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FINANCIAL OLIGOPOLIES AND PARALLEL EXCLUSION IN THE
CREDIT DEFAULT SWAP MARKETS*
Lawrence Kryzanowski
John Molson School of Business
Concordia University
Email: [email protected]
Stylianos Perrakis
John Molson School of Business
Concordia University
Email: [email protected]
Rui Zhong
UWA Business School
University of Western Australia
Email: [email protected]
* We thank Jennie Bai, Sean Cleary, George Constantinides, András Danis, Faye Diamantoudi, Darrell Duffie, Jan
Ericsson, Gordon Fisher, Jean-Sébastien Fontaine, Louis Gagnon, Genevieve Gauthier, Nikolay Gospodinov, Bing
Han, Zhiguo He, Jing-Zhi Huang, Sergey Isaenko, Robert Jarrow, Arben Kita, Laurence Lescourret, Jorge Cruz Lopez,
Chayawat Orthanalai, Wulin Suo, Lorne Switzer, Dragon Tang, Nancy Ursel, Sarah Wang, Hong Yan, Jun Yang,
Zhaodong Zhong and participants at the 23rd Annual Derivatives Securities and Risk Management Conference jointly
organized by FDIC, Cornell and the University of Houston, the 20th Annual Multinational Finance Society Conference,
the 2013 Northern Finance Association Conference, the 2013 Financial Management Association Conference,
Frontiers of Finance 2014, China International Conference in Finance 2014, 3rd International Conference on Futures
and Derivative Markets 2014, 2016 Biennial Athenian Policy Forum and seminars at Bank of Canada, the 3rd Annual
Volatility Institute Conference at NYU Shanghai, Central University of Finance and Economics, Concordia
University, Queen’s University, University of Victoria, University of Windsor and Warwick Business School for
helpful comments. Financial support from the Senior Concordia University Research Chair in Finance, RBC
Distinguished Professorship of Financial Derivatives, IFSID, Social Sciences and Humanities Research Council of
Canada (SSHRC) and National Natural Science Foundation of China (NNSFC, Project No.71501197) are gratefully
acknowledged. We thank the Credit Regulation Department of the Financial Industry Regulatory Authority (FINRA)
for the information that it supplied on the applicability of FINRA Rule 4240.
FINANCIAL OLIGOPOLIES AND PARALLEL EXCLUSION IN THE CREDIT DEFAULT
SWAP MARKETS
Abstract
Motivated in part by a recent antitrust case in the CDS market defined as "parallel exclusion" that
corresponds to deliberate obfuscation on the part of financial intermediaries (dealers), we formulate an
oligopoly model of simultaneous trading by dealers in the CDS and Loan CDS (LCDS) markets. The model
incorporates information asymmetry between incumbents and would-be entrants in the dealer function in
both markets, recognizes positive and negative quantities and includes realistic features such as margins
and bid-ask spreads. We show that in equilibrium it is optimal for the incumbent dealers to take suitably
designed opposite positions in the two markets using only observable data at contract time. We also show
that limiting information to incumbents constitutes a barrier to entry and preserves the intermarket arbitrage
profits even in the absence of collusion. We apply the model to all matured contract pairs in the two markets
and document very large and virtually riskless profits from such trading, much larger than the collective
fine levied in the court case. Extensive empirical tests support our model and reject competing theories.
Keywords: Oligopolies, Market Structure, Barriers to Entry, (Loan) Credit Default Swaps, Limits to
Arbitrage
JEL Classification: L13, L14, L16, G01, G13, G14, G3
1
FINANCIAL OLIGOPOLIES AND PARALLEL EXCLUSION IN THE CREDIT
DEFAULT SWAP MARKETS
1. Introduction
Credit derivatives are insurance products that allow the holders of credit instruments, bonds and credit
lines, to hedge their exposure to the default of the underlying loan instruments. These instruments are known
as Credit Default Swaps (CDS) and are financial agreements between protection buyers and protection
sellers to transfer the credit risk of referenced assets. Their market is an intermediated market whose
structure has never been studied in detail except in an aggregate version that tacitly assumes perfect
competition. In this paper we argue that this structure has very important implications for public policy,
which we illustrate by a theoretical model and validate empirically using a novel data base. We find strong
evidence that the intermediary market’s structure is oligopolistic and that the credit derivatives’ prices over
the time series of our data are consistent with highly profitable and essentially riskless intermarket arbitrage
operations. We also show that these profits, net of margins and transaction costs, cannot be rationalized as
rewards for risk and cannot be justified by conventional limits to arbitrage explanations.
The public policy implications of our findings are readily apparent from a recent court case that partially
motivated our study. In April 2016 the Southern District Court of New York approved a settlement that had
been reached in September 2015 with all defendants in a number of class action suits that had been
consolidated for litigation purposes in October 2013. The suits alleged price fixing in the CDS market by
a number of financial institutions that acted as dealers in that market. These institutions included almost all
the major investment banks, as well as the industry group International Swap and Derivatives Association
(ISDA) and the market data provider Markit Group Holdings Ltd. All defendants in that suit were members
of the Too Big To Fail (TBTF) group of “systemically important financial institutions” identified in a 2011
report by the Financial Stability Board (FSB).2 Further, several of these institutions were sanctioned in a
separate case for manipulating the London Interbank Borrowing Rate (LIBOR) market, as noted in Gandhi
2 FSB, 2011. Policy measures to address systemically important financial institutions, November 4. Available at:
www.fsb.org/wp-content/uploads/r_111104bb.pdf?page_moved=1
2
et al (2019). Although none of these defendants admitted fault under the settlement agreement, they agreed
to pay a $1.86 billion penalty, which was described as “one of the largest private antitrust class action
settlements of all time”.3 The highly concentrated nature of credit derivative markets led to the allegations
and regulatory investigations of anti-competitive behavior, and to an evolving regulatory policy dealing
with, for example, initial and variation margins imposed on CDS traders, whose implications for pricing
efficiency and participant fairness are only partly addressed in the literature.
A key element of the court case was the allegation that the defendants introduced artificial information
asymmetry, by refraining from reporting critical information about trades in real time to would-be entrants
that did not belong to the dealer group. In the theoretical part of this article we examine the market structure
consequences arising out of this asymmetry by formulating a Cournot-style oligopoly model at the
intermediation level with simultaneous trading in the CDS and Loan CDS (LCDS) markets. The oligopoly
recognizes both positive and negative quantities in the two markets and includes frictions such as margins
and transaction costs. We demonstrate that information asymmetry constitutes a barrier to entry, which is
illustrated with an example in our online appendix. This barrier is over and above the more conventional
barriers due to economies of scale and regulatory requirements included in the model and detailed in the
next section. The barriers to entry prevent intermarket arbitrage to a sufficient extent to eliminate profits,
in spite of the fact that the item traded is identical in both, namely the default probability of the underlying
firm within the contract maturity time. Because both CDS and LCDS contracts are written on the same
firm, the claims are triggered by the same default events, which are defined exogenously by the International
Swap and Derivatives Association (ISDA). The only difference between the markets is that for the CDS
contracts the referenced assets are corporate debts, whereas the referenced assets of LCDS are syndicated
bank loans that have priority in case of default. The oligopoly model predicts that in equilibrium the
intermediaries (dealers) will adopt opposite positions in the two markets whose relative sizes are functions
3 See Gilmartin (216, p. 470). Hereafter all information about the court case is drawn from that study.
3
of the recovery rate estimates in case of default, which are available in the data base ex ante to the incumbent
dealer group.
Our intermarket oligopoly model’s formulation and results are also valid if only one of the markets is
oligopolistic and the other competitive. The oligopoly is justified by the fact that in the LCDS market the
number of quotes within the time span of our data base never exceeded 10, while the median was only 2,
implying that it functioned as a tight oligopoly for almost the entire time. Further, since both CDS and
LCDS contracts are standardized as to maturity and non-cancellable, the Cournot game is played only once
for each date and each reference entity. Hence, the timing of information revelation is irrelevant, since it
always takes place after contracting time. This simplifies significantly the empirical tests to verify the
oligopoly model, which rely on a single assumption about the ex ante values of the recovery rates and are
otherwise model free.
We test our model’s predictions by forming suitably chosen ex ante portfolios taking opposite positions
in CDS and LCDS contracts on the same reference entity. We document ex post (out-of-sample) positive
and persistent profits net of margins and transaction costs with insignificant risk for all such portfolios
constructed from 5-, 3- and 1-year matured contracts in our data base, thus identifying a tradable anomaly.
Our model predicts that the observed profitable portfolios are a consequence of the oligopolistic
equilibrium, vary inversely with the net demand elasticities and the number of Cournot players that are
active in both markets, and will persist as long as barriers to entry exist in at least one of the two markets.
Our choice of the matured contracts sample also verifies the use of the recovery rate data in documenting
ex ante the tradable anomaly. Last but not the least, we evaluate the total potential profit from our portfolio
strategies using observed premiums and transaction costs as well as legally prescribed margins and find
that the assessed penalty constitutes a small fraction of it.
It is important to note that these observed profits do not come from transaction costs collected by the
dealers or from collusion in setting the premiums in the two markets. In intermediation markets the function
of the dealers is to minimize the search costs of would-be traders and eliminate counterparty risk. The bid-
ask spread is legitimate compensation for the former, whereas the margins deal with the latter. While such
4
market frictions are barriers to small-scale entry, especially because they are likely to be higher for entrants
than for large incumbents due to the netting out provisions, they have not been included in the estimated
profits. Further, our tests’ results found no evidence of collusion in pricing. Note also that the information
asymmetry documented in the court case that forms the basis of the entry barrier is over and above the one
noted in the CDS market by Acharya and Johnson (2007) and Kryzanowski, Perrakis and Zhong (2017),
which was attributed to informed trading or the traders’ superior ability to process information.
To our knowledge, this is the first empirical article to apply industrial organization (IO) modeling
principles to the study of financial derivatives markets. A large number of empirical studies have appeared
in the financial literature dealing with the CDS market, but their market structure assumptions have
implicitly or explicitly almost always assumed free entry and a perfectly competitive equilibrium. Any
evidence of abnormal profits or other anomalous behavior is rationalized under the catch-all term “limits to
arbitrage”, following the classic study by Shleifer and Vishny (1997). Commonly invoked such limits are
various types of frictions such as asymmetric information, transaction costs, insufficiency of capital,
margins, slow moving capital and market illiquidity.4 In most of this literature, however, the arbitrage
relations are model-based and their failure may be due to model error. What makes our setup unique is the
simplicity of the integration relationship and an almost model-free parity relation under various market
structures, which is clearly not supported by the data in its competitive no arbitrage format, and the
confirmation of the ex post profits from the large sample of matured contracts.5
Our theoretical model nests most of the above frictions and reproduces well-known results from the
financial economics literature derived in different contexts. For instance, transaction costs and margins
create a no trade (NT) zone as in the classic work of Constantinides (1986), in which market participants
refrain from trading. Insufficiency of capital appears explicitly as a low amount of initial wealth available
to the dealers. Illiquidity in financial markets is commonly measured by the regression coefficient of price
4 See Mitchell, Pulvino and Stafford (2002), Stein (2005), Duffie (2010), and Thompson (2010). 5 Mitchell, Pulvino and Stafford (2002) have a similarly model-free arbitrage setup, but their empirical evidence shows
significant losses by arbitrageurs due to the failure of prices to converge to their no-arbitrage values.
5
on volume and is thus closely related to the concept of elasticity, which corresponds to non-horizontal
demand or supply curves and plays a key role in our oligopoly model. 6 In our model information
asymmetries are created by incumbent dealers against would-be entrants, as alleged in the 2016 court case,
in several media articles,7 and in Gilmartin (2016, pp. 474-476) and Chang (2016, pp. 672-679). In our
robustness checks we revisit transaction costs, margins (initial and variation) and slow-moving capital and
show that they cannot account for our results.
Our study also contributes to the research on market power in financial markets, which is represented
by a few studies that do not adopt the perfect competition and free entry assumptions. Closely related
theoretical studies are Duffie, Garleanu and Pedersen (2005), Duffie and Strulovici (2012), and Fardeau
(2012). The empirical work includes Froot (2001) who uses market power to explain the anomalous
behavior in catastrophe risk-indexed instruments, Allen et al (2006), who document stock market
manipulation cases and note (p. 646) the paucity of empirical studies on the topic, and Dunne, Hau and
Moore (2015) on the European sovereign bond market. In CDS markets Atkeson et al (2013) and Bolton
and Oehmke (2013) focus on the market structure without using any data, whereas Gehde-Trapp, Gunduz
and Nasev (2015) study the liquidity premium that they attribute to market power without any formal proof.
In fact market power in the CDS markets, in spite of the paucity of studies that invoke it, has been at the
center of several other court cases that claim anticompetitive conduct on the part of some of the defendants
in the case that motivates this paper. This conduct includes price-fixing, as in re. Alaska Electrical Pension
Fund v. Bank of America, N.A., Lead Case No.: 14-cv-7126 (JMF), and boycotting upstart trading
platforms that they did not control, as in re. Interest Rate Swaps Antitrust Litigation, Southern District of
New York, No. 16-md-02704. This latter case, in particular, is consistent with our theoretical setup and
empirical findings. As we argue in the next section, control of the trading platform is essential for the
creation of informational asymmetry between incumbent CDS traders and would be competitors in the CDS
6 See the extensive discussion of illiquidity in Vayanos and Wang (2013), as well as in our Section 3. 7 See, for instance, Louise Story in the New York Times, Dec. 11, 2010, and Matt Levine in Bloomberg.Com, Sept. 11,
2015.
6
markets. This entry-preventing conduct by incumbent oligopolistic firms who are not necessarily acting
collusively has been termed “parallel exclusion” by Hemphill and Wu (2013) and Chang (2016), and has
been linked specifically to derivatives markets such as options and CDS.
Our results are also consistent with empirical studies that adopt implicitly the free entry assumption for
the CDS market but document only partial integration of the markets for the CDS and the underlying firms’
instruments such as equities, as in Kapadia and Pu (2012) and Qiu and Yu (2012), and bonds, as in Choi,
Shachar and Shin (CSS, 2018). In particular, our CDS quotes are endogenous and affected by demand
conditions, as in Qiu and Yu (2012), but are also affected in our study by the existence of the virtually
riskless profits from CDS-LCDS intermarket arbitrage. Our findings for the pricing of the CDS spread
relative to that for the corresponding LCDS spread for a large majority of the tradable anomalies is
consistent with the pricing of the CDS spread relative to that for the corresponding bond spread documented
by CSS.
The importance of our theoretical and empirical results transcends by far the realm of the two derivative
markets where they were applied. As argued by Stulz (2010), the CDS markets were blamed in many
popular venues for their responsibility in causing the 2008 financial crisis. This is not in itself surprising,
since several theoretical studies link financial crises to financial intermediaries’ credit crunches.8 Although
Stulz does not endorse this blame, he does refer (p. 84) to potential lack of transparency and to manipulation
and instability in these markets. It is also a fact that one of the biggest bailouts during the crisis was that of
American International Group (AIG), which almost went bankrupt partly because of its failure to deliver
on its short CDS positions.9 Although the type of systemic risk associated with financial crises lies beyond
the scope of this paper, our CDS market structure results have obvious implications for efficiency and
regulatory policy for these all-important financial intermediaries.
8 See Holmstrom and Tirole (1997), and Rampini and Viswanathan (2018).
9 See https://insight.kellogg.northwestern.edu/article/what-went-wrong-at-aig. AIG was identified on the FSB’s
initial list of nine multinational insurance groups it considered to be global systemically important insurers (G-SIIs).
FSB, 2013. Global systemically important insurers (G-SIIs) and the policy measures that will apply to them, July 18.
Available at: http://www.fsb.org/wp-content/uploads/r_130718.pdf
7
Our empirical work tests the oligopoly model against alternative explanations. After observing that the
riskless profits persist in the presence of most conventional limits to arbitrage nested in our model, we
examine slow-moving capital, which has been invoked by Mitchell, Pedersen and Pulvino (2007) for
mispricing in mutual funds experiencing withdrawals, and by Kapadia and Pu (2012) in analyzing the
convergence of the markets for CDS and equities. We use several tests of convergence towards the
competitive equilibrium relation to justify slow-moving capital as an impediment to arbitrage. All of them
confirm the oligopoly market’s predictions and reject the limits to arbitrage explanations. In particular,
when all frictions are taken into account the size of the profits turns out to be a highly significant
determinant of the persistence of a profitable arbitrage strategy. We conclude that market structure is the
most likely explanation for this apparent trading anomaly.
In the absence of detailed microstructure data that identifies the traders in both markets it is impossible
to confirm with certainty that the observed potential payoffs of our arbitrage strategy were realized during
our data period. We do observe, though, that in both CDS and LCDS markets a small number of very large
financial institutions act as dealers.10 This is in accordance with the stylized general equilibrium model of
the banking sector in the NBER study by Atkeson et al (2013), which shows that the market concentration
on the CDS dealer side arises under free entry equilibrium due to the differing sizes of the firms in the
banking sector even in the absence of entry deterrence conduct. In commenting on the NBER study, Bolton
and Oehmke (2013, p. 4) point out the possibility of collusion with such high concentration and cite
anecdotal evidence of highly lucrative trading in that market. Further, Peltonen et al (2014) present data
according to which in 2011 the 10 largest traders had a market share in excess of 70% in all CDS trading
subnetworks, implying that the barriers to entry in the dealer market in the CDS-LCDS market pair may be
due to economies of scale that allow profitable entry-deterring conduct.11 Surprisingly, such barriers do not
appear at all in most of the empirical financial economics literature that we surveyed. They are only
10 The CDS markets’ data is controlled by the Depository Trust and Clearing Corporation (DTCC), which has
restricted access to transactional data with the exception of researchers whose employers are entitled to access such
data by law. The authors of this paper are not employed by entities entitled to such an access. 11 This was first pointed out by Bain (1956). See also the extended discussion of entry deterrence in Section 3.
8
mentioned in Qiu and Yu (2012, p. 612) in order to be dismissed on the grounds that “the total number of
entities providing [CDS] quotes can be quite large”. This statement does not hold in our data because in the
full 5-year maturity sample there are on average 5.20 and 2.02 dealers quoting on the same firm’s CDS and
LCDS contracts. Last, our oligopoly model also shows that collusion in setting prices and quantities is not
required in order to produce profits from intermarket arbitrage and suggests that the strategies identified in
this article may have already been realized by dealers executing them on their behalf to the available depth
of counterparty traders.
The rest of the article is organized as follows. In Section 2 we briefly describe the CDS and LCDS
markets. Section 3 develops the simultaneous equilibrium oligopoly market model with and without trading
costs. Section 4 contains our main empirical evidence. Section 5 examines alternative explanations. Section
6 presents empirical evidence as robustness checks. Section 7 concludes.
2. CDS and LCDS markets
2.1. CDS and LCDS market overview
The CDS market was initiated in the late 1990s and grew quickly until the subprime financial crisis
starting in late 2007. The LCDS market was launched in 2006 in both the US and Europe, 12 and
subsequently grew very quickly because of the rapid growth in the underlying asset. LCDS contracts can
be divided into Cancellable LCDS (European LCDS) and non-cancellable LCDS (US LCDS) contracts. In
this study we concentrate on the US LCDS contract, where one commits to make (receive) payment in the
case of default.
Similar to an ordinary swap contract, there are physical and cash settlements for both CDS and LCDS
contracts once the settlement is triggered by a credit event. Under cash settlement, there is no delivery of
the reference obligation and the protection seller only pays to the protection buyer the difference between
par value and the market price after a credit event. Especially after the financial crisis, cash settlement has
12 See Table XIII of our online appendix.
9
become more popular because the physical delivery of a loan is cumbersome and time consuming. In the
cash settlement of a LCDS contract the final price of the underlying syndicated loan is determined by an
auction methodology.13 CDS and LCDS are essentially swap agreements between two counterparties to
transfer the exposure to the default risk of the underlying asset. Thus, there is no requirement to hold the
underlying assets, especially under cash settlement, which makes an arbitrage position feasible. In the
following analysis, we assume cash settlement for both CDS and LCDS contracts.
2.2. Regulation and barriers to entry
As noted in the introduction, the CDS contracts, together with other over-the-counter (OTC) traded
derivatives, were at the center of the discussions that followed the 2008-2009 financial crisis, prompted in
part by the near failure of AIG. These discussions included a recommended shift of derivatives trading from
OTC to centrally cleared platforms, which was to be enforced through differential margins for OTC and
central clearing. The relative advantages of central clearing vis-à-vis bilateral OTC are analyzed in
theoretical models by Duffie, Scheicher and Vuillemey (2015), which show that they depend on several
central clearing features such as, for instance, the number of clearing platforms.
As our data covers totally the financial crisis and partially overlaps with the ongoing regulatory reform
of the Dodd-Frank Act, our empirical results took place under differing regulatory regimes. Over the period
examined here CDS contracts have become more standardized, and electronic processing and central
clearing of trades have increased. Regulatory approvals by the Securities and Exchanges Commission
(SEC) on margin requirements include an interim pilot program for dealer members of FINRA introduced
in 2009 (Rule 4240). A central clearing corporation (CCP) was introduced by several trading platforms
during the period to clear standard contracts.
Under central clearing there is an intermediary between long and short positions that reduces
counterparty risk by guaranteeing the execution of the swap agreements. Institutions wishing to participate
as dealers could become CCP members provided they had an A credit rating and a net worth of at least $5
13 See the link: http://www.creditfixings.com/CreditEventAuctions/fixings.jsp for the details of CDS Auctions and
Table XIV of our online appendix.
10
billion. These are clearly scale barriers to potential entry into the dealer function, especially given the fact
that the A credit rating would rule out most hedge funds. Further, it was alleged in the antitrust class action
mentioned in the introduction that the conspiring institutions imposed on the Intercontinental Exchange
(ICE) trading platform to require participants to hold a large amount of capital in derivative units, and also
used their positions in order to restrict the release of market data so as to preserve the dealers’ information
advantage. 14 The entry barrier for non-CCP traders who could have participated in the profitable
transactions described in this paper becomes apparent if price discovery and transparency does not extend
outside the CCP members.
These information-based entry restrictions are probably responsible for the undeniable fact of high
concentration in the CDS market, documented in Atkeson et al (2013) and Peltonen, Scheicher and
Vuillemey (2014). Margins also play a role as barriers to entry, as traders are allowed to net out their margin
positions, and this netting out tends to favor large market participants. In our empirical work we examine
the role of margins using FINRA’s margin scheme, assuming the existence of variation margins separately
for each underlying. For these variation margins we apply the practice followed in futures markets adjusted
as per the most plausible interpretation of Rule 4240.15 Specifically, we adjust the margin account in each
existing bilateral CDS-LCDS position every quarter, depending on the new observed spreads at that time,
mirroring the marking to market of futures contracts. As these adjustments are random when the position
is established, they introduce an element of risk into our simulated portfolios and cannot be undone due to
the non-cancellability of the contracts and the differing maturities of new contracts. For matured contracts
the variation margins were inconsequential for one- and three-year contracts and can safely be ignored. For
the five-year positions the variation margin impact is also very low in the matured subsample, but a precise
14 As Gilmartin (2016, p. 473) noted, this condition “was prohibitive even for some large banks”. Further, in a
declaration in support of the plaintiffs, Darrel Duffie (2015, par. 8, p. 3) wrote: “Because this action sought to address
the historical lack of price transparency and competition in the CDS market, I agreed to serve as an expert witness for
the plaintiff class.” Last, in an earlier Brookings Institute publication, Litan (2010) stated that the main impediments
to meaningful financial reform were “the private actors who now control the trading of derivatives and all key elements
of the infrastructure of derivatives trading, the major dealer banks.” 15 The details of Rule 4240 of FINRA are available at: http://finra.complinet.com /en/display/display_main.html?
rbid=2403&element_id=8412. Further information on our application of this rule is in Section 5.
11
estimation of its ex ante risk for our portfolios is not feasible and transcends the scope of this article. In
conclusion, therefore, the evidence on the institutional environment faced by those willing to trade in the
CDS-LCDS market pair is that, although there are no formal regulatory barriers, there are economies of
scale and serious restrictions to entry into the dealer function in both markets, resulting in high
concentration of trading.
2.3. Sample and data for the empirical work
For the empirical part of this article we obtain our CDS and LCDS data from Markit who collects the
quotes on LCDS spreads from large financial institutions and other high quality data sources and produces
the LCDS spread database on a daily basis. Our sample is from August 1st, 2006 to December 31st, 2014,
which encompasses the credit crisis, the accompanying recession and the subsequent recovery.16 As a
robustness check on the size of the transaction costs we also match part of our CDS sample to the CDS data
in Bloomberg.
In the CDS market we select the contracts on senior unsecured debts because this type of contract is the
most liquid and is used frequently in the literature. In the LCDS market, we select the contracts on the first-
lien syndicated loans, which form the majority in our data source and are more liquid than those on the
second-lien loans. We restrict our CDS and LCDS contracts to those in the United States and denominated
in US dollars. To ensure that the first-passage default and survival probabilities of the CDS contracts are
exactly the same as those of the corresponding LCDS, we match the daily LCDS and CDS data based on
company name, denominated currency, restructure clauses and time to maturity. We focus on the contracts
with a 5-year maturity, the most liquid contracts and the most studied in the previous literature,17 and we
also study in some detail the 1-year, and 3-year maturities which are more prevalent in the matured contracts
subsamples.
16 We calculate the realized abnormal profits using this sample period. For the later multivariate analysis we have to
merge the CDS and LCDS data with other databases such as Compustat, CRSP, etc., resulting in shrinkage of the
sample period because of data availability. 17 See for instance Cao, Yu and Zhong (2010) and Qiu and Yu (2012).
12
We use the estimated recovery rates extracted from our Markit datasets, which are based on the raw data
providers’ estimates as proxies for the unobservable real recovery rates upon default.18 These recovery rate
expectations at time of issue may differ from subsequent expectations and from actual recovery rates.
Nevertheless, these Markit estimates represent the only available proxy for the real recovery rates19 and
have been used repeatedly in previous studies.20 We stress the fact that the recovery rate estimates in the
Markit data base concern only the ex ante choice of our portfolios and are not involved in the ex post (out-
of-sample) evaluation of realized profits for the matured contracts that use the observed real recovery rates
in the few default cases that took place. Even if one disbelieves the adjusted no arbitrage relation derived
from our oligopoly model and/or the validity of the recovery rate estimates he/she can consider our
portfolios as “black box” screening rules that use only observables and generate subsequent profits by
simultaneous trading in both markets.
[Insert Table 1 about here]
Table 1 reports the summary statistics for our full sample of 5-year contracts covering 347 firms and the
sub-samples classified by credit rating.21 We eliminate the observations whose CDS spreads (or LCDS
spreads) are greater than 1 and the single name contracts which have less than 120 consecutive daily
observations. In addition, we obtain the accounting variables from Compustat, economic macro variables
from Federal Reserve H.15 database and equity trading information from CRSP. This is the full data base
from which all empirical work is carried out.
3. An oligopoly equilibrium model of CDS and LCDS markets
We model the simultaneous market equilibrium in both markets assuming initially the absence of trading
costs (apart from initial margins) and an oligopoly at the dealer level. Our simplified model abstracts from
18 Based on Markit CDS and Bonds User Guide, their clients can also contribute their recovery rates. Data on recovery
rates are denoted throughout the Markit product as Client Recovery. 19 The real recovery rates are collected from Moody’s (2007) Default and Recovery Database and discussed in Section
4. 20 See, for instance, Zhang, Zhou and Zhu (2009). Loon and Zhong (2014, pp. 112-113) give a detailed description of
the Markit data collection procedures. 21 We provide the same statistics for the 1-year and 3-year contracts in Table II of our online appendix.
13
some realistic market features but is quite general in its assumptions, retains the necessary elements for the
equilibrium analysis and contains the competitive and monopoly structures as limit cases.
3.1. A Cournot oligopoly without trading costs at the dealer level
We follow the general approach of Duffie and Strulovici (2012) in analyzing the intermediation between
the two markets. For every single firm on which CDS and LCDS contracts are traded we distinguish three
categories of agents and two markets denoted by the subscript 1,2i for the CDS and LCDS respectively.
In each market ic and iR , 1,2i , denote the corresponding premium and recovery rate estimate contained
in the database. 21 R and 11 R denote the expected losses in the LCDS and CDS contracts, respectively,
in the event of default; recognition of the priority rule implies 2 11 1R R . Two classes of agents are
assumed to trade exclusively in each of the two markets for insurance or speculative purposes, who may or
may not hold the firm’s bonds and credit lines, respectively.
Each member of these two single-market trading groups takes a long or short position in a CDS or LCDS
contract, with a member of the third group, the intermediaries, acting as a counterparty. These
intermediaries can also trade on their own behalf, as noted below. In the frictionless market equilibrium it
does not matter which side the intermediaries trade, since the prices are the same for both positions. This
assumption is relaxed in the following subsection. We represent each single-market group’s joint decisions
by the function ( ), 1,2i
D iC c i , the net demand volume of contracts (long minus short, or the conventional
demand curve minus the conventional supply curve in the corresponding market) in markets 1,2i , a
continuously decreasing function over the positive real line that becomes negative for sufficiently high
values of the ic ’s indicating net short positions.22 For reference purposes we also consider the equilibrium
premiums at which both functions become 0, which equalize the traded volume of long and short contracts
22 We assume, for simplicity, that the two markets are partially segmented, insofar as the two net demands are functions
of their own price and not the price in the other market, as it would happen if all traders apart from the dealers are
specializing in one of the two markets. This assumption is inconsequential and can be relaxed easily if, as is plausible,
the cross-elasticity effect is dominated by the own price elasticity.
14
for each market, denoted by ˆ , 1,2ic i , which corresponds to zero net positions for the intermediaries. It
is assumed that the net demand functions are exogenous, and that the marginal revenues [ ( )]
, 1,2i
i D i
i
d c C ci
dc
increase as the prices increase or the quantities decrease, the usual assumptions for oligopoly equilibrium.
The single-market traders’ net positions are negative (positive) whenever i ic c ( i ic c ), with the
intermediaries’ net positions having the opposite sign in each case.
In a large class of models that have been used to value the CDS contracts the markets for these contracts
have been assumed to be perfectly liquid, implying that these net demand curves are horizontal and that
traders cannot affect the equilibrium premiums.23 Several empirical measures of illiquidity have also been
developed based on stylized models of equilibrium in asset markets. Often illiquidity is measured by the
slope of the time series regression between the volume of trade and the premium of the respective CDS and
LCDS instruments as in Vayanos and Wang (2013), the slope of the function ( ), 1,2i
D iC c i for the two
markets, which is a key component of the net demand elasticity. Such measurements, however, embody the
assumption that the net demands stay the same over time, which is not necessary for our empirical work.
More relevant is the measure of illiquidity by the number of quotes in the CDS market as in Qiu and Yu
(2012), which is also used in our empirical tests in Section 5.
We model explicitly the decisions of the third category of traders in the two markets, the 1J
intermediary traders termed arbitrageurs or dealers, who trade simultaneously in both markets and provide
the residual liquidity to clear the markets. Following Shleifer and Vishny (1997), these traders are assumed
to be “highly specialized investors using other people’s capital”. A key element of our model is the
assumption that membership in this group is exogenous, defined by their control of the trading platform
and timely access to information, as expressed in the court case and in several opinion articles. In other
words, they are the only ones who can observe the net demands ( ), 1,2i
D iC c i in real time, when the market
23 See, for instance, Leland and Toft (1996), Ong, Li and Lu (2012) and Cao, Yu and Zhong (2010).
15
equilibrium is established. Apart from that, the arbitrageurs may differ as to their preferences and initial
wealth.
We consider a two-period horizon (0 and T), with the terminal date corresponding to the maturity of the
contracts. Let , 1, 2iY i denote the arbitrageurs’ net demand in the two markets at time 0 when all
decisions are taken, for which we must have the clearing condition, omitting the time subscript:
( ) 0, 1,2i
D i iC c Y i (3.1)
Each arbitrageur 1,..., , [1, ]j J J is assumed to choose her contract volume j
iy , j
i i
j
y Y ,
1,2i by maximizing the expected utility of a function ( )j j
TU W of discounted terminal wealth j
TW at the
maturity of the contracts. The utility is assumed to be twice differentiable, increasing and concave and with
a non-decreasing second derivative as implied by risk aversion and the normally assumed decreasing
absolute risk aversion (DARA) property. As the product is homogenous in both markets, in the absence of
collusion the joint equilibrium is a Cournot oligopoly, with each arbitrageur choosing j
iy by the
maximization of expected utility, with (0, ]T denoting the random default time and ( )SP , ( )DP , the
corresponding probabilities of survival and default within the contract horizon T
1 2
1 2
,
,
0 0
{ [ ( )]}
{ ( ) ( ( ) ) ( ) ( ( ) ) }
1,...,
j j
j j
j j
Ty y
T T
S j j D j j
T Ty y
Max E U W
Max P U W S d P U W D d
j J
(3.2)
In this maximization all ,k
iy k j are taken as given, , 1,2j
i i
j
y Y i , as per the market equilibrium
condition (3.1), and the wealth constraint (3.3) holds, with 0
jW denoting the initial wealth and with ( )j
TW
given by (3.3). The initial wealth is a proxy for economies of scale at the dealer level and will be shown to
play an important role on entry further in this section. Initial wealth also represents the start up capital, the
capacity to cover required margins for the intraday financing of trades, which as Duffie (2010) pointed out
16
is a key component of dealer solvency. , 1,2j
im i denotes the cost of the corresponding margin, assumed
proportional to the size of the contract and independent of the spread, and j
i is equal to +1 or -1 depending
on whether the arbitrageur position is long or short, recognizing that margins may differ between
oligopolists because of the netting out provision.
0 1 1 1 1 1 2 2 2 2 2
0 1 1 1 1 2 2 2 2
{ [(1 ) ] [(1 ) ]} ( ) , [0, ]
{ ( ) ( )} ( ) , (survival) [0, ]
j j r j j j j j j j
T T
j j j j j j j j r j
T T
W W e y R c m y R c m W D if default at T
W W y c m y c m e W S if no default for all T
(3.3)
The wealth constraints (3.3) include the simplifying assumption that all premiums are paid or collected
at contract maturityT , an assumption that is inconsequential when there is no default but may introduce
in the case of default some positive or negative bias to the terminal wealth if both markets’ positions are
short or long respectively. As Propositions 1 and 2 below show, this bias is also likely to be inconsequential
because the positions have opposite signs in the two markets. Similarly, it is assumed that the dealers treat
the observed recovery rates as if they were equal to those realized upon default. Since our sample consists
of matured contracts, this assumption does not affect the ex post dealer payoffs, which use the realized
recovery rates. Further, the error in using the ex ante observed recovery rate estimates in the payoff
estimates is very small.
The maximization of the objective function (3.2) yields the following first order conditions (FOC) for
the joint equilibrium
0
0 0
1
(1 ) ( ) '( ( ) )
(1 )
( ) '( ( ) ) ( ) '( ( ) )
( ), 1, 2
T
D j j
i T jj ji
i i iT T i
S j j D j j i D
T T
Jj i
i D i
R P U W D dy
c mY
P U W S d P U W D d
y C c i
(3.4)
17
Where '( ( ) )j j
TU W D and '( ( ) )j j
TU W S denote the marginal utilities of the jth arbitrageur under firm
default and survival respectively, and
' ''( ) , , 1,2
i i ii ii D i D DD i Di
D i i
c C c C Cc C i
C Y c
denote the price elasticity
of demand in each market. Note that the elasticities here take both positive and negative values when i
DC
changes sign. At 0i
DC the elasticity is not defined, as its inverse is equal to 0. Note also that since
' 0i
DC the elasticity in (3.4) always is negative (positive) whenever 0iY ( 0).iY
Let now
* * *0
0 0
( ) '( ( ) )1
( ), ( )
( ) '( ( ) ) ( ) '( ( ) )
T
D j j
T
T TjS j j D j j
T T
P U W D d
j jJ
P U W S d P U W D d
(3.5)
denote, respectively, the common factor in the two equations of (3.4) evaluated at the optimal number of
contracts and its summation over j . Aggregating equations in (3.4) and dividing by J on both sides, we
eliminate the market shares from (3.4) and obtain the equilibrium relations for the average dealer
participating in the two markets:
* 1
1 1
1(1 ) (1 ) , ( ), 1,2
J Jj j j i
i i i i i D ii
D
R c J m y C c iJ
. (3.6)
Relations (3.4) and (3.6) are consistent with the conventional valuation relations of asset pricing theory.
Indeed, the left-hand-side (LHS) of both relations is the expected cost of default in the two markets in the
risk neutral world, where the default probabilities have been weighed by the arbitrageurs’ marginal utilities,
individually and as a market aggregate respectively. These risk-adjusted costs are equated to the individual
and aggregate marginal revenues.
Taking the ratio, we get the following result,
1
1 1 111 1
1 22 2 22
1
1(1 )
1
1 1(1 )
Jj j
D
Jj j
D
c J mJ R
Rc J m
J
(3.7)
18
In line with standard results for the Cournot game, relation (3.7) contains as special cases both
competition for J , when the elasticity effect disappears and the individual margins tend to 0, and
monopoly for 1J . Competition emerges as a special case of the oligopoly equilibrium in the dealer
market when there are infinitely many arbitrageurs, no minimum scale restrictions and constant recovery
rates, where each arbitrageur maximizes (3.2) given 1c and 2c ; see Ong, Li and Lu (2012).
In the absence of competition each contract premium must be modified by the elasticity and the number
of dealers. It will be multiplied by a term that is greater (smaller) than 1 if the corresponding elasticity is
negative (positive). In other words, if the observed ratio 1 1
2 2
1
1
c R
c R
, it may be either because there is
mispricing or because there is imperfect competition and market power at the dealer level. In the former
case we expect changes over time would converge to the “correct” ratio (slow moving capital). In the latter
case no such convergence is to be expected, as (3.7) holds and the equilibrium ratio also depends on the
demand elasticities and the number of Cournot dealers. In our model J is common to the two markets,
since the arbitrageurs provide liquidity to both. Those traders participating in only one of the two markets
are absorbed by the market demand curve.
The Cournot equilibrium shows how parallel exclusion may result in a barrier to entry. As we shall see
in the empirical section, the overwhelming majority of the dealers’ positions in the two markets are short
LCDS-long CDS, with the number of dealers corresponding in most cases to the LCDS market traders.
Under parallel exclusion would-be entrants are unable to observe even the number J of dealers, let alone
the premiums and contract volumes in real time. As we prove theoretically in the next section and illustrate
in our online appendix, this uncertainty may render entry into the dealer function unprofitable, thus
preserving the oligopoly and motivating the parallel exclusion in the lawsuit.
19
3.2. Properties of the frictionless Cournot equilibrium
An arbitrage between the CDS and LCDS markets is defined as an equilibrium in which1
jy and 2
jy have
different signs in the Cournot equilibrium relations (3.4) for every dealer. The following result, proven in
the appendix, shows that this equilibrium does, indeed, correspond to an arbitrage.
Proposition 1: If *
1
jy and*
2
jy denote the optimal quantities for the thj Cournot player then their signs
are opposite and the oligopolist acts as an arbitrageur between the two markets.
Proposition 1 implies that each Cournot player participates in opposite sides in the two markets and
1 2( ) 0j jsign y y , for all j , or that arbitrage trading is part and parcel of market equilibrium in the
oligopoly structure. Furthermore, such trading is not the result of collusion or otherwise non-competitive
behavior but appears as an optimal strategy in a competitive oligopoly game. The following result is also
shown in the appendix.
Proposition 2: If *j
iy and*k
iy , 1,2i denote the optimal contracts for two different Cournot players
then, under our assumptions about the margins, * *
1 1
j ky y implies * *
2 2
j ky y and vice versa. Further, the
aggregate market positions iY , 1,2i , have opposite signs and all dealers adopt the same long-short
strategy in both markets.
Proposition 2 implies that, if 1* *
1 1... Jy y , then 1* *
2 2... Jy y as well. Further, the opposite sign for the
aggregate market equilibrium position in the two markets implies also that the corresponding elasticities
also have opposite signs and, similarly, thatj
i has the same value, 1 or -1, for all j. This has very important
implications for our empirical work, which are highlighted by the following result, whose proof is obvious
from (3.7) and the sign of the elasticity in each market.
Corollary: In the frictionless intermarket equilibrium (3.7) the equilibrium premium is reduced
(increased) for the long (short) market position from the value ˆ , 1,2ic i prevailing under perfect
competition.
20
Propositions 1 and 2 and their corollary also show that the frictionless equilibrium always exists under our
assumptions, and that all J players participate in both markets. This last result is no longer true in the
presence of frictions, as noted in the next subsection. The number of Cournot players becomes endogenous,
depending both on the size of frictions but also on economies of scale in terms of start up capital.
3.3. Cournot equilibrium under trading costs and margins
Let , 1, 2ik i denote the trading costs. We assume that for any CDS-LCDS contract pair these costs
are platform-wide and exogenously determined, and applicable to all such pairs. In other words, our dealer
oligopoly determines jointly the trading costs for the platform, but lets the dealers compete as Cournot
players in each contract pair. This assumption is consistent with the description of the practices of the
conspiring firms and the ICE platform as described in Gilmartin (2016) and is in agreement with the widely
accepted definition of the bid-ask spread as legitimate compensation of the market making function. It also
results in the most conservative estimates of the aggregate oligopoly profits, as the trading cost revenue
from the intermediated positions of the non-dealer traders is not added to the arbitrageur’s profit. By
definition, at the competitive frictionless equilibrium premiums ˆ , 1,2ic i we have ˆ( ) 0, 1,2i
D iC c i .
The demand curves in the presence of trading costs become discontinuous, lowering (raising) the
positive (negative) quantity segment by , 1, 2ik i . Instead of equation (3.1) we now have
ˆ( ) ( ) 0, ( ) 0 ( <0) for , 1,2
ˆ( ) ( ) 0, ( ) 0 ( 0) for , 1,2
ˆ ˆ0, [ , ] 1,2
i i i
D i i i D i i D i i i i i i
i i i
D i i i D i i D i i i i i
i i i i i i
C c k Y C c Y if C c k Y c c k i
C c k Y C c Y if C c Y c c k i
Y if c c k c k i
(3.8)
In other words, the dealers provide the counterparty short (long) demand when the premium is
sufficiently low (high), whereas they refrain from trading for the intermediate premium values.
The presence of trading costs raises questions of the existence of an arbitrage equilibrium as we defined
in our oligopoly model, in the sense that several or even all of the J dealers may not find it profitable to
trade in both markets. Existence depends on the size of the trading costs and the (observable or unobservable)
demands, as discussed more extensively in the following subsection, in which we examine the entry
21
conditions for both dealer and non-dealer traders. For our empirical work we develop observable conditions
under which a (3.10a) or (3.10b) equilibrium exists for all, part or none of the J dealers participating in
both our markets, thus covering all of the contracts in our data base.
The objective function, equations (3.2)-(3.3), remains the same, with the difference that now instead of
ic we have i ic k and i ic k , 1,2 i , depending on the sign of the corresponding j
iy . Without loss of
generality we now redefine J as the number of dealers who find it profitable to participate in intermarket
arbitrage. It can also be easily shown that when an equilibrium outside the no trade zone exists then
Propositions 1 and 2 and their all-important Corollary also hold in the environment with frictions. In such
a case, setting 1
1, 1,2
j Jj
i i
j
m m iJ
and setting + or – as superscript to the elasticity corresponding to the
equivalent demand ( )i
D iC c or ( )i
D iC c , we have FOC instead of (3.4):
For a short position in CDS and long in LCDS
* 11 1 1 11
1
* 22 2 2 22
2
1 2
1 1 2 2
1 1
(1 ) ( ) ( )(1 )
(1 ) ( ) ( )(1 )
( ), ( )
jj
D
jj
D
J Jj j
D D
yR j c k m
Y
yR j c k m
Y
y C c y C c
(3.9a)
Conversely, for a long position in CDS and short in LCDS
* 11 1 1 11
1
* 22 2 2 22
2
1 2
1 1 2 2
1 1
(1 ) ( ) ( )(1 )
(1 ) ( ) ( )(1 )
( ), ( )
jj
D
jj
D
J Jj j
D D
yR j c k m
Y
yR j c k m
Y
y C c y C c
(3.9b)
Aggregating again over the participating dealers in both markets we observe that the frictionless
equilibrium (3.6) is replaced by the following pair of equations (3.10a)-(3.10b), corresponding,
respectively, to the case where the dealer is short (long) in the CDS and long (short) in the LCDS (CDS)
market.
22
* *
1 1 1 1 2 2 2 21 2
1 2
1 1 2 2
1 1
1 1(1 ) ( )(1 ) , (1 ) ( )(1 )
( ), ( )
D D
J Jj j
D D
R c k m R c k mJ J
y C c y C c
(3.10a)
* *
1 1 1 1 2 2 2 21 2
1 2
1 1 2 2
1 1
1 1(1 ) ( )(1 ) , (1 ) ( )(1 )
( ), ( )
D D
J Jj j
D D
R c k m R c k mJ J
y C c y C c
(3.10b)
Obviously, equivalent results to the premium ratio (3.7) in the presence of frictions also exist whenever a
type (3.10a) or (3.10b) equilibrium exists.
Equations (3.10a-b) are also applicable by setting 1J to the case where the arbitrageurs form a cartel
in order to fix the premiums 1c and 2c by maximizing the sum of expected profits. It can be shown by Jensen’s
inequality that this is an optimal behavior for any desired allocation among the members of the cartel.
3.4. Entry in the competitive Cournot equilibrium under frictions
In the frictionless market without information asymmetry (parallel exclusion) entry into the dealer
function is theoretically feasible at any scale. In practice such entry is limited by economies of scale at the
dealer level under the form of fixed entry costs that prevent small financial institutions from entering
(Atkeson et al, 2013, p. 11). Here we show that this result also holds theoretically in our model when there
are margins and trading costs, where individual dealers may not find it profitable to participate in either one
or both markets depending on their utility functions and their start up capitals. We also show that economies
of scale proxied by an increase in the initial endowment 0
jW may overcome the trading cost barriers to
small scale entry. Last but not least, we demonstrate the effectiveness of the parallel exclusion barrier to
entry, by showing that a minimal information asymmetry that prevents would-be entrants to observe the
premiums in real time has the same effects as a reduction in start up capital.
We elaborate on the entry conditions of the dealers under parallel exclusion. We assume that each
member of the group of dealers who control the trading platform has full information about its potential
23
Cournot competitors’ preferences and wealth levels. Hence, it can determine for each pair of premiums
, 1,2ic i whether entry is profitable and at what scale. This is formalized in the following three
propositions.
Suppose a type of (3.10a) or (3.10b) Cournot equilibrium exists and consider a “small-scale” entrant
' [1, ]j j J who considers entry at an infinitesimally small output and acts as a price taker. We then
prove the following in the appendix.
Proposition 3: Given a type (3.10a) or (3.10b) equilibrium, a price-taking entry for entrant
' [1, ]j j J is not feasible in both markets if the following conditions hold
11 2 2 2 1 1 1 2
2
1( )
1
Rc c k m k m c c
R
for a type (3.11a) equilibrium (3.11a)
11 2 2 2 1 1 1 2
2
1( )
1
Rc c k m k m c c
R
for a type (3.11b) equilibrium (3.11b)
(3.11a-b) define a no trade zone (NT) 1 1= ,c cZ given the corresponding CDS recovery rates, LCDS
spreads and recovery rates, whose width is equal to
11 2 1 2 2 2 1 1
2
1( ) ( ) 2[ ]
1
Rc c c c k m k m
R
. (3.12)
(3.11)-(3.12) also imply that if the two premiums are outside the NT zone and if the two recovery rates
are known with certainty then the dealers’ portfolios are riskless, producing the following payoffs per unit
CDS contract:
11 2 2 2 1 1 1 1
2
12 2 2 1 1 1 1 1
2
1 1 1
1
1
1
1
0
Rc c k m k m if c c
R
RPayoff c k m k m c if c c
R
if c c c
. (3.13)
24
Specifically, when the observed CDS spread is such that 1 1c c the arbitrageurs take a long position in
one share of the CDS contract with $1 notional amount and pay the CDS premium given that no default
occurs, whereas they participate in 1 21 1R R shares of the LCDS short contract with $1 notional
amount per contract and receive the LCDS premium. If there is no estimation risk associated with recovery
rates and no further market frictions the current and expected future payoffs for this portfolio are positive
and zero, respectively. An equivalent portfolio exists when the observed CDS spread is such that 1 1c c .
Last, the arbitrageurs refrain from trading when the two markets’ spreads are in the NT zone represented
by its limits in (3.11a, b).
As all variables and parameters in (3.13) are observable ex ante, we verify in the following section the
existence of equilibrium relations away from the boundaries of the NT zone and find a very large number
of such relations. The resulting portfolios also turn out to be highly profitable and virtually riskless ex post,
thus generating a tradable anomaly. In several cases these profitable portfolios appear in sequences of
several dates for a particular reference entity. A key question in such cases is why these profits do not attract
new entrants within or outside the fully informed dealer group to drive the CDS and LCDS premiums
sufficiently close to the NT zone once the profitability is observed on the first date of the sequence.
For traders outside the dealer group a partial answer to this question is provided by the following two
propositions that show the importance of start up capital for any type of entry and demonstrate that
asymmetric information is equivalent to a reduction in start up capital. Several other possible explanations
can also be conjectured on the basis of our oligopoly equilibrium. For instance, in the more commonly
observed equilibrium of the (3.10b) type price-taking small scale entry may be infeasible if the initial
margins faced by small entrants are sufficiently large to drive the CDS market premium above the lower
bound 1 2( )c c in (3.11b), even though this does not happen for the incumbent oligopolists. For traders within
the dealer group that have full information on market conditions, the decision to enter and the scale of
participation in the two markets is endogenous and depends on individual preferences and the size of start
up capital.; it may entail staying out of one or both markets. Unlike the frictionless case, the convergence
25
to the NT zone does not require a large number of oligopolists, as we show in a numerical example in our
online appendix.
The initial wealth 0
jW , the economies of scale factor, plays a role in the entry process, similar to that
of capital investment in the strategic entry deterrence literature.24 The next theoretical result shows that
increases in0
jW can overcome barriers to small scale entry when the prospective entrant faces higher
margins than the incumbents, but also that these increases cannot go above an upper limit because then
entry in the long market becomes unprofitable. In the appendix we first prove the following, under slightly
different assumptions.
Proposition 4: Under the DARA property, assuming constant probabilities ( )SP and ( )DP for all
and unchanged equilibrium premiums, an increase in 0
jW may eliminate the barriers to entry in the
short market but this increase cannot exceed an upper limit if it is to be profitable in the long market for
both types of equilibria (3.11a) and (3.11b).
Last, information asymmetry between the dealers (oligopolists) and new entrants due to the parallel
exclusion lack of transparency as documented for the CDS market by Gilmartin (2016, p. 473) is formally
shown to constitute an entry barrier, equivalent to a reduction in 0
jW , in the next result, for any type of
entry. We consider one of the simplest asymmetries, in which the incumbents observe the spreads , 1,2ic i
in real time, but prospective new entrants, although they know the number J of incumbents, can only
observe past realizations, from which they derive unbiased estimates , 1,2ic i of the spreads such that
[ ] , 1,2i iE c c i at the time participation in the CDS-LCDS market pair must be decided. We then prove
the following in the appendix.
24 See Dixit (1980), Eaton and Lipsey (1981), Schmalensee (1981), Perrakis and Warskett (1986) and more recently
Ito and Reguant (2016).
26
Proposition 5: In the Cournot equilibrium with frictions and for both types of equilibria (3.11a) and
(3.11b) the feasibility of entry for a new entrant ' [1, ]j j J with imperfectly observed spreads , 1,2ic i
such that [ ] , 1,2i iE c c i is strictly equivalent to entry with a lower start-up capital '
0
jW than the one
actually possessed by the entrant for any type of incumbent behavior.
Propositions 3-5 may not have empirical implications due to lack of data, but they provide key
theoretical support to the parallel exclusion argument that motivates this article and show the importance
of scale in determining the CDS markets’ competitive structure. In our online appendix we provide a
numerical demonstration of these results by applying the oligopoly model to symmetric oligopolies with
identical constant relative risk aversion (CRRA) utility functions for all traders and constant elasticity
demands for both markets. We show the effects of collusion and of start up capital on the two markets’
equilibrium, as well as the convergence towards the NT zone as the number of Cournot players increases.
In fact, for 7J the oligopoly equilibrium is no longer an intermarket arbitrage, since the CDS premium
increases above the NT lower bound. Further, we illustrate the power of information asymmetry in deterring
entry as in Proposition 5, by modeling the entry decision of a third trader in a a colluding duopoly under
full and partial information. . These results hold as well under general non-competitive conditions and
without any restrictions on dealer preferences beyond risk aversion and the DARA property. Still, they are
sufficient to test the oligopoly market structure hypothesis, as we show in the following section.
4. The main empirical tests: Pricing parity violations
In this section we examine whether the observed equilibrium premiums, transaction costs and recovery
rates, together with the prescribed margins, generate simultaneous market equilibria in the CDS and LCDS
markets that correspond to positive dealer payoffs as in (3.14). Such payoffs imply market power and
sufficient barriers to entry to preserve the oligopolistic market. We verify them net of both transaction and
margin costs for the matured 1-year, 3-year and 5-year contracts with real default events.
27
4.1. Transaction costs and margin costs
We match the single names in our sample with the Bloomberg database to extract the daily closing bid-
ask quote information for CDS contracts.25 Table 2 reports the summary statistics of both firm average and
daily average bid-ask spreads in both absolute and proportional terms. As the transaction costs in the LCDS
market should be greater because of higher illiquidity, we use twice the bid-ask ratio of CDS to calculate
the absolute bid-ask spreads for LCDS contracts.26
[Insert Table 2 about here]
Table 3 presents the numerical results of our portfolio strategies for the base case 5-year contracts based
on (3.13) in the presence of time-varying bid-ask spreads, assumed the same for every firm in our sample
and equal to the daily average of the Bloomberg sample.27 Table 4 presents the same results for the 1- and
3-year contracts. The results in both tables include both initial and variation margins and are disaggregated
by rating classes and contracting date relative to the FINRA rule effectiveness. A similar pattern of results
appears when we omit the margins or use initial margins only, and also when we vary the transaction cost
rate according to the data source, Markit or Bloomberg.
As the margin requirements rely on the bilateral exposure in order to mitigate counterparty risk, we
calculate the cost of margin by computing the costs of both initial and variation margins. Because the dealers
have the flexibility to choose their margin calculation model, there is no unique number for the initial
margin requirements. For our empirical analysis we use the initial margin scheme provided by FINRA28 for
long positions and twice that for short positions for both CDS and LCDS contracts. We select our portfolios
on the basis of a NT zone that includes both transaction costs and initial margins, but do not include the
25 As Bloomberg does not provide information about restructuring clauses, we can only match with firm name and we
need to assume that the restructure clauses are the same as for the single name contracts in the Markit database. 26 We checked our results using three or four times the bid-ask ratio of CDS to calculate the absolute bid-ask spreads
for LCDS contracts and find consistent results. 27The results summarized in Table III of our online appendix are very similar if we use real bid-ask spreads for our
Bloomberg and Markit intraday sub-samples. Note that, in view of the skewed distribution of the bid-ask spreads, the
use of the average overestimates the impact of the transaction costs in (3.13) and understates the payoffs of our
portfolio strategies. 28 4240. Margin Requirements for Credit Default Swaps, FINRA Manual. Available at:
http://finra.complinet.com/en/display/display_main.html?rbid=2403&element_id=8412
28
unobservable variation margins. For the latter, we mark-to-market the net bilateral exposure at the end of
each quarter and set the variation margin equal to the net bilateral exposure. As for the appropriate rates to
finance the initial and variation margin requirements, we follow Kan and Pedersen (2012), who state that
the party who receives the collateral is required to pay interest to the counterparty at the Fed funds rate, as
proxied by the Overnight Index Swap (OIS) rate. We also assume that the dealers borrow money at a cost
that is equal to the swap rate depending on the maturity. Thus the net cost of margin for dealers is
approximated by the difference between the swap rate and the OIS rate.
[Insert Table 3, Table 4 about here]
The variation margins are not relevant for our sample of matured contracts that were signed before the
first implementation of the FINRA rule in 2009. The CDS-LCDS portfolios’ realized payoffs were
evaluated under a variety of assumptions about transaction costs and margins: with transaction costs but
without margins, with costs and initial margins but no variation margins, and finally with costs and both
types of margins as in the above tables. In the absence of margin the ex post payoffs present very few
negative values in a few realized default cases for all three maturities, less than 0.06% of the total in the
worst case or about 50 contracts, all of which are concentrated exclusively in the short CDS-long LCDS
category. These cases, however, yield not only a very small negative left tail to the payoff distribution, but
also disappear when initial margins are included due to the widening of the NT zone, again for all three
maturities. Hence, in view of the very large sample of observations, the portfolios in the absence of variation
margins are ex ante riskless arbitrage portfolios in a statistical sense, in spite of the recovery rate
uncertainty.
As shown in Tables 3 and 4, this conclusion is maintained when the variation margin is included for the
post-FINRA rule cases. There are very few negative payoffs that generate an insignificant amount of losses
for all three maturities, as noted in the introduction. Further, Figure I in our online appendix shows that
more than 60% of the portfolios fall outside the NT zone, implying that the competitive equilibrium
corresponds to about 36% of the observations and constitutes the exception, rather than the rule, in the CDS
and LCDS markets. These conclusions would not have been true had the variation margins existed in the
29
pre-FINRA rule data, since the average variation margin was negative for all three maturities, as shown in
Table I of our online appendix. Nonetheless, the observed profits from our easily executed arbitrage
strategies constitute a clear and model-free result that can be attributed either to the imperfect competition
model presented in the previous section or is a tradable anomaly in a perfectly competitive model that needs
to be justified by the traditional limits to arbitrage. The rest of this article concentrates on assessing the
validity of the two competing hypotheses.
5. Empirical tests of possible explanations
If a zero net cost portfolio generates positive payoffs in a perfectly competitive no arbitrage model then
the most commonly invoked explanation is that the payoffs are rewards for risk. In our case it can only hold
when the underlying firm defaults prior to contract maturity, and arises either from incorrect estimates of
the recovery rates in (3.13) or from counterparty default. For the realized ex post payoffs, which have used
actual recovery rates and no counterparty default was observed, the reward for risk explanation implies that
investors refrained from adopting the arbitrage portfolios in spite of observing riskless profits for more than
8 years and is not credible. Alternative explanations in a no arbitrage context are the often invoked limits
to arbitrage such as margins, liquidity, insufficiency of arbitrage capital, or slow moving capital.29 With the
exception of the latter factor, the others are also characteristics of a non-competitive market structure and
have been incorporated into our oligopoly model. We deal with each one of them in turn.
5.1 Limits to arbitrage
We structure the empirical tests in two stages. First we examine the frictionless economy, without any
margins or transaction costs, in which the two competing hypotheses can be contrasted under simplified
conditions involving the entire sample of matured contracts. The hypotheses that form the core of the
empirical part of this article are:
29 Shleifer and Vishny (1997), Mitchell, Pulvino and Stafford (2002), and Duffie (2010).
30
H0: The observed prices and recovery rates are consistent with the perfectly competitive no arbitrage
structure of the dealer market.
H1: The observed prices and recovery rates are consistent with a non-competitive structure of that
market.
If H0 is rejected then it may still be because of conventional limits to arbitrage factors rather than market
power. These are examined in the second stage, in samples that take into account realistic trading conditions
such as margins and transaction costs as well as firm-specific and macro variables, concentrating on those
factors that distinguish the two alternatives.
5.1.1 Tests in the frictionless economy
In the frictionless economy the two-market equilibrium is represented by the following pair of relations
under the alternative H0 and H1 hypotheses, both extracted from (3.7) without and with the elasticity terms
respectively:
1 1
2 2
1
1 1
2 22
1ln ln = 0 (no arbitrage, H0)
1
1(1 )
1ln ln ln (oligopoly, H1)
11(1 )
D
D
c R
c R
c R J
c R
J
(5.1)
Under H1 the LHS of (5.1) changes sign depending on whether (3.9a) or (3.9b) holds, as determined by
the signs of the elasticities in the two-market equilibrium. For this reason we separate the sample into two
subsamples, corresponding to the positive or negative LHS and to the corresponding strategies of sell CDS-
buy LCDS or vice-versa of Proposition 1.30 Our tests allow us also to verify two subcases, collusive
behavior of the dealers in the two markets and possible competitive structure in the CDS market.
In both subsamples the following relations hold under hypothesis H1:
H1a: Under Cournot oligopoly the LHS of (5.1) decreases as the number J of dealers increases.
H1b: Under collusive oligopoly the LHS of (5.1) is unaffected by the number of dealers
30 We omit a small number of observations, less than 4% of the total, for which the LHS of (5.1) is too close to 0.
31
H1c: In a non-competitive CDS market the LHS of (5.1) decreases as the elasticity1
D increases in
absolute value.
By contrast, neither of these variables should be a significant factor under H0.31 We test, therefore, H0
against the alternative H1 by regressing the LHS of (5.1) separately for the positive and negative subsamples
against values representing J and 1
D available from the Markit data. Whereas these variables are not
directly observable, reasonable proxies are for J the minimum number of quotes in the market pair (almost
always associated with LCDS) and the difference in the number of quotes between the two markets for 1
D
representing non-dealer traders, almost always in the CDS market. Note that J is an upper bound on the
two-market traders that are defined as dealers, although their small and persistent numbers in the data imply
that the approximation is good. Further, the database does not identify trades but only quotes, which makes
the elasticity proxy a good indicator of market pressures that shift the demand rightward and “flatten” the
demand curve by increasing in absolute value its elasticity at every price level.32 Under H1 and Cournot
oligopoly both variables should have negative coefficients in all cases, given the signs of the elasticities in
both (3.10a) and (3.10b).
We estimate, therefore, the following regressions, whose results for the 5-, 3- and 1-year samples are
shown in Table 5, with one-day lags in the independent variables to mitigate possible endogeneity problems
if H1 is true:
2 1
0 1 , 1 ,t 1 . 1
1 2 ,
1 2
0 1 , 1 , 1 , 1
2 1 ,
1Sell_CDS: ln _ + _
1
1Buy_CDS: ln _ + _
1
i t i i t it
i t
i t i t i t it
i t
R cDiff Dealers Min Dealers Control
R c
R cDiff Dealers Min Dealers Control
R c
(5.2)
[Insert Table 5 about here]
31 Note that the converse of this statement does not hold, because it is possible for both variables to be insignificant
in (5.1) and for H0 to be false. This happens if the dealers behave collusively and the inverse elasticity in the CDS
market is 0. 32 This is virtually identical to the use of CDS quotes by Qiu and Yu (2012).
32
The results are a conclusive rejection of H0 for all three maturities. All 1 coefficients are negative and
strongly significant, contradicting H0. All coefficients for the long CDS-short LCDS category are
negative and strongly significant, while for the short CDS-long LCDS category they are significant only
for one-year maturity. Further, collusive behavior of the dealers does not seem to be prevalent over the
entire sample, and the CDS market is clearly non-competitive. As for the time factor that can also be
used to assess the effects of the crisis, its sign cannot be predicted a priori, as it is influenced by the frictions
that reduce the profitable dealer participations by higher transaction costs that widen the NT zone, but also
by the increased demand for insurance and the reduced willingness to adopt the short positions. The results
show mostly positive signs for the crisis years that are significant in only a few cases. The estimates remain
almost identical when we include time dummies. In Table IV of our online appendix we also carry out
robustness checks with lagged variables and interaction terms that leave all our results virtually unchanged.
The negative 1 coefficients contradict directly one of the limits to arbitrage explanations of the parity
deviations in (5.2). The variable _Diff Dealers , almost always the extra quotes in the CDS market over
LCDS, is positively associated with contract liquidity and with a lower premium 1c according to Vayanos
and Wang (2013), but implies a higher deviation from no arbitrage parity in both expressions in the LHS
of (5.2). The Table 5 results also seem to support the Cournot version H1a of the oligopoly, since the
coefficient of the number of dealers variable J , proxied by _Min Dealers in (5.2), is negative and strongly
significant. This variable, almost always associated with the LCDS market, has a median value of 2, almost
equal to its mean, and a maximum value of 10 in our entire sample of matured contracts. In the key case of
the long CDS (3.10b) equilibrium almost half of the matured 5-year contracts had exactly one LCDS quote.
In Table V of our online appendix we confirm that the profits behave as predicted by the Cournot oligopoly
model and there is no evidence of collusion.
We conclude that H0 is decisively rejected, given that the key relation (5.1) is strongly influenced by
factors related to the structure of the two markets both within and outside the NT zone. We now proceed to
33
the second stage to ascertain if frictions can explain the tradable anomaly of the profitable intermarket
arbitrage in Tables 3 and 4. Under H1 the two markets’ elasticities appear as the key element affecting the
pricing parity relation, and the frictionless results in Table 5 are consistent with it. In the next subsection
we proceed with an analysis of the factors that affect them.
5.1.2 Empirical tests with margins and trading costs
Since the net demands for CDS and LCDS vary across our sample because of economic conditions and
firm characteristics, we need to control for both firm-specific and macro variables that affect market
conditions and through them the elasticities, the default probability and ultimately the parity relation. These
variables are chosen from the existing credit spreads literature,33 taking into account multicollinearity and
data availability. All variables used in the empirical analysis are defined in the appendix and further
discussed in the online appendix B; their correlations are shown in Table XII of that appendix. We restrict
ourselves to the 5-year maturity case, with the other two maturities presented in Tables VII and VIII of the
online appendix.
A majority of our anomalous portfolios are on privately owned firms, for which there is no publicly
available firm-specific information. For this reason they are omitted from further empirical work, because
the missing information may bias the tests. For such firms information asymmetry between CDS-LCDS
dealers and non-dealer traders is going to be maximum even without parallel exclusion dealer strategies.
Table IX of our online appendix shows the characteristics of the two subgroups outside the NT zone. The
private subgroup has lower average profits but also with a very low standard deviation, whereas the median
profits are significantly higher than those of the public group. The CDS market is clearly less competitive
in the private subgroup, because the net demand is more inelastic as evidenced by the significantly lower
number of quotes. As for the LCDS market, there is very little difference between the two subgroups’
quotes, whose medians are equal although the public subgroup has a slightly but significantly higher mean.
33 See, for instance, Acharya and Johnson (2007) and Cao, Yu and Zhong (2010). We also considered the variable
Loan/Debt but its inclusion would have reduced in a major way the size of the sample, because information was
missing for about 20,000 observations. Furthermore, it was not statistically significant when included.
34
For the subgroup of publicly traded firms we filter further our sample by excluding firms with missing
information. In Table 6 we present a summary of the most important results from regressing the parity
violations profits against the control variables and the competition proxies for the sample that does not
include the observations in the NT zone, those results that concern the structure of the two markets. Table
VI of the online appendix shows the full results. In both tables the results are presented for separate samples
in terms of the strategies that dealers use to exploit them, short CDS or short LCDS as in (3.10a) and (3.10b)
respectively, with the latter sample accounting for more than 80% of the total. The corresponding dependent
variables are equal to,
11 1 1 2 2 2
2
1[ ]
1
Rc k m c k m VM
R
, and 1
2 2 2 1 1 1
2
1[ ( )]
1
Rc k m c k m VM
R
(5.3)
where VM denotes the variation margin. The larger long CDS sample is further disaggregated according to
the rating of the underlying debt, between investment and speculative bonds, with the latter accounting for
almost 80% of the total.
In Table 6 the market structure results are strongly significant and in the expected direction for the long
CDS-short LCDS sample and, especially, for its speculative rating component, which accounts for about
two thirds of the total observations for both strategies. In those two samples monopoly and duopoly are
strongly positively associated with the size of the profits, whereas the difference of their coefficients shown
in online Table VI is also strongly significant, confirming the lack of collusion observed in the frictionless
case. Similarly, the elasticity coefficients proxied by the Diff_Dealers variable, are negative and strongly
significant for both monopoly and duopoly as predicted by the oligopoly model, and also not significantly
different from each other. By contrast, none of the market structure variables is significant in the short CDS-
long LCDS sample, even though they all have the right sign. This weak support for the oligopoly model in
this subsample is attributed to the fact that the arbitrage strategy involves raising the premium in the short
CDS market, where market power is weaker. Further, only one of the coefficients in the extended Table VI
results is weakly significant.
35
The full results in Table VI for the long CDS sample and its subsamples, tell a consistent story in their
significant coefficients, also consistent with the fact that the investment grade bonds are less significant.
This is that oligopoly profits tend to be stronger when the ex ante default probability is higher and the CDS
recovery rate is likely to be lower, as in the speculative grade bonds, and also when CAL, TANG, LOGA
and TB5Y are low and IDIO and CBS are high. Of the macro variables CBS, the yield spread, should not
affect the size of the profits under no arbitrage, because the ratios of both credit spreads and recovery rates
move in the same direction and the 𝑐1 𝑐2⁄ ratio is closely correlated with CBS. In fact its coefficient is
positive and significant in both the entire sample and the speculative subsample, moving in the opposite
direction relative to the recovery rate ratio and confirming the Table 5 frictionless results. The move is also
strongly consistent with the “flattening of the demand curve” in the CDS market and the increase in 1
D ,
to which the second profit term in (5.3) responds.34
[Insert Table 6 about here]
5.3. Analysis of slow-moving capital
Each observed arbitrage portfolio is a one-shot deal, because it cannot be replicated under identical terms
given the day-to-day changing information. Nonetheless, such day-to-day changes are often small and leave
a firm’s default probability and the CDS and LCDS net demand curves unchanged. In such cases the
appearance of a profitable arbitrage acts as a signal and we observe sequences of such profitable contract
pairs. Under limits to arbitrage in the form of adverse selection and slow-moving capital these sequences
should be short, their duration should decrease with the size of the profits and relative spread changes should
converge to the transaction cost-adjusted parity relation. On the other hand, in the oligopoly model with
barriers to entry because of parallel exclusion the sequences should persist when the profits are high and
there should be no convergence to the parity relation, since the set of fully informed dealers is unchanged
34 Note that in almost all cases the change in competition takes place only in the CDS market, given the small number
of dealers providing quotes for LCDS. The tightening of the parity relation violations affects the payoffs no matter
which markets the dealers are short in.
36
and the net demand elasticities change slowly. The following three hypotheses are direct tests of limits to
arbitrage, with the oligopoly model being the alternative in all three cases:
H2: Persistence of observed arbitrageur profits states is lower than that of their absence.
H3: Duration of arbitrageur profits states decreases the higher the size of observed profits.
H4: In arbitrageur profits states the CDS and LCDS premiums should change towards the closest
boundary of the NT zone.
To test H2 we count the number of consecutive days on which a particular CDS-LCDS pair persists in
a profit state or stays in the NT zone once we observe an arbitrageur profit opportunity (or lack thereof)
according to the CDS-LCDS parity rule presented in the previous sections and report the results in Table X
of the online appendix. Based on those results, we find that the median number of days of persistence or
duration of profits is 5 (4) days in the long CDS-short LCDS (short CDS-long LCDS) case. For the cheap
CDS case in the aggregate sample and in four out of the five subsamples the highest persistence occurs in
the profit state. In other words, for this case which is by far the most prevalent the profit sequences are
longer than the stays in the NT zone, thus contradicting H2.
We test H3 by defining a variable that measures profit persistence as in an event study, by noting the
date that a particular pair of CDS-LCDS contracts first gave rise to a profitable intermarket arbitrage and
counting the days in the sequence that the arbitrage persisted. Under H3 this sequence should be inversely
related to the size of the observed profits in the first day of the sequence. Because prevailing economic
conditions and the underlying firm’s characteristics as in Table VI of the online appendix may also affect
the persistence, we include them as independent variables in the regression as well, adding to them the
variable CRISIS identifying the time period June 2007-April 2009. Given the fact that these variables also
affect the size of the arbitrage profits, we first regress the profits on the firm specific and macro variables
and include the residuals of the regression as independent variables. We refer to this as Profit_TC*. Last,
given the nature of our data we estimate a two-stage logistic regression as in Heckman (1979) to account
for selection bias, with the first stage identifying the cases that fall outside the NT zone.
[Insert Table 7 about here]
37
We present the results of both stages in Table 7 for the entire sample and separately for the buy and sell
CDS subgroups. The significant macro and firm-specific variables are broadly similar to those of Table VI
for the corresponding samples. The striking result of Table 7, however, clearly visible in the full sample
and in both subsamples, is the significance of the second stage coefficient for Profit_TC*, which is strong
for the full sample and the long CDS portfolios and weak but still clearly positive for the short CDS
subsample. Our expectation is that the coefficient estimates for Profit_TC* should be negative if H3 holds,
because capital should respond faster to higher arbitrage profit opportunities’ signals. Thus, H3 is decisively
rejected, contradicting slow-moving capital or, indeed, any other limits to arbitrage factors. The duration
of arbitrageur profits increases with an increase in the profits as predicted by the oligopoly market model
and in accordance with the decision of the antitrust case, a result that is the single most powerful rejection
of limits to arbitrage and fully supportive of the financial oligopoly hypothesis.
Last, for H4 we construct a diverging ratio (DR) to measure the persistence of all the possible
intermarket arbitrage opportunities based on parity violations. This measure is inspired by the K-metric
developed in Kapadia and Pu (2012) and is described in detail in online appendix D. It is a nonparametric
measure, independent of the time period because it accounts for all the pairings of CDS and LCDS and all
the possible combinations from the N observations. Furthermore, it is based on standard statistical
properties and is not impacted by nonlinearities. The DR results are shown in Table XI of the online
appendix for the full sample and various subsamples based on credit ratings or position in the economic
cycle, calculated using the overlapping windows with varying window sizes for each firm. In all cases the
median DR is not significantly different from 50%, showing conclusively that there is no pattern in the
movements of the relative spreads in connection to the observed parity violations, directly contradicting H4
and fully consistent with the parallel exclusion’s entry barriers.
5.4. Conclusions of the empirical tests
The model-free and virtually riskless positive payoffs to our intermarket arbitrage portfolios that depend
on ex ante available information are efficiency violations. Limits to arbitrage is the most popular
explanation among finance researchers for such violations, and the empirical tests in this section treat it as
38
the null hypothesis, with non competitive market structure as the alternative. The tests use different
methodological approaches and samples, covering both the frictionless economy that uses the largest
available sample and the more realistic market equilibrium in the presence of both transaction costs and
margins. For the alternative non-competitive structure hypothesis we rely on the evidence and the
theoretical analysis for an entry-deterring oligopoly in all CDS markets at the dealer level provided in
Sections 2 and 3. All empirical tests are consistent with the oligopoly model, whereas limits to arbitrage in
an otherwise competitive market structure are inconsistent with the observed structural features of the two
markets determining the occurrence of the violations, and with the absence or perverse market response to
the observed pricing parity violations and the size of the violations.
6. Counterparty risk and regulatory implications
In this section we examine briefly counterparty risk, and the regulatory implications of our findings in
connection to the financial crisis and the various measures that were taken that concern the CDS market.
6.1. Counterparty risk
As noted in the introduction, counterparty risk in a CDS market (i.e., the risk associated with a
counterparty failing to honor its obligations) was at the center of the 2008 financial crisis. As discussed in
Section 2, the evolving regulatory environment and the introduction of CCP’s and margins were in part
intended to eliminate it.35 Because it evolved during our data period and our data base does not distinguish
between trades that went through a CCP and the others, we cannot evaluate its role in explaining the positive
payoffs. Nonetheless, counterparty failure of honoring its obligations did not appear anywhere in the
observed default cases of our matured contracts sample, implying that at best it might be able to explain
only a very small portion of the observed profits.
35 The impact of the central clearing counterparty (CCP) on the CDS market’s counterparty risk is unclear. For
instance, Duffie and Zhu (2011) show an increase of counterparty risk in the presence of CCP whereas Loon and
Zhong (2014) document a decrease. Arora, Gandhi and Longstaff (2012) find that the magnitude of the counterparty
risk that is priced is vanishingly small. Due to the nature of counterparty risk transfer under our trading strategy, the
presence of CCP should not be able to explain the documented abnormal current deviations documented herein.
39
6.2. Regulatory implications of the CDS market structure
Our results on the documented potentially available riskless profits from the CDS-LCDS market pair
have important implications for the ongoing public debate on the role of credit derivatives in the 2008-2009
financial crisis. Several of the financial institutions deeply implicated in the crisis, and the efforts to deal
with it such as the Troubled Asset Relief Program (TARP), appear at the top of the list published by Atkeson
et al (2013, Figure 2) of the top bank holding companies involved in credit derivatives (e.g., Morgan
Stanley, Goldman Sachs, Bank of America and Citigroup). Hence, a failure of these institutions that could
have occurred had the government not intervened during the crisis would have also precipitated the failure
of our arbitrage strategies. This kind of systemic risk, however, is mitigated by the fact that these institutions
are also part of the TBTF group, implying that government intervention is to be expected and probably
accounts for the vanishingly small price of counterparty risk noted above. Note that incorporating systemic
risk and potential intervention to save the TBTF institutions from default into our two-period oligopoly
model presents significant challenges. A decision to adopt a profitable CDS-LCDS intermarket arbitrage
becomes now a function of the arbitrageur’s existing non-cancellable positions in the various reference
entities, since they affect the terminal wealth of the arbitrageur in the event of systemic default.
An important inference that can be drawn from our results concerns the innocuousness of the financial
penalties from the antitrust actions in view of the potentially realized high profits of our arbitrage portfolios.
The agreed-to penalty of $1.86 billion was described by Gilmartin (2016, p. 470) as “one of the largest
private antitrust class action settlements of all time”. We evaluate the size of the penalty by comparing it
to the size of the realized profits from our arbitrage portfolios, which were shielded from competition by
the incumbents’ parallel exclusion strategy. We find in our matured contracts data approximately 264,627
long CDS-short LCDS matured contract pairs, to which we apply our simulated long CDS-short LCDS
strategies at the average notional contract size of $5 million. Our portfolios would have generated total
profits of approximately $116.35 billion dollars in total, with the negative profits equal to $10 million for
the 5-year maturities and $17,000 and $7,000 for the 3- and 1-year maturities respectively – literally pennies
40
in front of a steamroller!36 Recall that this total does not include the “normal” income derived from the
dealers’ intermediation functions, which were assumed to be sufficient to cover the dealers’ costs.
In other words, the assessed penalty was less than 1.6% of the estimated essentially riskless profits
arising from our matured arbitrage portfolios in the years immediately before the settlement. More
substantive was the commitment on the part of the defendants to take actions to eliminate certain features
of their entry-deterring conduct by increasing price transparency, which are still being discussed as of this
writing (Gilmartin, 2016, pp. 477-479). Whereas neither the U.S. Department of Justice nor the European
Commission for anticompetitive agreements have sought financial penalties based on the conclusion that
the alleged anti-competitive conduct is being remedied,37 it remains to be seen whether these actions will
be sufficient to attract more participants and increase competitiveness in the CDS and LCDS markets. The
initial results are not very encouraging, although it may be a bit early for definitive conclusions. Chang
(2016, p. 714) finds virtually no change post-settlement in the CCP membership profiles and the dominance
of the major dealers. He also expects this situation to continue because of the outsized role played by the
major dealers in setting clearinghouse risk standards.38
The implementation of the variation margin in CDS trading, the only “new” regulatory practice that can
affect the ex ante identification of the profitability of at least some of the simultaneous CDS-LCDS trading
strategies, has two contradictory impacts on market efficiency and fairness. On the one hand, the reduction
36 The realized profits of $116.35 billion dollars are calculated using the matured CDS contracts whose actual recovery
rates can be observed in our sample. The actual default events and corresponding real recovery rates are extracted
from multiple sources, including Moody’s ultimate default and recovery database, and the CDS and LCDS auction
website. 37 DOJ won’t penalize banks in swaps investigation: WSJ, Reuters, Feb. 1, 2014. Lavoie, Chantal. Belgium: EU
competition investigation into Credit Default Swaps: The end in sight?, Monday, June 5, 2016. Available respectively
at: http://www.huffingtonpost.com/2013/12/02/doj-not-planning-to-penal_n_4370011.html; and
http://www.mondaq.com/x/493020/Antitrust+Competition/EU+Competition+Investigation+Into+Credit+Default+S
waps+The+End+In+Sight However, the European Commission made various commitments binding on ISDA and
Markit that would facilitate access to essential price data and indices for CDS exchanges and exchange products
(http://europa.eu/rapid/press-release_IP-16-2586_en.htm). This essentially dealt with the first of two significant
actions that the ISDA agreed to undertake as part of the settlement agreement; namely, to adopt a more transparent
licensing framework for its intellectual property that included a dispute resolution mechanism and “fair, reasonable
and nondiscriminatory” terms (Gilmartin, 2016, pp. 477-78). 38 See, e.g., ICE CLEAR CREDIT, CLEARING RULES § 201(b)(ii) (Mar. 29, 2016),
https://www.theice.com/publicdocs/clear_credit/ICE_Clear_Credit_Rules.pdf [https://perma.cc/UMW5-D4JH].
41
of the strategies’ profits from the variation margins and the discouragement of multiple positions that can
precipitate systemic risk are certainly desirable, because such profits tend to accrue disproportionately to
the largest institutions. On the other hand, the relative prices of the two markets will be even further away
from the competitive standard, which prevails when both markets’ elasticities tend to infinity, since there
will be fewer trades under variation margins and fewer firms participating in convergence trades (i.e.,
increased entry barriers). A similar contradiction affects also the initial margins, whose effect is identical
to that of transaction costs.
The resolution of this contradiction through an appropriate design and enforcement of regulatory
policies lies beyond the scope of this article but should be part of the ongoing regulatory debate.
7. Conclusions
Based on the documented highly concentrated structure of the CDS markets and a recently settled
antitrust case, we formulate a Cournot-style oligopoly model for intermarket trading in the CDS and LCDS
markets on the same reference entity. We extend the oligopoly model to include margins and proportional
transaction costs. Empirically, the observed abnormal positive current payoffs are related to structural
features of the two markets. These empirical evidence are consistent with our oligopoly model on the dealer
side in both markets and are confirmed with extensive empirical tests that reject the conventional limits to
arbitrage factors in favor of the competing oligopoly hypothesis.
This failure of intermarket trading to equalize the spreads in the CDS and LCDS markets is analyzed
theoretically and is formally documented here for the first time. Our theoretical and empirical analysis
confirms the related theoretical results by Atkeson et al (2013) and the conjectured and anecdotal evidence
by Bolton and Oemhke (2013), as well as the structure of CDS markets documented in Peltonen et al (2014)
and Duffie et al (2015). It is also strongly supported by the allegations formulated and essentially endorsed
in the recent settlement of a private antitrust class action suit alleging manipulation in the CDS market, as
analyzed by Gilmartin (2016).
42
Our results also have regulatory implications with respect to the advantages of a CCP and the recently
introduced variation margins, both of which lower counterparty risk but also benefit large traders. These
can only be assessed with detailed information and intraday data on actual margins, contract depths and
trading costs. Note also that two relevant theoretical oligopoly studies reach diametrically opposite welfare
implications. Shimomura and Thisse (2012) show that welfare increases with the entry of large firms,
whereas Atkeson et al (2013) show that welfare improves when some large dealers are removed and smaller
ones are encouraged to enter.
Examination of these factors requires access to microstructure data in the two markets. Given the
importance of the CDS markets in the recent financial crisis, such a microstructure study should be the
focus of future research.
43
Appendix A: Proof of the Propositions
Proof of Proposition 1:
The proof relies on the following auxiliary result, whose proof is obvious and will be omitted. It is a
specialized version of a similar result initially presented by Rothschild and Stiglitz (1970).
Lemma: Let ( )F x denote a concave function on the real line, and let also 1 2x x denote two values
and 1 1 2 2 1( ) ( , ) or ( , 1 )p x x p x p p a probability distribution. Then any mean-preserving change
x that reduces the distance of 1x and 2x increases the expectation 1 1 2 2[ ( )] ( ) ( )pE F x p F x p F x .
To prove the Proposition we apply the lemma to the utility function 1( )j jU W evaluated at the Cournot
equilibrium *, 1,2, 1,...,j
iy i j J , * * 1 *( )i j
i D i
j
c C y , with the following values of 1x and 2x
* * * *
1 0 1 1 1 1 1 2 2 2 2 2 1
* * * *
2 0 1 1 1 1 2 2 2 2 1
[(1 ) ] [(1 ) ]
( ) ( )
j j j j j j j j
j j j j j j j j
x W y R c m y R c m W D
x W y c m y c m W S
(A.1)
Assume that both *
1
jy and *
2
jy are positive, in which case 1 0 0jx W and 2 0 0jx W in (A.1).39 Then
by applying the lemma it can be easily verified that the strategy of reducing unilaterally *
1
jy and thus
raising the price 1c above *
1c (yielding a reduction of *
1
jy in the CDS volume) while simultaneously
increasing unilaterally *
2
jy and thus reducing 2c below *
2c (increasing the LCDS volume by *
2
jy ) and
such that *
1 2
*
2 1
(1 )
(1 )
j
j
y R
y R
would increase the expectation
1 1 2( ( )) ( ) (1 ) ( )j j D DU W P U x P U x and
preserve the mean 1 2( ) (1 )D D
pE x P x P x . Hence, *
1
jy and *
2
jy cannot both be optimal and positive
in a Cournot equilibrium. A similar proof also holds when both are assumed negative, thus proving the
Proposition.
39If
1 0 0jx W then the oligopolist’s utility is inferior to the one resulting from a strategy of doing nothing.
44
Proof of Proposition 2:
Applying the equilibrium relations (3.4) for any pair of traders ( , )j k and equating the terms equal to
the prices, we get,
* * * *11 1 1 1 1 1 11
1
* * * *22 2 2 2 2 1 22
2
(1 )[ ( ) ( )] ( )
(1 )[ ( ) ( )] ( )
j k j j k k
D
j k j j k k
D
cR j k y y m m
Y
cR j k y y m m
Y
(A.2)
Suppose now without loss of generality that 1Y is positive, implying that1 0D and assume that
1* *
1 1... Jy y and that *
1
jy and *
1
ky have the same sign, implying also by Proposition 1 that *
2
jy and *
2
ky also
have the same sign. In such a case j k implies that * *
1 1 0j ky y , the difference in margins at the RHS of
the first part of (A.2) is positive and similarly * *
1 1
j ky y has the same sign as* *( ) ( )j k , which in turn
implies that * *( ) ... (1)J . If 2 0Y then Proposition 1 is contradicted for at least some j , since we
must have 1 2( ) 0j jsign y y for all j . Hence, 2Y must be negative, in which case2
2 0DY . Since the LHS
of the second part of (A.2) is positive, from the RHS we get that* *
2 2 0j ky y and the margin difference is
similarly positive. Hence, 1* *
1 1... Jy y implies that1* *
2 2... Jy y as well. The rest of the Proposition follows
immediately by establishing a contradiction that arises when *
1
jy and *
1
ky have different signs, QED.
Proof of Proposition 3:
Consider the case of a (3.10b) equilibrium and suppose entry is feasible for some firm 'j at “small”
contract sizes 1 20, 0 that do not affect equilibrium in the CDS and LCDS markets respectively. In
such a case we must have from (3.9b)*
1 1 1 1(1 ) ( ')R j c k m and*
2 2 2 2(1 ) ( ')R j c k m . It is easy
to see that the signs of the elasticities imply that these two relations are incompatible with (3.11b), QED.
The case of a (3.10a) equilibrium is symmetric. Observe that while (3.11a,b) preclude entry in both markets,
they leave open the possibility of small-scale entry in only one of the markets. However, in such a case, the
45
entrant is no longer an arbitrageur. Observe also that the equilibrium (3.9b) implies the following relation
for any type of entry, given the signs of the elasticities:
*1 1 1 2 2 2
1 2
( ')1 1
c k m c k mj
R R
. (A.3)
For a small scale entrant we obviously have *
0( ') '( )jj U W , in which case (A.3) defines obvious
limits on0
jW in order to enter into the dealer market. These limits, however, do not apply for an entrant that
affects the equilibrium in the two markets.
Proof of Proposition 4:
The proof is trivial for small scale entry, given (A.3) for *
0( ') '( )jj U W . Assume, therefore, that this
last relation does not hold, that we have a (3.10b) equilibrium but that the prospective entrant ' [1, ]j j J
faces margins such that she is in the NT zone with 1 1 2( )c c c . We prove the result for entry in market 2
only, with identical proofs for the other cases. As shown in the proof of Proposition 3, feasibility of entry
for entrant ' [1, ]j j J implies *
2 2 1 2(1 ) ( ')R j c k m , which holds for the incumbents but not for the
prospective entrant because she faces higher margins. We need, therefore, to show that *( ')j decreases
or, equivalently, that 1 1
0 0
1 1
0 0
( ) '( ( ) ) '( ( ) )
( ) '( ( ) ) '( ( ) )
T T
S j j
S
T TD
D j j
P U W S d U W S dP
PP U W D d U W D d
increases with 0
jW . This last
relation is equivalent to
1 1
0 0
1 1
0 0
''( ( ) ) ''( ( ) )
'( ( ) ) '( ( ) )
T T
j j
T T
j j
U W S d U W D d
U W S d U W D d
(A.4)
Since the DARA property implies 1'''( ) 0jU W and obviously
1 1( ) ( )W S W D for all τ for a prospective
entrant considering entry with a short position in market 2, we have 1 1''( ( ) ) ''( ( ) )j jU W S U W D and
46
1 1'( ( ) ) '( ( ) )j jU W S U W D , from which (A.4) follows immediately, QED. Identical proofs apply for the lower
limit on*( ')j for entry in the long market, and also for entry in an (3.10a) equilibrium.
Proof of Proposition 5:
Assume that we have a type (3.10b) equilibrium and that the entry of 'j is feasible had the entrant
possessed the same information as the J incumbents, and let *' *'
1 2( , ) y y denote the equilibrium output choices
of the entrant. By definition, these output choices solve the problem (3.2) modified by the presence of
margins and transaction costs, and let * '
1[ ( )]j jE U W denote the resulting maximized expected utility. Let
now a tilde denote utility and wealth under restricted information for the 'j entrant and suppose now that
this maximization takes place under the imperfectly observed spreads , 1,2ic i , in which case the entrant’s
utility is '
1( )j jU W and she must solve the following problem:
' '1 2
' '1 2
'
1,
' ' ' '
1 1,
0 0
{ [ ( )]}
{ ( ) ( ( ) ) ( ) ( ( ) ) }
1,..., 1
j j
j j
j j
y y
T T
S j j D j j
y y
Max E U W
Max P U W S d P U W D d
j J
,
(A.5)
subject to
1 11 2
1 1 2 2
1 1
( ), ( ) J J
j j
D Dy C c y C c
.
Since the utility function is strictly concave, by Jensen’s inequality we have 1 2
' '
, 1 1[ ( )] ( )j j j j
c cE U W U W
, implying that the solution of (A.5) is strictly less than * '
1[ ( )]j jE U W . The latter function is, however,
monotone increasing in '
0
jW , implying that there exists a value ' '
0 0
j jW W equating it to the solution of (A.5),
QED.
Appendix B: Definition of the variables
47
Variable Definition
Profit_TC Realized return of CDS and LCDS pairs with transaction costs, initial and variation
margins.
LOGA The logarithm of total assets.
CAL The current ratio; that is the ratio of current assets over current liabilities.
LEV The leverage ratio that equals total debt divided by total assets.
TANG Tangible assets ratio that equals the value of tangible assets divided by total assets.
IDIO The idiosyncratic volatility of equity returns. We first calculate the daily returns using
1 1it it itr p p , where itp denotes the daily closing equity price for firm i at day t, and then
run the following regression using the Fama-French three-factor model to get the residual
it ,
1 2 3it t t t t itr rf R rf SMB HML
The idiosyncratic volatilities, ith , which are the conditional volatilities of the residuals,
are filtered by an EGARCH model, given as follows,
1 1 1 1
, ~ 0,
ln( ) ln( )
it itit it it
it it it it it
h N h
h E h
TB5Y The 5-year treasury bond yield in the U.S.
SL Slope of yield term structure, i.e., yield spread between 1-year and 5-year contracts.
CBS The yield spread between Aaa and Baa corporate bonds.
SP The total daily return of the S&P 500 index.
Diff_Dealers The difference of the number of distinct dealers providing quotes for a pair of CDS and
LCDS contracts.
Min_Dealers Minimum number of distinct dealers providing quotes for a pair of CDS and LCDS
contracts.
48
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52
Table 1: Descriptive Statistics of 5-year CDS and LCDS contracts
This table reports the means of 5-year CDS(LCDS) spreads, number of distinct dealers and quoted recovery
rates provided by Markit under various ratings. It covers the sample period from August 15, 2006 to
December 31, 2009 and includes all the 5-year matured contracts for the calculation of the realized returns.
CDS LCDS
No. of
Obs
Average
Spreads
(Unit:
bps)
Average
No. of
Dealers
Average
Quoted
Recovery
Rates
(%)
Average
Initial
Margin
Average
Spreads
(Unit:
bps)
Average
No. of
Dealers
Average
Quoted
Recovery
Rates
(%)
Average
Initial
Margin
Full
Sample 139721 675 5.26 38.70 % 14.69% 515 2.20 69.00% 12.62%
Invest 24133 223 6.83 39.40% 8.43% 223 1.62 65.86% 8.16%
Junk 115588 769 4.93 38.55% 16.00% 576 2.32 69.66% 13.55%
Table 2: Summary statistics of bid-ask spreads (Unit: basis points)
This table reports the summary statistics of bid-ask spreads. The Firm Averages show the average bid-ask
spread for each firm during the period from August 15th, 2006 to August 15th, 2015, depending upon data
availability. The Bid-ask spread and Bid-ask ratio are defined as below:
𝐵𝑖𝑑 − 𝑎𝑠𝑘 𝑆𝑝𝑟𝑒𝑎𝑑 = 𝑐𝑎𝑠𝑘 − 𝑐𝑏𝑖𝑑
𝐵𝑖𝑑 − 𝑎𝑠𝑘 𝑅𝑎𝑡𝑖𝑜 =2(𝑐𝑎𝑠𝑘 − 𝑐𝑏𝑖𝑑)
𝑐𝑎𝑠𝑘 + 𝑐𝑏𝑖𝑑
Where 𝑐𝑎𝑠𝑘 and 𝑐𝑏𝑖𝑑 denote the ask and bid price of CDS, respectively. The Daily(Firm) Average shows
the average bid-ask spread for each day (firm) across all the available firms (days). P represents percentile.
Panel A: Daily Average N Mean STD P5 P25 P50 P75 P95 SKEW
Bid-ask spread (bps) 2349 10.52 5.23 4.22 7.89 9.77 11.74 22.88 1.88
Bid-ask ratio (%) 2349 9% 4% 5% 7% 8% 11% 21% 1.64
Panel B: Firm Average N Mean STD P5 P25 P50 P75 P95 SKEW
Bid-ask spread (bps) 249 11.98 14.92 3.83 5.14 7.33 12.66 35.47 5.05
Bid-ask ratio (%) 249 9% 4% 5% 6% 8% 10% 16% 1.89
53
Table 3: Summary Statistics of Realized Profits for Matured 5-year Contracts
This table reports the summary statistics of the realized profits generated by the simulated portfolios when
the CDS and LCDS parity is violated for the cross-sectional daily observations for matured 5-year contracts.
It is assumed that the transaction costs are the same under CDS and LCDS market. The daily transaction
costs come from the daily average bid-ask spreads observed in the Bloomberg database. Std. Dev. refers to
the standard deviation. The notional amount of each CDS or LCDS contract is assumed to be 5 million
USD. The annualized realized return equals the dollar profits divided by the initial margin.
Panel A: Return Distribution across Trading Strategies for Matured 5-year Contracts
No. of
Obs P5 Median P95 Mean
Std.
Dev.
Skewnes
s
Negative
Return %
Full Sample 89138 0.99% 8.26% 29.54% 10.35% 12.32% 6.14 0.32%
Buy CDS &
Sell LCDS 76438 1.68% 8.53% 27.75% 10.56% 11.70% 6.95 0.33%
Buy LCDS
& Sell CDS 12700 0.26% 3.56% 39.83% 9.06% 15.46% 3.76 0.25%
Panel B: Return Distribution across Rating Classes for Matured 5-year Contracts
No. of
Obs P5 Median P95 Mean
Std.
Dev.
Skewnes
s
Negative
Return %
Investment 13982 0.62% 6.02% 12.41% 6.38% 4.17% 1.82 0.77%
Junk 75156 1.09% 8.58% 32.66% 11.09% 13.16% 5.81 0.24%
Panel C: Return Distribution pre- and post-FINRA’s pilot program in 2009 for
Matured 5-year Contracts
No. of
Obs P5 Median P95 Mean
Std.
Dev.
Skewnes
s
Negative
Return %
Pre 74788 1.77% 8.68% 31.01% 10.98% 11.28% 4.50 0.04%
Post 14462 0.35% 3.47% 21.45% 7.04% 16.25% 9.01 1.78%
54
Table 4: Summary Statistics of Realized Profits for Matured 1-year and 3-year contracts
This table reports the summary statistics of the realized profits generated by the simulated portfolios when
the CDS and LCDS parity relation is violated for the cross-sectional daily observations for matured 1-year
and 3-year contracts. Transaction costs are assumed to be the same in both CDS and LCDS markets. The
daily transaction costs come from the daily average bid-ask spreads observed in the Bloomberg database.
Std. Dev. refers to the standard deviation. The notional amount of each CDS or LCDS contract is assumed
to be 5 million USD. The annualized realized return equals the dollar profits divided by the initial margin.
Panel A Annualized Realized Return
No. of
Obs P5 Median P95 Mean
Std.
Dev. Skewness
Negative
Return %
Matured 1-year Contracts
Full Sample 16307
7 1.13% 15.02% 49.62% 21.85% 68.42% 8.39 0.57%
Buy CDS &
Sell LCDS
12626
8 1.40% 18.22% 55.97% 26.80% 70.16% 11.99 0.03%
Buy LCDS
& Sell CDS 36809 0.62% 7.47% 28.56% 4.84% 59.01% -11.51 2.40%
Matured 3-year Contracts
Full Sample 74533 1.13% 11.05% 42.30% 15.59% 34.53% 9.14 0.09%
Buy CDS &
Sell LCDS 61921 2.22% 11.63% 44.97% 17.10% 36.17% 10.34 0.04%
Buy LCDS
& Sell CDS 12612 0.26% 4.17% 38.65% 8.16% 23.54% -15.13 0.33%
Panel B: Return Distribution Pre- and Post-FINRA’s Pilot Program in 2009
No. of
Obs
Minimu
m
Maximu
m Mean Median
Std.
Dev. Skewness
Negative
Return %
Matured 1-year Contract
Pre 61416 2.14% 21.68% 55.83% 31.62% 98.67% 3.78 0.20%
Post 10166
1
0.87% 11.43% 44.43% 15.94% 39.17% 4.04 0.78%
Matured 3-year Contracts
Pre 59744 1.80% 11.85% 46.02% 17.13% 36.94% 8.81 0.07%
Post 14789 0.55% 4.83% 31.94% 9.34% 21.12% 8.91 0.18%
55
Table 5: Market Structure Tests without Margin and Transaction Costs
This table reports the OLS regression results for the following models:
2 1 1 2
1 2 2 1, ,
0 1 , 1 ,t 1 . 1
1 1Sell_CDS(or Buy_CDS) : ln ln
1 1
_ + _
i t i t
i t i i t it
R c R cor
R c R c
Diff Dealers Min Dealers Control
Min_Dealers denotes the minimum number of distinct dealers providing quotes in the CDS and LCDS
markets. Diff_Dealers denotes the difference of the number of distinct dealers providing quotes in the CDS
and LCDS markets. The statistically significant coefficients are indicated by ***, ** and * for significance
at the 1%, 5% and 10% levels, respectively. The standard errors are clustered by firm and reported in the
parentheses. N is the number of observations.
Buy_CDS Sell CDS
Panel A: Matured 5-year CDS contracts
0 1.188*** 1.117*** 0.932*** 0.855***
(0.081) (0.131) (0.164) (0.165)
Diff_Dealers -0.144*** -0.139*** -0.220*** -0.188***
(0.021) (0.019) (0.056) (0.049)
Min_Dealers -0.046*** -0.046*** -0.002 -0.000
(0.008) (0.008) (0.014) (0.014)
Year Fixed-Effect NO YES NO YES
Industry Fixed-
Effect NO YES NO YES
Adj. R-square 0.06 0.07 0.05 0.07
N 84,263 84,263 20,461 20,461
Panel B: Matured 3-year CDS contracts
0 0.995*** 0.924*** 0.547*** 0.661***
(0.078) (0.150) (0.078) (0.145)
Diff_Dealers -0.101*** -0.100*** -0.072*** -0.074***
(0.016) (0.018) (0.021) (0.023)
Min_Dealers -0.037*** -0.037*** -0.005 -0.005
(0.008) (0.008) (0.009) (0.010)
Year Fixed-Effect NO YES NO YES
Industry Fixed-
Effect NO YES NO YES
Adj. R-square 0.07 0.08 0.03 0.07
N 63,483 63,483 18,283 18,283
Panel C: Matured 1-year CDS contracts
0 1.234*** 1.331*** 0.582*** 0.748***
(0.080) (0.169) (0.047) (0.181)
Diff_Dealers -0.142*** -0.130*** -0.046*** -0.071***
(0.021) (0.023) (0.013) (0.014)
Min_Dealers -0.027*** -0.024** -0.014* -0.017**
(0.009) (0.010) (0.008) (0.008)
Year Fixed-Effect NO YES NO YES
Industry Fixed-
Effect NO YES NO YES
Adj. R-square 0.05 0.06 0.01 0.04
N 108,982 108,982 36,972 36,972
56
Table 6: Market Elasticity Test
This table reports the results for the following cross-sectional regression under various trading strategies
with matured 5-year CDS contracts:
, 0 1 ,t 2 ,t 3 ,t
4 , 5 ,t 6 ,t
7 ,t .
Pr _ _ 1* _ 2* _
_ + _ 1* _
2* _
i t i i i
i t i i
i i t it
ofit TC Min Dealers D Min Dealers D Min Dealers
Diff Dealers Diff Dealers D Diff Dealers
D Diff Dealers Control
Profit_TCi,t denotes the realized arbitrage profits with transaction costs, initial and variation margins.
Min_Dealers denotes the minimum number of distinct dealers providing quotes in the CDS and LCDS
markets. Diff_Dealers denotes the difference of the number of distinct dealers providing quotes in the CDS
and LCDS markets. D1 is an indicator that equals to one if Min_dealers is equal to one and zero otherwise.
D2 is an indicator that is equal to one if Min_dealers is equal to two and zero otherwise. Controli,t includes
LOGA, CAL, LEV, TANG, IDIO, TB5Y, SL, CBS and SP. All the variables are as defined in Appendix B.
Clustered standard errors are used to allow for residual autocorrelation and cross-sectional dependence as
in Petersen (2009). The statistically significant coefficients are indicated by ***, ** and * for significance
at the 1%, 5% and 10% levels, respectively. The standard errors clustered by year and industry are reported
in the parentheses. N is the number of observations.
Trading Strategy Rating Class of
Buy-CDS and Sell-LCDS
Buy CDS Sell CDS Investme
nt Grade
Speculative
Grade
Min_Dealers 0.001 -4.000 -0.007** 0.002
(0.001) (2.842) (0.004) (0.001)
Min_Dealers*D1 0.041*** 16.063 -0.031 0.051***
(0.009) (11.282) (0.032) (0.011)
Min_Dealers*D2 0.015*** 0.812 0.007 0.017***
(0.003) (1.818) (0.008) (0.003)
Diff_Dealers 0.002* -0.959 -0.002 0.002*
(0.001) (0.885) (0.002) (0.001)
Diff_Dealers*D1 -0.004** -1.225 0.001 -0.005**
(0.002) (1.409) (0.002) (0.002)
Diff_Dealers*D2 -0.004*** -2.785 -0.001 -0.005***
(0.001) (2.378) (0.002) (0.001)
Controls YES YES YES YES
N 34,010 6,306 6,962 27,048
Adjusted R2 0.13 0.10 0.33 0.15
57
Table 7: Regression Results for the Persistence of Arbitrage Profits
This table reports the results for the persistence of arbitrage profits for matured contracts using the following
Heckman two-stage procedure under various scenarios:
1st stage: 𝑇𝑟𝑎𝑑𝑒_𝑑𝑢𝑚𝑚𝑦𝑖,𝑡 = 𝛼0 + 𝛾𝐶𝑜𝑛𝑡𝑟𝑜𝑙𝑖,𝑡 + 𝜀𝑖,𝑡 based on a logistic regression
2nd stage: 𝑁 − 𝑑𝑎𝑦𝑠𝑖,𝑡 = 𝛼0 + 𝛼𝑃𝑟𝑜𝑓𝑖𝑡_𝑇𝐶𝑖,𝑡∗ + 𝛽𝜆𝑖,𝑡 + 𝛾𝐶𝑜𝑛𝑡𝑟𝑜𝑙𝑖,𝑡 + 𝜀𝑖,𝑡 based on a cross-sectional
regression
Trade_dummyi,t is equal to one if the observation falls outside the no-trade zone and zero otherwise for firm
i and time t. N-daysi,t denotes the logarithm of the total number of consecutive days for which arbitrage
profits persist after first presenting itself. Profit_TCi,t denotes the realized arbitrage profits with transaction
costs, initial and variation margins. 𝑃𝑟𝑜𝑓𝑖𝑡_𝑇𝐶𝑖,𝑡∗ is the residual from the regression: 𝑃𝑟𝑜𝑓𝑖𝑡_𝑇𝐶𝑖,𝑡 =
𝛼𝐶𝑜𝑛𝑡𝑟𝑜𝑙𝑖,𝑡 + 𝜀𝑖,𝑡 . 𝜆𝑖,𝑡 refers to the inverse Mills’ ratio estimated from the first stage regression. Controli,t
includes CRISIS, LOGA, CAL, LEV, TANG, IDIO, TB5Y, SL, CBS and SP as defined in Appendix B.
Clustered standard errors by year and industry are used to allow for residual autocorrelation and cross-
sectional dependence as in Petersen (2009). ***, ** and * indicate statistical significance at the 1%, 5%
and 10% levels, respectively. The standard errors are reported in the parentheses. N is the number of
observations.
Full Sample Buy CDS Sell CDS
Variables 1st stage 2nd stage 1st stage 2nd stage 1st stage 2nd stage
𝑷𝒓𝒐𝒇𝒊𝒕_𝑻𝑪𝒊,𝒕∗
7.012*** 24.39*** 5.352*
(2.552) (6.663) (3.204)
CRISIS 0.082 1.060 0.370** 1.814 -0.472* -3.425**
(0.055) (0.689) (0.157) (1.636) (0.258) (1.445)
LOGA -0.045** -0.945*** -0.075 -0.621* 0.067 0.510*
(0.019) (0.347) (0.063) (0.343) (0.118) (0.270)
CAL -0.003 -0.149 -0.029 -0.187 0.116 0.426
(0.024) (0.091) (0.051) (0.149) (0.141) (0.457)
LEV -0.083 -1.939*** -0.972*** -6.008 2.134*** 13.17**
(0.105) (0.695) (0.300) (4.260) (0.519) (6.495)
TANG -0.037 -0.961*** -0.140 -1.038 0.280 1.172
(0.049) (0.347) (0.150) (0.647) (0.342) (1.049)
IDIO 4.126 66.16** -31.07 -217.6 12.91 34.29*
(6.995) (28.14) (35.47) (158.2) (12.66) (20.07)
TB5Y -0.201*** -3.990*** -0.248** -1.886* 0.126 1.526**
(0.062) (1.479) (0.104) (1.143) (0.223) (0.595)
SL -17.26*** -332.8*** 3.749 -7.124 -51.90*** -269.3*
(6.347) (127.6) (12.05) (27.60) (18.12) (152.2)
CBS -12.44*** -234.6** -27.23*** -158.2 32.89 218.9**
(4.469) (92.41) (10.09) (123.5) (22.17) (104.2)
SP -5.207*** -108.1*** -3.244* -26.33* -5.063** -39.83**
(1.681) (39.40) (1.862) (15.94) (2.461) (16.62)
𝛌 30.62*** 8.325 6.648*
(11.85) (6.192) (3.452)
N 2737 1413 2737 1050 2737 352
Pseudo R2 0.58% 2.90% 2.76% 4.92% 8.71% 8.23%
1
For Online Publication
Financial Oligopolies and Parallel Exclusion in the
Credit Default Markets
Lawrence Kryzanowski Stylianos Perrakis Rui Zhong†‡
† We thank Jennie Bai, Sean Cleary, George Constantinides, András Danis, Faye Diamantoudi, Darrell Duffie, Jan
Ericsson, Gordon Fisher, Jean-Sébastien Fontaine, Louis Gagnon, Genevieve Gauthier, Nikolay Gospodinov, Bing
Han, Zhiguo He, Jing-Zhi Huang, Sergey Isaenko, Robert Jarrow, Arben Kita, Laurence Lescourret, Jorge Cruz Lopez,
Chayawat Orthanalai, Wulin Suo, Lorne Switzer, Dragon Tang, Nancy Ursel, Sarah Wang, Hong Yan, Jun Yang,
Zhaodong Zhong and participants at the 23rd Annual Derivatives Securities and Risk Management Conference jointly
organized by FDIC, Cornell and the University of Houston, the 20th Annual Multinational Finance Society Conference,
the 2013 Northern Finance Association Conference, the 2013 Financial Management Association Conference,
Frontiers of Finance 2014, China International Conference in Finance 2014, 3rd International Conference on Futures
and Derivative Markets 2014, 2016 Biennial Athenian Policy Forum and seminars at Bank of Canada, the 3rd Annual
Volatility Institute Conference at NYU Shanghai, Central University of Finance and Economics, Concordia
University, Queen’s University, University of Victoria, University of Windsor and Warwick Business School for
helpful comments. Financial support from the Senior Concordia University Research Chair in Finance, RBC
Distinguished Professorship of Financial Derivatives, IFSID, Social Sciences and Humanities Research Council of
Canada (SSHRC) and National Natural Science Foundation of China (NNSFC, Project No.71501197) are gratefully
acknowledged. We thank the Credit Regulation Department of the Financial Industry Regulatory Authority (FINRA)
for the information that it supplied on the applicability of FINRA Rule 4240. ‡ Lawrence Kryzanowski and Stylianos Perrakis are with the John Molson School of Business at Concordia University,
1455 De Maisonneuve Blvd West, Montreal, Quebec, Canada H3G 1M8. Rui Zhong is with UWA Business School
at University of Western Australia, 35 Stirling Hwy, Crawley, Western Australia, Australia, 6009.
2
Financial Oligopolies and Parallel Exclusion in the
Credit Default Markets
Online Appendix
This online appendix provides further evidence of the failure of the no arbitrage model to explain the
observed parity violations as rewards for recovery rate risk. It is organized as follows: Part A includes a
numerical demonstration of the oligopoly model described in the main text, using identical dealer firms and
constant elasticity demand curves. Part B describes the control variables used in the multivariate analysis
of realized profits. Part C describes the diverging ratios used in the empirical tests of Section 5. Part D
reports several tables and figures of the robustness checks referred to in the paper.
3
Part A: A Numerical Demonstration of the Oligopoly Model’s Theoretical results
We apply the Cournot oligopoly model to a symmetric duopoly or triopoly with identical for all firms
constant relative risk aversion (CRRA) utility functions: let 1
1 1( ) ( ) 1,2 or 3j j jU W W j and assume the
same value of 0
jW for all j. Assume also that the two net demand functions are of the constant elasticity
type within the relevant range, with1 1
1 2
D D
. Consider the equilibrium with frictions of the long CDS
type, given by (3.9b)-(3.10b). We obviously have, under the simplified assumption that default probabilities
are constant during the contract term, that
1 1* * *
1 1 1 1
'( ) ( )(1) (2)
'( ) '( ) ( ) ( )
j
D D
j j
S D S D
P U W D P W D
P U W S P U W D P W S P W D
, (A.1)
where, omitting the time factor and the superscript and including transaction costs, we have
1 0 1 1 1 1 1 2 2 2 2 2
1 0 1 1 1 1 2 2 2 2
[(1 ) ( ) ] [(1 ) ( ) ]
[ ( ) ( )]
W D W y R c k m y R c k m
W S W y c k m y c k m
. (A.2)
The equilibrium system (3.10b) now becomes
1 2
* *
1 1 1 1 2 2 2 21 2
1 1 1 1 2 2 2 2
1 1(1 ) ( )(1 ) , (1 ) ( )(1 )
( ) , ( ) , 2 or 3D D
D D
R c k m R c k mJ J
Jy A c k Jy A c k J
. (A.3)
This system provides an explicit solution for the two equilibrium spreads and numbers of contracts
( , ) 1,2i ic y i for given values of the RRA, default probability, initial wealth, transaction costs, margins,
recovery rates and demand and elasticity parameters. The case of colluding oligopolists, in which they
maximize the expected sum of the profits, is given by a similar system by replacing the 1
Jcoefficient of
the inverse elasticities by 1 in (3.10b). Another potentially interesting case is when there is competitive
entry in the CDS market and1
1 0D
. In such a case the spread 1c is exogenous and the equations (A.4)
4
determine the LCDS premium and number of contracts, as well as the number of long contracts in the CDS
market.
2
* *
1 1 1 1 2 2 2 22
2 2 2 2
1(1 ) , (1 ) ( )(1 )
2
2 ( ) D
D
R c k m R c k m
y A c k
(A.4)
Figure A1 and Table A1 show the equilibria * *( , ), 1,2i ic y i for the symmetric Cournot duopoly and
triopoly and the colluding duopoly for three values of 0
jW and for the following parameter values: 𝑅1 = 0.4,
𝑅2 = 0.7 , 𝑚1 = 𝑚2 = 0.003 , 𝜀𝐷1+ = −3 , 𝜀𝐷
2− = 4 , 𝐴1 = 3𝐸 − 4 , 𝐴2 = 9𝐸6 , 𝛼 = 4 , 𝑃𝐷 = 0.02 , 𝑃𝑆 =
1 − 𝑃𝐷, 𝑘1 = 0.001, 𝑘2 = 0.002. The table also shows the NT zone and the expected utility 1[ ( )]E U W in
each case, which should be compared with the initial utility 0( )U W .
Figure A1: Optimal Spreads and Demands in CDS and LCDS Markets
These figures show the optimal spreads and demands in equilibrium under a triopoly, duopoly and collusion
market structure in CDS and LCDS markets, respectively. We calculate the optimal solutions using the
calibration as follow: 𝑊0 = 3, 𝑅1 = 0.4, 𝑅2 = 0.7, 𝑚1 = 0.003, 𝑚2 = 0.003, 𝜀𝐷1+ = −3, 𝜀𝐷
2− = 4, 𝐴1 =3𝐸 − 4, 𝐴2 = 9𝐸6, 𝛼 = 4, 𝑃𝐷 = 0.02, 𝑃𝑆 = 0.98, 𝑘1 = 0.001, 𝑘2 = 0.002.
0.5 1 1.5 2 2.5 3 3.5 40.02
0.025
0.03
0.035
0.04
0.045
0.05
0.055
0.06
0.065
0.07 Panel A: CDS Market
y1
c1
-11 -10 -9 -8 -7 -6 -50.02
0.025
0.03
0.035
0.04
0.045
0.05
0.055
0.06
0.065
0.07 Panel B: LCDS Market
y2
c2
Triopoly
Triopoly
Duopoly
DuopolyCollusion
Collusion
5
Table A1: Optimal Solutions under Triopoly, Duopoly and Collusion Market Structures
This table reports the optimal solutions under a triopoly, duopoly and collusion market structure,
respectively. We calculate the optimal solutions using the calibrations as follow: 𝑅1 = 0.4, 𝑅2 = 0.7, 𝑚1 =0.003, 𝑚2 = 0.003, 𝜀𝐷
1+ = −3, 𝜀𝐷2− = 4, 𝐴1 = 3𝐸 − 4, 𝐴2 = 9𝐸6, 𝛼 = 4, 𝑃𝐷 = 0.02, 𝑃𝑆 = 0.98, 𝑘1 =
0.001, 𝑘2 = 0.002.
Initial Wealth Market
Structure 1c 2c 𝑦1 𝑦2 No-Trade Zone
[𝑐1, 𝑐1] U(W)
𝑊0 = 2
U(𝑊0)=-0.0417
Triopoly 0.0615 0.0448 0.6154 -15.0554 [0.1035, 0.0755] -0.0178
Duopoly 0.0560 0.0452 0.8090 -15.6123 [0.1043, 0.0763] -0.0175
Collusion 0.0428 0.0469 1.7851 -18.3441 [0.1079, 0.0799] -0.0156
𝑊0 = 3
U(𝑊0)=-0.0123
Triopoly 0.0473 0.0362 1.3304 -6.1473 [0.0864, 0.0584] -0.0115
Duopoly 0.0439 0.0370 1.6620 -6.7891 [0.0881, 0.0601] -0.0113
Collusion 0.0353 0.0403 3.1317 -9.6640 [0.0946, 0.0666] -0.0104
𝑊0 = 4
U(𝑊0)=-0.0052
Triopoly 0.0494 0.0374 1.1727 -7.1031 [0.0889, 0.0609] -0.0048
Duopoly 0.0455 0.0382 1.4899 -7.6903 [0.0903, 0.0623] -0.0048
Collusion 0.0361 0.0410 2.9315 -10.4105 [0.0960, 0.0680] -0.0045
The results illustrate very nicely the properties and economic implications of the oligopoly equilibrium.
For each level of start-up capital 0W the spreads and quantities move in the expected directions, with 1c
increasing and 2c decreasing as the market structure becomes progressively more competitive, moving from
collusion (monopoly) to Cournot duopoly and then triopoly. Note also that the distance of 1c from the lower
bound 1c of the NT zone decreases as well with increasing competition. As the number of participants in
the dealer intermarket arbitrage increases we would expect convergence to that zone. Indeed, we find that
for 0 7W the intermarket arbitrage breaks down since the resulting spreads under Cournot oligopoly lie
inside the NT zone.
The effect of the start-up capital for a given structure is asymmetric, insofar as both 1c and 2c increase
with 0W for the two higher levels 3 and 4 shown in the table (and also for levels above 4) but not for 0 2W
, where utility from the intermarket arbitrage is a much higher component of 1[ ( )]E U W than for the other
two levels. For small scale entry, we must have from the proof of Proposition 3
6
1 1 1 2 2 20 0
1 2
'( ) ( )1 1
c k m c k mU W W
R R
, implying limits on the start-up capital of
1 1
1 1 1 2 2 20
1 2
( ) ( )1 1
c k m c k mW
R R
. For 0 3W these imply that small scale entry in both markets to
be profitable, if feasible on other grounds, must have a start-up capital within the limits of
0 (1.7609,1.8493)W and 0 (1.7498,1.8813)W for the Cournot triopoly and duopoly respectively, while for
collusion the limits for small scale entry in both markets are considerably wider at 0 (1.7074,1.9767)W .
Outside these limits small scale entry is profitable only in one of the two markets.
Last, we examine the case of entry at a sufficiently large scale that changes the market equilibrium
and/or the incumbents’ positions. We use a particular example in order to illustrate the effectiveness of the
lack of transparency about CDS and LCDS market conditions as an entry barrier, as described in Proposition
5. Suppose that we are in a collusive duopoly equilibrium with 0 3W as in Table A1. A fully informed
prospective entrant with 0 2W wishes to participate in the intermarket arbitrage. While small scale entry
in both markets is not profitable for this level of start-up capital, there are entry-accommodating allocations
of the total amounts*
12y and *
22y that preserve the collusive equilibrium values of the premiums
*
1 0.0353c and*
2 0.0403c and make entry profitable for the prospective entrant. Let the entrant receive an
allocation of 1 21, 3y y , apportioned equally between the two members of the cartel. Under full
information it is easy to verify that for such values the entrant’s utility increases from the no entry level of
-0.0417 to 1[ ( )] 0.0382E U W , while the incumbents’ utility decreases somewhat to -0.0107 from the
collusive level of -0.0104. This last level is far above the levels that will prevail in a breakdown of the
collusion discipline even if entry is deterred, let alone if a full triopoly under Cournot conditions is
established.
7
Suppose, however, that the markets are non-transparent and the prospective entrant cannot observe the
two premiums or, for that matter, the structure of the two markets. Assume that she knows the spread levels
corresponding to the triopoly and the collusive result shown in Table A1, but is unable to distinguish which
one of the two prevails at the time of entry and considers them as equally likely. Her expected utility when
she receives the allocation 1 21, 3y y is now -0.0430, less than the no entry level of -0.0417 and
equivalent to a reduction of a little more than 2% in the start-up capital as shown in Proposition 5. We
conclude that lack of transparency is a powerful instrument for preventing entry and maintaining the
stability of a collusive equilibrium.
Part B: Detailed Explanation of Control variables for the multivariate analysis
a. Firm-specific variables
We use the logarithm of total asset (LOGA), current ratio (CAL), leverage ratio (LEV), tangible assets
(TANG) and idiosyncratic volatilities (IDIO) to control for the firm-specific characteristics. In particular,
we use idiosyncratic volatility as a firm-specific measure of pricing uncertainty or price informativeness or
informational asymmetry. We conjecture that higher idiosyncratic volatilities are associated with lower
market efficiency. In the oligopoly model these volatilities are also expected to reduce the demand elasticity
in both markets, although the net effect on the key relation (3.8) cannot be predicted. We also conjecture
that higher idiosyncratic volatilities would be associated with increased current payoffs.
b. Macro variables
Macro variables associated with the business cycle: There are four such variables, the 5-year US
treasury bond yield (TB5Y), the slope of the term structure (SL) measured by the difference between the
yields on 5- and 1-year US treasury bonds, the yield spread between Aaa and Baa corporate bonds (CBS),
and the return of the S&P 500 total return index (SP). The VIX is not included due to its high correlation
with the CBS and the relatively higher explanatory power of the CBS.
8
These four variables are leading indicators of the business cycle. With the exception of CBS, whose
increase is associated with weakening prospects for the economy, increases in the other three factors
indicate a stronger economy. The effects of these variables on the current payoffs of our portfolio strategies
are by their nature ambiguous, since they affect all four variables on both sides of the parity relation (3.8).
The CDS/LCDS spread ratio effect, which increases almost by definition when CBS increases, is likely to
dominate the indirect recovery rates ratio, thus increasing the divergence and predicting higher current
payoffs when CBS increases and a positive coefficient for this variable. We also expect under both
hypotheses a widening of the no trading zone during the crisis because of the increase in transaction costs.
The accounting variables, including total assets, book value of total liabilities, market value of equity,
current assets, current liabilities and tangible assets, are obtained from the Compustat database via the
WRDS platform. The data are updated quarterly. For our initial regressions, we convert the frequency from
quarterly to daily by keeping the value constant within each quarter and then take a one quarter lag. The
fixed income macro variables, including the yields on 1- and 5-year US treasury bonds, and Aaa and Baa
corporate bond yields are obtained from the US Federal Reserve H15 database. The equity prices and S&P
500 total return index data are obtained from Bloomberg.
Part C: Diverging Ratios
Assume that we have a window of N daily observations of a given pair of CDS and LCDS contracts
starting on a given date, the length of the observation period in our sample is denoted by , and is the
number of such periods within N , where 1 1N and N . As in equations (3.13), we define
the limits of the NT zone,
11 2 2 1 1
2
11 2 2 1 2
2
1
1
1
1
Rc c k k m
R
Rc c k k m
R
(C.1)
9
A diverging change in relative premiums for a position outside the NT zone is defined as a movement away
from NT in a time interval of , when one or both of the two markets’ spreads change. Thus, we have,
for 1 1 1( ), ( ), ( )c c c denoting the changes in the CDS spread and the relevant limit of the NT zone
that changes with the LCDS spread:
If we observe 1 1c c on day 0, we define the diverging changes as,
1 1
1 1 1 1
1 1 1 1
0, 0
0, 0
0, 0
c c
c c and c c
c c and c c
(C.2)
If we observe 1 1c c instead, we define the diverging changes as,
1 1
1 1 1 1
1 1 1 1
0, 0
0, 0
0, 0
c c
c c and c c
c c and c c
(C.3)
We define the diverging ratios for each firm outside the NT zone as,
1
1 1
1
N N
Diverging ChangekDR
N N
(C.4)
Table XI shows the average DR for N varying from 5 to 60 days for the full sample and various subsamples.
References
Bartlam, Martin and Karin Artmann, 2006, Loan-only credit default swaps, Orrick. Available at:
http://www.orrick.com/Events-and-Publications/Documents/787.pdf .
Merrill Lynch, 2007, Pricing cancellable LCDS, Credit Derivatives Strategy (Global, February 2007).
Petersen, Mitchell, 2009, Estimating standard errors in finance panel data sets: Comparing approaches,
Review of Financial Studies 22, 435-480.
Rothschild, M., and J. Stiglitz, 1970, Increasing risk I: a definition, Journal of Economic Theory 2, 225-
243.
10
Part D: Tables and Figures
Table I: Distribution of variation margins
Panel A Annualized Realized Return
No. of
Obs Minimum Maximum Mean Median
Std.
Dev. Skewness
% of
negative
variation
margins
1-year Contracts
Full Sample 137966 -0.90% 0.80% -9.55E-5 -7.88E-6 0.09% -1.43 57.31%
Buy CDS &
Sell LCDS 109552 -0.87% 0.80% -4.3E-5 -3.0E-6 0.08% -1.43 53.82%
Buy LCDS &
Sell CDS 28414 -0.90% 0.70% -0.03% 5.59E-5 0.13% -1.77 70.78%
3-year Contracts
Full Sample 68793 -1.78% 1.57% -0.03% -3.59E-6 0.27% -0.68 51.18%
Buy CDS &
Sell LCDS 57354 -1.75% 1.57% -0.02% 2.90E-6 0.25% -0.40 47.90%
Buy LCDS &
Sell CDS 11439 -1.78% -1.77% -0.10% -0.02% 0.36% -0.78 67.63%
5-year Contracts
Full Sample 89624 -15.00% 16.96% -0.75% -0.29% 2.79% -0.16 62.70%
Buy CDS &
Sell LCDS 78299 -15.00% 16.96% -0.66% -0.23% 2.78% -0.06 60.52%
Buy LCDS &
Sell CDS 11325 -14.18% 12.10% -1.37% -0.77% 2.79% -0.85 77.74%
11
Table II: Descriptive statistics of 3- and 1-year CDS and LCDS contracts
This table reports the means of 3- and 1-year CDS(LCDS) spreads, number of distinct dealers and quoted
recovery rates provided by Markit under various ratings. It covers the sample period from August 15, 2006
to December 31, 2011 for 3-year CDS(LCDS) contracts and August 15, 2006 to December 31, 2013 for 1-
year CDS (LCDS) contracts.
CDS LCDS
No. of
Obs
Average
Spreads
(Unit:
bps)
Average
No. of
Dealers
Average
Quoted
Recovery
Rates (%)
Average
Initial
Margin
Average
Spreads
(Unit:
bps)
Average
No. of
Dealers
Average
Quoted
Recovery
Rates
(%)
Average
Initial
Margin
Panel A: 3-year Contracts
Full
Sample 103982 554 5.77 38% 10% 451 2.38 69% 8%
Invest 19471 206 7.26 39% 5% 211 1.75 64% 5%
Junk 84511 634 5.43 38% 11% 507 2.53 70% 9%
Panel B: 1-year Contracts
Full
Sample 187528 306 5.37 38% 4% 256 1.98 67% 3%
Invest 42719 94 6.37 40% 2% 144 1.50 61% 2%
Junk 144809 369 5.07 38% 4% 289 2.13 69% 3%
12
Table III: Portfolio current payoffs with real bid-ask spreads
This table reports the summary statistics of the portfolio current payoffs for the 5-year maturity cross-
sectional observations with real bid-ask spreads from Bloomberg and Markit, respectively. In Panels A and
B, we match the observed bid-ask spreads from Bloomberg and Markit with the CDS-LCDS pairs,
respectively. In Panel C, we collect all the firms either in Bloomberg or Markit and select the maximum
bid-ask spreads for the observations available in both datasets. In Panel D, we collect all the firms in
Bloomberg and Markit and select the maximum bid-ask spreads for the observations available in both
datasets. It is also assumed that the CDS and LCDS contracts have the same absolute transaction costs that
can be observed in the CDS market.
No.
Observations Mean Median
Standard
Deviation
Panel A: Bloomberg Only
22395 0.0286 0.0073 0.0567
Panel B: Markit Only
14468 0.0191 0.0065 0.0471
Panel C: Bloomberg or Markit
28686 0.0259 0.0070 0.0551
Panel D: Bloomberg and Markit
8177 0.0206 0.0053 0.0463
13
Table IV: Market structure tests without margin and transaction costs
This table reports the OLS regression results for the following models:
Sell-CDS: 𝑙𝑛 ((1−𝑅2)𝑐1
(1−𝑅1)𝑐2)𝑖,𝑡
=𝛼0 + 𝛽1𝑁𝑢𝑚_𝐷𝑒𝑎𝑙𝑒𝑟𝑠_𝐶𝐷𝑆𝑖,𝑡−𝜏 + 𝛽2𝑁𝑢𝑚_𝐷𝑒𝑎𝑙𝑒𝑟𝑠_𝐿𝐶𝐷𝑆𝑖,𝑡−𝜏 +
𝛽3𝑁𝑢𝑚_𝐷𝑒𝑎𝑙𝑒𝑟𝑠_𝐶𝐷𝑆𝑖,𝑡−𝜏 × 𝑁𝑢𝑚_𝐷𝑒𝑎𝑙𝑒𝑟𝑠_𝐿𝐶𝐷𝑆𝑖,𝑡−𝜏 + 𝛽∙𝐶𝑜𝑛𝑡𝑟𝑜𝑙𝑖,𝑡−𝜏 + 𝜀𝑖𝑡
Buy-CDS: 𝑙𝑛 ((1−𝑅1)𝑐2
(1−𝑅2)𝑐1)𝑖,𝑡
=𝛼0 + 𝛽1𝑁𝑢𝑚_𝐷𝑒𝑎𝑙𝑒𝑟𝑠_𝐶𝐷𝑆𝑖,𝑡−𝜏 + 𝛽2𝑁𝑢𝑚_𝐷𝑒𝑎𝑙𝑒𝑟𝑠_𝐿𝐶𝐷𝑆𝑖,𝑡−𝜏 +
𝛽3𝑁𝑢𝑚_𝐷𝑒𝑎𝑙𝑒𝑟𝑠_𝐶𝐷𝑆𝑖,𝑡−𝜏 × 𝑁𝑢𝑚_𝐷𝑒𝑎𝑙𝑒𝑟𝑠_𝐿𝐶𝐷𝑆𝑖,𝑡−𝜏 + 𝛽∙𝐶𝑜𝑛𝑡𝑟𝑜𝑙𝑖,𝑡−𝜏 + 𝜀𝑖𝑡
𝑁𝑢𝑚𝐷𝑒𝑎𝑙𝑒𝑟𝑠_CDS and 𝑁𝑢𝑚𝐷𝑒𝑎𝑙𝑒𝑟𝑠_LCDS are the number of dealers in CDS and LCDS markets,
respectively. 𝜏 denotes the number of lagged days and equals to one. The statistically significant
coefficients are indicated by ***, ** and * for significance at the 10%, 5% and 1% levels, respectively. The
standard errors are clustered by firm and the corresponding t-statistics are reported in the parentheses.
Buy_CDS Sell CDS
Panel A: 5-year Contracts
0 1.206*** 1.065*** 0.421*** 0.411***
(13.75) (9.77) (5.25) (4.44)
𝛽1 -0.073*** -0.073*** -0.011 -0.013
(6.66) (6.61) (1.07) (1.29)
𝛽2 -0.152*** -0.154*** -0.054** -0.061**
(6.55) (6.62) (2.17) (2.49)
𝛽3 0.013*** 0.014*** 0.002 0.004
(4.75) (4.76) (0.73) (1.16)
Year Fixed-Effect NO YES NO YES
Industry Fixed-Effect NO YES NO YES
R-square 0.13 0.14 0.04 0.07
N 76,851 76,851 16,435 16,435
Panel B: 3-year Contracts
0 1.041*** 0.916*** 0.394*** 0.409***
(12.04) (8.64) (10.80) (3.56)
𝛽1 -0.056*** -0.055*** -0.011** -0.011**
(5.52) (5.39) (2.00) (2.14)
𝛽2 -0.113*** -0.112*** -0.035*** -0.037***
(5.02) (4.84) (2.75) (2.88)
𝛽3 0.009*** 0.009*** 0.002 0.002
(3.65) (3.59) (1.15) (1.15)
Year Fixed-Effect NO YES NO YES
Industry Fixed-Effect NO YES NO YES
R-square 0.09 0.09 0.02 0.04
N 57,304 57,304 15,514 15,514
Panel C: 1-year Contracts
0 1.153*** 1.233*** 0.510*** 0.361***
(11.47) (9.65) (10.22) (4.24)
𝛽1 -0.124*** -0.124*** -0.012 -0.012
(4.75) (4.70) (1.60) (1.65)
𝛽2 0.009*** 0.009*** -0.034** -0.042***
(3.10) (2.95) (2.26) (2.60)
𝛽3 -0.049*** -0.048*** 0.002 0.002
(4.18) (4.14) (0.85) (0.90)
Year Fixed-Effect NO YES NO YES
14
Industry Fixed-Effect NO YES NO YES
R-square 0.06 0.07 0.02 0.03
N 48,057 48,057 16,167 16,167
15
Table V: Arbitrage Profits as Functions of the Number of Cournot Players
This table reports the multivariate regression results to examine the impact of market structure on the
arbitrage profits of longing CDS and shorting corresponding LCDS contracts. D is an indicator that equals
one when Min_Dealers is equal to one (monopoly) or equal to 2 (duopoly) and zero otherwise. Min_Dealers
denotes the minimum number of distinct dealers providing quotes in the CDS and LCDS markets.
Diff_Dealers denotes the difference of the number of distinct dealers providing quotes in the CDS and
LCDS markets. The statistically significant coefficients are indicated by ***, ** and * for significance at
the 1%, 5% and 10% levels, respectively. The standard errors are reported in the parentheses. N is the
number of observations.
Panel A: Regression Results
5-year 3-year 1-year
Min_Dealers*D -0.198*** -0.081 -0.153** (0.064) (0.054) (0.062)
Min_Dealers*(1-
D) -0.153*** -0.095*** -0.135***
(0.028) (0.024) (0.030) Diff_Dealers -0.048*** -0.036*** -0.025**
(0.007) (0.008) (0.010) Intercept 1.204*** 0.894*** 1.365***
(0.154) (0.188) (0.195) Year Dummy YES YES YES
Month Dummy YES YES YES
Adj. R-square 0.07 0.08 0.06 N 84,263 63,483 108,982
Panel B: Effect of Min_Dealers on arbitrage profits computed from
the above results
Min_Dealers=1 -0.198 -0.081 -0.153
Min_Dealers=2 -0.396 -0.162 -0.306
Min_Dealers=3 -0.459 -0.285 -0.405
Min_Dealers=4 -0.612 -0.380 -0.540
16
Table VI: Market Elasticity Test for the Contracts with 5-year Maturity
This table reports the OLS results for the following regression under various trading strategies with matured
5-year CDS contracts:
, 0 1 ,t 2 ,t 3 ,t
4 , 5 ,t 6 ,t
7 ,t .
Pr _ _ 1* _ 2* _
_ + _ 1* _
2* _
i t i i i
i t i i
i i t it
ofit TC Min Dealers D Min Dealers D Min Dealers
Diff Dealers Diff Dealers D Diff Dealers
D Diff Dealers Control
Profit_TCi,t denotes the realized arbitrage profits with transaction costs, initial and variation margins.
Min_Dealers denotes the minimum number of distinct dealers providing quotes in the CDS and LCDS
markets. Diff_Dealers denotes the difference of the number of distinct dealers providing quotes in the CDS
and LCDS markets. D1 is an indicator that equals to one if Min_dealers equals to one and zero otherwise.
D2 is an indicator that equals to one if Min_dealers equals to two and zero otherwise. Controli,t includes
LOGA, CAL, LEV, TANG, IDIO, TB5Y, SL, CBS and SP. All the variables are as defined in Appendix B.
Clustered standard errors are used to allow for residual autocorrelation and cross-sectional dependence as
in Petersen (2009). The statistically significant coefficients are indicated by ***, ** and * for significance
at the 1%, 5% and 10% levels, respectively. The p-values are reported in the parentheses. N is the number
of observations.
Trading Strategy Rating Class of
Buy-CDS and Sell-LCDS
Sell CDS Buy CDS Investment
Grade
Speculative
Grade
Min_Dealers 0.001 -4.000 -0.007** 0.002 (0.001) (2.842) (0.004) (0.001)
Min_Dealers*D1 0.041*** 16.063 -0.031 0.051***
(0.009) (11.282) (0.032) (0.011)
Min_Dealers*D2 0.015*** 0.812 0.007 0.017***
(0.003) (1.818) (0.008) (0.003)
Diff_Dealers 0.002* -0.959 -0.002 0.002* (0.001) (0.885) (0.002) (0.001)
Diff_Dealers*D1 -0.004** -1.225 0.001 -0.005**
(0.002) (1.409) (0.002) (0.002)
Diff_Dealers*D2 -0.004*** -2.785 -0.001 -0.005***
(0.001) (2.378) (0.002) (0.001)
CRISIS 0.004 4.934 -0.005 0.007 (0.003) (4.745) (0.005) (0.004)
LOGA -0.002 1.884 -0.018** 0.001 (0.003) (3.003) (0.007) (0.004)
CAL -0.009*** -2.329 -0.009** -0.009***
(0.002) (3.537) (0.004) (0.003)
LEV 0.005 -19.683 -0.019 0.012 (0.022) (15.085) (0.037) (0.020)
TANG -0.018** 13.772 -0.098*** -0.012
(0.009) (10.678) (0.031) (0.010)
IDIO 0.073 23.236 16.710* 0.073 (0.065) (135.995) (8.990) (0.065)
TB5Y -0.013*** 15.949* -0.012*** -0.015***
(0.004) (9.405) (0.003) (0.005) SL 0.102 -518.196 0.905 0.035
17
(0.342) (1,045.818) (0.563) (0.392)
CBS 1.017*** 368.616 0.036 0.893**
(0.350) (793.850) (0.666) (0.412)
SP -0.013 -56.654 0.018 -0.017 (0.010) (83.233) (0.019) (0.011)
Year Fixed-Effect YES YES YES YES
Industry Fixed-
Effect NO NO NO NO
N 4,049 22,395 4776 17619
Adjusted R2 13.50% 13.32% 40.05% 14.78%
18
Table VII: Market Elasticity Test for the Contracts with 3-year Maturity
This table reports the results for the following regression under various trading strategies with matured 3-
year CDS contracts:
, 0 1 ,t 2 ,t 3 ,t
4 , 5 ,t 6 ,t
7 ,t .
Pr _ _ 1* _ 2* _
_ + _ 1* _
2* _
i t i i i
i t i i
i i t it
ofit TC Min Dealers D Min Dealers D Min Dealers
Diff Dealers Diff Dealers D Diff Dealers
D Diff Dealers Control
Profit_TCi,t denotes the realized arbitrage profits with transaction costs, initial and variation margins.
Min_Dealers denotes the minimum number of distinct dealers providing quotes in the CDS and LCDS
markets. Diff_Dealers denotes the difference of the number of distinct dealers providing quotes in the CDS
and LCDS markets. D1 is an indicator that equals to one if Min_dealers equals to one and zero otherwise.
D2 is an indicator that equals to one if Min_dealers equals to two and zero otherwise. Controli,t includes
LOGA, CAL, LEV, TANG, IDIO, TB5Y, SL, CBS and SP. All the variables are as defined in Appendix B.
Clustered standard errors are used to allow for residual autocorrelation and cross-sectional dependence as
in Petersen (2009). The statistically significant coefficients are indicated by ***, ** and * for significance
at the 1%, 5% and 10% levels, respectively. The p-values are reported in the parentheses. N is the number
of observations.
Trading Strategy Rating Class of
Buy-CDS and Sell-LCDS
Buy CDS Sell CDS Investment
Grade
Speculative
Grade
Min_Dealers 0.000 -0.013 -0.005 0.001 (0.001) (0.009) (0.005) (0.001)
Min_Dealers*D1 0.042*** -0.019 -0.032 0.048***
(0.009) (0.053) (0.036) (0.010)
Min_Dealers*D2 0.017*** -0.009 0.015 0.017***
(0.003) (0.016) (0.011) (0.003)
Diff_Dealers 0.002** -0.004 -0.002 0.001* (0.001) (0.004) (0.002) (0.001)
Diff_Dealers*D1 -0.004*** -0.002 0.003 -0.003*
(0.001) (0.006) (0.004) (0.002)
Diff_Dealers*D2 -0.004*** 0.002 -0.002 -0.005***
(0.001) (0.005) (0.003) (0.001)
CRISIS 0.014*** -0.000 0.008 0.014***
(0.004) (0.013) (0.007) (0.004)
LOGA -0.005* 0.007 -0.025*** -0.005 (0.003) (0.013) (0.008) (0.003)
CAL -0.003 0.001 0.009 -0.002 (0.002) (0.011) (0.011) (0.002)
LEV 0.001 0.151* 0.004 0.020 (0.024) (0.079) (0.036) (0.018)
TANG -0.017 -0.028 -0.115*** -0.002 (0.010) (0.023) (0.039) (0.011)
IDIO 0.036 0.437 4.678 0.034 (0.026) (1.297) (7.542) (0.024)
TB5Y -0.011*** -0.005 -0.018*** -0.010***
(0.003) (0.013) (0.005) (0.003) SL 0.307 -2.997 2.171*** -0.124
19
(0.385) (1.965) (0.708) (0.398)
CBS 0.239 4.933*** -1.176** 0.335 (0.412) (1.602) (0.554) (0.475)
SP -0.017 0.121** 0.014 -0.010 (0.013) (0.048) (0.020) (0.013)
Year Fixed-Effect YES YES YES YES
Industry Fixed-
Effect NO NO NO NO
N 28,548 6,272 6,067 22,481
Adjusted R2 0.18 0.38 0.44 0.21
20
Table VIII: Market Elasticity Test for the Contracts with 1-year Maturity
This table reports the results for the following regression under various trading strategies with matured 1-
year CDS contracts:
, 0 1 ,t 2 ,t 3 ,t
4 , 5 ,t 6 ,t
7 ,t .
Pr _ _ 1* _ 2* _
_ + _ 1* _
2* _
i t i i i
i t i i
i i t it
ofit TC Min Dealers D Min Dealers D Min Dealers
Diff Dealers Diff Dealers D Diff Dealers
D Diff Dealers Control
Profit_TCi,t denotes the realized arbitrage profits with transaction costs, initial and variation margins.
Min_Dealers denotes the minimum number of distinct dealers providing quotes in the CDS and LCDS
markets. Diff_Dealers denotes the difference of the number of distinct dealers providing quotes in the CDS
and LCDS markets. D1 is an indicator that equals to one if Min_dealers equals to one and zero otherwise.
D2 is an indicator that equals to one if Min_dealers equals to two and zero otherwise. Controli,t includes
LOGA, CAL, LEV, TANG, IDIO, TB5Y, SL, CBS and SP. All the variables are as defined in Appendix B.
Clustered standard errors are used to allow for residual autocorrelation and cross-sectional dependence as
in Petersen (2009). The statistically significant coefficients are indicated by ***, ** and * for significance
at the 1%, 5% and 10% levels, respectively. The p-values are reported in the parentheses. N is the number
of observations.
Trading Strategy Rating Class of
Buy-CDS and Sell-LCDS
Buy CDS Sell CDS Investment
Grade
Speculative
Grade
Min_Dealers 0.003 -0.011 0.015 0.005 (0.006) (0.007) (0.012) (0.007)
Min_Dealers*D1 0.077*** 0.047 0.044 0.055*
(0.026) (0.038) (0.052) (0.032)
Min_Dealers*D2 0.017*** 0.018 0.017* 0.015**
(0.006) (0.013) (0.009) (0.007)
Diff_Dealers 0.003 -0.003 0.003 0.003 (0.002) (0.002) (0.003) (0.003)
Diff_Dealers*D1 -0.003 -0.010** 0.001 0.005 (0.005) (0.004) (0.004) (0.009)
Diff_Dealers*D2 -0.003 -0.001 0.002 -0.004 (0.002) (0.004) (0.001) (0.003)
CRISIS 0.021** -0.018 -0.011 0.023** (0.010) (0.027) (0.018) (0.011)
LOGA -0.017** 0.004 -0.045** -0.007
(0.008) (0.009) (0.018) (0.012)
CAL 0.000 0.006 0.028 -0.001 (0.011) (0.010) (0.019) (0.010)
LEV 0.108 0.117*** 0.106 0.104 (0.093) (0.043) (0.075) (0.104)
TANG -0.018 -0.032 -0.091 -0.013 (0.037) (0.023) (0.058) (0.046)
IDIO -0.022 1.814 -5.552 -0.003 (0.021) (1.300) (9.958) (0.022)
TB5Y -0.017*** 0.005 -0.017** -0.019***
(0.006) (0.013) (0.008) (0.007) SL 2.360*** -0.203 2.942** 2.235**
21
(0.730) (1.564) (1.140) (0.957)
CBS -0.924 7.181*** -2.654*** -0.142 (0.990) (1.788) (0.988) (1.025)
SP 0.005 0.041 0.038 0.006 (0.025) (0.061) (0.031) (0.028)
Year Fixed-Effect YES YES YES YES
Industry Fixed-
Effect NO NO NO NO
N 56,756 17,984 18,064 38,692
Adjusted R2 0.16 0.27 0.40 0.20
22
Table IX Private and Public Firms’ sub-Samples outside the NT zone
Panel A: Private Firms’ Sample
Variable N Mean Std Dev 5th Pctl 25th Pctl Median 75th Pctl 95th
Pctl
Profit_TC 49310 0.0471 0.3518 -0.0109 0.0158 0.0367 0.0765 0.2619
CDS_Quotes 49310 4.6892 3.1387 2.0000 2.0000 3.0000 7.0000 11.0000
LCDS_Quotes 49310 2.2877 1.4772 1.0000 1.0000 2.0000 3.0000 5.0000
Panel B: Public Firms’ Sample
Variable N Mean Std Dev 5th Pctl 25th Pctl Median 75th Pctl 95th
Pctl
Profit_TC 40675 0.9755 27.1615 -0.0015 0.0138 0.0305 0.0602 0.1685
CDS_Quotes 40675 5.1783 3.1335 2.0000 2.0000 5.0000 7.0000 11.0000
LCDS_Quotes 40675 2.0058 1.3535 1.0000 1.0000 2.0000 2.0000 5.0000
Panel C: Difference Tests of Means and Medians
Means Medians
Un-
matched Matched
Difference
(p-value of
T-tests)
Un-
matched Matched
Difference
(p-value of
Wilcoxon)
Profit_TC 0.0471 0.9755 -0.9284***
(<.0001) 0.0367 0.0305
0.0062***
(<.0001)
CDS_Quotes 4.6892 5.1783 -0.4891***
(<.0001) 3.0000 5.0000
-2.000***
(<.0001)
LCDS_Quotes 2.2877 2.0058 0.2819***
(<.0001) 2.0000 2.0000
0.0000***
(<.0001)
23
Table X: Number of Consecutive Days with Arbitrage Profits and No Profits
This table reports summary statistics for the numbers of consecutive days on which the arbitrage profits are persistent once an arbitrage profit
opportunity is or is not observed according to the CDS-LCDS parity rule. First and third rows of each panel represent such opportunities. Mean
(Median) Diff equals the difference between the means (medians) of the number of consecutive days under buy CDS (LCDS) and under no-trading
strategies. The p-values for t-tests of the mean differences (Mean Diff) and Wilcoxon ranked tests of median differences (Median Diff) are reported
in the parentheses. ***, ** and * indicate 1%, 5% and 10% significance levels, respectively.
Min
Quantile
Mean Std Mean Diff Median Diff 25% 50% 75%
Panel A: Full Sample of Matured Contracts
1 1c c 1 2 5 20 31 75 13*** (<.0001) 1*** (0.0088)
1 1 1c c c 1 1 4 14 18 38
1 1c c 1 1 4 11 13 29 -5*** (0.0199) 0 (0.4364)
Panel B: Investment Grades for Matured Contracts
1 1c c 1 2 6 26 36 92 7*** (<.0001) 1 (0.7084)
1 1 1c c c 1 2 5 19 29 60
1 1c c 1 2 4 19 18 36 11*** (0.0002) -1 (0.6387)
Panel C: Junk Grades for Matured Contracts
1 1c c 1 1 5 20 29 71 13*** (<.0001) 1*** (0.0060)
1 1 1c c c 1 1 4 13 16 32
1 1c c 1 2 4 10 12 29 3** (0.0220) 0 (0.8053)
Panel D: Before Crisis (Aug, 2006 – May, 2007) for Matured Contracts
1 1c c 1 2 6 22 63 144 33*** (<.0001) -2 (0.2560)
1 1 1c c c 1 2 8 40 30 49
1 1c c 1 2 4 8 11 17 19*** (<.0001) -4*** (<.0001)
Panel E: Crisis Period: (June, 2007 – March, 2009) for Matured Contracts
1 1c c 1 1 5 24 30 62 14*** (<.0001) 2*** (0.0024)
1 1 1c c c 1 1 3 10 15 37
1 1c c 1 1 4 12 14 35 -1 (0.3060) 1 (0.4314)
Panel F: After Crisis Period: (April, 2009 – July, 2014) for Matured Contracts
1 1c c 1 2 4 14 16 32 -1 (0.9472) 0 (0.9375)
1 1 1c c c 1 2 4 15 17 32
24
1 1c c 1 1 3 6 8 14 -9*** (<.0001) -1** (0.0246)
Table XI: Diverging Ratios
This table reports descriptive statistics for the diverging ratios calculated using the overlapping windows with varying window sizes for each firm
for each arbitrage profit opportunity based on violations of the CDS-LCDS parity rule for matured contracts. This nonparametric measure is
independent of the time period since it accounts for all CDS-LCDS pairs and all the possible combinations from the total number of observations.
No. Win denotes the total number of windows under various scenarios.
Intervals No.
Win
DR
Mean
DR
Median
DR
STD
No.
Win
DR
Mean
DR
Median
DR
STD
Panel A: Full Sample Panel D: Before Crisis
(Aug, 2006 – May, 2007)
1 1c c
5-days 70345 45.35% 40.00% 31.31% 2753 38.32% 40.00% 30.37%
10-days 69650 46.64% 46.67% 27.40% 2739 39.69% 37.78% 26.17%
20-days 68317 47.59% 46.84% 25.26% 2723 41.31% 40.53% 23.03%
60-days 64852 48.57% 48.14% 21.98% 2682 48.57% 48.05% 20.60%
1 1c c
5-days 14733 50.15% 50.00% 31.23% 1531 46.34% 50.00% 31.76%
10-days 14518 51.55% 53.33% 27.09% 1523 48.86% 51.11% 26.70%
20-days 14137 53.32% 56.32% 25.00% 1515 52.06% 54.74% 23.70%
60-days 13416 56.30% 58.64% 20.75% 1535 62.21% 63.62% 18.91%
Panel B: Investment Grades Panel E: In Crisis
(June, 2007 – March, 2009)
1 1c c
5-days 15061 47.84% 50.00% 31.06% 24433 40.71% 40.00% 31.99%
10-days 14906 48.68% 48.89% 27.17% 24240 43.49% 42.22% 28.56%
20-days 14602 49.12% 48.42% 25.18% 23846 46.10% 45.79% 26.51%
60-days 13701 49.93% 49.10% 22.10% 22955 48.73% 49.49% 23.40%
1 1c c
5-days 1264 53.38% 60.00% 31.67% 3812 48.49% 50.00% 31.18%
10-days 1245 54.70% 57.78% 27.19% 3744 49.44% 51.11% 26.91%
20-days 1218 56.85% 61.58% 24.36% 3628 52.05% 55.26% 24.96%
60-days 1099 56.60% 57.91% 18.76% 3441 53.98% 56.33% 21.50%
Panel C: Junk Grades Panel F: Full Sample After Crisis
(April, 2009 – July, 2014)
25
1 1c c
5-days 55284 44.67% 40.00% 31.35% 43159 48.43% 50.00% 30.58%
10-days 54744 46.09% 46.67% 27.44% 42671 48.88% 48.88% 26.54%
20-days 53715 47.17% 46.32% 25.27% 41748 48.85% 47.89% 24.55%
60-days 51151 48.21% 47.85% 21.93% 39215 48.49% 47.51% 21.19%
1 1c c
5-days 13469 49.84% 50.00% 31.17% 9390 51.44% 50.00% 31.08%
10-days 13273 51.25% 53.33% 27.06% 9251 52.85% 55.56% 27.14%
20-days 12919 53.00% 55.79% 25.04% 8994 54.06% 56.84% 25.21%
60-days 12317 56.27% 58.70% 20.91% 8440 56.17% 58.59% 20.55%
Table XII: Correlation Matrix of the Variables for the 5-year maturity sample
This table reports the correlation matrix of firm specific and macro variables, including the current payoffs in the presence of transaction costs (PR),
publication of ISDA dummy (ISDA), total assets (LOGA), number of distinct dealers providing quotes for each CDS (CDS_L) and LCDS (LCDS_L)
contract, ratio of current assets over current liabilities (CAL), leverage ratio (LEV), tangible asset ratio (TANG), idiosyncratic volatility (IDIO), 5-
year US treasury bond yields (TB5Y), slope of the yield term structure (SL), the yield spread between Aaa corporate bonds and Baa corporate bonds
(CBS) and S&P 500 index return (SP). The numbers in the parentheses are the p-values of the Pearson correlation coefficients.
PR ISDA CDS_L LCDS_L LOGA CAL LEV TANG IDIO TB5Y SL CBS SP
PR 1.00
ISDA -0.06 1.00
(<.0001)
CDS_L -0.12 -0.19 1.00
(<.0001) (<.0001)
LCDS_L -0.07 -0.05 -0.15 1.00
(<.0001) (<.0001) (<.0001)
LOGA -0.23 0.02 0.39 -0.15 1.00
(<.0001) (0.00) (<.0001) (<.0001)
CAL 0.01 0.00 -0.06 0.13 -0.13 1.00
(0.00) (0.99) (<.0001) (<.0001) (<.0001)
LEV 0.23 -0.15 -0.09 0.11 -0.44 -0.26 1.00
(<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001)
TANG -0.03 -0.06 0.05 0.06 -0.15 -0.17 0.43 1.00
(<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001)
IDIO 0.22 -0.19 -0.07 0.11 -0.37 0.03 0.48 0.15 1.00
26
(<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001)
TB5Y 0.06 -0.66 0.15 0.01 0.05 0.01 0.00 0.03 0.03 1.00
(<.0001) (<.0001) (<.0001) (0.00) (<.0001) (0.04) (0.88) (<.0001) (<.0001)
SL 0.05 -0.60 0.13 0.01 0.06 0.01 -0.03 0.02 0.00 0.99 1.00
(<.0001) (<.0001) (<.0001) (0.05) (<.0001) (0.07) (<.0001) (<.0001) (0.63) (<.0001)
CBS 0.07 -0.43 0.14 0.05 -0.06 -0.01 0.21 0.08 0.30 0.06 -0.06 1.00
(<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (0.03) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001)
SP 0.01 -0.04 0.00 0.00 0.00 0.00 0.02 0.01 0.02 0.03 0.02 0.07 1.00 (0.13) (<.0001) (0.95) (0.81) (0.61) (0.72) (0.00) (0.20) (<.0001) (<.0001) (<.0001) (<.0001)
27
Figure I: Distribution of Trading Strategies for 5-, 3- and 1-year CDS-LCDS Contracts with Margins
and Transaction Costs
55% 56%
63%
9%11%
18%
36%33%
19%
0%
10%
20%
30%
40%
50%
60%
70%
5-year 3-year 1-year
buy_cds Sell_cds no_trade
28
Table XIII: Some details about the North American Loan CDS Documentation published on April 5,
2010 by the ISDA3
Document Name Abstract
Bullet Syndicated
Secured Loan Credit
Default Swap
Standard Terms
Supplement
“This template is designed to document credit default swap transactions
where the Deliverable Obligations are limited to Syndicated Secured
Loans of the Reference Entity. This form is primarily intended for use in
the North American market. The contract: (a) has a "bullet" maturity, i.e.
not subject to acceleration in the case where the Reference Entity's loans
are repaid; (b) is subject to a credit event determination by a
Determinations Committee; (c) provides for auction settlement if the
Participating Dealers vote to hold an auction under the Bullet LCDS
Auction Rules in relation to a Reference Entity and Designated Priority;
and (d) contains specific rules and procedures for determining Successors
to the Reference Entity (the procedures are contained in the Bullet LCDS
Continuity Procedures). If no auction is held or the auction fails or is
abandoned, Physical Settlement will apply to LCDS transactions under
the most recently-published form of LSTA Physical Settlement Rider,
which is available from the LSTA’s website.”
Bullet Syndicated
Secured Loan Polling
Rules
“This document contains the rules and procedures that apply to determine
whether a loan qualifies as a "syndicated secured" loan of the Reference
Entity, for purposes of the syndicated secured list.”
Bullet LCDS Auction
Rules and LCDS
Auction Settlement
Terms
“The Bullet LCDS Auction Rules and LCDS Auction Settlement Terms are
designed to facilitate the settlement of Bullet Syndicated Secured Loan
Credit Default Swap transactions.”
Bullet LCDS
Continuity
Procedures
“The Bullet LCDS Continuity Procedures contain the procedural rules for
determination of a Successor under the Bullet LCDS documentation.”
3 See also Merrill Lynch (2007) and Bartlam and Artmann (2006). The template forms of LCDS documentation were
published by International Derivative and Swap Association (ISDA) for the US and European LCDS market on 8th,
June 2006 and 2nd, May 2006, respectively. The abstracts are quoted from ISDA website:
http://www.isda.org/publications/isdacredit-deri-def-sup-comm.aspx#ra.
29
Table XIV: Restructuring clause
Restructuring Clause Details
Cum Restructuring (CR) or old
restructuring
Any restructuring event is qualified as a credit event and any bond
of maturity up to 30 years is deliverable. (1999 ISDA credit
derivative definition)
Modified Restructuring (MR)
Restructuring events are considered as a credit event and the
bonds with maturity of 30 months or less after the termination
date of the CDS contract are deliverable. (2001, ISDA credit
derivative definition)
Modified-Modified Restructuring
(MM)
Restructuring events are considered as a credit event and the
bonds with maturity of 60 months or less for the restructured
obligations and 30 months for all the other obligations after the
termination date of the CDS contract are deliverable. (2003, ISDA
credit derivative definition)
Ex-Restructuring(XR) or without
restructuring All the restructuring events are not considered as a credit event.