The CDS Bond Basis Spread in Emerging Markets: Liquidity and Counterparty Risk E ects (Draft)

Transcription

1 The CDS Bond Basis Spread in Emerging Markets: Liquidity and Counterparty Risk E ects (Draft) Ariel Levy April 6, 2009 Abstract This paper explores the parity between CDS premiums and bond spreads for emerging market sovereign entities. Previous studies found that this parity holds between bonds and CDSs for US corporate debt. We nd that this parity does not hold for Emerging Markets sovereign debt. In order to explain the pricing deviations we focus on two frictions, liquidity and counterparty risk. First, we present a model where the two market frictions account for the deviations in prices. Then, our empirical results strongly support the relevance of these two factors to the pricing of CDS contracts. We mange to restore much of the theoretical predictions of a zero basis spread once we account for liquidity e ects. 1 Introduction A Credit Default Swap (CDS) is a credit derivative that provides protection against a bond default. Theory suggests that under ideal market conditions, due to arbitrage forces, CDS premiums should be equal to the underlying bond yield spread over the risk-free rate. However, in sharp contrast to this theoretical prediction, we nd that CDS premiums consistently deviate from bond yield spreads for emerging market sovereign debt. Using an extensive data set we document a non-zero basis spread between CDSs and their underlying bonds. In order to account for these deviations we present a model with two market frictions. We rst allow for liquidity di erences between CDSs and bonds. Liquidity di erences introduce di erent liquidity premiums into the pricing of each asset, which consequently generate pricing inequalities between CDSs and bonds. Second, we allow for the existence of counterparty 1

2 risk in CDS trading. We show how the possibility that a CDS seller will default and not honor its contractual obligations has a negative e ect on CDS pricing. Again, this market friction consequently generates pricing di erences between CDSs and bonds, which violate the pricing equality under perfect market conditions. Finally, our new model yields testable predictions that allow us to empirically evaluate the relevance of these two market frictions using real data. Our empirical results strongly support the relevance of these two frictions to the pricing of CDSs. Once accounting for liquidity di erences we manage to restore much of parity between the pricing of CDSs and bonds, that is, restore the zero basis spread. Also, we show strong evidence for the negative e ect that counterparty risk has on CDS prices. After introducing our main results, we carry out several robustness tests such as using di erent measures for the risk free rate, alternative measures for counterparty risk, checking for xed e ects between countries and time e ects. The remainder of this paper is organized in the following way. In the next part we describe the the background and development of the CDS market. In Part 3 we describe the CDS contract and brie y discuss the parity that should hold between cash bonds and their CDSs. In Part 4 we review the existing literature. In Part 5 we introduce the model. At rst, we present the basic model for pricing the CDS contract and determining the CDS-bond zero basis. Then, we adjust the basic model to account for liquidity and counterparty risk e ects. In Part 6 we describe our empirical methodology and present the main ndings. In Part 7 we describe our data and in Part 8 and 9 we introduce our detailed empirical results. In Part 10 we carry out several robustness tests. Finally, in Part 11 we provide a summary of our paper and conclude. 2 Background CDSs began trading in the early 1990s as over-the-counter (OTC) transactions between banks, and mainly included attempts to lay o some of the credit exposure on their balance sheets. Since then, CDS contracts have become fairly standardized products that are used by multiple market participants, including banks, hedge funds, mutual funds and pension funds, with signi cant trading volume and high liquidity. CDSs today are the most widely traded instrument for transferring credit risk. Its market value has expanded dramatically over the past two decades, with notional global value of traded CDSs increasing from $40 billion in 1996 to an estimate of over $60 trillion in Bank of America, 2008; The World Bank, 2007; Packer and Suthiphongchai,

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4 CDS trading has expanded not only in volume and liquidity, but also in variety and related nancial products. More sophisticated forms of CDSs have emerged, such as basket CDSs and CDS indices. Even CDS derivatives were developed, such as CDS options and futures. Along with the global expansion of CDS markets, emerging market CDSs have grown as well, although at a slower pace. Emerging market CDSs currently cover a wide variety of sovereign entities and are traded with high liquidity. In 2003, emerging market CDS trading accounted for approximately 5 percent of their total credit trading, where three quarters of the volume of transactions concerned 10 countries. Annual trading volumes were estimated at almost $200 billion. 2 According to a World Bank report, in 2006, only three years later, quotes were then available on debt issued in more than 29 countries and trading volumes in emerging market CDSs rivaled those in emerging market cash bonds. For some countries, such as Hungary and Lithuania, the amount of outstanding CDSs dwarfs the amount of outstanding cash bonds by a factor of ten. 3 The rapid expansion of CDS trading makes it one of the most fascinating developments of the last two decades in nancial markets. Its rapid growth in volume, the ourishing of CDS related products, as well as its role during the current credit crisis indicate the importance of studying this relatively new nancial product. Moreover, the rapid growth in CDS trading and its changes in liquidity during the past decade further inspire the study of the implications of these changes to CDS pricing, as we carry out in this paper. 3 The Credit Default Swap A credit default swap is a contract that provides insurance against the risk of a default by a particular borrowing entity, which could be a corporate or sovereign entity. The entity is known as the reference entity of the CDS and the event of default of the entity is known as a credit event. Each CDS provides protection for a speci ed bond, which is known as the reference obligation. The contract has two sides: the buyer of protection and the seller of protection. The buyer of the insurance has the right to replace the bond for its par value when a credit event occurs. In return for this right, the buyer of the CDS pays the CDS seller periodic payments until the end of the life of the CDS or until a credit event occurs, whichever comes rst. These payments are known as the CDS premiums or the CDS spread. When a credit event occurs, the settlement of payments between the buyer of the CDS and the seller of the CDS can take one of the following two forms, depending on the terms 2 The World Bank, 2007; Emerging Market Traders Association, The World Bank,

5 speci ed in the contract. One form is physical delivery, where the buyer of insurance delivers the bond to the seller, and the seller in exchange pays the full face value of the bond. The second form is cash settlement, where the market value of the defaulted bond is determined, usually by calculating an average quote from a sample of di erent dealers some speci ed number of days after the credit event. The cash settlement is then the face value of the bond minus its determined market value. We can illustrate a simple example for a typical deal in the following way. Suppose that a buyer and a seller of a CDS enter into a ve year contract. The protection buyer wishes to insure his bond position of $1 million against the possibility of default for the next ve years. Assume the protection buyer agreed to pay 100 basis points every year for protection against the reference entity defaulting. If the reference entity does not default during the ve years, the protection seller receives from the buyer $10,000 each year for the ve years till the contract matures. The buyer receives no payments in this case. If a credit event does occur, after two years and a day for instance, then the buyer pays at the end of each one of the rst two years $10,000. The day after, once the credit event occurs, the CDS seller needs to make a substantial payment to cover the default loss. If the contract speci es physical settlement, the buyer has the right to sell $1 million par value of the reference obligation (the underlying bond) for $1 million to the CDS seller. Alternatively, if the contract requires cash settlement, the market value of the reference obligation will be determined after the credit event within a number of days according to the pre-speci ed conditions in the contract. For example, if the determined value of the reference obligation proves to be $40 per $100 par value, the CDS seller will pay the CDS buyer the loss of $600,000. The protection feature of the CDS is not a new feature in the xed income market. Cash bonds also contain an "insurance" aspect, which is captured in their yield spread over the risk-free interest rate. This yield spread is a compensation for the bond holder for baring the risk of default by the borrowing entity instead of investing in a risk-free bond. Since both assets, the CDS and the bond, o er compensation for the same event, that is, the default of the same reference entity, their pricing should also be equal. Thus, intuitively speaking, the value of the bond s yield spread over the risk-free rate should be close to the value of the CDS premium. The di erence between the CDS periodic premium and the bond s periodic yield spread is de ned as the Basis Spread. Hence, intuitively, one would expect the CDS-bond basis spread to be close to zero. 5

6 4 Literature Review Two pioneering papers by Du e (1999) and Hull and White (2000) set the framework for pricing CDS contracts and the CDS basis spread. These papers introduce two approaches to pricing CDSs. One is the "no arbitrage" approach, and the other is a direct pricing based on discounting the expected cash ow from the CDS contract. The rst approach, the no-arbitrage one, argues that an investor can construct a portfolio using a CDS and the underlying bond that replicated a risk free bond. By buying a risky bond and a CDS on the bond with the same maturity date, the investor eliminates the default risks associated with the bond. In the absence of arbitrage opportunities, the value of this portfolio should be equal to the value of a risk-free bond with the same maturity date. Hence, one can derive the CDS premium in the following way: if y is the yield to maturity on the bond and S is the annual CDS premium, the investor s net annual return is y S. Since this is a risk-free return, it should be equal to the risk free-rate. Otherwise, if y S is signi cantly di erent than the risk-free rate, arbitrage pro ts can be made. The second approach uses a reduced-form model, where default is treated as a random stopping time with a stochastic arrival intensity. Just like in the case of pricing bonds, the periodic CDS premium is determined by risk neutral valuation of the expected cash ow. Under the absence of arbitrage opportunities, the premiums collected by the CDS seller (the premium leg) should be equal to the expected insurance payments in the case of default (the insurance leg). This reduced form representation has become the more standard valuation procedure in the literature, and has been widely used later on in the empirical work testing CDS valuation. The simplicity of the zero basis spread obtained by the two theoretical papers of Du e (1999) and Hull and White (2000) inspired a sequence of empirical research examining how well the theoretical relation between CDS premiums and bond yield spreads holds in practice. However, most empirical comparisons of CDS and bond pricing have considered only corporate names with investment grade credit rating. These studies include Longsta et al. (2005) that nd signi cant di erences between credit default swap spreads and bond yield spreads. Other studies have mainly found that arbitrage forces CDS premiums to be approximately equal to the underlying bond spreads. For example, Blanco et al. (2005) nd CDS premiums to be quite close to bond yield spreads. They also nd that the CDS market leads the bond market so that most price discovery occurs in the credit default swap market. Hull et al. (2004) test the zero basis spread hypothesis for a list of corporate entities in the US and nd the results to strongly support it. In addition, by using two di erent interest rates as their risk free rate benchmark, the Treasury rate and the swap rate, they nd the swap rate 6

7 to match the zero basis spread hypothesis much better. Another aspect they explore is the extent to which credit rating announcements by Moody s are anticipated by participants in the CDS market. Zhu (2006) compares between the pricing of credit risk in the bond market and the CDS market. He nds that the theoretical prediction that bond spreads and CDS premiums move together holds in the long run. In the short run, Zhu nds that the CDS market often moves ahead of the bond market. There has been relatively little work to date on comparing CDS and bond pricing for emerging markets sovereign data. Jan De Wit (2006) uses a large data set of CDS and bond yield spreads, which includes some emerging market sovereign reference entities for the time period of However, the number of countries included in his study is limited, the analysis is mostly aggregated and not as detailed as in this paper. Additionally, the time period covered in his data is much shorter. In another paper, Chan-Lau and Kim (2004) look for lead-lag relationships among emerging market sovereign bond indices, CDS premiums, and national stock market indices, reporting somewhat inconclusive results. Their analysis, also, focuses only on a limited number of countries. Moreover, their data contains only indices for CDSs and bonds, which do not allow the breakdown into real CDS and bond series. As a result, it lacks the transparency to enable a price comparison between CDSs and their actual underlying bonds, as was carried out in the studies on corporate CDS and bond markets described above. Two papers that appear to be most relevant to the analysis undertaken here are very recent: one paper by Ammer and Cai (2007) and a working paper by Adler and Song (2007). Both papers explore the emerging market sovereign bond CDS basis spread for a large number of countries and cover a relatively long time period using rich data sets. Ammer and Cai test for nine emerging market sovereign borrowers between February 2001 and March 2005, and nd that sovereign CDS premiums and bond spreads do move in tandem in the long run. In the short run, when the prices deviate from their long-run equilibrium, CDS markets seem to lead bond markets in price discovery in some instances, but lag behind bond prices in other cases, with some evidence that the more liquid market tends to lead. The emphasis of their study is on the implications of the "cheapest-to-deliver" (CTD) option embedded in the standard CDS contract. They o er a variety of evidence that CDS premiums are a ected by the CTD option which makes them relatively more expensive. Adler and Song (2007) test the parity between CDS premiums and bond yield spreads for emerging market sovereign debt of 17 countries. They use a data set supplied by J.P. Morgan, which contains daily quotes of CDS premiums and bond prices from as early as 1998 until January Their results reject the parity relationship between CDS premiums and bond 7

8 yield spreads for 11 out of 17 countries. These results lay in sharp contrast with previous empirical studies of investment grade corporates. However, Adler and Song argue that this result does not necessarily indicate a market failure. They develop a model that shows how non-par bonds with xed coupons should result in a non-zero basis spread. Then, in order to measure whether the CDS and bond markets price risk similarly, they construct what they call implied bond yield spreads. The implied spreads are theoretical yield spreads for the bonds contained in their data set, based on default probabilities derived from the CDS premiums. If both markets, the CDS and the cash bonds, price credit risk similarly, then the theoretical and the actual prices should coincide. Carrying out this test results in rejecting the parity between CDS markets and cash bonds for only 3 out of the 17 countries. The contribution of this paper to the above literature, especially the two papers of Ammer and Cai (2007) and Adler and Song (2007), is primarily in its focus on the e ects of liquidity and counterparty risk on the basis spread. The issue of liquidity and CDS pricing is hardly addressed in the previous literature. One important paper addressing the topic is Longsta et al. (2004) who nd price di erences between CDSs and bonds, as mentioned above. These price di erences are then attributed to liquidity e ects, and a series of tests are carried out to examine how correlated they are with some measures of liquidity. Other studies that include some tests for liquidity do not nd any signi cant results, or obtain results that stand in contrast to the theoretical predictions, (Ammer and Cai, 2007; Zhu, 2006). The topic of counterparty risk is addressed in a number of papers, but as far as we know, no empirical work has so far tested the e ect of counterparty risk on CDS pricing. Hull and White (2001) address the e ect of counterparty risk from a theoretical point of view, and based on simulations they determine conditions under which CDS prices are a ected. They show how in most cases CDS prices are negatively a ected by the existence of counterparty risk. A number of other working papers and professional papers take a similar approach, 4 however, neither of them derive analytical results but rather use simulations to evaluate the in uence of counterparty risk on CDS pricing. In our work, we use a simple model to derive conditions under which counterparty risk has a negative e ect on CDS pricing. Also, using proxies for counterparty risk we estimate these e ects in real data and show results that are consistent with the model s predictions. Another important advantage of our work is the time period included in our data set, which ends in May This fact is important not only because the data set in use is richer, but also because it adds a signi cant time period in which CDS markets are more mature. 4 Leung and Kwok, 2005; Hamp et al., 2007; Mashal and Naldi, 2003; Brigo and Chourdakis,

9 As described above in the background section, CDS markets have been growing rapidly and there is a big di erence in their liquidity and trade volume between the years 2000 and This fact allows us to test the e ects of these changes on the pricing parity between CDSs and bonds. This could not have been carried out earlier when such structural changes in liquidity and counterparty risk were absent. Finally, as mentioned above, the previous work on emerging markets sovereign CDSs by Ammer and Cai considers only 9 countries, whereas this paper uses data on 16 di erent emerging market countries. In the next section we introduce the model for pricing the CDS contract and deriving the zero basis spread. 5 The Model As mentioned above, Du e (1999) and Hull and White (2000) provide the basic pricing equation for CDS contracts and the basis spread. We follow the framework suggested by Zhu (2006) who solves for the prices of CDS premiums and bonds separately and then constructs a portfolio that replicates the CDS contract. From this portfolio we derive the valuation of the basis spread. Then, we adjust the basic model for liquidity e ects and derive the new basis spread. Finally, we adjust the model for counterparty risk and derive its e ect on the pricing of the CDS. 5.1 The Basic Model We assume a risk neutral world with three assets: a risk-free bond, a risky bond and a CDS contract. Let f(t) be the default probability for a risky bond at time t. The survival probability for a risky bond until time t is denoted by F (t) and is equal to: F (t) = 1 R t f(x)dx. Let C be a xed coupon paid by a risky bond at each period t = 1; 2; 3::::N and 0 y be the periodic yield spread. The recovery rate for the risky bond out of its par face value upon default at time t is denoted by R t. r is the constant risk-free rate during t = 1; 2; 3::::N. Finally, S is the xed CDS premium, paid at times t = 1; 2; 3::::N whatever comes rst. till maturity or default, The CDS premium satis es the following condition: NX Se rt F (t) = Z N 0 e rt (100 R t )f(t)dt (1) 9

10 The left hand side is the premium leg of the CDS contract which is the expected sum of all payments to the CDS seller, discounted by the risk free rate, that are paid out in case there is no credit event. The right hand side is the protection leg of the CDS contract which is the expected sum of all payments to the CDS buyer, discounted by the risk free rate, which are due in case a credit event occurs. Under a risk neutral valuation these two payments should be equal. The value of the risky bond, B, is: NX B = Ce rt F (t) + 100e rn F (N) + 0 Z N R t e rt f(t)dt (2) The right hand side is just the discounted cash ow of the risky bond, weighted by the probability of receiving each payment. In each period t the bond holder receives the coupon C if there is no default. When the bond matures, the bond holder receives in addition to the coupon also the face value of the bond, again, in case there is no default. The third expression is the expected value of the bond in case a default does occur. The present value of the sum of all payments should then be equal to the bond s price. Equivalently, the value of a risk-free bond paying coupon r each period t is nothing but: NX 100 = re rt + 100e rn (3) The price of a risk-free bond that pays the risk-free interest rate as a coupon each period, is just the face value of the bond, that is, 100. Just like in the case of a risky bond, the price of the bond is equal to the present value of the bond s stream of payments till maturity. The value of a portfolio that shorts the risky bond and buys the risk-free bond (equations (3) (2)), is: NX 100 B = re rt + 100e rn (4) NX Ce rt F (t) 100e rn F (N) 0 Z N R t e rt f(t)dt From equation (4) we derive the following proposition: Proposition 1 In a frictionless market, the CDS premium equals the spread on a par risky xed-rate bond over the risk-free rate: S = y r 10

11 The proof of Proposition 1 is provided in Appendix 1. The intuition for Proposition 1 is the following. The risky bond s yield spread is a compensation for the bond holder for baring the risk of default instead of investing in a risk-free bond. Since the CDS and the yield spread both price the same event, that is, the default of the same reference entity, their pricing should also be equal. Thus, under ideal market conditions, due to arbitrage forces, the CDS premium should be equal to the underlying bond yield spread over the risk-free rate. 5.2 Adjusting for Liquidity To account for liquidity we follow the same motivation which generates liquidity costs as presented in Du e et al. (2005). In their paper liquidity costs arise in over-the-counter (OTC) markets from traders who look for counterparties with di erent opportunity costs. These di erent opportunity costs can arise from di erent needs for cash that di erent investors are faced with or adverse correlation between a particular asset and other assets held by the investor. A search model is then applied to derive the liquidity premium for the particular asset at stakes. We present a simpli ed model which abstracts from Du e et al. (2005) and is speci cally employed to our framework. We assume two types of traders: one trader with high liquidity that bears no holding costs. A second trader with low liquidity has a holding cost of d. We denote these two types by type h and type l. The fair-priced CDS premium for type i is denoted by S i. The market price for the CDS premium is denoted by S. e Let p h be the probability of nding an h type trader in a single search, and p l = (1 p h ) be the probability of nding an l type trader in a single search. Based on equation (1) we know that the following holds for the high liquidity type, NX S h e rt F (t) = Z N 0 e rt (100 R t )f(t)dt Similarly, the following holds for the low liquidity type, NX S l e (r+d)t F (t) = Z N 0 e (r+d)t (100 R t )f(t)dt Since the l type incurs an additional holding cost of d, his discount factor is adjusted accordingly. 11

12 From these two equations we can derive the CDS premium for each type, S h = NR 0 e rt (100 R t )f(t)dt NP e rt F (t) (5) and S l = NR 0 e (r+d)t (100 R t )f(t)dt NP e (r+d)t F (t) (6) Type i will buy the CDS contract (buy insurance) only if S e < S i ; Type i will sell the CDS contract (provide insurance) only if S e > S i. If S e = S i, i.e., if the market price for the CDS contract is equal to type i s risk neutral valuation of the CDS contracts, then type i is indi erent. Assume S l > S h, then we get the following conditions: If S e > S l then all types want to sell the CDS If S e < S h then all types want to buy the CDS Hence, trade occurs only if S l S e S h, where type i faces one of the following alternatives: Type i meets its own type and trades at S i Type h sells insurance to type l at e S The trading process then takes the following form: a CDS buyer (l type) searches for a CDS seller. Once he samples a potential seller he gives him a take-it-or-leave-it o er. The buyer in each search can either sample a high type with probability p h, or sample a low type with probability p l and continue searching for a high type, bearing the search cost of C. Hence, the value of the search process, V, for the CDS buyer is: V = p h S h + p l (V + c) (7) A market maker can o er the CDS buyer a CDS contract at V for which the buyer would be indi erent between independently searching for a buyer and buying directly from the market maker. Solving for V we get, Re-arranging, we get: V = p hs h + Cp l 1 p l V = S h + 12 Cp l (1 p l )

13 Hence, the market price e S is es = V = S h + Cp l p h (8) where Cp l p h is the liquidity premium. In a similar way we can derive the liquidity premium for the bond yield. For simplicity, let s j denote these additional spreads for each asset j (the bond and the CDS) over its fair price in the frictionless market, as described above in the basis model. In other words, where, s j Cp l p h 1. s cds is the additional premium per annum for trading the CDS. 2. s bond is the additional premium per annum for trading the bond. The market price for the bond yield and the CDS premium, which now contains a liquidity premium component, can be described in the following way: 1. Let e S be the market price for the CDS contract. Then: e S = S + scds 2. Let ey be the market yield on the bond. Then: ey = y + s bond Proposition 2 The CDS premium equals the spread on a par risky xed-rate bond over the risk-free rate minus the di erence in transaction costs: es = ey r (s bond s cds ) The proof for Proposition 2 is provided in Appendix 2. The intuition for Proposition 2 is straightforward. The parity between the CDS contract and the risky bond should hold only for the pure risk component that is priced into the two assets. If one asset is more liquid than the other the parity would be violated due to pricing di erent liquidities into the assets. Once we deduct these di erent liquidity premiums the parity should be restored. An important result from Proposition 2 is that the more illiquid is the CDS relatively to the risky bond, the higher is the CDS premium relatively to the bond yield spread. Thus, we can expect a non-zero basis spread when liquidity di erences exist. 13

14 Figure 3 Protection Leg Payoff Tree 0 0 Pr(D,CP) Pr(D,CP) Pr(D,CP) Pr(D,CP) CDS Continues Pr(D,CP) Pr(D,CP) CDS Continues... 1-M 1-M Pr(D,CP) Pr(D,CP) 0 0 t=0 t=2 5.3 Adjusting for Counterparty Risk A second element that should be taken into account when pricing a CDS contract is counterparty risk. Since a CDS is an insurance contract, the value of the insurance depends on the ability of the insurer to pay back the guaranteed principal in case of a credit event. In order to account for counterparty risk we make the following adjustments to the basic model presented above. 5 Let CP denote the event where the counterparty defaults, and CP denote the event where the counterparty does not default. Equivalently, let D denote the event where the underlying bond defaults, and D denote the event where the underlying bond does not default. P r(; ) t denotes the probability of event (; ) at time t. For instance, P r(d; CP ) t denotes the probability of the event where the bond does not default and the counterparty does default at time t. Finally, the new CDS premium once accounting for counterparty risk is denoted by b S. The tree describing the payments of the protection leg of the CDS throughout the life of the contract is described in the Figure 3. If the counterparty defaults at time t, the contract terminates and the payo is zero. That is, the seller of the CDS defaults and thus does not honor its insurance obligation to the CDS buyer, whether the bond defaulted or not. If at time t the counterparty does not default and the bond does default, the CDS seller pays the recovery rate of 1 R t and the contract terminates. If at time t neither the counterparty 5 We develop a framework similar to the one suggested by Hamp et al. (2007). 14

15 Figure 4 Premium Leg Payoff Tree 0 0 Pr(D,CP) Pr(D,CP) Pr(D,CP) S Pr(D,CP) S... Pr(D,CP) Pr(D,CP) S S Pr(D,CP) Pr(D,CP) 0 0 t=0 t=2 nor the bond default, the CDS contract remains valid till the next period. Summing up the stream of payments of the protection leg till the maturity of the CDS contract at time N, we get the following expression: P rotection Leg = P r(d; CP ) (1 R t )e r + P r(d; CP ) P r(d; CP ) t=2 (1 R t )e 2r + :::: In each period the CDS buyer gets his loss given default, (1 R t ), with probability P r(d; CP ) that the counterparty did not default and the bond did default. These payments are also contingent on the survival of the counterparty till the time of the bond default, P r(d; CP ) t. Simplifying the above expression we get: P rotection Leg = N P P r(d; CP ) t (1 R t )e rt t Q 1 i=0 P r(d; CP ) i (9) The tree describing the payments of the premium leg throughout the life of the CDS contract is presented next in Figure 4. Periodic payments of the CDS premiums are made as long as the seller does not default. Once the seller defaults premium payments from the buyer to the seller also stop. When the underlying bond defaults a nal single payment of premium is made to the CDS seller. Summing up the stream of payments of the premium leg till the maturity of the CDS at time N, we get the following expression: P remium Leg = P r(d; CP ) Se b r + P r(d; CP ) Se b r +P r(d; CP ) P r(d; CP ) t=2se b 2r + P r(d; CP ) P r(d; CP ) t=2se b 2r +:::: 15

16 Premium payments are paid in each period only in two cases: when the bond did not default and the counterparty did not default, with probability P r(d; CP ) t ; and when the bond defaulted but the counterparty did not default, with probability P r(d; CP ) t. Simplifying the above expression we get: P remium Leg = b S N P f[p r(d; CP ) t + P r(d; CP ) t ] t Q 1 i=0 P r(d; CP ) i g (10) Under a risk neutral valuation the protection leg should be equal to the premium leg. Thus from equations (9) and (10) we derive: bs N P f[p r(d; CP ) t + P r(d; CP ) t ] t Q 1 i=0 P = N P r(d; CP ) t (1 R t )e rt t Q 1 P r(d; CP ) i And solving for the CDS premium, we get: i=0 P r(d; CP ) i g (11) bs = NP P r(d; CP ) t (1 R t )e rt t Q 1 i=0 P r(d; CP ) i NP f[p r(d; CP ) t + P r(d; CP ) t ] t Q 1 P r(d; CP ) i g i=0 (12) To simplify equation (12) we assume that the recovery rate is constant for all t, and thus we get: NP P r(d; CP ) t e rt t Q 1 P r(d; CP ) i i=0 bs = (1 R) NP f[p r(d; CP ) t + P r(d; CP ) t ] t Q 1 P r(d; CP ) i g i=0 (13) Proposition 3 A risky protection seller receives lower CDS premiums compared to a risk-free one when the default of the protection seller is positively correlated with the default of the underlying bond. When they are independent, the CDS premiums are identical for the risky protection seller and the risk-free one. The proof of Proposition 3 is provided in Appendix 3. The intuition for Proposition 3 is the following. The existence of counterparty risk generates a tradeo in pricing. On the one hand, the possibility that the protection seller will default reduces the value of the insurance and thus has a negative e ect on CDS prices. On the 16

17 other hand, once the counterparty defaults the buyer of the CDS contract stops paying periodic payments to the seller, which has a positive e ect on CDS premiums. If the default probabilities are correlated then Proposition 3 states that the negative e ect is stronger than the positive one and the CDS premium decreases. If the default probabilities of the underlying bond are not correlated with the default probabilities of the counterparty, then these two e ects cancel out each other. One way to understand this result is the following. Once the counterparty defaults the CDS buyer always has the option to engage in a new CDS contract with a new protection seller. The overall e ect of the tradeo described above depends on the expected future costs of engaging in a new protection contract. If expected future costs are higher than the present costs, then the overall protection costs increase due to the existence of counterparty risk, resulting in a current reduction of CDS prices. If expected future costs are identical to the present ones, then the overall protection costs do not change even when the counterparty defaults, and current CDS prices should not change either. The expected future protection costs depend on the correlation between the default probabilities of the counterparty and the underlying bond. If they are not correlated, then, on average, the counterparty default will not be accompanied by a deteriorating credit quality of the underlying bond. However, if the default probabilities are correlated, a counterparty default is likely to be accompanied with a deteriorating credit quality of the underlying bond. This deterioration increases expected future protection costs, thus resulting in a reduction in current CDS premiums. 6 Empirics So far we showed three results which are summarized in propositions 1, 2 and 3. Starting from the basic model in section 1, which provides a benchmark for further adjustments, we showed that in a market under ideal condition with no frictions and no counterparty risk, the basis spread should be equal to zero. This idea is expressed in Proposition 1. Then, adjusting for liquidity in the price of the two assets in section 2, we showed how the property of the zero basis spread is maintained if correcting for the liquidity components of the CDS and the bond. More speci cally, the CDS premium is equal to the bond s spread after subtracting the liquidity premiums per annum from each asset. This notion was expressed in Proposition 2. Finally, when the protection provided by the CDS seller is not guaranteed and there exists a risk that the CDS seller will default, the CDS premium decreases and is worth less than under a risk-free insurance. This result is captured by Proposition 3. 17

18 These three results provide us with three testable predictions: 1. Under the assumptions of Proposition 1, in the following regression = 0 and = 1: S t = + (y t r t ) + " t (14) 2. Under the assumptions of Proposition 2, in the following regression = 0, = 1 and = 1: S t = + (y t r t ) + (s cds;t s bond;t ) + " t (15) 3. Proposition 3 states that the existence of counterparty risk should have a negative e ect on CDS premiums. In other words, in the following model, S t = + (y t r t ) + CP R t + " t (16) if CP R t is a measure for counterparty risk, then the model predicts that < 0. In the liquidity regression, since the liquidity premiums are unknown, we use bid-ask spreads instead as a proxy for liquidity. Thus, instead of equation (15) we use, S t = + (y t r t ) + (bid:ask cds;t bid:ask bond;t ) + " t (15a) In this regression, since the bid-ask spread is just a proxy for the liquidity premium, we do not expect the value of to be equal to the predicted value of 1, but just to be positive, > 0. Also, we add a fourth regression that includes both adjustments for liquidity and counterparty risk, S t = + (y t r t ) + (bid:ask cds;t bid:ask bond;t ) + CP R t + " t (17) where, again, we expect > 0 and < 0. In estimating the above regressions we get the follwoing main results. The estimates for the frictionless model (Proposition 1) deviate signi cantly from their predicted values. After accounting for the two frictions of liquidity and counterparty risk the estimates improve signi cantly. First, their e ect on CDS pricing proves to be signi cant and consistent with the models predictions: the relative illiquidity of CDSs has a positive e ect on CDS premiums; countreparty risk has a negative e ect on CDS premiums. Second, correcting for these two frictions also improves the estimates for the relation between the bond s yield spread and 18

19 the CDS premium to be much closer to 1. Finally, controlling for counterparty risk reveals a large component in the negative basis spread in the basic model which is due to counterparty risk. In addition to the regression results we also plotted the time series for the bid-ask spreads for both the CDSs and the bonds for all countries included in the sample (Appendix 6). The time series show a clear decreasing trend in the CDS bid-ask spreads over time. Especially in the cases of Brazil, Mexico, Panama, Peru, South Africa and Turkey, the declining trend is seen very clearly. For instance, in Mexico and Panama bid-ask spreads were around 50 bps in 2001, whereas in 2008 they reached levels lower than 10 bps. On the other hand, the bid-ask spread patterns for the bond market have not experienced serious changes over time for either one of the countries, and are rarely traded in levels higher than 10 bps. These di erences indicated a maturity process through which the CDS market has gone in these emerging markets during the past decade. These patterns in the bid-ask spreads fortify the regression results and the role of liquidity in pricing CDS premiums. In the next section we describe the data we use followed by our regression results. 7 The Data In order to estimate Propositions 1,2, and 3 several time series were located. 1. Daily quotes for 5-year emerging market sovereign CDS premiums. 2. Daily quotes for 5-year emerging market sovereign bond yields. 3. Daily quotes for 5-year US Treasury rates as the risk-free rate. 4. Daily bid-ask spreads for the corresponding CDS premiums and bond yields as a proxy for their liquidity premium. 5. Daily quotes for the 5-year swap spread as a proxy for the level of counterparty risk, or the capital adequacy of major banks. All data was downloaded from Bloomberg. The CDS data covers the time period from January 1st, 2000, till May 16th, 2008, and was downloaded for the 25 emerging market countries included in the Lehman Brothers MSCI Emerging Market Index. For each of the sovereign reference entities we estimated a matching bond yield with exactly 5-years to maturity using a linear interpelation method. All bonds and CDSs are dollar denominated. For the risk free 19

20 rate we use daily quotes for the 5-year US Treasury yields. Another alternative for the risk free rate is the 5-year swap rate, which is most commonly used by market practitioners. For the coherence of the study we rst use a single measure for the risk-free rate, the 5-year US Treasury yields, which is more commonly used in the academic literature. However, later on in the robustness tests section we examine and discuss how our results change due to the di erent choices of risk free rates. After ltering the data to include only countries with enough available dates for matching bond-cds quotes, our nal data set ended up including 16 countries with 1,230 trading days on average (about 4 years) of matching bond-cds quotes per country. A more detailed description of the data, the bond estimation method, and a breakdown of the basic statistics at the country level are presented in Appendix 4. 8 Regression Results As mentioned above, we are interested in estimating the three predictions derived from the model, which are expressed in equations (14), (15a), (16) and (17), and test whether the estimates con rm the values predicted by the model. The results for each regression are presented and discussed in the following sections. 8.1 The Basic Regression Table 1 presents the regression results for equations (14), (15a),( 16) and (17) when all observations were pooled together. Staring with the basic regression, the estimated slope between the bond s yield spread and the CDS premium for the entire sample is 1.28, as opposed to an expected value of = 1. In addition, the estimate for the intercept is -53 basis points, as opposed to a predicted value of zero, = 0. These results indicate deviations from the parity predicted by the basic model and Proposition 1, assuming a frictionless market and no counterparty risk. 8.2 The Liquidity Regression The liquidity regression shows signi cant improvement in the model s parameter estimations and we get results that are consistent with Proposition 2. The slope coe cient between the bond s yield spread and the CDS premium is much closer to the predicted value of = 1: including liquidity in the regression yields an estimate of 1.09 for, as opposed to 1.28 in the model without liquidity. The intercept which is predicted by the model to be zero, 20

21 Table 1 Rgression Results - Basic, Liquidity & Counterparty Risk This table reports OLS panel data estimates for the Basic Regression, Liquidity Regression, Counterparty Risk Regression and estimates for both effects combined: liquidity and counterparty risk together. The coefficient for the bond yield spread over the risk free rate is β, for the liquidity effect is γ, and for the counterparty risk is δ. The 1% significance level is denoted by (*), 5% significance level is denoted by (**), and 10% significance level is denoted by (***). The total umber of observations is 20,053. Estimate [ 95% Conf. Interval ] Adj. R-Square Basic Regression α (bps) * β 1.28* Liquidity Regression α (bps) * β 1.09* γ 2.14* Counterparty Risk Regression α (bps) 48.75* β 1.29* δ -2.05* Liquidity & Counterparty Risk Regression α (bps) 34.54* β 1.13* γ 1.72* δ -1.37*

22 is still signi cantly di erent than zero, but its deviation drops from -53 bps to 28 bps after accounting for liquidity. Finally, another consistent result with the model s predictions is the estimate for the liquidity coe cient,, which is signi cantly positive. A positive liquidity coe cient means that the larger the di erence in bid-ask spreads between CDSs and bonds is, which indicates a more illiquid CDS market, the higher is the CDS premium. 8.3 The Counterparty Risk Regression In the third test, the counterparty risk regression, we see that there are no major di erences between the estimates for the bond yield spread,, using the basic regression and the counterparty risk one. However, the estimate for the coe cient of the counterparty risk variable,, con rms the prediction of Proposition 3 and is signi cantly negative. Moreover, a major change between the two regressions is the size of the intercept. The intercept is still far from zero, = 48 bps. However, the estimated intercept for the basis model was -53 bps. This result suggests that the negative xed basis spread originally included a major counterparty risk component which reduced the value of the CDS premium. After correcting for the counterparty risk element in the regression, this negative "pressure" is taken o the intercept and is explicitly captured by the negative counterparty risk coe cient,. Another possible explanation for the change of the intercept is addressed in the robustness tests section when testing for the swap rate as an alternative risk free rate. 8.4 Liquidity and Counterparty Regression The fourth regression, which includes both liquidity and counterparty risk factors in the regression, combines some of the above results. The estimate for the coe cient of the bond yield spread,, is closer to 1 compared the basic regression (1.14 as opposed to 1.28), but is a little larger than the regression for liquidity alone (1.14 as opposed to 1.09). The intercept is again positive and has the same value as in the regression for counterparty risk alone. Both estimates for the liquidity factor, ; and the counterparty risk factor,, are consistent with their predictions: > 0 and < Country Level Results Here we provide a breakdown of the regression results at the country level. The basic regression, the liquidity regression and the counterparty risk regression were this time carried 22

23 Table 2 Basic Regression - By Country This table reports OLS estimates for the Basic Regression for each country separately. α is the regression constant and β is coefficient for the bond yield spread over the risk free rate. The 1% significance level is denoted by (*), 5% significance level is denoted by (**), and 10% significance level is denoted by (***) Country α (bps) [ 95% Conf. Interval ] β [ 95% Conf. Interval ] Adj. R-Square Brazil * * Chile * * China * Columbia * * Malaysia -9.94* * Mexico * * Panama * * Peru * * Philippine * * Poland * * Russia * ** South Africa * ** South Korea 9.09* * Turkey * * Ukraine 52.36* * Venezuela * * out for each individual country separately. The results for each regression are presented in Tables 2,3 and The Basic Regression Results for the basic regression at the country level are presented in Table 2. For some countries the coe cient is close to one, such as Russia (1.01), South Africa (0.97), Panama (1.12) and Venezuela (1.13). However, in most cases the estimates for are more than 20 percent away from the predicted value of = 1, with the highest estimates for Brazil (1.40) and Columbia (1.34). The lowest results are for South Korea (0.41) and China (0.42). The estimates of the intercept also vary from one country to the other. For some countries the estimate is close to zero but for most of them the deviation is above 30 basis points. China (not signi cantly di erent than zero), South Korea (9 basis points) and Malaysia (-9 basis points) are close to zero, whereas the highest deviations are for Brazil (-89 bps), Columbia, Turkey and Ukraine (all around a 50 bps deviation). 23

24 Table 3 Liquidity Regression - By Country This table reports OLS estimates for the Liquidity Regression for each country separately. α is the regression constant, β is coefficient for the bond yield spread over the risk free rate and γ is the liquidity coefficient. The 1% significance level is denoted by (*), 5% significance level is denoted by (**), and 10% significance level is denoted by (***) Country α (bps) [ 95% Conf. Interval ] β [ 95% Conf. Interval ] γ [ 95% Conf. Interval ] Adj. R-Square Brazil 11.35* * * Chile * * * China 11.52* * * Columbia * * * Malaysia -7.94* * * Mexico -3.36* * * Panama 26.67* * * Peru ** * Philippine * * * Poland * * * Russia * * * South Africa * * * South Korea 4.13* * * Turkey * * * Ukraine 52.24* * Venezuela * * The Liquidity Regression Table 3 presents the liquidity regression results at the country level. The changes between the basic regression and the liquidity regression are clear at the country level as well. For many countries the slope between the bond s spread and the CDS premium,, is now much closer to one. Brazil, Chile, Mexico, Peru, Russia, and Venezuela have estimates for that are within 10 percent from the predicted value of = 1. Other countries also improve their coe cient, such as Turkey (1.20 including liquidity compared to 1.32 in the basic case) and Columbia (1.21 including liquidity compared to 1.34 in the basic case). However, some countries remain with low values for the slope, like China, Malaysia and South Korea. Looking at the values for the intercept,, again, we see a signi cant improvement. For 7 countries (Brazil, China, Malaysia, Mexico, Peru, South Korea and Venezuela) the estimates of are around 10 bps or less. Only a smaller group of countries have now estimates for that are greater than 30 bps. Finally, the coe cient for the liquidity e ect is positive for all countries with the exception of Ukraine (which is not signi cantly di erent than zero). This uniform result is consistent with the prediction from Proposition 2: > 0. 24

25 Table 4 Counterparty Risk Regression - By Country This table reports OLS estimates for the Counterparty Risk Regression for each country separately. α is the regression constant, β is the coefficient for the bond yield spread over the risk free rate and δ is the counterparty risk coefficient. The 1% significance level is denoted by (*), 5% significance level is denoted by (**), and 10% significance level is denoted by (***) Country α (bps) [ 95% Conf. Interval ] β [ 95% Conf. Interval ] δ [ 95% Conf. Interval ] Adj. R-Square Brazil * * *** Chile 23.58* * * China 10.37* * * Columbia 66.83* * * Malaysia * * Mexico 25.01* * * Panama 79.57* * * Peru * * * Philippine 46.04* * * Poland * * * Russia 40.21* * * South Africa 26.74* * * South Korea 39.15* * * Turkey 27.50* * * Ukraine 58.88* * * Venezuela 77.09* * * The Counterparty Risk Regression Table 4 presents the results of the counterparty regression at the country level. Again, the estimate for the coe cient of the counterparty risk variable is negative and signi cant for all countries, as Proposition 3 predicts. Additionally, for most countries the intercept is positive after accounting for the counterparty risk, as opposed to the basic case. These results follow a similar pattern to the ones obtained in the pooled regression presented in Table 1 and discussed above. 9 Robustness Tests This section addresses a few robustness tests to examine how the results we presented so far depend on the choice of variables and the test formats. More speci cally, we examine the following points: (1) How the choice of the risk free rate a ects the results - US Treasury rates vs. the swap rate. (2) We introduce into the pooled regressions xed e ects to account for di erences between countries. (3) We introduce into the pooled regressions time e ects to account for di erences between years. (4) We account for the par pricing of bonds and measure the scope of potential errors. (5) Suggest an alternative proxy for counterparty risk. These issues are addressed in the following sections. 25

26 Table 5 Alternative Risk-Free Rates This table reports OLS estimates for the panel data using two different risk-free rates: the 5-year swap rate and the 5-year US Treasury rate. All three regressions are reported: the Basic Regression, Liquidity Regression and Counterparty Risk. α is the regression constant, the coefficient for the bond yield spread over the risk free rate is β, for the liquidity effect is γ, and for the counterparty risk is δ. The 1% significance level is denoted by (*), 5% significance level is denoted by (**), and 10% significance level is denoted by (***). The total umber of observations is 20,053. Swap Rate US Treasury Rate Estimate [ 95% Conf. Interval ] Estimate [ 95% Conf. Interval ] Basic Regression α (bps) 9.95* * β 1.29* * Liquidity Regression α (bps) 23.07* * β 1.13* * γ 1.78* * Counterparty Risk Regression α (bps) 48.61* * β 1.29* * δ -0.76* * The Choice of Risk Free Rate The choice of the risk free rate is not an obvious one. The US Treasury rate is often used in the academic literature as the risk-free rate whereas the swap rate is more commonly used among market practitioners as a benchmark rate. The choice of the Treasury rate as the risk-free rate is based on the argument that a bond issued by a government in its own currency has no credit risk so that its yield should equal the true risk-free interest rate. However, market practitioners claim that the actual borrowing rates in the market are more accurately captured by swap rates. These rates are based on the LIBOR curve and re ect borrowing costs for nancial institutions with high credit rating. In order to examine the e ect that di erent benchmark interest rates have on our results, we repeat the three regressions described in the previous sections and compare between using Treasury rates and swap rates as the benchmark interest rate. Table 5 presents the results for the pooled regressions using Treasury Rates and swap rates. In all three cases there are no big di erences in the coe cients. The liquidity coe cient does not change much either, from 2.14 for the Treasury to 1.78 for the swap rate. 26

27 The more signi cant changes are in the intercept and the counterparty risk coe cient,. Using the swap rate the intercept a changes in the basic regression from -53 bps to 9 bps. The counterparty risk coe cient changes from to A possible reason for the change in a is the following. The swap rate is the borrowing rate for major nancial institutions and thus incorporates the risk of an event of default by these institutions, (see Appendix 4 for a more detailed discussion). Recall that our previous results show that the CDS market indeed prices counterparty risk, as expressed in the negative estimates for in the counterparty risk regression (see Table 5). Since the counterparties are typically these same major investment banks which borrow close to LIBOR, as a result, using LIBOR as the borrowing rate in our regression essentially factors in counterparty risk. In this way, counterparty risk is no longer estimated only through the intercept,, but is partially accounted for by the slope. As a result the constant term becomes less negative. This change is similar to the change in between the basic regression and the counterparty risk regression using the Treasury Rate, as we mentioned earlier. Similarly, the estimate for the counterparty risk coe cient,, is less negative under the swap rate regression (-0.76 compared with -2.06) for the same reason. Part of the counterparty risk is already accounted for by the use of the swap rate as the borrowing rate. Interestingly, once adding up the combined e ect of the swap rate on the CDS premium, i.e.,, we get the same value as the original estimate for under the regression using the Treasury rate (-2.06). This result reinforces the signi cance of the e ect of counterparty risk on the pricing of CDS by the market. 9.2 Fixed E ects Another re nement of the results obtained by the pooled regression is to account for xed effects between the di erent countries. Di erent countries have di erent nancial institutions, nancial regulations and di erent frictions that may a ect the results from one country to another. Estimating these xed e ects will provide a more re ned insight into how these di erences in uence the CDS market. We use the following regression, P S t = + (y t r t ) + (bid:ask cds;t bid:ask bond;t ) + CP R t + I i D i + " t which accounts for liquidity and counterparty risk for the pooled sample, and includes a dummy variables for each country i to account for xed e ects. Regression results are presented in Table 6. As can be seen in Table 6, the di erent countries can be divided roughly into three groups by the level of their. Russia, Poland, Malaysia and South Africa have values of that 27 i=1

28 Table 6 Fixed Effects - By country This table reports OLS estimates for the panel data regression using all three factors: bond yield spreads, liquidity and counterparty risk, but controlling for fixed effects for the different countries. α is the regression constant, the coefficient for the bond yield spread over the risk free rate is β, for the liquidity effect is γ, and for the counterparty risk is δ. α is the coefficient for the fixed effect of each country and should be added to the constant α to calculate each country's total constant. The 1% significance level is denoted by (*), 5% significance level is denoted by (**), and 10% significance level is denoted by (***). The total umber of observations is 20,053. Estimate [ 5% Conf. Interval ] α (bps) 13.26* β 1.07* γ 2.16* δ -1.05* α Fixed Effects Per Country: Brazil 33.62* Chile China 14.35* Columbia 57.87* Malaysia -8.31* Mexico 9.76* Panama 2.90*** Peru 44.35* Philippine 44.83* Poland Russia * South Africa * South Korea 11.24* Turkey 39.17* Ukraine 35.91* Venezuela

29 are lower than 10 bps in absolute values, indicating a very small xed basis spread between bonds and CDS premiums. Another group of countries including Venezuela, South Korea, Panama, Mexico, China and Chile have values that are between bps. Finally, Brazil, Columbia, Peru, Philippine, Turkey and Ukraine have values of that are higher than 50 bps indicating a large xed basis between CDSs and bonds. The rst group is probably the more advanced countries among the list of emerging market countries, which could explain the lower xed basis. However, it s hard to distinguish between the two other groups, whether geographically or by the level of their economic or institutional development. 9.3 Time E ects In the next step we turn to examine the time e ects on the CDS basis. Similarly to the xed e ects per country, we run the pooled regression, accounting for liquidity and counterparty risk, P S t = + (y t r t ) + (bid:ask cds;t bid:ask bond;t ) + CP R t + I i Y ear i + " t and includes dummies for each year. The years included in our sample are , however since there are only a few observations for the year of 2000 we do not account for that year. Table 7 presents regression results for this test. Starting with the year 2001, is large and negative (-128 bps, the sum of and for 2001). In 2002 becomes smaller (-26 bps). In the intercept is around zero and then becomes slightly positive in (around 10 bps). In the intercept starts declining slightly again. This pattern in the xed basis spread along the years is consistent with the maturity process that the CDS has gone through during same time period. As we describe in the introduction, in the beginning of the 2000 s CDS markets were still young, especially in the emerging markets sector, and only in later years both volume of trade and the number of underlying entities increased. Another possible explanation for the pattern of changes is the ending of nancial crisis times in Latin America during the years , where Argentina defaulted on its debt and political instability in Brazil which a ected bond yields and perhaps added to the insecurity of CDS markets. Consistent with this explanation, we also see a slight decline in the value of a to a negative basis area during , a time period that includes the rst year of the recent global credit crisis. Last, the years of also have less data in our sample (approximately one third of available quotes for the other years, which might a ect the estimates as well. 29 i=1

30 Table 7 Time Effects - By Year This table reports OLS estimates for the panel data regression using all three factors: bond yield spreads, liquidity and counterparty risk, but controlling for time effects for each year. α is the regression constant, the coefficient for the bond yield spread over the risk free rate is β, for the liquidity effect is γ, and for the counterparty risk is δ. α is the coefficient for each year's time effect and should be added to the constant α to calculate each year's total constant. The 1% significance level is denoted by (*), 5% significance level is denoted by (**), and 10% significance level is denoted by (***). The total umber of observations is 20,024. Estimate [ 5% Conf. Interval ] α (bps) * β 1.19* γ 1.59* δ -0.91* α Time Effects Per Year: * * * * * * * *

31 9.4 Par and Non-Par Bonds An important element in Propositions 1,2 and 3 is that bonds are priced at par. Unfortunately, bonds traded at par throughout the entire sample time period are very rare, since bond prices uctuate and are traded with a premium or discount according to changes in their yields. One way to overcome this issue is by using Bloomberg s Fair Market Curve data. Bloomberg provides for some bonds estimates for par priced yield curves, based on the entire outstanding bonds for the same issuer. Using the 5-year point on the fair market par yield curve estimates allows for completely avoiding the discount or premium problem. However, Bloomberg provides fair market data for only 9 emerging market countries, as opposed to 16 in our sample. Nevertheless, in order to test the accuracy of our estimates and the margin of error due to non-par pricing in our data, we carry out the following additional tests. First, as a benchmark to our results, we compare all three regression results (for Proposition 1,2 and 3) based on our sample with those based on Bloomberg s estimates for par bond yields, for the conjoint 8 countries. Next, we regress for the 8 conjoint countries the 5-year par-bond estimates on the non-par estimates to examine how close these two estimates are to each other. Finally, this last test is repeated at the country level as well. Table 8 presents the comparison between using the fair market estimates (par) and our sample (non-par) for the same set of countries. As can be seen there are very marginal di erences between the results for both tests, especially in the basic regression and the counterparty risk one. The only signi cant change is the coe cient for the bond s spread in the liquidity regression, which drops under the par bond estimates to 1.01, very close to the predicted value of = 1, as opposed to an estimate of 1.06 for when using the non-par bonds. The nearly similar results obtained by using the par and non-par bond yields suggest that the scope of error due to the premium or discount pricing of the bond is relatively marginal. To further enforce this claim we also regress the two time series on each other, i.e., the nonpar yields on the par yields, and check how correlated they are. Table 9 presents the results for the entire sample and at the country level. For the entire sample the slope coe cient indicates that on average changes in both estimates are the same, with a constant di erence of only 10 bps on average between the two series. At the country level too, for almost all countries the deviation is no more than 5%. The only exceptions is the case of Peru where the deviations seem to be higher, which might be explained by the poor number of observation available on Bloomberg for the par estimates - less than one year of data. Overall, these results further support the relatively marginal e ect of the error in our estimations due to the premium or discount factors in the bond data. 31

32 Table 8 Par & Non-Par Comparison This table reports OLS estimates for the panel data using two different estimates for bond yields: the original nonpar linearly interpolated yield estimates and Bloomberg's par fair market 5-year yield quotes. All four regressions are reported: the Basic Regression, Liquidity Regression, Counterparty Risk and all combined. α is the regression constant, the coefficient for the bond yield spread over the risk free rate is β, for the liquidity effect is γ, and for the counterparty risk is δ. The 1% significance level is denoted by (*), 5% significance level is denoted by (**), and 10% significance level is denoted by (***). The total umber of observations is 10,054. Par Estimates Non-Par estimates Estimate [ 95% Conf. Interval ] Estimate [ 95% Conf. Interval ] Basic Regression α (bps) * * β 1.34* * Liquidity Regression α (bps) * * β 1.06* * γ 2.61* * Counterparty Risk Regression α (bps) β 1.33* * δ -1.47* * Liquidity & Counterparty Risk Regression α (bps) 23.52* * β 1.07* * γ 2.48* * δ -0.91* *

33 Table 9 Par & Non-Par Bond Correlation This Table reports OLS estimates for regressing Bloomberg's par fair market 5-year yield quotes on the 5-year non-par linearly interpolated yield estimates we originally used. α is the regression constant and β is the bond's slope coefficient. The total umber of observations is 10,054. α (bps) Std. Error β Std. Error All Countries Brazil China Columbia Mexico Peru Philippine Turkey Venezuela Alternative Measure for Counterparty Risk The proxy chosen above for measuring counterparty risk was the swap spread. Another alternative is to use an index of CDS quotes for nancial institutions which typically function as market makers in the CDS market. The CDS quotes of these nancial institutions measure their own risk of default and thus could naturally function as a proxy for counterparty risk. In order to construct such an index, 9 global investment banks with available CDS quotes were chosen 6 and their daily CDS quotes were downloaded from Bloomberg. Then, the average of their daily quotes was taken to construct the actual index. Based on this new index we repeated the counterparty risk regression. Table 10 presents the results. As can be seen in Table 10, using the alternative index yields again a negative estimate for the counterparty risk coe cient,. This result is consistent with the prediction of Proposition 3, just like our previous results based on the swap spread. However, using the CDS index yields an estimate of 0:5 for, as opposed to 1:47 based on the swap spread. The change in the size of the estimate could probably be explained in relation to the true borrowing costs by market players. As discussed earlier in this section, there are a few possible borrowing rates that could function as the benchmark rate. If the swap rate is the true borrowing rate for investors, then in the counterparty risk regression the swap spread variable captures an additional negative correlation with the CDS pricing. It accounts not only for counterparty 6 The nine investment banks include: Bank of America, Bear Sterns, CitiGroup, Goldman Sachs, HSBC, JPMorgan, Lehman Brothers, Merrill Lynch and Morgan Stanley. 33

34 Table 10 Swap Spread vs. CDS Index Counterparty Risk Regression This table reports OLS estimates for the panel data Counterparty Risk Regression using two different proxies for counterparty risk: the 5-year swap spread and a basket of 5-year CDS quotes for major investment banks. The 9 investment banks included are: Bank of America, Bear Sterns, CitiGroup, Goldman Sachs, HSBC, JPMorgan, Lehman Brothers, Merrill Lynch and Morgan Stanley. α is the regression constant, the coefficient for the bond yield spread over the risk free rate is β and for the counterparty risk is δ. The 1% significance level is denoted by (*), 5% significance level is denoted by (**), and 10% significance level is denoted by (***). The total umber of observations is 16,569. Swap Spread CDS Index Estimate [ 95% Conf. Interval ] Estimate [ 95% Conf. Interval ] α (bps) 13.29* * β 1.35* * δ -1.47* * risk, but also for additional borrowing costs in excess of the Treasury rate. Thus, the coe cient contains two components when using the swap spread: one component that captures the excess borrowing cost (i.e., ), and one component that captures the "clean" counterparty risk. Since is close to 1, we get an estimate smaller almost by 1 using the swap spread compared to the CDS index ( 1:47 as opposed to 0:5). A similar e ect should be found when using the swap rate as the risk free benchmark, since it allows to separate between the two components. Indeed, a similar change in the estimates for happens when we use the swap rate as the benchmark borrowing costs (see Table 5). We discussed this matter above once we compared between the use of Treasury rates and swap rates in the counterparty risk regression. A similar e ect is also re ected in the di erences for the constant term estimates in both regressions,. The constant term is much smaller using the CDS index compared to using the swap spread. The reason is, that the undervalued borrowing costs of Treasury rates have to be accounted for either directly by introducing the swap spread or indirectly by the constant term. When using the CDS index, the reduction in the size of the constant captures the excess borrowing costs beyond Treasury rates since there is no other variable related to it directly. 10 Summary In this paper we addressed pricing anomalies between CDSs and their underlying bonds for sovereign debt in emerging markets. We focus on two factors, liquidity and counterparty risk, 34

35 to explain the pricing deviations. Under ideal market conditions, due to arbitrage forces, theory suggests that CDS premiums should be equal to the underlying bond yield spread over the risk free rate. However, using extensive data on 16 emerging market countries we documented a consistent non-zero basis spread between CDSs and their underlying bonds. In order to show the relevance of liquidity and counterparty risk for the basis spread and the di erent asset prices, we adjusted the models to account for liquidity and the existence of counterparty risk. We rst allow for liquidity di erences between CDSs and bonds. Liquidity di erences introduce di erent liquidity premiums into the pricing of each asset, which consequently generate pricing inequalities between CDSs and bonds. Second, we allow for the existence of counterparty risk in CDS trading. We show how the possibility that a CDS seller will default and not honor its contractual obligations has a negative e ect on CDS pricing. Again, this market friction consequently generates pricing di erences between CDSs and bonds, which violate the pricing equality under perfect market conditions. Our new model yields testable predictions that allow us to empirically evaluate the relevance of these two market frictions using real data. The empirical results show strong support for the relevance of these two factors to the pricing of CDS contracts. The estimated basic model, which does not take into account any market frictions or counterparty risk, deviates signi cantly from its predicted values. After correcting for liquidity and counterparty risk the estimates improve signi cantly. First, the e ect of the two frictions on CDS pricing proved to be signi cant and consistent with the model s predictions: the relative illiquidity of CDSs has a positive e ect on CDS premiums and countreparty risk has a negative e ect on CDS premiums. Second, correcting for these two factors also improves the estimates for the relation between the bond s yield spread and the CDS premium. Under the new model is much closer to the predicted value of 1. We nd further support for our ndings in the time series for the bid-ask spreads of CDSs and bonds plotted in Appendix 6. The time series show a clear decreasing trend in the CDS bid-ask spreads over time. On the other hand, bid-ask spreads for the bond market have not experienced serious changes over time. These di erences indicate a maturity process through which the CDS market has gone in these emerging markets during the past decade. These patterns in the bid-ask spreads fortify the regression results and the role of liquidity in pricing CDS premiums. 35

36 Appendix 1 In this appendix we provide the proof for Proposition 1. We start by modifying the pricing equation for the risk-free bond, equation (3), to the following form, using the default probabilities of the risky bond: NX 100 = re rt F (t) + 100e rn F (N) + 0 Z N 100e rt f(t)dt (18) The rst two expressions are the stream of payments of the risk-free bond under "no-default" states of the risky bond. The third expression is the risk-free bond s value under a "default state" of the risky bond. This somewhat arti cial presentation of the pricing of the risk-free bond modi es equation (3) to a similar structure of the pricing equation of the risky bond and will prove to be useful later on. The value of a portfolio that shorts the risky bond and buys the risk-free bond (equations (18) (2)), is: 100 B = NX re rt F (t) + 100e rn F (N) + NX Ce rt F (t) 100e rn F (N) Z N 0 Z N 0 100e rt f(t)dt (19) R t e rt f(t)dt Rearranging we get: 100 B = NX (r C)e rt F (t) + Z N 0 (100 R t )e rt f(t)dt (20) Substituting equation (1) into equation (20), we get: Rearranging again, we get: 100 B = NX (r C)e rt F (t) + NX Se rt F (t) 100 B = (S + r C) 36 NX e rt F (t)

37 and nally we have, 100 B NP e rt F (t) = S (C r) (21) Notice the following result from equation (21): When the defaultable bond is traded at par, i.e., B = 100, we get: 0 = S (C r) (22) Since a xed coupon on a par bond is also equal to the bond s yield to maturity, i.e., C = y, we can re-write equation (22) in the following way: 0 = S (y r) (23) And since the right hand side is nothing but the CDS-Bond Basis Spread, S (y r) Basis Spread which leads us to our nal result that, 0 = S (y r) Basis Spread (24) 37

38 Appendix 2 In this appendix we provide the proof for Proposition 2. Recall that we described the market price for the bond yield and for the CDS premium, which now contain a liquidity premium component, in the following way: 1. Let e S be the market price for the CDS contract. Then: e S = S + scds 2. Let ey be the market yield on the bond. Then: ey = y + s bond Re-arranging the two equations, we get S = e S s cds (25) and, y = ey s bond (26) Substituting the values of y and S given by equations (25) and (26) in equation (23) we get: 0 = S (y r) = ( S e s cds ) (ey s bond r) Which gives us the nal result for a market with frictions: es = ey r (s bond s cds ) (27) 38

39 Appendix 3 In this appendix we provide the proof for Proposition 3. Notice, that we can rewrite the probabilities in the following way: 1. P r(d; CP ) t = P r(d) t P r(d; CP ) t Where P r(d) t is the total probability for default by the reference entity and P r(d; CP ) t is the joint probability of default by the reference entity and the counterparty. 2. P r(d; CP ) t = 1 (P r(d) t + P r(cp ) t P r(d; CP ) t ) The probability of no default by either the bond or the counterparty is one minus the probability of default by either one of the parties. 3. Also, the value of the joint probability P r(d; CP ) t can be expressed as: P r(d; CP ) t = P r(d) t P r(cp ) t + corr(d; CP )f(d; CP ) t where f(d; CP ) is some function of the probabilities of D and CP. Plugging these values in the CDS premium, we get: bs = (1 R) N P P r(d; CP ) t e rt t Q 1 i=0 P r(d; CP ) i NP f[p r(d; CP ) t + P r(d; CP ) t ] t Q 1 P r(d; CP ) i g i=0 = (1 R) N P [P r(d) t P r(d; CP ) t ]e rt t Q 1 i=0 P r(d; CP ) i NP f[p r(d) t P r(d; CP ) t + 1 (P r(d) t + P r(cp ) t P r(d; CP ) t )] t Q 1 P r(d; CP ) i g Now, we can de ne = (1 R) NP [P r(d) t P r(d; CP ) t ]e rt t Q 1 NP f[1 P r(cp ) t )]e rt t Q 1 g(t) e rt t Q 1 i=0 i=0 P r(d; CP ) i i=0 P r(d; CP ) i P r(d; CP ) i g i=0 (28) 39

40 and thus re-write equation (28) as, NP [P r(d) t P r(d; CP ) t ]g(t) bs = (1 R) NP [1 P r(cp ) t )]g(t) If we assume all probabilities to be constant over time (a at term structure for the default probabilities), we can simplify equation (29) to, NP [P r(d) t P r(d; CP ) t ]g(t) bs = (1 R) NP [1 P r(cp ) t )]g(t) = (1 R) = (1 R) Based on number 3 above we know that, P r(d) P r(d; CP ) 1 P r(cp ) P r(d) P r(d; CP ) 1 P r(cp ) NP g(t) NP g(t) P r(d; CP ) t = P r(d) t P r(cp ) t + corr(d; CP )f(d; CP ) thus plugging this expression in equation (30) we get, P r(d) P r(d; CP ) bs = (1 R) 1 P r(cp ) P r(d) (P r(d)p r(cp ) + corr(d; CP )f(d; CP ) = (1 R) 1 P r(cp ) P r(d)[1 P r(cp )] corr(d; CP )f(d; CP ) = (1 R) 1 P r(cp ) Now, comparing between the case where counterparty risk exists and where it does not exist we have the following: 1. When there is no counterparty risk, i.e., P r(cp ) = 0, we have (29) (30) (31) bs = (1 R)P r(d) 2. When there is counterparty risk, i.e., P r(cp ) > 0, we have P r(d)[1 P r(cp )] corr(d; CP )f(d; CP ) bs = (1 R) 1 P r(cp ) We distinguish between the case where there is correlation between the default of the underlying bond and the counterparty and the case where there is no correlation: 40

41 When there is no correlation between D and CP, i.e., corr(d; CP ) = 0, we get the same result as in 1, S = (1 R)P r(d) When there is positive correlation between D and CP, we get, corr(d; CP ) > 0 P r(d)[1 P r(cp )] corr(d; CP )f(d; CP ) bs = (1 R) 1 P r(cp ) which is smaller than in the rst case, when there is no counterparty risk. Also notice, that the larger the correlation between the defaults of the counterparty and the underlying bond, the smaller is the CDS premium. 41

42 Appendix 4 - Description of the Data We located the following time series: 1. Daily quotes for 5-year emerging market sovereign CDS premiums 2. Daily quotes for 5-year emerging market sovereign bond yields 3. Daily quotes for 5-year US Treasury rates as the risk-free rate 4. Daily bid-ask spreads for the corresponding CDS premiums and bond yields as a proxy for their liquidity premium 5. Daily quotes for the 5-year swap spread as a proxy for the level of counterparty risk, or the capital adequacy of major banks. The description of the data in use is provided in the following sections. All data was downloaded from Bloomberg. CDS Data The CDS data covers the time period from January 1st, 2000, till May 16th, 2008, and was downloaded for the 25 emerging market countries included in the Lehman Brothers MSCI Emerging Market Index. The CDS premium data are averages taken by data agencies that collect daily quotes from di erent CDS brokers and then average them to provide a single daily end-of-day quote. Therefore, even though the quotes do not re ect any actual transactions, they are constructed out of aggregate data of various transaction quotes by several dealers and thus re ect better the total market trading zone for each day. Not all countries have continuos quotes throughout the desired time period, and for some of the countries CDS quotes begin only in a later than January, Some of the reasons for the absence of quotes are that for some countries active CDS markets fully developed only later than the year Also, the availability of quotes depends on the time when Bloomberg started collecting the data for the particular country. 42

43 Five year Bond Yields For each of the sovereign reference entities a matching bond with exactly 5-years to maturity had to be matched. Ideally, we would like to nd a matching 5-year bond at each observation date from which the sovereign bond spread could be determined. In reality, the number of outstanding bonds is limited and it is very rare to nd bonds that exactly match the 5-year maturity of the credit default swaps for any of the observation dates in the sample. To overcome this problem we follow previous work, such as Blanco et al. (2005), Hull et al. (2004) and others, and use a linear interpolation method. For each reference entity we located on Bloomberg a bond with between 3.5 and 5 years left to maturity, and another bond with between 5 and 6.5 years to maturity, for each observation date. In this way we constructed a window of 1.5 years around the 5-year maturity date horizon for each observation date, which is bounded above and bellow with bonds with available quotes. By linearly interpolating their yields, we are able to estimate a 5-year yield to maturity on a daily basis. In order to locate such bonds the following method was taken: all CUSIP s of bonds with maturities between January 1st, 2005, and January 1st, 2015, that were available on Bloomberg were determined for each country included in the Lehman Brothers MSCI Emerging Market Index. The characteristics of each issue were downloaded and the bonds to be included were selected using the following major criteria: 1. Bonds must not have any embedded options: no puttable, callable or convertible bonds; only bullet bonds were retained. 2. Bonds must not be subordinated, structured or securitized. 3. Bonds must be in USD with xed rate coupons. 4. The issue must not be a private placement. The Risk Free Rate As a risk free rate we use daily quotes for the 5-year US Treasury yields. Another alternative for the risk free rate is the 5-year swap rate, which is most commonly used by market practitioners. For the coherence of the study we rst use only one measure for the risk free rate, the 5-year US Treasury yields, which is more commonly used in the academic literature. However, later on in the robustness tests section we examine and discuss how our results change due to the di erent choices of risk free rates. 43

44 Bid-Ask Spreads As a proxy for the liquidity premium there are several measures in the literature. Two of the most common and signi cant proxies for liquidity are volume of trade and bid-ask spreads. Unfortunately, since both bond and CDS markets are over-the-counter markets there is no available data on volume of trade. Thus, we downloaded daily quotes of the bid-ask spread for bonds and CDSs as a proxy for their liquidity. By using the bid-ask spread we are not trying to capture the actual liquidity premium, but to suggest a variable that is expected to be highly correlated with the liquidity of the asset, which in return determines the size of liquidity premium. Nevertheless, one nice property of the bid-ask spread measure is that it is actually a premium charged by the market maker in addition to the "clean" price of the asset. However, what share of that spread is actually charged as a premium remains unclear. Counterparty Risk As a proxy for the risk of default by the counterparty, i.e., the protection seller, we use the 5-year swap spread. Since swap spreads represent the di erence between swap rates and Treasury yields, they re ect the di erence in the default risk of the nancial sector quoting Libor rates and the U.S. Treasury. Thus, this measure tracks the ability of nancial institutions to pay back their obligations. Since these institutions are typically also the market makers in CDS markets, it can function as a proxy for their ability to back their insurance obligations in case of a credit event by the reference entity. The use of the swap spread as a measure for credit worthiness for major nancial institutions is very common among market practitioners. In the academic literature there are several studies that investigate what factors account for the swap spread. Two important papers by Du e et al. (1997) and Liu et al. (2006) study the share of liquidity and default risk imbedded in the credit spread of swap rates. Both studies use a reduced-form credit framework with two components, a liquidity process and a default process. These studies nd empirical evidence that support the signi cancy of both components. However, Du e et al. (1997) nd that the liquidity factor a ects the spread in the short term only whereas the default risk a ects longer term contracts (beyond two years). Moreover, Liu et al. (2006) show that the default-risk component in the swap rate credit spread is much larger than the liquidity component. Based on these sources we use the swap rate as a proxy for the default risk of the nancial sector. 44

45 Final Sample For many of the emerging market countries it was hard to match an estimated 5-year bond to a corresponding CDS quote. In many cases the number of outstanding dollar bonds was very limited and did not enable us to create the required 1.5-year window around the 5 year horizon. For instance, the Check Republic, Indonesia and Pakistan have only one outstanding bond in our sample; Thailand has only two and Hungary has only three. Also, other countries have very inactive CDS markets, such as Jordan and Morocco. After ltering the data to include only countries with enough available dates for matching bond-cds quotes, the nal data set ended up including 16 countries with 1,230 trading days on average (about 4 years) of matching bond-cds quotes per country. A summary of our nal sample is presented in Table 11. Basis Spread (Swap) Basis Spread (Treasury) Date (bps) (bps) Country Begin End Observations Mean* Median Min Max Mean* Median Min Max Brazil 10/12/2001 5/14/2008 1, , ,381.4 Chile 1/24/2003 5/14/2008 1, China 1/24/2003 5/14/2008 1, Columbia 1/24/2003 5/14/2008 1, Malaysia 12/3/2003 1/11/ Mexico 10/12/2001 5/15/2008 1, Panama 11/3/2003 5/14/2008 1, Peru 10/20/2003 5/14/2008 1, Philippine 9/13/2002 5/14/2008 1, Poland 1/5/2007 5/15/ Russia 11/17/2000 5/16/2008 1, South Africa 12/13/2001 5/14/2008 1, South Korea 10/18/2002 5/14/2008 1, Turkey 11/21/2001 5/15/2008 1, Ukraine 9/5/2005 5/16/ Venezuela 8/4/2003 5/16/2008 1, * Mean of absolute values Table 11 Summary of Basic Statistics 45

46 Appendix 5 Figure 5 5-Year CDS Premiums & Bond Yield Spreads (basis points) CDS Premiums Bond Yields 46

47 Figure 5 - Continued 5-Year CDS Premiums & Bond Yield Spreads (basis points) CDS Premiums Bond Yields 47

48 Figure 5 - Continued 5-Year CDS Premiums & Bond Yield Spreads (basis points) CDS Premiums Bond Yields 48

49 Figure 5 - Continued 5-Year CDS Premiums & Bond Yield Spreads (basis points) CDS Premiums Bond Yields 49

50 Figure 5 - Continued 5-Year CDS Premiums & Bond Yield Spreads (basis points) CDS Premiums Bond Yields 50

51 Figure 5 - Continued 5-Year CDS Premiums & Bond Yield Spreads (basis points) CDS Premiums Bond Yields 51

52 Figure 5 - Continued 5-Year CDS Premiums & Bond Yield Spreads (basis points) CDS Premiums Bond Yields 52

53 Figure 5 - Continued 5-Year CDS Premiums & Bond Yield Spreads (basis points) CDS Premiums Bond Yields 53

54 Appendix 6 Figure 6 Bid-Ask Spreads for CDS Premiums & Bond Yields (basis points) CDS Premiums Bond Yields 54

55 Figure 6 - Continued Bid-Ask Spreads for CDS Premiums & Bond Yields (basis points) CDS Premiums Bond Yields 55