 0,2742 (0,1068) 0,1709 (0,2433) DMX -2 0,3574 (0,1519) 0,2247 (0,1249) DSK -1 0,0184 (0,0129) 0,1092 * (0,0083) 0,2356 (0,1672) 0,1772 (0,6249) DSK -2 0,0716 (0,2555) 0,0024 * (0,0006) 0,0685 (0,0542) 0,0592 (0,0307) DUS -1 0,3886 (0,2552) 0,0026 (0,0018) DUS -1 0,2131 (0,1507) 0,0328 (0,0280) 2 R 0,1581 0,1317 0,1148 0,2422 Response of DSA o DUS Response of DSA o DSK Response of DSA o DMEX Response of DUS o DSA 2 Response of DUS o DSK 2 Response of DUS o DMEX Response of DSK o DSA Response of DSK o DUS Response of DSK o DMEX Response of DMEX o DSA Response of DMEX o DUS Response of DMEX o DSK Figure 2. Impulse responses of 10-year bond yield changes (Time (in days) and percenage poins are measured on he x- and y-axes respecively) Invesmen Analyss Journal No

10 Table 7: Esimaes of GARCH-DCC models DCC coefficien c 0,0872 DSA [0,0469] DCC coefficien c 0,3027 DSA [0,2273] DCC coefficien c 0,3910 * DSA [0,0082] DCC coefficien c 0,0327 DUS [0,0241] DCC coefficien c 0,0062 DUS [0,0054] c 0,3228 * DUS [0,2139] c 0,5988 DMEX [0,3415] c 0,1685 * DSK [0,0284] c 0,4305 DMEX [0,2139] c 0,0431 * DSK [0,0429] DSA 0,4116 * [0,1149] DSA 0,1862 * [0,0119] DSA 0,2543 [0,1822] DUS 0,1551 [0,0922] DUS 0,2950 * [0,1359] DUS 0,0229 * [0,0058] DMEX 0,3612 * [0,0948] DSK 0,1061 [0,3018] DMEX 0,5983 * [0,0076] DSK -0,3351 [0,1932] DSA 0,3308 * [0,1095] DSA 0,2018 [0,7211] DSA 0,2427 [0,4063] DUS -0,3738 * [0,0139] DUS 0,5027 [0,2653] DSA 0,3514 * [0,0798] DMEX 0,6057 [0,4548] DSK 0,3394 [0,1557] DMEX -0,1113 [0,3829] DSK 0,0816 [0,0292] dcc 0,6132 * DSA [0,2250] dcc 0,1845 DSA [0,2833] dcc 0,3512 DSA [0,1887] dcc 0,6698 * DUS [0,2256] dcc 0,2812 DUS [0,1163] dcc 0,5417 * DUS [0,1286] dcc -0,3221 DMEX [0,2196] dcc 0,1332 DSK [0,0941] dcc 0,4027 * DMEX [0,1257] dcc 0,1708 DSK [0,1342] LogL 118,365 DSA,DUS LogL -25,80 LogL 42,179 DSA,DMEX DSA,DSK LogL -37,21 DUS,DMEX LogL 64,9 DUS,DSK Noe: 1/ dcc denoes he dynamic condiional correlaion coefficien (i.e., α+β) in Equaion 6. 2/ he numbers in[ ] refer o sandard errors 3/ LogL is he log-likehood funcion 4/ * denoes saisical significance a he saisical significance a he 5% level. The noable excepions involve he bivariae correlaion beween he US and Souh Africa, and he bivariae relaionship beween Souh Korea and Mexico. In he case of he dynamic correlaion beween he US and Souh Africa, here is a clear downrend in he degree of correlaion. In paricular, he graph poins o a seady decrease in he exen of correlaion beween hese bond marke yields over he sample period. In paricular, a he sar of he sample (i.e., 2002) he correlaion in 10-year bonds beween hese markes was close o 0,50, from here i rends erraically (bu wih a pronounced downward bias). This dynamic correlaion reaches a low of -0,3 a he end of Thereafer, he dynamic correlaion rises o zero a he end of he sample. The decline in he ime-varying correlaion value reflecs he divergen moneary policies pursued by he respecive cenral banks and he de-synchronisaion of business cycles beween hese economies. The bivariae dynamic condiional correlaion beween Souh Korea and Mexico also differs from he oher pairwise correlaion pahs in wo regards. Firs, he correlaion beween hese markes is a around -0,25 a he sar of he sample (in 2002). Thereafer, he correlaion quickly rises in he firs 3 monhs o zero, afer which i flucuaes wihin a narrow band around zero, while he oher correlaion pairs display wide ampliudes wih respec o he zero correlaion mark. The rise in he correlaions may be due o an emerging crisis (e.g., he Argenina financial crisis of 1999 o 2002), which may have affeced bond yields in oher emerging markes. 4.5 Asymmeric DCC - GARCH Reurn correlaion is known o rise in a down marke, hereby amplifying he impac of naional bond marke volailiy. Tha is, a negaive shock ends o hi many naional bond yields simulaneously, causing an increase in yields. In his case, i is possible o have an increase in marke volailiy wihou any increase in he volailiy of he emerging marke bond yields. To furher explore his aspec of dynamic correlaions in emerging marke yields, we evaluae he Asymmeric DCC (ADCC) model in a bivariae seing. The evaluaion of asymmeric correlaion responses (o negaive reurns) is examined hrough he (leverage) parameer,. 5 Table 8 presens our findings. The 5 As can be seen, he ADCC model reduces o he sandard DCC-GARCH when Invesmen Analyss Journal No

11 empirical resuls sugges he exisence of asymmeric condiional correlaions. The asymmeric (or leverage) erm is found o be saisically significan in only wo cases, boh involving Mexico. In paricular, he dynamic correlaions are found o have a saisically significan asymmeric componen in he case of Mexico and Souh Africa, and Mexico and Souh Korea. The leverage parameer ranges from 0,00029 (Souh Africa versus Mexico) and 0682 (Souh Africa versus Souh Korea). For all oher markes, he asymmeric effec is no saisically differen from zero. The ADCC resuls also indicae low correlaions among he various bond markes. 5. ASSESSING TIME VARIATION IN PORTFOLIO CONSTRUCTION In order o evaluae if here are benefis from recognising he impac of ime-variaion (of correlaions and volailiies) in porfolio consrucion, we es he proposiion (or hypohesis) ha if correlaions and volailiies are indeed ime-varying, hen a porfolio consrucion mehod ha ignores his feaure of he daa will lead o riskier porfolios ex-pos han a porfolio consrucion mehod ha accouns for imevariaion. In oher words, if an invesor minimises porfolio risk based on he uncondiional correlaion marix, while he rue correlaion dynamic is imevarying, hen he invesor s porfolio will no be risk minimal ex pos. Based on Bayes heorem we consruc a risk raio defined below: (9) where is he risk raio; is an indicaor variable denoing he uncondiional correlaion marix given ha he rue correlaion marix is ime varying; represens he minimum risk porfolio and capures he disribuion of he uncondiional correlaion marix. Table 9 shows ha, while invesors may have divergen views in relaion o he expeced bond reurns, i is imporan (especially where he US marke is concerned) o ake ime-variaion of he covariance marix ino accoun, because his leads o lower porfolio risk. Examining he case of Souh Africa and US, he use of he uncondiional marix insead of he ime-varying covariance marix increases he realized risk by 35,8%, 22,8%, 26,3% and 68,2% in Cases 1, 2, 3 and 4, respecively. The lower risk of he porfolios consruced wih he condiional DCC covariance marices is in line wih he empirical fis of he DCC models, which have already indicaed ha a consan covariance marix is no appropriae. In he case of ineracions beween emerging markes, he porfolio risk is less, suggesing ha i is more imporan in he case of ineracions where he US is concerned han where inra emerging markes ineracions are concerned. Our resuls show ha beer performing porfolios could be creaed if invesors incorporae ime variaion in heir modelling framework. Indeed our ou-of-sample experimen indicaes ha porfolio performance was beer when ime variaion is no ignored. This is paricularly rue for cases involving he US bond marke. This in urn suggess ha accouning for ime variaion may be more imporan in larger and more sophisicaed deb markes like hose of he US compared o he emerging markes used in our sudy. 4. CONCLUSION Analyzing bond marke co-movemens is imporan for risk diversificaion of an inernaional porfolio. The exen of linkages in hree large emerging fixed income markes (Mexico, Souh Africa and Souh Korea), along wih he US, are sudied by examining he ime series properies of he reurns and he volailiy of heir respecive (local currency) benchmark 10-year bonds from April 01, 2002 o April 29, Our sudy expands he scope of he dynamic correlaions lieraure in emerging markes by focusing on fixed income given his asses reurn and diversificaion benefis - and by employing recen economeric echniques which permi a richer analysis of he imevarying naure of bond yield daa. We begin by using esablished co-inegraion echniques in order o gauge he exen of comovemens of bond yields in emerging markes and beween hese markes and he US. Our findings indicae ha emerging marke bonds do no display a long-erm rend neiher amongs hemselves nor wih respec o he US. This, in urn, suggess ha sysemic risk can be diversified away as movemens in bond yields are no linked in a predicable direcion. On he basis of VAR analysis, we find evidence refuing boh he exisence of shor-erm or long-erm relaionships. Impulse response funcions allowed us o examine he sensiiviy of emerging marke bond marke yields o each oher and o he US. The impulse responses of long-erm bond yield changes indicae ha shocks o volailiy dissipae very quickly and/or are saisically insignifican. Invesmen Analyss Journal No

12 US vs. Souh Africa.6 US. vs Souh Korea US vs. Mexico Souh Africa vs. Souh Korea Souh Korea vs. Mexico Souh Africa vs. Mexico Figure 3. Time-varying condiional correlaions (The year and he correlaion are measured on he x- and y- axes respecively) Table 8: ADCC-GARCH(1,1) esimaes a 1 b 1 Mean Maximum Minimum Sandard deviaion SA vs. MEX 0,00342 * 0,00029 * 0, , , , ,08644 SA vs. SK 0, , , , , , ,12052 SA vs. US 0,07438 * 0, ,00022 * -0,0798 0, , ,20136 MEX vs. SK 0, ,00177 * 0, , , , ,10191 MEX vs. US 0,00031 * 0, , , , , ,10756 SK vs. US 0,13162 * 0, ,00241 * 0, , , ,13359 Noes: 1/ This Table presens he esimaed coefficiens from he ADCC model in a bivariae framework for he fixed income markes (yield changes) for he emerging markes under sudy (and he US oo), 2/ A number of descripive saisics of he ime-varying correlaions are also produced including values of he mean, maximum, minimum and sandard deviaion values of he esimaed correlaions among he seleced bond markes, 3/ * denoes significance a he 5% level of significance. 36 Invesmen Analyss Journal No

13 Table 9: Assessmen marix of ime-variaion in porfolio consrucion Scenario Case 1 Case 2 Case 3 Case 4 Porfolio composiion 0,00/1,00 0,25/0,75 0,50/0,50 1,00/0,00 Souh Africa vs. US 135,8 122,8 126,3 168,2 Souh Korea vs. US 114,2 182,3 163,71 178,9 Mexico vs. US 177,6 134,7 122,4 185,1 Souh Africa vs. Souh Korea 103,2 102,4 100,7 0,992 Souh Africa vs. Mexico 105,8 101,8 100,6 103,5 Souh Korea vs. Mexico 100,6 104,7 101,2 100,2 Noes: 1/The expeced excess reurn raes are sandardised (since only he relevan magniude of he expeced excess reurn raes is relevan for porfolio opimisaion). We nex explore bond marke linkages beween our sample counries over ime using correlaion coefficiens ha were adjused for changing volailiy (heeroskedasiciy) of reurns. In paricular, we used he dynamic condiional correlaion GARCH model o examine he dynamic behaviour of bivariae correlaions. We find evidence of ime-variaion in correlaion dynamics. In general, we find ha correlaions flucuae erraically around zero among he various counry pairings. In he case of Souh Africa and he US, we observe a downward rend ha evenually sabilizes a zero. In he case of Souh Korea and Mexico, a negaive correlaion quickly sabilizes around zero. Esimaes from he DCC- GARCH model, in general, poin o low (or weak) correlaions. A key finding of he paper is ha here are no subsanial inernaional cross-marke linkages among emerging bond markes. Furhermore, he impac of he US on hese markes is very limied. The imporance of he US 10-year noe is fel mos acuely by changes in he 10-year Souh African bond yield. To invesigae he role of asymmery in condiional correlaions, we esimae he asymmeric DCC- GARCH model. On he basis of his model, we find ha he asymmeric erm is found o be saisically significan in wo cases: Mexico agains boh Souh Korea and Souh Africa, respecively. These correlaions are, however, of comparaively low magniude. This means ha he dynamic correlaions beween hese bond yields have a sronger response (i.e., are more sensiive) o negaive news (or shocks), raher han posiive news. Finally, we assess he relevance of accouning for ime-variaion (of correlaions and volailiies) in porfolio consrucion. In paricular, we evaluae he rade-off an invesor is subjec o if he invesor minimizes porfolio risk based on he uncondiional correlaion marix, while in fac he acual correlaion dynamic is ime-varying. Our resuls show ha accouning for ime-variaion is imporan, especially in ineracions where he US is concerned. In relaion o he ineracion beween emerging markes, incorporaing for ime-variaion is shown o be less imporan. REFERENCES Andersson M Using inraday daa o gauge financial marke responses o Fed and ECB moneary policy decisions. Working Paper 726, European Cenral Bank. Andrizky JR, Banniser GJ and Tamirisa NT The impac of macroeconomic announcemens on emerging marke bonds. Emerging Markes Review, 8: Balduzzi P, Elon EJ and Green C Economic news and bond prices: Evidence from he U.S. Treasury Marke. Journal of Financial and Quaniaive Analysis, 36(4): Benelli R and Ganguly S Financial linkages beween he US and Lain America: Evidence from daily daa. Inernaional Moneary Fund Working Paper. WP/07/262. Washingon D.C.: Inernaional Moneary Fund. Bank for Inernaional Selemens (BIS) The developmen of bond markes in emerging economies. BIS Papers No 11, June Bank of America Merrill Lynch Guide o local markes deb. Global Emerging Markes (GEMS) Paper No. 6 (20 Sepember, 2011). Blommesein H and Saniso J New sraegies for emerging domesic sovereign bond markes. OECD Developmen Cenre, Working Paper, No. 260, April. Cappiello L, Engle R and Sheppard K Asymmeric dynamics in he correlaions of global Invesmen Analyss Journal No

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