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Faculty of Business and Law School of Accounting, Economics and Finance
Financial Econometrics Series
SWP 2014/08
An Analysis of Price Discovery from Panel Data
Models of CDS and Equity Returns
P.K. Narayan, S.S. Sharma, K. Thuraisamy
The working papers are a series of manuscripts in their draft form. Please do not quote without obtaining the author’s consent as these works are in their draft form. The views expressed in this paper are those of the author and not necessarily endorsed by the School or IBISWorld Pty Ltd.
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An Analysis of Price Discovery from Panel Data
Models of CDS and Equity Returns
Paresh Kumar Narayan1, Susan Sunila Sharma2, Kannan Thuraisamy3
Mailing Address
Paresh Kumar Narayan
Alfred Deakin Professor
School of Accounting, Economics and Finance
Faculty of Business and Law
Deakin University
221 Burwood Highway
Burwood, Victoria 3125
Australia
Telephone: +61 3 9244 6180
Fax: +61 3 9244 6034
Email: [email protected]
1 Alfred Deakin Professor, Research Professor, Financial Econometrics Group, School of Accounting, Economics and Finance, Deakin University 2 Lecturer in Financial Econometrics, Financial Econometrics Group, School of Accounting, Economics and Finance, Deakin University 3 Senior Lecturer in Finance, Financial Econometrics Group, School of Accounting, Economics and Finance, Deakin University
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An Analysis of Price Discovery from Panel Data
Models of CDS and Equity Returns
ABSTRACT
We propose a panel data model of price discovery. We find that the stock market contributes
to price discovery in most sectors while the Credit Default Swap (CDS) market contributes to
price discovery in only a few sectors. We discover that in sectors where both the stock market
and the CDS market contribute to price discovery, it is the stock market that dominates the
price discovery process. When we consider investment grade stocks, the importance of the
CDS market in price discovery improves but the stock market still dominates the price
discovery process. The results for different sizes of stocks generally suggest that both markets
are important for price discovery but it is the stock market that dominates. We also find that
while the price discovery process was affected by the 2007 global financial crisis, the stock
market still dominated the price discovery process. Finally, in an economic significance
analysis, we show that investors in the CDS market are able to make relatively more profits
from a forecasting model that takes into account price discovery compared to a model that
simply ignores the role of price discovery.
Key words: Price Discovery; CDS Spread; Panel Data; Sectors; Sizes.
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1. Motivation
There is now a large body of literature (see, inter alia, Kapadia and Pu, 2012; Riordan and
Storkenmaier, 2012; and Trutwein et al., 2011) that investigates the relationship between stock
returns and CDS spreads. However, literature that specifically examines evidence for price
discovery in the stock and CDS spread markets is scarce. Therefore, our contribution to this
literature is timely. We count at least three factors that motivate us to re-visit the price discovery
process in the stock and CDS spread markets. First, as we gauge from the literature, there is
tension when it comes to the question of whether the CDS market leads the stock market or
whether the stock market leads the CDS market. Norden and Weber (2009) and Forte and Pena
(2009), for instance, find it is the stock market that generally leads the CDS market. Acharya
and Johnson (2007) find the opposite; they discover evidence of information flowing from the
CDS market to the equity market, with stronger relationships for organisations that have
cliental relationships with banks. Longstaff et al.’s (2003) finding, compared to the studies
alluded to above, is somewhere in the middle: they claim there is no clear-cut evidence that
either market is a leader. In their analysis, stock returns predict CDS premium for 17 stocks
while CDS premium predicts returns for 12 stocks. Moreover, the study by Fung et al. (2008)
contributes to the existing tensions when they find that the stock market leads the CDS market
only for investment grade firms, while, for high yield firms, it is the CDS market that leads the
stock market. Therefore, we opine that the literature has reached a point of tension, which needs
a response.
The second feature of the literature motivating us to re-visit the search for price discovery is
that few attempts have been made respecting the CDS spread heterogeneity across stocks.
While it seems rather obvious that stocks belonging to different sectors are characterised by
different levels of risk, as measured by the CDS spread, in testing for price discovery these
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risks have not been accounted for. Failure to do so renders evidence on price discovery
susceptible to CDS spread heterogeneity bias. We believe this represents one avenue for
extending this literature, prompting us to entertain the possibility that price discovery,
regardless of whether it is found in the stock or CDS markets, is likely to be sector-specific.
We also recognise that a second source of heterogeneity bias, as revealed in the work of
Narayan and Sharma (2011), is stocks of different sizes. Therefore, price discovery may also
be size-dependent. To progress this idea further, we present some statistical facts that confirm
the sectoral and size-based heterogeneity with respect to the CDS spread, measured in natural
logarithmic form. In Figure 1, using four panels, we plot the mean CDS spread (of the S&P
500 companies) and its standard deviation (SD) by sector in panels A and B, respectively, and
the mean and SD of CDS returns by size in panels C and D, respectively. We find the following
features in the data. There are clearly some sectors, such as consumer discretion, information
technology, and financials, which have relatively high CDS spreads, suggesting that these
sectors are most risky. Compare this with the industrial, health care, and consumer staples
sectors, where CDS spreads are almost half of those found for the most risky sectors. The
volatility of the CDS spread, as measured by the SD, also shows a clear sectoral pattern; in
some sectors volatility is high while in others it is low.
INSERT FIGURE 1
Turning to panels of stocks categorised by size, we observe a similar type of heterogeneity with
respect to both mean CDS spread and the SD of CDS spread. We observe that the largest stocks
(sizes 1 and 2) are the least risky while the smallest stocks (sizes 9 and 10) have relatively high
CDS spreads, suggesting that these stocks are most risky. When we read evidence on the SD
of CDS spread by size, we conclude with the understanding that the most volatile CDS spreads
are typically associated with the largest and smallest sized stocks. Stocks of medium sizes
(sizes 5-7) have the lowest volatility. The main implication here is that testing for price
5
discovery in size-based stocks is imperative to obviate any heterogeneity bias due to the size
of the stocks.
The third feature of the literature is that the investigation of price discovery is silent about the
specific constituents of the CDS spread, such as high yield (HY) spread and investment grade
(IG) spread. We address this issue as well. We not only consider the 212 stocks which have
CDS spread data, but we also separately consider a subset of 166 stocks which are investment
grade. This is an important consideration because the CDS spread of IG stocks is different
compared to all stocks, as can be seen from Figure 2, where we plot the mean (panel A) and
SD (panel B) of CDS spreads for all stocks and IG stocks. The mean CDS spread is lower for
IG stocks compared to all stocks. This is true even if we exclude the IG stocks from all stocks.
This suggests that the price discovery relationship between the stock market and the CDS
market consisting of IG stocks can potentially be different. Whether or not this is the case, is
an empirical issue which we test.
INSERT FIGURE 2
Our approach to addressing these three less-understood issues with respect to price discovery
in the stock and CDS spread markets is as follows. Using the Global Industrial Classification
System, we categorise S&P 500 stocks into 10 different sectors. Using market capitalisation of
stocks, we also divide stocks into different sizes. The sector and size classifications of stocks
and CDS spreads ensure that we have on hand panels of stocks that are relatively homogeneous.
This will ensure that our estimates of price discovery will be relatively free from the commonly
observed heterogeneity bias. We end up with no fewer than 40 panel data models of stock
prices and CDS spreads. We then propose a panel co-integration framework, which, conditional
on a co-integrating relationship between the two price variables, allows us to specify a panel
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vector error correction model (PVECM). Using the PVECM, we show how one can extract the
price discovery coefficients, following the time series price discovery proposals of Hasbrouck
(1995) and Gonzalo and Granger (1995).
Briefly, foreshadowing the main results, we find that while the stock market contributes to
price discovery in nine sectors, the CDS spread contributes to price discovery in only six
sectors. In the six sectors where both the stock and the CDS markets contribute to price
discovery, it is the stock market that dominates the price discovery process. When we consider
only the investment grade firms, we observe a rise in the role of the CDS market in price
discovery: in seven of the 10 sectors, the CDS market contributes to price discovery but does
not dominate the price discovery process, the stock market does. Size-based panels of stocks
reveal strong evidence of size effects. In firms of most sizes, both the stock and the CDS
markets contribute to price discovery; however, it is the stock market that dominates the price
discovery process. Sectoral and size heterogeneity with respect to this price discovery process
is clear though: the magnitude of sectoral price discovery varies and is in the range of 60% to
73%, while for size-based panels the range is 56% to 89%, suggesting strong sectoral and size
effects. Finally, in an economic significance analysis, we show that investors in the CDS
market are able to make relatively more profits from a forecasting model that takes into account
price discovery (a VECM-based forecasting model) compared to a model (a VAR-based
forecasting model) that simply ignores the role of price discovery.
The rest of the paper is organised as follows. In Section 2, we present the panel data framework
for price discovery. The focus of this section is on establishing the motivation for a panel data
model of price discovery and explaining the panel data econometric framework for modelling
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price discovery. Data and results are explained in Section 3. The final section concludes with
the main findings.
2. A panel data framework for price discovery
In this section, we propose computing price discovery in the CDS spread and stock markets by
using a panel data framework. This computation involves two distinct yet related steps. The
first step is to test for panel co-integration. To proceed to the second step, one needs to ascertain
that CDS spread and stock prices are panel co-integrated. Panel co-integration is, therefore, a
prerequisite for estimating a PVECM in the second step. The objective here is to extract the
coefficients of the one-period lagged panel error correction terms (PECT). These PECT
coefficients together with the covariance matrix are then used to compute the lower bound and
upper bound panel price discovery coefficients. Essentially, we extend the time series price
discovery approach proposed by Hasbrouck (1995). The PECT coefficients are also used to
compute a second measure of price discovery, effectively extending the Gonzalo and Granger
(1995) time series proposal. Our panel proposal is very similar to the Blanco et al. (2005) time
series version of the price discovery model. Let us consider these two steps in some detail now.
Three things need to be clarified before we begin with the estimation. First, the definition of
price discovery is imperative because it has been used in different contexts by the literature.
Second, we need to be clear about the relationship between the concept of price discovery and
econometric models. Typically, when two markets are related theoretically, any shock (news)
will impact both markets. Therefore, if two markets (as in our case) are related, the news is
perceived to be common to both markets. In econometric terms, the relationship between two
markets (over the historical period of time) is known as co-integration (long-run relationship).
The question then is: which of the two markets responds to news more quickly? In econometric
8
terms, this is known as the speed of adjustment. In econometric models, this speed of
adjustment appears in the error correction model in the form of news lagged one period, which
are nothing but innovations from the co-integrated model. Typically, because these error
correction coefficients measure the speed of adjustment to equilibrium in each of the two
markets, it allows one to compute the market in which the speed of adjustment is the highest.
Third, why should equity price and CDS spreads be integrated and share a long-run (co-
integration/co-movement) relationship? This is a relevant question as limited empirical work
has been undertaken on this subject; therefore, little is known about it. The empirical link
between equity and CDS markets has been documented, unsurprisingly, by many studies.
These studies have been cited earlier. The empirical evidence that information flows from CDS
markets to equity markets, and vice versa, has roots in the theoretical work presented in Merton
(1974), namely, his structural model of credit risk. The main implication of the Merton model
is that changes in credit spread and stock price must co-move to prevent arbitrage. Kapadia and
Pu (2012) argue in favour of credit and equity market integration, and claim that the two
markets will be more integrated when: (a) impediments to arbitrage are limited; and (b) firms’
equity and credit markets are characterised by greater liquidity. From a statistical point of view,
this type of co-movement over short periods of time is known as common cycles, while, over
long periods of time, is known as co-integration. Evidence of co-integration—that is, a long-
run relationship between equity and CDS markets—suggests zero/limited opportunities for
arbitrage consistent with the Merton model. Therefore, a test for co-integration between the
equity and CDS markets is motivated by the tenets of the Merton model. Moreover, our goal
of testing for integration and co-integration between these two markets is supported by the
findings of Kapadia and Pu (2012, p. 561), who write: “… empirical tests of structural models
of credit risk need to be implemented over horizons that are sufficiently long to ensure
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integration”. We use the longest possible time series of data and use daily data for empirical
tests.
What do the data reveal? We plot the S&P 500 index together with a (constructed) equally-
weighted CDS portfolio using the Bloomberg system. Using the 5-year tenor, the Bloomberg
system generated 260 CDS series belonging to the member firms of the S&P 500 index. Figure
3 captures these two plots of the series. To make our point clear about the co-movement of the
two markets, we highlight five regions representing eventful market movements. Region 1
shows the initial phase of the 2007 global financial crisis. Region 2 depicts shocks being
experienced by both markets triggered by a confidence crisis when Lehman Brothers filed for
bankruptcy protection on 15 September 2008. Over the three months from July to September
2008, the high yield CDX and the investment grade CDX widened by 136 basis points and 39
basis points, respectively. Simultaneously, the S&P 500 declined by 8.8%. Regions 3 and 4
show further evidence of the co-movement of the two markets. By April 2010, the CDS market
widened following the sovereign difficulties experienced in the Euro area. In July 2011, Fitch
downgraded its sovereign rating for Greece from B+ to CCC, which triggered a repricing in
the CDS and equity markets. From the late 2011 to the early 2012 period, however, asset prices
showed signs of recovery, together with a tightening of spreads in the credit market. The main
message emerging from the graphical illustration is that equity and CDS markets co-move over
time, suggesting a potential long-run (co-integrating) relationship between the two markets.
INSERT FIGURE 3
Lastly, our empirical illustration would be incomplete if we did not provide a discussion of the
non-stationary nature of the CDS spread. This literature has found credit risk to be an integrated
process. Consider, for instance, the following works. Longstaff and Schwartz (1995) show the
10
mean reverting properties of credit spreads of industrial and utility bonds. Their regression
results show that the half-life of deviations from the long-run means stay in the range of 0.7 to
1 year, and 1.5 to 4 years, for the industrial spreads and the utility spreads, respectively. Pedrosa
and Roll (1998), using credit spread indices belonging to the US market, find a systematic risk
in credit spread contributing to a unit root behaviour in credit spreads across different maturities
and credit classes. They report empirical evidence of a unit root behaviour of credit spreads
and attribute the interest rate factor and perceptions about volatility and asset values as reasons
for this unit root behaviour of spreads. Batten et al. (2000) extend the theoretical framework
for co-integration analysis of Hall et al. (1992) for riskless Treasury Bills to risky Australian
dollar bonds, and show that credit spreads are unit root processes.
While the literature has considered credit spreads, we consider CDS spread which is just a
subset of credit spread. Therefore, we extend the theoretical insights of Merton by substituting
credit risk with CDS spread. The reason we are able to do this is because CDS spread is very
highly and statistically significantly correlated with the different measures of credit risk. For
example, the correlations between the CDS portfolio and CSA (credit spread based on A rating
bonds), CSAA (credit spread based on AA rating bonds), CSBBB (credit spread based on BBB
rating bonds), and CSHY (credit spread based on high yield bonds) are 0.88, 0.87, 0.80, and
0.94, respectively. The null hypothesis that the correlations are equal to zero is rejected at the
1% level in all four cases.
2.1. Panel co-integration
Our panel co-integration test is based on the procedure developed by Larsson et al. (2001,
henceforth, LLL). LLL developed a maximum likelihood-based co-integration test in
heterogeneous panel data models. The model follows in the spirit of the time-series version of
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the co-integration model proposed by Johansen (1995). The panel test is, essentially, based on
the mean of the individual rank trace statistics. To understand the model, consider 𝑁 cross-
section, which in our application is stocks, say 𝑖, where 𝑖 = 1,… ,𝑁, which contains a time
series dimension, say 𝑡, where 𝑡 = 1, … , 𝑇. We have a two-variable model, denoted by the
vector 𝑋𝑖𝑡 = (𝑥𝑖𝑡1 , 𝑥𝑖𝑡
2 )′, where 𝑥𝑖𝑡1 and 𝑥𝑖𝑡
2 can be thought of as our variables, stock returns and
CDS spread returns, respectively. It follows that we have the following panel 𝑉𝐴𝑅(𝑞𝑖) model:
𝑋𝑖𝑡 = ∑ Π𝑖𝑞𝑋𝑖,𝑡−𝑞
𝑞𝑖
𝑞=1
+ 𝜇𝑖𝑡, 𝜇𝑖𝑡~𝑁𝑧(0, Ω𝑖) (1)
LLL then draw on the Engle and Granger (1987) error correction model framework (ECM) and
propose a PVECM as follows:
Δ𝑋𝑖𝑡 = Π𝑖𝑋𝑖,𝑡−1 + ∑ Γ𝑖𝑞
𝑞𝑖−1
𝑞=1
∆𝑋𝑖,𝑡−𝑞 + 𝜖𝑖𝑡 (2)
Let us fix notations: 𝑧 represents the number of variables in our system; therefore, Π𝑖 is of order
𝑧 × 𝑧; the error term has the same properties as those from the VAR model; Π𝑖 = 𝛼𝑖𝛽𝑖′, if Π𝑖
is of reduced rank, where 𝛼𝑖 and 𝛽𝑖 are of order 𝑧 × 𝑟𝑖 and of full column rank. As LLL
recommend, the time series dimension of the panel should be sufficiently large to ensure that
the model is parsimoniously estimated. LLL propose the co-integrating rank hypothesis as
follows: 𝐻(𝑟): rank(Π) ≤ 𝑟 against the alternative 𝐻(𝑝): rank(Π) = 𝑝. The likelihood ratio
test, referred to as the trace statistic, has the following form:
−2𝑙𝑛𝑄𝑇{𝐻(𝑟)|𝐻(𝑝)} = −𝑇 ∑ 𝑙𝑛(1 − �̂�𝑖)
𝑧
𝑖=𝑟+1
(3)
where �̂�𝑖 is the 𝑖th eigenvalue—see LLL (2001) for further details.
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2.2 Price discovery in panel data models
To estimate price discovery, let us re-write our PVECM as follows:
[Δ𝑙𝑛𝑆𝑃𝑖𝑡
Δ𝑙𝑛𝐶𝐷𝑆𝑖𝑡] = [
𝑐𝑖1 + 𝛼1(𝑙𝑛𝑆𝑃𝑖𝑡−1 − 𝛽𝑖𝑡𝑙𝑛𝐶𝐷𝑆𝑖𝑡−1)
𝑐𝑖2 + 𝛼2(𝑙𝑛𝑆𝑃𝑖𝑡−1 − 𝛽𝑖𝑡𝑙𝑛𝐶𝐷𝑆𝑖𝑡−1)]
+
[ ∑ −𝐴1𝑗
1𝑞
𝑗=1Δ𝑙𝑛𝑆𝑃𝑖𝑡−𝑗 + 𝐴1𝑗
2 Δ𝑙𝑛𝐶𝐷𝑆𝑖𝑡−𝑗
∑ −𝐴2𝑗1
𝑞
𝑗=1Δ𝑙𝑛𝑆𝑃𝑖𝑡−𝑗 + 𝐴2𝑗
2 Δ𝑙𝑛𝐶𝐷𝑆𝑖𝑡−𝑗]
+ [𝜖1𝑖𝑡
𝜖2𝑖𝑡] (4)
As we will show later, both 𝑙𝑛𝑆𝑃𝑖𝑡 and 𝑙𝑛𝐶𝐷𝑆𝑖𝑡 follow a random walk process:
𝑙𝑛𝑆𝑃𝑖𝑡 = 𝑙𝑛𝑆𝑃𝑖𝑡−1 + 𝜂𝑖𝑡1 (5)
𝑙𝑛𝐶𝐷𝑆𝑖𝑡 = 𝑙𝑛𝐶𝐷𝑆𝑖𝑡−1 + 𝜂𝑖𝑡2 (6)
The error terms may be contemporaneously and serially correlated:
𝑐𝑜𝑣(𝜂𝑖𝑡1 , 𝜂𝑖𝑡
2 ) = 𝜔𝑖𝑡 (7)
𝑣𝑎𝑟(𝜂𝑖𝑡1 ) = 𝜎𝜂𝑖1
2 (8)
𝑣𝑎𝑟(𝜂𝑖𝑡2 ) = 𝜎𝜂𝑖2
2 (9)
The evidence on price discovery is based on the error correction coefficients, 𝛼1 and 𝛼2. These
coefficients measure the speed of adjustment. When 𝛼1 < 0 and statistically significant, it
implies that the CDS market is contributing to any disequilibrium in stock returns. In other
words, the stock market adjusts to information contained in CDS spreads. On the other hand,
if 𝛼2 > 0 and statistically significant, it implies that the stock market contributes to any
disequilibrium in CDS returns. In this case, the stock market will contribute to price discovery
as the CDS spread market will adjust to information contained in the stock market. Indeed, if
both coefficients are statistically significant then both markets are contributing to price
discovery (Blanco et al., 2005). The inclusion of error correction terms in the model is based
13
on the assumption that both variables are co-integrated. Co-integration implies that at least one
market will adjust, in which case that market is inefficient because its price reacts to
information contained in another price. The concept of co-integration and adjustment of the
kind discussed here has been motivated by the Granger representation theorem (Engle and
Granger, 1987).
Blanco et al. (2005) show how one can utilise the coefficients of the error correction terms and
the covariance matrix of 𝜖1𝑡 and 𝜖2𝑡, represented by 𝜎12, 𝜎12, and 𝜎2
2, to obtain the Hasbrouck
(HAS, 1995) and the Gonzalo and Granger (GG, 1995) measures of price discovery. They show
this in the case of time series co-integrating models. We use the same framework, and propose
the following HAS and GG measures of price discovery in cases where two price variables are
panel co-integrated. The lower bound HAS (𝐻𝐿𝑊) and upper bound HAS (𝐻𝑈𝑃) price
discovery (contribution of stock market to CDS spread market) coefficients are:
𝐻𝐿𝑊 =
𝛼22 (𝜎1
2 −𝜎12
2
𝜎22 )
𝛼22𝜎1
2 − 2𝛼1𝛼2𝜎12 + 𝛼12𝜎2
2 , 𝐻𝑈𝑃 =(𝛼2𝜎1 − 𝛼1
𝜎12
𝜎1)2
𝛼22𝜎1
2 − 2𝛼1𝛼2𝜎12 + 𝛼22 (10)
Lower and upper bounds of the price discovery coefficients result when the two error terms
from the vector ECM are correlated. In our panel data models, these error terms are strongly
correlated in that they are statistically significant; detailed results are available upon request.
In this case, Baillie et al. (2002) suggest that one should use the average of the upper and lower
bounds. Therefore, our measure of HAS price discovery is: 𝐻𝐴𝑆 = (𝐻𝐿𝑊 + 𝐻𝑈𝑃) 2⁄ . On the
other hand, the GG price discovery in the CDS market contributed by the stock market can be
obtained by the following expression involving the error correction terms:
𝐺𝐺1 =𝛼2
𝛼2 − 𝛼1 (11)
14
When, in a two-variable PVECM, there is a co-integrating relationship, then GG must satisfy
𝐺𝐺1𝛼1 + 𝐺𝐺2𝛼2 = 0 (orthogonality condition) and 𝐺𝐺1 + 𝐺𝐺2 = 1 (equality condition). Since
the error correction term in the stock market equation is expected to be negative, and positive
in the CDS spread equation, the GG measure is expected to be in the [0,1] range. This will not
be the case, however, if the error correction coefficients appear with incorrect (unexpected)
signs. In this case, there is no evidence of price discovery, therefore, GG can be outside the
[0,1] range.
3. Data and Results
3.1 Data
The equity price and CDS spread data are obtained from the Bloomberg system and
Datastream. For the CDS spread (denominated in basis points so that 100 basis points equates
to 1 percentage point), we only consider the 5-year tenor series contracts as these instruments
are known to have adequate liquidity and are, therefore, widely used in empirical analysis. We
have daily data for 10 sectors of the S&P 500. Of the 500 stocks, only 212 stocks with
corresponding CDS spreads have sufficient time series data with a clean price history.
Therefore, consistent with the aim of the paper, the remaining 287 stocks were excluded. For
the 212 stocks organised into sectors and sizes, we provide a distribution of their size based on
market capitalisation. Some relevant statistics are presented in Table 1. The first point to note
here is that the 212 firms in our sample cover around 60% of the market represented by the
S&P 500 index. The sectoral representation in terms of firm size ranges from 2.1% of total
market capitalisation for the utility sector up to 11% for the financial sector. Similarly, the size-
based portfolios indicate that the size effects are appropriately captured. Stocks categorised in
size 1 (the largest sized stocks) have a market capitalisation valued at 25%, whereas, stocks
contained in the smallest size portfolio (size 10) account for only 0.8% of the total market
15
capitalisation. The main implication from this size distribution on relative market
capitalisation, particularly for our size-based panels of stocks, is that we have on hand a size
portfolio that clearly represents the different sizes of stocks and appropriately distinguishes
between small and large stocks.
INSERT TABLE 1
In our sample, there are investment grade (IG) and high yield (HY) firms as well. In order to
eliminate the effects of downgrades and upgrades during the sample period, we systematically
tracked down the credit rating of each firm, as released by Standard & Poor’s, and isolated
those firms that experienced an upgrade/downgrade during the sample period. Of the 187
investment grade firms that we began with, 21 companies had experienced a downgrade and,
therefore, were removed from the IG sample. In this way, our final sample of IG firms
concluded at 166.
By comparison, we only have 25 HY firms, which is insufficient for sectoral panel data analysis
as, when we form sectors, we end up with six sectors, four of which have only two firms each.
For this reason, we do not categorise HY stocks into panels and we exclude them from further
analysis. The sectors are listed in column 1 of Table 1. The data span the period 7/02/2004 to
3/30/2012. This provides no fewer than 2021 observations per stock. All data are converted
into natural logarithmic form before application, and, because daily panel data models are
characterised by cross-sectional dependence and heteroskedasticity, we standardise our data
set. Typically, to account for cross-section dependence, the literature simply demeans the data
series by subtracting from the actual series its mean (see Westerlund, 2007). On the other hand,
to account for heteroskedasticity, studies (see, for instance, Garcia, 2013) simply divide the
series by its SD. We follow this literature and divide the demeaned data by the SD. The biggest
16
concern with panel data models is with respect to cross-sectional dependence; therefore, we
spend a little more space on this issue. To make the point clear about how our data set accounts
for the cross-section dependence with our approach, following the proposal of Pesaran et al.
(2008), we estimate the cross-sectional dependence (average pair-wise cross-sectional
correlation) of returns for each panel. We do this with unadjusted returns and with adjusted
(our standardised) returns, and report the results in Table 1 (panel C). The average pair-wise
cross-sectional correlations from our standardised data set are substantially less compared to
the correlations obtained from the unadjusted returns. Excluding the telecommunication sector,
which has only four firms, the range of average correlations for the unadjusted returns is 0.393,
0.698, whereas, for the standardised returns, the average cross-correlations fall in the -0.024,
0.0001 range.
We conclude the data section with an explanation of why we prefer a panel data model. Our
proposal of a panel data model of price discovery is based on the fact that a panel data model
offers a rich characterisation of the data set by simply combining the “members” of a panel
with its time series. The key advantages are two-fold. First, it allows us to extract and, therefore,
take advantage of the additional (or heterogeneity of) information that may exist with respect
to each member (firm) of the panel. That the literature (see Narayan and Sharma, 2011) has
shown firms in panels to be heterogeneous adds to our motivation. Second, since our interest
is on price discovery, it is essential that we pick up information at the firm-level as this
information has direct implications for price discovery. The alternative, and to some extent a
short-cut, approach of averaging the information across firms and creating a portfolio of time
series data on equity and CDS spread will, effectively, dilute any firm-specific information
there may be. This is not to say that the ‘averaging of data’ approach should not be entertained.
Our main point here is simply that given the research issue on hand is about price discovery,
17
the most relevant set-up to investigate price discovery at the firm-level is to deal with it in a
panel data framework, which allows us to collect and make use of any firm-level information
on prices.
3.2 Main findings
A prerequisite for panel co-integrating modelling is that all variables need to be non-stationary
in their level form. To ascertain the integrational properties of our two price variables, we
applied the Hadri (2000) panel stationarity test that examines the null hypothesis of stationarity.
The results are extensive as they include 20 sector-based panels and 20 size-based panels. In
total, we estimated 40 panel data models. To conserve space, we do not present all the results
here. We only report results for all CDS sectors and IG sectors in panel A of Table 2. The
detailed results can be obtained upon request. We find that the null hypothesis of stationarity
is comfortably rejected for both variables across all sectors and sizes. This is true for all panel
data models. Therefore, we find strong evidence that stock prices and CDS spreads for all
panels of stocks are non-stationary. The main implication is that these findings pave the way
for us to conduct a formal test of panel co-integration.
The results from panel co-integration based on the Larsson et al. (2001) procedure are reported
in panel B of Table 2. We only report sectoral panel co-integration test results and, to conserve
space, we do not report results from size-based panels; these results are obviously available
upon request. Strong evidence of co-integration is found in all 40 panel data models. The main
implication of this evidence of co-integration is that we can specify a PVECM, as proposed
earlier, allowing us to estimate the price discovery coefficients. We do this next and discuss
the main findings.
INSERT TABLE 2
18
We begin with results on price discovery for each of the 10 sectors. The results are reported in
Table 3. The first column contains the sectors; columns 2-5 report the coefficients of the error
correction terms, 𝛼1 and 𝛼2, and their significance level as measured by the t-statistics, which
examine the null hypothesis that 𝛼1 = 0 and 𝛼2 = 0, respectively. The last two columns report
the GG and the HAS measures of price discovery, that is, the contribution of stock prices to
price discovery in the CDS spread market. We begin with a note on the error correction terms.
We notice that in nine out of 10 sectors, 𝛼2 is positive and statistically significant at the 1%
level, indicating that the stock market actually contributes to price discovery in the CDS spread
market. The exception is the telecommunication sector, where 𝛼2 is statistically insignificant,
which is not surprising given that telecommunication is the smallest panel with only four firms.
Meanwhile, 𝛼1 is only significant (at the 5% level or better) in six (energy, finance, materials,
consumer discretion, health care, and industrial) out of 10 sectors, suggesting that while CDS
spreads contribute to price discovery in stock markets, their role is limited and specific to only
a few sectors. Therefore, in these six sectors where both the stock market and the CDS market
are contributing to price discovery, the role of the stock market is dominant. Based on both the
GG and HAS measures, on average the stock market contributes around 60% and 75%,
respectively, to price discovery in the CDS spread market.
INSERT TABLE 3
In panel B of Table 3, we report the corresponding results for investment grade stocks. We find
that both error correction terms appear with the correct sign and while 𝛼2 is statistically
significant at the 10% level or better for all sectors, 𝛼1 is only statistically significant in seven
sectors. In three sectors, 𝛼1 is not statistically different from zero. These sectors are information
technology, utility, and consumer staples. On the whole, then, while the stock market
contributes to price discovery in all sectors, the CDS market does so only in seven sectors. The
stock market dominates the price discovery process in these two markets.
19
In Table 4 we report size-based evidence on price discovery. We find clear evidence of size
effects when it comes to price discovery on a number of fronts. First, the error correction terms
are correctly signed and statistically significant in all panels except size 3. By comparison, on
average across all sizes, the GG measure reveals that the stock market contributes around 70%
to price discovery. Second, we observe that for large-sized stocks (sizes 1-5), the stock market
contributes around 73% to price discovery, while, for small-sized stocks (sizes 6-10), the stock
market, while still dominating the price discovery process, contributes only around 65%. Third,
while it is true that the stock market contributes and dominates price discovery in the CDS
market in nine out of 10 sizes of stocks, the magnitude of price discovery varies from one size
to another. For example, based on the GG measure, the range of price discovery is 56% (size
8) to 76% (size 5). Size-based results for the IG panel of stocks, reported in panel B of Table
4, are very similar.
INSERT TABLE 4
3.3 Was price discovery affected by the global financial crisis?
Some recent studies analysing the relationship between stock markets and CDS spread markets
have shown that the 2007 global financial crisis has affected this relationship; see, for instance,
Eichengreen et al. (2012) and Grammatikos and Vermeulen (2012). There are two reasons why
the global financial crisis matters for the stock market and CDS market relationship. First, the
global financial crisis represents a financial shock and, since the onset of the financial crisis in
2007, there have been some ‘mini-crises’, such as the collapse of the Lehman Brothers in 2008,
which actually led to the persistence of the global financial crisis. Given this, several studies
argue that shocks emanating from the financial crisis are likely to be transmitted more strongly
during the crisis period (see Grammatikos and Vermeulen, 2012). Second, Kapadia and Pu
(2012) study the determinants of equity-credit market integration and find that measures of
20
credit market liquidity and idiosyncratic volatility are important during the pre-2007 financial
crisis but not over the crisis period. That equity volatility does not explain this market
integration and it is attributed to the fact that: “… during the crisis period, liquidity in a firm’s
markets is closely associated with the credit risk of the firm” (p. 559). From this literature, it is
clear that the dynamic relationships between the equity and CDS markets, including the
transmission of shocks over the crisis period, are likely to be different compared to the pre-
crisis period. Therefore, there is no reason to believe that our evidence of price discovery is not
affected by the global financial crisis. It follows that the one question that remains is: is price
discovery affected by the 2007 global financial crisis? In this section, we answer this question.
Our approach is as follows. We sub-sample the data to include the period without the financial
crisis. We extract specific date of the crisis from the Federal Reserve Bank of St. Louis’ crisis
timeline. According to this timeline, 27 February 2007 is considered to be the start of the crisis.
Therefore, we specify our pre-crisis sample period as 9 September 2004 to 26 February 2007.
The crisis officially ended in December 2009; therefore, we have a crisis sub-sample spanning
the period 27 February 2007 to 30 December 2009. Since the results from the HAS and GG
measures are broadly similar, to conserve space, we only report results based on the GG
measure. The results are reported in Table 5. Our main findings can be summarised as follows:
Evidence from all 212 firms suggests that the stock market dominates price discovery
in both the pre-crisis and crisis period.
In all sectors, the magnitude of the stock market’s contribution to price discovery has
been higher in the crisis period compared to the pre-crisis period. On average across all
sectors (for all 212 stocks), the stock market contributes 56% to price discovery in the
pre-crisis period, while, in the crisis period it contributes around 61%.
21
Results from IG firms provide similar evidence, that is, while the stock market
dominates price discovery, the magnitude of contribution is relatively high (on average)
in the crisis period (76%) compared to the pre-crisis period (51%).
Regarding size effects, evidence from all 210 stocks, where both 𝛼1 and 𝛼2 are
statistically significant, suggests two things: (1) that the stock market (over 62%)
dominates the price discovery process in both the pre-crisis and crisis periods; and (2)
the size effects are obvious in both the pre-crisis and crisis periods: in the pre-crisis
period the range for price discovery is 0.56 to 0.78, whereas, in the crisis period the
range is 0.51 to 0.71. A similar trend in the results is observed for panels of IG stocks.
From these results, we conclude that the global financial crisis has indeed affected price
discovery, in that while the stock market dominates the price discovery process, its contribution
in the pre-crisis period is different compared to that in the crisis period.
Our finding that it is the stock market that dominates the price discovery process is consistent
with the findings from Norden and Weber (2009) and Forte and Pena (2009). We extend this
literature by confirming that the stock market’s dominance of price discovery goes beyond the
market to sectors and sizes of stocks. Equally interestingly, our contribution is that although
we find that the price discovery process is dominated by the stock market, this dominance is
very much sector and size-specific. The main reason for this pattern in the results has roots in
our motivation. We began by showing that sectors and sizes of firms were heterogeneous. Some
sectors and sizes of stocks were not only relatively more risky (in terms of CDS spread) but
were also much more volatile than others. Therefore, the sectoral and size variations in price
discovery that we find, mirror the heterogeneity of the stocks. The main implication here is that
even though the stock market dominates the price discovery process, the information it contains
22
varies not only from sector to sector, but also from size to size. Investors can, potentially,
explore the different magnitude of the information contained in the stock market to predict
CDS returns. Generally, there is limited work on the predictability of CDS returns. Our results
suggest that one of the predictors of CDS returns is, indeed, the stock market. In the next
section, we build on this finding and explore the economic significance of the stock market’s
dominance of price discovery.
INSERT TABLE 5
3.4 Economic significance
The goal of this section is to provide a test of the economic significance for our price discovery
evidence. The main finding is that the stock market dominates price discovery in a model where
the CDS market is the second and only other market containing pricing information. Since the
stock market dominates the price discovery in the CDS market, investors in the CDS market
should be able to track the information contained in the stock market to predict the CDS market.
If this is true, the key question is: can investors in the CDS market use the information in the
stock market to make profits from the PVECM? What is the role of price discovery in these
profits (assuming profits can be made)? Alternatively, the question is: can investors in the CDS
market make more profits from using our proposed PVECM as opposed to, say, a model that
ignores the role of price discovery (that is, the error correction coefficients), which is nothing
but a panel VAR model (PVARM). To answer this question, we adopt the following steps:
For those sectors where both the CDS and the equity markets contribute to price
discovery and where the equity market dominates price discovery, we forecast CDS
spread returns using both the PVARM and the PVECM. We also verify whether the
23
stock market still dominates the price discovery process over the in-sample period
(which is now set to 50% of the sample).4
In forecasting CDS spread returns from the PVARM, we simply restrict the PVECM
by setting 𝛼1 = 0 and 𝛼2 = 0. This restriction implies that the PVARM ignores the role
of price discovery. The lag lengths in the PVARM are chosen using the Schwarz
Information Criterion. The same lag lengths are used in the PVECM model. The
optimal lag lengths are reported in parentheses beside each sector and size in column 2
(for All stocks) and column 3 (for IG stocks).
In generating the forecasts (recursively), we use an out-of-sample period consisting of
50% of the sample, following the recent literature on forecasting published in this
journal (see Narayan et al., 2013).
Once we have obtained the forecasts for CDS spread returns, we utilise a mean-variance
utility function, similar to the one used by Narayan et al. (2013), and estimate investor
profits. We do not repeat the trading strategy here as this is clearly spelt out in papers
published in this journal, such as Narayan et al. (2013, pp. 3887-3888), which is exactly
what we follow.
Using the mean-variance investor framework, we first estimate profits from the
PVARM-based forecasts (PVARMp) and then from the PVECM-based forecasts
(PVECMp). We then annualise these profits and compute the difference, say 𝑑, as
PVECMp – PVARMp. If 𝑑 > 0 it suggests that investors who utilise a PVECM-based
4 We also test, using the GG measure, evidence for price discovery over 50% of the sample for the six sector and
10 size-based stocks. To conserve space, we do not tabulate the results here; instead, we provide a summary of
the main findings. The detailed table is available upon request. Generally, we find strong evidence that the stock
market dominates the price discovery process. For the sectors taken together, in nine out of 12 cases the stock
market dominates the price discovery process. For the size-based stocks, when considering all stocks, as before,
in nine out of the 10 sizes, the stock market dominates the price discovery process. When we consider IG stocks,
while, over the full sample period the stock market dominated the price discovery process in all sizes, over 50%
of the sample, in only 60% of sizes the stock market dominates the price discovery process. The results, as before,
suggest no evidence that the CDS market dominates the price discovery process. In cases where the stock market
is not dominating the price discovery process, the GG coefficient turns out to be statistically insignificant.
24
model to forecast CDS spread returns make relatively more profits compared to those
who use a PVARM-based forecasting model. In other words, it also implies that
evidence of price discovery and the dominance of the stock market in the price
discovery process actually translates into economic profits for investors in the CDS
market.
The forecasts are generated for all sectoral and size-based panels (PVARM versus PVECM)
where the stock market dominates the price discovery process. The results are reported in Table
6. The results are promising, and, unsurprisingly, support the fact that the dominance of the
stock market in the price discovery process actually leads to economic profits for investors in
the CDS market. This is true for all stocks and IG-based stocks. The only exception though is
the energy sector amongst the IG-based stocks, where investors actually end up being worse-
off when using the PVECM compared to a PVARM. With sectors from the all CDS category,
profits (in annualised percentage) fall in the [3.4, 24.7] range and, across the six sectors,
average around 9.9% per annum. With regard to profits obtained for the six IG-based sectors,
profits average around 6.5% per annum. When considering the size-based panels, we again
find strong evidence that by following forecasts from a PVECM model, investors in the CDS
market are able to make significant profits across eight of the 10 size-based panels, with an
average profit of around 9% per annum. Amongst IG-based stocks, the annual average profits
across all 10 sectors turn out to be around 7.1%.
INSERT TABLE 6
On the whole, our results from the trading strategy suggest that price discovery that is
dominated by the stock market translates into profits for investors in the CDS market. Our
work, therefore, makes the connection between the statistical evidence of co-integration and
price discovery between the CDS and equity markets, and economic profits.
25
4. Concluding remarks
This paper is motivated by the fact that the extant literature, while scarce, has failed to build
consensus on whether the stock market leads the CDS market, or vice versa. The literature has
documented mixed evidence. We take a position in this literature by doing three things
differently. First, we propose a panel data model of price discovery. We identify that sectors
and sizes of firms are heterogeneous with respect to the CDS spread; therefore, we form panels
of stocks based on sectors and sizes of firms and apply panel co-integration and panel VECM
to estimate price discovery. Second, we not only examine all 212 stocks but also consider the
166 investment grade stocks, and examine whether evidence of price discovery is different for
investment grade stocks compared to all stocks. Third, we provide an economic significance
test of the relevance of price discovery for investors.
We find that while the stock market contributes to price discovery in nine sectors (all except
the telecommunication sector), the CDS spread contributes to price discovery in only six
sectors. In the six sectors where both the stock and the CDS markets contribute to price
discovery, it is the stock market that dominates the price discovery process. When we consider
only the investment grade firms, we observe a rise in the role of the CDS market in price
discovery: in seven of the 10 sectors, the CDS market contributes to price discovery but it does
not dominate the price discovery process, the stock market does.
Size-based panels of stocks reveal strong evidence of size effects. In most sizes of stocks, both
the stock and CDS markets contribute to the price discovery process; however, it is the stock
market that dominates the price discovery process. The magnitude of price discovery also
varies with size. The results are robust to the HAS measure of price discovery and hold, even
when we consider investment grade stocks.
26
We also test whether the 2007 global financial crisis affected the evidence on price discovery.
We find that it did. While the stock market dominates the price discovery process, its
contribution is higher in the crisis period compared to the pre-crisis period. Price discovery in
both periods is very much size-dependent. Our final contribution is that we develop the link
between price discovery and economic significance. In sectors where both markets contribute
to price discovery and the stock market dominates the price discovery process, we forecast
CDS returns using our proposed PVECM as well as using a PVARM (which simply ignores
the role of price discovery in forecasting CDS returns). We find strong evidence that a mean-
variance investor will be able to make relatively more profits from a price discovery model
(PVECM) as opposed to a model that simply ignores the role of price discovery.
27
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Figure 1: Mean and standard deviation of log CDS spreads by sector
In this graph we have four plots. Panel A contains the mean of log CDS spread for each of the 10 sectors; panel
B contains the standard deviation of log CDS spread for each of the 10 sectors; panel C contains the mean of log
CDS spread for each of the 10 sizes of firms, where 1 represents the largest size firm and 10 represents the smallest
size firm; and the last panel includes a plot of the standard deviation of log CDS spread for each of the 10 sizes.
00.5
11.5
22.5
33.5
44.5
5
Panel A: Mean of Log CDS spread by sector
0
0.2
0.4
0.6
0.8
1
1.2
Panel B: Standard deviation of Log CDS spread by sector
0
1
2
3
4
5
6
Size1
Size2
Size3
Size4
Size5
Size6
Size7
Size8
Size9
Size10
Panel C: Mean of Log CDS spread by size
0
0.2
0.4
0.6
0.8
1
1.2
Size1
Size2
Size3
Size4
Size5
Size6
Size7
Size8
Size9
Size10
Panel D: Standard deviation of Log CDS spread by size
32
Figure 2: A comparison of log CDS spreads of all stocks versus IG stocks
In this figure, we plot the mean log CDS spread for all stocks, and for IG stocks in panel A, and the mean of the
coefficient of variation of log CDS spread for all stocks and IG stocks in panel B.
Panel A: Mean CDS spread by sector
Panel B: Standard deviation of CDS spread by sector
00.5
11.5
22.5
33.5
44.5
5
All CDS stocks IG Stocks
0
0.2
0.4
0.6
0.8
1
1.2
All CDS stocks IG Stocks
33
Figure 3: A Plot of S&P 500 Index and CDS portfolio
In this figure we plot the equity market (represented by the S&P 500 index) and the CDS market. The CDS market
is represented by an equally weighted basket of CDS series attached to the member firms of the S&P 500 index
generated using the CIX page of the Bloomberg system.
34
Table 1: Distribution of firms in our sample
This table outlines the distribution of firms in our sample relative to the total market capitalisation (MC), and the
average pair-wise sector-based cross-sectional correlations. Panel A reports the distribution of market
representation with respect to each of the 10 sectors with the number of firms in each sector appearing in square
brackets, while Panel B reports the distribution of firms by size. Capturing the cross-sectional dependence, Panel
C reports the average pair-wise cross-sectional correlations based on a test proposed by Pesaran et al. (2008).
Columns 2 and 3 of panels A and B report the sum of all individual firm level market capitalisations relative to
the total market capitalisation in percentage form and in dollar (billions) form, respectively. Columns 4 and 5 of
panels A and B represent the mean and the standard deviation (SD) of firm level market capitalisation expressed
as a percentage of the total market capitalisation, respectively. The sample of firms covered in this study represents
about 60% of the US market. It should be noted that the last 3 firms were excluded in creating the size-based
panels to maintain a uniform number of firms in each size. Column 2 of panel C reports average correlations for
panels of unadjusted returns, whereas column 3 reports average correlations for the standardised (adjusted) panel
returns.
% of MC Mean MC (US$
billions)
Mean relative % of
firm level MC
SD firm level
mean relative
MC
Panel A: Sector-based distribution
Information technology[9] 3.538 44 0.393 0.449
Material[15] 2.285 17 0.152 0.108
Consumer discretionary[40] 7.003 20 0.175 0.163
Consumer staples[27] 9.750 40 0.361 0.469
Energy[17] 3.686 24 0.217 0.192
Financial[33] 11.021 37 0.334 0.412
Health care[19] 8.507 50 0.448 0.431
Utility[19] 2.101 12 0.111 0.079
Telecommunication[4] 2.626 73 0.657 0.599
Industrial[29] 8.471 33 0.292 0.444
Market 11,190
Panel B: Size-based distribution
Size 1 25.276 135 1.2036 0.4445
Size 2 10.149 54 0.4833 0.0716
Size 3 6.249 33 0.2976 0.0270
Size 4 4.688 25 0.2232 0.0221
Size 5 3.494 19 0.1664 0.0101
Size 6 2.876 15 0.1370 0.0097
Size 7 2.292 12 0.1092 0.0072
Size 8 1.756 9 0.0836 0.0068
Size 9 1.315 7 0.0626 0.0083
Size 10 0.837 4 0.0399 0.0054
Market 11,190
Panel C: Average pair-wise cross-sectional correlations (APCC)
Sectors APCC—unadjusted returns APCC—adjusted returns
Telecommunication 1.000 -0.024
Information technology 0.469 -0.018
Materials 0.565 -0.009
Energy 0.698 -0.008
Utility 0.658 -0.011
Health care 0.416 -0.002
Consumer staples 0.393 -0.004
35
Industrials 0.550 0.0001
Financials 0.553 -0.005
Consumer discretion 0.502 0.004
36
Table 2: Co-integration test results for sectoral and size panels
This table reports the Hadri panel unit root and panel co-integration test results in panels A and B, respectively.
The panels of stocks categorised into sectors are reported in column 1 of panels A and B. The trace statistics are
reported in column 2 for testing the null hypothesis of 𝑟 = 0 and 𝑟 = 1. The panels of stocks, categorised into 10
different sizes, are reported in column 1 of panels C and D. Market capitalisation of stocks is used to categorise
stocks into sizes. Size 1 represents the largest size firms, while size 10 represents the smallest sized firms. The
critical value at the 5% level, obtained from Larsson et al. (2001) is 1.645.
Panel A: Hadri tests for stationarity
All stocks IG stocks
Sectors Equity CDS Equity CDS
Telecommunication
20.081***
(0.0000)
18.177***
(0.0000)
19.428***
(0.0000)
11.409***
(0.0000)
Energy
55.056***
(0.0000)
39.118***
(0.0000)
47.807***
(0.0000)
30.799***
(0.0000)
Information technology
41.283***
(0.0000)
36.871***
(0.0000)
31.141***
(0.0000)
17.038***
(0.0000)
Materials
51.404***
(0.0000)
35.799***
(0.0000)
50.409***
(0.0000)
34.179***
(0.0000)
Utilities
66.382***
(0.0000)
42.553***
(0.0000)
67.004***
(0.0000)
38.342***
(0.0000)
Health care
56.684***
(0.0000)
55.065***
(0.0000)
49.632***
(0.0000)
48.894***
(0.0000)
Consumer staples
76.639***
(0.0000)
55.176***
(0.0000)
59.64***
(0.0000)
51.69***
(0.0000)
Industrials
52.332***
(0.0000)
59.158***
(0.0000)
50.859***
(0.0000)
56.973***
(0.0000)
Financials
61.895***
(0.0000)
71.968***
(0.0000)
58.137***
(0.0000)
66.342***
(0.0000)
Consumer discretionary
81.891***
(0.0000)
78.856***
(0.0000)
55.644***
(0.0000)
56.234***
(0.0000)
Panel B: Co-integration
All stocks IG stocks
Sectors 𝑟 = 0 𝑟 = 1 𝑟 = 0 𝑟 = 1
Telecommunication 20.04 5.66 8.32 7.79
Energy 33.46 13.47 25.58 10.84
Information technology 33.51 4.47 3.22 2.00
Materials 33.95 8.51 27.64 6.99
Utilities 59.9 21.09 51.31 18.57
Health care 64.06 8.78 49.52 7.87
Consumer staples 80.02 19.57 71.7 14.94
Industrials 73.3 16.76 71.17 16.59
Financials 346.1 26.36 197.4 23.03
Consumer discretionary 179.1 18.64 98.62 10.2
37
Table 3: Price discovery sector-based
In this table we report results on price discovery for each of the sectors. Column 1 contains the sectors; columns
2-5 report the error correction terms and the associated t-test statistics. The GG and HAS coefficients are reported
in the last two columns. Results are reported for all stocks categorised into sectors (panel A) and IG stocks
categorised into sectors (panel B). The GG coefficients in bold suggest that both error correction terms appear
with the correct sign and are statistically different from zero.
Panel A: All Stocks
ECT1 t-stat ECT2 t-stat GG HAS
Energy -0.0004 -2.8564 0.0006 4.6806 0.5954 0.7388
Finance -0.0005 -4.8203 0.0007 7.1327 0.5967 0.7020
Materials -0.0005 -3.0067 0.0006 4.5186 0.5766 0.7057
Consumer discretion -0.0003 -3.9791 0.0005 6.4575 0.6220 0.7338
Telecommunication 0.0000 -0.1676 0.0004 1.2369 0.9184 0.9880
Information technology -0.0001 -1.1422 0.0006 3.6639 0.8232 0.9204
Utility -0.0001 -0.8394 0.0007 4.6745 0.8916 0.9749
Health care -0.0057 -6.4888 0.0064 17.8149 0.5290 0.8827
Consumer staples 0.0000 0.2762 0.0005 4.8666 1.0445 0.9938
Industrial -0.0004 -3.7387 0.0009 6.0256 0.7073 0.7217
Panel B: IG Stocks
ECT1 t-stat ECT2 t-stat GG HAS
Energy -0.0006 -2.6050 0.0011 5.1252 0.6617 0.8048
Finance -0.0005 -4.5370 0.0007 7.0300 0.6086 0.7223
Materials -0.0006 -3.2223 0.0008 4.8050 0.5990 0.6981
Consumer discretion -0.0005 -4.4366 0.0010 6.2541 0.6545 0.6735
Telecommunication -0.0015 -1.7085 0.0014 1.7925 0.4820 0.5248
Information technology 0.0001 0.3921 0.0007 1.8458 1.1220 0.9545
Utility 0.0000 -0.0686 0.0013 6.0643 0.9932 0.9998
Health care -0.0006 -3.4281 0.0008 4.1823 0.5451 0.6006
Consumer staples -0.0002 -1.6299 0.0007 4.8380 0.8211 0.9062
Industrial -0.0004 -3.9527 0.0010 6.2037 0.7099 0.7167
38
Table 4: Price discovery size-based
In this table we report results on price discovery for each of the sizes of stocks. Column 1 contains the sizes;
columns 2-5 report the error correction terms and the associated t-test statistics. The GG and HAS coefficients are
reported in the last two columns. Results are reported for all stocks categorised into sizes (panel A), and IG stocks
categorised into sizes (panel B). Market capitalisation is used to form stock size. Size 1 contains the smallest sized
firms, while the largest sized firms are in size 10. The GG coefficients in bold suggest that both error correction
terms appear with the correct sign and are statistically different from zero.
Panel A: All stocks
ECT1 t-stat ECT2 t-stat GG HAS
Size 1 -0.0003 -2.8039 0.0007 5.1558 0.7372 0.7885
Size 2 -0.0003 -2.6039 0.0009 5.6375 0.7168 0.8410
Size 3 -0.0002 -1.3787 0.0008 5.6006 0.8285 0.9518
Size 4 -0.0003 -2.6425 0.0006 5.4800 0.7076 0.8246
Size 5 -0.0003 -2.4082 0.0010 5.6619 0.7588 0.8586
Size 6 -0.0004 -2.9032 0.0007 4.7458 0.6553 0.7355
Size 7 -0.0004 -3.2998 0.0008 4.9742 0.6499 0.7013
Size 8 -0.0004 -3.8654 0.0006 5.2795 0.5615 0.6589
Size 9 -0.0002 -2.2329 0.0006 4.6956 0.7170 0.8242
Size 10 -0.0003 -2.2811 0.0006 6.0235 0.6674 0.8872
Panel B: IG Stocks
ECT1 t-stat ECT2 t-stat GG HAS
Size 1 -0.0003 -2.6069 0.0007 4.4395 0.7226 0.7613
Size 2 -0.0004 -2.5860 0.0009 4.7958 0.7107 0.7884
Size 3 -0.0005 -2.5418 0.0010 6.1118 0.6782 0.8678
Size 4 -0.0008 -3.3962 0.0013 5.8464 0.6268 0.7565
Size 5 -0.0004 -2.8226 0.0010 5.6536 0.6999 0.8125
Size 6 -0.0006 -3.2370 0.0012 5.6569 0.6534 0.7656
Size 7 -0.0003 -1.9378 0.0011 4.8313 0.7917 0.8702
Size 8 -0.0008 -4.4609 0.0010 5.2828 0.5515 0.5864
Size 9 -0.0005 -3.4921 0.0008 5.3123 0.6184 0.7057
Size 10 -0.0006 -3.6487 0.0011 5.3084 0.6359 0.6845
39
Table 5: GG sectoral and size price discovery results, pre-crisis and crisis periods
This table reports the GG measure of price discovery over the pre-crisis and crisis period. The pre-crisis period
considered is 9 September 2004 to 26 February 2007, while the crisis period is considered to be from 27 February
2007 to 30 December 2009. The results are organised into two panels. Panel A contains results for sectoral panels
and includes all the 212 stocks and the 166 IG stocks. Panel B reports results for size-based panels. We consider
a total of 10 firm sizes. Market capitalisation is used to form stock size. Size 1 contains the largest sized firms,
while the smallest sized firms are in size 10. The GG coefficients in bold suggest that both error correction terms
appear with the correct sign and are statistically different from zero.
Panel A: Sectoral results
All stocks IG stocks
Pre-crisis Crisis Pre-crisis Crisis
Energy 0.4424 0.5646 0.4744 0.5409
Financial 0.6682 0.5254 0.7846 0.5033
Materials 0.4930 0.5828 0.6320 0.6410
Consumer discretion 0.8471 0.6412 0.7999 0.6293
Telecommunication 0.5462 1.2193 0.1213 0.6957
Information technology 0.4105 1.0929 0.4233 0.9489
Utility 14.7826 1.5296 0.8713 1.7315
Health care 0.5569 0.6679 0.2774 1.1150
Consumer staples 0.5433 1.2182 0.7147 0.9999
Industrial -3.3077 0.6453 -2.3514 0.6480
Panel B: Size results
All stocks IG stocks
Pre-crisis Crisis Pre-crisis Crisis
Size 1 0.7331 0.6253 0.8095 0.6149
Size 2 0.7798 0.8086 0.6605 0.7739
Size 3 0.5953 0.7902 0.6819 0.7494
Size 4 1.1224 0.5674 0.7055 0.5926
Size 5 0.5992 0.7101 0.7448 0.6574
Size 6 0.5600 0.7387 0.2663 0.6272
Size 7 0.9800 0.6674 0.8417 0.7793
Size 8 0.7732 0.5134 0.8144 0.5925
Size 9 0.7370 0.6819 0.8226 0.4958
Size 10 0.6109 0.6526 0.9083 0.5442
40
Table 6: Economic profits from a mean-variance trading strategy
This table reports the difference between profits obtained based on forecasts generated from a PVECM and a
PVAR model. The difference is in annualised form and a positive profit suggests that investors in the CDS market
gain from the price discovery dominance of the equity market (by following forecasts from a PVECM) as opposed
to a model that simply ignores the role of price discovery (PVAR model). The results are based on panels (sectors
and sizes) where the stock market dominates the price discovery process. Panel A contains the sectors for all
stocks and IG-based stocks, while panel B contains profits for size-based panels of all stocks and IG stocks. The
optimal lag lengths used to estimate the PVAR model and PVECM are obtained using the Schwarz Information
Criterion. The lag lengths are reported in square brackets in columns 2 and 3, beside the annualised profits.
Panel A: Annualised profits (%) for sectors of stocks
Sectors All stocks IG stocks
Energy 8.652 [2] -15.436 [2]
Materials 8.318 [3] 9.250 [3]
Health care 24.668 [3] 19.904 [3]
Industrials 7.705 [2] 6.489 [2]
Financials 6.463 [2] 6.907 [2]
Consumer discretionary 3.394 [2] 11.834 [2]
Panel B: Annualised profits (%) for sizes of stocks
Sectors All stocks IG stocks
Size 1 9.829 [2] 5.773 [2]
Size 2 28.377 [2] 23.204 [3]
Size 3 23.663 [3] 22.137 [2]
Size 4 13.131 [3] -14.969 [3]
Size 5 4.654 [3] 9.683 [3]
Size 6 -9.779 [3] 3.091 [3]
Size 7 6.124 [2] -7.310 [2]
Size 8 11.447 [2] 6.276 [2]
Size 9 -0.939 [3] 14.348 [2]
Size 10 4.340 [3] 9.106 [2]
