Credit Default Swap Contract

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					An Empirical Analysis of the CDS-Bond
   Basis in Sovereign Debt Markets
              Scott Smith
              April, 2006




                   1
Introduction

A credit default swap (CDS) is an over-the-counter financial instrument that permits the transfer
of credit risk between parties. In a credit default swap, a protection seller agrees to compensate a
protection buyer in the event that a particular entity (the reference entity), such as a corporation
or sovereign country, experiences a credit event. In return, the protection buyer pays the seller a
periodic fee. Thus, CDS contracts are basically a form of insurance.

CDS contracts are linked to cash bond markets by arbitrage relationships much like equity and
bond futures are linked to their respective cash markets. However, unlike many derivative
markets, the arbitrage is less apparent. CDS contracts are not written on individual securities;
instead, they are written on an issuer. Any bond or loan associated with the reference entity can
be delivered in the event of default, creating a natural cheapest-to-deliver option for protection
buyers that are not present in the cash market. Further, CDS generally are written for a tenor of
five years, meaning that it is difficult or impossible to create a maturity-matched hedge for a
given instrument. Finally, since default is an ill-defined concept, there may be disagreement as
to whether a credit event has actually occurred. As a result of these and other factors, spreads in
the two markets often diverge even though they represent similar underlying credit risks. The
dynamics of this difference between CDS and cash bond spreads, or basis, is thus a natural target
for relative value traders.

In this paper, we will begin with an overview of CDS contracts. We will explain the most
common uses and derive a valuation model. We will then present a method for comparing
spreads in the two markets using risk-neutral default intensities. Using this technique, we will
calculate the CDS-bond basis for a number of sovereign issuers. We will analyze the statistical
behavior of the basis, determine whether a non-zero basis persists, and look for causal
relationships between spreads in the two markets.


Overview of Credit Default Swaps

A CDS contract is an unfunded instrument that transfers credit risk from a protection buyer to a
protection seller in exchange for a period fee. This fee is set such that the present value of the
fee payments equals the expected present value of the potential obligations of the protection
seller in the event of a default event. Thus, a CDS contract has zero value at initiation.

If the reference entity does not experience any credit events, then the protection buyer simply
continues paying the protection seller a fee until the contract expires (usually after five years). In
the event that a credit event does occur, then the buyer can deliver any obligation of the reference
entity to the seller at par (although cash, rather than physical, settlement is becoming more
common). Thus, a CDS contract behaves much like a put option on the firm’s debt for the
protection buyer.




                                                  2
Often, parties will want to terminate a contract before it matures. This can be achieved in a
number of ways. A party (xxx)

Since the term “credit event” can be defined in many different ways, market participants have
agreed on a set of definitions laid out by the International Securities Dealers Association (ISDA)
in 2003. ISDA’s 2003 definitions include several types of credit events1:

    1.        Failure to pay: if an entity fails to make scheduled payment of coupon or principal
    2.        Bankruptcy: if an entity files for bankruptcy
    3.        Obligation default or acceleration: if any of the entity’s obligations have become
              payable prior to maturity (generally excluded in corporate contracts but still used in
              some emerging market contracts)
    4.        Repudiation or moratorium: if a government or other authority enacts laws that
              make it impossible for an entity to repay its debt
    5.        Restructuring: if the principal or interest due on an obligation is decreased or the
              maturity date extended; could also be triggered by changing the priority of obligations
              or the currency in which they will be paid

As an example of the ambiguity inherent in the term “credit event”, one could look to the case of
Xerox in the summer of 20022. Xerox’s creditworthiness had been steadily declining before this
time. Shortly before a substantial bank revolver came due, Xerox negotiated an extension of the
repayment date. The extension was agreed to by both parties, but according to the terms of many
CDS contracts, it could have been defined a credit event. As a result of this case, ISDA updated
its definitions to include the word “mandatory” in the restructuring clause to prevent bilateral
agreements from triggering a credit event.

The restructuring clause has been by far the most contentious aspect of CDS contracts. ISDA
now has four different versions of the restructuring clause. This means that contracts on the
same reference entity may have different terms and trade at different spreads. In an attempt to
standardize the market (to improve transparency and liquidity), many market participants are
advocating dropping this clause completely.


Uses of Credit Derivatives

The primary participants in the CDS market are banks, insurance companies, corporations, and
asset managers. Banks and corporations are net buyers of protection, while insurance companies
are net sellers3. Among asset managers, some players sell protection in order to enhance returns,
while others (such as convertible bond arbitrageurs) use them to hedge credit risk in their
strategies.

Hedging credit risk


1
  Francis, p. 62.
2
  Francis, p. 63.
3
  Taksler, p. 8.


                                                   3
Many market participants who buy protection are looking to hedge exposure to an entity. For
instance, banks often extend loans to corporations. Rather than securitizing these loans (which
may damage the bank’s relationship with its customer), the bank can simply buy protection in the
CDS market and nullify its credit exposure. Similarly, firms such as pension funds, and
insurance companies often use CDS contracts to limit exposure to bonds that are experiencing
credit erosion. Instead of selling the bonds and incurring a mark-to-market loss, the firms
continue to hold the bonds and simply buy protection via CDS contracts.

Regulatory capital relief
Banks are a major player in the CDS market. According to the terms of the Basel Accord, banks
need to hold capital in relation to their loan exposure. However, since the rules favor OECD
banks and sovereigns (exposure to an A-rated OECD bank requires less capital than exposure to
an AAA-rated corporation)4. As a result, banks often use credit derivatives to transfer exposure
from corporations to OECD banks. They will buy protection from an OECD bank on their
corporate portfolios in order to minimize the amount of capital they need to hold.

Yield enhancement
When yields are low, entities such as investment banks and hedge funds often sell protection in
the CDS market. Such a strategy is similar to the strategy of writing deep out-of-the-money puts
on a firm in an attempt to enhance yields.

Arbitrage

Many hedge funds use CDS contracts as a part of their trading strategies. For instance, firms
who engage in convertible bond arbitrage generally purchase convertible bonds and buy
protection. This leaves them with an option on common equity that is stripped of credit risk5.
Thus, much like interest-rate derivatives can be used to hedge curve risk in trading strategies,
CDS can be used to hedge credit risk.


Arbitrage Principles

The cash bond and CDS markets are linked by arbitrage principles like all cash-derivative
markets. In order to determine the nature of this relationship, one needs to find a portfolio of
tradable instruments that replicates the cash flows of the CDS contract. Disregarding
counterparty risk, the following trades would replicate the cash flows of a CDS contract:

          Buy a bond corresponding to the reference entity in the cash market
          Finance the bond by selling it in the repo market
          Sell an interest rate swap to hedge the interest rate risk inherent in the cash bond

Combining these trades with protection from a CDS contract yields a trade with no cash flows at
either initiation or at termination. In the event of no default, the loan is repaid with the principal

4
    Meissner, p. 85-87.
5
    Taksler, p. 31.


                                                     4
payments from the bond. In the event of default, the CDS will be triggered, thus providing the
difference between the bond’s par value and its recovery rate. In either case, the net principal
payments for the trade will be zero.

By no-arbitrage principles, since there is no initial outlay, the value of the cash flows from the
trade should be zero. We have just demonstrated that the combination of the cash bond and
protection offsets the loan payment. All that is left are the intervening payments: the coupons
from the bond, flows from the swap, loan payments, and protection payments. Thus, the net
value of these payments must also be zero6.
                          Principal Payments (no default)   Principal Payments (default)         Coupon Payments          Initial Payments
Buy Cash Bond                            B                          B*RecovRate                       Rbond                        -B
Sell Interest Rate Swap                  0                                0                        LIBOR-Rswap                      0
Repo                                    -B                               -B                           -Rrepo                        B
Buy Protection                           0                        B*(1-RecovRate)                      -Scds                        0
Total                                    0                                0                Rbond+LIBOR-Rswap-Rrepo-Scds             0



Rearranging the payments, we find the following:

Rbond  LIBOR  Rswap  Rrepo  S cds  0
S cds  ( Rbond  Rswap )  ( LIBOR  Rrepo )
S cds  S bond  S repo

Thus, the CDS spread should equal the spread to swaps of a cash bond less the repo spread (or
the “specialness” of the repo). If S cds  S bond , then it would be profitable to buy the cash bond
and buy protection. Since highly rated firms can buy cash bonds and fund close to LIBOR, they
will exploit this situation and drive the spreads together ( S repo is essentially zero in this case
since the firm is funding on their balance sheet at or near LIBOR). Thus, these situations are
exceedingly rare. In contrast, if S cds  S bond , then it would be profitable to short the cash bond
and sell protection. However, in many cases, S repo is negative (it is difficult to short bonds).
Therefore, it is possible for CDs spreads to exceed cash spreads for extended periods of time (the
spread will be bounded by S repo ).


Valuation

The valuation of a credit default swap requires a number of inputs including default rates,
recovery rates, and interest rates. Most valuation models fall into two categories: structural and
reduced form. Structural models are generally based on Merton’s option pricing model. They
attempt to model the path of an entity’s assets and liabilities. Using these predictions, a
probability of default (when assets fall below liabilities) can be determined.

Reduced form models attempt to derive default probabilities from cash bond prices. There are
two degrees of freedom associated with reduced-form models: the probability of default and the

6
    Francis, p. 13-14.


                                                                   5
recovery rate. Since prices can only eliminate one degree of freedom, the other must be
determined exogenously. Generally, recovery rates are estimated based on historical default
data. In the corporate market, recovery rates are generally a function of sector and somewhere in
the neighborhood of 40%. Sovereign recovery rates are often lower since there is no legal
structure to enforce asset distribution (for instance, a sovereign could simply refuse to pay its
debt, whereas a corporation would be forced to liquidate and distribute its assets to bondholders).
Cash bond prices are then used to calculate the probability of default.

One of the most common reduced form models was proposed by Hull and White7. It assumes
that default rates, recovery rates, and interest rates are independent and that there is no
counterparty risk (although the latter constraint was lifted in a subsequent paper).

To derive their model we must first define the following:
h(t ) : risk-neutral default intensity density at time t (conditional)
s (t ) : survival probability at time t
q (t ) : risk-neutral default probability density at time t (unconditional)
                 1
DF (t )                 : discount factor at time t
             (1  rt ) t
A(t ) : accrued interest at time T
 ˆ
R : risk-neutral recovery rate

Using this model, the first step in pricing a plain vanilla CDS involves finding the risk-neutral
default probability density function q (t ) .

We start with the survival probability s (t ) . The unconditional probability of default is simply
                                   Pdefault (t, t  dt)  s(t )  s(t  dt) .
                                       uncon


The conditional probability of default is
                                                      s(t )  s(t  dt )
                             Pdefault (t , t  dt ) 
                               con
                                                                          h(t )dt .
                                                             s(t )
Rearranging yields
                                                          1 ds(t )
                                              h(t )               .
                                                        s(t ) dt
Integrating leads to
                                                             

                                            s (t )  e 0
                                                           h ( ) d
                                                          .
This is the survival probability as a function of the hazard rate. The risk-neutral probability
density is then simply the product of the hazard rate and the survival probability:
                                                                        

                                     q (t )  h(t ) s (t )  h(t )e 0
                                                                    h ( ) d
                                                                               .

The probability that a credit event will occur by time T can be defined as


7
    Hull, 2000.


                                                         6
                                                            T
                                                           0
                                                                q (t ) dt .
Likewise, the probability that no credit event will occur is
                                                                       T
                                                      1   q(t )dt .
                                                                       0
In the event that a default does occur, the protection buyer will receive a payment equal to
                                                           ˆ
                                           1  [1  A(t )] R .
Integrating this over the default density function and discounting to the present yields
                                         T
                                                           ˆ
                              V                
                                      {1  [1  A(t )] R}q(t ) DF (t )dt .
                                floating
                                                0
This is the value of the contingent leg of the swap.

To value the fixed leg, one must discount the conditional fixed payments back to the present.
Thus, the value of the fixed leg is simply
                                                                T
                                           V fixed  C  s (t i ) DF (t i ) .
                                                                i 1


The spread that equates the value of these two legs is thus the “price” of the contract:

                                           T
                                                                ˆ
                                 C
                                          0
                                               {1  [1  A(t )] R}q (t ) DF (t )dt
                                                                                     .
                                                        T

                                                        s(t ) DF (t )
                                                       i 1
                                                                       i      i




Comparing CDS Spreads to Bond Spreads

In order to compare CDS spreads to spreads in the cash market, a par-implied spread should be
calculated for a bond8. Often, spreads in the bond market are quoted as Z-spreads, or the amount
by which the curve would need to shift in parallel for the discounted value of a riskless bond
with the same cash flows to be equal to the observed market price of the bond. This technique
suffers from a major drawback, however: CDS contracts are struck at par whereas bonds can
trade at any value. In the no default case, this is not significant, but in the event of default, it is.

Let us assume that investor A were to buy a bond at $80 and investor B were to sell protection in
the CDS market. If the bond were to default with a recovery value of $40, investor A would
realize a loss of $40. However, investor B would be delivered a bond worth $40 and be
obligated to exchange it for $100 (par), resulting in a loss of $60. Thus, a protection seller is
exposed to more risk than a bond holder when bonds are trading below par. This means that
comparable CDS spreads should be wider than predicted by bond Z-spreads. Similarly,
comparable CDS spreads should be lower than bond Z-spreads when bonds are trading at a
premium.



8
    Taksler, p. 24-27.


                                                                    7
The solution is to derive the “par CDS equivalent spread” from cash bonds9. To calculate this, a
hazard rate is found that correctly prices the cash bond using the equation:
                                     n
                          Pbond  c  s (t i ) DF (t i )  100 s (T ) DF (T )  R  q ( ) DF ( )d .
                                                                                ˆ T

                                                                                 0
                                    i 1
Thus, the price of a bond can be expressed as the sum of the coupon and principal payments
discounted back to the present and adjusted for the probability of default plus the value upon
recovery in the event of default. The right side can be expressed purely as a function of interest
rates (which are readily observable), the recovery rate (which can be determined exogenously),
and the hazard-rate. Inputting the bond parameters and a market price, a risk-neutral value for
the hazard rate can thus be determined.

Using the CDS pricing formula derived in the previous section, a CDS spread can be calculated.
Since this spread uses the set of interest rates, recovery rates, and hazard rates that correctly price
the cash bond, it is therefore “equivalent” and can be used to measure the magnitude of the basis
more effectively than Z-spreads.


Drivers of the CDS-Bond Basis

A number of factors drive the basis (the difference between spreads in the cash and derivative
markets). These include illiquidity in the cash bond market, supply/demand imbalances in the
protection market, the presence of a cheapest-to-deliver option in the CDS contract, and
counterparty risk10.

Illiquidity in the cash bond market
In general, the CDS market is more liquid than the cash bond market. This can result in either a
positive or negative basis. If market participants are looking to gain exposure to an entity with
little outstanding debt, then the basis will generally tighten (decrease or become negative)
because of the presence of many participants looking to sell protection. Alternatively, one could
look at this situation and say that the holders of illiquid bonds are receiving additional
compensation for the liquidity risk they are bearing.

Alternatively, if there is significant demand for a firm’s debt, than it may be the case that cash
investors are willing to accept lower compensation for the risk they are bearing (as may be the
case with bonds that are part of major indices). As a result, the cash bond market may trade
tighter than the CDS market.

Supply/Demand imbalances in the CDS market
In some cases, there may be instances of heightened demand for protection via the derivative
market. For instance, when an entity moves closer to default, other firms may elect to hedge
their exposure by buying protection. Suppliers might want to buy protection in the event that a
firm cannot make timely payments. As a result of this increase in demand for protection, the

9
    Taksler, p. 87-89.
10
     Francis, p. 36-40.



                                                              8
price of protection (the credit spread) will increase. Consequently, it is also the case that as the
riskiness of an entity increases, the basis often widens (that is, spreads in the CDS market widen
more than those in the cash market).

Presence of a cheapest-to-deliver option in the CDS market
In the event of a credit event, a protection buyer can deliver any loan or bond that is pari-passu
(equivalent) with the instrument defined in the CDS contract. Since these instruments may trade
at different prices, it is possible that a protection buyer will be holding the cheapest of these
instruments. A protection seller is obligated to pay the difference between par and the value of
the delivered instrument, and as a result, the magnitude of this obligation is uncertain. In
essence, the buyer is long (and the seller short) an option to deliver the cheapest bond available.
Thus, the seller expects additional compensation (a higher spread) in return for being short this
option.

Counterparty Risk
In a CDS contract, the protection buyer is exposed to risk on two fronts: from the reference entity
and from the counterparty. Since there is a risk (however slight) that the reference entity and
counterparty will simultaneously default, the contingent payout upon reference default is risky.
Thus, the price a protection buyer is willing to pay should be depressed (resulting in lower
spreads).


Empirical Results

Existence of the Basis
In order to examine the properties of the CDS-bond basis, we first looked at various sovereign
CDS levels versus the spread to LIBOR of the corresponding JP Morgan EMBI+ Index.
Although the effects caused by bonds trading away from par are present in these series, they
provide a straightforward mechanism to indicate (a) the presence/absence of a basis and (b) the
presence/absence of a causal link between the two markets.

Analyses were run on five countries: Brazil, Mexico, Russia, Turkey, and Venezuela. A CDS
spread was calculated to match the average life of the bonds in the index by interpolating the
CDS curve as downloaded from JP Morgan. This mitigated effects caused by differences in the
tenor of the two securities.

The basis was calculated by calculating the difference between the CDS spread and the cash
bond index spread. First, the basis was tested for statistical significance. In all cases except
Russia, the basis exhibited a significant positive value at a confidence level of 99%. In the case
of Russia, the average value was positive, but the value was less statistically significant. The
resulting plots appear in appendix A.

Figure 1: Average CDS-EMBI+ Index Basis




                                                  9
  country     start     end    mean            se      t stat
   Brazil  30-Nov-98 21-Apr-06 0.474          0.042    11.201
  Mexico    4-Oct-99 21-Apr-06 0.854          0.012    68.797
  Russia    3-Jan-01 21-Apr-06 0.411          0.366     1.123
  Turkey    3-Jan-01 21-Apr-06 0.818          0.046    17.810
 Venezuela 30-Nov-98 21-Apr-06 0.731          0.065    11.305

After confirming the presence of a basis, the hypothesis that the basis will widen as overall
spreads widen (presumably due to the increased demand for protection as risk increases). To
verify this hypothesis, the basis was regressed against the index spread. In all cases, a
statistically significant relationship emerged: the basis was clearly positively related to spreads.
The magnitude of this effect ranged from 0.08 to 0.66, but in all cases, it was present.

Figure 2: Regression Results for CDS-EMBI+ Index Basis vs. EMBI+ Index Spreads

  country     start     end    alpha alpha t          beta   beta t R-squared
   Brazil  30-Nov-98 21-Apr-06 (1.48) (18.01)         0.24   26.45     0.27
  Mexico    4-Oct-99 21-Apr-06 (0.14) (4.36)          0.66   31.94     0.38
  Russia    3-Jan-01 21-Apr-06 0.01    0.77           0.09   25.49     0.33
  Turkey    3-Jan-01 21-Apr-06 0.38    8.77           0.08   11.00     0.08
 Venezuela 30-Nov-98 21-Apr-06 (1.88) (21.87)         0.32   32.36     0.36

These findings are consistent with the theoretical propositions put forth earlier. CDS spreads
rarely trade significantly below cash bond spreads because it is easy to exploit the arbitrage that
would result. Large positive values can persist, however, because of the difficulty in shorting
cash bonds. Similarly, the proposition that increased demand for protection as spreads widen
would cause the basis to widen was also confirmed. The regression analysis can be found in
Appendix B.

Causality

Although there may be biases present between spreads in the two markets, effects in one market
should be reflected in the other market since they have similar credit exposures. For instance, if
cash bonds widen by 100bps on news of a currency devaluation, then CDS spreads should
simultaneously widen by a similar magnitude. If this effect is not instantaneous, then an
arbitrage opportunity may result. One market would be cheap relative to another and so relative
value traders would buy the now cheaper bonds and sell protection expecting CDS spreads to
widen relative to cash bonds (equivalently, expecting the basis to revert to its former level). This
effect would drive CDS spreads out until the markets were trading on a roughly equal footing.

The question is how quickly information flows between these two markets. Assuming market
efficiency, both markets should move simultaneously. In order test for any lagged effects being
transmitted from one market to the other, Granger causality tests were run on the five sets of
CDS/EMBI+ Index spreads. Using a lag of five, there was no significant causality in either
direction for any of the five countries. Thus, neither market leads the other on the scale of days.
Possibly, effects may emerge on a finer frequency, but it is difficult to detect because these
markets have modest liquidity, significant bid-ask spreads, and limited transparency.



                                                 10
Individual Bond Basis

In order to examine whether the basis observed in the EMBI+ Index spreads is caused by bonds
trading away from par, par implied spreads were calculated by deriving default probabilities
from individual cash bonds using the methodology discussed in the section “Comparing Bond
Spreads to CDS Spreads”. Par implied spreads were calculated using recovery rate assumptions
of 20% and 40% to test the model sensitivity to this exogenous parameter. Once again, maturity-
matched CDS spreads were calculated by interpolating the CDS curve. Plots of the resulting
spreads appear in appendix C.

For each of the six bonds, there was a statistically significant positive basis. With the exception
of the case of Brazil following the Argentine crisis in 2002, CDS traded wider than cash bonds
throughout the period. The model output did not appear to be highly sensitive to changes in the
recovery rate (the model simply derived a lower hazard-rate in the 20% recovery case to
correctly price the cash bond, offsetting the effect of the lower recovery rate).

Figure 3: Implied CDS-Bond Basis for Select Emerging Market Bonds
                   Mexico                         Brazil                        Turkey
       8.125 Dec 2019 11.375 Oct 2016 14.5 Oct 2009 10.125 May 2027 12.375 Jun 2009 10 Sep 2007
avg        112.61          134.72         164.00         57.16           129.68        160.81
se          9.19            13.57          15.06         15.06            11.88        11.56
t-stat      12.25           9.93           10.89          3.79            10.91        13.91

It is interesting to note that, even in a very tight spread environment, a significant basis can exist.
Looking at Mexico during the past few months, the 11.375s of Oct 2016 have been trading with
an implied spread of around 50bps. Ten year CDS contracts are trading around 150bps.

As in the analysis involving the basis relative to the EMBI+ Index, the basis for the individual
bonds was regressed on the spread level. In this case, that was the par implied spread for the
bond using a recovery rate of 20%. In the index analysis, we found that there was a strongly
positive relationship between spreads and the basis. In four of the six individual bonds, similar
trends were found. In one case the relationship was weakly positive (the Brazilian 10.125s of
May 2027), and in one it was weakly negative (the Turkish 12.327s of June 2009).

Figure 4: Regression of individual bond basis on implied par spread
country         bond           alpha          alpha t          beta            beta t        R-squared
Mexico    8.125 Dec 2019            25.10          1.19                0.31          4.51          0.27
Mexico    11.375 Oct 2016          (17.07)        (0.57)               0.56          5.57          0.27
Brazil    14.5 Oct 2009             76.52          3.72                0.13          5.41          0.30
Brazil    10.125 May 2027           68.68          4.27               (0.01)        (0.83)         0.01
Turkey    12.375 Jun 2009          110.58          4.61                0.04          0.92          0.01
Turkey    10 Sep 2007                4.61          2.81                0.92          6.32          0.31


Overall, it seems that, after accounting for the effects of bonds trading away from par, there still
seems to be a widening of the basis associated with higher spreads. This is consistent with the
story that, as risk increases, demand for protection in the CDS market as drives up the cost of
protection.


                                                  11
Possible Sources of the Basis

Although effects related to maturity mismatches and bond premiums/discounts were mitigated in
this analysis, there are still several factors present in CDS spreads that are not present in cash
bond spreads. Most significantly, there is counterparty risk and an implied cheapest-to-deliver
option present in CDS contracts. As discussed earlier, both of these effects should drive up the
cost of protection since they represent risks to protection sellers. Thus, the presence of a basis
after accounting for maturity and bond prices may not be a sign of market inefficiency but
simply compensation for more subtle risk factors.

In order to examine the effects of counterparty risk, one would need to model the default
correlations between CDS issuers and their reference entities. A pricing model incorporating
counterparty default risk was proposed by Hull and White in a follow-on paper.

In terms of the cheapest-to-deliver option, one would need to examine all obligations for a given
issuer. The price of cheapest issue would represent an approximate lower bound for the recovery
rate. However, since it is unlikely (or impossible) for all protection buyers to deliver the
cheapest issue, the actual exposure of protection sellers is probably less than that related to the
cheapest obligation.

Summary

In conclusion, we found that there was a significant positive basis in sovereign CDS relative to
both the JP Morgan EMBI+ Indices and individual cash bonds. In both cases, the basis also
appeared to be positively correlated with spreads. Although spreads in the two markets do not
converge, relative value trading opportunities may emerge if mean reversion is present
(additional tests for mean reversion using individual bonds and higher frequency data would be
needed to test this hypothesis for tradability). Presence of a causal link between the two markets
was not found, indicating that signaling effects in one market are quickly reflected in the other
market. Although there may be trading opportunities on time frames shorter than a day, none
appeared when looking at daily data for CDS contracts and the EMBI+ Indices.




                                                12
     Appendix A
CDS and EMBI+ Index Spreads




            13
                               Spread (%)




                  0
                      5
                          10
                               15
                                       20
                                            25
                                                 30
                                                      35
     11/30/1998

      2/28/1999

      5/30/1999

      8/30/1999

     11/30/1999

      2/29/2000

      5/30/2000

      8/30/2000

     11/30/2000

      2/28/2001

      5/30/2001

      8/30/2001

     11/30/2001

      2/28/2002

      5/30/2002




14
                                                           EMBI+ Spread




      8/30/2002

     11/30/2002

      2/28/2003

      5/30/2003
                                                           CDS Spread
                                                                          Brazil CDS and EMBI+ Index Spreads




      8/30/2003

     11/30/2003

      2/29/2004

      5/30/2004

      8/30/2004

     11/30/2004

      2/28/2005

      5/30/2005

      8/30/2005

     11/30/2005

      2/28/2006
                             Spread (%)




                 0
                     1
                         2
                                3
                                          4
                                              5
                                                  6
     10/4/1999

      1/4/2000

      4/4/2000

      7/4/2000

     10/4/2000

      1/4/2001

      4/4/2001

      7/4/2001

     10/4/2001

      1/4/2002

      4/4/2002

      7/4/2002

     10/4/2002




15
                                                      EMBI+ Spread




      1/4/2003

      4/4/2003

      7/4/2003

     10/4/2003
                                                      CDS Spread




      1/4/2004
                                                                     Mexico CDS and EMBI+ Index Spreads




      4/4/2004

      7/4/2004

     10/4/2004

      1/4/2005

      4/4/2005

      7/4/2005

     10/4/2005

      1/4/2006

      4/4/2006
                             Spread (%)




                 0
                     2
                         4
                             6
                                     8
                                          10
                                               12
                                                    14
      1/1/2001
      3/1/2001
      5/1/2001
      7/1/2001
      9/1/2001
     11/1/2001
      1/1/2002
      3/1/2002
      5/1/2002
      7/1/2002
      9/1/2002
     11/1/2002
      1/1/2003
      3/1/2003
      5/1/2003
      7/1/2003




16
                                                         EMBI+ Spread




      9/1/2003
     11/1/2003
      1/1/2004
      3/1/2004
                                                         CDS Spread




      5/1/2004
                                                                        Russia CDS and EMBI+ Index Spreads




      7/1/2004
      9/1/2004
     11/1/2004
      1/1/2005
      3/1/2005
      5/1/2005
      7/1/2005
      9/1/2005
     11/1/2005
      1/1/2006
      3/1/2006
                                 Spread (%)




                 0
                     2
                         4
                             6
                                    8
                                              10
                                                   12
                                                        14
                                                             16
      1/2/2001
      3/2/2001
      5/2/2001
      7/2/2001
      9/2/2001
     11/2/2001
      1/2/2002
      3/2/2002
      5/2/2002
      7/2/2002
      9/2/2002
     11/2/2002
      1/2/2003
      3/2/2003
      5/2/2003
      7/2/2003




17
                                                                  EMBI+ Spread




      9/2/2003
     11/2/2003
      1/2/2004
      3/2/2004
                                                                  CDS Spread




      5/2/2004
                                                                                 Turkey CDS and EMBI+ Index Spreads




      7/2/2004
      9/2/2004
     11/2/2004
      1/2/2005
      3/2/2005
      5/2/2005
      7/2/2005
      9/2/2005
     11/2/2005
      1/2/2006
      3/2/2006
                               Spread (%)




                  0
                      5
                          10
                                            15
                                                 20
                                                      25
     11/30/1998

      2/28/1999

      5/30/1999

      8/30/1999

     11/30/1999

      2/29/2000

      5/30/2000

      8/30/2000

     11/30/2000

      2/28/2001

      5/30/2001

      8/30/2001

     11/30/2001

      2/28/2002

      5/30/2002




18
                                                           EMBI+ Spread




      8/30/2002

     11/30/2002

      2/28/2003

      5/30/2003
                                                           CDS Spread




      8/30/2003
                                                                          Venezuela CDS and EMBI+ Index Spreads




     11/30/2003

      2/29/2004

      5/30/2004

      8/30/2004

     11/30/2004

      2/28/2005

      5/30/2005

      8/30/2005

     11/30/2005

      2/28/2006
     Appendix B
Basis vs. EMBI+ Index Spread




             19
                         Brazil Basis vs. EMBI+ Index Spread

            10




            8




            6
                                                                    y = 0.2425x - 1.4859
                                                                         R2 = 0.2739
            4
Basis (%)




            2




            0
                 0   5    10                  15               20    25                    30


            -2




            -4
                                   EMBI+ Index Spread (%)




                                         20
                                Mexico Basis vs. EMBI+ Index Spread

             3




            2.5


                                                                            y = 0.6648x - 0.1427
                                                                                 R2 = 0.3832
             2
Basis (%)




            1.5




             1




            0.5




             0
                  0   0.5   1              1.5              2         2.5          3               3.5
                                          EMBI+ Index Spread (%)




                                                 21
                               Russia Basis vs. EMBI+ Index Spread

              2




            1.5

                                                                          y = 0.0941x + 0.0145
                                                                               R2 = 0.3285

              1
Basis (%)




            0.5




              0
                   0   2   4                6               8        10         12               14



            -0.5




             -1
                                          EMBI+ Index Spread (%)




                                                22
                               Turkey Basis vs. EMBI+ Index Spread

            3.5


              3


            2.5


              2


                                                                          y = 0.0776x + 0.3846
            1.5
                                                                               R2 = 0.0835
Basis (%)




              1


            0.5


              0
                   0   2   4                6               8        10     12                   14

            -0.5


             -1


            -1.5
                                          EMBI+ Index Spread (%)




                                                23
                             Venezuela Basis vs. EMBI+ Index Spread

            8




            6

                                                                            y = 0.3173x - 1.8794
                                                                                 R2 = 0.3609

            4
Basis (%)




            2




            0
                 0   2   4       6          8            10       12   14       16             18



            -2




            -4
                                         EMBI+ Index Spread (%)




                                                24
    Appendix C
CDS and Cash Bond Spread




           25
                                        Spread (bps)

     Ap




                0
                    500
                          1000
                                 1500
                                         2000
                                                2500
                                                       3000
                                                              3500
                                                                     4000
                                                                            4500
        r-0
     Ju 1
       n-
           0
     Au 1
       g-
           0
     O 1
       ct
          -0
     D 1
      ec
          -0
     Fe 1
       b-
           0
     Ap 2
        r-0
     Ju 2
       n-
           0
     Au 2
       g-
           0
     O 2
       ct
          -0
     D 2
      ec
          -0
     Fe 2
       b-
           0
     Ap 3
        r-0
     Ju 3
       n-
           0
     Au 3
       g-
                                                                                   Cash Bond (R=20%)




           0




26
     O 3
       ct
          -0
     D 3
      ec
          -0
     Fe 3
       b-
           0
     Ap 4
        r-0
     Ju 4
       n-
           0
     Au 4
                                                                                   Cash Bond (R=40%)




       g-
           0
     O 4
       ct
                                                                                                       CDS and Cash Bond Spread: Brazil 14.5 Oct 2009




          -0
     D 4
      ec
          -0
                                                                                   CDS




     Fe 4
       b-
           0
     Ap 5
        r-0
     Ju 5
       n-
           0
     Au 5
       g-
           0
     O 5
       ct
          -0
     D 5
      ec
          -0
     Fe 5
       b-
           06
     N
         ov




                     0
                         1000
                                2000
                                       3000
                                              4000
                                                     5000
                                                            6000
              -9
     Fe          8
       b-
          99
     M
      ay
         -9
     Au 9
       g-
          9
     N 9
      ov
         -9
     Fe 9
       b-
          0
     M 0
      ay
         -0
     Au 0
       g-
          0
     N 0
      ov
         -0
     Fe 0
       b-
          0
     M 1
      ay
         -0
     Au 1
       g-
          0
     N 1
      ov
         -0
     Fe 1
       b-
          0
     M 2
      ay
                                                                   Cash Bond (R=20%)




         -0
     Au 2




27
       g-
          0
     N 2
      ov
         -0
     Fe 2
       b-
          0
     M 3
      ay
         -0
     Au 3
       g-
          0
     N 3
                                                                   Cash Bond (R=40%)




      ov
         -0
     Fe 3
       b-
          0
     M 4
                                                                                       CDS and Cash Bond Spread: Brazil 10.125 May 2027

                                                                   CDS




      ay
         -0
     Au 4
       g-
          0
     N 4
      ov
         -0
     Fe 4
       b-
          0
     M 5
      ay
         -0
     Au 5
       g-
          0
     N 5
      ov
         -0
     Fe 5
       b-
          06
                                      Spread (bps)

     Ju




                0
                    100
                          200
                                300
                                       400
                                              500
                                                     600
                                                           700
                                                                 800
                                                                       900
       n-
           0
     Au 1
       g-
           0
     O 1
       ct
          -0
     D 1
      ec
          -0
     Fe 1
       b-
           0
     Ap 2
        r-0
     Ju 2
       n-
           0
     Au 2
       g-
           0
     O 2
       ct
          -0
     D 2
      ec
          -0
     Fe 2
       b-
           0
     Ap 3
        r-0
     Ju 3
       n-
           0
     Au 3
       g-
           0
     O 3
                                                                             Cash Bond (R=20%)




28
       ct
          -0
     D 3
      ec
          -0
     Fe 3
       b-
           0
     Ap 4
        r-0
     Ju 4
       n-
           0
     Au 4
       g-
           0
                                                                             Cash Bond (R=40%)




     O 4
       ct
          -0
     D 4
                                                                                                 CDS and Cash Bond Basis: Mexico 8.125 Dec 2019




      ec
          -0
                                                                             CDS




     Fe 4
       b-
           0
     Ap 5
        r-0
     Ju 5
       n-
           0
     Au 5
       g-
           0
     O 5
       ct
          -0
     D 5
      ec
          -0
     Fe 5
       b-
           06
                                 Spread (bps)
     Ja
       n-




                 0
                     200
                           400
                                 600
                                          800
                                                1000
                                                       1200
                                                              1400
           9
     Ap 9
        r-9
             9
      Ju
         l-9
     O 9
       ct
          -9
     Ja 9
       n-
           0
     Ap 0
        r-0
             0
      Ju
         l-0
     O 0
       ct
          -0
     Ja 0
       n-
           0
     Ap 1
        r-0
             1
      Ju
         l-0
     O 1
       ct
          -0
     Ja 1
       n-
           0
     Ap 2
        r-0
             2
                                                                     Cash Bond (R=20%)




      Ju




29
         l-0
     O 2
       ct
          -0
     Ja 2
       n-
           0
     Ap 3
        r-0
             3
      Ju
         l-0
     O 3
       ct
          -0
                                                                     Cash Bond (R=40%)




     Ja 3
       n-
           0
                                                                                         CDS and Cash Bond Basis: Mexico 11.375 Oct 2016




     Ap 4
        r-0
             4
                                                                     CDS




      Ju
         l-0
     O 4
       ct
          -0
     Ja 4
       n-
           0
     Ap 5
        r-0
             5
      Ju
         l-0
     O 5
       ct
          -0
     Ja 5
       n-
           06
                                 Spread (bps)
     Ja
       n-




                 0
                     200
                           400
                                 600
                                          800
                                                1000
                                                       1200
                                                              1400
           9
     Ap 9
        r-9
             9
      Ju
         l-9
     O 9
       ct
          -9
     Ja 9
       n-
           0
     Ap 0
        r-0
             0
      Ju
         l-0
     O 0
       ct
          -0
     Ja 0
       n-
           0
     Ap 1
        r-0
             1
      Ju
         l-0
     O 1
       ct
          -0
     Ja 1
       n-
           0
     Ap 2
        r-0
             2
                                                                     Cash Bond (R=20%)




      Ju




30
         l-0
     O 2
       ct
          -0
     Ja 2
       n-
           0
     Ap 3
        r-0
             3
      Ju
         l-0
     O 3
       ct
          -0
                                                                     Cash Bond (R=40%)




     Ja 3
       n-
           0
                                                                                         CDS and Cash Bond Basis: Turkey 12.375 Jun 2009




     Ap 4
        r-0
             4
                                                                     CDS




      Ju
         l-0
     O 4
       ct
          -0
     Ja 4
       n-
           0
     Ap 5
        r-0
             5
      Ju
         l-0
     O 5
       ct
          -0
     Ja 5
       n-
           06
                                 Spread (bps)
     O
       ct




                 0
                     200
                           400
                                 600
                                          800
                                                1000
                                                       1200
                                                              1400
          -9
     Ja 8
       n-
           9
     Ap 9
        r-9
      Ju 9
         l-9
     O 9
       ct
          -9
     Ja 9
       n-
           0
     Ap 0
        r-0
             0
      Ju
         l-0
     O 0
       ct
          -0
     Ja 0
       n-
           0
     Ap 1
        r-0
      Ju 1
         l-0
     O 1
       ct
          -0
     Ja 1
       n-
           0
     Ap 2
        r-0
                                                                     Cash Bond (R=20%)




             2




31
      Ju
         l-0
     O 2
       ct
          -0
     Ja 2
       n-
           0
     Ap 3
        r-0
             3
      Ju
         l-0
     O 3
       ct
                                                                     Cash Bond (R=40%)




          -0
     Ja 3
                                                                                         CDS and Cash Bond Basis: Turkey 10 Sep 2007




       n-
           0
     Ap 4
        r-0
                                                                     CDS




      Ju 4
         l-0
     O 4
       ct
          -0
     Ja 4
       n-
           0
     Ap 5
        r-0
      Ju 5
         l-0
     O 5
       ct
          -0
     Ja 5
       n-
           06
References

Bomfim, Antulio. Understanding Credit Derivatives and Related Instruments, 2004.

Francis, Chris et al. Credit Derivate Handbook 2003. Merrill Lynch Global Securities Research
   & Economics Group, April 2003.

Hull, John and A. White. “Valuing Credit Default Swaps I: No Counterparty Default Risk,”
   University of Toronto, 2000.

Meissner, Gunter. Credit Derivatives: Application, Pricing, and Risk Management, 2005.

Taksler, Glen et al. Credit Default Swap Primer 2nd Edition. Bank of America Debt Research,
   January 2006.




                                             32

				
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