Journal of Derivatives & Hedge Funds

, Volume 20, Issue 1, pp 10–27

Persistence of volatility of sovereign credit risk in presence of structural breaks

  • Geoffrey Ngene
  • Hannah Carley
  • Mohammad Kabir Hassan
Original Article

DOI: 10.1057/jdhf.2014.9

Cite this article as:
Ngene, G., Carley, H. & Hassan, M. J Deriv Hedge Funds (2014) 20: 10. doi:10.1057/jdhf.2014.9
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Abstract

The credit risk of a sovereign borrower is priced using bond spreads (BS) and credit default swaps (CDS). In this study, we investigate how structural breaks affect persistence of volatility of sovereign credit risk of seven countries. Using Kappa-1 and Kappa-2 tests, we identify multiple structural breaks in variance of both CDS and BS. Using exponential generalized autoregressive conditional heteroskedasticity model with and without structural breaks, we find that BS are more persistent than CDS hence informed trading takes place in sovereign bond market. The structural breaks are not only jointly significant in influencing volatility of sovereign credit but they reduce persistence of volatility and associated half-life of BS and CDS. The results have important implications on cost of borrowing of sovereigns, efficiency of CDS and BS markets as well as pricing of both credit risk measures.

Keywords

credit default swap bond spread sovereign volatility structural breaks persistence EGARCH 

INTRODUCTION

Credit default swaps (CDS) were introduced in 1997 by J.P. Morgan. Since then, CDS together with bond spreads (BS) have become the two most prevalent measures of credit or default risk of corporate and sovereign borrowers (reference entities). Duffie (1999) and Hull et al (2004) formalized the relationship between these two credit risk measures. If an investor is holding a zero-coupon par value bond with T-years to maturity and a yield to maturity equal to y, the BS is equal to y less risk free rate of US Treasury bond with equivalent T-years to maturity. The same bondholder1 will buy protection or insurance against default by the bond issuer by paying the CDS premium or spread, usually expressed in basis points. The purchase of insurance makes the bond default risk free. Theoretically, CDS and BS should be equal at equilibrium. However, they are rarely equal, and it is not uncommon to encounter non-zero basis (CDS less BS) occasioned by market frictions (transaction costs, funding requirements for bonds, counter-party risks and restrictions on shorting bonds) in addition to features such as cheapest to deliver options embedded in CDS contracts. Nevertheless, CDS and BS still remain largely effective pointers of the credit risk of the same reference entity. The higher the credit risk, the higher the CDS and BS.

In this study, we focus on two important issues regarding sovereign BS and CDS of seven emerging markets. First, which of the two instruments used to price credit risk exhibit higher persistence of volatility? Second, how do structural breaks affect this persistence of volatility?

The volatility of asset returns is important in the pricing of financial assets, predicting volatility, managing risk and asset allocation in a portfolio. As Ang et al (2006) argue, time-varying volatility either triggers changes in expected future returns or changes in risk-return trade-off. This will ultimately result in variation of investment opportunity set. This is important to policymakers trying to stabilize financial markets, investors trying to hedge risk, and fund managers seeking to rebalance their portfolios and hedge risk. For example, as the prices of sovereign bonds increase (bond yield and risk of default decreases), we would expect the prices of risk (measured by sovereign CDS) to decline. Conversely, as sovereign bonds held by hedge funds experience a dip in prices (yield and default risk increases), we would expect changes in CDS to increase to hedge against increased risk. We would thus expect an inverse relationship between percentage of bond return and changes in CDS. Figure 12 illustrates this point by showing the negative correlations between changes in sovereign CDS of six emerging markets and percentage of return of Eureka emerging markets’ fixed income hedge fund index (HFI).
Figure 1

Source of Eureka emerging markets fixed income HFI.

Source: www.eurekahedge.com.

Ross (1989) shows that volatility of asset returns is directly related to the rate of information flow information to the market. As market participants use information to price the assets, the rate of information flow has important implications for efficient pricing of sovereign credit risk using BS and CDS, especially in the absence of arbitrage process. Therefore, volatility and its persistence form a solid foundation of testing efficient market hypothesis in BS and CDS.

As CDS and BS are intimately related and price credit risk of the same sovereign reference entity, we expect the prices and volatilities of the two securities to be linked in asset pricing models, an argument expounded by Fleming et al (1998). However, because of market frictions, especially in the bond market, the persistence of volatility of the two assets may differ. It is imperative to understand why persistence of volatility (not just volatility) is important. First, volatility of credit risk indicates uncertainty regarding the default risk of the borrower. As long as this uncertainty persists, the cost of sovereign borrowers will continue to rise. This may limit and prolong the borrower’s ability to access capital markets to raise additional debt to fund projects. Second, the persistence of volatility of asset prices also has implications regarding the degree of informed trading and information flow. Ross (1989) argues that in the absence of arbitrage opportunities, the volatility of stock price is equal to the volume of information flow, whereas the variance of stock return is proportional to variance of information flows. Further studies by Llorente et al (2002), Black (1986) and Kyle (1985) suggest that informed trading can be inferred from relative persistence of volatility in spot (bond) and derivative (CDS) markets. For example, if CDS returns3 exhibit higher persistence of volatility, this would confirm the theory that CDS markets are the principal locus of informed trading where informed investors trade on positive private information. Changes in price are likely to persist as the investors buy and drive up the price. Therefore, increase in amount of information available to traders in CDS market may produce information symmetry, which subsequently magnifies volatility of bond market.

Third, a counter view espoused by Attanasio (1990), Singleton (1987), and Grossman and Stiglitz (1980) argue that incomplete and asymmetric information in derivative market may intensify persistence of volatility. The authors rationalize that in a market with asymmetric or imperfect information, uninformed traders will intensify their ‘noise’ and prevent prices from fully revealing private signals or information by informed traders. This will magnify volatility in the spot prices.

Fourth, Starica and Granger (2005) show that the variance of asset returns may experience sudden shifts, depending on the magnitude of news or information received in the market. This has an important implication on pricing of other assets. In fact, Belke and Gokus (2011) provide evidence of volatility spillovers among the CDS, bond and equity markets. Therefore, volatility in the CDS market may trigger persistent volatility and price changes in both equity and bond markets. This affects efficient pricing of government debt of any country that has important implications for diversification of risk by hedge fund managers4, lenders and policymakers striving to stabilize financial markets.

Volatility and its persistence can be best modeled using the generalized autoregressive conditional heteroskedasticity (GARCH) models some of which offer the advantage of capturing the leverage effects of Black (1976) and the mean reversion. However, these models are unable to capture sudden shifts in conditional volatility which, according to Lamoureux and Lastrapes (1990), Ewing and Malik (2005) and Cagli et al (2011) among others, could result not only in specious volatility modeling, but also overestimation of persistence parameters because of omission of variables, videlicet, structural breaks.

In this article, we contribute to existing literature by investigating persistence of volatility of sovereign credit risk and how structural breaks affect this persistence. This is particularly important because past studies in this area have found that ignoring structural breaks in volatility modeling tends to overestimate persistence of volatility. Moreover, past studies on persistence of volatility have focused on stock markets of developed countries. To the best of our knowledge, this is one of the first papers to investigate the short-term dependence nature of volatility of instruments used to price sovereign credit risk in presence of structural breaks. The rest of the article is organized as follows: the next section details the sources and features of BS and CDS data; the section after that explains the econometric methodology utilized to gather evidence; the penultimate section discusses the empirical evidence while the final section summarizes and concludes.

DATA SOURCES AND CHARACTERISTICS

We gather daily, US dollar-denominated, standard 5-year sovereign CDS and emerging market BS. Specifically, for each of the seven sovereigns, we use Emerging Market Bond Index Global (EMBIG) sovereign BS from J.P. Morgan research and market database. The EMBIG spread is a market capitalization-weighted average of spreads on US dollar-denominated Brady bonds, Eurobonds and traded debt issued by sovereign and quasi-sovereign entities. Data from J.P. Morgan has been extensively used in academic research to price default risk sovereign US dollar-denominated public debt.

We use the standard 5-year BS since any variation in the maturities and types of bonds (sovereign and quasi-sovereign bonds) in the EMBIG could possibly distort the arbitrage relation between the BS and CDS. In some cases, this could lead to negative or positive basis wrongly occasioned by varying maturities rather than arbitrage processes in the two markets. This also ensures that our results are not adulterated by the maturity structures of the data.

As of September 2011, the most heavily traded sovereigns CDS contracts (by gross national amount) were France, Italy, Germany and Spain. However, we focus on seven emerging markets as our sample for various reasons. First, France, Italy, Germany and Spain are all developed countries in European Union (EU) and became heavily traded just recently as most developed countries started experiencing financial problem during and 2007–2008 global financial crises. Their history is thus transient, and the historical data going back to pre-crisis period cannot truly and adequately capture the spirit of our study. As the International Monetary Fund (IMF) report indicates5, the importance of sovereign BS and CDS especially in developed economies has been growing rapidly since 2008. We therefore focus on seven emerging markets’ sovereign or reference entities that have been consistently heavily traded (albeit some have toppled from top 10 from the onset of financial crisis).

Second, unlike developed countries in the EU, the emerging markets we study are highly susceptible to sudden structural breaks in volatility as they experience the destabilizing internal shocks from the social, economic and financial markets restructuring of political upheavals. These markets are also subject to external shocks emanating from financial markets of developed countries. We cannot gainsay the exigent need to incorporate structural breaks in estimation of volatility persistence coefficients for emerging markets as opposed to developed markets that have been largely stable in all aforementioned fronts.

Third, most post-crisis studies in sovereign BS and CDS have ignored emerging markets and focused almost entirely on EU. Therefore, we take a beeline in this study and focus on seven emerging markets, videlicet, Argentina, Brazil, China, Colombia, Mexico, Philippines and South Africa. The BS and CDS data for all sovereign nations have different starting dates but they have a mutual ending sample period ending date of 30 March 2012.

ECONOMETRIC METHODOLOGY

In this study, we use Kappa-1 (K1) and Kappa-2 (K2) tests of Sanso et al (2004). The two tests identify structural breaks in variance of time series. Both tests are nested in iterated cumulative sums of squares algorithm of Inclan and Tiao (IT henceforth, 1994), who developed the original structural break test called IT. We adopt the K1 and K2 tests for three main reasons. First, the Inclan and Tiao (IT) test is premised on the restrictive assumptions of homoskedasticity and mesokurtic (independent and Gaussian) distribution of disturbances in each regime identified. Andreou and Ghysels (2002) show that because of this inherent problem, the IT test tends to overestimate the number of structural breaks in variance. The K1 test corrects for this weakness especially the issue of kurtosis or fourth moment in distributions. The K2 corrects for dependence or persistence nature of volatility in presence of time-varying or conditionally heteroskedastic disturbances. Second, Rapach and Strauss (2008) find that the IT test is fraught with size distortions if serial correlations among the residuals, problem not prevalent in K1 and K2 tests. Third, the preliminary tests indicate that changes in CDS and BS are characterized by non-normal distributions (Jarque Bera (JB) test), serial correlation of residuals (Breusch–Godfrey test (BG)), conditional heteroskedasticity (autoregressive conditional heteroskedasticity (ARCH) effects), and leptokurtic or fat-tail distribution. These features violate the conditions necessary for the application of IT test, hence we adopt the K1 and K2 tests.

To elaborate on K1 and K2 tests, we start with the original work of Inclan and Tiao (1994) who proposed to use the IT statistics to identify structural breaks in variance as follows:

First, IT developed Open image in new window statistics to test the null of constant unconditional variance.
where Ck=∑t=1kɛt2 for =1, ….., T is the cumulative sum of squares of ɛt that is assumed to be ɛtiid N(0, σ2) under the IT test. Then, IT⇒supr|√T/2Dk|, where √T/2 standardizes the distribution. The asymptotic distribution of the test, annotated as IT, is given by

According to Sanso et al (2004), ⇒ represents weak convergence of probability measures associated with the test, W(r) is the standard Brownian motion while W*(r)≡Wr−rW(1) is a Brownian bridge.

The Gaussian process advocated by IT test implies that kurtosis or fourth moment is equal to η4=3σ4. However, granted the fat-tail or leptokurtic distribution of returns, then η4>3σ4 which will generate higher frequency of rejecting the null hypothesis of homoskedasticity. Sanso et al (2004) adjusted the IT test to remove the nuisance parameter of iid residuals. The developed K1 test as follows:

and Open image in new window

The asymptotic distribution of the K1 test is premised on the idea that if ɛtiid and E(St4η4<∞, then, K1⇒supr|W*(r)|

To overcome the assumption of independence of returns in data-generating process inherent in both IT and K2 but still incorporate heteroskedasticity, Sanso et al (2004) assumed, under some conditions6 that the sample data can be viewed as a sequence of random variables, {ɛt}t=1. This led to development of K2 test, where
Open image in new window is a consistent estimator of ω4, and ω4 can be estimated non-parametrically as follows7:

where ω(l,m)=1−(l/(m+1)). In addition, if Open image in new window, then Open image in new window

According to Cumby et al (1993) and Cheng et al (2001), exponential generalized autoregressive conditional heteroskedasticity (EGARCH) offers three main advantages relative to GARCH model. First, EGARCH model does not require ARCH and GARCH coefficient estimates to be restricted to positivity. Second, EGARCH formulation captures both the sign and size of the past shocks affecting contemporaneous variance of returns. Finally, EGARCH models standardized residuals as a moving average that is able to capture the asymmetry of positive and negative news or shocks (leverage effects) that characterize most stationary time series. According to Black (1976), the leverage effects capture the tendency of negative news to magnify conditional volatility more than good news of the same magnitude. The EGARCH model of Nelson (1991) is as follows:
In equation (7), ϖ is unconditional volatility, α coefficient captures the size effect of a standardized previous shock (|ɛt-1|), whereas γ captures the leverage effects. β coefficient estimates indicate persistence of conditional volatility, σ2. The coefficients α and γ should be positive and negative, respectively, while the closer β is to unity, the higher the persistence of volatility. Lamoureux and Lastrapes (1990) states that conventional EGARCH models tend to overestimate persistence of volatility if structural breaks in variance are not accounted for. Therefore, to get more reliable estimates for the persistence of uncertainty of default risk of sovereign borrowers, we add structural breaks to our univariate EGARCH model as follows:

DUMn is a set of dummy variables that takes a value of 1 from the structural break date onward and 0 otherwise. To estimate the model parameters, we maximize the log-likelihood using the Berndt et al (1974) algorithm. We also use generalized error distribution to capture fat-tail distribution of CDS and BS returns.

EMPIRICAL EVIDENCE

The descriptive statistics in Table 1 capture the main features of the sovereign CDS and BS returns. The returns of all credit risk measures except China and South Africa’s CDS returns and Philippines and South Africa’s BS returns indicate positive skew. With exception of the Argentina’s BS returns, the BS and CDS returns have positive excess kurtosis (kurtosis greater than 3) thus exhibit leptokurtic or fat-tail distributions.
Table 1

Descriptive statistics, ARCH and serial autocorrelation tests

Country

Mean

Q1

Q3

Standard deviation

skew

kurtosis

JB-test

n

ARCH(16)

BG(16)

Argentina

 BS

0.00032

−0.006

0.0072

0.0233

1.131

1.451

***552.07

1762

***4.701

***6.581

 CDS

0.00046

−0.016

0.0152

0.0325

0.633

6.285

***909.91

1762

***7.531

***15.824

Brazil

 BS

−0.0007

−0.012

0.0098

0.0264

0.704

8.341

***3468.74

2729

***35.261

***5.862

 CDS

−0.0008

−0.021

0.0179

0.0411

0.375

10.838

***7049.28

2729

***20.617

***4.635

China

 BS

0.00048

−0.002

0.0033

0.0153

2.338

127.017

***1538292.96

2397

0.100

***39.726

 CDS

0.00001

−0.028

0.0279

0.0642

−0.31

10.788

***6096.51

2397

***3.355

***2.890

Columbia

 BS

−0.0007

−0.011

0.0101

0.0313

0.601

31.661

***82185.40

2397

***35.199

***3.687

 CDS

−0.0008

−0.019

0.0147

0.0398

0.368

12.129

***8377.96

2397

***14.976

***6.386

Mexico

 BS

−0.0003

−0.011

0.0118

0.0280

0.200

7.195

***2020.29

2730

***41.568

***3.189

 CDS

−0.0003

−0.022

0.0202

0.0474

0.495

20.162

***33612.83

2730

***16.933

***3.423

Philippines

 BS

−0.0005

−0.002

0.0095

0.0253

−0.14

27.573

***60920.65

2421

***67.616

***10.307

 CDS

−0.0005

−0.016

0.0142

0.0352

0.184

10.877

***6273.17

2421

***52.404

***4.353

South Africa

 BS

−0.0001

−0.016

0.0217

0.0435

−0.29

3.282

***45.82

2588

***15.145

***9.992

 CDS

0.00003

−0.023

0.0232

0.0690

−0.19

93.115

***875693.95

2588

***5.244

***10.855

*** represents statistical significance at 1 per cent significance level.

Notes: Q1 and Q3 are first and third quartiles mean return. JB is the Jacque–Bera test of normal distribution of returns while n is the number of observations. ARCH (16) is the Autoregressive conditional heteroskedasticity test of Engle (1982) up to 16 lags while BG (16) is the Breusch—Godfrey serial autocorrelation test of Godfrey (1978) and Breusch (1979) up to 16 lags.

Although the skew is relatively small, the positive (negative) skew implies that trading on both CDS and BS generates higher probability of positive (negative) returns. The Jacque and Bera (JB) (1987) test whose null is normal distribution or asset returns, is decisively rejected indicating non-normal distribution of CDS and BS returns. Given the relatively small skewness, we can conclude that non-normality is largely driven by leptokurtosis. The ARCH test of Engle (1982), which have a null of constant variance (homoskedasticity) rejects the null at 16 lags. The Breusch (1979) and Godfrey (1978) tests (BG (16) of serial autocorrelation or dependence up to 16 lags of residuals (the null is zero autocorrelation) strongly reject the null at 1 per cent significance level. The existence of heteroskedasticity, non-normality, fat-tails and autocorrelation of residuals justify adoption of EGARCH modeling. These features are also inherent in returns of other securities especially stocks.

We then test for unit root or non-stationary features of CDS and BS at levels. We use the more efficient Dickey–Fuller Generalized Least Squares (DG-GLS) test of Elliott et al (1996) which tests the null of unit root against the alternative of stationary. We also use unit root test of Kwiatkowski et al (1992) test based on the null hypothesis stationary against non-stationary. Finally, we use Zivot and Andrews’ (1992) test which has a null hypothesis of unit root test excluding exogenous structural breaks at the intercept (du) and at intercept and trend (du and dt), respectively. The results are presented in Table 2. The Kwiatkowski, Phillips, Schmidt and Shin (KPSS) test rejects stationarity in all cases and thus confirms unit root. The DF-GLS rejects unit root for Brazil’s BS and South Africa’s BS and CDS. Using Zivot and Andrews (ZA) test8, we reject the null for Brazil’s BS and CDS, and China and Argentina’s BS. For the remaining CDS and BS returns, we fail to reject unit root excluding structural break at the intercept and at the intercept and trend. In sum, we find that BS and CDS at levels have a unit root using at least one of the three tests. Therefore, we use the log of first difference (CDS and BS returns) for subsequent analysis. Having confirmed that CDS and BS at levels are integrated of order one [I(1)] at levels, we compute the log of first difference to make the data stationary. The results of stationarity test are not presented to conserve space. We denote the first difference as BS and CDS returns. We use the returns, and the Sanso et al’s (2004) tests to endogenously identify structural breaks in volatility.
Table 2

Unit root tests using level time series data

Country

DFGLS1

DFGLS2

KPSS1

KPSS2

ZA1

t-stat1

Tb1

ZA2

t-stat2

Tb2

Argentina

 BS

−1.663

−2.146

***1.419

***0.513

**−4.92

−2.82

1001

−2.31

−2.72

800

 CDS

−1.744

−2.077

***0.968

***0.562

−2.97

−2.66

1039

−3.14

−3.74

843

Brazil

 BS

−0.260

−1.878

***3.634

***0.768

***−9.1

−4.26

261

***7.26

−7.24

261

 CDS

−1.333

*−2.578

***2.946

***0.606

***−12.1

−4.28

301

***−9.6

−8.63

262

China

 BS

−0.485

−1.662

***2.735

***0.268

**−4.90

−2.48

2202

4.16

−3.87

1615

 CDS

−1.909

−1.942

***2.217

***0.322

3.148

−4.61

1290

−2.36

−4.83

1468

Colombia

 BS

0.028

−1.527

***2.441

***0.549

3.298

−4.41

1396

−1.18

−4.34

1406

 CDS

0.325

−1.062

***3.256

***0.843

3.192

−4.74

1401

2.95

−4.50

1162

Mexico

 BS

−0.599

−1.703

***0.845

***0.690

3.802

−4.53

1742

−1.49

−4.61

1742

 CDS

−0.854

−1.759

***0.769

***0.701

3.223

−4.33

1730

−1.16

−4.33

1768

Philippines

 BS

−0.159

−2.052

***2.802

***0.437

3.468

−4.64

1428

−0.82

−4.64

1428

 CDS

−0.216

−2.079

***3.454

***0.619

3.528

−4.77

1393

2.16

−5.19

1303

South Africa

 BS

***−2.568

*−2.688

***0.953

***0.428

2.578

−3.26

1436

−1.22

−3.28

1436

 CDS

***−2.656

*−2.691

***1.046

***0.542

3.405

−4.44

1468

−0.04

−4.37

1468

Critical Values

 1%

−2.566

−3.480

0.739

0.216

−5.34

−5.57

 5%

−1.941

−2.890

0.463

0.146

−4.80

−5.08

 10%

−1.617

−2.570

0.347

0.119

−4.58

−4.80

*, ** and *** shows statistical significance at 10 per cent, 5 per cent and 1 per cent significance levels, respectively.

Notes: DFGLS1 (DFGLS2) is the Dickey—Fuller Generalized Least Squares test of Elliot et al (1996) with intercept (intercept and trend). KPSS1 (KPSS2) is Kwiatkowski, Phillips, Schmidt and Shin’s (1992) test with intercept (intercept and trend). ZA1 and ZA2 is the ZA (1992) unit root test with structural break at the intercept (du) and intercept and trend (du and dt), respectively. t-stat1 and t-stat2 is the standard t-statistics testing for unit root test with du and du and dt structural break tests.. Tb1 and Tb2 are the structural break dates when testing for structural break at the intercept (du) and intercept and trend (both du and dt), respectively.

Therefore, there is no potential for data mining in testing for breaks in volatility. The K1 and K2 tests correct for serial interdependence, heteroskedasticity and non-normal distribution of returns. These features characterize the BS and CDS returns. We report in Table 3 the results of structural break tests. First, we find multiple structural breaks in variance of CDS and BS. Second, the break points or dates vary across sovereigns. Third, majority of breaks seem to have occurred around the 2007/2008 global financial crisis as most of the structural break dates fall in either 2008 or 2009.
Table 3

Structural break dates of variance using K1 and K2 tests

Country

TB (k1)

  

NB

TB (k2)

  

NB

Argentina

BS

11 June 2007

22 October 2008

1 January 2009

11 June 2007

1 January 2009

11 December 2007

12 September 2008

5

2

CDS

3 October 2005

6 June 2007

11 June 2007

1 January 2009

29 June 2006

29 June 2009

4

2

Brazil

BS

5 December 2001

8 August 2003

24 March 2008

3 June 2002

7 November 2002

8 August 2003

3 June 2002

27 January 2004

12 September 2008

28 June 2002

1 May 2003

27 January 2004

28 June 2002

17 June 2004

31 October 2008

7 November 2002

12 June 2007

1 January 2009

 

1 May 2003

13

6

CDS

19 July 2007

29 October 2008

25 May 2011

18 September 2007

17 December 2008

18 September 2007

17 December 2008

11 November 2011

12 September 2008

4 June 2010

12 September 2008

4 June 2010

5 March 2012

9

29 October 2008

25 May 2011

6

China

BS

30 April 2009

4 June 2010

2

17 July 2007

23 May 2011

CDS

30 April 2009

4 June 2010

2

30 April 2009

4 June 2010

4

Colombia

BS

14 April 2004

11 June 2007

12 September 2008

7 June 2004

19 September 2007

22 October 2008

7 June 2004

17 August 2007

22 October 2008

10 March 2005

26 June 2008

1 December 2008

10 March 2005

26 June 2008

1 December 2008

11 June 2007

12 September 2008

8

7 February 2006

10

CDS

31 August 2004

30 August 2008

3 August 2011

7 June 2004

27 September 2007

22 October 2008

3 January 2005

17 December 2008

14 December 2011

10 March 2005

26 June 2008

1 December 2008

31 January 2006

1 February 2011

28 February 2012

11 June 2007

12 September 2008

12 September 2008

10

8

Mexico

BS

31 May 2007

12 September 2008

31 December 2008

31 May 2007

12 September 2008

31 December 2008

24 March 2008

30 October 2008

5

24 March 2008

30 October 2008

5

CDS

4 January 2002

19 July 2007

12 September 2008

31 May 2007

12 September 2008

31 December 2008

25 March 2004

19 September 2007

23 October 2008

24 March 2008

30 October 2008

5 January 2005

18 April 2008

18 December 2008

6 July 2006

10

5

Philippines

BS

20 May 2004

12 May 2006

11 September 2008

20 May 2004

12 May 2006

11 September 2008

4 March 2005

1 December 2006

2 December 2008

6

4 March 2005

1 December 2006

2 December 2008

6

CDS

13 December 2005

17 January 2008

26 November 2008

13 December 2005

17 January 2008

26 November 2008

13 July 2007

22 September 2008

25 November 2010

8 June 2007

2 September 2008

 

15 August 2007

24 October 2008

22 July 2011

9

5

South Africa

BS

1 May 2003

17 August 2007

12 September 2008

1 May 2003

17 August 2007

12 September 2008

12 December 2006

5 February 2008

1 January 2009

6

12 December 2006

5 February 2008

1 January 2009

6

CDS

23 March 2004

4 January 2005

30 October 2008

1 May 2003

17 August 2007

12 September 2008

3

12 December 2006

5 February 2008

1 January 2009

6

Notes: TB (K1) and TB (K2) are structural break dates or points for BS and CDS variance dates using K1 and K2 tests. NB is the number of structural breaks.

This is a confirmation that a global event such as a global financial crisis emanating from developed countries such as the United States can trigger a fundamental shift in variance or uncertainty of sovereign credit risks.

Having identified the structural breaks in volatility of BS and CDS, we then test how the breaks affect persistence of volatility of sovereign credit risk. However, to assess the impact of the breaks on persistence of volatility, we first run a base EGARCH model without incorporating structural breaks. Table 4 presents the estimates of α coefficient (effects of size of shock on conditional volatility), γ (leverage effect) and β (persistence of volatility). We find interesting results.
Table 4

Persistence of variance without structural breaks

Country

α

γ

β

ARCH(16)

Half-life

Argentina

 BS

***0.1802

−0.0054

***0.9976

0.199

288.5

 CDS

***0.3119

***−0.0836

***0.8991

1.001

6.5

Brazil

 BS

***0.2126

***−0.0291

***0.9907

0.227

74.2

 CDS

***0.2154

***−0.0433

***0.9593

1.588

16.7

China

 BS

***0.1960

*−0.0134

***0.9729

0.684

25.2

 CDS

***0.4581

***−0.1030

***0.8202

0.249

3.5

Columbia

 BS

***0.2096

*−0.0214

***0.9863

0.012

50.2

 CDS

***0.3541

***−0.0534

***0.9527

0.728

14.3

Mexico

 BS

***0.2167

**−0.0233

***0.9918

0.385

84.2

 CDS

***0.1972

***−0.0570

***0.9604

0.238

17.2

Philippines

 BS

***0.2556

*−0.0268

***0.9722

1.028

24.6

 CDS

***0.2862

*−0.0297

***0.9672

0.461

20.8

South Africa

 BS

***0.1630

−0.0051

***0.9959

1.047

168.7

 CDS

***0.3327

***−0.0629

***0.9244

0.544

8.8

*, ** and *** shows statistical significance at 10 per cent, 5 per cent and 1 per cent significance levels, respectively.

Notes: ARCH (16) is the Engle (1982) test with the null of constant variance (homoskedasticity) of residuals.

First, volatility of both BS and CDS returns is highly persistent with all sovereigns recording a persistence of 0.90 or higher except China’s CDS. This evidence is captured by β coefficient estimates. The high degree of persistence of uncertainty of sovereign credit risk implies shocks to conditional volatility will dwindle slowly over time. Therefore, sovereigns are likely to pay high cost of borrowing as long as this uncertainty persists. This could also constrain the sovereign borrower from accessing new credit from lenders until volatility or uncertainty peters out. This may exacerbate liquidity problem of the borrower. A classic case in point is Greece where sovereign CDS have been consistently high as uncertainties regarding burgeoning budget deficits and potential default have persisted for almost the past 2 years.

One notable finding is that the persistence parameter for BS is consistently higher than that of CDS for all the sovereigns in which case the sovereign bond market is the vehicle of price leadership in price discovery process. Using Ross’s (1989) argument, this could suggest that informed trading occurs in the sovereign bond market. A counter argument by Attanasio (1990), Singleton (1987) and Grossman and Stiglitz (1980) states that it can also be argued that the asymmetric or imperfect information in bond market will enhance trading by uninformed traders who will intensify their ‘noise’ and prevent true prices of credit risk from being fully revealed by private signals or information from informed traders in the CDS market. This will magnify volatility in the bond prices and increase persistence of such volatility. In this model, persistence of volatility is caused by uninformed trading9.

Second, the half-life, which according to Lamoureoux and Lastrapes (1990) shows the number of periods (days) a shock to conditional variance takes to shrink to half its initial size varies across the sovereigns. For example, shocks to conditional variance of Argentina’s BS will take 288 days (more than 1 year trading days) to revert to original size, whereas a shock to conditional variance of China’s CDS returns will take only 3.5 days to shrink to original size. The shorter the half-life, the faster the uncertainty dissipates.

Third, the asymmetry or leverage effect coefficients (γ) is significant and negative for all sovereigns. This implies that bad news or negative shocks intensify or have destabilizing effects on conditional volatility of both BS and CDS more than positive shocks (good news) of equal magnitude. Finally, we find that in all cases, coefficient of persistence, β is greater than α. This suggests that large shocks to the market do not trigger significant revisions in future conditional volatility. Satisfying this condition, together with the fact that almost all the coefficient estimates are statistically significant, indicates the EGARCH model is stationary.

The EGARCH model with (without) structural breaks may be considered as unrestricted (restricted), hence both models are nested in each other. In Table 5, we summarize the results of EGARCH model which account for structural break. The results are based on breaks identified by K1 and K2 tests. To preserve space and without loss of information, we report the leverage effect coefficient γ and persistence of volatility coefficient, β. We document interesting evidence. First, in Argentina and South Africa, CDS returns exhibit higher persistence of volatility than BS, a reversal of evidence without structural breaks. In these two countries, CDS market may be dominated by informed traders. The persistence of volatility of BS remains higher than that of CDS in the remaining sovereigns. Second, with exception of China’s CDS, the persistence of volatility register significant declines after accounting for structural breaks, suggesting that ignoring structural breaks in volatility tends to overestimate persistence parameter, β. Moreover, the half-life also declined by significant percentages hence in presence of structural breaks, shocks to conditional volatility take lesser days to revert to half of original size. Third, to test the fit of the model, we compute the likelihood ratio (LR) to test the null hypothesis that the unrestricted EGARCH model (with breaks) does not fit the data significantly better than restricted EGARCH model (without breaks). The LR is computed from the log likelihood estimates of the two models. The LR is strongly significant, evidence that the EGARCH model with breaks (using dummies) fits significantly better than restricted EGARCH model without breaks.
Table 5

Persistence of volatility in presence of Structural breaks

Country

Security

γ

β

Percentage of change

half-life

F-(DUM)

LR

ARCH (16)

Panel A: Using k1 breaks

Argentina

BS

−0.043

***0.602

−39.61

1.37

***6.316

***72.33

0.509

 

CDS

−0.083

***0.869

−3.32

4.94

1.357

***7.57

0.917

Brazil

BS

***−0.053

***0.926

−6.57

9.02

***3.461

***117.5

0.126

 

CDS

***−0.057

***0.872

−9.06

5.06

***3.839

***45.82

0.132

China

BS

−0.007

***0.928

−4.60

9.28

***21.905

***43.84

0.908

 

CDS

−0.114

***0.834

+1.74

3.82

***12.152

***97.88

0.172

Colombia

BS

0.010

***0.955

−3.13

15.05

***7.340

***128.40

0.147

 

CDS

***−0.071

***0.819

−14.03

3.47

***3.170

***69.07

1.329

Mexico

BS

***−0.037

***0.917

−7.57

8.00

***7.659

***111.60

0.315

 

CDS

**−0.049

***0.783

−18.51

2.83

***2.922

***40.87

0.138

Philippines

BS

−0.019

***0.912

−6.16

7.53

***4.234

***126.9

0.532

 

CDS

**−0.045

***0.874

−9.60

5.15

***2.438

***50.71

1.757

South Africa

BS

**−0.053

***0.647

−35.00

1.59

***3.148

***131.40

0.301

 

CDS

***−0.050

***0.730

−21.03

2.20

***212.625

***569.50

0.692

Panel B: Using k2 breaks

Argentina

BS

−0.036

***0.803

−19.55

3.16

***11.689

***63.09

0.514

 

CDS

−0.079

***0.883

−1.77

5.57

1.000

***3.31

0.997

Brazil

BS

***−0.052

***0.920

−7.15

8.31

***8.034

***112.80

0.111

 

CDS

***−0.045

***0.927

−3.40

9.14

**2.646

***20.60

1.473

China

BS

−0.007

***0.928

−4.60

9.28

***21.905

***43.84

0.908

 

CDS

***−0.075

***0.855

+4.23

4.43

***3.235

***−57.12

0.214

Colombia

BS

−0.01

***0.964

−2.24

18.91

***10.794

***118.8

0.086

 

CDS

**−0.051

***0.923

−3.13

8.65

**1.989

***20.36

0.567

Mexico

BS

***−0.055

***0.826

−16.69

3.63

***4.740

***108.9

0.279

 

CDS

***−0.042

***0.925

−3.69

8.89

**2.367

***14.57

0.245

Philippines

BS

−0.019

***0.912

−6.16

7.53

***4.234

***126.90

0.532

 

CDS

−0.028

***0.914

−5.45

7.71

***3.476

***29.62

0.32

South Africa

BS

**−0.053

***0.647

−35.00

1.59

***3.148

***131.40

0.301

 

CDS

**−0.035

***0.272

−70.53

0.53

***32.238

***422.80

1.643

*, ** and *** shows statistical significance at 10 per cent, 5 per cent and 1 per cent significance levels, respectively.

Notes: LR is the likelihood ratios computed as 2[Lb)−L0)], where Lb) and L0) are the log-likelihoods for EGARCH models with and without structural breaks in variance. F(DUM) is the F-statistics for the joint test of joint significance of the dummy variables (DUM). Percentage of change represents the percentage of change in persistence with and without the breaks. The half-life for EGARCH model is computed as –ln(2)/ln(β). ARCH (16) is Engle’s (1982) ARCH-LM test up to 16 lags.

We also conduct Wald F-statistics test to investigate whether inclusion of the dummies significantly improves the fit of the model. Specifically, we test the null that all dummy coefficients are simultaneously equal to 0 (Ho: dn1= dn2=……=dnn=0, where dn are dummies 1 … n coefficient estimates). We decisively reject the null using F-statistics (F-DUM) suggesting that including dummies to proxy for structural breaks significantly improves our results. The ARCH test up to 16 lags indicates that the residuals are homoskedastic. In sum, ignoring breaks caused by fundamental shifts in volatility may yield incorrect results and inference therefrom.

SUMMARY AND CONCLUSION

In this study, we investigate persistence of volatility of sovereign credit risk and how multiple structural breaks in volatility affect volatility persistence. This is one of the first studies to investigate the volatility dependence behavior of sovereign BS and CDS. We find that BS and CDS returns are characterized by skewness, fat-tail distributions, heteroskedasticity and serial correlation of residuals. Unlike past studies in other asset returns that use IT test, we use K1 and K2 tests and endogenously identify multiple structural breaks. These two tests correct for dependence of assets returns, heteroskedasticity and non-normal distribution of returns features that were found in BS and CDS returns. Using EGARCH model without breaks, we find that BS have higher persistence of volatility than CDS. We also find not only multiple structural breaks, but also that these structural breaks significantly reduce persistence of volatility of sovereign credit risk and corresponding half-life. Therefore, failure to account for structural breaks in volatility tends to overestimate persistence and half-life and may yield incorrect inferences for policy purposes. Moreover, BS generally seems to have higher persistence of volatility before and after accounting for structural breaks. This may suggest that either informed trading takes place in the bond market or presence of asymmetric information and noise trading in the bond markets. Our findings have important implications on cost of borrowing by sovereigns, pricing of sovereign credit risk, and the efficiency of CDS and BS markets. The fact that volatility persists and is predictable suggests that future changes in BS and CDS prices can be predicted from current price changes. This is a violation of efficient market hypothesis. Hedge fund managers, arbitrageurs and speculators can also use the results to formulate pairs trading strategies and engaging in arbitrage process.

Footnotes
1

In naked CDS, speculators, who are not bondholders, pay CDS premium to speculate that the reference entity is going to default. This misuse of CDS was one of the major triggers of 2007/2008 financial meltdown.

 
2

HFI is the monthly percentage of return of Eureka emerging market fixed income hedge fund index. BRA, ARG, COL, MEX, PHN and SAF are the monthly percentage of return of sovereign CDS for Brazil, Argentine, Colombia, Mexico, Philippines and South Africa.

 
3

In this study, we use stationary data. Therefore, we use log of first difference of level BS and CDS that we consistently refer to BS and CDS returns, respectively.

 
4
 
5

‘A new look at the role of sovereign credit default swaps’, Financial Stability Report, April 2013, IMF.

 
6

See Sanso et al (2004) for more information.

 
7

In derivation of K1 and K2, the bandwidth selection is based on Newey–West methodology.

 
8

In ZA test, we report the higher of the two ZA values: The one generated by ZA test on intercept only and the one generated by ZA test of structural break in intercept and trend.

 
9

In this study, we are not testing for the appropriate theory that can explain persistence of volatility but we attempt to offer competing theories that can explain our results.

 

Copyright information

© Palgrave Macmillan, a division of Macmillan Publishers Ltd 2014

Authors and Affiliations

  • Geoffrey Ngene
  • Hannah Carley
  • Mohammad Kabir Hassan
    • 1
  1. 1.Department of Economics and FinanceUniversity of New OrleansNew OrleansUSA

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