The Structure and Degree of Dependence in Government Bond Markets

Our study provides new evidence on asymmetric dependencies in international government bond markets, by examining bonds from developed, emerging, and frontier countries, using a quantile regression methodology. We find that the dependence structure for emerging and frontier markets significantly changes during financial crisis periods, which we show has important implications for international diversification of investment strategies. Moreover, we also examine in detail stock-bond correlations and uncover several instances of decoupling. In contrast, developed markets exhibit a more stable dependence pattern. In addition, we document that the degree and structure of dependence vary when foreign currencies are hedged or unhedged, and across bond maturity segments.


Introduction
We examine the degree and structure of dependence in international government bond markets. Measuring dependence is of high relevance for asset allocation and risk management, especially since the structure of the dependence helps to assess potential diversification benefits during both tranquil and crisis periods; see Baur (2013). Correct estimation of dependence is particularly essential for a proper understanding of the functioning and performance of government bond markets, which are often assumed to be risk-free in nominal terms for local investors. International investors, however, are facing the risk of a sovereign (selectively) defaulting on its debt or exchange rate risk involved with holding foreign assets (Arellano and Ramanarayanan, 2012;Bhatta et al., 2017;Lustig and Verdelhan, 2019). Understanding better how these financial market risks vary in periods with and without stress is of crucial importance to investors constructing a diversified government bond portfolio.
The literature on the dependencies across financial markets is extensive, with a majority of studies concentrating on the modeling of dependence and utilizing: correlations, extreme value techniques, or copula-based frameworks. 1 The copula models have been used to address asymmetric dependence structures between financial variables, such as: dependence across international equity markets (Hu, 2006;Rodriguez, 2007;Okimoto, 2008;Chollete et al., 2009;Markwat, 2014;Okimoto, 2014); exchange rates dependence (Patton, 2006); equity and foreign exchange market dependence (Ning, 2010); and equity and bond market dependence (Garcia and Tsafack, 2011). 1 For approaches based on correlation and extreme value techniques, see Longin and Solnik (2001), Ang and Chen (2002), Beine et al. (2010), and Bhatti and Nguyen (2012). For a detailed discussion on modeling dependence, see Embrechts et al. (2002) and Garcia and Tsafack (2011). See also Patton (2012) for a comprehensive overview of the literature on copula-based models for economic and financial time series. dependence structure in global equity markets, commodities, and exchange rates, he does not examine dependence structures in government bond markets. We fill that gap in the literature with this study. To be more precise, we address four research questions. First, we examine the degree and structure of dependence for three categories of government bond markets (developed, emerging, and frontier) relative to global bond market. We specifically focus on whether the dependence structure is asymmetric in the sense of exhibiting different upper and lower tail dependence. Furthermore, we analyze the role of bond maturity by examining differences in the degree and structure of dependence for short-, medium-, and long-term bonds. 2 Second, we investigate whether the dependence structure is affected by the [2007][2008] global financial crisis and the Eurozone debt crisis. Third, we examine the currency implications in the analysis of dependence structure using: (i) local currency returns converted to US dollar, (ii) returns hedged to US dollar using currency derivatives, and (iii) returns on US dollar-denominated government bonds. Fourth, we analyze the existence of flights-to-quality and contagion from global stock market to developed, emerging, and frontier bond markets.
This study contributes to the literature in four aspects. First, we provide a comprehensive analysis of the degree and structure of dependence in international government bond markets. In particular, we segment government bond markets into three categories: developed, emerging, and frontier, and analyze their dependence on the global bond market. We pay special attention to differences in dependence patterns across three categories of these bond markets. The distinction between the three aforementioned categories of bond markets is essential for proper international asset allocation management. Building on a common perception of emerging market bonds as "equity-like assets" and frontier markets bonds as "the next generation of emerging bond markets issuers" (Piljak and Swinkels, 2017a), our study provides useful insights for international portfolio managers, especially applicable in periods labeled as crisis times.
Furthermore, we utilize the quantile-based approach proposed by Baur (2013) to decompose the dependence into its degree and structure. Finally, we investigate contagion in the degree and the structure of dependence during the global financial crisis and the Eurozone debt crisis, reexamining findings in Hu (2006) that financial turmoil can affect changes in both the degree and structure of dependence. To that end, we improve understanding of the contagion phenomenon by analyzing whether the contagion is more dominant for extreme returns (tails of the distribution) than for average returns.
Second, in addition to examining dependence for three categories of bond markets on the aggregate level, we also provide analysis on the regional and country level for emerging and frontier markets. The added value of regional and country perspectives is related to the fact that both emerging and frontier bond markets are heterogeneous groups with compelling differences in terms of sovereign credit ratings and levels of market integration (Christopher et al., 2012;Piljak, 2013;Šimović et al., 2016;Agur et al., 2019;Chaieb et al., 2019). Hence, we contribute to the growing body of literature on bond market integration in the domain of emerging and frontier markets.
Third, we examine the currency aspect of dependence by comparing returns hedged to the US dollar using currency derivatives with non-hedged returns. This insight is essential as the currency component of investing in foreign bonds can be the dominant driver of returns (Adler and Dumas, 1980;Burger and Warnock, 2007;Piljak and Swinkels, 2017b;Burger et al., 2018;Amstad et al., 2020). The currency aspect of dependence is essential for our study as we observe three categories of markets having different denomination practices. For developed markets, we use local-currency government bond markets, which are by far the largest debt markets for this Electronic copy available at: https://ssrn.com/abstract=3886486 group of countries and characterized by an investment-grade credit rating and free movement of capital. In the analysis, we examine returns converted and hedged to a common currency, namely the US dollar. For frontier markets, government bonds available to international investors are most frequently denominated in US dollars (Jeanneret and Souissi, 2016;Ottonello and Perez, 2019). The denomination of government bonds in US dollars reduces incentives of (the central banks of) these governments to revert to uncontrolled increases in money supply to fund repayment of the existing government debts (Farhi and Maggiori, 2018;Gennaioli et al., 2018).
Simultaneously, bond denomination in US dollars protects foreign investors from domestic currency devaluation and enables the preservation of their purchasing power (Eichengreen et al., 2003). Emerging markets issue government bonds denominated both in local currency or US dollars (see, Cayon et al., 2018;Gilchrist et al., 2019), and we include each of these bond denominations in our analysis.
Finally, we contribute to the literature on stock-bond correlations and flight-to-quality, especially in the part of the literature devoted to emerging markets. Previous studies on stockbond correlations in emerging markets concentrated on co-movement between stocks and bonds within individual emerging countries and analyzing factors that affect co-movement (Li andZou, 2008, Panchenko andWu, 2009;Christopher et al., 2012;Bianconi et al., 2013;Dimic et al., 2016). We extend this line of research by focusing on the co-movement between global stock market and three different categories of bond markets (emerging, frontier, and developed) while incorporating currency and hedging aspects, and testing for flight-to-quality and contagion during the global financial crisis and the Eurozone debt crisis.
The remainder of the paper is organized as follows. Section 2 provides a literature review, Section 3 describes our data, and Section 4 presents the methodological framework. In Section 5, we discuss our empirical results. Finally, Section 6 concludes.

Literature review
Our paper focuses on financial market dependencies. Still, it is closely related to the strands of literature concentrating on financial contagion, integration and co-movement dynamics in government bond markets, and stock-bond correlation with consequent flight-to-quality. Thus, we provide here a brief description of related literature.

Financial contagion
One of the central issues in the financial contagion literature is examining changes in dependencies during the financial crisis period compared to tranquil periods. Different methodological approaches have been used to address this issue. In particular, a straightforward method to study contagion in equity markets is based on linear dependence measure; see Forbes and Rigobon (2002). More advanced techniques include co-exceedance measures in multinomial logistic regressions (e.g., Bae et al., 2003;Markwat et al., 2009) or in quantile regressions (Baur and Schulze, 2005); Markov switching models (Ang and Bekaert, 2002); switching-parameter copulas (Rodriguez, 2007), quantile-based approach (Baur, 2013;Cappiello et al., 2014).
In the vein of contagion in bond markets, Dungey et al. (2006) examine contagion in international bond markets during the Russian crisis in 1997, showing that both emerging and developed markets caught contagion during the crisis period. More recent studies concentrate on spillovers and contagion in Eurozone during the European sovereign debt crisis (Claeys and Vašícek, 2014; Gómez-Puig and Sosvilla-Rivero, 2014;Samarakoon, 2017;Bekiros et al., 2018;Caporin et al., 2018). In particular, Gómez-Puig and Sosvilla-Rivero (2014) provide evidence of contagion in the aftermath of the Eurozone sovereign debt crisis, while Claeys and Vašícek Electronic copy available at: https://ssrn.com/abstract=3886486 (2014) and Caporin et al. (2018) conclude that contagion has remained subdued. Samarakoon (2017) reports negative contagion stemming from the crisis countries to other stock markets. He also establishes that both debt and equity markets in crisis countries function as main transmission channels of the crisis. Bekiros et al. (2018) utilize a dynamic copula approach to analyze the time-varying dependence structure between the European government bond markets around the Eurozone debt crisis.

Integration and co-movement in government bond markets
Another strand of related literature focuses on integration and co-movement in international government bond markets. 3 The major part of this literature pertains to the developed bond markets, mainly in the Eurozone and G-7 economies (e.g., Kumar and Okimoto, 2011;Abad et al., 2014;Christiansen 2014). The broad conclusion from those studies is reflected in the evidence of the time-varying nature of the government bond market integration, with the degree of integration decreasing after the beginning of the global financial crisis. Similarly, Ehrmann and Fratzscher (2017)
(2005) examine stock-bond correlations with respect to stock market uncertainty, while d' Addona and Kind (2006) utilize affine asset pricing model to jointly value stocks and bonds and document correlations in post war period in the sample of seven developed countries. The scope of the literature has been extended during the last decade to cover also emerging markets Electronic copy available at: https://ssrn.com/abstract=3886486 (Li and Zou, 2008;Panchenko and Wu, 2009;Christopher et al., 2012;Bianconi et al., 2013;Dimic et al., 2016). The issue of stock-bond correlations in emerging markets is mainly examined by looking at co-movement of stocks and bonds within individual emerging countries and analyzing factors that affect co-movement, such as policy and information shocks (Li and Zou, 2008), sovereign credit ratings (Christopher et al., 2012), the US financial stress (Bianconi et al., 2013), macroeconomic fundamentals and market uncertainty (Dimic et al., 2016), and stock market integration (Panchenko and Wu, 2009).
One specific part of the stock-bond literature focuses on the "flight-to-safety" phenomenon characterized by a negative stock-bond correlations during crisis periods, which lead to potential diversification benefits. The most notable early contributions among others are Gulko (2002) who analyzes "decoupling effect", and Hartmann et al. (2004)

Data
Our dataset consists of weekly data for different indices classified into three categories of government bond markets: developed, emerging, and frontier. We use total return indices, meaning that they incorporate both bond price changes and coupon payments. The sample period spans from 10 May 2002 to 29 December 2017.
The category of emerging markets encompasses three different subcategories: (i) USDdenominated government bonds represented by the JP Morgan Emerging Markets Bond Index Plus (EMBI+), (ii) local currency government bonds with returns hedged to the USD using currency derivatives, and (iii) local currency government bonds converted to USD without currency hedging. 4 The EMBI+ is a commonly used sovereign bond emerging market benchmark, which tracks the performance of USD-denominated debt instruments issued by governments of emerging markets, and it includes Brady bonds, loans, and Eurobonds. The local currency government bonds are proxied by the JP Morgan Government Bond Index-Emerging Markets (GBI-EM). 5 For GBI-EM, we also use subindexes for different maturities: short (1-5 years), medium (5-10 years), and long term (15+ years).
The frontier government bond markets are captured with the JP Morgan Next Generation Markets Index (NEXGEM), which tracks USD-denominated government debt issued by frontier markets. The frontier markets group consists of smaller and less liquid markets that are called "next-generation issuers" since they are considered as the next wave of emerging markets. The requirement for classification into the frontier group is that the country must have a rating of Ba1/BB+ or lower by both Moody's and S&P. At the same time, inclusion criteria require that bonds have a current face amount outstanding of at least USD 500 million and remaining maturity longer than 2,5 years. The frontier markets have lower ratings than traditional emerging markets, but due to their usual higher yields and less integrated economies, they represent an alternative investment opportunity and a potential source of additional diversification benefits (see, Piljak and Swinkels, 2017a). Inevitably, the indexes that we use occasionally change country composition over time, as countries are added when they issue qualifying bonds or removed when they no longer have qualifying bonds outstanding. Therefore, to thoroughly capture all of their movements in addition to the aggregate level indices, for emerging and frontier markets, we also perform analysis on the regional and country level. 6 These fixed income asset classes are accessible to investors around the world through exchange traded funds or mutual funds. For example, the 'iShares J.P. Morgan USD Emerging Markets Bond ETF' (Ticker: EMB) can be used to access USD-denominated emerging markets, 'SPDR Barclays Capital Emerging Markets Local Bond ETF' (Ticker: EBND) for local-currency emerging markets bonds, and the 'NN Frontier Markets Debt (Hard Currency) Fund' (ISIN: LU0990547431) for frontier bond markets. These are illustrations of funds, but investors have more options, depending on their geographical location. Our insights can also benefit portfolio managers of fixed income funds who manage portfolios by allocating to individual bonds and can choose between different types of bonds that we analyze in this paper.
Our dataset also includes a global bond market portfolio, which is proxied by the JP Morgan Global Aggregate Bond Index (GABI). We choose the GABI as our global benchmark constructed combining 5,500 instruments issued in more than 60 countries with the denomination in over 25 currencies, and its total market value averaging about USD 20 trillion. 6 The NEXGEM has four regional indices (Africa, Asia, Latin America, and Middle East), while EMBI+ has regional coverage of Africa, Asia, Latin America, and Europe. For country level analysis of frontier markets we include countries that have sufficient period of data availability without time breaks (Dominican Republic, Ecuador, Egypt, and Pakistan), while for emerging markets we focus on countries that have relatively higher country weights in the EMBI+ composition and longer periods of data availability (Brazil, Colombia, Mexico, Panama, Peru, Philippines, Russia, South Africa, and Turkey).
The developed markets are proxied by JP Morgan Government Bond Index Broad (GBI Broad), which tracks bond issuances from high-income countries worldwide. For GBI Broad, we also use subindexes for different maturities: short (1-5 years), medium (5-10 years), and long term (15+ years). We consider returns converted to a common currency, the US dollar (USD) in our case, and returns hedged to USD using currency derivatives. Analyzing both currency-hedged and open currency returns enables us to examine the effect of exchange rates on international bond returns. Provided that most of the constituents of GBI Broad are also constituents of our benchmark for the global bond market (GABI), we select France, Germany, Japan, the UK, and the US as representatives of developed markets subsample. Consequently, we report country-level instead of aggregate-index level analysis for the subsample of developed markets. shows also slight drop in value (but of the smaller magnitude) at the same time, while on the contrary local-currency emerging markets bond index GBI EM (with returns hedged to the USD using currency derivatives) exhibit very little variability during the crisis and over entire sample period. A similar pattern regarding difference between hedged and unhedged returns is also observed across developed markets.
Insert Figure 1 here Insert Table 1 here Electronic copy available at: https://ssrn.com/abstract=3886486 Table 1 displays descriptive statistics of weekly bond index returns for all indices. 7 The statistics show that the highest average weekly return among our three observed categories of the markets is at the level of 0.20% and for the group of frontier markets. The observed return in frontier markets is slightly higher than the 0.18% average return on USD-denominated emerging market index. The average weekly return on local currency emerging market index in the case of USD-hedged returns is 0.08%, which is almost on the same level as the USD-hedged returns on developed markets. Also, frontier markets appear to be the most volatile ones, closely followed by USD-denominated emerging market index. Table 1 also includes descriptive statistics for the MSCI All Country World Equity Index in US dollars, which is used to represent the global stock market used in the stock-bond correlation analysis.

Methodology
Utilizing the quantile-based methodology proposed by Baur (2013), we analyze the degree and the structure of the dependences of global government bond markets. 8 The base quantile regression model is in the following form: where ri denotes the returns of government bond market i; rm is the return on global bond market portfolio; ( | ) denotes the τth conditional quantile of ri given the explanatory variables 7 Descriptive statistic for regional and country level for emerging and frontier markets is given in Appendix A ( The estimated quantile regression coefficients determine the dependence relationship between the global bond market returns (rm) and τth conditional quantile of emerging, frontier, and 9 The VIX Index is used as a control variable in the model. We tested also the MOVE Index (the Merrill Lynch Option Volatility Estimated Index) as a proxy for bond market uncertainty and the results are qualitatively similar to the ones obtained by using VIX. 10 For the global financial crisis, we use the same timeline as Baur (2013), which is based on the timeline given by Federal Reserve Board of St. Louis (2010) and the Bank for International Settlements (BIS; see Filardo et al., 2010). For the Eurozone debt crisis, the choice of the beginning date of the Eurozone debt crisis is the time when the Greek Prime Minister, George Papandreou, announced Greece's severe fiscal problems. The end of the crisis period is chosen when Mario Draghi, the president of the ECB, disclosed publicly that "the ECB is ready to do whatever it takes to preserve the Euro" (see Bloomberg, 2012). This timeline is also in accordance with Lane (2012). developed bond markets returns (ri). The complete dependence structure is determined by the pattern of the estimated coefficients across all quantiles. If estimated coefficients do not change across quantiles, then the dependence structure is constant. By contrast, if estimated coefficients for low and high quantiles are statistically different from each other, then the observed structure is asymmetric.
In addition to the structure of dependence, quantile regression also enables determining the degree of dependence (defined as the average over 99 quantile regression coefficients).
Specifically, the degree of dependence in the non-crisis period is average of the terms ( ), while the change in the degree of dependence due to the global financial crisis is average of the terms 1 ( ) and the change in the degree of dependence due to the Eurozone debt crisis is average of the terms 2 ( ).

Empirical results
In this section, we report empirical results of the structure and degree of dependence in international government bond markets. In the Sections 5.1, 5.2, and 5.3 we describe the estimation results of the quantile regression given in Equation (1). Tables 2, 3, and 4 report the coefficient estimates of β, γ1, and γ2 respectively for selected quantiles and the degree of dependence for emerging (Panel A), frontier (Panel B), and developed markets (Panel C). 11 The parameter γ1 models the change of the dependence during the global financial crisis period, while γ2 models the change of the dependence during the Eurozone debt crisis period. The aggregate or full effect for a specific quantile in the global financial crisis period is calculated as the summation of the coefficient estimates β and γ1. Similarly, the aggregate effect for a specific quantile in the Eurozone debt crisis period is given by the sum of coefficient estimates β and γ2. Figures 2 and 3 provide a graphical illustration of the dependence structure and changes in the dependence structure associated with the global financial crisis and Eurozone debt crisis. In Section 5.4 we display the results of the test for inter-quantile differences ( Table 5) and analysis of asymmetry (Table 6). In Section 5.5 we show results from our analysis on bond maturity segments (Table 7 and Figure 4).
Finally, in Section 5.6 we report results on contagion and flights from global stock to bond markets (Table 8), while in Section 5.7 we provide portfolio management application (Table 9). To facilitate interpretation of the results from the currency aspect, in the following three sub-sections, we present the results separately for local-currency emerging markets, USD-denominated emerging and frontier markets, and developed markets.

Dependence in local-currency emerging bond markets
Emerging markets local currency unhedged returns have a different dependence pattern from emerging markets hedged returns (as shown in Figure 2, Panel A However, as for the unhedged returns, the beta coefficient is close to 0.8 (left tail) and 0.6 (right tail), and during both crisis periods, the dependencies shoot up in the left tail. Only during the global financial crisis, the right-tail dependence shoots down. This observed pattern indicates that during the crises emerging markets currency returns move more together with the global bond market index than emerging local currency bond returns.

Insert Figure 2 here
Further examination of the degree of dependence shows that its level in normal times (average of β coefficients across all quantiles) is around 0.68 for unhedged returns, vs.
approximately 0.15 for hedged returns. This evidence indicates substantial variation in the degree of dependence contingent on whether emerging markets local currency returns are hedged or unhedged. The further evidence suggests that the global financial crisis and the Eurozone debt crisis led to a negative change in the degree of dependence for both hedged and unhedged returns. At the same time, the magnitude of change during the global financial crisis (γ1) is higher than during the Eurozone debt crisis (γ2). More substantial effects during the global financial crisis can be explained by the fact that this crisis originated from equity markets, and investors perceive emerging markets bonds as "equity-like assets" (Piljak, 2013). On the contrary, the Eurozone debt crisis emanated from uncertainty in debt markets, and its most significant and immediate impact was witnessed in European developed markets (see, Gómez-Puig and Sosvilla-Rivero, 2014).

Dependence in USD-denominated emerging and frontier bond markets
Electronic copy available at: https://ssrn.com/abstract=3886486 Emerging markets USD-denominated returns (shown in Figure 2, Panel B) exhibit a similar dependence pattern to emerging markets local currency unhedged returns in the global financial crisis, albeit with a larger magnitude. This finding is in line with Agur et al. (2019), who report that emerging market USD-denominated debt markets are more internationally integrated than emerging markets local currency bond markets. Furthermore, credit spreads for emerging market debt move in line with emerging market currencies. During the Eurozone debt crisis, the dependence pattern for emerging USD-denominated debt and unhedged local currency debt is the same in the left tail but different in the right tail. In particular, dependence in the right tail is increasing for unhedged local currency sample, but decreasing for emerging USD-denominated sample. Apparently, this pattern indicates that the currency denomination of emerging markets bonds plays a vital role in reacting to the Eurozone debt crisis, which was also the crisis of the  statistical significance in extreme left and right tail quantiles), with the exception of South Africa (both tails) and Philippines (left tail).
The dependence of frontier markets bond return relative to the global bond market (shown in Figure 3, Panel B) is similar to one observed by emerging markets USD-denominated return. The only difference arises during the Eurozone debt crisis in the left tail. In that instance, the dependence for the emerging markets USD-denominated index is approximately 1.5 in the left tail, vs. near zero for frontier markets. This observed dependence behavior in the left tail cannot be captured with the linear dependence structure approach implemented in Piljak and Swinkels (2017a). Our ability to report this type of results stems from the application of the quantile regression approach. To offer further insights into the dependence patterns of frontier markets, we conduct regional and country analysis. 14 The pattern observed in every individual country is not the same as the pattern on the aggregate level. In particular, in pre-crisis period there is a statistical significance only in left tail (quantiles 1-10) on the aggregate level, while in certain countries (Egypt and Ecuador) there is also statistically significant dependence in right tail (quantiles 90-99).
Furthermore, a set of results derived from observation of regional bond markets reveals that the Latin American region has a much larger magnitude of dependence in both left and right tail than other regions during two examined crises events. In particular, during the Eurozone debt crisis, Turning attention to the degree of dependence, the results show that the degree of dependence in normal times (average of β coefficients across all quantiles) is around 0.51 for emerging markets USD-denominated return (aggregate index level). Furthermore, regional analysis confirms that the degree of dependence is very similar across regions, while on the country level the degree shows bigger variations and it ranges from 0.30 in Turkey to 0.83 in Brazil. 17 In contrast to emerging markets, the degree of dependence for frontier markets bond return on the aggregate index level is very low and amounts to 0.09. This finding outlines that frontier bond markets have more considerable diversification potential than emerging bond markets and that international investors should not neglect them in asset-allocation decisions. Looking at the regional level, the results show that frontier markets in Latin America have the lowest degree of dependence in the period before the crisis and hence the highest diversification potential. However, the degree of dependence is increasing during both crises events, consistent with the contagion and observed patterns in the 15 See, for example, Bloomberg (20 December 2020): "Desperate need for yield pushes investors into frontier debt". https://www.bloomberg.com/news/articles/2020-12-20/desperate-need-for-yield-pushes-investors-into-frontiermarkets 16 Certain markets (such as Egypt and Nigeria) included in NEXGEM Index have been labeled as "fallen angels" due to increased default risk and their earlier status of emerging market has been downgraded to frontier.  (-0.009) and Asian region the highest negative change (-0.256) during the global financial crisis. The observed regional difference indicates that emerging market bonds from European countries are perceived as safer than those of Asian countries.
However, the magnitude of change in dependence due to the Eurozone debt crisis is very similar in all regions.
Focusing to the frontier markets results, we show that despite a noticeable change in the degree of dependence in both crises events, the overall level of dependence is still much lower than for emerging markets. This finding provides evidence that frontier bond markets might yet have important diversification potential even during crisis events. This is also in line with literature pointing out that frontier bond markets have lower integration level with global markets (Piljak and Swinkels, 2017a). The regional analysis further shows that there are differences in the magnitude of crisis effects (for instance, African region appeared to be less vulnerable to crises in comparison to Latin American region), which confirms previous finding that frontier markets should not be perceived by investors as homogenous groups of markets.

Dependence in developed bond markets
The developed markets return dependence is rather flat over quantiles in the non-crisis period, no matter whether hedged or unhedged returns are considered (as shown in Figure 3).
France and Germany (unhedged returns) have a slight U-shape pattern for the Eurozone debt crisis.
Japan is less affected by the Eurozone debt crisis. The dependence pattern for the US returns is rather flat in non-crisis, but during both crises periods, there is a left tail dependence. The degree of dependence in normal times (average of β coefficients across all quantiles) is in the range from 1.37 (Japan) to 1.61 (France) for unhedged returns, while the corresponding range for hedged returns is from 0.13 (Japan) to 0.56 (the UK). This result shows that the degree of dependence is much higher for unhedged than for hedged returns, which is a similar finding as in the local currency emerging bond markets. Hedged and unhedged returns also show different patterns with regard to changes in the degree of dependence during crises episodes. In particular, during the Eurozone debt crisis the degree is decreasing for hedged returns, which is consistent with decoupling, while at the same time the degree is increasing for unhedged returns (except UK and US), consistent with contagion. This finding illustrates that unhedged bond returns were more vulnerable to the Eurozone debt crisis than hedged bond returns.
Insert Figure 3 here Insert Table 5 here

Tests for inter-quantile differences and asymmetric dependence
The next question is whether there is an asymmetric impact in negative and positive bond market conditions. 18 In this respect, we perform tests over a range of quantiles (quantile 1-10 versus 18 For further information on the importance of asymmetric dependence in financial markets please see Ang and Chen (2002), Yuan (2005), and Baur and Schulze (2009) among others. [90][91][92][93][94][95][96][97][98][99] to test whether the impact is equal in extreme lower and higher quantiles. such as Japan (hedged and unhedged returns) and USD-denominated (emerging and frontier) markets in some cases.
Insert Table 6 here

The role of bond maturity
In this section we extend the analysis by examining the role of bond maturities. In particular, we investigate differences in degree and structure of dependence between short-, medium-, and long-term bond maturities. Furthermore, we analyze whether changes in degree or structure of dependence during the global financial crisis and the Eurozone debt crisis are more prevalent in 19 The results for remaining four cases (6 th and 94 th , 7 th and 93 th , 8 th and 92 th , and 9 th and 91 th ) are not shown in the Table 6 in order to conserve space. long-term bonds than in short-term bonds. For this purpose, we use short-term (1-5 years), mediumterm (5-10 years), and long-term (15+ years) bond indices of local currency-denominated emerging and developed markets. 20 The results for degree of dependence are reported in Table 7. All analyzed markets exhibit the same pattern during non-crisis period that degree of dependence is increasing as maturity is increasing. Regarding the change in the degree of dependence during the global financial crisis and the Eurozone debt crisis, there is a clear pattern for emerging markets which shows that the change is larger for longer maturities. A similar pattern is observed for most of developed markets during the global financial crisis, but during the Eurozone debt crisis there is a deviation from this pattern, especially for unhedged returns. With respect to hedging perspective, the results show that the degree of dependence is higher for unhedged returns than for hedged across emerging and developed markets.
Insert Table 7 here Figure 4 shows the structure of dependence for different bond maturities in emerging (Panel A) and developed markets (Panel B). 21 The results in both panels confirm the previous finding that dependence and crises-induced changes of dependence are higher for unhedged returns than for hedged. Furthermore, the changes in the structure of dependence are more prevalent in long-term bonds than in short-and medium-term bonds for both emerging and developed markets.
Insert Figure 4 here

Contagion and flight-to-quality
This section examines contagion and flight-to-quality from global stock market to bond markets. We follow the econometric framework proposed by Baur and Lucey (2009) were not statistically significant, confirming finding of Piljak and Swinkels (2017a) that frontier bond markets have lower level of market integration, which makes them less vulnerable to global crisis events.
Insert Table 8 here

Portfolio management application
What do the results above mean for an investor in global bond markets? In this section we focus on the returns in the extreme quantiles, and therefore analyze the worst weekly returns in the global aggregate bond market in more detail, and show the effect on a naively diversified portfolio of unhedged government bonds. The naïve portfolio is a portfolio with equal weights in the global developed government bond index, emerging markets local currency index, emerging markets USD-denominated bond index, and frontier markets index. Table 9 shows that this diversified portfolio ('DIV') had a return of an annualized 8.21% and an annualized volatility of 7.42%, compared to an average return of 5.21% and volatility of 5.74% for the global aggregated bond market. Now we zoom in on the downside risk of investing in the global aggregate bond market by ranking each of the weeks of our sample based on the market return. The average return over the worst 10 weeks is -2.21%. While local currency emerging bond markets experienced a lower return during these weeks, on average -3.22%, frontier markets bonds did relatively well with a negative return of -1.01%. This is consistent with the low degree of dependence level of frontier markets, and higher average dependence of emerging markets local currency debt that we already saw in Table 2. While the diversified portfolio had a substantially higher volatility over the whole sample, the downside risk is on average the same as for the aggregate market index. 22 Insert Table 9 here During the global financial crisis, frontier markets did relatively poor during periods that the aggregate bond market did bad, with an average return of -2.03%. This is primarily due to an extreme negative return of -11.59% in the week ending 10 October 2008. Emerging markets bonds offset this huge negative week with a positive return of similar magnitude in the week ending 31 October 2008, but frontier markets did not. This positive correlation of frontier markets in the tail of the distribution of aggregate market returns is consistent with the significant increase in dependence that we reported in Table 3. During the Eurozone debt crisis, frontier markets hold out well, with an average return of -0.58%. Local currency emerging markets are relatively bad asset class during this period with -1.90% return on average, and even a -6.69% return during the week ending 7 May 2010. The naïve diversified portfolio (again) shows slightly better returns than the aggregate market during the 10 worst weeks of this crisis period. This portfolio application shows that investors can use knowledge of the degree and structure of dependence between government bond markets to manage the downside risk of their government bond portfolios. As full portfolio optimization requires additional information on the required returns by investors and their attitudes for the entire risk profile, we leave that for further research. This section is an illustration of the practical use of the econometric techniques that we used earlier. 22 The most extreme return is lower for the diversified portfolio, as the week ending 21 June 2013 had a negative return of -4.59% versus the market -2.69%. The second largest drop in the aggregate market, ending 13 June 2008, was -2.68%, whereas the diversified portfolio did relatively well with -1.79%.

Conclusions
This paper studies the degree and structure of dependence in international government bond markets. Specifically, we focus on three categories of government bond markets (developed, emerging, and frontier) and analyze their dependence on the global bond market. We investigate whether the dependence structure is asymmetric (different upper and lower tail dependence) and affected by the [2007][2008] global financial crisis and Eurozone debt crisis, and what is the role of bond maturity. Furthermore, we also examine the currency aspect in the analysis of dependence structure by using: (i) returns converted to USD, (ii) returns hedged to USD using currency derivatives, and (iii) returns on USD-denominated government bonds.
The results lead to several conclusions. First, the study provides new evidence on asymmetric dependencies in international government bond markets. In particular, the dependence structure for emerging and frontier markets changes substantially due to the global financial crisis and Eurozone debt crisis, while developed markets exhibit a more stable dependence pattern. The results indicate that average dependence is not sufficient to describe a complete dependence structure in international government bond markets, meaning that the upper and lower tail dependence should also be considered as essential elements in measuring dependence. Second, regarding the currency aspect of the analysis, the results show that the degree of dependence varies substantially depending on whether local currency returns are hedged or unhedged. Third, degree of dependence and crisisinduced change in the dependence are increasing for longer maturities. Fourth, our finding that frontier markets exhibit a very low degree of dependence on the global bond market returns in both no-crisis and crisis times underscores the importance of their diversification potential for international investors in asset-allocation decisions. Fifth, results on regional and country analysis reveal that emerging and frontier markets cannot be treated as homogenous groups, and consequently regional and country aspect is important in analyzing the sensitivity of those markets to crises events. Finally, results of contagion analysis from global stock to bond markets during the global financial crisis confirm "equity-like" properties of emerging markets bonds.
In summary, the study has important practical implications for international investors in terms of asset allocation decision-making and the formulation of their investment strategies. Our application shows that investors can increase portfolio diversification in scenarios where the aggregate bond market experiences negative returns. By diversifying risk among emerging markets debt in both local and hard currencies, and frontier market bonds, downside risks are reduced. Our analyses indicate that there is not one specific asset class that always reduces fixed income portfolio risk, but rather that different asset classes may help during different crisis periods.   (1). T-statistics are in parentheses. The last column shows degree of dependence.  (-0.89) (-0.76) (-2.14) (-3.04) (-4.39) (-5 (-0.03) (-0.65) (-0.04) (-0.03)