2009_Norden_Weber_The Comovement of Credit Default Swap Bond and Stock Markets an Empirical Analysis

European Financial Management, Vol. 15, No. 3, 2009, 529–562doi: 10.1111/j.1468-036X.2007.00427.x

The Co-movement of Credit DefaultSwap, Bond and Stock Markets: anEmpirical Analysis

Lars Norden and Martin WeberDepartment of Banking and Finance, University of Mannheim, L 5.2, 68131 Mannheim, Germany,and Centre for Economic Policy Research (CEPR), London, UKE-mail: [email protected]; [email protected]

Abstract

We analyse the relationship between credit default swap (CDS), bond and stockmarkets during 2000–2002. Focusing on the intertemporal co-movement, we ex-amine monthly, weekly and daily lead-lag relationships in a vector autoregressivemodel and the adjustment between markets caused by cointegration. First, wefind that stock returns lead CDS and bond spread changes. Second, CDS spreadchanges Granger cause bond spread changes for a higher number of firms thanvice versa. Third, the CDS market is more sensitive to the stock market than thebond market and the strength of the co-movement increases the lower the creditquality and the larger the bond issues. Finally, the CDS market contributes moreto price discovery than the bond market and this effect is stronger for US thanfor European firms.

Keywords: credit risk, credit spreads, credit derivatives, lead-lag relationship

JEL classification: G10, G14, G21

1. Introduction

In efficient markets default risk of firms should be reflected by market prices of financialclaims on these firms. Theory suggests that there is a close link between market prices

We are particularly grateful to an anonymous referee for helpful comments. In addition, wewish to thank Klaus Dullmann, Jens Grunert, Rainer Jankowitsch, Volker Kleff, MarkusMentz, Ingmar Nolte, Winfried Pohlmeier, Monika Trapp, Andreas Trauten, Valeri Voev,participants of the CFS Workshop on credit derivatives and CDOs in Frankfurt, Germany(2004), the 11th Annual Meeting of the German Finance Association in Tubingen, Germany(2004), the 8th Conference of the Swiss Society for Financial Market Research in Zurich,Switzerland (2005), the 4th C.R.E.D.I.T. Conference in Venice, Italy (2005), and theDeutsche Bundesbank research seminar. We also thank two members of the credit derivativesdepartment from the bank who provided the CDS data for helpful comments and suggestions.Financial support of the German National Science Foundation is gratefully acknowledged.Correspondence: Lars Norden.

C© 2007 The AuthorsJournal compilation C© 2007 Blackwell Publishing Ltd.

530 Lars Norden and Martin Weber

of different claims, for example stocks and bonds, because their value depends onthe distribution of the market value of a firm’s assets. Less obvious is the empiricalrelationship between market prices of different credit-sensitive claims for the samefirm. In particular, the link between the heavily growing credit derivatives market (seeFitch Ratings (2003), British Bankers’ Association (2004), and European Central Bank(2004) for an overview) and traditional markets has only been marginally explored. Themarket of single name credit default swaps (CDS) is of particular interest because theseinstruments should reflect pure issuer default risk and no facility or issue specific risk,making them a potentially ‘ideal’ benchmark for measuring and pricing credit risk. Inaddition, CDS have turned out to clearly dominate other types of credit derivatives suchas credit linked notes or total return swaps in terms of market volume and standardisation.Therefore, we empirically analyse the co-movement of single name CDS, bond and stockmarkets to study if and how these markets are connected and whether default-risk relatedinformation is reflected earlier in certain markets than in others. More specifically, weaddress the following three issues: 1. What is the relationship between CDS, bondand stock markets? In particular, can we detect lead-lag relationships? 2. If lead-lagrelationships exist, what is their strength and which factors influence their magnitude?3. What role do CDS and bond markets play for price discovery?

Our paper contributes in three ways. First, we expand the very small number ofrelated studies by providing evidence for new issues. We find that the CDS marketis more sensitive to the stock market than the bond market and the magnitude of thissensitivity is related to a firm’s average credit quality, the liquidity of corporate bondsbut not to its market capitalisation. In addition, the contribution to price discoveryof the CDS market relative to the bond market is substantially stronger for US thanfor non-US reference entities. Furthermore, the result that CDS spread changes areGranger-causal for bond spread changes at most of the firms (and not vice versa) canbe detected for firms with and without cointegrated credit spreads. Second, from amethodological perspective, we compare aggregate results of a pseudo-panel analysiswith findings from firm-specific regressions. Third, we are able to substantiate existingempirical evidence by means of a considerably richer data set covering a larger numberof firms, a longer time-period, different data frequencies (monthly, weekly, and daily)as well as US and non-US reference entities. In particular, different data frequenciesand the international sample composition allow us to investigate the influence of newinformation and liquidity effects on the relationship between the three markets.

Analysing time-series data from 58 individual firms over the period 2000–2002, wefind that stock returns clearly lead both CDS and bond spread changes from the samefirm. Furthermore, at higher data frequencies CDS spread changes Granger cause bondspread changes for a higher number of firms than vice versa. A cointegration analysisof CDS and bond spreads and a corresponding vector error correction model reveal thatthe CDS market mainly contributes to price discovery.

Our findings may be useful for market participants who rely on price data fromdifferent markets for trading, monitoring, or hedging against credit risk (see, e.g.,Berndt et al. 2005). In addition, regulators increasingly pay attention to the evolutionof markets for credit risk transfer, investigating the opportunities from an improved riskallocation in the financial system and threats from a potential increase in systemic risk(see Bank for International Settlements, 2003; European Central Bank, 2004; DeutscheBundesbank, 2004). It is noteworthy that for the first time the Basel Committee onBanking Supervision (2004) recognises credit risk transfer instruments like CDS in anew capital adequacy framework for banks.

C© 2007 The AuthorsJournal compilation C© 2007 Blackwell Publishing Ltd

Credit Default Swap, Bond and Stock Markets 531

The remainder of the paper is organised as follows. In Section 2, we review theliterature and propose a set of hypotheses. Section 3 describes the data. In Section 4, weanalyse lead-lag relationships between markets and perform various robustness checks.In Section 5, we examine the strength of the lead-lag relationships and test for potentialdeterminants. In Section 6, we study the adjustment process between CDS and bondspreads. Section 7 concludes.

2. Existing Literature and Hypotheses

Subsequently, we briefly review the empirical literature that relates to our threeresearch questions and propose a set of hypotheses. Early research that deals with thecontemporaneous and intertemporal co-movement of stock and corporate bond returnsfinds a small, significantly positive relationship (see, e.g., Blume et al., 1991; Cornelland Green, 1991; Fama and French, 1993). However, these studies are based on aggregateportfolio performance data at a relatively low frequency.

More recent studies investigate the bond-stock market relationship at the individualfirm-level, in a lead-lag framework, and with data of higher frequency (weekly, daily,hourly). For example, Kwan (1996) attempts to explain weekly changes of corporatebond yields with changes of same-maturity treasury yields and contemporaneous,leading and lagging stock returns. The main results are that bond yield changes aresignificantly positively affected by changes in treasury yields, significantly negativelyinfluenced by contemporaneous and lagged stock returns but not significantly associatedwith lagged bond yield changes. Alexander et al. (2000) investigate the relationshipbetween daily stock and high-yield bond returns at the individual firm-level during theperiod 1994–97. They find a significantly positive but economically weak correlationbetween daily high-yield bond returns and excess stock returns. Hotchkiss and Ronen(2002) analyse the informational efficiency of the high yield corporate bond marketusing daily and hourly price data from the year 1995. Applying a vector autoregressive(VAR) model, they do not find support for the view that stock portfolio returns leadbond portfolio returns. They detect a significantly positive but economically weakcontemporaneous correlation between stock and bond returns which is judged as non-causal. However, it is unclear whether these results hold for firms from the investment-grade level as well. Longstaff et al. (2003) examine weekly lead-lag relationshipsbetween CDS spread changes, corporate bond spreads and stock returns of US firms.They find that both stock and CDS markets lead the corporate bond market whichprovides support for the hypothesis that information seems to flow first into stockand credit derivatives markets and then into corporate bond markets. However, in theirsample there is no clear lead of the stock market with respect to the CDS market andvice versa. In light of this literature, we propose the following hypotheses H1 and H2.

H1: Positive stock returns are associated with negative CDS spread changes andnegative bond spread changes.

As stated by Kwan (1996), we expect that stock and bond prices move in the samedirection when new information relates to the expected firm value. If the latter rises,for example, due to unexpectedly high earnings, the stock price will go up becausestockholders will benefit from improved earnings and the price (credit spread) ofcorporate debt will rise (fall) because default risk is reduced. Note that this inverse



relationship between stock returns and credit spread changes is consistent with studiesthat have analysed the determinants of credit spreads (see, e.g., Collin-Dufresne et al.,2001; Aunon-Nerin et al., 2002; Blanco et al., 2005; Avramov et al., 2004).1

H2: Stock and CDS markets lead the bond market.

We expect the stock market to lead the bond market for the following reasons. First,there is some prior empirical evidence which suggests that information is reflectedearlier in the stock than in the bond market (see Kwan, 1996). Second, institutionalfeatures of the stock market facilitate a continuous flow of transactions which is not thecase in the bond market where short positions are more difficult to establish. Third,the number of traders, trades and the trading volume and liquidity is clearly higher inthe stock market than in the corporate bond market. The CDS market is also expectedto lead the bond market because of the first two arguments mentioned above.

With regard to our second question about the strength of the market co-movementand potential influence factors, we state the following hypotheses H3 and H4:

H3: The link between CDS and stock markets is stronger than the link betweenbond and stock markets.

In the CDS market pure issuer credit risk is traded whereas in the bond market issue-specific credit risk and market risk are traded in a bundle. Accordingly, hypothesisH3 postulates that CDS spread changes should exhibit a stronger sensitivity to stockreturns than bond spread changes. Empirical evidence is provided by Blanco et al.(2005). They follow Collin-Dufresne et al. (2001) in analysing the determinants ofCDS spread changes and corporate bond spread changes and find that the impact offirm-specific stock returns is stronger on CDS spreads changes than on corporate bondspread changes.

H4: The strength of the relationship between CDS/bond spread changes andstock returns becomes more pronounced (a) the lower a firm’s credit quality, (b)the bigger the firm, and (c) the higher the liquidity of corporate bonds.

CDS and bond spread changes from low-grade firms should exhibit a higher sensitivityto stock returns than those from high-grade firms. This relationship has been detected forbond spread changes and stock returns (see Blume et al., 1991; Cornell and Green, 1991;Kwan, 1996; Collin-Dufresne et al., 2001, and Avramov et al., 2004). The underlyingreasoning is as follows: equity bears the ultimate form of credit risk because it representsthe most subordinated claim in the capital structure of a firm. Hence, CDS and bondspread changes from high risk firms should be linked more strongly to stock returnsthan those from low risk firms. Moreover, CDS and bond spread changes from relativelysmall firms should exhibit a higher sensitivity to stock returns than those from relativelylarge firms if size is related to default risk. In addition, CDS and bond spread changesfrom firms that issue large bonds should be related more strongly to stock returns than

1 Alternatively, it can be argued that positive stock returns may be associated with positiveCDS and bond spread changes when new information relates to the volatility of the firm’sasset return. However, Kwan (1996) cannot provide empirical evidence for this volatility-based reasoning.



those from firms with smaller bond issues due to a higher liquidity in the bond market.The latter is important for the CDS market as well because the size, number and liquidityof outstanding bonds determine the set of reference and deliverable obligations in CDScontracts. Moreover, there is some evidence that bond and CDS spreads consist of defaultrisk and liquidity components (see Longstaff et al., 2005; Buhler and Trapp, 2006).

Finally, the adjustment of firm-specific credit spreads from different markets has beeninvestigated by Blanco et al. (2005) for a sample of 33 firms (16 from the USA, 17from Europe) from January 2001 to June 2002. The analysis reveals that price discoverytakes place predominantly in the CDS market. In a similar study, Zhu (2006) examinesthe same question for a sample of 24 firms (hereof 19 from the USA) during the period1999–2002. According to that study, spread levels in both markets can considerablydeviate from each other in the short run but they are strongly linked in the long-run.With respect to our third question we will test the following hypothesis H5:

H5: Price discovery takes place mainly in the CDS market.

This hypothesis can be motivated as follows. First, the CDS market is more flexibleand less capital-intense because only premia but no bond prices have to be paid. Second,CDS traders can easily go long and short in credit risk while shortening bonds is moredifficult. Third, bond spreads from the secondary market depend on the available numberand specifics of outstanding bonds which are related to the issuance activity of the firmswhile the CDS market is more standardised and less dependent on primary marketissuances.

3. Data Description

3.1. Data collection and sample composition

CDS data is provided by CreditTrade and a large European bank2 which is among theworld’s top 25 credit derivatives counterparties. Raw data covers the time period 2 July1998 to 2 December 2002 and includes CDS quotes and contractual information formore than 1,000 reference entities. CDS quotes are selected in the following manner.First, we exclude all quotes on sovereigns due to the lack of stock prices for theseentities. Second, we calculate the mid spread from bid and offer quotes. Third, we takethe mean per day if multiple mid spreads and/or transaction spreads were observed ona given day. Fourth, since the number of CDS price observations per firm is relativelylow in 1998 and 1999, we select all firms with at least 100 daily senior CDS quotes forthe benchmark maturity of five years in each of the years 2000–2002.

Moreover, daily default-free interest rate term structures are collected. Besidesgovernment bond yield curves from the Federal Reserve Board, the Bank of Englandand the Deutsche Bundesbank, we also consider swap rate curves for USD, GBP andEUR from Thomson Financial DataStream since there is evidence that swap rates mightbe the more appropriate benchmark (see, e.g., Hull et al., 2004; Houweling and Vorst,2005). Additionally, we include a synthetic Euro yield curve from the Statistical Officeof the European Communities.

2 The bank wishes to remain anonymous.



To obtain a sample of suitable corporate bonds from Bloomberg, several filter rules areapplied.3 In addition to generic mid-market closing bond prices and yield to maturities,we gathered bond characteristics like issue and maturity date, coupon, notional, currencyetc. Since daily CDS spreads refer to a constant maturity, we have to compare thesespreads with constant maturity bond spreads. As the latter do not exist, we create, ifthe corresponding bond data is available, a synthetic five-year constant maturity bondspread for each firm by linearly interpolating the daily yields of two bonds with amaturity above and below five years and subtract the five-year default-free interest rate(see Longstaff et al., 2003, 2005, Hull et al., 2004, Blanco et al., 2005, for a similarmethodology).4

We then add daily common stock closing prices from Thomson Financial Datastreamand firm-specific implied stock volatility of put options from Bloomberg. The data iscompleted with individual firm characteristics (market capitalisation in local currencyand Euro, region, industry code) from Thomson Financial DataStream and histories ofcredit ratings from the three major rating agencies from Bloomberg.

The final data set consists of 58 firms with observations from the years 2000–2002(see Appendix A). It covers 70% of the world’s top 20 most actively traded corporatereference entities in terms of frequency of occurrence (see Fitch Ratings, 2003). 35of the 58 firms (=60%) come from Europe, 20 from the USA (=35%) and 3 fromAsia (=5%). The most important industries are financials (=31%), telecommunication(=14%) and automotive (=12%). Table 1 presents characteristics of the firms and bondsincluded in our final sample.

Panel A reveals that both average firm size and average credit quality decline overthe sample period. The first observation is due to the overall baisse in the Europeanand North American stock markets and, additionally for US firms, partially due to thedevelopment of the US dollar-euro exchange rate. The deterioration of the firms’ ratingsreflects the rise of leverage and/or earnings problems in some industries (e.g. telecom-munication or automotive). Panel B presents characteristics of 58 synthetic five-yearconstant maturity bonds which have been created as described before (see Appendix B).Notionals of the bonds below and above five years to maturity amount to roughly0.5 billion euro. Approximately 45% of the bonds are denominated in euro and USdollar respectively and the remainder in pound sterling.

3.2. Descriptive analysis

In this section, we succinctly describe the market data and analyse the contemporaneouslink between markets with correlations. Table 2 exhibits five-year senior CDS spreads(CDS) and five-year constant maturity bond spreads (BSS) over swap rates and

3 We require that (1) bonds are issued with a fixed coupon and are non-callable, non-puttableand not convertible, (2) bonds are quoted in US-dollar, pound sterling or euro, (3) bondsrank senior unsecured (required seniority for deliverable assets according to the ISDA MasterAgreement for CDS), (4) bond price time series exist during 2000–2002 and indicate liquidtrade (matrix priced bonds were excluded).4 This model-independent approach, if used for pricing issues, may underestimate the defaultrisk in investment-grade bonds and overestimate it for low-grade bonds (see Longstaff et al.2005). This problem does not affect our study as almost all firms in our sample exhibitinvestment grade ratings over the entire sample period.



Tabl

e1

Firm

and

bond

char

acte

rist

ics.

Pane

lA

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irm

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size

and

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2000

4,73

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225

44,3

78Ju

n20

014,

981

30,0

3811

3,40

447

,546

Dec

2002

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79,6

3532

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Rat

ing

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910

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2000

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116

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1.8

1.8

14.3

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01.

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86.

72.

1



Tabl

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Con

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lB

:B

onds

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mat

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Table 2

Mean CDS and bond spreads by year and rating.

This table reports mean CDS and bond spreads for different years and rating grades. The variable CDSrepresents a five-year maturity CDS spread that refers to senior unsecured debt. The variables BSS andBSG are the differences between a synthetic five-year constant maturity corporate bond yield and theequivalent currency five-year LIBOR interest swap rate or government bond yield. The table showsmean spreads per year and rating category. Spreads come from 58 firms and are noted in basis points.In brackets, the underlying number of observations is reported.

Variable Year \ rating 1 2–4 5–7 8–10 11–13 Total(AAA, Aaa) (AA, Aa) (A, A) (BBB, Baa) (BB, Ba)

CDS 2000 – 24.51 43.05 65.97 – 41.53(2,940) (7,162) (1,605) (11,707)

2001 – 27.56 62.12 133.99 357.81 71.09(2,519) (8,400) (2,905) (8) (13,832)

2002 – 36.88 76.49 189.00 647.76 118.95(2,157) (6,616) (4,091) (324) (13,188)

Total – 29.02 60.25 147.46 640.78 78.45(7,616) (22,178) (8,601) (332) (38,727)

BSS 2000 – 18.46 47.43 74.25 – 42.97(3,382) (5,783) (1,824) (10,989)

2001 – 20.60 56.94 111.90 136.89 61.78(2,594) (7,940) (2,886) (9) (13,429)

2002 – 25.63 59.98 138.10 330.5 84.56(2,111) (6,581) (3,820) (332) (12,844)

Total – 21.02 55.22 115.58 325.39 64.08(8,087) (20,304) (8,530) (341) (37,262)

BSG 2000 – 66.34 121.80 153.08 – 109.91(3,275) (5,587) (1,767) (10,629)

2001 – 59.44 105.31 155.71 189.43 107.38(2,490) (7,604) (2,783) (7) (12,884)

2002 – 52.80 92.96 166.38 370.51 115.40(2,034) (6,336) (3,685) (320) (12,375)

Total – 60.60 106.02 159.92 366.64 110.89(7,799) (19,527) (8,235) (327) (35,888)

government bond yields (BSG) by year and rating. First, one can easily notice thatmean spreads are in accord with the ordinal ranking by credit ratings. Second, we findan increasing average spread per rating category during the sample period for CDS andBSS. This observation may be due to the decline of swap rates, a deterioration of theaverage credit qualities within each grade, or to a rise in the average risk premia (seeBerndt et al., 2005). Third, for investment-grade levels, CDS spreads are much closerto BSS than BSG which is consistent with Hull et al. (2004), Blanco et al. (2005) andHouweling and Vorst (2005). Therefore, we do not consider the variable BSG for thesubsequent analyses.



ratedate

micds5sen mbs5swap

03jan2000 02dec2002

0

50

100

150

200

ratedate

meicds5sen mebs5swap

03jan2000 02dec2002

0

50

100

150

200

a: Mean spreads b: Median spreads

Fig. 1. Time-series of CDS and bond spreads.

Figure 1a (Figure 1b) displays times series of daily cross-sectional mean (median) spreads. CDSspreads are indicated by a solid line, bond spreads by a dotted line. Data comes from 58 firms overthe period 2000–2002.

Figure 1 displays time series of daily cross-sectional means and medians of CDS andBSS during the entire sample period. It can be seen that CDS and bond spreads wererelatively close to each other in the years 2000 (CDS: 41 bps, BSS: 43 bps) and 2001(CDS: 71 bps, BSS: 62 bps). On the one hand, since mid 2001, we observe a positivebasis for mean spreads (CDS: 119 bps, BSS: 85 bps) which persists until the end of thesample period (see Figure 1a). On the other hand, Figure 1b reveals that median spreadsremain quite close to each other although a small positive basis becomes visible (seeO’Kane and McAdie (2001) for a discussion of the CDS basis).

In the next step, we examine stationarity and serial correlation of the individual CDS,bond and stock time series. This is important because if time-series are non-stationaryand serially correlated, the usual OLS regression approach is no longer applicable.In particular, one may find a spurious relationship between the two variables. Theapplication of three different stationarity tests5 yields that the null hypothesis that leveltime-series (i.e. stock prices, CDS and BSS) are non-stationary (stationary) is rejectedfor a small (large) number of firms. The opposite is found for daily time-series of stockreturns and spread changes. In at least 54 of 58 cases the time-series of returns and firstdifferences are no longer considered to be non-stationary. The analysis of autocorrelationreveals that it is high for level time-series but very low for weekly and daily change dataexcept for daily bond spread changes at lag 1. Therefore, we consider stock returns andspread changes for the subsequent analyses.

To get an impression of the contemporaneous co-movement of the three markets, weexamine pairwise rank correlation of monthly and daily time-series at the firm-level.The corresponding results are summarised in Table 3.

The mean rank correlation of monthly stock returns and CDS spread changes is −0.30with 30 of 58 individual correlation coefficients being significantly different from zeroat the 0.10-level. Interestingly, CDS spread changes exhibit a significantly stronger

5 Note that the Augmented Dickey-Fuller and the Phillips-Perron test have a null hypothesisof non-stationarity whereas the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test has a nullhypothesis of stationarity. We consider tests with different null hypotheses to ensure thatresults are robust to the power of the tests.



Tabl

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negative correlation with stock returns than bond spread changes (−0.30 vs. −0.22,p<0.01). Differentiating by the geographic origin of a firm, we find that stock returnsof US firms exhibit a stronger negative correlation with CDS than European firms.Across industries, we detect a much stronger correlation of stock returns with CDS andbond spread changes (−0.47, −0.37) for telecommunication firms than for other firms(−0.28, −0.19). In addition, CDS and bond markets are much closer inter-linked inthe case of telecommunication firms (0.76) than in the case of other firms (0.45). Thecorrelation of stock returns and CDS spread changes for financials is higher than fornon-financial firms. Finally, the analysis of sub-samples reveals that all three types ofcorrelations become stronger in the second half (June 2001 to December 2002). Similarresults are found for the correlation of daily changes.

4. Lead-lag Relationships between CDS, Bond and Stock Markets

4.1. Methodology and results

In this section, we analyse the intertemporal co-movement of CDS spread changes, bondspread changes and stock returns (i) at the aggregate level and (ii) at the firm-specificlevel. More specifically, we aim to explain current stock returns, CDS spreads changesand bond spread changes with a three-dimensional vector autoregressive model. A VARmodel is appropriate to analyse the co-movement of markets because it captures lead-lag relationships within and between stationary variables in a simultaneous multivariateframework (see Engsted and Tanggaard (2004) for an analysis of the co-movement ofUS and UK stock markets with a VAR model). Our basic model specification is thefollowing:6

Rt = α1 +P∑

p=1

β1p Rt−p +P∑

p=1

γ1p�CDSt−p +P∑

p=1

δ1p�BSSt−p + ε1t

�CDSt = α2 +P∑

p=1

β2p Rt−p +P∑

p=1


p=1

δ2p�BSSt−p + ε2t

�BSSt = α3 +P∑

p=1

β3p Rt−p +P∑

p=1


p=1

δ3p�BSSt−p + ε3t (1)

with Rt: stock return in t, �CDSt: CDS spread change in t, �BSSt: change of a synthetic5-year corporate bond spread in t, p: lag order index, ε t: disturbance term in t.

Subsequently, we apply this model to monthly, weekly and daily firm-specific time-series from the three markets. Monthly data offers the advantage to minimise potentialproblems due to liquidity effects. The weekly analysis is carried out to allow forcomparability with related studies. In addition, we focus on daily data because differentmarkets may exhibit different levels of liquidity and may respond differently to new

6 Note that our approach differs from Longstaff et al. (2003) with regard to the followingthree aspects: i) they analyse weekly data, we examine monthly, weekly, and daily data,ii) their sample is confined to US firms while our data is international, iii) they calculatebond spreads above US Treasury bond yields whereas we consider the swap rate which hasbecome the benchmark for the risk-free rate in recent years.



information in the short term but they are likely to align after some days. We refrainfrom analysing the contemporaneous relationship of stock returns and spread changesbecause, in the absence of intraday data, we are not able to detect lead-lag effects on thebasis of closing prices from the same day. For the above model specification, the lagstructure and the maximum lag order P has to be determined. Since the maximum lagorder should consider the overall information processing and aggregation time in eachof the three markets, we choose a specification without gaps and a maximal lag of order2 for monthly and weekly data and one of order 5 (spanning one week) for daily data.7

In a first step, we examine the aggregate co-movement of markets by meansof a pseudo-panel regression analysis. Specifically, we estimate fixed-effects panelregression models with stock returns, CDS spread changes and bond spread changesas dependent variables to explore the average lead-lag relationships between markets.Table 4 reports the results.

Panel A reveals that there are several intertemporal linkages between the three marketsat the monthly level. As stated in H1, it clearly turns out that lagged stock returns havea significantly negative impact on CDS spread changes and on bond spread changes.Moreover, bond spread changes are the most and stock returns the least forecastablevariable. However, we also observe two-way linkages across markets which are notconsistent with H2. Panel B and C report the panel analysis results for weekly anddaily data. As previously, we find support for H1 since lagged stock returns display astrong negative impact on �CDS and �BSS which becomes weaker for higher lags.Furthermore, most of the lags of �BSS (�CDS) are significantly positively relatedto �CDS (�BSS), indicating again two-way linkages across markets which are not inline with H2. However, note that the panel analysis provides aggregate results that maybe driven by intertemporal and cross-sectional relationships. In particular, this analysisdoes not allow to disentangle firm-specific from time-series effects in the explanatoryvariables since the estimated coefficients are the same across firms.

Therefore, in a second step we investigate the lead-lag relationships in a moredifferentiated manner with firm-specific regressions. Table 5 reports VAR modelestimation results for the individual firms based on monthly (Panel A), weekly (Panel B)and daily data (Panel C). Columns 3, 6 and 9 display the number of coefficients that aresignificantly different from zero at the 0.01-level. We report the number of cases in whichthe coefficients are jointly different form zero (Granger-causal, see Granger, 1969) incolumns 4, 7 and 10. When interpreting these numbers, note that our findings becomeseriously stronger if we adopt a significance level of 0.05 or 0.10 for the estimatedregression coefficients and Granger causality tests. From Panel A, it can be seen thatstock returns are the least forecastable and bond spread changes the most forecastablevariable at a monthly frequency. More important, the CDS market leads the bond marketfor a higher number of firms than vice versa. In particular, note that lags 1–2 of �CDShave a significantly positive impact on �BSS at 22 firms while the same is true for lags1–2 of �BSS for only 13 firms. However, the coefficients reported here are smallerthan in Table 4 since they are medians.

7 For weekly (daily) data the Akaike information criterion suggests a lag order of 2 (4),the Hannan-Quinn criterion one of 1 (2) and a likelihood-ratio test one of 3 (9). Numbersare medians of the individual criteria from all 58 firms. For comparison, Kwan (1996) andLongstaff et al. (2003) include weekly lags 1 and 2 as well.



Table 4

Aggregate lead-lag analysis with pseudo-panel regressions.

For each market (stock, bond, and CDS) we estimate panel regressions to study aggregate lead-lag relationships across markets for different frequencies (monthly, weekly, daily data). We reportcoefficients and p-values from fixed-effects models. Note that random-effects models produce similarresults. Monthly data refers to mid-month observations, weekly data to the Wednesday-Wednesdayinterval. For each of the three equations in each panel we show the overall R2 (which is close to thewithin R2). Data stems from 58 firms over the period 2000–2002.

Panel A: Monthly data

Dep. Var. Rt �CDSt �BSSt

Coeff. p-val. Coeff. p-val. Coeff. p-val.

Rt−1 −0.04 0.199 −123.62 0.000 −95.99 0.000Rt−2 −0.05 0.104 −65.65 0.000 −51.97 0.000�CDSt−1 0.00 0.623 −0.49 0.000 −0.10 0.002�CDSt−2 −0.00 0.357 0.01 0.801 0.06 0.075�BSSt−1 0.00 0.090 0.35 0.000 −0.11 0.023�BSSt−2 0.00 0.077 −0.24 0.002 −0.25 0.000Const. 0.02 0.000 2.92 0.041 2.16 0.018

Obs. 1,390 1,390 1,390R2 0.0066 0.1190 0.1228

Panel B: Weekly data



Rt−1 −0.08 0.000 −39.15 0.000 −17.22 0.000Rt−2 −0.03 0.019 −21.93 0.000 −9.52 0.000�CDSt−1 −0.00 0.135 −0.02 0.094 0.15 0.000�CDSt−2 −0.00 0.499 0.01 0.608 0.09 0.000�BSSt−1 0.00 0.000 0.19 0.000 −0.23 0.000�BSSt−2 0.00 0.300 0.10 0.000 −0.01 0.610Const. −0.00 0.169 0.40 0.058 0.41 0.007

Obs. 8,700 8,700 8,700R2 0.0085 0.0419 0.0663

Panel C: Daily data



Rt−1 −0.01 0.176 −29.59 0.000 −19.79 0.000Rt−2 −0.04 0.000 −13.48 0.000 −9.07 0.000Rt−3 −0.03 0.000 −10.13 0.000 −0.16 0.888Rt−4 −0.01 0.018 −4.63 0.005 −0.27 0.820Rt−5 −0.00 0.381 −6.09 0.000 −7.26 0.000�CDSt−1 −0.00 0.001 −0.08 0.000 0.09 0.000�CDSt−2 0.00 0.952 0.01 0.019 0.07 0.000



Table 4

Continued.

Panel C: Daily data



�CDSt−3 0.00 0.629 −0.11 0.000 0.04 0.000�CDSt−4 0.00 0.805 0.06 0.000 0.01 0.101�CDSt−5 0.00 0.378 0.03 0.000 −0.01 0.000�BSSt−1 −0.00 0.076 0.23 0.000 −0.12 0.000�BSSt−2 −0.00 0.001 0.21 0.000 −0.01 0.007�BSSt−3 0.00 0.000 0.08 0.000 −0.05 0.000�BSSt−4 0.00 0.043 0.07 0.000 0.02 0.000�BSSt−5 −0.00 0.802 −0.02 0.012 −0.05 0.000Const. −0.00 0.000 0.06 0.207 0.07 0.042

Obs. 38,675 38,675 38,675R2 0.0041 0.0758 0.0488

Panel B reveals that the results based on weekly data are qualitatively similar andquantitatively even stronger in comparison to Panel A.8 Whereas lagged CDS and bondspread changes have little impact on stock returns, the latter significantly lead CDSspread changes in 19 of 58 cases at the 0.01-level. Note that the relationship is negativefor all firms which provides evidence in favour of hypothesis H1 and which is consistentwith results from the contemporaneous co-movement analysis (see Table 3). In addition,the CDS market seems to lead the bond market at lag 1 in 23 of 58 cases at the 0.01-level (33 of 58 at the 0.10-level) which is support for hypothesis H2. Note that boththe frequency of statistically significant coefficients and the magnitude of the mediancoefficient tends to decline if one moves from lag 1 to lag 2 in most of the cases.Furthermore, there is clear indication that the residuals of each equation come from awhite noise process on the basis of a Ljung-Box test (including lags 1–8). Additionally,applying Bartlett’s periodogram-based test the white noise property of the residualscannot be rejected for any of the firms. Overall, the analysis of residuals indicates thatOLS assumptions are respected.

Finally, Panel C reports the results for the daily VAR model with lags 1–5. Thenumber of firms whose lagged CDS and bond spread changes significantly explaincontemporaneous stock returns is relatively low and median coefficients are close tozero. In contrast, lags 1–5 of stock returns Granger cause CDS spread changes at 39 of58 firms. Note that, as found beforehand, the relationship is negative, which is consistentwith H1, and the magnitude of the median coefficient and the number of significantcoefficients of lagged stock returns decreases as the lag order ascends. Bond spreadchanges are predictable with past CDS spread changes (lags 1–5 are jointly significant or

8 Stock returns and spread changes in Table 5, Panel B (and Table 4, Panel B) refer to theWednesday-Wednesday interval. The model was also estimated for other day-of-the-weekintervals and the results (number of significant coefficients, magnitude of the coefficients,average R2 for each equation) are very similar.



Table 5

Firm-specific lead-lag analysis with a VAR model.

The firm-specific VAR model consists of three-equations with the log stock return (Rt), the CDSspread change (�CDSt), and the bond spread change (�BSSt) as dependent variables respectively. Inthis table, we report median coefficients (columns 2, 5, and 8) and the absolute frequency of firms forwhich the coefficient of the explanatory variable is significantly different from zero at the 0.01-level(columns 3, 6, and 9). Columns 4, 7, and 10 report the number of firms for which we can reject the nullhypotheses at a 0.01-level (Wald test) that lags 1 to P have no joint explanatory power (the Wald test forp = 5 corresponds to a Granger causality test). Monthly data refers to mid-month observations, weeklydata to the Wednesday-Wednesday interval. For each equation we additionally show the median R2,median p-value from a standard F-Test and the number of firms which exhibit a F-test p-value below0.01. The hypothesis that the residuals come from a white-noise process is tested with a Ljung-Box(LB) test (weekly data: lags 1–8, daily data: lags 1–40) and Bartlett’s test (B) for each equation andfirm separately. Data comes from 58 firms over the period 2000–2002.

Panel A: Monthly data

Column: (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)


Rt−1 −0.03 3 −42.36 17 −45.75 18Rt−2 −0.17 2 −5.04 3 14 −26.42 8 13�CDSt−1 0.00 1 −0.37 11 0.16 4�CDSt−2 0.00 5 2 0.14 7 0.24 18 9�BSSt−1 0.00 4 0.08 6 −0.41 19�BSSt−2 0.00 5 2 −0.12 7 2 −0.33 15Const. −0.02 5 1.40 2 0.53 3

Median R2 0.2253 0.4201 0.4323Median p-val. F 0.3731 0.0724 0.0209No. F-test p<0.01 1 18 22Residuals:No. LB-p. < 0.01 0 0 0No. B-p. < 0.01 0 0 0


Column: (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)


Rt−1 −0.06 5 −15.62 19 −5.93 4Rt−2 −0.03 1 −5.25 2 13 −5.40 5 5�CDSt−1 0.00 3 0.01 9 0.16 23�CDSt−2 0.00 0 2 0.01 9 0.09 8 24�BSSt−1 0.00 2 −0.01 3 −0.18 26�BSSt−2 0.00 2 4 0.00 6 6 −0.08 10Const. 0.00 0 0.18 0 0.21 0

Median R2 0.0568 0.0952 0.1281Median p-val. F 0.1799 0.0189 0.0021No. F-test p < 0.01 9 27 35



Table 5

Continued.


Column: (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)


Residuals:No. LB-p. <0.01 2 11 9No. B-p. <0.01 0 0 1

Panel C: Daily data

Column: (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)


Rt−1 −0.01 9 −14.67 32 −9.27 21Rt−2 −0.04 5 −7.09 20 36 −6.21 6 21Rt−3 −0.02 4 −5.70 15 35 −1.44 0 20Rt−4 −0.01 3 −4.25 12 37 −2.89 2 20Rt−5 −0.02 1 −0.68 2 39 −1.19 1 19�CDSt−1 0.00 3 −0.02 23 0.08 20�CDSt−2 0.00 2 4 −0.01 15 0.05 12 23�CDSt−3 0.00 1 5 −0.02 11 0.05 10 25�CDSt−4 0.00 0 5 0.02 12 0.04 8 30�CDSt−5 0.00 0 5 0.01 4 0.03 9 33�BSSt−1 0.00 2 0.03 16 −0.27 47�BSSt−2 0.00 2 2 0.02 13 19 −0.09 28�BSSt−3 0.00 6 6 0.00 6 18 −0.08 22�BSSt−4 0.00 2 4 0.01 4 19 0.00 10�BSSt−5 0.00 1 4 0.00 5 19 0.00 6Const. 0.00 0 0.04 0 0.04 0

Median R2 0.0323 0.0977 0.1479Median p-val. F 0.0991 0.0000 0.0000No. F-p. <0.01 12 54 57Residuals:No. LB-p. <0.01 4 27 16No. B-p. <0.01 0 0 0

Granger-causal for 33 of 58 firms) and, for a smaller number of firms, with lagged stockreturns. Again, the economic impact of the stock market on bond spreads tends to declineif the lag length increases. With regard to the intertemporal relationship between CDSand bond spread changes, Granger causality tests for a 0.01-level of significance revealthat i) �CDS exclusively cause �BSS at 18 firms, ii) �CDS cause �BSS and viceversa at 15 firms, iii) �BSS cause �CDS at 4 firms and iv) neither �CDS cause �BSSnor vice versa at 21 firms. While there is reciprocal Granger causality for a considerablenumber of firms, we find that the one-way impact of lagged �CDS on �BSS is observedmore often than the opposite relationship which is support for H2. Similarly to monthly



and weekly data, the fraction of variance explained and the number of firms with verylow F-test p-values is smallest for the stock market and highest for the bond marketequation. Hence, individual firm regressions with daily data represent support for H2too. Finally, note that the statistical properties of the residuals are predominantly in linewith the OLS assumptions.

In summary, the panel analysis and the firm-specific regressions provide evidence fora significantly negative co-movement of stock returns and CDS/bond spread changes.In addition, the firm-specific regressions show that the stock market clearly leads bothother markets, which supports the view that the stock market is relatively more sensitiveto new information and more liquid than the two other markets. Moreover, at a weeklyand daily frequency, CDS spread changes Granger cause bond spread changes for ahigher number of firms than vice versa while there is no clear lead-lag relationshipbetween both markets at the monthly level. One interpretation for this finding is thatliquidity problems reduce the ability of the bond market to reflect information as timelyas the CDS market at higher data frequencies.

4.2. Robustness tests

Subsequently, we carry out various tests to study the robustness of previous findingsbased on daily data. First, we investigate whether the observed lead-lag relationships areinfluenced by asynchronous price observations. Since previous results suggest that thestock market leads both other markets, but stock prices do not exactly refer to the samepoint in time as CDS spreads and bond spreads, we repeat our analyses for stock returnsthat are lagged by one day to explicitly favour both other markets. Essentially, resultsare very close to those obtained previously: even stock returns lagged by one day arethe least forecastable and bond spread changes remain the most forecastable variable.

Second, we split our data into the first and second half (Jan 2000 to Jun 2001,Jul 2001 to Dec 2002) of the sample period and re-estimate the VAR model with datafrom each sub-sample respectively. Note that related studies do not provide any insightsabout the intertemporal stability of the co-movement of different markets. Basically, ourestimation results for the sub-periods are similar to those reported in Table 5. However,it is noteworthy that the leading role of the stock market in comparison to both othermarkets increases over time. Furthermore, the CDS market does not lead the bondmarket in the first half while it clearly does in the second half, reflecting the increasingimportance of the CDS market. Finally, the R2 increases over time in all markets withoutaltering the finding that stock returns are the least and bond spread changes the mostforecastable variable. This result is consistent with the detected increase in monthly anddaily correlations of the contemporaneous variables (see Table 3). It is also in line withHunter and Simon (2005) who find that the return correlation of US, UK and Germangovernment bonds has risen substantially during the last ten years.

Third, we include additional explanatory variables in the VAR model to study itsrobustness with respect to a potential omitted variable problem. We add contemporane-ous and lagged changes of the five-year swap rate (�SWAP) as an exogenous variablein the VAR model to control for changes in the interest rate levels. Furthermore, weinclude changes of the firm-specific implied stock volatility (�VOL) which representsan important determinant of credit spreads (see, e.g., Collin-Dufresne et al. 2001).The implied volatility is derived from at-the-money put options on the individualfirms’ stocks because these derivatives are, like bonds or credit derivatives, sensitive todecreases in the value of a firm. Results are reported in Table 6.



Table 6

Firm-specific analysis with an augmented VAR model.

This firm-specific VAR model is based on the VAR model presented in Table 5, Panel C, whichwe have augmented by including contemporaneous and lagged daily changes of the five-year swaprate (�SWAPt) and the implied stock volatility (�VOLt) derived from at-the-money put options. Themodel is estimated on a reduced sample of 55 firms over the period 2000–2002 because �VOLt wasnot available for three firms.

Column: (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)


Rt−1 −0.03 15 −12.82 28 −6.15 16Rt−2 −0.05 9 −5.88 18 30 −4.33 6 14Rt−3 −0.02 4 −7.07 13 35 −1.10 0 14Rt−4 −0.02 2 −4.06 11 36 −2.06 3 14Rt−5 −0.01 2 −0.76 2 34 −1.04 1 14�CDSt−1 0.00 3 −0.02 23 0.08 18�CDSt−2 0.00 3 4 −0.01 13 0.06 12 24�CDSt−3 0.00 1 7 −0.02 10 0.04 7 25�CDSt−4 0.00 0 5 0.02 10 0.03 7 26�CDSt−5 0.00 2 5 0.01 4 0.03 7 31�BSSt−1 0.00 1 0.04 14 −0.22 41�BSSt−2 0.00 1 2 0.03 10 17 −0.07 21�BSSt−3 0.00 4 3 0.01 6 17 −0.05 13�BSSt−4 0.00 2 2 0.01 5 17 0.00 10�BSSt−5 0.00 1 3 0.00 4 18 0.00 8�SWAPt 0.00 43 −0.03 12 −0.25 46�SWAPt−1 0.00 4 −0.01 1 −0.01 19�VOLt −0.01 34 0.05 16 0.00 11�VOLt−1 −0.00 10 0.03 5 0.00 3Const. 0.00 0 0.03 0 −0.02 0

Median R2 0.1197 0.1218 0.2551Median p-val. F 0.0000 0.0000 0.0000No. F-p. <0.01 48 51 55

While the contemporaneous swap rate changes exhibit a significant impact on stockreturns and �BSS for a relatively large number of firms, the impact on �CDS is clearlyless frequent. A noteworthy impact of lagged swap rate changes is only observed on�BSS. Moreover, there is a significantly negative influence of �VOLt on stock returnsat 34 firms and a positive impact on �CDS (�BSS) at 16 (11) firms. Coefficientsare less frequently significant for the volatility change at lag 1. As expected, the R2 ofeach equation has been considerably increased indicating that interest rate changes andimplied volatility changes are important explanatory factors. However, stock returnsremain the least forecastable variable (median R2 = 0.1197) and �BSS the mostforecastable variable (median R2 = 0.2551). Most important, the finding that �CDSGranger causes �BSS for a considerably higher number of firms (n = 31) than viceversa (n = 18) remains robust after the inclusion of control variables. In addition, tostudy the impact of liquidity in the corporate bond market, we split up the sample in twogroups (below and above median bond notional in euros) and estimate the augmented



VAR model for each group separately. Essentially, results are similar to those for theentire sample in terms of statistical significance. We find that the lead of the CDS marketrelative to the bond market is only slightly smaller for firms that issue big bonds. Forsmall (big) bond issues, we obtain that �CDS Granger cause �BSS at 15 (16) firmswhile the opposite is observed at 8 (10) firms. However, we obtain significant differencesin the magnitude of the coefficients across both groups. This finding will be discussedin more detail in the next section.

Fourth, we include relative CDS and bond spread changes calculated as the differenceof the log spreads in the VAR model. The results do not differ very much from previousones that are based on absolute spread changes.

Summarising, various tests of robustness suggest that there is a robust negativerelationship between stock returns and CDS/bond spreads changes and that the firstclearly lead the latter. In addition, CDS spread changes are more frequently able toforecast bond spread changes in recent years than vice versa. The latter result is inaccord with findings from Longstaff et al. (2003). However, in contrast to that study, wefind a definite lead of the stock market relative to the CDS market. One reason for thisdifference may be the sample composition: while Longstaff et al. (2003) exclusivelyanalyse US firms, we examine an international sample with 35 of 58 firms comingfrom Europe. If the CDS market for US reference entities is more developed than forEuropean firms, which is not implausible, results can be reconciled. We will revisit thisissue in more detail in Section 6.

5. Lead-lag Relationships: Strength and Influence Factors

Having thus far investigated the existence and the direction of lead-lag relationshipsbetween markets, we now analyse the magnitude of the previously estimated coefficientsand test for potential influence factors.

An examination of the sensitivity of contemporaneous CDS and bond spread changesto lagged stock returns indicates that the CDS market is significantly more sensitive tostock returns than the bond market (weekly data: −15.62 vs. −5.93, daily data: −14.67vs. −9.27) which represents support for H3 and is in line with findings from Blanco etal. (2005). Applying a non-parametric Wilcoxon sign rank test to the difference of β 2,t−1

and β 3,t−1 shows that β 2,t−1 is significantly smaller (in absolute terms higher) at the0.01-level for weekly data and at the 0.05-level for daily data. The difference becomessignificant at the 0.01-level for daily and weekly data if we compare the firm-specificsum of the significant lag coefficients.

Moreover, as stated in H4, we carry out univariate tests to investigate whether themagnitude of the coefficients β 2,t−p and β 3,t−p is related to (a) credit risk, (b) firmsize and (c) the size of bond issues. With respect to the first aspect, we compare thefirm-specific coefficients with the duration-weighted 17-grade rating scale. Results forall firms and daily data are plotted in Figure 2.

It can be seen that the estimated sensitivity of �CDS and �BSS on lagged stockreturns is negatively associated with a firm’s average creditworthiness. While thisrelationship is quite pronounced for the CDS market,9 indicated by a rank correlation

9 Related event-study based evidence is provided by Norden and Weber (2004). They findthat both the CDS and the stock market react more strongly to negative rating announcementsfor firms with a relatively bad ‘old’ rating than for firms with a relatively good ‘old’ rating.



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a: β2, t-1 vs. rating b: β3, t-1 vs. rating

Fig. 2. Sensitivity of CDS and bond spread changes to lagged stock returns by rating.

Figure 2a displays the sensitivity of daily CDS spread changes (�CDS) to past stock returns (β 2,t−1)by rating while Figure 2b exhibits the sensitivity of daily bond spread changes (BSS) to lagged stockreturns (β 3,t−1) by rating. Note that each number represents a sensitivity-rating pair of one firm (seeAppendix A for firm numbers). Spearman’s rank correlations are −0.46∗∗∗ for Figure 2a and −0.09for Figure 2b. Data comes from 58 firms over the period 2000–2002.

coefficient of −0.46 that is significantly different from zero at the 0.01-level, it is notsignificant for the bond market at all. Note that this result also holds for the sum ofsignificant coefficients and for the subsample of firms that exhibit coefficients thatare significant at the 0.01-level. These findings provide partial evidence in favour ofH4a since the hypothesised relationship has been found for the CDS but not for thebond market. Repeating the same kind of analysis for firm size measured by the marketcapitalisation of firms, we note an insignificant relationship between the magnitudeof β 2,t−p and β 3,t−p and firm size. This result leads to a rejection of H4b for bothmarkets because the expected influence of a firm’s size is not significant. In addition,univariate tests of H4c reveal that the sensitivity of �CDS to lagged stock returns isnegatively correlated with the size of the bond issue (rank correlation of −0.28, p<0.05)and the corresponding result for �BSS is even more pronounced (rank correlation of−0.36, p<0.01). These findings provide clear evidence in favour of H4c, indicatingthat a higher liquidity of bonds markets leads to a stronger (negative) co-movement ofCDS/bond markets with stock markets. We also test whether the size of the bond issueis related to the market co-movement at different data frequencies. Interestingly, we findthat the bond notional is only significantly negatively related to the spread sensitivities atthe daily level but not at the weekly or monthly level. This result is in line with findingsfrom Section 4.1 and supports the view that liquidity effects place the bond market at adisadvantage relative to the other markets in the short-run.

To gain further insights, we study the impact of potential determinants of thestrength of market co-movement in a multivariate setting. Specifically, we estimate twocross-sectional regressions with the spread sensitivities β 2,t−1 and β 3,t−1 as dependentvariables respectively and the duration-weighted rating, the firm size, bond notional,and dummy variables that mark telecommunication firms, financial firms and region asindependent variables. Results are reported in Table 7.

Panel A reveals a significantly negative impact of the average credit rating MRAT ofa firm and the telecommunication dummy on the sensitivity of CDS spreads changes tolagged stock returns (β 2,t−1). Panel B shows the results for the sensitivity of bond spreadchanges to lagged stock returns (β 3,t−1). We observe a significantly negative impact of



Table 7

Cross-sectional determinants of the strength of market co-movement.

Panel A displays results for cross-sectional determinants of the average daily sensitivity of CDSspread changes to stock returns in t−1 (β i, 2,t−1) and Panel B shows the corresponding results forthe average daily sensitivity of bond spread changes to stock returns in t−1 (β i, 3,t−1). MRAT is theduration-weighted credit rating of firm i, logMV the log market capitalisation, logBN the log of themean notional of the two bonds (one bond below and one above five years maturity) which we use tocalculate the synthetic constant-maturity bond spreads BSS, US (TEL, FIN) a dummy taking the valueone for US firms (telecommunication firms, financial institutions). We use logarithms of MV and BNbecause those variables exhibit a relatively skewed distribution. P-values are calculated on the basisof robust standard errors. Data comes from 58 firms over the period 2000–2002.

Panel A: Determinants of the sensitivity of Panel B: Determinants of the sensitivity ofCDS spread changes to past stock returns bond spread changes to past stock returns

Dep. Var.: β i,2,t−1 Dep. Var.: β i,3,t−1

Coeff. p-val. Coeff. p-val.

MRATi −6.07 0.008∗∗∗ −1.64 0.369LogMVi −0.28 0.920 −0.06 0.963logBNi −2.45 0.515 −8.01 0.050∗∗USi −10.17 0.116 −13.86 0.037∗∗TELi −20.05 0.045∗∗ 1.75 0.856FINi −1.36 0.815 0.41 0.938Const. 58.10 0.279 106.03 0.066∗

Obs. 58 58R2 0.3504 0.1756

the log bond notional logBN and the US dummy variable. Note that firm size logMV isnot significant in both regressions while the rating matters for the co-movement CDSand stock markets (Panel A) and the bond notional is important for the co-movementof bond and stock markets (Panel B). Consequently, the multivariate analysis confirmsH4a for the CDS market, rejects H4b for both markets and confirms H4c in case of thebond market. Finally, a re-estimation of both models with the sum of the stock returncoefficients β 2,t−p and β 3t−p with p = 1, . . . , 5 as dependent variables leads to highlysimilar results in terms of economic and statistical significance.

6. The Adjustment Process between CDS and Bond Spreads

In this section, we continue our analysis with a test of hypothesis H5. Since two relatedstudies indicate that CDS spreads and corporate bonds spreads from the same firm tendto be cointegrated (see Blanco et al., 2005: Zhu, 2006), we take a closer look at theadjustment and price discovery process between both two credit markets and leave thestock market aside.

The existence of a cointegration relationship between the levels of two non-stationaryvariables means that a linear combination of these variables is stationary and should beexplicitly taken into account in a VAR-analysis of change data (see Engle and Granger,



1987, p. 259). Cointegrated variables move together in the long run but may deviatefrom each other in the short run which can be interpreted as a permanent adjustmentprocess towards an economic equilibrium (see Figure 1). A model that considers thisadjustment process is called a vector error correction model (VECM) and correspondsto a vector autoregressive model that is augmented by an error correction term. In theremaining analysis, we adopt the specification of Blanco et al. (2005) and estimate thefollowing two-dimensional VECM:

�CDSt = α1 + λ1 Zt−1 +P∑

p=1

β1p�CDSt−p +P∑

p=1

γ1p�BSSt−p + ε1t

�BSSt = α2 + λ2 Zt−1 +P∑

p=1

β2p�CDSt−p +P∑

p=1

γ2p�BSSt−p + ε2t

with Zt−1 = CDSt−1 − α0 − β0BSSt−1 (2)

Given the observation that CDS frequently exceed BSS (see Table 2), the coefficientsλ1 and λ2 of the error correction term Zt−1 can be interpreted as follows. If the bondmarket contributes to the adjustment, λ1 will be significantly negative and if the CDSmarket contributes to the adjustment, λ2 will be significantly positive. In the casethat both markets play a role, we expect both coefficients to be significant and signedas explained before. Subsequently, we first test whether there exists a significantcointegration relationship between CDS and BSS for each firm. Second, we estimate aVECM for all firms at which spreads are cointegrated and then interpret the coefficientsof the error correction term. Main results from these two steps are summarised in Table 8.

As reported in Panel A, we detect a significant cointegration relationship between thespreads at 36 of 58 firms.10 It turns out that the share of firms with cointegrated spreadsis higher among US firms (15/20 = 75%) than among European firms (20/35 = 57%)which is consistent with results from Blanco et al. (2005) and Zhu (2006). Analysingthe relative importance of the CDS and bond market for price discovery, we find thatmean and median λ1 is negative and λ2 is positive for all firms. The Gonzalo-Grangermeasure, defined as GG = λ2 / (λ2 – λ1) with λ1 �= λ2, indicates which of both marketscontributes more to price discovery (see Gonzalo and Granger, 1995).11 For all firmsat which cointegration between spreads exists, the mean (median) of the GG-measureamounts to 0.69 (0.79) indicating that most of the price discovery occurs in the CDSmarket which provides evidence in favour of hypothesis H5. In comparison, Blancoet al. (2005) find that the CDS market contributes roughly 80% to price discovery.Differentiating across regions, it turns out that the CDS market is more important forprice discovery than the bond market for US reference entities (mean GG = 0.84) thanfor European firms (mean GG = 0.58). This difference is significant at the 0.05-levelon the basis of a non-parametric Wilcoxon rank sum test. Note that results get more

10 Blanco et al. (2005) find cointegration at 27 of 33 firms. Zhu (2006) detects cointegrationat 14 of 24 firms.11 If both coefficients are significantly different from zero, correctly signed and the GG-measure is equal to 0.5, both markets contribute to price discovery at the same degree. ForGG = 0 only the bond market contributes and for GG = 1 only the CDS market contributesto price discovery.



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Fig. 3. Error correction coefficients for European and US firms

Figure 3a (Figure 3b) displays the coefficients λ1 and λ2 from a two-equation vector error correctionmodel (VECM) for European (US) firms for which cointegration of CDS and bond spreads cannot berejected at the 0.10-level. Note that each number represents a λ1-λ2 pair of one firm (see Appendix Afor firm numbers). Data comes from 58 firms over the period 2000–2002.

pronounced, in particular the difference between US and European firms, for the 21firms at which cointegration is even significant at the 0.01-level.

Panel B presents the number of significant coefficients and their sign for firms atwhich a cointegration of spreads cannot be rejected at the 0.10-level (0.01-level inbrackets). Basically, these numbers confirm results of Panel A in the sense of statisticalsignificance. We find that for 19 firms price discovery takes place significantly only inthe CDS market and for an additional 8 firms in the CDS and the bond market. In the caseof 8 firms CDS spreads adjust to changes of the bond spreads.12 Moreover, the exclusivecontribution of the CDS market relative to the bond market is more frequently significantfor US firms (10/15 = 67%) than for European firms (8/20 = 40%). In addition, weinvestigate whether the origin of the reference entity or the currency in which the bondsare denominated is better suited to summarise the adjustment behaviour of spreads. Wefind that both variables are, as expected, highly correlated but that the origin of the firmand not the currency matters. For example, the spread adjustment process for Ericssonwhose sampled bonds are denominated in USD, is more alike to other European firmsthan to US firms.

Figure 3 displays the error correction coefficients λ1 and λ2 for all firms withcointegrated spreads differentiating by the geographical origin of the firm. It is evidentthat the CDS and the bond market both contribute to price discovery for European firms,while for US firms the CDS market is clearly more important for price discovery thanthe bond market. We obtain similar results if we distinguish between firms with a marketcapitalisation above and below the median. Interestingly, a differentiation by the proxyfor bond market liquidity, i.e. the size of bond issues, does not produce a systematicdifference for price discovery. Price discovery takes mainly place in the CDS marketfor most of the firms, independently from the liquidity of their bond issues.

In addition to these findings, it is noteworthy that the fraction of variance explainedin the two-equation-VECM is higher for �BSS (median R2 = 0.1481) than for �CDS(median R2 = 0.0814). Moreover, the R2 of the VECM-equation with �CDS (�BSS)

12 Zhu (2006) finds that the CDS market accounts for price discovery at 15 firms, the bondmarket at 5 firms, and both markets at 2 firms.


Credit Default Swap, Bond and Stock Markets 553Ta

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as a dependent variable exhibits a significantly negative (positive) rank correlation withthe GG-measure. In other words: the higher the R2 is in the �BSS-equation, the closerthe GG-measure is to one, indicating the leading role of the CDS market. However,although we have explicitly taken into account the cointegration of spreads, the model’sability to explain spread changes does not increase much in comparison to the VARmodel from Section 4.1.

Finally, testing for Granger causality in the VECM leads to the following results forfirms at which cointegration of spreads has been detected: i) �CDS cause �BSS (andnot vice versa) for 10 firms, ii) �BSS cause �CDS (and not vice versa) for only 3 firms,iii) �CDS cause �BSS and vice versa for 11 firms and iv) neither �CDS cause �BSSnor vice versa for 12 firms. Applying the same tests to firms at which no significantcointegration of spreads has been found yields: i) �CDS cause �BSS (and not viceversa) for 8 firms, ii) �BSS cause �CDS (and not vice versa) at only 1 firm, iii) �CDScause �BSS and vice versa at 4 firms and iv) neither �CDS cause �BSS nor viceversa at 9 firms. Obviously, there are no significant differences in Granger causality forfirms with and without cointegrated spreads which indicate that results from Section 4are robust.

7. Conclusions

In this paper, we investigate the relationship between the heavily growing credit defaultswap (CDS), the corporate bond and the stock market for an international sample over theperiod 2000–2002. We focus on the intertemporal co-movement, in particular on lead-lag relationships at different data frequencies and on the dynamic adjustment processbetween markets.

First, analysing the aggregate and the firm-specific market co-movement, we findthat stock returns are significantly negatively associated with CDS and bond spreadchanges. Second, stock returns are the least predictable and bond spread changes the mostpredictable variable at all data frequencies. Moreover, at a weekly and daily frequencyCDS spread changes Granger-cause bond spread changes for a considerably highernumber of firms than vice versa. Third, the negative intertemporal relationship betweenthe CDS and stock market is more pronounced than the one between the bond and stockmarket. Fourth, the sensitivity of the CDS market to prior stock market movementsis significantly related to the firm’s average credit quality and the size of bond issuesbut not to firm size. CDS spread changes from low-grade firms are more sensitive tolagged stock returns than those from firms with a relatively good rating. There is no suchrating dependency for the sensitivity of bond spread changes to lagged stock returns.Bond spreads changes react more strongly to lagged stock returns the larger the sizeof bond issues which can be interpreted as a consequence of liquidity effects in corporatebond markets. Fifth, for the majority of firms we detect cointegration of CDS and bondspreads. A vector error correction model reveals that the CDS market contributes moreto price discovery than the bond market which is consistent with findings from Blancoet al. (2005). Whereas the adjustment process for European firms occurs in both markets,it mainly takes place in the bond market for US firms indicating the leading role of theCDS market. Finally, a comparison of Granger causality tests for firms with and withoutcointegrated spreads confirms that in both groups CDS spread changes Granger causebond spread changes for a higher number of firms than vice versa.

Despite some limitations due to data imperfections and methodological issues, wethink that our analysis essentially captures the intertemporal relationship between the



three markets. Besides the need for a larger international data set, and, if available,transaction prices instead of quotes, further research should consider institutionalfeatures of the CDS market (e.g. credit events, settlement terms) and their influenceon the relationship of CDS spreads to prices of other credit risk sensitive claims forthe same firm. Moreover, a corresponding study (without the stock market analysis)could be carried out for a sample of sovereign reference entities which represent themost liquid segment of the CDS market. Insights about the co-movement of sovereignCDS and bond spreads may be useful for financial regulators and investors to constructmarket-based indicators of credit risk. Finally, additional avenues for further researchare to analyse default and non-default components (see, e.g., Longstaff et al. 2005)and risk compensation and risk premia (see, e.g., Amato, 2005) in credit spreads fromdifferent markets over time.

Appendix A: Sample composition by firms

No. Company name obs.

1 Commerzbank AG 6362 Dresdner Bank AG 7313 Volkswagen AG 7394 Deutsche Bank AG 6505 Iberdrola SA 7426 Societe Generale 7407 Renault SA 7008 Tokyo Electric Power 5389 Toyota Motor Corp 56410 Korea Development Bank 65411 Kon Philips Electronics NV 73912 Volvo AB 36313 Merrill Lynch & Co Inc 73914 Citigroup INC 70315 Altria Group 74116 Morgan Stanley Dean Witter & Co 73517 Goldman Sachs Group Inc 75718 Telefonica SA 75019 France Telecom SA 76120 BNP Paribas SA 65521 BT Group – British Telecom 75922 National Grid Group PLC 74223 Sainsbury J Ltd 33824 Imperial Chemical Industries PLC 67825 Investor AB 69026 Ericsson AB 72227 Bank of America Corp 71228 Ford Motor Credit Co 69229 Sanpaola Imi SPA 70930 Wells Fargo & Co 64131 Walt Disney Co 67832 Lehman Brothers Holdings Inc 73433 Bear Stearns Inc 73134 General Motors Acceptance Corp 705



Appendix A. Continued.

No. Company name obs.

35 Pearson PLC 63736 Marks & Spencer PLC 73937 Endesa SA 70438 Deutsche Telekom AG 75039 Household Finance Corp 71940 Boeing Corp 71041 IBM Corp 68942 Carrefour SA 73943 Repsol YPF SA 73044 KPN NV 75645 DaimlerChrysler AG 74646 Fiat Spa 75947 Lockheed Martin Corp 71048 TotalFinaElf SA 71549 Vodafone Group PLC 76150 United Utilities PLC 58851 Cox Communications Inc 53952 Bank One Corp 72953 Deere & Co 69254 Hilton Hotels Corp 49455 Koninklijke Ahold NV 70556 British American Tobacco PLC 68757 Lafarge SA 67558 Banco Santander Central Hispano 708



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