Determinants of CDS premium and bond yield spread

Determinants of CDS premium and bond yield spread

Yusho KAGRAOKA

Musashi University, 1-26-1 Toyotama-kami, Nerima-ku, Tokyo 176-8534, Japantel: +81-3-5984-4059, fax: +81-3-3991-1198

e-mail: [email protected]

Abstract

A reduced-from model for credit risk is applied to evaluation of credit de-fault swaps (CDSs) and corporate bond spreads. For each reference entity,the term structure of default intensity in the reduced-form model is estimatedfrom CDS premiums. The CDS-implied bond spread of a market-traded cor-porate bond is calculated by using the term structure of default intensity.The market and CDS-implied bond spreads are examined by fixed-effectspanel data analysis. As a byproduct, a new method to estimate the risk-freeinterest rate is developed. The method is appealing to practitioners since theresultant term structure of the risk-free rate is consistent with both sovereignCDS premiums and government bond spreads. Empirical study on Japanesemarket is conducted based on a quarterly dataset from 2005 to 2011. Empir-ical study unveils the following facts: (i) CDS-implied bond spread comprisesof credit and firm-specific liquidity premiums, (ii) market bond spread com-prises of credit, firm-specific and bond-specific liquidity premiums.

Preprint submitted to Financial Markets and Portfolio Management October 28, 2012

1. Introduction

Growing credit derivatives market shows strong demand by financial mar-ket participants for credit-risk management vehicles because many investorsare exposed to credit risk resulting from corporate bonds in their portfolios.Investing in corporate bonds is definitely a long-position in credit risk. In-vestors were not able to take a short-position in credit risk until the advent ofcredit derivatives in early 1990’s. Credit default swaps (CDSs) are one of themost popular instruments among the credit derivatives. Brokers constantlyquote CDSs’ premiums and one can observe current premiums on financialinformation terminals such as Bloomberg. In this paper we use the terms”default risk” and ”credit risk” interchangeably.

Credit risk of an issuing company are reflected in CDS premium as wellas yield spread. Hull, Predescu and Vorst (2004) and Blanco, Brennanand Marsh (2005) compared CDS premiums and corporate spreads andconcluded that CDS premium was consistent with corporate bond spreads.Their results can be biased since they employed fixed-rate corporate bondsin place of floating-rate corporate bonds. Cashflows from CDS are replicatedby a long position in a par default-free floating-rate note (FRN) and a shortposition in a par defaultable FRN issued by the reference entity. Duffie andLiu (2001) show that if a issuer’s default risk is risk-neutrally independentof interest rates, floating-fixed spreads are determined by a term structure ofthe risk-free forward rate.

Credit risk models are useful to compare CDS premiums and corporatebond spreads on a comparative basis 1. The models are categorized into twotypes, structural and reduced-form models. Structural model is first devel-oped by Black and Scholes (1973) and practically applied by KMV (Vasicek(2001)). The structural model requires information on the current financialstructure of a firm. It is difficult to apply the structural model for timelyvaluation of credit risk since financial reports are disclosed only quarterly.Reduced form models are developed by Jarrow, Lando and Turnbull (1997),Duffie and Singleton (1999), Jarrow (2001), Madan, Guntay, and Unal(2003), and Das and Sundaram (2007). The reduced-form models are moreappropriate for evaluation of the credit risk than the structural one sincemodel parameters in the reduced-form models can be estimated from market

1Credit risk models are reviewed in many textbooks such as Duffie (2003), Lando(2004), and Schonbucher (2003), Bielecki and Rutkowski (2010), and so forth.

2

prices of CDSs or corporate bonds.Longstaff, Mithal, and Neis (2005) apply a reduced-form model to valua-

tion of CDS premiums and corporate bond spreads and study their relation-ship empirically. They regard that CDS is very liquid and its risk premiumcontains mainly credit risk; if an investor want to liquidate a CDS position,it is easy to enter into a new swap in the opposite direction. The differencebetween CDS premiums and corporate bond spreads comprises of a liquidityrisk of corporate bonds. They report that the default component represent51% of the spread for AAA/AA-rated bonds, 56% for A-rated bonds, 71%for BBB-rated bonds, and 83% for BB-rated bonds. Houweling and Vorst(2005) apply a reduced-form model and investigate relationship between CDSpremiums and corporate bond prices. They parametrize the default inten-sity as constant, linear, quadratic or cubic function of term to maturity, andconsider three types of interest rates as the risk-free rate; government, swap,and repo curves They conclude that a quadratic model that use the repocurve works well for investment grade issuers and the underestimation ofCDS premiums for speculative grade issuers is substantial.

Our objective is two-fold. Firstly, we empirically examine a relationshipbetween CDS premium and corporate bond spread by applying a reduced-form of credit risk model. Secondly, we identify the determinants of CDSpremium, corporate bond spread, and the difference between them by in-vestigating the default intensity in the reduced-form model. We calculateCDS-implied bond spread from the default intensity which is estimated fromCDS premium. We have a large data set of quarterly market quotes onJapanese CDSs from 2005Q3 to 2011Q3 at our disposal. We expect that thedifference between the CDS-implied and market spread of corporate bondarising from liquidity risk as Longstaff, Mithal, and Neis (2005). Our studyexpands Houweling and Vorst (2005) in three ways. Firstly we use premiumsof CDSs with various maturities and estimate term structure of the defaultintensity. Secondly we simultaneously estimate the risk-free rate and thedefault intensity from the government from sovereign CDS premiums andgovernment bond prices. They recommend repo rate as proxy for the risk-free rate, however, it is impossible to get long-term repo rate. Thirdly weestimate CDS-implied bond spreads from CDS premiums while they estimateCDS premiums using bond spreads.

The remainder of the paper is organized as follows. In section 2, a reduce-form model of credit risk is presented. In section 3, our data sets on CDSand corporate bonds are explained. In section 4, our empirical study is

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conducted. The default intensity in the credit risk model is estimated fromCDS and corporate bond. The determinants of CDS premium, corporatebond spread, and the difference between them are investigated. Section 5summarizes the paper and includes discussions on our model.

2. Model

2.1. Reduced-form model of credit risk

We review Houweling and Vorst (2005) to introduce our notations and toexplain our extension. We assume that default event of a reference entity ismodelled by a point process with deterministic intensity. Let p(t, T ) denotefor the time-t value of default-free discount bond maturing at time T withface value 1. Let λ(t) and Pr(t, T ) denote default intensity at time t andmartingale survival probability at time t up to time T , respectively. Thefollowing relationship holds for them,

Pr(t, T ) = Et

[exp

(−∫ T

t

ds λ(s)

)]. (1)

Houweling and Vorst (2005) assume default intensity as constant, linear,quadratic, or cubic function with respect to term-to-maturity. We assumethat the default intensity λ(t) is expressed by a piecewise constant func-tion which is discontinuous at simple knots [ 0, 1, 2, 3, 4, 5, 7, 10 ]. Ourparametrization has an advantage that we can fit theoretical CDS premiumsto the corresponding market premiums.

Let us investigate the value of a defaultable fixed-rate bond maturing attime tn. The defaultable bond has a stream of coupon payment c at timest = (t1, t2, . . . , tn). The value of the bond, v(t, t, c), is given by

v(t, t, c) =n∑

i=1

p(t, ti)Et

[c1{τ>ti}

]+ p(t, tn)E

[1{τ>tn}

]+ Et

[p(t, τ)δ1{τ≤tn}

]=

n∑i=1

p(t, ti)c Pr(t, ti) + p(t, tn) Pr(t, tn)

+

∫ tn

t

ds p(t, s)δφ(s), (2)

4

where τ is a stopping time at which default occurs and φ is a probabilitydensity function of Pr(t, T ). The last term in eq. (2) is approximated bydiscretizing the time interval [t, tn] into series of time {s0, s1, . . . , sm} (sj−1 <sj) so as to s0 = t and sm = tn. We finally obtain a valuation formula,

v(t, t, c) =n∑

i=1

p(t, ti)c Pr(t, ti) + p(t, tn) Pr(t, tn)

+m∑

i=1

p(t, si)δ (Pr(t, si−1) − Pr(t, si)) . (3)

Next let us evaluate a CDS with payment dates T = (T1, T2, . . . , TN),premium p, notional 1, and cash settlement at time t. We discretize the timeinterval [t, Tn] into series of time {S0, S1, . . . , SM} (Sj−1 < Sj) so as to S0 = tand SM = TN . The value of a fixed leg is given by

V (t, T , p) =N∑

i=1

p(t, Ti)α(Ti−1, Ti)pEt

[1{τ>Ti}

]+ E

[p(t, τ)α(T (τ), τ)p1{τ≤TN}

]=

N∑i=1

p(t, ti)α(Ti−1, Ti)p Pr(t, Ti) +

∫ TN

t

ds p(t, s)α(T (s), s)pφ(s)

=N∑

i=1

p(t, ti)α(Ti−1, Ti)p Pr(t, Ti)

+M∑i=1

p(t, Si)α(T (si), Si)p (Pr(t, Si−1) − Pr(t, Si)) , (4)

where α(t, S) is the year fraction between time t and S, and T (S) = maxi=0,...,N(Ti :Ti < S). The last term corresponds to an accrual payment; the holder ofCDS is required to pay the part of the premium payment that has accruedsince the last payment date. The value of a floating leg is expressed as

V (t, T ) = Et

[p(t, τ)(1 − δ)1{τ≤Tn}

]=

∫ TN

t

ds p(t, s)(1 − δ)φ(s)

=M∑i=1

p(t, Si)(1 − δ) (Pr(t, Si−1) − Pr(t, Si)) . (5)

The CDS premium is set to the level at which it holds V (t, t, p) = V (t, T ).

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2.2. Risk-free rate

Traditionally practitioners and academics have taken it for granted thatthe interest rate estimated from the government bonds corresponds to therisk-free rate, however, non-zero sovereign CDS premiums imply that thegovernment bonds are risky. The Japanese Governmental Bonds (JGBs) aretraded very actively in the OTC market, and they are highly liquid. Weassume that the JGBs have no liquidity risk. We simultaneously estimatethe risk-free rate and the default intensity of the government by applying thereduced-form model of credit risk. Denote instantaneous forward rate at timet maturing at time T by f(t, T ). We assume that the instantaneous forwardrate is expressed by a piecewise constant function with discontinuities atsimple knots [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ]. The time-t value of default-freediscount bond maturing at time T with face value 1 is expressed as

p(t, T ) = exp

(−∫ T

t

ds f(t, s)

). (6)

2.3. Explanatory variables for the spread

We investigate the CDS-implied and market spread of corporate bond.The CDS-implied bond prices are calculated by using the reduced-form modelwhose parameters are estimated from CDS premiums, and the CDS-impliedbond prices are converted into spreads over the risk-free rate. We identify therisk factors generating the CDS-implied and market spread, and investigatethe differences between the CDS-implied and market spreads.

We assume that risk factors are additive. Credit risk is traditionallyevaluated by credit rating, and we use an ordinal number to express creditrating; 1 for AAA, 2 for AA, 3 for A, and so forth. We assign 9 to the worstrating of C. We adopt logarithm of the issue amount and yield discrepancy asliquidity measure. The yield discrepancy is proposed as a liquidity measureby Kagraoka (2010). it is a difference in yields of a corporate bond betweenthe highest and the lowest of quoted yields by brokerage firms. If a corporatebond is liquid, quoted prices by brokerage firms are very close to each other.If a bond is illiquid, quoted prices by brokerage firms vary widely. Therefore,we expect that the yield discrepancy is greater for less liquid bonds. Weinclude a dummy variable for firms belonging to a financial sector.

We summarize our regression model for the spreads and their difference

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in the following,

(market spread) = β1(rating) + β2 log(issue amount)

+ β3(yield discrepancy) + β4(financial sector) + β5, (7)

(CDS-implied spread) = β1(rating) + β2 log(issue amount)


(market spread) − (CDS-implied spread)

= β1(rating) + β2 log(issue amount)


The coefficient parameters are estimated by panel analysis with time-fixedeffect

3. Data

Our database records quarterly CDS premiums and bond prices from2005Q3 to 2011Q3. The numbers of observations of CDSs and corporatebonds are given in Table 1. CDS maturity ranges from one to ten year; everyone year up to five year, seven and ten year. Time series of CDS premium ofJapan and that of recovery rate of Japan are depicted in Fig. 1. Time seriesof average CDS premium of Japanese firms by rating class are depicted inFig. 2-5.

JGB and corporate bond data are provided by the Japan Securities Deal-ers Association (JSDA). The JSDA has published the reference yields forover-the-counter bond transactions from August 2002. The reference yieldsare calculated by the JSDA, based on quotations reported by the designated-reporting members of the JSDA. The yield discrepancy is calculated from thehighest and lowest quotation by the designated-reporting members of theJSDA. We select corporate bonds by the following criterion; their couponrates are fixed, coupons are paid semi-annually, principal amount is fully re-paid at the maturity, without call or put provisions, and remaining term tomaturity of a bond is greater than one year.

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4. Empirical result

4.1. Estimation of the CDS-implied spread

We regard that the JGBs are not risk-free and sovereign CDS premiums ofJapan reflect its credit risk. We simultaneously estimate the term structureof the risk-free rate and the term structure of the default intensity of Japanby minimizing sum of squared pricing errors of the JGBs under constraintsthat theoretical premiums of the sovereign CDS exactly coincide with thecorresponding market premiums. The sum of squared pricing errors is definedas ∑

i

(PJGB,i − PJGB,i

PJGB,i

)2

, (10)

where PJGB,i and PJGB,i are the CDS-implied and market price of i-th JGB,respectively. The CDS-implied price of the JGB is calculated from eq. (3)with the default intensity estimated from the sovereign CDS premiums ofJapan. The theoretical premium of CDS is calculated from eqs. (4) and (5).Time series of the estimated term structure of the forward rate and that ofthe default intensity of Japan are shown in Fig. 6 and Fig. 7, respectively.

We assume that default risk of a firm is perfectly reflected in CDS pre-mium. We estimate term structure of the default intensity for each referencecompany so that the theoretical premiums of CDS exactly coincide with thecorresponding market premiums. Then CDS-implied price of a corporatebond is calculated by using eq. (3) 2. CDS-implied price of a corporate bondis estimated by using the risk-free rate and the default intensity of the is-suing company. The CDS-implied and market spread of a corporate bondis calculated from the corresponding CDS-implied and market bond price,respectively.

We calculate non-credit spread by subtracting the CDS-implied spreadfrom the market spread. Scatter plots of the CDS-implied and market spreadare provided in Fig. 8-14. Histograms of the non-credit spread are given inFig. 15-21.

2We verify that recovery rate does not affect our result. We set the recovery ratedepending on the credit rating. We also estimate the default intensity by taking thecommon recovery rate at 0.35, and we obtain similar result for the CDS-implied priceof corporate bond. This is because the fact that lower recovery rate is compensated byhigher level of default intensities and vice versa. Das and Hanouna (2009) discuss how toestimate the recovery rate from the market data.

8

4.2. Panel data analysisWe apply panel data model to three kinds of spreads; the market spread,

the CDS-implied spread, the non-credit spread defined as a difference betweenthe market and CDS-implied spread. If CDS has no liquidity risk, the CDS-implied spread purely arises from credit risk, and the difference betweenthe market and CDS-implied spread corresponds to non-credit risk, whichconsists of liquidity and other risk factors. Panel data model has manyversions, and we employ fixed-effects for time variable since CDS premiumsfluctuate wildly in the period as seen in Fig. 2-5. After the turmoil of thesub-prime loan crisis, CDS premiums are very high and corporate bonds areover-priced compared to CDS. Empirical results of the panel analysis aresummarized in Table 2-4.

We first examine the result for the market spread shown in Table 2. Theempirical result shows that all of the explanatory variables are statisticallysignificant. The adjusted R2 for the market spread is 0.684039. The creditspread is well explained by the credit rating; the coefficient to the credit rat-ing is 0.186671, and it implies that spread widen as credit rating deteriorates.The coefficient to the logarithm of issue amount is −0.039613, and it meansthat the larger issue amount has the tighter spread. Among the explanatoryvariables, the yield discrepancy is the most statistically significant, and thecoefficient to the yield discrepancy is 2.865461. This is another evidence thatthe yield discrepancy is an effective measure for liquidity risk. The coefficientto the financial sector is 0.265402, and it captures the fact that corporatebond spread for financial firm is higher than other firms.

Next we examine the result for the CDS-implied spread. The empiricalresult shows that all of the explanatory variables are statistically significant.The adjusted R2 for the CDS-implied spread is 0.684483, and it is comparableto the result for the market spread. All of the magnitude of the regressioncoefficient for the CDS-implied spread is greater than that for the marketspread. The credit spread is well explained by the credit rating; the coef-ficient to the credit rating is 0.212409, and it is slightly greater than thecoefficient for the market spread. It means that the CDS-implied spreadreflect bond credit rating stronger than the market spread. On contrary toour assumption that CDS has no liquidity risk, the result suggests that CDSpremium reflects the liquidity risk. The coefficient to the yield discrepancyis 4.108213. The coefficient to the logarithm of issue amount is 0.019584,however, it is not statistically significant at 95% confidence level. It is inter-esting to notice that one of the liquidity measure, the yield discrepancy, is

9

statistically significant while another measure, the logarithm of issue amountis not. This distinction is interpreted as follows. There exist two type of liq-uidity risk for corporate bonds, firm-specific and bond-specific ones. Theyield discrepancy is attributed to firm-specific liquidity risk, and the loga-rithm of issue amount is directly related to bond-specific liquidity risk. Thecoefficient to the financial sector is 0.435846, and it is also greater than themarket spread.

We investigate the results on liquidity proxies, yield discrepancy and loga-rithm of issue amount. We conjecture that there exists two types of liquidityrisk, company-specific liquidity and bond-specific one. The yield discrepancyreflects the company-specific liquidity, and it is statistically significant in themarket and CDS-implied spreads. The logarithm of issue amount is thebond-specific liquidity, and is statistically significant for the market spreadsbut the CDS-implied spread.

Finally, we examine the result for the non-credit spread. The result forthe CDS-implied spread suggests that it is not appropriate to call the differ-ence between the market and CDS-implied spread as the non-credit spread,however, we continue to use the term ”non-credit spread” for backward con-sistency. The adjusted R2 is 0.334428, and it is quite low compared to theresults for the market and CDS-implied spread. Except the coefficient tothe logarithm of the issue amount, signs of the coefficient for the non-creditspread are opposite to that for the market and CDS-implied spread. Thecoefficient to the logarithm of issue amount is −0.059196 and it is statisti-cally significant. Regarding the fact that the CDS-implied spread does notreflect the bond-specific liquidity risk, this is consistent with the result forthe market and CDS-implied spread. The coefficient to the credit rating, theyield discrepancy, and dummy variable for financial sector are −0.025739,−1.242753, and −0.170444, respectively. It is difficult to interpret these re-sult, and further investigation is needed.

5. Conclusion

Combining data on CDS premiums and corporate bond spreads, we studycredit risk embedded in the market and CDS-implied spreads of corporatebonds. The CDS-implied spreads are calculated by applying the reduced-form model for default risk and estimating the default intensity from CDSpremiums. Both spreads as well as their difference are investigated by paneldata analysis with time-fixed effects. Empirical study unveils that the market

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and CDS-implied spreads are well explained by the credit and liquidity mea-sures. It is found that CDS does not bear only credit risk but also liquidityrisk. The CDS-implied spread is explained by one of the liquidity measure,the yield discrepancy. The yield discrepancy is comparable for a firm, andthe yield discrepancy is a useful measure for firm-specific liquidity. In ourfuture study, we investigate the firm-specific liquidity risk in detail.

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References

Bielecki, Tomasz R., and Marek Rutkowski, 2010, Credit Risk: Modeling,Valuation and Hedging, Springer, Springer Finance.

Black, Fischer, and Myron Scholes, 1973, The pricing of options and corpo-rate liabilities, Journal of Political Economy 81, 637–654.

Roberto Blanco, Simon Brennan, and Ian W. Marsh, 2005, An EmpiricalAnalysis of the Dynamic Relation between Investment-Grade Bonds andCredit Default Swaps, The Journal of Finance 60, 2255–2281.

Das, Sanjiv R., and Paul Hanouna, 2009, Implied recovery, Journal of Eco-nomic Dynamics & Control 33, 1837–1857.

Das, Sanjiv R., and Rangarajan K. Sundaram, 2007, An integrated modelfor hybrid securities, Management Science 53, 1439–1451.

Duffie, Darrell, 2003, Credit Risk: Pricing, Measurement, and Management,Princeton University Press, Princeton Series in Finance.

Duffie, Darrell, and Jun Liu, 2001, Floating-fixed credit spreads, FinancialAnalysts Journal 57-3, 76–87.

Duffie, Darrell, and Kenneth J. Singleton, 1999 Modeling term structures ofdefaultable bonds, The Review of Financial Studies 12, 687–720.

Houweling, Patrick, and Ton Vorst, 2005, Pricing default swaps: Empiricalevidence, Journal of International Money and Finance 25, 1200–1225.

Hull, John, Mirela Predescu, and Alan White, 2004, The relationship betweencredit default swap spreads, bond yields, and credit rating announcements,Journal of Banking and Finance 28, 2789–2811.

Jarrow, Robert, 2001, Default parameter estimation using market prices,Financial Analysts Journal 57-5, 72–92.

Jarrow, Robert A., David Lando, and Stuart M. Turnbull, 1997, A Markovmodel for the term structure of credit risk spreads, The Review of FinancialStudies 10, 481–523.

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Kagraoka, Yusho, 2010, A time-varying common risk factor affecting corpo-rate yield spreads, The European Journal of Finance 16-6, 527–539.

Lando, David, 2004, Credit Risk Modeling: Theory and Applications, Prince-ton University Press, Princeton Series in Finance.

Longstaff, Francis A., Sanjay Mithal, and Eric Neis, 2005, Corporate yieldspreads: Default risk or liquidity? New evidence from the credit defaultswap market, The Journal of Finance 60, 2213–2253.

Unal, Haluk , Dilip Madan, and Levent Guntay, 2003, Pricing the risk ofrecovery in default with absolute priority rule violation, Journal of Banking& Finance 27, 1001–1025.

Schonbucher, Philipp J., 2003, Credit Derivatives Pricing Models: Model,Pricing and Implementation, Wiley.

Vasicek, Oldrich Alfons, 2001, EDFTM

credit measure and corporate bondpricing, Moody’s Analytics, working paper.

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Table 1: Description of observations.

date CDS bond2005Q3 60 5782005Q4 89 7112006Q1 101 8162006Q2 135 9142006Q3 154 9362006Q4 138 9022007Q1 156 9792007Q2 149 9442007Q3 153 9682007Q4 162 9892008Q1 145 9562008Q2 165 10272008Q3 162 10042008Q4 168 9732009Q1 168 9782009Q2 163 9652009Q3 164 9902009Q4 176 10262010Q1 175 10492010Q2 179 10722010Q3 150 10102010Q4 148 9882011Q1 137 9782011Q2 149 10082011Q3 147 1016

The numbers of observations of CDSs and corporate bonds are given. Thesecond and third column are the number of CDS and that of corporate bonds,respectively. We select firms which are assigned as reference entities of CDSsand issue corporate bonds.

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Table 2: Panel analysis for the market spread.

Coefficient Std. Error t-Statistic Prob.rating 0.186671 0.005905 31.6142 0.0000

log(amount) -0.039613 0.007119 -5.5640 0.0000yield discrepancy 2.865461 0.016954 169.0140 0.0000

financial 0.265402 0.010448 25.4012 0.0000interception 0.697658 0.176600 3.9505 0.0001

R2 0.684422Adjusted R2 0.684039

The result of panel analysis with period-fixed effect is given. The marketspread of a corporate bond is regressed by

(market spread) = β1(rating) + β2 log(issue amount)

+ β3(yield discrepancy) + β4(financial sector) + β5,

15

Table 3: Panel analysis for the CDS-implied spread.

Coefficient Std. Error t-Statistic Prob.rating 0.212409 0.008670 24.4986 0.0000

log(amount) 0.019584 0.010454 1.8733 0.0610yield discrepancy 4.108213 0.024895 165.0220 0.0000

financial 0.435846 0.015342 28.4082 0.0000interception -0.970817 0.259317 -3.7438 0.0002

R2 0.684866Adjusted R2 0.684483

The result of panel analysis with period-fixed effect is given. The CDS-implied spread of a corporate bond is regressed by

(CDS-implied spread) = β1(rating) + β2 log(issue amount)


The CDS-implied price is estimated from CDS premiums.

16

Table 4: Panel analysis for the non-credit spread.

Coefficient Std. Error t-Statistic Prob.rating -0.025739 0.006735 -3.8217 0.0001

log(amount) -0.059196 0.008120 -7.2898 0.0000yield discrepancy -1.242753 0.019338 -64.2657 0.0000

financial -0.170444 0.011917 -14.3021 0.0000interception 1.668475 0.201430 8.2831 0.0000

R2 0.335237Adjusted R2 0.334428

The result of panel analysis with period-fixed effect is given. The non-creditspread which is defined as a difference of the market and CDS-implied spreadis regressed by

(market spread) − (CDS-implied spread) = β1(rating) + β2 log(issue amount)


17

01/01/06 01/01/07 01/01/08 01/01/09 01/01/100

2

4

6

8

10

CDS premium for Japan

01/01/06 01/01/07 01/01/08 01/01/09 01/01/100

10

20

30

40

50

CDS recovery for Japan

1y

2y

3y

4y

5y

7y

10y

Figure 1: CDS premium of Japan.CDS premium and recovery rate of Japan.

18

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0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

CDS premium for Japanese Entities: 1 year

07/07/05 11/19/06 04/02/08 08/15/09 12/28/10 05/11/120

0.05

0.1

0.15

0.2

0.25

0.3

0.35


AAA

AA

A

BBB

BB

B

CCC

CC

C

NR

NUL

AAA

AA

A

BBB

BB

B

CCC

CC

C

NR

NUL

Figure 2: CDS premium of Japanese company.CDS premium of Japanese firm is averaged by rating class. The symbol ’NR’represents ’Not Rated’. The symbol ’NUL’ means that its rating data is notfulfilled.

19

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0.05

0.1

0.15

0.2

0.25

0.3

0.35


07/07/05 11/19/06 04/02/08 08/15/09 12/28/10 05/11/120

0.05

0.1

0.15

0.2

0.25


AAA

AA

A

BBB

BB

B

CCC

CC

C

NR

NUL

AAA

AA

A

BBB

BB

B

CCC

CC

C

NR

NUL


20

07/07/05 11/19/06 04/02/08 08/15/09 12/28/10 05/11/120

0.05

0.1

0.15

0.2

0.25


07/07/05 11/19/06 04/02/08 08/15/09 12/28/10 05/11/120

0.05

0.1

0.15

0.2

0.25


AAA

AA

A

BBB

BB

B

CCC

CC

C

NR

NUL

AAA

AA

A

BBB

BB

B

CCC

CC

C

NR

NUL


21

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0.05

0.1

0.15

0.2

0.25


AAA

AA

A

BBB

BB

B

CCC

CC

C

NR

NUL


22

1y 2y

3y 4y

5y 6y

7y 8y

9y10y

2005

2006

2007

2008

2009

2010

-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

Forward rate: JGB is risky

Figure 6: Risk-free rate by regarding JGBs are risky.The risk-free rate is estimated by regarding JGBs are risky. The CDS pre-miums of Japan is used to estimate their credit risk. The instantaneousforward rate is a step function with discontinuities at every one year in term-to-maturity.

23

1y

2y

3y

4y

5y

7y

10y

2005

2006

2007

2008

2009

2010

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Default intensity: JGB is risky

Figure 7: Default intensity of Japan.The default intensity of Japan in the reduced-form model is estimated. Thedefault intensity is a step function with discontinuities at every one year upto five year, seven and ten years.

24

-5 0 5 10 15 20

x 10-3

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

20050930

bond spread

cds-implied spread

-0.01 0 0.01 0.02 0.03 0.040

0.005

0.01

0.015

0.02

0.025

0.03

0.035

20051230

bond spread

cds-implied spread

Figure 8: Scatter plot for market and CDS-implied spreadsScatter plot for market and CDS-implied spread. X-axis is the market spread.Y-axis is the CDS-implied spread. The CDS-implied price is calculated byapplying the reduced-form model whose parameters are estimated from CDSpremiums.

25

-0.01 0 0.01 0.02 0.03 0.040

0.005

0.01

0.015

0.02

0.025

0.03

0.035

20060331

bond spread

cds-implied spread

-0.01 0 0.01 0.02 0.03 0.040

0.005

0.01

0.015

0.02

0.025

0.03

20060630

bond spread

cds-implied spread

0 0.01 0.02 0.03 0.04 0.050

0.01

0.02

0.03

0.04

0.05

20060929

bond spread

cds-implied spread

0 0.01 0.02 0.03 0.040

0.005

0.01

0.015

0.02

0.025

0.03

20061229

bond spread

cds-implied spread


26

0 0.01 0.02 0.03 0.040

0.005

0.01

0.015

0.02

0.025

0.03

20070330

bond spread

cds-implied spread

0 0.01 0.02 0.030

0.005

0.01

0.015

0.02

0.025

20070629

bond spread

cds-implied spread

0 0.02 0.04 0.06 0.080

0.005

0.01

0.015

0.02

0.025

0.03

0.035

20070928

bond spread

cds-implied spread

0 0.1 0.2 0.3 0.40

0.005

0.01

0.015

0.02

0.025

0.03

0.035

20071228

bond spread

cds-implied spread


27

0 0.2 0.4 0.6 0.80

0.01

0.02

0.03

0.04

0.05

0.06

20080331

bond spread

cds-implied spread

0 0.1 0.2 0.3 0.4 0.50

0.01

0.02

0.03

0.04

0.05

0.06

0.07

20080630

bond spread

cds-implied spread

0 0.2 0.4 0.6 0.80

0.05

0.1

0.15

0.2

20080930

bond spread

cds-implied spread

0 0.2 0.4 0.6 0.80

0.1

0.2

0.3

0.4

20081230

bond spread

cds-implied spread


28

0 0.2 0.4 0.6 0.80

0.05

0.1

0.15

0.2

20090331

bond spread

cds-implied spread

0 0.1 0.2 0.3 0.40

0.02

0.04

0.06

0.08

0.1

20090630

bond spread

cds-implied spread

0 0.1 0.2 0.3 0.40

0.05

0.1

0.15

0.2

20090930

bond spread

cds-implied spread

0 0.1 0.2 0.3 0.40

0.02

0.04

0.06

0.08

0.1

20091230

bond spread

cds-implied spread


29

0 0.05 0.1 0.15 0.2 0.250

0.01

0.02

0.03

0.04

0.05

0.06

20100331

bond spread

cds-implied spread

0 0.05 0.1 0.15 0.20

0.02

0.04

0.06

0.08

0.1

20100630

bond spread

cds-implied spread

0 0.05 0.1 0.15 0.2 0.250

0.05

0.1

0.15

0.2

0.25

20100930

bond spread

cds-implied spread

0 0.1 0.2 0.3 0.40

0.1

0.2

0.3

0.4

20101230

bond spread

cds-implied spread


30

0 0.05 0.1 0.15 0.2 0.250

0.02

0.04

0.06

0.08

20110331

bond spread

cds-implied spread

0 0.05 0.1 0.15 0.2 0.250

0.01

0.02

0.03

0.04

0.05

0.06

20110630

bond spread

cds-implied spread

0 0.1 0.2 0.3 0.40

0.1

0.2

0.3

0.4

20110930

bond spread

cds-implied spread


31

-0.15 -0.1 -0.05 0 0.050

50

100

150

200

20050930

[bond spread] - [cds-implied spread]

-0.15 -0.1 -0.05 0 0.050

50

100

150

200

20051230


Figure 15: Histogram of the non-credit spreadHistogram of the non-credit spread. The CDS-implied spread is subtractedfrom the market spread. The CDS-implied price is calculated by applying thereduced-form model whose parameters are estimated from CDS premiums.

32

-0.15 -0.1 -0.05 0 0.050

20

40

60

80

100

120

20060331


-0.15 -0.1 -0.05 0 0.050

50

100

150

200

20060630


-0.15 -0.1 -0.05 0 0.050

50

100

150

200

20060929


-0.15 -0.1 -0.05 0 0.050

50

100

150

200

20061229



33

-0.15 -0.1 -0.05 0 0.050

50

100

150

200

20070330


-0.15 -0.1 -0.05 0 0.050

50

100

150

20070629


-0.15 -0.1 -0.05 0 0.050

20

40

60

80

100

120

20070928


-0.15 -0.1 -0.05 0 0.050

20

40

60

80

100

120

140

20071228



34

-0.15 -0.1 -0.05 0 0.050

10

20

30

40

50

60

20080331


-0.15 -0.1 -0.05 0 0.050

10

20

30

40

50

60

20080630


-0.15 -0.1 -0.05 0 0.050

10

20

30

40

50

20080930


-0.15 -0.1 -0.05 0 0.050

5

10

15

20

25

30

20081230



35

-0.15 -0.1 -0.05 0 0.050

5

10

15

20

25

30

20090331


-0.15 -0.1 -0.05 0 0.050

10

20

30

40

50

60

70

20090630


-0.15 -0.1 -0.05 0 0.050

10

20

30

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50

60

20090930


-0.15 -0.1 -0.05 0 0.050

10

20

30

40

50

20091230



36

-0.15 -0.1 -0.05 0 0.050

10

20

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50

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20100331


-0.15 -0.1 -0.05 0 0.050

10

20

30

40

50

60

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20100630


-0.15 -0.1 -0.05 0 0.050

20

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80

20100930


-0.15 -0.1 -0.05 0 0.050

20

40

60

80

20101230



37

-0.15 -0.1 -0.05 0 0.050

10

20

30

40

50

60

20110331


-0.15 -0.1 -0.05 0 0.050

20

40

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100

20110630


-0.15 -0.1 -0.05 0 0.050

10

20

30

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20110930



38

Documents

Determinants of CDS premium and bond yield spread