Regional Stochastic Dynamics and Market Integration of Emerging Market Sovereign Eurobonds
Kannan Thuraisamy
School of Accounting, Economics andFinance
Faculty of Business and Law
Melbourne Campus at Burwood
Phone: +61 3 9244 6913
Fax: +61 3 9244 6283
Email:
Gerard Gannon*
School of Accounting, Economics andFinance
Faculty of Business and Law
Melbourne Campus at Burwood
Phone: +61 3 9244 6243
Fax: +61 3 9244 6283
Email:
Abstract
This paper models the cross-market dynamics in an emerging market regional setting using US dollar denominated risky sovereign Eurobonds issued by major Latin American economies. We employJohansen’s and a modified three-step procedure,which can generate portfolio adjustment weights whilst accounting for common volatility effects across markets. The bonds are grouped by maturities across different markets in the Latin American region. The analysis uncovers evidence of cross-market links – creating a sub-regional formation across the Latin American region.
JEL classification code: G15; G12
Keywords: Common stochastic trend, Market integration, Latin America, Long-run dynamics, Sovereign bonds.
* Corresponding author G.L.Gannon .
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Regional Stochastic Dynamics and Market Integration of Emerging Market Sovereign Eurobonds
1.Introduction
Understanding the nature of cross-market dynamics and emerging market integration underpinning the behaviour of sovereign bonds issued in international markets in a regional setting has important implications for market participants, market practitioners and policy makers. The importance of regional dynamics has been emphasised in recent research (see, for example, Diaz-Weigel and Gemmill 2006; Kamin and Kleist 1999; Eichengreen and Mody1998). Obtaining vital information on long-run equilibrium relationships is important for fund managers to enable them to make necessary adjustments to their portfolios to monitor and manage their risk exposure. In addition, to make interest rate and pricing decisions,policy makers and practitioners require vital information on long-run equilibrium relationships across markets with different credit classes of seemingly homogenous instruments, such as Latin American sovereign Eurobonds issued in international markets.
Investigation into the notion of emerging market integration with global market forces has been mainly examined across national equity markets anddifferent regions (see Bekaert and Harvey 1995;Bekaert, Harvey and Lumsdaine 2002; Bekaert, Erb, Harvey and Viskanta 1998;Carrieri, Errunza and Hogan 2007; de Jong and de Roon 2005;Chambet and Gibson 2008). These studies focused on integration versus segmentation of global equity markets. On the other hand, investigation of the issue of bond market integration has concentrated on mature markets (see Ilmanen 1995; Clare, Maras and Thomas 1995; Mills and Mills 1991; Arshanapalli and Doukas 1994; Sutton 2000; Barr and Priestley 2004; Yang 2005;Kim, Lucey and Wu 2006).
Ilmanen (1995)examined the effect of integration of six markets (US, UK, Canada, France, Germany and Japan) using long-maturity government bonds. He found strong evidence of integration across mature bond markets. On the other hand, Clare, Maras and Thomas (1995) using the daily yield of mature market bonds (US, UK, West Germany and Japan) found no cointegrating relationship between these markets. The study focused on bonds with less than 5-year maturity to test market integration through a multivariate cointegration framework. Similarly, Mills and Mills (1991), investigating four major bond markets, find no integration.Arshanapalli and Doukas (1994)investigated the temporal relationship between Eurodeposit instruments of five different maturities for different currencies[1]and found several cointegrating factors binding them together for the period between 1986 and 1992. Their multivariate cointegration test for dependency on five maturity sets of seven dimensional systems reveals that the cointegrating structure is stronger at the short end rather than at the long end of the maturity spectrum.Focusing on a particular maturity sector,Sutton (2000) examined the 10-year bond yield of five mature markets and found the term premia at the long end of the term structure to be both time-varying and positively-related across the markets. Barr and Priestly (2004) investigate bond market integration using bond index data belonging to five mature markets and the World index. Using asset pricing methodology,they find partial integration of national bond markets into world markets.Yang (2005) confirms the existence of linkages across industrialized countries.Kim, Lucey and Wu (2006) examine the time-varying level of financial integration of European markets using government bond indices of Europeaneconomies (Czech Republic, Hungary, Poland, Belgium, France, Ireland, Netherlands, UK and Germany) in the region. Their test was to see how the Euro zone markets were integrated with Germany. They found strong evidence of linkages between Euro zone markets and Germany. However, the nature of financial market integration,allowing for Autoregressive Conditional Heteroskedastic ARCH effects in the system and uncovering the true dimension of the systems, was not explored in the above research.
The literature in the area of cointegration testing, in the context of ARCH effects, is still developing. For low-dimensioned systems, Lee and Tse (1996) and Silvapulle and Podivinsky (2000) indicate that while the Johansen (1988) cointegration test tends to over-reject the null hypothesis of no cointegration in favour of finding cointegration, the problem is generally not very serious. However, Hoglund and Ostermark (2003) conclude that the Eigen values of the long-run information matrix for the Johansen (1988) cointegration test are highly sensitive to conditional heteroskedasticity and the multivariate statistic may only be reliable in the context of homoskedastic processes. This latter finding, regarding the size of the cointegration test, becomes increasingly pronounced the more integrated the ARCH process being considered. Empirical contributions in modelling common stochastic trends in higher dimensioned currency series with ARCH effects accounted for, are reported in Alexakis and Apergis (1996), Gannon (1996) and Aggarwal and Muckley (2010), and for equity series, in Pan, Liu and Roth (1999). Reported results indicate that the ARCH effects and their variants exert a significant and deleterious impact on the statistical test’s power properties. There are a number of other important and interesting issues to consider.First, in cases where higher dimensioned systems may exhibit a less-integrated ARCH effect, the gains for allowing for ARCH effects may be diminished. For example, Thuraisamy (2010) finds significant lead-lag effects in BEKK_MGARCH models within pairwise Latin American international sovereign bonds. These lead-lag effects in conditional volatility diminish the contemporaneous integration ARCH effects.
Generally we observe strong contemporaneous conditional volatility (integrated ARCH) effects across sets of currencies and international stock market indices observed on a daily basis. There can be interesting cases in higher-dimensioned systems where contemporaneous ARCH effects are less important because of the nature of the market mechanisms. This can be the case for international bond markets where portfolio unwinding is more protracted.
There is a second important modelling issue related to the evolution of macroeconomic data reported in Johansenand Juselius (1990), and for financial prices observed at relative high frequency reported in Gannon (1996). Generally, currency returns can be well characterized as I(0) series with zero mean. It follows that the observed currency levels can be characterized as I(1) series with non-zero mean. Stock indexreturns could be generally well-characterized as I(0) series with non-zero mean (the return on holding the assets above the risk-free rate). It follows that the observed stock index levels can be characterized as I(1) series with non-zero mean and drift (linear trend). Sovereign bond returns can be characterized as (0) series with non-zero mean and drift. Then sovereign bond levels may be characterized as I(1) series with non-zero mean and linear and quadratic trends.
The third consideration is of the dimensionality of the system of equations and the number of common stochastic trends incorporated in the tests. Inclusion of irrelevant variables leads to comparison with an overdimensioned critical value which assumes the dimension of the system to be correct. A common problem with likelihood ratio statistics and one often reported in multivariate applications in detecting the appropriate number of zero eigenvalues, is that q = 0 is often strongly rejected while Likelihood Ratio tests q < 1< (p-1), < q are often insignificant. Overspecifying the number of variables entering the system reduces the power of the multivariate procedure, since the adopted degrees of freedom for the test can severely overstate the underlying degrees of freedom for the true sub-system. The application of Johansen’s Likelihood ratio testing procedure presupposes knowledge of p, the correct number of variables linked by one or more cointegrating vectors.
In response to the preceding discussion, the Johansen (1988) and a modified Johansen testing procedure is estimated and reported. Specifically, following Gannon (1996), we adopt a modified test for common roots in which we account for Generalised Autoregressive Conditional Heteroskedastic (GARCH) effects in the correlating combinations of residuals. The same Latin American international sovereign bond dataset is employed as reported in Thuraisamy (2010) where significant lead-lag effects in conditional volatility are reported in subsets of countries. The following specific modifications to the testing procedures of Johansen (1988) and Gannon (1996) are incorporated:
(i) Sovereign bond returns are characterized as (0) series with non-zero mean and drift. The sovereign bond levels are then characterized as I(1) series with non-zero mean and linear and quadratic trend.
(ii) We sequentially reduce the dimension of the variable set to uncover important links within the multivariate frameworks. As well, the second moment effects are allowed to enter via a modified test statistic constructed from the canonical weights. This modified test is a truncatedversion of Johansen’s likelihood ratio test which is constructed from the largest root from the system and allows for common GARCH effects. In the absence of common GARCH effects, the limiting parameter value for the test reduces to the square root of the maximum eigenvalue from Johansen’s canonical correlations procedure.
As well as considering the above econometric issues, we also focus on a neglected area for this empirical research application. There is a gap in the literature in terms of risky sovereign bond issues denominated in a single currency, belonging to different emerging markets, in a regional setting. This study attempts to fill this gap in the literature by investigating the cross-market dynamics of Latin American risky sovereign Eurobonds denominated in US dollars. Markets with the higher credit quality tend to dominate the price behavior of the region, and the lower credit quality markets usually follow the dominant players forming sub-regional clusters (see Batten, Hogan and Pynnonen 2000)[2]. In the event of a credit shock in the region, the behavioural dynamics can drastically change, prompting credit quality driven regrouping.
The paper is organised as follows: In Section 2 we outline the methods used in this study. Section 3 outlines data used in this study and reports the results. Section 4 concludes the paper.
2.Method
The standard Vector Autoregressive (VAR) representation of the levels of processes is a function of its own past values and the past values of other variables in the system, plus an error term. Generally, the structure is symmetric in that p equal-lags of all variables in the system enter each of the N equations in the system.
(1)
cis the constant term andtis anassumed independent GaussianN-dimensional with mean zero and variance
The VAR model is defined by placing no restrictions on the parameters(c, pEquation (1) can be extended to include either or both linear (ct) and quadratic trends().
A convenient representation ofthe common stochastic trend of the same model is:
(2)
is an assumed independent Gaussian N-dimensional with mean zero and variance .
The VAR model is defined by letting the parametersbeunrestricted.Equation (2) can also be presented by incorporating the mean and linear trend (ct),implying a linear trend and quadratic trend in the levels equation. Including a trend in Equation (2) with initial values X-k’………………….,X0and errors that are assumed identically and independently distributed in N-dimensions , then can be represented as:
(3)
a stationary process with in Equation (3) has a quadratic trend and the stochastic part of is a non-stationary I(1) process, but they become stationary when they are differenced.The parameters are decomposed to let indicate the deterministic part of the model. The quadratic trend can be eliminated by linear combination which then containsa linear trend which cannot be eliminated by the cointegrating relations. It is possible that bond series, especially excessively volatile emerging market series, may contain a quadratic trend which requires the application of the theory of Johansen (1991) for I(2) and I(1) with trend processes.
2.1Common stochastic trends
The residual generating process of the Johansen (1988)procedure involves two steps. The first step of the Johansen procedure involves testing the order of integration of the variables in the system. The second step involves generating a vector of residuals and from the vector of differences of the series, and the vector of lagged level of the series in the first step. The residuals and enter the second step of the Johansen procedure by identifying the common roots via a canonical correlation procedure. This residual generating process is captured by the following auxiliary regressions for the differences and the lagged levels.
(4a)
(4b)
When equation (4b) contains a constant, linear trend and quadratic trend, equation (4a) contains a constant and linear trend. This is the procedure we follow in the analysis in this paper.The Error Correction Model for these types of processes can be represented as where is a linear combination of. In a finite Gaussian VAR, the log likelihood iswhere is the variance-covariance matrix of and A*(0) has been normalised to INwith defined by .In the presence of known, this is just a Seemingly Unrelated Regression (SUR) system. The Johansen procedure concentrates all parameters from the log likelihood function in two steps. Both steps rely on the information content of so that the log likelihood can be sequentially concentratedusing Equation (5).
(5)
The estimate of the error variance is . The maximum value of the likelihood function is captured by .The maximum likelihood estimate of is found by solving and the hypothesis testing the number of unit roots ≥q is tested via the likelihood ratio test statistic in the Johansen procedure. In this study, we use a finite sample adjustment of the trace statistics, defined in Bartlett (1941), where is replaced by in calculating the Q(r) calculated value of the test statistic. is the number of observations in the current sample;P is the lag of the VAR and N the dimension of the system. We report results using 4 lags and also the optimal number of lags as determined by the Akiake Information Criterion (AIC). Further technical detail of the Johansen procedure is documented in Appendix A.
2.2Three step procedure
The vectors of residuals of andin the Gannon (1996) procedure are,essentially,residuals from the auxiliary regressions equations (4a) and (4b). The vectors of residuals andare generated followingthe suggestion of Johansen and Juselius (1990). Their procedure can be viewed as similar to the unit root test of Said and Dickey (1984), where the lagged level enters at rather than.A1, and A2 of Equations (6a) and (6b) can be estimated by OLS, as in Equations (4a) and (4b).
(6a)
(6b)
As is the case with equations (4a) and (4b), when equation (6b) contains a constant, linear trend and quadratic trend, equation (6a) contains a constant and linear trend. This is the procedure we follow in the analysis in this paper.
In modelling the first step of the three-step procedure, we first estimate the residuals and through a VAR process represented by the auxiliary regressionscapturedby equations(6a) and (6b). Step 2 of this procedure estimates the canonical correlations of the stacked residuals from step 1,with lagged level residuals at time entering for. Canonical weights to for the dependent variable and to for the independent variable are generated and stored for generating weighted residuals for step 3.In this application, only the first roots and of the stored weights are used to generate the weighted residuals by attaching the weights to the original residuals fromand from step 1, and are named as and ,respectively. Equations (6a) and (6b) express variates and as the linear combinations of original un-standardized error terms, but have mean zero.
(7a)
(7b)
t = 1 . . . . . T
where r refers to the ith pair of canonical variates of U and V orthogonal to all other U and V.Equations (7a) and (7b) can be generated to express all r pairs of canonical correlations so that the notation can be augmented for r > 1. We have also generated the weights for and from the orthogonal residuals in step 1. We expect that in some cases for high dimensional systems where the first and second roots of the system may be significant and, therefore, important when establishing the stochastic portfolio weights. This can occur, for example, in a four-dimensional system where separate pairs of price process are highly correlated with pairs but not across pairs. Casual observation of the loadings of the standardised canonical weights reveals these linkages. The third step involves the estimation of OLS and GARCH equationsU1 and V1for I =1, ……..,Nmax.