Illiquidity Commonality
across
Equity and Credit Markets
Miriam Marra
∗
Warwick Business School
Working Paper
This Version: 20 August 2012
∗ Finance
Group, Warwick Business School, University of Warwick, Coventry, UK (Office: C2.26, WBS Scarman
Road Building; email:Miriam.Marra@wbs.ac.uk). I thank Gordon Gemmill and Anthony Neuberger for very helpful
suggestions, Alex Stremme, Dion Bongaerts, and Jérôme Dugast for valuable comments on an earlier version, and
all participants to: Cambridge-Oxford-Warwick Spring Doctoral Conference (April 2011), Finance Series Workshop
in Warwick Business School (June 2011), Fourth Liquidity Conference in Rotterdam Erasmus University (July 2011),
Glasgow University Workshop (May 2012), and Transatlantic Doctoral Conference in London Business School (May
2012).
Illiquidity Commonality
across
Equity and Credit Markets
Miriam Marra
Working Paper
Abstract
This paper examines whether illiquidity propagates across equity and credit markets and, if
so, through which mechanisms. Equity and CDS illiquidity co-movements are detected for a large
sample of firms, but the extent of the illiquidity commonality changes over time and increases
over crisis periods. For most firms illiquidity spills over from one market to the other.
We view equity and credit default swaps as claims written on the same underlying firm’s
assets and show that, besides the effect of traders’ funding constraints, market volatility, and
firm’s systematic risk, the equity-CDS illiquidity co-movements are strongly related to the debtto-equity hedge ratio (based on the Merton 1974 model). The hedge ratio captures the arbitrage
linkage between the two assets and the extent of cross-market activity of traders for hedging and
speculative purposes and contributes to explain the existence of cross-market illiquidity spillovers.
Finally, the paper disentangles common components of CDS and equity bid-ask spreads at
individual firm level: hedging and information costs, besides funding costs and market volatility,
are found significantly priced CDS bid-ask spreads.
The paper sheds some lights on how the demand of liquidity for hedging and speculative
trading across two fundamentally-linked assets can generate and enhance cross-market contagion
phenomena besides the well-documented effects of volatility and shortage of liquidity supply.
Keywords: Credit Default Swap, Equity, Bid-Ask Spreads; Illiquidity Commonality; Illiquidity
Spillovers; Hedging; Capital Structure Arbitrage; Merton (1974) Model.
1
Introduction
This paper examines whether a lack of liquidity (illiquidity) spreads across equity and credit markets
and, if so, through which mechanisms. Although the study of such commonality has important implications for asset pricing and risk management, the extent and causes of the cross-market illiquidity
co-movement have not yet been reported in the literature.
Structural-form models based on Merton (1974) view the equity of the firm as equivalent to a
long call position on the firm’s assets and the risky debt of the firm as a short put position on the
firm’s asset plus a long position on a riskless bond. As a result, equity and credit markets have strong
inter-linkages. In addition, the increased use of credit derivatives to hedge risky positions in equity
is bringing the relationship between these two assets even closer1 and prompting the expectation of
illiquidity transmission mechanisms. Therefore, the study of CDS-equity illiquidity co-movements
is important to understand whether, and at which extent, more integrated markets might be less safe.
The literature on illiquidity commonality has flourished in the last decade. Academics have highlighted that the illiquidity of individual assets is affected by the illiquidity of the overall market
and that this commonality represents risk which is priced across securities2 . Many studies have
provided some evidence of illiquidity commonality in the U.S. equity market (Chordia, Sarkar, and
Subrahmanyam 2005, Halka and Huberman 2001, Hasbrouck and Seppi 2001). Other papers have
extended the analysis of illiquidity commonality to corporate bonds, options, CDSs, and international equity markets (Chakravarty and Sarkar 2003, Houweling, Mentink, and Vorst 2005, Karolyi,
Kuan Hui, and van Dijk 2007, Mahanti, Nashikkar, and Subrahmanyam 2010, Kapadia and Pu 2012,
Cao and Wei 2010). Some studies have also attempted to offer demand-side or supply-side explanations for the phenomenon (Brockman and Chung 2002, Coughenour and Saad 2004, Bauer 2004, Fabre
and Frino 2004, Domowitz, Hansch, and Wang 2005, Zheng and Zhang 2006, Kamara, Lou, and
Sadka 2008, Koch, Ruenzi, and Starks 2004, Hameed, Kang, and Viswanathan 2010).
Meanwhile, the fast growth of the (over-the-counter) credit derivative market3 in the last ten
years has fueled a large amount of literature on the relationship between equity, debt, and credit
default swaps (the most popular credit derivative product). Some papers have provided evidence of:
lead/lag relationships between returns in CDS, equity, and bond markets (Norden and Weber, 2009;
and Marsh and Wagner, 2010); CDS and bond spreads’ dependence on equity liquidity risk (De Jong
and Driessen 2005, Das and Hanouna 2009); time-varying integration between equity and CDS markets (Kapadia and Pu 2012); effects of credit news and insider trading in the CDS market on the
equity market (Acharya and Johnson 2007, Qiu and Yu 2012); and reciprocal volatility spillovers
among CDS, bond, and equity for a group of firms (Meng, Ap Gwilym, and Varas 2009). These findings support the hypothesis that, as investors trade across different asset classes, the link between the
CDS, bond, and equity markets strengthens. A few researchers have attempted to detect the existence of illiquidity co-movements across equity, CDS, and bond markets (Tang and Yan 2006, Jacoby,
Jiang, and Theocharides 2009), but have not provided insights and explanations for this phenomenon.
1 See
Meng et al (2009)
fact, an investor would require a higher risk premium for holding an asset expected to become illiquid during market
illiquidity events; i.e. when liquidity is most needed.
3 See Meng, ap Gwilym, and Varas (2009) for relevant statistics
2 In
1
The literature lacks an accurate and comprehensive investigation of the extent and causes of
credit-equity illiquidity linkages. Our study fills this gap: it examines whether there is robust evidence of CDS-equity illiquidity commonality and sets out an appropriate framework to explain its
determinants. The research question is interesting for academics, but is also of particular interest for
investors engaged in cross-market trades, for risk managers, and for regulators. Understanding the
influence of the joint movements of asset illiquidity has major implications for portfolio management,
financial risk management, and derivatives pricing.
In this paper, we differentiate the concepts of illiquidity commonality (also defined co-movement)
and illiquidity spillover (also defined contagion). Illiquidity commonality is the common surge of
illiquidity in equity and credit assets, while illiquidity spillovers comprise transmission of illiquidity
shocks from one asset to the other. Illiquidity spillovers imply illiquidity commonality, but illiquidity
commonality does not necessarily imply the existence of spillovers. In fact, equity and credit assets
might be influenced by exogenous factors which cause an increase in their respective illiquidity without generating illiquidity transmissions across the two markets.
We measure illiquidity commonality as the positive co-movement between equity and CDS bidask spreads4 . We analyze 51 U.S. investment-grade firms over the period April 2003 - December
2009. Correlation analysis and graphic analysis suggest that equity and credit illiquidity co-move
over time, but the extent of this commonality changes over time: commonality is much higher in
2003 than during the period 2004-2006 and then it rises again during the crisis period 2007-2009.
We also test for the existence of illiquidity spillovers and find that for most firms illiquidity is
transmitted across markets either from CDS to equity or in both directions, but not from equity to
CDS. We notice that the direction of the illiquidity spillovers at firm level has no one-to-one correspondence with the directions of return spillovers and for one third of firms it follows the direction
of volatility spillovers5 . Moreover, we analyze how market-wide illiquidity and firm-specific volatility affect equity and CDS bid-ask spreads. At individual firm level we find that CDS and equity
illiquidity are influenced by general market illiquidity, but CDS bid-ask spreads are also significantly
affected by firm’s asset volatility.
After examining the characteristics of equity-CDS illiquidity commonality and illiquidity spillovers,
the paper investigates possible explanations consistent with the reported evidence. Several illiquidity transmission mechanisms are likely to be in place across the two markets, in particular during
periods of higher volatility (Frank, González-Hermosillo, and Hesse 2008). Previous literature argues
that during periods of turbulence market-wide factors such as higher cost of funding and increase
in market volatility can prevent market makers from providing liquidity to both equity and credit
markets, thereby increasing their illiquidity commonality. The recent sub-prime crisis offers an ex4 We
select the bid-ask spread as measure of illiquidity in equity and credit markets. However, in Appendix A2 we
perform Principal Component Analysis on different illiquidity proxies (for trading costs, trading frequency, and trading
impact on prices) to investigate on the informativeness of bid-ask spreads as measures of illiquidity in both markets.
5 For all firms, return and price spillovers run from equity to CDS; for a large number of firms volatility spillovers run
from CDS to equity.
2
ample of the scale of these market-wide factors on cross-market illiquidity transmission. The early
literature on limits to arbitrage (Schleifer and Vishny 1997, Kyle and Xiong 2001, Xiong 2001, Gromb
and Vayanos 2002) argues that wealth constraints experienced by traders give rise to withdrawal of
market liquidity. Similarly, the Brunnermeier and Pedersen (2009) model shows how the ability of
traders to provide market liquidity across multiple markets depends on the availability of funding.
The Gromb and Vayanos (2010) model shows that arbitrageurs’ financial constraints create a linkage
across otherwise independent assets, i.e. fundamental and supply shocks to one arbitrageur’s investment opportunity affect the liquidity and risk premia of all her opportunities. Comerton-Forde et al
(2010), Garleanu and Pedersen (2011), Hameed et al (2010), and Ben-David et al (2012), amongst
others, provide empirical evidence for the mentioned theories. Cespa and Foucault (2011) model
departs from this earlier literature: in this model the illiquidity spillovers across securities with correlated payoffs rely on dealers’ attention to prices across markets. Since the dealers in one security
pay attention to the price of the other security, when one market is less liquid, its price noisier, and
the price-embedded information less transparent, liquidity declines also in the other market.
Besides the theory on funding constraints and market volatility, our paper proposes and tests an
additional channel of illiquidity propagation across asset-markets. Equity and credit are fundamentallyrelated since they both represent claims written on the same underlying firm’s assets (contingentclaim approach of Merton (1974) structural model). Consistently, prices in the equity and credit
markets appear to co-move substantially over time6 . Sophisticated arbitrageurs with informational
advantage -also know as capital structure arbitrageurs- trade on this fundamental (arbitrage) linkage. They take simultaneous positions in equity and credit to benefit from mispricings across the
two markets. Other traders simply exploit the credit-equity linkage for hedging purposes. All these
traders decide the amount of equity and credit to be held in their portfolios according to the hedge
ratio estimated from the structural model. This ratio measures the sensitivity of debt to changes
in equity value and ensures that traders can correctly cover the risk of their credit exposures in the
equity market. The cross-market positions are therefore proportional to the hedge ratio.
When the credit conditions of a firm worsen and when the firm’s assets become more volatile,
the hedge ratio increases. This means that credit and equity markets become more integrated. The
increased linkage translates in higher credit risk and larger trade-rebalancing needs for those traders
who hold positions contemporaneously in CDS and equity claims of the same firm. This paper illustrates how and tests whether higher hedging and arbitrage trading across markets can trigger
larger bid-ask spreads in both equity and credit markets, therefore causing a surge in their illiquidity
commonality7 .
6 See
Figure 1 displaying a close relation between average CDS premium and inverse of average equity price for the firms
in our sample.
7 The intuition behind this channel of cross-market illiquidity transmission is explained in Section 3.5
3
We use panel analysis to test whether the illiquidity spillovers across credit and equity can be
explained by the hedge ratio. We find that the hedge ratio (estimated from the Merton model8 ) is
a main determinant of illiquidity commonality and its contribution remains economically and statistically significant even after controlling for funding illiquidity, systematic risk factors, and market
volatility.
Additionally, we examine the determinants of CDS bid-ask spread, using some of the insights
from the previous analysis. After controlling for CDS bid-ask serial correlation, cost of funding,
and market volatility, we find that hedging costs and informed trading flows across CDS and equity
markets (indicative of sophisticated arbitrage trading) increase the CDS bid-ask spread.
The rest of the paper is organized as follows. Section 2 describes the data employed and carries
on statistical analysis to detect equity-CDS illiquidity co-movements. Section 3 presents preliminary
analysis on illiquidity, return, and volatility spillovers and explains potential drivers of the illiquidity
co-movement. This section also describes an arbitrage/hedging channel of cross-market illiquidity
transmissions and formulates the main hypothesis to be tested in the rest of the paper. Sections 4
and 5 explain the empirical methodology for two different tests of the arbitrage/hedging channel and
examine the respective results. Section 6 concludes.
2
Statistical Analysis on Equity and CDS Bid-Ask Spreads:
Detecting Illiquidity Commonality
In this Section we perform an analysis of co-movements between equity and CDS illiquidity using
equity and CDS percentage bid-ask spreads9 ,10 . We employ data on 51 U.S. investment-grade companies which are components of the Dow Jones 5-years On-the-run CDX North America Investment
Grade Index (CDX.NA.IG). The CDX.NA.IG index is composed of 125 firms; however, 51 companies
(6 financial and 45 industrial firms) remain after excluding those recording missing values in the CDS
prices series for more than 20 consecutive days. We include only investment-grade firms in our sample
because they do no suffer from distress or restructuring events over the period considered and from
structural illiquidity. The companies have large market capitalization and are typically followed by a
large number of analysts. For each firm we select the corresponding stock and the 5 years on-the-run
credit default swap. We collect daily quotes (bid and ask prices) and daily close trading data (price
and volume) for firms’ stocks from the CRSP Daily Stock dataset. The sample period goes from
8 We
calibrate the Merton model in order to estimate the sensitivity of debt to equity (hedge ratio) which determines
the size of the equity position relative to the CDS position in the arbitrage/hedging strategy. One of the underlying
assumptions is that sophisticated investors use Merton’s structural model to perform arbitrage trading across equity
and credit markets. This assumption is not far from the actual practice of capital structure arbitrageurs - mainly
hedge funds - who refer to modified implementations of Merton’s model (the most popular proprietary models used
are Moody’s KMV and RiskMetrics’ CreditGrades).
9 Equity bid and ask prices are quoted in dollar terms, while CDS bid and ask prices are quoted in basis points. Therefore,
for CDS bid-ask spread we use the difference between quoted bid and ask prices (in percentage units), while for equity
bid-ask spread we used the ratio between quoted bid-ask spread and midquote price (in percentage units).
10 Most prior literature has examined illiquidity using different proxies for each specific market (Spiegel 2008). In
Appendix A2 we ascertain that the percentage bid-ask spread can be good a measure of illiquidity for both equity
and CDSs by performing Principal Component Analysis across a number of illiquidity proxies at weekly frequency:
Amihud measure, Roll measure, effective spread, percentage bid-ask spread, run length, and inverse turnover index.
4
April 2003 to December 2009. The CRSP stock dataset includes all transactions and quotes from
NYSE, AMEX, and NASDAQ. Daily quotes and prices for CDSs are available on Bloomberg. We
use only CDS contracts with a maturity of five years because the trading liquidity is highest in this
maturity. The CDS data provided by Bloomberg are daily price information contributed by some of
the leading market participants. Bloomberg constructs a composite quote called Bloomberg Generic,
which reflects the arithmetic average across the CDS spreads offered by various market participants.
When calculating the generic time-series, Bloomberg excludes the infrequent quotes, but not the
outliers. Bid and ask prices are daily averages of market quotations, rather then transaction-based
prices. This has some advantages, as highlighted by Völz and Wedow (2009). Firstly, the Bloomberg
Generic time series covers a wide range of CDS price information from various participants, rather
than being broker-specific information that might not reflect true conditions of the inter-dealer market. Secondly, the average provides the advantage that prices are not distorted by the evaluation of a
single market participant. Finally, while some CDSs may only be rarely traded, the indicative quotes
reflect the broader picture of market activity. Appendix A1 provides all details on the treatment and
filtering of the data employed.
In Figures 2, 3, and 4 the normalized percentage equity and CDS bid-ask spreads are compared
over the whole sample and in two sub-samples, before and after the recent financial crisis (i.e. July
2003-December 2006 and January 2007-December 2009). Equity and CDS bid-ask spreads are closely
related: both are downward trending over the pre-crisis period, jump upwards during the crisis period
and decline towards the end of the sample. Table 1 displays summary statistics on aggregate equity
and CDS bid-ask spreads at weekly frequency over the whole sample (April 2003 - December 2009).
On average equity bid-ask spread is larger and more volatile than CDS bid-ask spread11 .
Table 2 shows Pearson, Kendall’s Tau, and Spearman’s Rho measures of correlation between
weighted-average equity and CDS bid-ask spreads. The three estimated correlations are used as
alternative measures of illiquidity commonality. Pearson correlation (ψ) measures the degree of
linear association between equity and CDS bid-ask spreads. Rank correlation coefficients, such as
Spearman’s rank correlation (ρ) and Kendall’s rank correlation (τ ), measure how well the relationship between the two variables can be described using a monotonic function, without requiring the
function to be linear12 . Time average correlations are quite high, in the range of 20%-55% for the
whole sample period, and respectively 36%-77% and 15%-45% in the period 2003-2006 and 20072009. Table 3 shows the distributions of the time-average measures of correlation across all 51 firms
in the sample. Despite the dispersion of values being quite wide, the estimated measures remain
mostly positive (over the whole sample period, as well as over the pre-crisis and crisis sub-samples).
Correlation distributions present insignificant or slightly negative mean values only in the middle
of the period (2005-2006, results available upon request). Figure 5 illustrates the three measures of
correlation between equity and CDS bid-ask spreads in cross-sectional average. The average correlation measures are larger (in the range of 10-20%) over periods of higher turbulence (from the second
11 Our
result contradicts the finding of Hilscher et al (2011). They calculate that the CDS bid-ask spread is higher then
the equity bid-ask spread on average and speculate that informed trading privileges the most liquid market (i.e. the
equity one). Consistently with their conjecture and our results, we should instead support the hypothesis that most
informed trading may take place in the CDS market (as in Acharya and Johnson, 2007).
12 In our study Fisher z-transformation (inverse hyperbolic function) is applied to all sample correlation coefficients r
1+r
(where r = (ψ, τ, ρ)): z = 0.5ln( 1−r
) (See Section 4 at 4.1).
5
quarter of 2003 to the beginning of 2004; and from the third quarter of 2007 until the third quarter
of 2009) than in the middle and at the end of the sample.
To summarize this preliminary statistical analysis, we have found illiquidity commonality across
equity and CDS using different measures of association between equity and CDS bid-ask spreads of
51 firms. However, the illiquidity co-movement varies over time and becomes more prominent over
periods of higher market turbulence, that is in 2003 and in 2007-2009.
3
Drivers of Equity-Credit Illiquidity Co-movements
Statistical analysis has detected the existence of illiquidity commonality across equity and CDS bidask spreads and found that the co-movement is substantial during crisis periods. The next step of
the analysis is to investigate on: (1) the existence (and direction) of illiquidity spillovers across the
two assets; and (2) the sources of the illiquidity co-movement.
While the simultaneous increase in equity and CDS bid-ask spreads can be the consequence of
a rational response of dealers in segmented equity and CDS markets to market-wide frictions or
to adverse movements in the firm’s fundamentals (for example, an increase in asset volatility or a
decrease in asset quality), the existence of illiquidity spillovers (in one or both directions) could be
ascribed to trading patterns across equity and CDS markets.
3.1
Illiquidity Spillovers
We test for the existence of illiquidity spillovers across equity and credit markets for the 51 firms
in our sample by performing pair-wise Granger causality tests at individual firm level for CDS and
equity bid-ask spreads. We use daily data and include two and four lags. The sample period runs
from April 2003 to December 2009. We also perform vector autoregressive (VAR) analysis at individual firm level including daily equity and CDS bid-ask spreads and prices. The VAR analysis can
however detect only lead/lag relationships and not causality across equity and CDS markets.
Tables 4 and 5 show the results of Granger causality tests between CDS and equity bid-ask
spreads including 2 lags: the causality runs from CDS to Equity for 27 firms and in both directions
for 21 firms (but for 13 of these firms the evidence of casuality running from CDS to equity is much
stronger than the other way round). When we increase the number of lags to 4 we find even stronger
evidence in favour of CDS-to-equity causality for 34 firms. Since the causality relationship may be
(but not necessarily is) reflected in a “lead” of the CDS market on the equity market, we perform
VAR analysis on daily individual firms’ CDS and equity bid-ask spreads and prices to obtain more
robust results in terms of illiquidity spillovers . The lags included in the VAR are set using Schwartz
information criterion. The VAR tests show that, after controlling for past prices effects, lead/lag
illiquidity connections between equity and CDS markets exist for 45 firms over 51. For 13 firms
lagged values of CDS bid-ask spreads affect current equity bid-ask spread but not the other way
round; for 8 firms lagged values of equity bid-ask spread affect current CDS bid-ask spread but
not the other way round; while for 24 firms both effects are present13 . The VAR results are quite
13 Detailed
results of VAR analysis at firm level are not reported for brevity, but they are available upon request. VAR
6
conservative because the VAR performs controls also on past price effects. However, the VAR tests
show that there are illiquidity connections across the two markets and the Granger causality tests
detect a more pronounced evidence of contagion running from CDS to equity.
3.2
Return and Volatility Spillovers
Next, we gather some preliminary evidence on possible sources of cross-market illiquidity spillovers.
We start with analysing the relationship between CDS and equity returns. The worsening of firm’s
asset quality can trigger an increase in both CDS and equity bid-ask spreads. Meanwhile, it also
causes an increase in the firm’s CDS premium and a decrease in its equity price. If the same information on asset quality is impounded in both returns (prices) and bid-ask spreads, consistently with
the results on illiquidity spillovers’ direction, we should observe stronger evidence of CDS returns
(premia) Granger causing equity returns (prices). Therefore, we examine the causality relationship
between equity and credit returns for each company in the sample. We find that for almost all firms
equity returns Granger cause CDS returns, but not the other way round (see Tables 6 and 7). The
same results are found for returns calculated on both transaction prices and midquote prices and for
equity-CDS prices (unreported for brevity, but available upon request)14 .
Next, we study the relationship between CDS and equity volatility. Since a surge in volatility also
determines an increase in bid-ask spreads, we investigate whether the existence and the direction of
the illiquidity spillovers are consistent with the results of the Granger causality tests for equity and
CDS volatilities (Tables 8 and 9). All volatilities are computed at daily frequency as exponentially
weighted moving averages on a rolling window of 120 days of CDS and equity return data. The
study of volatility spillovers reveals that higher CDS volatility drives higher equity volatility more
frequently than the other way round (in 18 cases versus 6, while for 16 firms volatility spillovers
are detected in both directions). However, at individual firm level, the results on the direction of
Granger causality for CDS-equity bid-ask spreads and volatilities match only for 27% of the firms in
the sample.
While these findings indicate that illiquidity spillovers may not only be a by-product of returns
and volatility spillovers across equity and credit markets, they also suggest that different sets of
information might be anticipated in one market and then transmitted to the other one. For example,
while new information affecting the average performance of the firm may be firstly incorporated in
the equity returns/prices and then transmitted to the CDS returns/premia, more extreme shifts in
beliefs that generate higher volatility of firm’s assets and increase in bid-ask spreads for a large set
of firms may be detected first in the CDS market and then transmitted to the equity market.
analysis has been also performed on prices and on returns (without bid-ask spreads). In all cases we detect price
and return influences across both markets. This evidence offers some support to Cespa and Foucault (2011) theory
that illiquidity spillovers might be explained by dealers’ attention to prices across markets. However, their behavioral
explanation may result incomplete or insufficient when the markets analyzed share common fundamentals. Equity
and CDS illiquidity commonality might be explained by rational dealers’ attention to common fundamentals affecting
prices in both markets, rather than by their passive attention to prices across market. Moreover, the idea of separate
trading over segmented markets can be challenged by the hypothesis of traders taking positions in both markets for
arbitrage and hedging purposes.
14 This result is consistent with the result of Norden and Weber (2009) who find that equity returns lead CDS price
changes much more frequently than the other way round.
7
The contingent-claim approach offers some support to this conjecture. According to Merton
(1974) model the equity of an investment-grade firm (as those in our sample) corresponds to an
in-the-money option written on the underlying firm’s assets; while the CDS is equivalent to a deep
out-the-money put option with same underlying. Zhou (2005) finds that in-the-money options attract investors who possess mild firm-specific information (on price), while deep out-of-the-money
options catch the attention of those who possess extreme information (on volatility).
Consistently, Acharya and Johnson (2007) find that CDS can lead equity when there are bad
news about a specific company; Qiu and Yu (2012) show that most of the information flow from the
CDS to the equity market takes place before adverse credit events; and Marsh and Wagner (2012)
find that CDS markets lag equities in pricing good news about the general economy, but they quickly
impound firm-specific bad news.
From the Grange causality tests in our paper CDS volatility appears to lead equity volatility,
while equity returns lead CDS returns. Since the empirical literature suggests that volatility is more
affected by past negative news than by past positive news (see, for example, Dufour et al, 2008)15 ,
our results are compatible and consistent with the hypothesis of CDS market quickly impounding
(extreme) bad news and transmitting them to the equity market. The equity and CDS daily data and
the Granger causality tests we have employed suggests the possibility of a trading channel through
which negative information and illiquidity are transmitted for CDS to equity markets.
While this paper is focused on an investigation of CDS-equity illiquidity co-movements, future
research can be done on a more extensive identification of the sources and nature of information
flows across equity and credit markets and their effect on prices and bid-ask spreads of the relative
claims. This research would expand the flourishing literature on the topic16 .
3.3
Market-wide vs Firm-specific Drivers of CDS and Equity Illiquidity
The final test we perform in this Section aims at disentangling the separate contributions of marketwide and firm-specific factors to CDS and equity bid-ask spreads. We define market-wide sources
of illiquidity those frictions which might affect the transaction costs of different assets within the
same market (i.e. stocks of different companies, or CDSs issued on the debt of different companies).
We define asset-specific sources of illiquidity the variables that might affect both equity and CDS
contract of a firm as claims written on the underlying firm’s assets.
15 Chen
and Ghysels (2011) find that moderately good (intra-daily) news reduces volatility (the next day), while both
very good news (unusual high intra-daily positive returns) and bad news (negative returns) increase volatility, with the
latter having a more severe impact. Additionally, the ARCH literature has assessed that negative equity returns lead
to higher impact on future volatility than positive returns (see the reviews by Bollerslev, Engle, and Nelson, 1994; and
Andersen, Bollerselv, Christoffersen, and Diebold, 2006). Recent work has also found evidence of this relationship using
high frequency returns (see Bollerslev, Litvinova, and Tauchen, 2006; Barndorff-Nielsen, Kinnebrock, and Shephard,
2010; Visser, 2008). Patton and Sheppard (2011) also find that future volatility is much more strongly related to the
volatility of past negative returns than to that of positive returns.
16 Future work employing intra-daily and actual transaction data in CDS and equity markets would be very valuable in
shedding further light on this issue.
8
According to the contingent claims approach of the structural models (see Appendix B) when a
firm’s asset volatility increases, equity price decreases while CDS premium increases. The effect of
asset volatility could be extended -in theory- to CDS and equity bid-ask spreads: when firm’s fundamentals worsen and asset volatility increases, dealers rationally increase CDS and equity spreads.
Therefore, a shift in asset volatility might cause an inverse movement in equity and CDS prices and
a positive co-movement in equity and CDS bid-ask spreads.
We test separately for CDS and equity of each firm whether bid-ask spreads are affected by
market-wide and/or asset-specific factors. We perform regressions of CDS (equity) bid-ask spread
on CDS (equity) market average illiquidity and firm’s asset volatility. Newey-West standard errors
(robust to heteroskedasticity and serial correlation) are computed using GMM. Asset volatility is
estimated as in Schaefer and Strebulaev (2008) from a linear combination of firm’s equity and debt
variance and their covariance (see Appendix B). We perform this regression only for the 45 industrial
firms in our sample, given the different nature of financial companies’ balance sheets.
The regressions reveal that for all firms equity and CDS bid-ask spreads are affected by average
market illiquidity; however, while for 22 firms over 45 (half sample) CDS bid-ask spread is also
strongly positively affected by the firm’s asset volatility, for 80% of the sample this variable has
no significant positive effect on equity bid-ask spread (see Table 10)17 . In (unreported) regression
analysis on CDS and equity prices, we find for a larger number of firms a significant effect of asset
volatility on CDS premium but not on equity price, after controlling for aggregate market effects18 .
These results suggest that firm-specific asset volatility shocks have larger impact on CDS liquidity
and price than on the equity. This may reflect the CDS nature of deep out-the-money put option
written on the firm’s assets, therefore with larger exposure to volatility risk.
3.4
Re-Cap of the Preliminary Results
Our analysis shows so far that: (i) Bid-ask spreads on individual equities and CDSs are closely related, particularly in turbulent periods; (ii) There exist CDS and equity illiquidity spillovers which
for most firms travel from CDS to equity market and do not perfectly reflect the direction of returns
and volatility spillovers across markets; (iii) For almost all firms equity returns spill over CDS returns, while for a large number of firms volatility spillovers display an opposite direction; and (iv)
For a large number of firms asset volatility has positive influence on CDS illiquidity, while only for
few firms it affects equity illiquidity (after controlling for the general level of market illiquidity).
Thus, the co-movement in equity and CDS illiquidity may not only be the consequence of higher
asset volatility, worse asset quality, or higher general illiquidity, producing a separate response of
equity and CDS dealers. The illiquidity spillovers across CDS and equity may be the result of crossmarket trading activity. We define an alternative channel of illiquidity transmission across equity
and credit and call it “Equity-CDS Arbitrage/Hedging Channel”.
17 This
evidence does not change substantially between more volatile and calmer periods. Moreover, no significant
cross-sectional differences among firms (by sector, industry, and size) are found in the results of this analysis.
18 Also this evidence does not change substantially between more volatile and calmer periods and no significant crosssectional differences among firms (by sector, industry, size) are found in the results.
9
3.5
Arbitrage/Hedging Channel of Illiquidity Commonality across Equity
and CDS Markets
In this Section we attempt to provide some intuition on a channel of illiquidity transmission across
equity and credit markets based on the behaviour of different groups of traders, which will be then
used to formulate the central hypothesis of the paper. The intuition is supported by our empirical
results in Section 3 and by recent literature on CDS and equity microstructure (see Qiu and Yu,
2012, amongst others19 ) to which we refer throughout the exposition.
3.5.1
Some Basic Facts on CDS and Equity Market Microstructure
In normal times, equity and CDS are highly liquid markets. In particular, the CDS market is much
more liquid than the bond market20 . While the traders’ composition in the equity markets is very
heterogeneous, the CDS market is mainly a venue for speculative and hedging activity of institutional investors. For example, hedge funds and private equity firms use CDSs for a variety of trading
strategies (popularly known as capital structure arbitrage) that attempt to arbitrage across equity
and credit markets21 .
Dealers in CDS and equity markets are different. The CDS market is a bilateral dealership
over-the-counter market, with no centralized quote disclosure mechanism and with a less than fully
competitive network of (private) dealers, usually controlled by a group of major banks22 . In the CDS
market many banks act as dealers by posting bid and ask quotes for CDS protection. Apart from
their role as dealers, banks use CDSs also for managing the risk connected to their own loan exposure
(and they are net buyers of CDS protection)23 . Therefore, some of the dealers in the CDS market
have potentially access to companies’ private credit information. As Qiu and Yu (2012) notice: “ this
blurs the traditional boundary between dealers and non-dealers; rather it is the decision of supply
19 Further
research is needed however to develop a partial equilibrium market microstructure model for illiquidity commonality and contagion between pairs of assets with correlated payoffs and fundamental linkages.
20 Corporate bond markets often lack liquidity, which explains the presence of a substantial liquidity premium in bond
yields. According to different studies, CDS spreads incorporate a lower liquidity premium than bonds (see Longstaff
et al. 2005; Cossin and Lu, 2005; Crouch and Marsh, 2005; and Zhu, 2006), especially for the 5-year maturity, which
is the most traded maturity. The CDS market is the market investors are likely to turn to when they want to liquidate
their credit positions. Several factors underpin the greater liquidity of the CDS market, as explained by Coudert and
Gex (2010). First, when an investor wants to liquidate a CDS position, he does not have to sell it back on the market,
but he can write another contract in the opposite direction, which is of course not possible for bonds. Second, CDS
contracts are not in limited supply like bonds, so they can be sold in arbitrarily large amounts. Third, the CDS market
on a given borrower is not fragmented as the bond market, being made up of all its successive issuances. Fourth, a
number of investors, such as insurance companies or pension funds, purchase bonds as part of a “buy and hold” strategy,
whereas CDS sellers are more active on the market. For corporates, the CDS market has nearly outsized the bond
market, as it reached USD 9.7 trillion versus USD 10.0 trillion for long-term debt securities in September 2009 (BIS,
Quarterly Review, March 2010).
21 Hedge funds constitute a major force in the CDS market. Between 2004 and 2006 they doubled their market share
and with 30% of volume traded on both sides of the market, they became the second largest group in the CDS market,
after banks.
22 According to a survey by Fitch (2009), conducted amongst 26 banks which play a major role in the CDS market, the
5 largest banks were responsible for 88% of notional amount bought and sold
23 Banks’ trading activity constitutes respectively 33% and 36% of total volume of CDS sold and bought (BBA, 2006).
Banks’ loan portfolio activity represents instead 7% of total sold volume of CDS, and 18% of total bought volume
(BBA, 2006). On the sell side of the CDS market insurance companies are also particularly active and provide around
18% of total CDS supply (BBA, 2006).
10
or take liquidity that distinguish the participants” in the CDS market. The role of the dealers in
the equity market is much less ambiguous as they are at all effects liquidity-providers with no particular information advantage on the shares they provide a market for. Moreover, firms’ stocks are
exchange-traded and all dealers can access a centralized and transparent quote disclosure mechanism.
Despite their differences, in both CDS and equity markets the fundamental role of the dealers
is to provide liquidity in the relative assets. The dealer buys a security on its own account (at the
bid price) or sell a security from its own account (at the ask price). The bid-ask spread is the cost
of a round-trip transaction and also represents the compensation earned by a dealer for providing
liquidity. Dealers try to make a profit by maximizing the spreads they earn, given the costs they
have to bear. Below we analyse some of these dealership costs and their possible effects on the
co-movement between equity and CDS bid-ask spreads.
3.5.2
The Behaviour of Traders across CDS and Equity Markets
Let us consider the three groups of agents examined by most market microstructure models: i) Wellinformed risk-neutral arbitrageurs; ii) Risk-averse noise traders; and iii) Risk-averse dealers. In the
CDS market the dealers can be informed or uninformed agents, while noise traders are uninformed
agents mostly in demand for CDS protection24 . In the equity market dealers and noise traders are
uninformed agents. Noise traders trade mainly for liquidity reasons.
When firms’ credit conditions worsen25 , the debt-to-equity hedge ratios of the firms increase26
and noise traders demand more CDS insurance to protect themselves against the higher likelihood
of firms’ defaults and losses on their bond positions. Qiu and Yu (2012) find that higher hedging
demand triggers more supply from CDS dealers only when markets are relatively calm. Instead, during periods that precede steep increases in CDS premia and in the hedge ratios, fewer CDS dealers
supply liquidity to the CDS market.
Building on this result, we conjecture that if the firm’s default risk is moderate and its hedge
ratio not too high, then the CDS dealer provides additional liquidity supply. Being risk-averse, the
CDS dealer hedges her short position in CDS (say X) by shorting corresponding equity (hX). If the
default event becomes more likely and hedging increasingly difficult, the CDS dealers reduces her
24 For
example, bond market investors with passive hedging demand. The CDS market is vastly populated by traders
who take position only for hedging purposes and non-speculative desires. CDS dealers are in fact net sellers of CDS
to noise traders
25 This expository choice is consistent with the observation that the illiquidity commonality phenomenon appears mainly
during crisis periods
26 Credit protection is conceptually similar to a put option on the underlying firm value. For firms with better credit
ratings, which tend to be far from default, such puts are further out of the money. The elasticity H of the CDS (or put
option) to equity is equal to the debt-to-equity hedge ratio h = ∂CDS/∂E (or delta) multiplied by the ratio of equity
price to CDS (or put option) price (see Appendix B). A higher hedge ratio means that credit quality deteriorates,
credit risk is higher, and credit and equity markets are more integrated (i.e. credit price reacts more to changes in
equity). If a trader wants to invest Y in the CDS market and hedge for underlying fundamental value risk, she should
invest hY in the equity market. Similarly, if a trader wants to invest Y in the equity market and hedge for underlying
fundamental value risk, she should invest (1/h)Y in the CDS market. The bigger is h, the more difficult is to hedge
a CDS position, as this requires an increasing position in equity. However, when h increases, the incentive to hedge
CDS position in the equity increases as well.
11
supply of CDSs (by taking the opposite position on the CDS contract) and liquidates her position in
the “hedging”-equity. The implicit cost of this liquidation is the bid-ask spread of the “hedging” and
it is charged by the dealer in the bid-ask she sets in the CDS market27 .
The hedging costs of market making have been analysed by Cho and Engle (1999), Kaul, Nimalendran, Zhang (2004), Landsiedl (2005), Petrella (2006), and Neri and Engle (2010) in the option
market microstructure literature, where an explicit connection between equity and option bid-ask
spreads is established via the hedging activity of dealers. In this paper we attempt to verify the
existence of hedging costs for CDS and equity bid-ask spreads. The hedging channel can be a source
of firm-specific illiquidity commonality. If CDS and equity bid-ask spreads co-move in proportion to
the delta-hedge of the cross-market position, then the illiquidity commonality increases with the size
of the hedge ratio28 (and this should be also large enough to have any recognizable effect).
Furthermore, the reduction of CDS supply from CDS dealers (while demand for protection is
high) may generate a supply-demand imbalance. This can cause credit premia to set above their
fair value. The rise of a mispricing fuels arbitrage trading across the CDS and equity markets for a
specific firm. Arbitrageurs (in particular hedge funds) are well-informed traders. They can evaluate
the intrinsic value of credit spreads by setting them equal to synthetic option-based spreads from
a sophisticated model based on the company’s liability structure and equity volatility. When an
arbitrageur recognizes a mispricing between equity and relative CDS, she may decide to perform
credit-equity arbitrage (so-called capital structure arbitrage)29 . If the arbitrageur believes that the
credit spread observed for a specific firm is too high with respect to its equity value, she takes a
short position (Z) in CDS and a short position (hZ) in the corresponding equity. Suppose that a
group of arbitrageurs believe that for the same firm CDS is overvalued. Hence, they perform trading
across credit/equity of the identified firm: they go short on the corresponding CDS and short on
the corresponding equity. This cross-market trading should narrow the mispricing between CDS and
equity. The size of the cross-market position is determined by delta hedging, therefore it is equal or
27 Once
the dealer sells the CDS, it sells the corresponding equity as well paying the bid-ask spread on the equity as cost
of the round trip transaction. The bid-ask spread that the dealer charges on the CDS transaction in this case should
include the cost borne to hedge the positions (Cho and Engle, 1999) which is given by the size of the position on the
equity (delta determined by the hedge ratio) times the equity bid-ask spread paid.
28 Moreover, this is a potential channel for the illiquidity spill-overs asymmetry. Since it is easier to hedge equity position
with CDS than the other way around when the hedge ratio is particularly high, we should expect a stronger effect of
spillovers from CDS bid-ask spread to equity bid-ask spread, than the opposite. This is consistent with our result in
Section 3.1.
29 In more general terms, the capital structure arbitrage (CSA) is a trading strategy that attempts to exploit mispricing
between a company’s liabilities, most commonly between equity and straight or convertible debt. In recent years such
strategies have become increasingly popular, particularly among hedge funds, possibly as a result of the development
of the credit default swap market that has allowed market participants to take short positions in a credit risk more
easily (Currie and Morris, 2002). Yu (2005) analyses CSA convergence trades involving credit default swaps (CDS) and
equity. He finds these trades to be “quite risky” and, in particular, prone to large losses when CDS spreads rise quickly.
However, in this analysis Yu (2005) also finds that “when the individual trades are aggregated into monthly capital
structure arbitrage portfolio returns, the strategy appears to offer attractive Sharpe ratios”. In related analysis, Duarte,
Longstaff, and Yu (2005) find that CDS-based capital structure arbitrage and find that this can produce promising
Sharpe ratios of approximately 0.8. Finally, Kapadia and Pu (2012) analyse the limited arbitrage across equity and
CDS, due to arbitrageurs’inattention and funding limitations, as source of persistent misalignment between CDS and
equity prices
12
proportional to the debt-to-equity hedge ratio estimated using the sophisticated structural model30 .
An increase in the hedge ratio commands larger cross-market positions for delta-hedging and - therefore - larger liquidity demand across markets from arbitrageurs/informed traders31 .
If arbitrageurs are more informed than noise traders and dealers in both CDS and equity markets,
then, according to the mainstream microstructure models of asymmetric information (see, amongst
others, Glosten and Milgrom, 1985; Kyle, 1985; Amihud and Mendelson, 1986; Easley and O’Hara,
1987; and Admati and Pfleiderer, 1988), the bid-ask spreads should increase in both markets. The
cross-arbitrage would in fact generate informed flows in both the CDS and equity markets (respectively, Z and hZ)32 . Accordingly, when credit-equity arbitrage become possible (i.e. the CDS
mispricing and h are significantly above 0) bid-ask spreads should increase in both markets due to
a surge in adverse selection. This is another potential source of illiquidity commonality33 . While
it is hardly arguable that sophisticated arbitrageurs are more informed than equity dealers, to the
extent that the CDS market liquidity can be provided by both informed and uniformed dealers, the
relationship between informed arbitrage trading and CDS bid-ask spread remains an empirical issue.
On the one hand, the dominant role played by potentially informed dealers (i.e. banks) may set the
CDS apart from equity market (Qiu and Yu, 2012). On the other hand, it is highly probable that
when credit events increase (as for example in the 2007-08 financial crisis), the CDS dealers who
remain available to supply liquidity to noise traders are mainly uninformed agents.
In conclusion, when firms’ credit conditions worsen, co-movements between CDS and equity bidask spreads can arise because of:
1) Higher hedging needs of CDS dealers:
The dealers recover these hedging costs by setting higher CDS bid-ask spreads, in proportion to the
bid-ask spreads paid on the equity-“hedging” market (i.e. hedge ratio times equity bid-ask spread);
2) Larger demand of liquidity across CDS and equity markets from capital structure arbitrageurs:
Uniformed dealers will seek protection against superior information of capital structure arbitrageurs
by setting higher bid-ask spreads in equity and credit markets, respectively in proportion to the size
of the CDS informed flow (Z) and the size of the equity informed flow (hZ).
30 Yu
(2005) reports that: “From what traders describe in media accounts, the equity hedge is often ”static“, staying
unchanged through the duration of the strategy. Moreover, traders often modify the model-based hedge ratio according
to their own opinion of the particular type of convergence that is likely to occur”. For example “the trader may decide
to underhedge” or “he may overhedge.”
31 A model by Fernando et al (2008) suggests that the commonality in illiquidity is higher for securities traded in markets
where a small group of traders operate and pursue similar trading strategies. This is compatible with the cross-market
trading generated by capital structure arbitrage hedge funds.
32 If a dealer could hedge all the risk related to her CDS position in the equity market, no cost related to the risk of
informed trading in the CDS market would arise. Nevertheless, not all risk related to the unbalanced exposure can be
hedged. The hedging activity requires the dealer to have simultaneous active and frictionless exposure to both equity
and CDS markets. The decentralization in market making can be a problem for the coordination of risk management
decisions and it can render the hedging activity more expensive. It is more likely that the dealer applies a form of
partial, rather than perfect, hedging or no hedging at all. Therefore, she remains exposed to the risk of losses due to
informed trading.
33 The literature on liquidity shocks transmission across correlated assets via arbitrage trading has seen some developments
in very recent times (see, for example, the theoretical model by Gromb and Vayanos, 2010, and the empirical work on
equities and ETFs by Franzoni et al, 2012).
13
Accordingly, we derive the following hypothesis:
Hypothesis. Equity-CDS Arbitrage/Hedging Channel of Illiquidity Commonality:
The commonality of illiquidity across equity and credit markets increases with the hedge ratio.
In the reminder of the paper we set and perform some tests to disentangle whether equityCDS illiquidity commonality can be significantly explained by the arbitrage/hedge trading channel
- proxied by the hedge ratio - even after controlling for the effect of exogenous frictions (funding,
market, and systematic risk factors). In fact, as previous literature has pointed out, the ability
of market makers to provide liquidity depends also on their funding availability and aversion to
systematic risk. The equity-CDS arbitrage/hedging channel implies instead that illiquidity can comove and spill over across equity and CDS markets even in the absence of systematic risk (Das and
Hanouna, 2009), just as a result of specific trading patterns which intensify during crisis periods34 .
4
4.1
Empirical Test of Determinants of Linkages between Equity
and Credit Illiquidity
Empirical Modelling
In this Section we test the Hypothesis of an arbitrage/hedging channel of illiquidity commonality
across equity and credit markets.
In this test the illiquidity commonality variable CommBA
i,t is represented by the Kendall’s Tau
measure of correlation35 (Fisher-transformed) between daily equity and CDS bid-ask spreads constructed over each quarter from April 2003 to December 2009 for each firm.
As first step we perform a preliminary analysis to filter the illiquidity commonality variable from
the effects of some variables which previous market microstructure literature has found significant in
affecting the cost of market making:
- Firm’s systematic risk (Fama-French three factors M ktRf , SM B, and HM L):
Higher exposure of a firm to market, size, and book-to-market risk factors may cause higher inventory
costs for dealers operating in the CDS and equity market for the specific firm, which then translate
in higher bid-ask spreads.
- Tightening of funds (proxied by the spread between 3-months LIBOR rate and 3-months T-Bill
yield, T ED):
34 We
have shown how the hedging/arbitrage trading can increase illiquidity commonality taking a “directional” view,
i.e. assuming that during the crisis periods higher CDS demand would trigger higher equity-hedging needs and a CDS
mispricing fuelling CDS-equity arbitrage. We cannot completely rule out the possibility that during the crisis a forced
sale of stocks can cause equity to be undervalued, rather than CDS to be overvalued. The CDS-delta factor which
applies in this case is 1/h and it would lead to opposite conclusions: a counter-effect of hedge ratio h on illiquidity
co-movements. Firstly, this is not what we will observe in our data (see Section 4). Secondly, several papers (amongst
others, Dick-Nielsen et al, 2012) have shown that the crisis period has been characterized by a misalignment between
credit prices and equity fundamentals. In particular, bond and CDS spreads have risen above the level predicted by
different structural models of credit risk.
35 Kapadia and Pu (2012) use the Kendall’s Tau to measure the concordance between CDS and equity price changes.
They stress two advantages of using this measures: firstly, the Kendall’s Tau does not need a parametric setup;
secondly, being intuitively related to the variable’s co-movement, it is not affected by interpretation-ambiguity, unlike
other measures such as the coefficient of determination.
14
The increased cost of funding represents a burden on dealers’ costs across many different markets.
Generally, dealers fund and maintain their positions by borrowing (the cost of funding represents also
an opportunity-cost). Therefore, the lack of funding liquidity can generate unwinding of positions
across multiple markets, fire-sales, and large illiquidity discounts on assets. Additionally, the higher
risk of assets’ devaluation can cause further pressure on dealership costs.
- Increase in volatility of markets (measured by the implied S&P500 option volatility index, V IX):
Higher volatility can increase inventory dealership costs and cause dealers to impose larger bid-ask
spreads across all markets where they provide liquidity.
We perform the following preliminary panel least squares regression where we also add a control
for firms’ unobservable fixed effects:
CommBA
i,t = α0 +β1 M ktRft +β2 SM Bt +β3 HM Lt +δ1 T EDt +δ2 V IXt +α1 F irm1 +...+α17 F irm17 +i,t
(1)
where i = 1, . . . , 18 is the firm index; t = 1, . . . , 27 is the time (quarter) index.
The analysis is performed on a sub-sample of 18 non-financial companies which display stationarity in both the illiquidity commonality and the hedge ratio series36 . F irmi represents the fixed
effect (dummy) for firm i (i=1. . . 18).
As second step, we use the residuals from this model Res.CommBA
i,t (so-called filtered illiquidity
commonality) to analyze the effect of the hedge ratio. Using the filtered variable should strongly reduce the possibility that we attribute illiquidity commonality to equity and credit common exposure
to exogenous risk factors (systematic risk, funding illiquidity, and market volatility), rather than to
the hedge ratio which instead captures the extent of credit-to-equity sensitivity and cross-market
trading.
We perform the test using panel least squares regression and estimating firm clustered standard
errors. The estimated equation is:
SS
Res.CommBA
i,t = γ0 + θHi,t + ui,t
(2)
where i = 1, . . . , 18 is the firm index; t = 1, . . . , 27 is the time (quarter) index.
SS
On the right-hand side of Equation (2) we have Hi,t
, the estimated debt-to-equity elasticity (hedge
ratio) for firm i in quarter t. Appendix B describes the two methodologies followed (from Vassalou and Xing, 2004, and Schaefer and Strebulaev, 2008) to estimate the debt-to-equity hedge ratios
on a weekly basis for each firm (sample: April 2003-December 2009)37 using the Merton (1974)
model approach. The two methodologies are called respectively VX and SS for brevity. In the regression specification (2) we employ the hedge ratio obtained from SS methodology. In a further
specification we augment the right-hand side of Equation (2) with Qtr2003:2 , ..., Qtr2009:3 , which
36 Test
of unit roots have been performed on illiquidity commonality and hedge ratio to select these firms. The test are
run using Augmented Dickey-Fuller equation with number of lags lags set by Schwartz information criterion and 5%
confidence level.
37 In addition to equity price data from CRSP and CDS premia from Bloomberg, we employ firms’ accounting information
from COMPUSTAT.
15
represent the fixed quarter of the year effect (dummy). In particular, controlling for time effects
represents a robustness check for the effect of the hedge ratio on illiquidity commonality since time
dummies can capture the effects of extreme events (2003 stock market drop, 2007-07 subprime crisis).
The analysis performed so far could be too conservative if some of the exogenous risk factors
were also influenced by a contemporaneous worsening of firms’ credit conditions and assets volatility,
which ultimately determine the firms’ hedge ratios. In this case the filtering in the first step would
eliminate part of the effect of the hedge ratio. Therefore, we perform another panel regression where
the hedge ratio variable is added to the right-hand side of Equation 1. This analysis allows us also
to evaluate and compare the relative contributions of the hedge factor and the market volatility,
funding, and systemic factors to the increase in equity-CDS illiquidity commonality.
We estimate the augmented equation with least squares and call this second estimation exercise
the “All-in Regression”:
SS
CommBA
i,t = α0 +β1 M ktRft +β2 SM Bt +β3 HM Lt +δ1 T EDt +δ2 V IXt +θHi,t +α1 F irm1 +...+α17 F irm17 +υi,t
(3)
Finally, we repeat the entire analysis replacing the hedge ratio with its component orthogonal
to general market default risk and volatility (H SS,ORT ). This further check is necessary to test
whether the hedge ratio’s influence on the equity-CDS illiquidity commonality does not simply pick
up the increase in default risk and volatility at market level, particularly over the crisis period. A
change in economic conditions can in fact influence the likelihood of all firms’ default and their
hedge ratios. Therefore, to isolate the orthogonal component we regress the hedge ratio on: i) the
difference between the return on Moody’s AAA Index of long-term corporate bonds and the longterm (20 years) government bond yield (default risk factor DEF ) and ii) the V IX index, and take
the residuals from this regression.
4.2
Results of Test of Equity-CDS Arbitrage/Hedging Channel of Illiquidity Commonality
BA
BA
As proxies of illiquidity commonality we consider: ψi,t
, τi,t
, and ρBA
i,t , respectively the Fisher’s
z-Transformation of Pearson Correlation, Kendall’s Tau Rank Correlation, and Spearman’s Rho
Rank Correlation between equity and CDS bid-ask of firm i estimated over each quarter t. We also
consider the same correlation measures for equity and CDS returns of firm i estimated over each
RET
RET
quarter t: ψi,t
, τi,t
, and ρRET
. Table 11 and 12 report respectively the pair-wise correlation
i,t
and (Granger) causality matrices for relevant variables. The hedge ratio is highly correlated with
all alternative measures of illiquidity and return commonality and all these variables are also closely
related to default risk, VIX index, and TED spread (see Table 11). Table 13 display the summary
statistics of these variables. The pair-wise Granger causality matrix in Table 12 identifies for each
pair of variables which causality relationship is most likely. Stronger evidence on causality directions
suggest that all commonality proxies are influenced by the hedge ratio which in turn is affected by
bond market default risk and VIX index. The relationship between illiquidity and return commonality remains instead ambiguous.
16
To test whether the illiquidity commonality can be explained by the hedge ratio and verify the
main hypothesis of the paper, we first need to filter out the effects of firm systematic risk factors
(i.e. exposure to Fama-French factors: size, book-to-market, and market risk), funding cost, and
market volatility from the illiquidity correlation measures between equity and CDS bid-ask spreads
for the 18 non-financial firms. From the preliminary panel regression analysis all these variables are
found positively significant to explain an increase in illiquidity co-movement across equity and credit
of the firms (Table 14, Panel A). Moreover, the likelihood ratio tests of redundancy reveal a limited
contribution of firms’ fixed effects.
Next, using the residuals of the previous panel regression we test the main hypothesis of the
paper. We regress the residual series on the hedge ratio obtained through the SS methodology. The
hedge ratio represents a first approximation of the arbitrage relationship between equity and CDS;
in fact it is obtained as the elasticity of the CDS value to the equity value of the firm (see Appendix
B). When this elasticity changes, the arbitrage relationship between equity and credit changes: informed traders who exploit it (arbitrageurs or speculators) have to rebalance their relative positions
across the two markets. Their rebalancing need represents an act of liquidity-consumption from
informed traders to which dealers (liquidity-providers in the equity and CDS markets) react by increasing equity and credit bid-ask spreads. Moreover, dealers who hedge their credit imbalanced
positions in the equity market will have to pay a higher price for rebalancing the strategy and will
increase the bid-ask spreads to recover the higher equity-hedging costs. Therefore, an increase in
illiquidity co-movement may be driven by an increase in the hedge ratio (or debt-to-equity elasticity).
Figure 6 illustrates the time-series plot of the value-weighted average of the hedge ratio across all
firms. It shows that the average hedge ratio H SS gradually decreases from 2003 over the following
years; it then rises again from the second semester of 2007 and decreases towards the end of 2009.
Figure 7 displays a similar pattern of the average hedge ratios estimated with SS and VX methodology (April 2003-November 2008). Figure 8 shows that the time-pattern of the average hedge ratio
closely tracks CDS market average premia and bid-ask spread. Noticeably, Figure 9 reveals a very
close relation between average hedge ratio and CDS-equity illiquidity commonality over time. This
relation is the object of our investigation.
The results of the panel regression for Equation (2) reported in Table 14 (Panel B) confirm the
existence of a positive relationship between equity-CDS illiquidity co-movements and the hedge ratio.
The hedge ratio is a significant explanatory variable for co-movements of illiquidity only during crisis
periods (2003, and 2007-2009). It must be noted that the sample is composed of investment-grade
firms with low leverage and hedge ratio over calmer periods (2004-2006) when also the illiquidity
correlation across equity and credit is negligible or even slightly negative38 . As a robustness check,
the positive effect of the hedge ratio on the illiquidity commonality survives also when we control for
fixed effects of time (quarters) and when we replace the hedge ratio with its component orthogonal
to market default risk and volatility (Table 14).
When we perform the All-in Panel Regression (Equation 3) we can evaluate the separate influence of the hedge ratio versus exogenous frictions. Panel analysis at individual firm level in Table 15
38 These
intuitive results are unreported, but available upon request
17
(Panel A) reveals a positive significant effect of TED spread, VIX index, and systematic risk factors
on illiquidity commonality, but also a positive influence of the hedge ratio, after controlling for firms’
unobservable fixed effects. In Table 15 (Panel B) we notice that the economic significance of the
hedge ratio in terms of standard deviations impact is around 0.16, while the aggregate economic
significance of all other exogenous factors is about 0.52. When we use the hedge ratio as regressor for
the filtered illiquidity commonality (Equation 2) its economic significance is around 0.12. Consistent
with our concern, we find that the results in terms of hedge ratio effect are typically stronger without
the filtering.
For robustness checks we repeat the previous analysis using:
1) As alternative dependent variables (measure of illiquidity commonality) the Spearman rank measure of association and the Pearson correlation between equity and CDS bid-ask spreads;
2) As alternative proxy for arbitrage/hedging trading the hedge ratio estimated with Vassalou and
Xing (2004) methodology. When we use the hedge ratio from VX Methodology instead of SS Hedge
Ratio we consider a restricted time sample running from April 2003 to October 2008.
A comparison between the results of the three alternative regressions in Panel A of Table 16 shows
that using Spearman instead of Kendall correlation does not change the results, while in the regression that employs the Pearson correlation the hedge ratio and the size factor are the only significant
variables. The economic significance of the hedge ratio remains in a range between 0.13-0.16 standard
deviations impact.
If we replace the hedge ratio estimated using the SS methodology with the one estimated using the
Vassalou-Xing (2004) methodology we find that the latter is also significant in the panel data equations (Table 16, Panel B) and has the same economic significance as the SS hedge ratio. However,
the R-squared halves with respect to the case when we use SS hedge ratio (Table 16, Panel A), so
the VX measure of hedge ratio is less useful than the SS measure.
To conclude this Section, the central hypothesis of the paper cannot be rejected in all performed
tests: the effect of the hedge ratio on equity-CDS illiquidity commonality is strongly significant, both
statistically and economically, even after controlling for relevant exogenous risk factors39 .
39 Given
the unavailability of trading data for CDS markets, to verify that the firm-specific channel of illiquidity commonality is trading-based we rely on a proxy of traders’ changing exposure across markets (the hedge ratio). The frequency
of the analysis is low. However, this should bias the results towards under-detecting the incidence of cross-market
hedging and arbitrage on illiquidity transmission, since the relative trading happens at higher frequency. The data
and tests we have employed are suggestive of the existence of a trading channel for cross-market illiquidity movements.
However, future work employing better proxies for cross-arbitrage and hedging activity, perhaps using intra-day data
on actual transactions in CDS markets, would be valuable in shedding further light on this issue.
18
5
Empirical Test of Determinants of CDS Bid-Ask Spread
One of the insights of the arbitrage/hedging channel of CDS-equity illiquidity commonality illustrated in Section 3.5 is that the dealers in the CDS market: 1) can hedge the risk exposure of their
imbalanced positions on fair market terms in the equity market; and 2) can protect themselves from
potential losses arising from trading with better informed traders (capital structure arbitrageurs).
Furthermore, the dealers need to hold some capital to finance their market making activity and the
hedging and to absorb unhedged risks (hedging and raising external funds are costly). As a consequence, the bid-ask spreads in the CDS markets should be set by dealers upon the cost of the funding
needed and the compensation for an increase in market volatility (which augments the risk of keeping
imbalanced positions and freeze the funding), and also upon the cost of hedging and informed trading
across equity and credit markets. The effects of hedging costs on the CDS bid-ask spread should be
larger when the demand for CDS protection is higher (i.e. when the firm’s credit conditions worsen).
Asymmetric information costs should affect the CDS bid-ask spread more when the CDS mispricing
(and so arbitrageurs’ interest) increases.
In this Section we test whether hedging costs and costs related to trading on private information
across equity and credit markets represent additional determinants of CDS bid-ask spreads.
5.1
Empirical Modelling
We perform the test at weekly frequency. The following elements represent desirable properties of
this test when compared to the previous one performed on the illiquidity commonality variable: (i)
the test is executed on CDS bid-ask spreads directly, therefore it needs not to rely on estimated
measures; (ii) the frequency of the analysis increases from quarterly to weekly; and (iii) the test
employs data for all 45 non-financial companies in the sample after assessing the stationarity of the
relevant variables.
Firstly, we control for the influence on CDS bid-ask spread of its five lagged values, since the
bid-ask spreads have a strong autocorrelated component. We take the residual CDS bid-ask spread
after removing its autocorrelated component and regress it on: (i) TED spread (proxy for funding
constraints), (ii) VIX index (proxy for market volatility), (iii) equity and CDS private information
flows (proxy for asymmetric information costs); and finally (iv) hedging costs represented by the
equity bid-ask spread times the delta-hedging factor.
The following panel regression is estimated:
SS
CDS
Res.BACDS
= αCDS + γ CDS T EDt + δ CDS V IXt + ζ CDS Φi,t + λCDS (BAE
i,t
i,t × hi,t ) + i,t
(4)
Res.BACDS
is the residual CDS bid-ask spread of firm i at time t; T EDt is the (exogenous) cost
i,t
of external funding at time t proxied by the TED spread; V IXt is the (exogenous) proxy for market
SS
volatility40 ; BAE
i,t × hi,t is the cost of hedging an opened credit position on the equity market. Φi,t
represents the private information relative to firm i at time t and includes:
40 VIX
index is also considered a proxy for market risk aversion
19
(1) Information anticipated in CDS returns (according to the discussion in Section 3.2, this could
be mainly related to changes in asset volatility)
(2) Information anticipated by equity returns (according to the discussion in Section 3.2, this could
be mainly related to changes in asset value).
We follow the methodology of Acharya and Johnson (2007) to construct the components (1) and
(2) of Φi,t , which are defined respectively CDS and equity innovations41 . We regress CDS returns
∆CDSi,t (equity returns ∆Ei,t ) on contemporaneous equity (CDS) returns in order to extract the
residual component. We do this by means of separate time-series regressions for each firm i, also
including five lags of CDS and equity returns to absorb any lagged information transmission within
the credit and equity markets. To account for the nonlinear relation between CDS and equity returns,
the regression specification for CDS includes interactions of equity returns (both contemporaneous
and lagged) with inverse CDS level, while the regression specification for equity returns includes
interactions of CDS returns (both contemporaneous and lagged) with CDS level.
P5
P5
CDS
CDS
CDS
∆CDSi,t = αiCDS + k=0 (βi,t−k
+ γi,t−k
/CDSi,t−k )∆Ei,t−k + k=1 δi,t−k
∆CDSi,t−k + uCDS
i,t
P
P
5
5
E
E
E
+ γi,t−k
CDSi,t−k )∆CDSi,t−k + k=1 δi,t−k
∆Ei,t−k + uE
∆Ei,t = αiE + k=0 (βi,t−k
i,t
The residuals u
d
i,t from each regression represent independent news arriving in the credit (or equity)
market at time t that is either not relevant or simply not appreciated by the equity (or credit)
d
\
CDS = CDS Inn and u
E =
market at time t. We will define them CDS (or equity) innovations: u
i,t
i,t
Equity Inn.
5.2
Results of the Test
In panel regression analysis at weekly frequency for CDS bid-ask spreads (Table 17) the hedging and
private information cost components enter significantly in the estimated equations also when TED
spread and market-wide volatility are used as explanatory variables. Both funding costs and market
volatility are positively significant for CDS illiquidity. The two exogenous variables have a larger impact if we perform the analysis only for the crisis period 2007-2009 (unreported results). The panel
analysis allows a direct comparison of the economic impact of hedging and information costs versus
other determinants of the bid-ask spreads. A one standard deviation (SD) change in hedging costs
generates an increase of around 0.04 SD in CDS illiquidity. The economic impact of 1 SD increase
in CDS innovations have more than double impact on CDS bid-ask spreads (0.09). TED and VIX
together have instead an economic impact between 0.08 to 0.12 in the various regression specifications.
CDS and equity innovations (proxies for private information trading in the respective markets)
carry the expected signs: information anticipated in higher CDS returns - more likely related to an
increase in assets’ volatility - move the bid-ask spread upwards; while information anticipated in
positive equity returns - more likely related to an increase in assets’ value - reduce bid-ask spreads.
However, the CDS bid-ask spread is significantly affected only by CDS innovations. This means that
only private negative information in the credit markets can reduce CDS market liquidity through a
widening of the bid-ask spread set by CDS dealers, while private information in the equity market has
no effect on CDS liquidity. To verify whether this result is consistent with the mechanism described
41 Acharya
and Johnson (2007) uses this definition and methodology only for CDS innovations, however this work extends
it to stock innovations.
20
in Section 3.5 we test whether the impact of CDS informed flows widens when CDS mispricing is
substantially positive and high. For the CDS mispricing we use the residual component of CDS
premia regressed on structural variables (leverage ratio, equity volatility, and interest rate). We then
interact the CDS innovations variable with the lagged value of CDS mispricing. Table 17 shows that
the interaction term is significantly positive: more informed flows in the CDS market increase bid-ask
spreads; furthermore, their effect is stronger when the CDS mispricing is larger. A larger CDS mispricing may fuel in fact trading interest of well-informed capital structure arbitrageurs across CDS
and equity markets. In terms of economic significance, on average the interaction term adds 0.00642
to the impact of CDS innovations, which is around 0.09.
The hedging cost component is also found positively significant. In Section 3.5 we conjecture
that if higher demand for CDS protection from noise traders initially triggers larger supply from
CDS dealers, then it also fosters more hedging activity of CDS dealers in equity markets to reduce
the risk of their credit imbalanced positions. The effect of hedging costs should be then more effective
when the CDS demand from noise traders is higher. Since we do possess CDS trading data, we use
as proxy for CDS demand the lagged change in CDS price. The hedging costs interacted with the
proxy for CDS demand has a significant positive coefficient, which supports our conjecture. In terms
of economic significance, on average the interaction term adds 0.0743 to the impact of the hedging
factor, which is around 0.04.
To conclude this Section, the effects of hedging and private information costs are strongly supported by the data, also after controlling for funding and market volatility which are both statistically
and economically significant cost components of CDS bid-ask spreads of individual firms. The hedging and information cost contribute more to CDS illiquidity respectively when CDS demand (from
noise trader seeking protection) is higher, and when the mispricing across CDS and equity is wider
and cross-market trading more attractive to sophisticated arbitrageurs.
42 This
number is calculated by multiplying the economic significance (standardized beta) of the interaction term 0.04
by the average lagged positive CDS mispricing 0.13%.
43 This number is calculated by multiplying the economic significance (standardized beta) of the interaction term 0.09
by the average lagged positive CDS price change 0.78%.
21
6
Conclusions
This paper examines linkages between illiquidity in equity and CDS markets for 51 investment grade
firms and sets a theoretical framework to identify and test the determinants of their co-movements.
The paper demonstrates that part of the illiquidity contagion across equity and credit market is based
on their arbitrage linkage. Equity and CDS are almost substitute assets trading highly-correlated
(firm’s equity and credit) risks, therefore a wave of illiquidity originating in one market can be easily
transmitted to the other.
The paper demonstrates that: (i) Illiquidity co-moves in equity and credit markets, but the
commonality varies in magnitude over time; (ii) There exist illiquidity spillovers across CDS and
equity markets; (iii) Equity and CDS illiquidity are affected by general market-wide illiquidity, but
CDS illiquidity is also particularly sensitive to shifts in firm’s asset volatility; (iv) The equity-CDS
illiquidity transmission is significantly explained by a firm-specific factor (hedge ratio) representing
arbitrage/hedging trading across the two markets, even after controlling for the effect of exogenous
common risk factors (funding and systematic risks); and (v) Hedging and information costs are
significant explanatory variables for bid-ask spreads in the CDS market, even after controlling for
market-wide frictions.
Thus, this work shows that the transmission of illiquidity across markets can be partially explained by an arbitrage/hedging channel. To the best of our knowledge, this channel has never been
considered in previous empirical and theoretical literature. During credit events higher demand for
CDS liquidity provisions can push dealers to equity-hedge more their exposures. When dealers withdraw from providing CDS liquidity, CDS mispricing may raise and fuel CDS-equity arbitrage trading.
Equity and CDS dealers protect themselves from the likelihood of informed trades of sophisticated
arbitrageurs by increasing the bid-ask spreads respectively on equity and CDS.
Rather than identifying only external determinants of equity-CDS illiquidity commonality - such
as an increase in funding costs or general market volatility - this paper shows that the debt-to-equity
hedge ratio alone (as first general approximation of the equity-credit linkage) can explain a significant part of the co-movement. The illiquidity commonality increases with the hedge ratio, even after
controlling for systematic and funding risk factors.
To sum up, this paper makes several important contributions to the emerging literature on illiquidity commonality across asset markets. First, unlike any previous study it examines explicitly the
extent and causes of linkages between the illiquidity of equity and credit (CDS). Second, building on
previous theoretical literature on limits to arbitrage, the paper confirms the contribution of funding
costs and risk-aversion to the increase of illiquidity commonality across equity and credit markets.
This analysis appears of critical importance since the credit crisis, which was mainly characterized
in its early stages by a market-illiquidity contagion episode, exacerbated by traders’ lack of financial
resources which affected their ability to provide liquidity across multiple markets. Third, to the best
of our knowledge, it is the first paper to apply the Merton (1974) structural model to capture the
transmission of illiquidity shocks across correlated equity and credit markets. In particular, we employ Merton’s model to estimate the debt-to-equity hedge ratio and predict illiquidity co-movements
22
across CDS and equity markets due to arbitrage/hedging trading. Last, the paper provides a novel
framework for modelling CDS bid-ask spreads and reveals a significant influence of hedging and information costs, besides funding and risk aversion components, on CDS market illiquidity.
The results of this work can be used to formulate recommendations for regulators and investors to
monitor more closely the transmission of illiquidity shocks across assets, in particular when they are
characterized by common fundamentals, arbitrage connections, and correlated payoffs. In portfolio
allocation and risk management these pairs of assets need to be considered together given that, under
certain conditions, their functionality can be profoundly interrelated: if one asset experiences a drop
of liquidity, it is likely that the other one ceases to function in the same time.
This paper is mainly empirical in nature. However, it also provides some inputs for the development of a consistent theory of illiquidity contagion based on arbitrage linkages and information flows
across correlated assets. This model will provide a natural extension to the paper itself as well as a
continuation of this relatively new research on cross-market illiquidity commonality.
23
References
Acharya, V. V., and T. C. Johnson (2007): “Insider Trading in Credit Derivatives,” Journal of
Financial Economics, (84), 110–141.
Admati, A. R., and P. Pfleiderer (1988): “A Theory of Intraday Patterns: Volume and Price
Variability,” Review of Financial Studies, 1(1).
Amihud, Y. (2002): “Illiquidity and Stock Returns: Cross-Section and Time-Series Effects,” Journal
of Financial Markets, 5, 31–56.
Amihud, Y., and H. Mendelson (1986): “Asset Pricing and the Bid-Ask Spread,” Journal of
Financial Economics, 17, 223–249.
Andersen, T. G., T. Bollerslev, R. F. Christoffersen, and F. X. Diebold (2006): “Volatility and Correlation Forecasting,” Handbook of Economic Forecasting, by G. Elliott, C. Granger,
and A. Timmermann. North Holland Press., 4.
Barndorff-Nielsen, O. E., S. Kinnebrock, and N. Shephard (2010): “Measuring Downside
Risk – Realised Semivariance,” Volatility and Time Series Econometrics: Essays in Honor of
Robert F. Engle, ed. by T. Bollerslev.
Bauer, W. (2004): “Commonality in Pure Order-Driven Markets,” Working Paper.
Ben-David, I., F. Franzoni, and R. Moussawi (2012): “ETFs, Arbitrage, and Contagion,”
Working Paper.
Bharath, S. T., and T. Shumway (2008): “Forecasting Default with the Merton Distance to
Default Model,” Review of Financial Studies, 21(3), 1339–1369.
Black, F., and J. C. Cox (1976): “Valuing Corporate Securities: Some Effects of Bond Indenture
Provisions,” Journal of Finance, 31(2), 351–367.
Black, F., and M. Scholes (1973): “The Pricing of Options and Corporate Liabilities,” Journal
of Political Economy, 81(3), 637–654.
Bollerslev, T., R. F. Engle, and D. B. Nelson (1994): “ARCH Models,” Handbook of Econometrics, 4.
Bollerslev, T., J. Litvinova, and G. Tauchen (2006): “Leverage and Volatility Feedback
Effects in High-Frequency Data,” Journal of Financial Econometrics, 4(3), 353.
Brockman, P., and D. Y. Chung (2002): “Commonality in Liquidity: Evidence from an OrderDriven Market Structure,” Journal of Financial Research, 25(4), 521–539.
Brunnermeier, M., and L. Pedersen (2009): “Market Liquidity and Funding Liquidity,” Review
of Financial Studies, 22(6), 2201–2238.
Cao, M., and J. Wei (2010): “Option Market Liquidity: Commonality and other Characteristics,”
Journal of Financial Markets, 13, 20–48.
24
Cespa, G., and T. Foucault (2011): “Dealer Attention, Liquidity Spillovers, and Endogenous
Market Segmentation,” Working Paper.
Chakravarty, S., and A. Sarkar (2003): “Trading Costs in Three U.S. Bond Markets,” Journal
of Fixed Income, 13(June), 39–48.
Chen, X., and E. Ghysels (2011): “News–Good or Bad–and Its Impact on Volatility Predictions
over Multiple Horizons,” Review of Financial Studies, 24(1), 46–81.
Chordia, T., A. Sarkar, and A. Subrahmanyam (2005): “An Empirical Analysis of Stock and
Bond Market Liquidity,” Review of Financial Studies, 18(1), 85–129.
Comerton-Forde, C., T. Hendershott, C. M. Jones, P. C. Moulton, and M. S. Seasholes
(2010): “Time Variation in Liquidity: The Role of Market-Maker Inventories and Revenues,”
Journal of Finance, 65(1), 295–331.
Cossin, D., and H. Lu (2005): “Are European corporate bonds and default swap markets segmented?,” Working Paper 153, FAME.
Coudert, V., and M. Gex (2010): “Credit default swap and bond markets: which leads the other?,”
Banque de France - Financial Stability Review: Derivatives – Financial innovation and stability,
(14), 1980–2022.
Coughenour, J. F., and M. M. Saad (2004): “Common Market Makers and Commonality in
Liquidity,” Journal of Financial Economics, 73(1), 37–69.
Cremers, K. J. M., J. Driessen, and P. Maenhout (2008): “Explaining the Level of Credit
Spreads: Option-Implied Jump Risk Premia in a Firm Value Model,” Review of Financial Studies,
21(5), 2209–2242.
Crosbie, P., and J. Bohn (2003): “Modelling Default Risk-Modelling Methodology,” Moody’s KMV
Paper.
Crouch, P., and I. W. Marsh (2005): “Arbitrage relationships and price discovery in the autos
sector of the credit market,” Cass Business School Working Paper.
Currie, A., and J. Morris (2002): “And now for capital structure arbitrage,” Euromoney.
Das, S. R., and P. Hanouna (2009): “Hedging Credit: Equity Liquidity Matters,” Journal of
Financial Intermediation, 18, 112–123.
De Jong, F., and J. Driessen (2005): “Liquidity Risk Premia in Corporate Bond Markets,” Tilburg
University Working Paper.
Dick-Nielsen, J., P. Feldhütter, and D. Lando (2012): “Corporate Bond Liquidity before and
after the Onset of the Subprime Crisis,” Journal of Financial Economics, 103(3), 471–492.
Domowitz, I., O. Hansch, and X. Wang (2005): “Liquidity Commonality and Return Comovement,” Journal of Financial Markets, 8, 351–376.
Duarte, J., F. Longstaff, and F. Yu (2007): “Risk and Return in Fixed Income Arbitrage:
Nickels in front of a Steamroller?,” Review of Financial Studies, 20.
25
Dufour, J., R. Garcı́a, and A. Taamouti (2008): “Measuring Causality between Volatility
and Returns with High-Frequency Data,” Universidad Carlos III de Madrid - Departamento de
Economı́a Working Paper.
Easley, D., and M. O’Hara (1987): “Price, Trade Size, and Information in Securities Markets,”
Journal of Financial Economics, 19, 69–90.
Engle, B., and B. Neri (2010): “The Impact of Hedging Costs on the Bid and Ask Spread in the
Options Market,” Working Paper.
Engle, R., and Y. Cho (1999): “Modeling the Impact of Market Activity on Bid-Ask Spreads in
the Option Market,” NBER Working Paper.
Eom, Y. H., J. Helwege, and J. Huang (2004): “Structural Models of Corporate Pricing: An
Empirical Analysis,” Review of Financial Studies, 17(2), 499–544.
Fabre, J., and A. Frino (2004): “Commonality in Liquidity: Evidence from the Australian Stock
Exchange,” Accounting and Finance, 44(3), 357–368.
Fernando, C. S., R. J. Herring, and A. Subrahmanyam (2008): “Common Liquidity Shocks
and Market Collapse: Lessons from the Market for Perps,” Journal of Banking and Finance, 32,
1625–1635.
Frank, N., B. González-Hermosillo, and H. Hesse (2008): “Transmission of Liquidity Shocks:
Evidence from the 2007 Subprime Crisis,” IMF Working Paper.
Garleanu, N., T. Hendershott, and H. Pedersen, L. (2011): “Margin-Based Asset Pricing
and Deviations from the Law of One Price,” Review of Financial Studies, 24(6), 1980–2022.
Glosten, L., and P. Milgrom (1985): “Bid, ask and transaction prices in a specialist market with
heterogeneously informed traders,” Journal of Financial Economics, 14, 71–100.
Gromb, D., and D. Vayanos (2002): “Equilibrium and Welfare in Markets with Financially Constrained Arbitrageurs,” Journal of Financial Economics, 66, 361–407.
(2010): “Financially Constrained Arbitrage and Cross-Market Liquidity Contagion,”
INSEAD-LSE Working Paper.
Halka, D., and G. Huberman (2001): “Systematic Liquidity,” Journal of Financial Research, 24,
161–178.
Hameed, A., W. Kang, and S. Viswanathan (2010): “Stock Market Declines and Liquidity,”
Journal of Finance, 65(1), 257–293.
Hasbrouck, J., and D. J. Seppi (2001): “Common Factors in Prices, Order Flows and Liquidity,”
Journal of Financial Economics, 59, 383–411.
Hilscher, J., J. M. Pollet, and M. Wilson (2011): “Are Credit Default Swaps a Sideshow?
Evidence that Information flows from Equity to CDS Markets,” Working Paper.
Houweling, P., A. Mentink, and T. Vorst (2005): “Comparing possible Proxies of Corporate
Bond Liquidity,” Journal of Banking and Finance, 29, 1331–1358.
26
Jacoby, G., G. J. Jiang, and G. Theocharides (2009): “Cross-Market Liquidity Shocks: Evidence from the CDS, Corporate Bond, and Equity Markets,” Working Paper.
Jones, E. P., S. P. Mason, and E. Rosenfeld (1984): “Contingent Claims Analysis of Corporate
Capital Structures: An Empirical Investigation,” Journal of Finance, 39(3), 611–625.
Kamara, A., X. Lou, and R. Sadka (2008): “The Divergence of Liquidity Commonality in the
Cross-section of Stocks,” Journal of Financial Economics, 89(3), 444–466.
Kapadia, N., and X. Pu (2012): “Limited Arbitrage between Equity and Credit Markets,” Journal
of Financial Economics, 105, 542–564.
Karolyi, G. A., L. Kuan Hui, and M. A. van Dijk (2007): “Common Patterns in Commonality
in Returns, Liquidity, and Turnover around the World,” Working Paper.
Kaul, G., N. Nimalendran, and D. Zhang (2004): “Informed Trading and Option Spreads,”
Working Paper.
Koch, A., S. Ruenzi, and L. Starks (2004): “Commonality in Liquidity: A Demand-Side Explanation,” Working Paper.
Kyle, A. S., and W. Xiong (2001): “Contagion as a Wealth Effect,” Journal of Finance, 56,
1401–1440.
Lando, D. (2004): Credit Risk Modeling: Theory and Applications. Princeton University Press.
Landsiedl, F. (2005): “The Market Microstructure of Illiquid Option Markets and Interrelations
with the Underlying Market,” Working Paper.
Longstaff, F. A., S. Mithal, and E. Neis (2005): “Corporate Yields Spreads: Default Risk or
Liquidity? New Evidence from the Credit Default Market,” Journal of Finance, 60(5), 2213–2253.
Longstaff, F. A., and E. S. Schwartz (1995): “A Simple Approach to Valuing Risky Fixed and
Floating Rate Debt,” Journal of Finance, 50(3), 789–819.
Mahanti, S., A. Nashikkar, and M. G. Subrahmanyam (2010): “Liquidity and Arbitrage in
the Market for Credit Risk,” Working Paper.
Marsh, I. W., and W. Wagner (2010): “Why is Price Discovery in Credit Default Swap Markets
News-Specific?,” Duisenberg School of Finance - Tinbergen Institute Working Paper.
Meng, L., O. Ap Gwilym, and J. Varas (2009): “Volatility Transmission among the CDS, Equity,
and Bond Markets,” Journal of Fixed Income, 4, 33–46.
Norden, L., and M. Weber (2009): “The Co-movement of Credit Default Swap, Bond, and Stock
Markets: an Empirical Analysis,” European Financial Management, 15(3), 529–562.
Patton, A. J., and K. Sheppard (2011): “Good Volatility, Bad Volatility: Signed Jumps and
the Persistence of Volatility,” Oxford-Man Institute of Quantitative Finance University of Oxford
Working Paper.
27
Petrella, G. (2006): “Option Bid-Ask Spread and Scalping Risk: Evidence from a Covered Warrants Market,” Journal of Futures Markets, 26(9).
Qiu, J., and F. Yu (2012): “Endogenous Liquidity in Credit Derivatives,” Journal of Financial
Economics, 103, 611–631.
Roll, R. (1984): “A Simple Implicit Measure of the Effective Bid-Ask Spread in an Efficient Market,”
Journal of Finance, 39(4), 1127–1139.
Schaefer, S. M., and I. A. Strebulaev (2008): “Structural Models of Credit Risk are useful:
Evidence from Hedge Ratios on Corporate Bonds,” Journal of Financial Economics, 90, 1–19.
Schleifer, A., and R. Vishny (1997): “The Limits of Arbitrage,” Journal of Finance, 52, 35–55.
Spiegel, M. (2008): “Patterns in Cross-Market Liquidity,” Financial Research Letters, 5, 2–10.
Tang, D. Y., and H. Yan (2006): “Liquidity, Liquidity Spillover, and Credit Default Spread,”
Working Paper.
Vassalou, M., and Y. Xing (2004): “Default Risk in Equity Returns,” Journal of Finance, 59(2),
831–868.
Visser, M. (2008): “Forecasting S&P 500 Daily Volatility using a Proxy for Downward Price Pressure,” Kortewegde Vries Institute forMathematics, University of Amsterdam Working Paper.
Xiong, W. (2001): “Convergence Trading with Wealth Effects,” Journal of Financial Economics,
62, 247–292.
Yu, F. (2006): “How Profitable Is Capital Structure Arbitrage?,” Financial Analysts Journal, 62(5),
47–62.
Zheng, X., and Z. Zhang (2006): “Commonality in Liquidity in Emerging Markets: Evidence from
the Chinese Stock Market,” University of Durham Working Paper.
Zhou, X. (2005): “The Dynamics of Information Flow across Individual Stocks, Options and Corporate Bonds,” Cornell University Working Paper.
Zhu, H. (2006): “An empirical comparison of credit spreads between the bond market and the credit
default swap market,” Journal of Financial Services Research, 29(3), 211–235.
28
A
Data Treatment and Analysis of Illiquidity Measures for
Equity and CDSs
A.1
Data Filtering
We employ data on 51 U.S. investment-grade companies which are components of the Dow Jones
5-years On-the-run CDX North America Investment Grade Index (CDX.NA.IG). We choose sample
firms among the components of CDX.NA.IG Index to ensure continuous series of data for CDS quotes
and prices, but we exclude from our sample those companies recording missing values in CDS series
for more than 20 consecutive days. We therefore remain with 51 firms. For each firm we delete all
observations which exhibit for equity (CDS) at least one of the following conditions:
-Null bid or ask price;
-Negative quoted spread (Ask price - Bid price<0);
-Daily absolute change in equity (CDS) price higher than the 99% percentile over the period;
-Daily absolute change in equity (CDS) ask-price higher than the 99% percentile over the period;
-Daily absolute change in equity (CDS) bid-price higher than the 99% percentile over the period.
We remain with an equity daily dataset of 71598 observations and a CDS daily dataset of 69174
observations.
A.2
Analysis of Illiquidity Measures
The literature offers a broad range of measures of illiquidity which reflect three main dimensions:
trading costs, trading frequency, and trade impact on prices. We construct and compare different measures of illiquidity at weekly frequency to show that bid-ask spreads are suitable measure
of illiquidity for both equity and CDS markets and justify their use in the analysis of illiquidity
commonality.
A.2.1
Equity Illiquidity Measures
I. Measures of Transaction Cost at weekly frequency:
• The Roll measure (Roll 1984) is computed over a 21-days rolling window. It is based on
the magnitude of transitory price movements which induce negative serial correlation in price
changes. For each company i the daily measure is constructed as:
 p
2 −Cov(∆P , ∆P
i,t
i,t−1 ), if Cov(∆Pt , ∆Pt−1 ) < 0.
(5)
Rolli,t =
0
otherwise.
∆Pi,t represents the price change (return) for firm i stock at the end of day t. The measure is
averaged over each week (5 business days);
• The percentage bid-ask spread is obtained as the ratio between the quoted bid-ask spread
and the mid-quote price. For each company i over each day t, the measure is constructed as
Aski,t − Bidi,t
0.5(Aski,t + Bidi,t )
and then it is averaged over each week (5 business days);
29
(6)
• The effective spread is obtained as absolute spread between transaction price and mid-quote
price over mid-quote price. For each company i over each day t, the measure is constructed as
|Pi,t − 0.5(Aski,t + Bidi,t )|
0.5(Aski,t + Bidi,t )
(7)
and then it is averaged over each week (5 business days).
II. Measures of Trading Frequency at weekly frequency:
• For each day t the Run length measure is computed as the total number of consecutive days
when either:
-Equity returns keep the same sign, i.e. trade direction remains invariant. Over two consecutive
days we observe Buy - Buy; or Sell - Sell;
-Or equity returns are equal to zero, i.e. no trade is registered on consecutive days. Over two
consecutive days we observe No trade - No trade;
-Or equity returns switch from positive (negative) to zero, i.e. trading switches from active to
inactive. Over two consecutive days we observe Buy - No Trade; or Sell - No Trade;
The run length is short when assets are actively traded or when the price impact is low, as
the variation in the asset series swamps directionality. Therefore, liquid assets have short run
lengths, while illiquid assets have longer run lengths. To construct a weekly measure of run
length we take the maximum value recorded for this measure over 5 business days.
• The inverse turnover index is obtained as ratio between number of outstanding shares and
total traded number of shares over the day. The daily measure is averaged over each week (5
business days).
III.Measures of Market Depth (Price Impact of Trading) at weekly frequency:
• The weekly Amihud Illiquidity Measure (Amihud 2002) is calculated for each company i
over each week w (5 business days) as weekly average ratio between the absolute price change at
the end of the day t and the total amount of dollar volume traded during the day (approximately
equal to total number of shares traded times price per share).
Amihudi,w =
5
i
i
X
− Pt−1,w
|
|Pt,w
t=1
i
V olt,w
(8)
i
where Pt,w
is the closing price for firm i stock on day t in week w.
A.2.2
CDS Illiquidity Measures
For CDSs the same illiquidity measures are constructed as for equities, with the omission of the
inverse turnover, the effective spread, and the Amihud illiquidity measure. Bloomberg does not
provide traded volume data for CDSs.
30
A.2.3
Winsorizing the 0.5% highest value of all Illiquidity Measures and Treatment of
Missing Values
We winsorize the 0.5% highest value of all illiquidity measures. For each illiquidity measure we rank
all observations in 200 groups (0 - 199) in ascending order. Each group contains 0.5% of total observations. We assign the maximum value recorded for the observations falling in the 198th group to all
observations included in the 199th group (i.e. the 0.5% observations recording the highest values).
Although missing values in the weekly illiquidity measure series are few, especially for equity, to
avoid gaps we interpolate each variable using a linear method.
Figures 10-15 in Appendix C show the cross-sectional average for some equity and CDS illiquidity
measures. The cross-sectional average is value-weighted on all 51 firms. From a comparison across
Figures 10 to 13 we notice that the pattern of the equity percentage bid-ask spread is similar to the
patterns of the effective spread, the Roll measure, and the Amihud measure, while Figures 14 and
15 show an increasing pattern over the crisis period for both average CDS bid-ask spread and run
length measure.
A.2.4
Principal Component Analysis and Combined Illiquidity Indexes
Principal Component Analysis has been used in previous literature on the study of illiquidity proxies
(see Dick-Nielsen et al, 2012, for the corporate bond market; and Jacoby et al, 2009, for bonds,
equity, and CDSs). Following the methodology of these papers, we perform Principal Component
Analysis (PCA) across all equity (and CDS) normalized illiquidity measures to evaluate the weight
of the bid-ask spread in the First Principal Component (FPC). The Principal Components are computed on the correlation matrix of the variables. We also obtain a Composite Illiquidity Index.
This is computed at weekly frequency for equity and CDS of individual firms as a linear combination of the selected illiquidity proxies with an average positive loading in the FPC higher than 10%44 .
Aggregate results from Principal Component Analysis conducted across all weekly illiquidity measures for equity and CDS of all firms are displayed in Figures 16-19 in Appendix C. Figures 16 and
18 show that for both equity and CDS, the average First Principal Component explains around 40%
of common variation across different illiquidity proxies. Dick-Nielsen et al (2012) find the same result
across illiquidity measures for corporate bonds. On average bid-ask, effective spread, Roll measure,
and Amihud measure have positive weights in the equity First Principal Component, going from 75%
of bid-ask spread to 48% of Roll measure (see Figure 17). Trading frequency measures behave in
a dissimilar fashion and are mainly captured by the less significant Second Principal Component.
Bid-ask and run length have on average positive weights in the CDS First Principal Component,
respectively 50% and 45% (see Figure 19). CDS Roll measure displays instead a different pattern.
44 The
weight of each proxy in the linear combination is the same across all firms because it is set equal to the valueweighted average loading of the proxy in the First Principal Components.
31
The results of this analysis support the use of bid-ask spreads as a proxy for market illiquidity.
In fact, given the available data, we observe that:
- For CDS illiquidity, the bid-ask spread is consistent on average with the pattern of the other illiquidity measure (run length) with positive loading in the FPC and therefore with the CDS Combined
Illiquidity Index (obtained as a linear combination of bid-ask and run length);
- For equity illiquidity, the time pattern of the bid-ask spread is in line with other measures of equity
transaction costs and price impact of trades (Amihud measure, Roll measure, and effective spread)
and with the Combined Illiquidity Index. In fact, the PCA reveals that these four measures behave
very similarly in the First Principal Component of equity illiquidity, though bid-ask spread displays
the highest loading (75%).
32
B
Estimation of the hedge-ratio, using the Merton Model
(1974)
To quantify the “arbitrage/hedging relationship” between CDS and equity bid-ask spreads and the
relative size of cross-market positions, we estimate the sensitivity of debt to equity, i.e. the hedge
ratio. Schaefer and Strebulaev (2008) show that even a simple version of Merton (1974) model can
capture well the debt-to-equity sensitivity. Under the assumptions of the Black-Scholes (1973) model,
the Merton (1974) model prices equity and risky debt of a firm as contingent claims written on the
firm’s assets. Equity is priced as a call option on the assets of the firm with strike price equal to the
face value of firm’s debt. The risky debt of the firm is evaluated as a short put position on the firm’s
asset with strike equal to the promised debt payment and a long position on a riskless bond45 .
Suppose that the total value of a firm’s assets is equal to A0 at time 0 and the volatility of assets’
value is constant over time and equal to σA . The firms’ liabilities consist of risky debt B - with face
value D and maturity T - and equity E. We call L the leverage ratio (the ratio between present
−rT
value of debt promised payment and total value of assets): L = DeA0 , where r is the continuously
compounded risk-free interest rate in the market. According to the Black-Scholes pricing formula for
non-dividend paying European call options (Black and Scholes 1973), at time 0 the equity value E0
is given by:
E0 = C BS (A0 , σA , D, r, T ) = A0 N (d1 ) − De−rT N (d2 )
(9)
where N(.) is the cumulative function for the standard Normal distribution,
d1 =
ln(
A0
−rT
De√
σA
T
)
+
√
σA T
2
=
−ln(L)
√
σA T
+
√
σA T
2
√
and d2 = d1 − σA T
The sensitivity (first derivative) of equity to firm’s total assets value is determined by the call option
delta: N (d1 ) = ∆C .
At time 0, debt value is given by the difference between total assets’ value and equity value:
B0 = A0 − E0
(10)
B0 = De−rT N (d2 ) + A0 N (−d1 )
(11)
B0 = De−rT − (De−rT N (−d2 ) − A0 N (−d1 )) = P V (D) − P BS (A0 , σA , D, r, T )
(12)
Using equations (9) and (10) we obtain:
This implies:
45 There
is a large literature which extends Merton’s model in order to overcome the limitations of its simplified assumptions (Black and Cox 1976, Longstaff and Schwartz 1995). Merton’s model and its extensions have been extensively
tested. Some tests of structural models (Jones, Mason, and Rosenfeld 1984, Eom, Helwege, and Huang 2004) focus on
corporate bond pricing and find that structural models generally under-predict spreads. However, recent research has
more clearly assessed that the failure of the models has more to do with corporate bond market peculiarities, such as
liquidity and tax effects, than with their ability to explain credit risk. Although the basic Merton (1974) model has
revealed inaccurate to price credit instruments, it is very powerful to predict their sensitiveness to underlying equity
(i.e. debt-to-equity hedge ratio) which can be used to hedge long (short) position on credit risk with long (short)
position in corresponding equity (Schaefer and Strebulaev 2008, Cremers, Driessen, and Maenhout 2008).
33
As previously mentioned, the debt value at time 0 is equal to the present value of a long position on
a riskless bond with face value D plus the value of a short position on a put option (derived from the
Black-Scholes pricing formula for no-dividends paying European put options). Equation (11) can be
used to calculate the sensitivity (first derivative) of risky debt value to assets’ value which is given
by the delta of the put option N (−d1 ) = ∆P . The sensitivity of debt value to equity value is then
given by:
∂B
N (−d1 )
∂B
1
∂A
=
= ∂E
=
−1=h
(13)
∂E
N
(d
)
∆
1
c
∂A
The elasticity of debt-to-equity (hedge ratio) is obtained as:
H=(
∂B E
1
)( ) = h( − 1)
∂E B
L
(14)
We perform the estimation of the debt-to-equity hedge ratio H following the two approaches: (i)
the traditional methodology set by Vassalou and Xing (2004) - henceforth VX Methodology; and
(ii) the methodology implemented by Schaefer and Strebulaev (2008) - henceforth SS Methodology.
The VX methodology requires the knowledge of outstanding debt of the firm, equity value, and
equity volatility to estimate the value and volatility of firm’s assets from a system of two non-linear
equations. We estimate equity volatility as historical annualized volatility, and equity value as the
product between the firm’s equity price and the number of outstanding shares. Following Vassalou
and Xing (2004) we also obtain the outstanding amount of debt as book value of the firm’s current
debt plus one half of long-term debt value.
Following the VX Methodology, we recall equation (9) and notice that since equity is a function
of assets’ value, it is possible to apply Ito’s Lemma to determine the instantaneous volatility of equity
σE from total assets’ volatility σA (Jones, Mason, and Rosenfeld 1984).
dEt = df (At , t) = (
∂Et
σ2
∂Et
∂ 2 Et
∂Et
+ µA At
+ A A2t
)dt + (σA At
)dWt .
2
∂t
∂A
2
∂A
∂A
It follows
E0 σE = A0 σA
∂E
= A0 σA N (d1 ).
∂A
(15)
(16)
Therefore,
σE =
σA A0 N (d1 )
.
E0
(17)
Equations (9) and (17) represent two equations in two unknowns (A0 and σA ). We can determine the
unknowns by solving the non-linear equations. In practice, we adopt a recursive procedure -known
as the KMV method (Lando 2004)- that involves inverting the Black-Scholes formula (Vassalou and
Xing 2004, Crosbie and Bohn 2003, Bharath and Shumway 2008)46 .
46 Crosbie
et al (2003) explain that the model linking equity and asset volatility described by the system of Equations
(1) and (6) holds only instantaneously. In practice market leverage moves around in a substantial way and the system
does not provide reasonable results. Instead of using the instantaneous relationship given by Equations (1) and (6),
we follow Crosbie et al (2003) and produce the hedge ratio using a more complex iterative procedure to solve for the
asset volatility. Crosbie et al (2003) describe it as a procedure that “uses an initial guess of the volatility to determine
the asset value and to de-lever the equity returns. The volatility of the resulting asset returns is used as the input to
the next iteration of the procedure that in turn determines a new set of asset values and hence a new series of asset
returns. The procedure continues in this manner until it converges.”
34
The SS Methodology estimates asset volatility in a “more direct, model-free approach that is
based only on observables” and “recognizes that debt bears some asset risk and that equity and
debt covary” (Schaefer and Strebulaev 2008). We draw the basic idea from their methodology and
estimate the asset volatility for each firm i at time t as square root of:
2
2
2
σA(i,t)
= (1 − Li,t )σE(i,t)
+ Li,t σD(i,t)
+ (1 − Li,t )Li,t σED(i,t)
(18)
σD(i,t) is the time t unconditional volatility of firm i debt - estimated by historical annualized volatility of CDS; σE(i,t) is the time t unconditional volatility of firm i equity - estimated by historical
annualized volatility of equity; σED(i,t) is the time t covariance between firm i debt and equity - estimated by historical annualized covariance between equity and CDS returns; and Li,t is the leverage
ratio of firm i at time t. Once A and σA are estimated we can estimate N (d1 ) and the CDS-to-equity
hedge ratio H at time t.
35
C
Figures and Tables
Figure 1: Cross-sectional average of standardized CDS Premium and inverse Equity price
(Weekly Frequency, March 2003 - December 2009, Cross-Section of 51 Firms)
Figure 2: Cross-sectional average of standardized CDS and equity bid-ask spreads; All Sample
(Weekly Frequency, July 2003 - December 2009, Cross-Section of 51 Firms)
36
Figure 3: Cross-sectional average of standardized CDS and equity bid-ask spreads; Pre-Crisis Sample
(Weekly Frequency, July 2003 - December 2006, Cross-Section of 51 Firms)
Figure 4: Cross-sectional average of standardized CDS and equity bid-ask spreads; Crisis Sample
(Weekly Frequency, January 2007 - December 2009, Cross-Section of 51 Firms)
37
Figure 5: Cross-sectional average of CDS-equity liquidity correlations measures (Pearson, Kendall, and
Spearman)
(Measured in decimals, Quarterly Frequency, March 2003 - December 2009, Cross-Section of 51 Firms)
Figure 6: Cross-sectional average of debt-to-equity hedge ratio (Merton model calibration - SS Methodology)
(Measured in decimals, Weekly Frequency, March 2003 - December 2009, Cross-Section of 51 firms)
38
Figure 7: Cross-sectional average of debt-to-equity hedge ratio (Merton model calibration - SS vs VX
Methodology)
(Measured in decimals, Weekly Frequency, March 2003 - November 2008, Cross-Section of 51 firms)
Figure 8: Cross-sectional averages of CDS premium, CDS bid-ask spread, and debt-to-equity hedge ratio
(Merton model calibration - SS Methodology)
(CDS premium measured in 10 percentage units, CDS bid-ask spread in percentage units, hedge ratio in
decimals, Weekly Frequency, March 2003 - December 2009, Cross-Section of 51 firms)
39
Figure 9: Cross-sectional averages of CDS-equity liquidity correlations measures (Kendall and Spearman)
and debt-to-equity hedge ratio (Merton model calibration - SS Methodology)
(Measured in decimals, Quarterly Frequency, April 2003 - December 2009, Cross-Section of 45 non-financial
firms)
40
Figure 10: Cross-sectional weekly average of equity Roll measure
(Measured in decimals, Weekly Frequency, July 2003 - December 2009, Cross-Section of 51 Firms)
Figure 11: Cross-sectional weekly average of equity percentage bid-ask spread
(Measured in decimals, Weekly Frequency, July 2003 - December 2009, Cross-Section of 51 Firms)
41
Figure 12: Cross-sectional weekly average of equity effective spread
(Measured in decimals, Weekly Frequency, July 2003 - December 2009, Cross-Section of 51 Firms)
Figure 13: Cross-sectional weekly average of equity Amihud measure of price impact
(Measured in decimals, Weekly Frequency, July 2003 - December 2009, Cross-Section of 51 Firms)
42
Figure 14: Cross-sectional average of CDS quoted bid-ask spread
(Measured in basis points, Weekly Frequency, July 2003 - December 2009, Cross-Section of 51 Firms)
Figure 15: Cross-sectional average of weekly maximum value of CDS run length measure
(Measured in N o of days, Weekly Frequency, July 2003 - December 2009, Cross-Section of 51 Firms)
43
Figure 16: Equity PCA: Cross-sectional average of proportions of variance explained by each PC
(Measured in decimals, July 2003 - December 2009, Cross-Section of 51 Firms)
Figure 17: Equity PCA: Cross-sectional average of weights of illiquidity measures in the First PC
(Measured in decimals, July 2003 - December 2009, Cross-Section of 51 Firms)
44
Figure 18: CDS PCA: Cross-sectional average of proportion of variance explained by each PC
(Measured in decimals, July 2003 - December 2009, Cross-Section of 51 Firms)
Figure 19: CDS PCA: Cross-sectional average of weights of illiquidity measures in the First PC
(Measured in decimals, July 2003 - December 2009, Cross-Section of 51 Firms)
45
Table 1: Summary statistics of cross-sectional weighted average (W.A.) Equity and CDS bid-ask
spreads
(51 Firms, Weekly frequency, April 2003 - December 2009)
Obs.
Mean
Std. Dev.
Median
Minimum
Maximum
W.A. Equity Bid-Ask
366
0.0888
0.0735
0.062
0.0275
0.435
W.A. CDS Bid-Ask
366
0.0566
0.0181
0.049
0.0334
0.1155
Table 2: Correlations between cross-sectional weighted average Equity and CDS Bid-Ask Spreads
(51 Firms, Weekly frequency, April 2003 - December 2009)
All Sample
Pearson
Spearman
Kendall
0.557
0.3132
0.1997
Pre-Crisis Sample (2003-2006)
Pearson
Spearman
Kendall
0.772
0.522
0.364
Crisis Sample (2007-2009)
Pearson
Spearman
Kendall
0.448
0.245
0.154
0.5966
0.2239
0.3286
0.2897
0.1486
0.2208
Pre-Crisis Sample
Pearson
Kendall
Spearman
Crisis Sample
Pearson
Kendall
Spearman
0.268
0.1426
0.2055
0.6557
0.2232
0.3296
0.4943
0.1894
0.2776
Median
0.1575
0.1107
0.1596
0.1774
0.0967
0.1341
0.1918
0.0968
0.1374
Std. Dev.
0.1379
0.1123
0.1703
0.2418
0.1151
0.1599
0.3018
0.1352
0.1962
Inter-quartile Range
Figure 20: All Sample - Histograms of Equity-CDS Bid-Ask Spread Measures of Correlation
0.4572
0.1903
0.2818
All Sample
Pearson
Kendall
Spearman
Mean
Table 3: Distributions of Pearson, Kendall, and Spearman Correlations
between Equity and CDS Bid-Ask Spreads at firm level
(51 Firms, Weekly frequency, April 2003 - December 2009)
-0.2019
-0.1304
-0.1941
0.0994
-0.0489
-0.0531
-0.0050
0.0036
0.0046
Lowest
0.6533
0.4678
0.668
0.8445
0.4196
0.587
0.7975
0.4185
0.6052
Highest
Obs
1477
1319
1470
1402
1293
1411
1378
1426
1461
1408
1477
1357
1496
1449
1438
1239
1324
1502
1457
1357
1489
1411
1438
1466
1433
Company Name
Honeywell International
EI du Pont de Nemours
Goodrich
IBM
ConocoPhillips
Kroger
General Mills
Caterpillar
Deere
Boeing Capital
Dow Chemical
Lockheed Martin
Motorola
FirstEnergy
Progress Energy
Halliburton
Alcoa
Northrop Grumman
Raytheon
Campbell Soup
Walt Disney
Hewlett-Packard
Duke Energy
Arrow Electronics
Omnicom Group
9.65655
0.02757
12.9241
1.31877
12.8915
16.3281
0.93471
5.26131
1.88282
3.63554
0.69962
2.85577
6.59504
0.52073
0.45748
6.84928
2.07183
0.40535
4.93599
1.0173
1.55099
4.72621
11.4569
9.53989
7.58392
F-Stat
0.00007
0.97280
0.00000
0.26780
0.00000
0.00000
0.39290
0.00530
0.15250
0.02660
0.49690
0.05790
0.00140
0.59420
0.63300
0.00110
0.12640
0.66680
0.00730
0.36180
0.21240
0.00900
0.00001
0.00008
0.00050
P-value
Reject
Accept
Reject
Accept
Reject
Reject
Accept
Reject
Accept
Accept
Accept
Accept
Reject
Accept
Accept
Reject
Accept
Accept
Reject
Accept
Accept
Reject
Reject
Reject
Reject
Test Result
Null Hypothesis Tested:
Equity BA does not Granger cause CDS BA
72.0589
16.4846
94.7041
0.91107
13.0634
59.1789
12.8862
8.04736
24.2157
70.3464
29.8767
22.3741
53.2859
18.9554
3.77172
11.58
14.6745
16.7724
31.055
22.762
44.4972
32.8771
49.0586
63.6657
32.8313
F-Stat
0.00000
0.00000
0.00000
0.40230
0.00000
0.00000
0.00000
0.00030
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.02320
0.00001
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
P-value
Reject
Reject
Reject
Accept
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Accept
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Test Result
Null Hypothesis Tested:
CDS BA does not Granger cause Equity BA
Both directions*
CDS to Equity
Both directions*
No causality
Both directions
Both directions*
CDS to Equity
Both directions
CDS to Equity
CDS to Equity
CDS to Equity
CDS to Equity
Both directions*
CDS to Equity
CDS to Equity
Both directions
CDS to Equity
CDS to Equity
Both directions*
CDS to Equity
CDS to Equity
Both directions*
Both directions*
Both directions*
Both directions*
Causality Direction
(2 Lags included, Daily frequency, ∗ indicates that evidence is stronger for CDS to Equity than the other way round as the difference between their respective F-stats is > 20)
Table 4: Pair-wise Granger Test of Causality for Equity and CDS Bid-Ask Spreads - Panel A
Obs
1440
1475
1273
1315
1320
1400
1412
1370
1311
944
1465
1495
1397
1551
1464
1478
1496
1470
1425
1434
1421
1492
1433
1333
1388
1478
Company Name
Computer Sciences
McDonald’s
Target
Burlington Northern SF
Wal-Mart Stores
ConAgra Foods
Nordstrom
Chubb
Norfolk Southern
Newell Rubbermaid
Dominion Resources
American Intern. Group
Anadarko Petroleum
Carnival
Safeway
Time Warner
ACE
Eastman Chemical
Simon Property Group
Valero Energy
Hartford Fin.Services Group
Marriott International
Sempra Energy
Devon Energy
MetLife
Kraft Foods
6.06369
3.1774
0.18758
2.29332
12.7869
10.2588
0.55032
3.10743
2.39611
1.82804
2.38068
3.55763
1.49916
3.98564
8.22348
1.89036
5.59855
9.18974
7.09729
2.17625
44.622
0.49772
7.80696
0.58351
9.95191
2.93716
F-Stat
0.00240
0.04200
0.82900
0.10130
0.00000
0.00004
0.57690
0.04500
0.09150
0.16130
0.09280
0.02870
0.22370
0.01880
0.00030
0.15140
0.00380
0.00010
0.00090
0.11380
0.00000
0.60800
0.00040
0.55810
0.00005
0.05330
P-value
Reject
Accept
Accept
Accept
Reject
Reject
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Reject
Accept
Reject
Reject
Reject
Accept
Reject
Accept
Reject
Accept
Reject
Accept
Test Result
Null Hypothesis Tested:
Equity BA does not Granger cause CDS BA
3.05712
46.7617
14.2473
28.3297
9.35591
46.5928
5.15584
14.9602
7.51527
11.5742
28.4344
20.874
7.01297
6.79041
57.5242
34.1322
38.5151
54.5439
17.1519
16.0766
54.4471
19.4288
17.1864
1.06841
23.3621
44.7342
F-Stat
0.04730
0.00000
0.00000
0.00000
0.00009
0.00000
0.00590
0.00000
0.00060
0.00001
0.00000
0.00000
0.00090
0.00120
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.34390
0.00000
0.00000
P-value
Accept
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Accept
Reject
Reject
Test Result
Null Hypothesis Tested:
CDS BA does not Granger cause Equity BA
Equity to CDS
CDS to Equity
CDS to Equity
CDS to Equity
Both directions
Both directions*
CDS to Equity
CDS to Equity
CDS to Equity
CDS to Equity
CDS to Equity
CDS to Equity
CDS to Equity
CDS to Equity
Both directions*
CDS to Equity
Both directions*
Both directions*
Both directions
CDS to Equity
Both directions
CDS to Equity
Both directions
No causality
Both directions
CDS to Equity
Causality Direction
(2 Lags included, Daily frequency, ∗ indicates that evidence is stronger for CDS to Equity than the other way round as the difference between their respective F-stats is > 20)
Table 5: Pair-wise Granger Test of Causality for Equity and CDS Bid-Ask Spreads - Panel B
Obs
1476
1318
1469
1402
1292
1410
1377
1425
1460
1407
1476
1356
1495
1448
1437
1238
1323
1501
1456
1356
1488
1410
1437
1465
1432
Company Name
Honeywell International
EI du Pont de Nemours
Goodrich
IBM
ConocoPhillips
Kroger
General Mills
Caterpillar
Deere
Boeing Capital
Dow Chemical
Lockheed Martin
Motorola
FirstEnergy
Progress Energy
Halliburton
Alcoa
Northrop Grumman
Raytheon
Campbell Soup
Walt Disney
Hewlett-Packard
Duke Energy
Arrow Electronics
Omnicom Group
22.5254
16.5996
12.0712
21.6103
16.5660
3.5061
1.8178
35.8506
22.8571
15.5715
21.8746
1.8347
14.8009
31.0695
9.9939
16.5024
20.5129
11.3915
6.4501
0.7341
10.3409
8.9610
4.2866
43.3120
19.7300
F-Stat
0.00000
0.00000
0.00001
0.00000
0.00000
0.03030
0.16280
0.00000
0.00000
0.00000
0.00000
0.16010
0.00000
0.00000
0.00005
0.00000
0.00000
0.00001
0.00160
0.48010
0.00003
0.00010
0.01390
0.00000
0.00000
P-value
Reject
Reject
Reject
Reject
Reject
Accept
Accept
Reject
Reject
Reject
Reject
Accept
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Accept
Reject
Reject
Accept
Reject
Reject
Test Result
Null Hypothesis Tested:
Equity Ret. does not Granger cause CDS Ret.
(2 Lags included, Daily frequency)
0.8284
0.0044
0.9293
0.7024
1.5302
1.7045
0.8072
0.7449
2.4517
1.1175
4.5982
0.5797
3.0415
1.0539
2.7832
0.1917
0.5764
0.1740
1.7575
1.3428
0.6174
1.2891
0.6868
2.2501
0.1598
F-Stat
0.43700
0.99560
0.39510
0.49560
0.21690
0.18220
0.44630
0.47500
0.08650
0.32740
0.01020
0.56020
0.04810
0.34880
0.06220
0.82560
0.56210
0.84030
0.17280
0.26150
0.53950
0.27590
0.50330
0.10580
0.85240
P-value
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Reject
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Test Result
Null Hypothesis Tested:
CDS Ret. does not Granger cause Equity Ret.
Table 6: Pair-wise Granger Test of Causality for Equity and CDS Returns - Panel A
Equity to CDS
Equity to CDS
Equity to CDS
Equity to CDS
Equity to CDS
No causality
No causality
Equity to CDS
Equity to CDS
Equity to CDS
Both directions
No causality
Equity to CDS
Equity to CDS
Equity to CDS
Equity to CDS
Equity to CDS
Equity to CDS
Equity to CDS
No causality
Equity to CDS
Equity to CDS
No causality
Equity to CDS
Equity to CDS
Causality Direction
Obs
1439
1474
1273
1315
1320
1399
1411
1369
1310
943
1464
1494
1396
1550
1463
1477
1495
1469
1424
1433
1420
1491
1432
1332
1387
1477
Company Name
Computer Sciences
McDonald’s
Target
Burlington Northern SF
Wal-Mart Stores
ConAgra Foods
Nordstrom
Chubb
Norfolk Southern
Newell Rubbermaid
Dominion Resources
American Intern. Group
Anadarko Petroleum
Carnival
Safeway
Time Warner
ACE
Eastman Chemical
Simon Property Group
Valero Energy
Hartford Fin.Services Group
Marriott International
Sempra Energy
Devon Energy
MetLife
Kraft Foods
5.1909
3.1670
8.0365
17.6678
7.2472
6.4537
38.8123
20.2430
26.8072
11.8539
6.8437
16.9218
20.1116
7.3039
4.3313
22.1372
42.6476
32.2516
33.9180
30.1477
43.4927
36.9348
13.6967
10.5095
34.4126
3.4567
F-Stat
0.00570
0.04240
0.00030
0.00000
0.00070
0.00160
0.00000
0.00000
0.00000
0.00001
0.00110
0.00000
0.00000
0.00070
0.01330
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00003
0.00000
0.03180
P-value
Reject
Accept
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Accept
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Reject
Accept
Test Result
Null Hypothesis Tested:
Equity Ret. does not Granger cause CDS Ret.
(2 Lags included, Daily frequency)
1.9757
2.3948
0.4572
0.1708
4.1119
3.7718
1.6191
3.5390
0.0170
0.9385
0.6302
7.3920
0.4528
0.0959
0.3468
0.8263
0.0376
0.3471
1.2383
1.2658
1.8302
2.0099
1.1088
0.1466
2.5251
2.7806
F-Stat
0.13900
0.09150
0.63320
0.84300
0.01660
0.02320
0.19840
0.02930
0.98310
0.39160
0.53260
0.00060
0.63600
0.90850
0.70700
0.43790
0.96310
0.70680
0.29020
0.28230
0.16080
0.13440
0.33020
0.86360
0.08040
0.06230
P-value
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Test Result
Null Hypothesis Tested:
CDS Ret. does not Granger cause Equity Ret.
Table 7: Pair-wise Granger Test of Causality for Equity and CDS Returns - Panel B
Equity to CDS
No causality
Equity to CDS
Equity to CDS
Equity to CDS
Equity to CDS
Equity to CDS
Equity to CDS
Equity to CDS
Equity to CDS
Equity to CDS
Equity to CDS
Equity to CDS
Equity to CDS
No causality
Equity to CDS
Equity to CDS
Equity to CDS
Equity to CDS
Equity to CDS
Equity to CDS
Equity to CDS
Equity to CDS
Equity to CDS
Equity to CDS
No causality
Causality Direction
Obs
1549
1517
1563
1459
1513
1539
1537
1505
1530
1512
1525
1536
1544
1556
1550
1509
1534
1563
1538
1566
1533
1512
1548
1564
1546
Company Name
Honeywell International
EI du Pont de Nemours
Goodrich
IBM
ConocoPhillips
Kroger
General Mills
Caterpillar
Deere
Boeing Capital
Dow Chemical
Lockheed Martin
Motorola
FirstEnergy
Progress Energy
Halliburton
Alcoa
Northrop Grumman
Raytheon
Campbell Soup
Walt Disney
Hewlett-Packard
Duke Energy
Arrow Electronics
Omnicom Group
5.32693
0.96815
0.19327
2.71322
1.17301
2.02711
0.11188
2.24694
1.65853
2.08635
2.06503
0.82183
6.36213
3.34316
11.2197
3.28885
9.4765
6.53175
2.44959
0.85412
9.24651
4.30404
0.82741
5.72523
0.69593
F-Stat
0.00490
0.38000
0.82430
0.06670
0.30970
0.13210
0.89420
0.10610
0.19080
0.12450
0.12720
0.43980
0.00180
0.03560
0.00001
0.03760
0.00008
0.00150
0.08670
0.42590
0.00010
0.01370
0.43740
0.00330
0.49880
P-value
Reject
Accept
Reject
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Reject
Accept
Reject
Accept
Reject
Reject
Accept
Accept
Reject
Accept
Accept
Reject
Accept
Test Result
Null Hypothesis Tested:
Equity Vol. does not Granger cause CDS Vol.
(2 Lags included, Daily frequency)
11.9133
4.78274
0.19562
6.13909
6.20588
5.92694
0.4156
9.88471
11.2271
4.65806
1.66296
7.32844
0.34717
4.65785
4.79218
13.5669
5.42228
11.1753
5.39561
0.76645
11.1033
9.31248
7.40831
15.4489
1.69638
F-Stat
0.00001
0.00850
0.82230
0.00220
0.00210
0.00270
0.66000
0.00005
0.00001
0.00960
0.18990
0.00070
0.70670
0.00960
0.00840
0.00000
0.00450
0.00002
0.00460
0.46480
0.00002
0.00010
0.00060
0.00000
0.18370
P-value
Reject
Reject
Accept
Reject
Reject
Reject
Accept
Reject
Reject
Reject
Accept
Reject
Accept
Reject
Reject
Reject
Reject
Reject
Reject
Accept
Reject
Reject
Reject
Reject
Accept
Test Result
Null Hypothesis Tested:
CDS Vol. does not Granger cause Equity Vol.
Table 8: Pair-wise Granger Test of Causality for Equity and CDS Volatility - Panel A
Both directions
CDS to Equity
Equity to CDS
CDS to Equity
CDS to Equity
CDS to Equity
No causality
CDS to Equity
CDS to Equity
CDS to Equity
No causality
CDS to Equity
Equity to CDS
CDS to Equity
Both directions
CDS to Equity
Both directions
Both directions
CDS to Equity
No causality
Both directions
CDS to Equity
CDS to Equity
Both directions
No causality
Causality Direction
Obs
1536
1524
1515
1536
1494
1549
1536
1543
1531
1550
1542
1539
1547
1538
1537
1544
1551
1563
1525
1539
1545
1554
1551
1514
1524
1542
Company Name
Computer Sciences
McDonald’s
Target
Burlington Northern SF LLC
Wal-Mart Stores
ConAgra Foods
Nordstrom
Chubb
Norfolk Southern
Newell Rubbermaid
Dominion Resources
American Intern. Group
Anadarko Petroleum
Carnival
Safeway
Time Warner
ACE
Eastman Chemical
Simon Property Group
Valero Energy
Hartford Fin.Services Group
Marriott International
Sempra Energy
Devon Energy
MetLife
Kraft Foods
19.9354
8.09558
6.07164
0.11477
1.63434
1.6611
4.85863
14.1185
1.22545
4.27579
1.3423
46.2559
4.28249
1.69174
3.51825
0.71915
26.5361
12.6982
0.70557
4.76093
13.648
4.64991
12.7352
9.70201
17.3873
0.33171
F-Stat
0.00000
0.00030
0.00240
0.89160
0.19540
0.19030
0.00790
0.00000
0.29390
0.01410
0.26160
0.00000
0.01400
0.18450
0.02990
0.48730
0.00000
0.00000
0.49400
0.00870
0.00000
0.00970
0.00000
0.00007
0.00000
0.71770
P-value
Reject
Reject
Reject
Accept
Accept
Accept
Reject
Reject
Accept
Accept
Accept
Reject
Accept
Accept
Accept
Accept
Reject
Reject
Accept
Reject
Reject
Reject
Reject
Reject
Reject
Accept
Test Result
Null Hypothesis Tested:
Equity Vol. does not Granger cause CDS Vol.
(2 Lags included, Daily frequency)
2.25889
19.2949
15.4058
0.39538
11.0373
1.94036
10.4275
7.68667
0.54135
5.76115
14.1147
23.8591
1.92212
2.08267
10.3127
2.04066
13.9356
13.3616
5.63519
0.55913
27.7733
3.35204
2.25406
17.5007
8.62053
0.07701
F-Stat
0.10480
0.00000
0.00000
0.67350
0.00002
0.14400
0.00003
0.00050
0.58210
0.00320
0.00000
0.00000
0.14660
0.12490
0.00004
0.13030
0.00000
0.00000
0.00360
0.57180
0.00000
0.03530
0.10530
0.00000
0.00020
0.92590
P-value
Accept
Reject
Reject
Accept
Reject
Accept
Reject
Reject
Accept
Reject
Reject
Reject
Accept
Accept
Reject
Accept
Reject
Reject
Reject
Accept
Reject
Accept
Accept
Reject
Reject
Accept
Test Result
Null Hypothesis Tested:
CDS Vol. does not Granger cause Equity Vol.
Table 9: Pair-wise Granger Test of Causality for Equity and CDS Volatility - Panel B
Equity to CDS
Both directions
Both directions
No causality
CDS to Equity
No causality
Both directions
Both directions
No causality
CDS to Equity
CDS to Equity
Both directions
No causality
No causality
CDS to Equity
No causality
Both directions
Both directions
CDS to Equity
Equity to CDS
Both directions
Equity to CDS
Equity to CDS
Both directions
Both directions
No causality
Causality Direction
Table 10: Regressions of CDS and Equity Bid-Ask Spreads on Asset Volatility and Market Illiquidity
Market Illiquidity=Value-weighted average of bid-ask spreads across the 44 remaining firms. Newey-West SE estimated.
Dep. Var. Equity Bid-Ask Spread
Permno
Ticker
Equity Market Ill
10145
11703
12140
12490
13928
16678
17144
18542
19350
19561
20626
21178
22779
23026
23114
23819
24643
24766
24942
25320
26403
27828
27959
29209
30681
40125
43449
49154
50227
55976
56274
57817
60986
64311
64936
70332
75154
76149
77418
80080
85269
85913
86136
87137
89006
HON
DD
GR
IBM
COP
KR
GIS
CAT
DE
BA
DOW
LMT
MOT
FE
PGN
HAL
AA
NOC
RTN
CPB
DIS
HPQ
DUK
ARW
OMC
CSC
MCD
TGT
BNI
WMT
CAG
JWN
NWL
NSC
D
APC
CCL
SWY
TWX
EMN
VLO
MAR
SRE
DVN
KFT
Coeff
0.9127
0.7095
1.2947
0.7442
0.9451
0.7274
1.1031
0.9141
0.8704
0.6745
0.8822
2.0731
1.7936
2.1069
0.9714
1.1143
0.8955
1.1949
0.9591
1.2514
0.6358
0.5683
1.1297
0.7554
0.5606
1.7570
0.2519
0.2794
0.4397
0.2768
0.5374
1.1609
1.0236
1.0680
1.9557
0.9337
1.9054
0.6973
1.3812
1.0327
0.7816
1.2102
0.8180
0.9887
0.4462
p-value
0.0001
0.0000
0.0000
0.0000
0.0081
0.0079
0.0000
0.0000
0.0000
0.0000
0.0000
0.0003
0.0000
0.0030
0.0000
0.0016
0.0000
0.0000
0.0098
0.0001
0.0000
0.0000
0.0001
0.0006
0.0001
0.0061
0.0012
0.0768
0.0484
0.0017
0.0000
0.0002
0.0033
0.0001
0.0058
0.0001
0.0000
0.0000
0.0000
0.0002
0.0002
0.0000
0.0004
0.0015
0.0017
Asset Vol
Coeff
-0.0026
0.0185
0.0415
0.0239
0.0108
-0.1506
-0.0066
0.0627
0.0298
0.0363
0.0817
0.0720
0.3197
-0.0580
0.0393
0.0501
0.0867
0.0559
-0.0471
0.0439
0.0209
-0.0296
0.0781
0.0541
-0.0095
-0.0412
0.0067
-0.0091
-0.0882
-0.0564
0.0046
0.0517
0.1358
-0.0489
0.0215
0.0521
-0.0072
-0.0129
0.0471
0.0526
0.0773
0.0746
-0.0198
-0.0126
0.0247
p-value
0.9017
0.1747
0.0883
0.1849
0.6225
0.0023
0.8730
0.0290
0.0988
0.0030
0.0001
0.1482
0.0000
0.0492
0.3044
0.1443
0.0000
0.2146
0.1600
0.3552
0.3212
0.2380
0.0014
0.2016
0.7880
0.4200
0.8520
0.5817
0.0054
0.0278
0.9268
0.0598
0.0000
0.1250
0.6875
0.0083
0.6473
0.7992
0.3028
0.1295
0.0001
0.0016
0.5074
0.5586
0.2493
Dep. Var. CDS Bid-Ask Spread
CDS Market Ill
Coeff
0.9334
0.9179
0.6977
0.7956
0.6203
0.7314
0.4410
1.7590
1.1517
1.3947
2.9490
0.8362
2.7295
0.7234
0.6667
0.4850
5.2807
0.8489
0.7163
0.1627
0.9670
0.9634
0.1846
2.0952
2.3112
0.5096
0.3642
1.2647
0.7158
0.7477
0.3484
2.9263
0.9752
0.7198
0.4879
1.3697
3.0202
0.7673
1.2639
1.3878
0.5905
2.4101
0.4755
0.2252
0.6190
p-value
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0041
0.0000
0.0000
0.0023
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0019
0.0000
Asset Vol
Coeff
-0.0407
0.0382
0.0021
-0.0406
-0.0036
-0.0002
0.0347
0.0653
0.0478
0.0706
0.0994
-0.0756
0.1173
0.0308
-0.0956
-0.0115
0.2015
0.0646
-0.0700
0.0561
0.0077
-0.0505
0.0038
-0.0200
-0.0200
-0.0035
0.0272
0.0165
-0.0622
-0.0521
0.0206
0.1400
0.0674
-0.0552
-0.0477
0.0535
-0.0054
0.0206
0.0363
-0.0431
0.1769
0.1775
-0.0001
0.0118
0.1007
p-value
0.0000
0.0000
0.5217
0.0000
0.1384
0.9743
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0008
0.0000
0.0000
0.0000
0.0000
0.1224
0.0000
0.3758
0.0003
0.0362
0.3270
0.1076
0.0029
0.0000
0.0000
0.0009
0.0000
0.0000
0.0000
0.0000
0.0000
0.2321
0.0003
0.0000
0.0000
0.0000
0.0000
0.9908
0.0124
0.0000
0.251053
9.033028
<0.00001
0.258303
9.312236
<0.00001
0.109773
3.846441
0.0001
0.188536
6.686281
<0.00001
0.177576
6.284526
<0.00001
Hedge Ratio
t-Statistic
p-value
TED
t-Statistic
p-value
VIX
t-Statistic
p-value
Default
t-Statistic
p-value
0.173902
6.15039
<0.00001
0.187813
6.659684
<0.00001
0.110083
3.857447
0.0001
-0.072636
-2.536464
0.0113
-0.068303
-2.384421
0.0173
Ret.Comm (K)
t-Statistic
p-value
Ill.Comm (S)
Ret.Comm (S)
t-Statistic
p-value
0.995381
361.1159
<0.00001
Ill.Comm (S)
t-Statistic
p-value
Ill.Comm (K)
-0.249649
-8.979128
<0.00001
-0.22052
-7.874163
<0.00001
-0.100302
-3.511029
0.0005
-0.254563
-9.167993
<0.00001
0.996432
411.1636
<0.00001
Ret.Comm (K)
-0.2503
-9.004082
<0.00001
-0.222179
-7.93645
<0.00001
-0.098
-3.429677
0.0006
-0.256957
-9.26028
<0.00001
Ret.Comm (S)
0.521315
21.27631
<0.00001
0.551195
23.00773
<0.00001
0.215783
7.696638
<0.00001
Hedge Ratio
TED
0.78663
44.37234
<0.00001
0.74499
38.89642
<0.00001
Table 11: Pearson Correlation Matrix:
Time Sample: 2003Q2-2009Q4; Number of Total Quarterly Observations: 1215; Number of Cross-section: 45 Firms
Comm (K) = Kendall Tau Measure of Association; Comm (S) = Spearman Measure of Association
0.950148
106.1322
<0.00001
VIX
Table 12: Pair-wise Granger Causality Test Matrix
Null Hypothesis: X does not Granger cause Y
Time Sample: 2003Q2-2009Q4; Number of Total Quarterly Observations: 1215; Number of Cross-sections: 45 Firms
Comm (K) = Kendall Tau Measure of Association; Comm (S) = Spearman Measure of Association
X
Hedge Ratio Ill.Comm (K) Ill.Comm (S) Ret.Comm (K) Ret.Comm (S)
Y
Hedge Ratio
0.59798
0.49305
5.84912
5.67158
0.55010
0.61090
0.00300
0.00350
Ill.Comm (K)
26.3359
4.2486
<0.00001
0.0145
Ill.Comm (S)
24.8627
3.89849
<0.00001
0.0205
Ret.Comm (K)
45.5806
3.82037
<0.00001
0.02220
Ret.Comm (S)
46.887
3.18702
<0.00001
0.04170
VIX
3.08414
4.78519
4.14365
9.96393
9.52758
0.04620
0.00850
0.01610
0.00005
0.00008
Default
9.85346
2.0633
1.57617
5.81489
5.42138
0.00006
0.12750
0.20720
0.00310
0.00450
Default
57.8109
<0.00001
28.3934
<0.00001
26.2406
<0.00001
59.2915
<0.00001
60.9786
<0.00001
163.278
<0.00001
-
VIX
22.045
<0.00001
29.6549
<0.00001
27.1447
<0.00001
52.9075
<0.00001
54.6119
<0.00001
123.675
<0.00001
Mean
Median
Maximum
Minimum
Std. Dev.
2.19
1.83
50.52
-62.29
12.76
Ill.Comm (K)
3.09
2.71
71.01
92.99
18.49
Ill.Comm (S)
-4.03
-3.74
26.42
-44.54
10.28
Ret.Comm (K)
-5.90
-5.37
41.43
-67.57
15.19
Ret.Comm (S)
3.38
0.53
15.06
0
4.77
Hedge Ratio
0.59
0.35
2.35
0.18
0.53
TED
Table 13: Summary Statistics:
Time Sample: 2003Q2-2009Q4; Number of Total Quarterly Observations: 1215; Number of Cross-sections: 45 Firms
All Variables are measured in percentage units;
Comm (K) = Kendall Tau Measure of Association; Comm (S) = Spearman Measure of Association
VIX
20.36
16.66
58.61
11.04
10.55
0.79
0.61
1.85
0.47
0.34
Default
Dep.Var.
Filtered Kendall
Correlation
Dep.Var.
Kendall
Correlation
II
II
I
I
II
II
I
I
Model
-0.0086
-3.05
-0.0083
-2.20
-0.0045
-1.62
-0.0083
-2.20
Int.
0.3970
3.38
0.3825
2.31
0.2068∗
1.69
0.3825
2.31
0.3840
2.02
0.5186
2.20
0.2575
1.36
0.5186
2.20
7.84%
0.17%
8.79%
0.62%
7.57%
0.20%
8.53%
1.29%
Panel B.
Analysis of Residuals from Preliminary Regression
H SS
H SS,ORT
Adj − R2
2.5494
0.0001
2.6676
0.0001
No
2.4842
0.0001
No
2.4725
0.0001
No
LR Test (Time)
Fixed Effects
No
Panel A.
Preliminary Regression of Equity-CDS Illiquidity Commonality on Exogenous Risk Factors
Model
Int.
MktRf
Smb
Hml
TED
VIX
Adj − R2 LR Test (Firm)
Fixed Effects
I
-0.0410 21.3075
30.0406
6.7020
7.0610
6.69%
1.0739
-3.46
3.25
2.97
0.99
4.55
0.38
II
-0.0615 19.3255
25.9097
11.7533 4.1235 0.1874
7.45%
0.3676
-4.12
1.63
2.47
3.06
2.11
2.13
1.08
The panel regressions are estimated with least squares; Panel dataset includes 18 non-financial companies and 27 quarters (from 2003:2 to 2009:4); Estimated standard errors are
robust to firm clustering; t-statistics are reported in italic; Likelihood tests of fixed effects (FE) redundancy use the panel regressions with no fixed effects as baseline for comparison:
F-statistics and p-values (in italic) are reported; No = No FE included; Coefficients in bold when regressors are significant at 5% C.L.; Coefficients marked with ∗ when regressors
are significant at 10% C.L.; All variables are measured in decimals.
Table 14: Test of Hypothesis H.1: Arbitrage/Hedging Channel of Equity-CDS Illiquidity Commonality - Two-Steps Panel Regressions
Dep.Var.
Kendall
Correlation
Dep.Var.
Kendall
Correlation
IV
III
IV
Model
III
IV
IV
III
III
IV
IV
III
Model
III
Panel A.
Regression of Equity-CDS Illiquidity Commonality on Exogenous Risk Factors and Hedge Ratio
LR Test (Firm)
SS
SS,ORT
2
Int.
MktRf
Smb
Hml
TED
VIX
H
H
Adj − R
Fixed Effects
-0.0435 16.3739 23.0302 10.4497 5.8369
0.5434
8.40%
0.9582
-3.69
2.49
2.25
1.51
3.76
3.27
0.50
-0.0436 16.2548 22.8609 10.5402∗ 5.8073
0.5565
8.53%
No
-3.05
2.51
2.36
1.95
3.12
4.37
-0.0453 16.4088 22.9595 10.7479 5.6216 0.0172 0.5195
8.21%
0.9572
-2.57
2.47
2.22
1.49
2.59
0.13
2.05
0.51
-0.0445 16.2556 22.8045 10.6950∗ 5.7003 0.0082 0.5468
8.34%
No
-2.49
2.51
2.33
1.75
2.36
0.08
2.87
-0.0394 17.4670 25.3686
6.8913
7.1215
0.4983
7.49%
1.0832
-3.33
2.59
2.48
1.03
4.59
2.29
0.37
-0.0394 17.4670 25.3686
6.8913
7.1215
0.4983
7.21%
No
-2.72
2.90
2.51
1.27
3.87
2.69
-0.0551 16.9347 23.4450 10.5931∗ 4.9270 0.1390∗
0.3765∗
7.76%
1.0864
-3.44
2.57
2.24
1.46
2.36
1.40
1.53
0.36
-0.0551 16.9347 23.4450 10.5931 4.9270 0.1390
0.3765
7.48%
No
-3.40
2.73
2.31
1.72
1.99
1.75
1.69
Panel B.
Economic Significance of Regressors
LR Test (Firm)
SS
SS,ORT
2
MktRf
Smb
Hml
TED
VIX
H
H
Adj − R
Fixed Effects
0.1674
0.1049
0.0728 0.2413
0.1619
8.53%
No
2.51
2.36
1.95
3.12
4.37
0.1674
0.1046
0.0738∗ 0.2368 0.0068 0.1591
8.34%
No
2.51
2.33
1.75
2.36
0.08
2.87
0.1798
0.1164
0.0476
0.2959
0.1113
7.21%
No
2.90
2.51
1.27
3.87
2.69
0.1744
0.1076
0.0731∗ 0.2047 0.1148∗
0.0841∗
7.48%
No
2.73
2.31
1.72
1.99
1.75
1.69
The panel regressions are estimated with least squares; Panel dataset includes 18 non-financial companies and 27 quarters (from 2003:2 to 2009:4); Estimated standard errors are
robust to firm clustering; t-statistics are reported in italic; Likelihood tests of fixed effects (FE) redundancy use the panel regressions with no fixed effects as baseline for comparison:
F-statistics and p-values (in italic) are reported; No = No FE included; Coefficients in bold when regressors are significant at 5% C.L.; Coefficients marked with ∗ when regressors
are significant at 10% C.L.; All variables are measured in decimals; For the analysis of economic significance standardized betas are obtained by multiplying the estimated betas by
the ratio between standard deviation of relative explanatory variable and standard deviation of dependent variable.
Table 15: Test of Hypothesis H.1: Arbitrage/Hedging Channel of Equity-CDS Illiquidity Commonality - All-in Panel Regression
IV
Dep.Var.
Pearson
Correlation
Dep.Var.
Kendall
Correlation
IV
Dep.Var.
Spearman
Correlation
-0.0154
-1.17
-0.0659
-2.63
-0.0445
-2.49
Int.
8.0886
1.02
23.5711
2.48
0.1669
16.2556
2.51
0.1674
MktRf
39.5789
2.89
0.1499
33.5391
2.23
0.1059
22.8045
2.33
0.1046
Smb
-6.3317
-0.94
14.1709
1.39
10.6950
1.75
Hml
4.7113
1.58
8.0997
2.63
0.2315
5.7003
2.36
0.2368
TED
-0.1281
-1.15
0.0239
0.13
0.0082
0.08
VIX
0.5321
2.29
0.1277
0.7888
2.37
0.1579
0.5468
2.87
0.1591
H SS
Coeff
t-stat
Econ.Sign.
Coeff
t-stat
Econ.Sign.
IV
-0.0093
-0.86
0.0090
1.00
Int.
-3.8054
-0.71
-5.7458
-1.05
MktRf
11.6913
1.12
14.9055
1.52
Smb
-6.6383
-1.08
-9.0884
-1.42
Hml
-0.5774
-0.26
1.5265
1.29
TED
0.1705
1.45
VIX
1.0813
1.84
0.1480
1.2799
2.39
0.1715
HV X
Panel B.
All-in Panel Regression - Alternative Hedge Ratio (Vassalou and Xing)
Coeff
t-stat
Econ. Sign.
Coeff
t-stat
Econ. Sign.
Coeff
t-stat
Econ. Sign.
III
Model Spec.
IV
Dep.Var.
Kendall
Correlation
Model Spec.
4.97%
4.73%
Adj − R2
3.61%
8.37%
8.34%
Adj − R2
Panel A.
All-in Panel Regressions: Comparison between Three Alternative Dependent Variables
The All-in panel regressions are estimated with least squares; Panel regressions includes 18 non-financial companies and 27 quarters (from 2003:2 to 2009:4) when Hedge SS is used;
Panel regressions includes 30 non-financial companies and 23 quarters (from 2003:2 to 2008:4) when Hedge VX is used; Estimated standard errors are robust to firm clustering;
t-statistics are reported in italic; No firms’ fixed effects included; Coefficients in bold when regressors are significant at 5% C.L.; Coefficients marked with ∗ when regressors are
significant at 10% C.L.; All variables are measured in decimals; For the analysis of economic significance standardized betas are obtained by multiplying the estimated betas by the
ratio between standard deviation of relative explanatory variable and standard deviation of dependent variable.
Table 16: Test of Hypothesis H.1: Arbitrage/Hedging Channel of Equity-CDS Illiquidity Commonality - Robustness Checks
Dep.Var.
Res. CDS
Bid-Ask
-0.00080
-5.51
-0.00062
-5.05
-0.00067
-5.76
-0.00033
-5.59
Coeff
t-stat
Econ.Sign.
Coeff
t-stat
Econ.Sign.
Coeff
t-stat
Econ.Sign.
Coeff
t-stat
Econ.Sign.
Int.
0.00086
2.72
0.0559
0.00054
1.81
0.0349
0.00057
1.82
0.0368
0.00057
3.66
0.0369
H SS × Equity BA
0.00048
4.90
0.0874
0.00049
4.99
0.0890
0.00051
4.64
0.0919
H SS × Equity BA
× CDS Return(Lag1)
0.00020
6.54
0.09
0.00020
6.58
0.0926
0.00019
6.25
0.0912
0.00018
6.56
0.0855
CDS Inn
0.00025
1.90
0.04
0.00024
1.89
0.0431
CDS Inn ×
CDS Mispricing(Lag1)
-0.00013
-1.99
-0.03
-0.00012
-1.87
-0.0285
-0.00010
-1.52
-0.0234
0.00001
0.05
0.0013
Equity Inn
0.00058
3.96
0.06
0.00024
1.62
0.0548
0.00023
1.62
0.0227
0.00074
3.23
0.0726
TED
The panel regressions are estimated with least squares; Panel dataset includes 45 non-financial companies and 300 weeks (Sep 2003 to Dec 2009); Estimated standard errors are
robust to firm clustering; t-statistics are reported in italic; No firms’ fixed effects included; For the analysis of economic significance standardized betas are obtained by multiplying
the estimated betas by the ratio between standard deviation of relative explanatory variable and standard deviation of dependent variable.
Table 17: Test of CDS Bid-Ask Spread Determinants:
Effect of Hedging Costs, Private Information Costs, Market Volatility and Funding Costs on Residual CDS Bid-Ask Spreads
0.00003
3.92
0.0619
0.00003
3.50
0.0577
0.00003
2.72
0.0570
VIX
3.5%
3.7%
3.2%
2.6%
Adj-R2