Relation Between Corporate Credit and Credit Default

8/13/2019 Relation Between Corporate Credit and Credit Default

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Empirical study of liquidity effects in the relation betweencorporate credit spread and Credit Default Swaps

Christian [email protected]

Project Coordinator: Prof. Tim Johnson

Word count: 9,175

June 2006


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Empirical study of liquidity effects in the relation between Christian VilloutaCorporate credit spread and Credit Default Swaps Masters in Finance London Business School

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Index of Contents

1. Executive Summary...............................................................................................3

2.

Introduction...........................................................................................................4

2.1. Motivation of the project ............................................................................................... 42.2. Why the results of this study are important to investors? ......................................... 5

3. Credit Arbitrage.....................................................................................................63.1. Theoretical Framework for Valuation of Bonds and CDSs......................................63.2. Trading strategies in Credit Arbitrage .......................................................................... 7

3.2.1. CDS Basis positive ................................................................................................. 73.2.2. CDS Basis negative ................................................................................................ 8

4. Data Analysis....................................................................................................... 104.1. Selection of Markets and companies.......................................................................... 10

4.2.

Data Quality ................................................................................................................... 114.3. Constructing the CDS Basis ........................................................................................ 12

4.4. Liquidity Portfolios ....................................................................................................... 144.4.1. Liquidity of Bonds................................................................................................154.4.2. Liquidity of CDS .................................................................................................. 17

5. Results ................................................................................................................. 185.1. CDS Liquidity ................................................................................................................ 185.2. Bonds Liquidity..............................................................................................................205.3. Combined Liquidity measures: CDS & Bonds ......................................................... 22

5.3.1. Friedman Test.......................................................................................................245.3.2. Kolmogorov-Smirnov Test.................................................................................24

5.4.

Effect of liquidity in Credit Arbitrage strategies.......................................................30

6. Conclusions of the study .....................................................................................35

Appendix A ................................................................................................................37

References.................................................................................................................. 41


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1. Executive SummaryThe motivation of this study was to construct an empirical test to observe whether liquidity inFixed Income and Credit Derivative markets have an effect on the theoretical relationship thatlink these markets.

The test was performed taking daily quotes for 4,943 bonds and Credit Default Swap (CDS)Premiums for 3, 5, 7 and 10 years for 614 companies from UK and US markets. The total datacollected amounted to more than 5 million singles quotes, which is considerably higher thanprevious empirical studies on the Credit Derivatives market.

Liquidity effects were tested empirically through the construction of equally weighted portfoliosbased in measures that capture liquidity of securities. Each portfolio was rebalanced in a dailybasis using information from 01/01/2003 to 31/03/2006.

The main conclusions of this empirical study are:

- Liquidity has empirical effects to the behaviour of the CDS Basis in a range of +22 to+80 basis points, and substantial increases in volatility were observed for all maturities.

- Liquidity effect is different across maturities, eliminating the possibility to hedge positionsusing trading strategies in different maturities.

- Bid-Ask spread is not enough to explain the deviations in the CDS Basis in low liquidityenvironments. When maturity increases, the explanation power of the bid-ask spread andtransaction cost is not enough for the empirical deviation in the CDS Basis.

- Credit Arbitrage trading strategies perform badly in low liquidity environments, even afteradjusting for liquidity.


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2. Introduction2.1.Motivation of the project

In the last years, the market for Credit Default Swaps (CDS) has been growing exponentially. In

2004 the notional outstanding value has reached levels higher than USD 5 trillions, and projectedfigures for 2006 are in the range of USD 7.8 9.3 trillion.

CDS are considered the building blocks for more complex securities in Credit Derivativesmarket. Its power comes from the possibility to transfer credit risk between counterparties in themarket.

Thus, CDS form a financial linkage between Fixed Income and Credit Derivatives market.Because of that, the price of a CDS, which is called CDS Premium, can be derived througharbitrage relationships reflecting the interaction between these markets.

In the professional and academic literature it is possible to find several studies devoted todeveloping models to correctly price a CDS, and subsequently more complex structures ofsecurities. Most are based on the theoretical linkages between the markets, and only a few ofthem are empirical works trying to prove how well the relations work in reality.

In addition, investors like Hedge Funds involved in Credit Arbitrage strategies, are trading inthese markets with complex analytical and quantitative models, trying to generate arbitrageprofits from these deviations. Arbitrage not in the rigorous academic form, but with a risk-return considerably higher than normal investments in Fixed Income markets.

These trading strategies are not always profitable, mainly because there are some collateral effects

not well defined in pricing models. Trading strategies are based primarily on how broad is thedifference between corporate bond spreads and CDS Premiums, which is called the CDS Basis.

There are some empirical studies about issues affecting the behaviour of the CDS Basis. Most ofthem attributed liquidity as being one of the factors behind the CDS Basis behaviour over time.

However, there was not a broad empirical study regarding the effect of liquidity, first in thebehaviour of CDS Basis, and secondly, the effects on trading strategies trying to profit fromCredit Arbitrage between Fixed Income and Credit Derivative markets.

Therefore, the objective of this study is to provide empirical answers for two main questions:

- Is liquidity of bonds and/or CDS a factor affecting the behaviour of the CDS Basis?- How affected are Credit Arbitrage strategies because of deviations in CDS Basis

attributable to liquidity of securities?


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2.2.Why the results of this study are important to investors?Liquidity is an easy concept to understand, but very difficult in practice to measure with accuracy.

Actually, it is easier to describe liquidity in relative than in absolute terms. We can compareliquidity from one security to another, or from one market with another.

Investors trying to hedge or get away of some position can face liquidity issues. If liquidity werelow, the investor would be willing to pay more to buy or offer at discount over market prices tosell the security.

If liquidity has economic effects significant enough, then a price for a CDS computed by modelsusing relative value, e.g. reduced-forms models, need to be revised and properly adjusted beforeselling, buying or trading in the market.

This situation is especially important when deviations tend to persist over time, i.e. the relativespread between the markets does not converge quickly.

In addition, these effects of liquidity could have an impact in trading strategies of CreditArbitrage. These strategies use a threshold (basis points of deviation) to enter in the trades.Liquidity could imply the need to adjust the threshold to minimize the risk of the strategy.


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3. Credit Arbitrage3.1.Theoretical Framework for Valuation of Bonds and CDSs

Credit Default Swaps (CDS) are the most important and widely used instruments in the credit

derivatives market. In essence a Credit Default Swap is an agreement, which transfers a definedcredit risk from one party to another. The buyer of credit protection pays a periodic fee to aninvestor in return for protection against a Credit Event experienced by a Reference Entity.

The valuation of a CDS could be made through the use of a structural method of credit risk,derived through the seminal work of Black and Scholes (1973) and Merton (1974), which arefocused on the use of option pricing theory in the capital structure of a company. Otherpossibility arises using the so-called reduced-form methods, where information is extractedfrom securities traded in the market, which allows pricing a CDS. The latter approach is based inthe fact that the CDS price (or premium) can be interpreted as the risk-neutral default intensityfor a company. This is the method followed by Jarrow and Turnbull (1995) and Duffie and

Singleton (1999). Valuation of credit spreads can be made under no-arbitrage conditions usingthe Martingale approach. This valuation were used to price Credit Default Swaps by Acharya etal. (2002), Das and Sundaram (2000), Das et al. (2003), Duffie (1999), Hull and White (2000,2001, 2004), Jarrow and Van Deventer (2005), Jarrow and Yildirim (2002) and many others.

Reduced-form models are not only popular in academic research. These models are the mostcommon pricing methods used by practitioners in the market.

Reduced-form models for credit risk provide an interesting linkage between bond spreads andCDS Premium. Using no-arbitrage conditions and Martingale approach for the defaultprobability, it is simple to derive the parity relation:

CDS Premiummaturity T =Bond SpreadBond maturity T "Risk_ freerate

In the real markets, there are reasons allowing for violations of the equality. These can besummarized as:

- The risk free rate is assumed to be constant, which is not true in reality.- The relation holds theoretically for par floating bonds, while the most available bonds in

the market are coupon fixed. Duffie and Liu (2001) showed that the effect could berelatively small.

- In case of default, the buyer of a CDS needs to pay the accrued premium, which affectsthe CDS Premium.

- Most CDS contracts have an implicit cheapest-to-deliver option. This option wouldimply a higher CDS Premium to compensate the seller of the CDS with the embeddedoption.

- The definition of a credit event/default could lead to conflicting views in the CDS pricefrom the perspective of buyers and sellers of default protection.

- Transaction costs easily erode all the small deviations arising from arbitrageopportunities between the two markets.

Finally, there is the fact that it is not necessarily the same investors participating in each market,which supports the existence and persistence of such deviations during long periods of time.


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3.2.Trading strategies in Credit ArbitrageWhen the CDS Basis is high (or low) enough, there are some trading strategies that can beapplied to try to profit from the deviation. The basic objective is to lock in trades using both theFixed Income and Credit Derivatives markets, delivering profit after taking into account the

transaction costs involved in such a series of trades.

This type of strategy has been used by a number of Hedge Funds during the last years trading inthe area of the capital structure arbitrage. They enter in the strategy only when a substantialdeviation allow for a profitable arbitrage. There are variations of this strategy, using as analternative the equity market, but the scope of this study was only the Fixed Income market.

Therefore, such trading strategies and its implications could not be tested with the data collected.

Credit Arbitrage strategy is based in the fact that a CDS could be seen as a financed purchase of abond with an additional hedge of the interest rate. It is a transaction with no upfront payment.

To replicate the position it is necessary to finance a bond transaction in the repo market

(repurchasement agreement), or vice versa through a reverse-repo if it is a hedging transaction.In this sense, the price of a CDS Premium can be obtained through a benchmark with an assetswap in the bonds of the company.

3.2.1. CDS Basis positiveIf the CDS Basis is positive, the following trades are made (described in Figure 1):

- In the Repo market, lend cash in exchange for a bond, which is given as collateral.- Sell the bond in the Fixed Income market.- Sell a CDS in the Credit Derivative market, receiving the CDS Premium fees, and giving

protection in case of a default event.- In the Swap market, go short in a fixed-for-floating swap, to eliminate the duration and

convexity exposure of the bond sold.

Figure 1: Trading strategy to profit from a positive CDS Basis


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If the repo rate is the same as the floating leg in the swap transaction, the net proceedings ofthese trades is the difference between the CDS Premium payments and the credit spread of thebond sold in the market.

An important assumption in the previous trades is that in the repo transaction a haircut is not

considered. A haircut is the compensation for risk that the lender takes from the loan, whichtypically is 1-2% of the loan. The risk is not only the market risk of the collateral bond, but alsothe counterparty risk.

To profit from this trade, the hedge fund or investor is expecting that the CDS Basis converge.This could happen in two ways (independently or at the same time):

- The bond spread increase over time. When the trade is unwound, the bond is bought at acheaper price in the market, and subsequently a profit can be obtained.

- CDS Premium could decrease. Entering in offsetting positions in the market, it wouldallow profiting through the differences in the CDS Premiums received and paid.

Nevertheless, this strategy has an intrinsic risk. If instead of converging to zero, the CDS Basisdiverges growing in time, the investor would incur losses were the trade terminated. In addition,some mark-to-market positions in the CDS could imply losses will be realized during the life ofthe trade and not only at the termination.

3.2.2.CDS Basis negativeIn a similar kind of strategy as before, an investor could enter in a trading strategy to profit froma negative CDS Basis observed in the market (described in Figure 2):

- In the Repo market, receive cash in exchange for a bond, which is pledged as a collateral.- Buy the bond in the Fixed Income market.- Buy a CDS in the Credit Derivative market, paying the CDS Premium fees, and receiving

protection in case of a default event.- In the Swap market, go long in a fixed-for-floating swap, to eliminate the duration and

convexity exposure of the bond bought.

If the repo rate paid is the same as the floating leg in the swap transaction, the net proceeds ofthese trades is the positive difference between the credit spread of the bond bought and the CDSPremium fees.

To profit from this trade, the hedge fund or investor is expecting that the CDS Basis willconverge. This could happen in two ways (independently or at the same time):

- Bond spreads decrease over time, pushing the CDS Basis closer to zero. When the tradeis unwound, the bond is sold at a higher price in the market, and subsequently a profitcan be obtained.

- CDS Premium could increase. Entering in offsetting positions in the market, would allowprofiting through the differences in the CDS Premiums received and paid.

As the previous trading strategy, the risk in this strategy is that the CDS Basis not converges to

zero.


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Figure 2: Trading strategy to profit from a negative CDS Basis

In comparison, the second strategy where the CDS Basis is negative is easier to execute. First,you need to go long both in the CDS and in the Fixed Income market. In the first tradingstrategy you need to sell protection through the CDS, and this could be difficult to some type ofinvestors. A second reason is the fact that it is not always is possible to find counterparty in therepo market to lend money in exchange of a bond. The other way around is much more commonand available in the market.


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4. Data Analysis4.1.Selection of Markets and companies

To derive conclusions in the study with statistic significance, it was required to obtain a large

number of data from the market. The main markets in terms of activity in the Credit DerivativesMarkets are United Kingdom and United States. Focusing on that, it was conducted a research ofinformation providers. It was found that Thomson Financial Datastream has daily quotes forCDS, including Bid/Ask spread, for a significant numbers of companies.

It was possible to obtain daily quotes for CDS Premiums of 83 companies in the UK market and531 in the US.

For all these companies, the data obtained was daily quotes from a period of time between01/01/2001 to 31/03/2006, for CDS with maturities of 1, 3, 5, 7 and 10 years. In addition, it waspossible to get quotes for the bid and ask prices in a daily basis.

It is worth mentioning that for some companies the information was not available for all datesthe period, but it was collected for the longest extent possible.

For each of these 614 companies, the study required to select bonds that accomplish thefollowing criteria:

- Traded closest to Par value- Fixed coupon bonds- Coupons not linked to any index or floating- Not convertibles, and without special features- Currency denominated in GBP, USD, EUR or JPY

It was possible to obtain 4,943 different bonds from Datastream (4,368 from the US and 531from the UK), i.e. an average of 8.05 bonds per company.

For each one of these bonds, all the information regarding daily quotes (Bid, Ask and MediumPrice and Yield) was obtained in the period 01/01/2001 to 31/03/2006. In addition, it wascollected static information like ISIN Code, Coupon (%), Issued Amount (in USD) and finalMaturity.

The total amount of data collected was approximately 3.4 millions of different daily quotes for

bonds, and 1.7 million daily quotes for the companys CDS under study. The total amount ofinformation was more than 5 million of daily quotes from the market. This amount of data isconsiderably higher than previous empirical studies focused in the Credit Derivatives market.


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4.2.Data QualityAll the downloaded data was subject to a review process, to check for missing information,outliers, or inconsistency.

- Swap interest rates data was very clean information, mainly because the information inDatastream is obtained through a big number of traders and vendors. In addition, theForeign Exchanges (FX) markets are known to be very liquid and because of that, thedata is substantially reliable.

- Bond yields and prices obtained were, for most of the companies, very good data. Butsometimes in Datastream (possibly due to lack of trades) prices get pegged for asignificant number of consecutive days (sometimes weeks and months). This anomaly inthe data needed to be checked, and it was decided to eliminate completely or partially

where bond data had this problem in a significant number of consecutives days (i.e. morethan two weeks). In addition, the data was checked for outliers and manually removed

data points if they were not consistent with the information of the remaining companybonds.

An important issue was the elimination of the data in the latest days of the life of eachbond, because when maturity approaches, the yield reported in Datastream does notreflect accurately economic reality, mainly because of low liquidity of the security. Crosschecks with other information providers like Bloomberg were performed and resulted ina decision to discard data for each bond in its maturity year.

- CDS Premiums were the most noisy data obtained. There were significantly moreoutliers to be smoothed. The premiums among different maturities were used to achieve

consistency in the information. It is important to mention that it was common to findsome pegged values (or price runs) in the time series. This situation was carefullyanalysed, in order to decide if this situation was attributable to some missing information,or it could be attributable to lack of liquidity, which is the main characteristic in study inthis project.

From July 2005, Datastream was collecting data provided by iBoxx, and subsequently, thereliability of the information in the CDS market increased sharply. This noisiness ofCDS data was almost eliminated in the period from July 2005 to March 2006.

In addition, a number of consistency checks were performed at different stages in the study. Ifsome abnormality was detected, all the data regarding that company was reviewed. In thesesituations, it was very common to observe a particular bond with a different behaviour that theremaining. Subsequently the bond was removed, and the process was run again.


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4.3.Constructing the CDS BasisTo construct the CDS Basis, we need to compare the CDS Premium with the credit spread of abond with the same maturity. To get a time series of CDS Basis, it is necessary to get the creditspread of a synthetic constant maturity bond from the available bonds in the market for each

company.

There are at least two methods to get the credit spreads of a synthetic constant maturity T bond:

a) Interpolate the yields of the bonds series, and subtract the risk-free rate with maturity T.(Figure 3).

b) Use the risk-free rate series to compute the credit spread of each bond. Then interpolateto get the credit spread for a bond with maturity T. (Figure 4 and 5).

In both methods, to compute the credit spread, it is necessary to use a proxy for the risk-freerate. Houweling and Vorst (2005) showed that swap rates and repo-rates are better proxies for

riskless rates in this kind of Credit Derivatives markets. Repo rates might be the most proper oneto use, as they reflect collateralised rates used when some investors wants to engage in creditarbitrage.

Swap rates, which are in between the LIBOR and repo rates, were the choice for this study,mainly because they are quoted in maturities ranging from 1 to 25 years while repo rates are onlyavailable for short-term maturities, at the most 1 to 2 years.

Figure 3: Method (a), interpolate the yield for a bond with maturity T, and thensubtract the T-year risk-free rate to get the credit spread

The process of interpolating the swap curve to obtain the credit spread of a particular bond, isknow as the I-spread method. An even better measure of the spread could be obtained throughthe Z-spread method, which is the difference in basis points between the bond-equivalent yieldand interpolated risk-free rate corresponding to the bonds weighted average life. The Z-spreadcalculation need the entire stream of cash flows of all bonds to proper deliver the results.

The I-spread was chosen not only because the data availability, but also the differences could bereduced significantly if bonds traded at discount were eliminated from the sample, which was oneof the conditions used to obtain the bond daily quotes at data collection.


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Figure 4: Method (b): I-spread. Interpolate the risk-free rate for each bonds maturity in thedataset. Then subtract from the yield to get the credit spread

Figure 5: Method (b), second part. Interpolate the series of credit spreads to get the creditspread for a synthetic T-years maturity bond.

In both methods, (a) & (b), its necessary to interpolate to get the proper numbers. In the study,two methods of interpolation were tested: Linear and Cubic Splines.

To interpolate the risk-free curve, Cubic Splines worked better, because a complete term-structure is available for each day. Subsequently, the results were smooth interpolations.

To interpolate bond yields and credit spreads, the term-structure was incomplete. Because of this,a Splines interpolation would sometimes not deliver stable results over time. Both methods weretested when the available information was enough for it. The results were slightly different, butthis did not alter the results of this study. The statistical difference was not significant at all.

For some companies, the amount of bonds denominated in a single currency was not enough torun the procedure to get the credit spread (i.e. there were not enough maturities).


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Jankowitsch and S. Pichler (2003) showed that in arbitrage-free markets, the credit spread for anissuer has to be equal across different currencies if the factor processes driving the credit risk ofthe issuer are uncorrelated with the exchange rates deflated by the continuously compoundedmoney market account in the reference currency.

This result was used to run the interpolation procedure with the credit spreads, i.e. it wasassumed that exchange rates were uncorrelated with the credit risk in an aggregated level whichis the purpose of this study, and not assuming that it is true for each individual company.

In addition, the greater part of the bonds collected was currency denominated in USD (75%),and smaller proportions in GBP (13%), EUR (10%) and JPY (2%). Because of that, theuncorrelated assumption was used in a relatively low proportion.

For each bond was determined the credit spread using the proper risk-free rate for the bonddenominated currency.

The interpolation procedure was repeated for each day in the period of the sample (i.e. thesynthetic bond was again computed with the new information for the next day), and formaturities of 3, 5, 7 and 10 years, to match the data obtained of the CDS Premiums.

The quotes for CDS Premium of 1 year were discarded, because to construct the interpolationwas essential to have always the yield of a bond with maturity shorter than 1 year. Because of thediscarding procedure mentioned in 4.2, there was not information to construct a synthetic 1-yearmaturity bond to compare with the 1 year CDS Premium.

Finally, in order to compute the CDS Basis for each company name and for the differentmaturities, the credit spread was subtracted from the CDS Premium for the correspondingmaturity.

4.4.Liquidity PortfoliosAn empirical test was developed to test the liquidity effect in the behaviour of the CDS Basis, ,consistent in the construction of 4 equally weighted dynamic portfolios depending of the liquidityof companys bonds and companys CDS.

For each day in the sample, each company was assigned to some of the 4 portfolios called LL,LH, HL and HH, as is showed in the following table:

Bonds LiquidityLow High

Low LL LH

CDS

Liquidity

High HL HH

These portfolios were constructed for each one of the different maturities of the CDS Premiums,e.g. 3, 5, 7 and 10 years. Therefore, the total number of liquidity portfolios was 16.


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To use this measure in a dynamic way, it was defined a moving window of the last 30trading days of a bond, and counted how many missing prices or days with equal price thedata had. The low liquidity was assigned if the count delivers more than one observationin the past 30 trading days.

Bid-Ask Spread

This is probably the most often measure used to compute liquidity in the markets, whichhas an economic interpretation in the fact that market makers and traders set a wide bid-ask spread when they know the liquidity is not enough to go away in some unwantedposition.

The information available from Datastream had data constraints, in the sense that: 1) notall the bonds have a quote for the bid and ask prices, and 2) this measure was notavailable during the entire time period of the sample.

With each of these measures, a threshold was defined, and then computed a weighted average, inorder to give a bond a qualification of low or high liquidity. The following table resumes thethreshold for each variable, as well as the weights used:

Measure Threshold Weight Weight *)Issued Amount + USD 250 million!high liquidity 8% 20%

Coupon Coupons higher than 6%!low liquidity 6% 15%Age Maturity lower than 2 years!low liquidity 8% 20%

Missing Prices/ Price run

1+ observations in the last 30 trading days!low liquidity

18% 45%

Bid-Ask spread Spread greater than 20 bps!low liquidity 60% (*) --(*) When this measure was not available, the remaining 4 were adjusted in order to complete the 100% of the weights.

With the score of each bond was possible to assign a particular company to some of the liquidityportfolios for a particular date. Because of the construction, the main objective is not to get anabsolute measure rather than a comparative one between the data. Using this result it waspossible to select if the company needs to be allocated with portfolio xL or xH, with x beingthe measure of CDS liquidity.

Because of the dynamic construction of a synthetic T-year maturity bond, each day, the bondsused for the interpolation process were changing depending of the actual data available. As a

result, the measure of liquidity depends only for those particular bonds in that day. The liquidityscore for a company was computed using the weights of the interpolation process, but appliedto the liquidity score of each bond.

The final result of this dynamic liquidity score for each company allowed dynamic assignation foreach company in some of the liquidity portfolios. Is important to note that because of itsdynamic construction, some company could change for one portfolio to another. Moreover, acompany could have different assignation if the construction was a 3 years or 10 years maturitysynthetic bond.


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5. ResultsThe empirical test was run first using only the information of CDS Liquidity. At this point onlythe information relating to liquidity of Bonds was used. And finally, both pieces of liquidityinformation were used to construct the liquidity portfolios as described in 4.4.

This three part application of the empirical test was designed to determine and analyze theisolated effects of liquidity of only one of the markets (and then vice versa). Finally ending up

with the blend of information in order to observe joint effects resulting from Fixed Income andCredit Derivatives market.

5.1.CDS LiquidityUsing only the information regarding the liquidity of the CDS, e.g. not considering theinformation of the liquidity of Bonds, the following results were obtained:

3 years 5 yearsHigh

Liquidity LowLiquidity HighLiquidity LowLiquidityMean (bps) -11.77 -4.11 -9.31 41.16St. Deviation (bps) 11.44 56.66 9.56 72.49

7 years 10 yearsHigh

Liquidity LowLiquidity HighLiquidity LowLiquidityMean(bps) -9.18 34.11 -5.74 74.21St. Deviation(bps) 10.53 30.31 8.47 37.58

We can note that with the exception of T = 3 years, the mean of the CDS basis is below -10 basispoints for high liquidity CDS and higher than 34 basis point for low liquidity. In the four cases,the standard deviation of the data is considerable higher for low liquidity CDS ranging [+30 bps ;72 bps], while for high liquidity, the standard deviation is around 10 basis points in all cases.

Plotting the CDS Basis for High Liquidity CDS (Figure 6), we can observe that almost all thetime the CDS Basis is between the range [-20 bps ; +10 bps], with the exception of the period

between 01/01/2003 and 01/01/2004, where was observable higher CDS Basis, reaching -30 bpsfor T = 5 and 7 years, and -40 bps for T = 3 years.

In the case of Low liquidity CDS, we can observe higher levels for the CDS Basis in the range[-200 bps ; +300 bps]. (see Figure 7).

Detailed graphs comparing CDS Basis for High and Low liquidity CDS portfolios are shown inAppendix A.


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Figure 6: CDS Basis for High Liquidity CDS quotes

Figure 7: CDS Basis for Low Liquidity CDS quotes


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5.2.Bonds LiquidityWhen only the information of liquidity of Bonds was used, e.g. not taking in account theinformation of CDS liquidity, the following results were obtained:

3 years 5 yearsHigh

Liquidity LowLiquidity HighLiquidity LowLiquidityMean(bps) -12.94 -22.96 -6.46 -6.55St. Deviation(bps) 19.46 45.79 8.62 37.73

7 years 10 yearsHigh

Liquidity LowLiquidity HighLiquidity LowLiquidityMean(bps) -1.12 21.71 6.84 62.79

St. Deviation(bps) 9.38 54.80 11.96 92.19

We can note that with the exception of T = 5 years, the mean of the CDS basis is consistentlybelow for high liquidity bonds than low liquidity ones. In the case of T = 10 years the differenceis considerably high (56 bps). In the four cases, the standard deviation of the data is considerablehigher for low liquidity Bonds in the range [+37 bps ; +92 bps], and for high liquidity bonds, thestandard deviation is only in the range [+9 bps ; +20 bps].

Plotting the CDS Basis for High Liquidity Bonds (Figure 8), we can observe that almost all thetime the CDS Basis is between the range [-20 bps ; +20 bps], with the exception of the periodbetween 01/01/2003 and 01/07/2003, where was observable higher CDS Basis, reaching -80 bpsfor T = 3, and +55 bps for T = 10 years.

In the case of Low liquidity bonds, we can observe higher levels for the CDS Basis in the range [-100 bps ; +100 bps], with the exception of the period 01/01/2003 to 01/07/2003, when levelsof -200 bps were observable for T=3 years and +500 bps for T=10 years. (see Figure 9).

Detailed graphs comparing CDS Basis for High and Low liquidity bonds portfolios are shown inAppendix A.


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Figure 8: CDS Basis for High Liquidity bonds

Figure 9: CDS Basis for High Liquidity bonds


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5.3.Combined Liquidity measures: CDS & BondsUsing the approach described in 4.4 for the construction of the dynamic liquidity portfolios, theresults obtained through the combination of the liquidity information of Bonds and CDS. Thefollowing tables show the main results.

Dispersion of data

3 yearsH(cds) H(b) H(cds) L(b) L(cds) H(b) L(cds) L(b)

Mean(bps) -11.47 -24.91 -2.46 -10.62St. Deviation(bps) 11.34 37.58 58.73 85.53

5 yearsH(cds)H(b) H(cds) L(b) L(cds) H(b) L(cds) L(b)

Mean(bps) -8.80 -32.49 37.59 29.31St. Deviation(bps) 9.30 39.12 73.58 75.62


Mean(bps) -9.00 -18.37 33.66 39.64St. Deviation(bps) 10.53 35.89 32.27 56.73


Mean(bps) -6.02 10.76 72.06 87.79St. Deviation(bps) 8.35 35.89 36.74 98.70

The mean of the CDS Basis is ranging -6 to -11 bps for the HH Liquidity portfolio when thematurity changes, and in the other portfolios the range is considerable higher, reaching levels of88 bps in the case of portfolio LL for maturity 10 years.

The standard deviations are substantially higher (56 to 99 bps) for portfolios with Low Liquidityin both the CDS and the Bond markets, and substantially lower for portfolios with High

Liquidity in both markets (8 to 11 bps).

It is interesting to mention that the standard deviation of the CDS Basis didnt increase withmaturity. In most of the cases it actually decreased.

Figure 10 shows a comparative graph with the dispersion of the data of CDS Basis for differentmaturities.


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5.3.1. Friedman TestTo complete the statistical analysis of this information, a Friedman Testwas performed. This test isusually called a two-way analysis on ranks, and allows testing the Hypothesis that distributionsof ranks within rows are unrelated between rows. In the test, a sufficiently small p-value suggests

that at least one column-sample median is significantly different than the others; i.e., there is amain effect due to factor that differs in the columns.

One of the main strengths of this statistical test is the fact that there is no assumption regardingthe distribution of the data. The test only needs that the data comes from a continuousdistribution. In the case of the CDS Basis of the different portfolios, some trading days there isnot data for all the maturities. These days were removed from the data used to perform the test,leaving a data series for 848 trading days.

The data was properly formatted, and the Friedman Test was applied for each one of thematurities. The result are shown in the following table:

Maturity Effect Chi-Squares tat i s t i c p-valueLiquidity of Bonds 31.12 2.4248 x10-8

3 yearsLiquidity of CDS 207.00 0Liquidity of Bonds 54.8 1.33671 x10-13

5 yearsLiquidity of CDS 596.33 0Liquidity of Bonds 0.67 0.4141

7 yearsLiquidity of CDS 1266.53 0Liquidity of Bonds 73.04 0

10 yearsLiquidity of CDS 1564.42 0

(*) In blue colour and bold is highlighted when there is not statistical significance in the p-value of the Friedman test

In almost all the cases it was found that there is statistical evidence of the effect of Liquidity inthe behaviour of the CDS Basis. The only one exception is the liquidity of the Bonds in thematurity T = 7 years.

This statistical significance drives one of the most important results in the study, which is theempirical confirmation that both the liquidity of CDS and the securities in the Fixed Incomemarket are responsible for deviations showed by the CDS Basis.

In addition, comparing the Chi-square statistics of the test, it is possible to conclude that

Liquidity of the CDS has a stronger effect that Liquidity of the Bonds.

5.3.2.Kolmogorov-Smirnov TestThe data was subject of a statistical test, in order to detect differences across maturities for eachliquidity portfolio. To test if each one of the maturities were different realizations of the sameunderlying distribution, a Kolmogorov-Smirnov Test was performed to the data.

The Kolmogorov-Smirnov Test is used to test whether or not these two samples may reasonablybe assumed to come from the same distribution. The null hypothesis for this test is that two

samples of data are drawn from the same continuous distribution. The alternative hypothesis isthat they are drawn from different continuous distributions.


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The following tables present the p-values obtained from the Kolmogorov-Smirnov Test.

Liquidity Portfolio HH

3 years 5 years 7 years 10 years3 years 4.9441 x10-6 1.3526 x10-9 3.8638 x10-19

5 years 0.0414 9.882 x10-11

7 years 1.2104 x10-7

Liquidity Portfolio HL


5 years 4.8805 x10-10 3.1149 x10-63

7 years 2.7454 x10-32

Liquidity Portfolio LH


5 years 1.1985 x10-27 1.9588 x10-116

7 years 4.1905 x10-74

Liquidity Portfolio LL


5 years 6.6937 x10-10 2.4239 x10-24

7 years 6.3559 x10-23

As we observe across the tables, all the p-values are significant at the 5% level, and only one (5and 7 years in portfolio HH) is not significant at 1% level. In all the other cases, the p-value isconsiderably lower than 0.0005%.

Now, we can empirically conclude that the CDS Basis behaviour changes with the maturity,leading to an increase in the mean of the CDS Basis for all types of Liquidity portfolios.

In Figures 11 to 14 is showed the CDS Basis for different portfolios across maturities.

p-value not statistically significant at1%level. Still, it is statisticallysignificant at 5% level.


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Figure 11: CDS Basis of liquidity portfolio HH across 4 different maturities


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Figure 12: CDS Basis of liquidity portfolio HL across 4 different maturities


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Figure 13: CDS Basis of liquidity portfolio LH across 4 different maturities


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Figure 14: CDS Basis of liquidity portfolio LL across 4 different maturities


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5.4.Effect of liquidity in Credit Arbitrage strategiesBid-Ask spread is one of the major measures of liquidity, not only in this study, but also in realsituations when trading strategies are placed to profit from Credit Arbitrage.

The trading strategies in Credit Arbitrage have other costs not considered in the previousanalysis. Examples of such costs are: differences in repo rate, haircut charged, or requirementsof cash or collaterals in margin accounts. Under assumptions similar to those in Find (2005),around 20 bps in the CDS Basis could be explained through these costs.

The Scattered plots in Figures 15 to 18 show the amount of the deviation in the CDS Basis inbasis points that can be explained because of the bid-ask spread. These graphs were constructedusing Bid-Ask spread for bonds and CDS. When Bid-Ask prices were not available, the spreadused was constructed considering a weighted average of similar spreads for otherbonds/companies with closest measures of liquidity.

When the data in the graphs is outside the red borders then the deviation of the CDS Basis wasgreater than the effect of bid-ask spread. In addition, drawn in magenta are limits at -20 bpsand +20 bps from the red range.

- Portfolio HH: Observations outside the extended border are the exception. The vastmajority is inside the area. Importantly, the red area is very narrow, andstill a significant number of observations are inside.

- Portfolio HL: A significant proportion of observations for T= 3, 5 and 7 years are belowthe range, and above the range for T = 10 years. Only in the case of T=3years the percentage inside the area is higher than 50%.

- Portfolio LH: A high percentage of observations is inside the range, but there are atendency to go above through the years, reaching an absolute value in

T=10 years, when most of the observations are not only outside the redarea, but also the magenta area.

- Portfolio LL: It is very common find observations outside the range. For T=3 years,there are extreme values above and below, which implies a very volatilestrategy in Credit Arbitrage. For T=5 years, the tendency is to go abovethe range, which increase through the years, reaching values of +200 bpsin T=5 years, +300 bps in T=7 years and +500 bps in T=10 years.


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Figure 16: Basis points of CDS Basis explained because of Bid-Ask spread. Liquidity Portfolios HL


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Figure 18: Basis points of CDS Basis explained because of Bid-Ask spread. Liquidity Portfolios LL


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6. Conclusions of the studyThe analysis and results of the empirical test presented in the previous chapters, leads to thefollowing conclusions:

a) Liquidity has empirical effects in the behaviour of CDS BasisThe CDS Basis, reflecting the relationship between the Fixed Income and Credit Derivativesmarkets, has statistical significant effects due to the liquidity of the securities traded in themarket.

It was shown that liquidity of CDS securities have an impact of +43 to +80 basis point inaverage when maturity of the contracts is between 5 and 10 years. For all maturities, thestandard deviation of the CDS Basis increases substantially in a range of +20 to +63 basispoints depending on the maturity.

When liquidity of bonds is considered, the average impact in the CDS Basis is only significantfor long maturities, +22 basis point from 7 years and +55 basis points for 10 years. The

volatility of the CDS Basis increases for all maturities, in a range of +26 to +81 basis points.

Considering both effects of liquidity together, the main effect is on the volatility of the CDSBasis, which always increases its value for all maturities. The effect in the mean is significant

when the comparison is between a high-high liquidity portfolio with a low-low liquidityportfolio, and it increases with the maturity.

b) Effects impact is different through different maturities.In portfolios with the same liquidities, the behaviour of the CDS Basis is statistically differentacross maturities. Even for portfolios with high liquidity in the securities, the statistical valuesconfirm that the differences are very depth. For low liquidity, the values are really extreme inthe tail of the distribution.

This situation leads to eliminate any possibilities to hedge positions using trading strategiesthat aim to take positions in different maturities. The different behaviour could lead to evenhigher differences, and the positions could imply huge losses due to these movements.

c) Bid-Ask spread is not enough to explain CDS Basis in low liquidity environments.A plausible explanation for the deviations of the CDS Basis is the fact that when liquidityarises, the bid-ask spread tends to widen.

In the study, it was proven that in fact, this increase in the spread because of this conditionhas an impact on the CDS Basis, and its one of the explanations of the deviation. Actually,this increase in the spread is an excellent explanation for a high-high liquidity portfolio.

For less liquid portfolios, the amount of the deviation in the CDS Basis is much more than

the bid-ask spread. Including transaction costs the deviation still is even further. In addition,the maturity of the contract has an impact too. When maturity increases, the explanation


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Appendix A

Graphs for CDS Basis with Low and High Liquidity CDS portfolios, not using Bond liquidity.


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Documents

Relation Between Corporate Credit and Credit Default