Treasury Yields_ Equity Returns_ and Credit Spread Dynamics

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					Treasury Yields, Equity Returns, and Credit Spread Dynamics




                                            Yun Li*

                                            March 2003




*
 The author is a Ph. D. student in Finance from the University of Toronto.
Address for correspondence: Yun Li, Ph.D. student in Finance, Joseph L. Rotman School of
Management, University of Toronto, 105 St. George Street, Toronto, ON, Canada M5S 3E6
E-mail: yun.li02@rotman.utoronto.ca Bus: (416) 978-6648 Fax: (416) 978-5433
Treasury Yields, Equity Returns, and Credit Spread Dynamics                          Yun Li




                                         Abstract



This paper investigates how credit spreads respond to changes in the Treasury market and

the Equity market both in the short and long run. The analysis shows that various proxies

affect daily credit spread changes differently. As credit quality deteriorates, credit spread

changes become dependent on the short-end slope. The Fama and French systematic risk

factors are significant and negative. In the long run, credit spread is positively related to

volatility, two-year and 30-year Treasury yields; and is negatively related to S&P500

level. However, there is no cointegration in any pairs of credit spreads and Treasury

yields.




Keywords: corporate credit spread, Treasury yield, Equity return, cointegration




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Treasury Yields, Equity Returns, and Credit Spread Dynamics                        Yun Li


1. Introduction

In recent years, corporate credit risk has become an increasingly important and active

area of research. This issue plays a central role in the fixed income literature, primarily

because of its importance in the pricing of risky debt and credit derivatives.

   Existent theoretical models to quantify the effects of credit risk on bonds prices have

developed into two major branchesthe structural (also called the firm value) models

(e.g., Merton (1974), Leland (1994), Longstaff and Schwarz (1995), and Briys and de

Varenne (1997)), and the reduced-form (also called intensity) models (e.g., Jarrow and

Turnbull (1995), Jarrow et al. (1997), Duffie and Singleton (1999), Bielecki and

Rutkowski (2000), and Madan and Unal (2000)). Both approaches take into account

credit spreads as a central component in their pricing models.

   Credit spread is generally defined as the difference between yield-to-maturity on a

coupon-paying corporate bond and yield-to-maturity on a coupon-paying government

bond of the same maturity. A great many of empirical researches, such as Delianedis and

Geske (2001), and Elton et al. (2001), have been done subsequently to test the theoretical

results on credit spreads. They investigate the components of corporate credit spreads and

find that default and recovery risks are not the primary components of corporate credit

spreads, contrary to the traditional views as suggested by theories. They conclude that

taxes, jumps, liquidity, market risk factors, and interest rate factors all play a role in

explaining the credit spread.

   Two empirical papers are directly related to this paper. Collin-Dufresne et al. (2001)

use monthly quotes on straight industrial bonds for the period July 1988 through

December 1997 to investigate the determinants of credit spread changes. Their results


                                                2
Treasury Yields, Equity Returns, and Credit Spread Dynamics                        Yun Li


suggest that monthly credit spread changes are principally driven by local supply/demand

shocks that are independent of both credit-risk factors and standard proxies for liquidity.

Variables that should in theory determine credit spread changes have rather limited

explanatory power. Neal et al. (2000) use cointegration to model the monthly series of

Moody’s Aaa and Baa seasoned bond indices and 10-year constant maturity Treasury

bond rates for the period January 1960 to December 1997, for a total of 456 observations.

They find that Aaa, Baa, and Treasury rates are jointly cointegrated and the relation

between credit spreads and Treasury rates depends on the time horizon. In the short-run,

an increase in Treasury rates causes credit spreads to narrow. This effect is reversed over

the long run and higher rates cause spreads to widen.

   The purpose of this paper is to investigate how corporate credit spreads respond to

changes in the Treasury market and the Equity market both in the short run and in the

long run. This paper contributes to the literature in four ways.

   First, this paper studies the effects of Treasury yield curves on credit spreads in more

detail. Instead of using one short-run Treasury rate (e.g. Duffee (1998), and Delianedis

and Geske (2001)) or one long-run Treasury rate (e.g. Collin-Dufresne et al. (2001), and

Joutz et al. (2001)) as a measure of Treasury yield level, this paper examines how

corporate credit spreads respond to changes of different rates along the Treasury yield

curve. Furthermore, the impacts on credit spreads of different measures of slopes of

Treasury yield curve such as short-end slope and long-end slope are also examined.

   Second, this paper examines the roles of Equity market returns and volatilities in

credit spread changes.




                                                3
Treasury Yields, Equity Returns, and Credit Spread Dynamics                         Yun Li


   Third, this paper uses cointegration analysis to explore the long-run relations among

credit spreads, Treasury term structure characterized by the levels and the slopes, and

Equity market performance characterized by the level and volatilities.

   Fourth, due to the difficulty of collecting clean corporate bond data of all the ratings,

the existent practice of calculating credit spread from groups of bonds or bond indexes

and the Benchmark Treasury yield at the similar maturity using monthly dealer’s quotes

introduces inconsistency across different ratings more or less. This paper utilizes

expertise of Goldman Scachs and uses their daily spread of corporate bond index to

Treasuries of seven different ratings directly to avoid inconsistency of the credit spread

across different ratings brought by imprecise matching and rough calculation. These

spreads serve as an indicator of the level of credit spreads for many investors.

Furthermore, this data makes it possible to examine the properties of daily movements of

credit spread.

   I find that daily series of credit spreads of all the ratings are non-stationary. Changes

in credit spread of different ratings behave in different ways, and each has its own set of

explanatory factors. Economic variables that are suggested by theories to explain changes

in credit spread have rather limited explanatory power for the best rating AAA and the

worst rating CCC. Various proxies of Treasury market and Equity market affect change

in credit spread of different ratings in different ways. The sign of the yield level is not

simply negative as reported by many previous researchers. As credit quality deteriorates,

changes in credit spread become dependent on the short-end slope of the Treasury yield

curve. The Fama and French systematic risk factors are significant and negative as

expected most of the time.


                                                4
Treasury Yields, Equity Returns, and Credit Spread Dynamics                           Yun Li


   Credit spreads of ratings A, BB, and B are cointegrated with their significant

explanatory variables. The cointegrating relation can be interpreted as an equilibrium

expression for the determinants of credit spreads. In the long run, credit spread is

positively related to Equity market volatility, two-year Treasury yield, and 30-year

Treasury yield; and is negatively related to S&P 500 index level. The analysis suggests

different impacts of ten-year Treasury yield and the short-end slope of the Treasury yield

curve on credit spreads. The error correction coefficient is negative and statistically

significant for all the ratings. However, in contrast to Joutz et al. (2001), there is no

cointegration in any pair of credit spreads of all the seven ratings and different proxies for

the Treasury market viz. two-year Treasury yield, ten-year Treasury yield, 30-year

Treasury yield, and the short-end slope.

   The rest of this paper is structured as follows. Section 2 describes the data set of

corporate credit spreads and variables used to explain credit spread dynamics. Section 3

examines the effects of Treasury yields and Equity returns on credit spreads. Section 4

presents the cointegration analysis between credit spreads and their significant

explanatory variables. Section 5 estimates error-correction models. Section 6 concludes

the paper.



2. Data and Their Statistical Properties

The first objective of this paper is to investigate how well the proxies for the Treasury

market and the Equity market as suggested by theories explain observed changes in credit

spreads. Corporate credit spreads and proxies for both markets are discussed as follows.




                                                5
Treasury Yields, Equity Returns, and Credit Spread Dynamics                          Yun Li


A. Corporate Credit Spreads

Goldman Scachs’ daily spreads of corporate bond index to Treasuries of seven different

ratings (AAA, AA, A, BBB, BB, B, and CCC) for the period 26 July 2001 through 31

December 2002, for a total of 356 observations, are retrieved from Bloomberg. Table 1

provides descriptive statistics for credit spreads. The mean and standard deviation of

credit spreads increase as ratings decline. This increase becomes larger as credit quality

deteriorates from investment to speculative grade.

                                    Table 1 about here

B. Treasury Markets

Treasury rate level and the slope characterize Treasury yield curve. Instead of using one

short-run Treasury rate (e.g. Duffee (1998), and Delianedis and Geske (2001)) or one

long-run Treasury rate (e.g. Collin-Dufresne et al. (2001), and Joutz et al. (2001)) as a

measure of Treasury yield level, this paper examines how corporate credit spreads

respond to changes of different rates along the Treasury yield curve. Therefore,

Datastream’s daily series of one-month Treasury yield, three-month Treasury yield, six-

month Treasury yield, two-year Treasury yield, ten-year Treasury yield, and 30-year

Treasury yield are employed in this paper.

   Furthermore, two slopes of Treasury yield curve are defined in this paper. One is the

short-end slope (SLP1), defined as the difference between Datastream’s two-year and

one-month Treasury yields. The other is the long-end slope (SLOPE), defined as the

difference between Datastream’s 30-year and one-month Treasury yields. Slope can be

interpreted as both an indication of expectations of future short rates, and as an indication




                                                6
Treasury Yields, Equity Returns, and Credit Spread Dynamics                          Yun Li


of overall economic health. I also include the prime rate as a proxy for the overall state of

the economy.

C. Equity Markets

Equity returns and volatilities characterize Equity market. I use the Fama and French

factors to measure systematic risk on the Equity market, which includes the excess return

on the market (EXCRET) i.e. the value-weighted return on all NYSE, AMEX, and

NASDAQ stocks minus the one-month Treasury bill rate, SMB (Small Minus Big) i.e.

the average return on the three small portfolios minus the average return on the three big

portfolios, and HML (High Minus Low) i.e. the average return on the two value

portfolios minus the average return on the two growth portfolios. The excess return on

the market measures the overall health of the Equity market. I also include daily series of

value-weighted return with dividends (VWRETD) from CRSP. It is only for a market of

stocks as identified by the S&P 500 Composite Index. To detect the potential

cointegration between corporate credit spreads and the Equity market, I also include level

of the Standard & Poor's Composite (SPIDX) retrieved from CRSP.

   To measure the Equity market volatility, two volatility indexes are employed in this

paper. One is the VIX index, which measures the volatility of the U.S. Equity market

based on the implied volatility of OEX (S&P 100) index options. The other is VXN

index, which is the newest benchmark of “tech stock” volatility based on the implied

volatility of Nasdaq-100 index options.

   Before performing any econometric analysis, it is important to check stationarity of

the time series under study. Table 2 reports the Augmented Dickey-Fuller test statistic for

credit spreads of seven ratings and their explanatory variables. The Augmented Dickey-


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Treasury Yields, Equity Returns, and Credit Spread Dynamics                             Yun Li


Fuller test equation includes an intercept and tests for unit root in level with two lagged

differences.

                                     Table 2 about here

   Table 2 shows that the hypothesis of unit root, with stationarity as the alternative, is

rejected for all the credit spreads. These results confirm the findings of Pedrosa and Roll

(1998) and Joutz et al. (2001) that credit spreads are non-stationary. For the Treasury

market variables, yields in the short end such as one-month, three-month, and six-month

are stationary at the 5%, 5%, and 10% level of significance respectively, while yields

with longer maturity such as two-year, ten-year, and 30-year have a unit root. Slopes

exhibit opposite patterns. Short-end slope has a unit root, whereas long-end slope is

stationary at the 10% level of significance. Prime rate, a proxy for the overall state of the

economy, is stationary at the 10% level of significance.

   For the Equity market variables, various equity returns including the Fama and French

systematic risk factors and value-weighted return with dividends on S&P 500 Composite

Index are stationary at the 1% level of significance, as expected. Volatilities and S&P 500

index have a unit root.

   Table 2 also provides the results of the stationarity test on the first differences of credit

spreads and their explanatory variables. The evidence suggests that first differences are

stationary at the 1% level of significance.



3. Determinants of Credit Spreads

In this section, I examine whether the economic variables suggested by theories have a

statistically significant effect on changes in credit spreads of different ratings from AAA


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Treasury Yields, Equity Returns, and Credit Spread Dynamics                                             Yun Li


to CCC. The explanatory variables in the regression for changes in credit spreads involve

one-month Treasury yield (TB1M), three-month Treasury yield (TB3M), six-month

Treasury yield (TB6M), changes in the two-year Treasury yield (TB2Y), changes in the

ten-year Treasury yield (TB10Y), changes in the 30-year Treasury yield (TB30Y),

changes in the short-end slope (SLP1), long-end slope (SLOPE), prime rate, the excess

return on the market (EXCRET), SMB, HML, value-weighted return with dividends on

S&P 500 (VWRETD), changes in the level of the S&P 500 (SPIDX), changes in VIX,

and changes in VXN. To complete the regression, the constant term, the autoregressive

term of lag one, and the moving average term are also included in the regression, totalling

19 variables. The choice of lag one is basically for parsimony as well as based on the

theory that the lag-one variable in general contains the most information.

    The objective of this empirical test is to show what economic factors are statistically

significant in explaining changes in credit spreads of each rating. To this end, I include

all of the 19 variables in the regression for each rating at the very start. Next, I exclude

the most insignificant variable from the regression based on the p-value and perform

another regression on the remaining variables.1 This procedure continues until each of the

remaining variables is statistically significant at the 10% level of significance at least.

The resulting model is the “best” economic model for the examined credit spread changes

and is reported in Table 3.

                                            Table 3 about here

    Table 3 shows that changes in credit spread of different ratings behave in different

ways, and each has its own set of explanatory factors. Economic variables that are


1
  A variable is regarded as the most insignificant variable in a regression if its p-value is over 0.1 and is the
largest among all.
                                                          9
Treasury Yields, Equity Returns, and Credit Spread Dynamics                         Yun Li


suggested by theories to explain changes in credit spread have rather limited explanatory

power for the best rating AAA (9%) and the worst rating CCC (8%). For the rest of

investment grades, economic variables suggested by theories explain 23% to 28% of

changes in credit spreads. These results are consistent with Collin-Dufresne et al. (2001).

However, economic variables suggested by theories have much more power in explaining

changes in credit spreads of speculative grades. They explain 64% and 44% of changes in

credit spreads for ratings BB and B respectively.

   Overall, change in credit spread of lag one is statistically significant in explaining

change in credit spread of each rating except rating B at the 0.1% level of significance.

Change in credit spread increases with change in credit spread of lag one, except that

change in credit spread of rating AAA moves in the opposite direction. Various proxies

of Treasury market and Equity market affect change in credit spread of different ratings

in different ways.

   The “best” economic model suggests that more than one yield on the Treasury yield

curve is significant in the regression across ratings. Different ratings have different

significant yields. The sign of the yield level is not simply negative as reported by many

previous researchers. Changes in credit spread may move in the same direction as some

yields but may move in the opposite with other yields along the curve. This

diversification in signs helps fit complicated changes of credit spread of different ratings

in the reality.

   In contrast to Collin-Dufresne et al. (2001), slopes are not always negative in the

regression either. Changes in credit spread of rating AA and CCC increase with slopes.

And slopes do not have explanatory power for rating B. As credit quality deteriorates,


                                                10
Treasury Yields, Equity Returns, and Credit Spread Dynamics                          Yun Li


changes in credit spread become dependent on the short-end slope of the Treasury yield

curve. Besides, prime rate is statistically significant for the investment grade and displays

a negative sign.

   Changes in Equity market volatilities are significant only for ratings AA, B, and CCC

with a sign of negative, negative, and positive respectively. Interestingly, change in credit

spread for investment grade AA is negatively related to “tech stock” volatility (VXN)

change. Whereas, changes in credit spread for speculative grades B and CCC move with

the overall Equity market volatility (VIX) change. The Fama and French systematic risk

factors are significant and negative as expected most of the time. On the whole, S&P 500

value-weighted return and change in S&P 500 level are significant in explaining changes

in credit spread of investment grade and are positively related to changes in credit spread.



4. Cointegration Analysis

The fact that daily series of credit spreads and their significant explanatory variables are

non-stationary induces a test for a cointgrating vector. The essence of a cointegrating

relationship is that a linear combination of non-stationary variables can be stationary.

Thus, a cointegrating vector indicates a long-run relationship between the variables. The

test for the presence of a cointegrating vector between credit spreads and their significant

explanatory variables suggested by the “best” economic model is performed using the

Johansen maximum likelihood procedure with two lags (similar to the ADF tests) and is

reported in Table 4.

                                    Table 4 about here




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Treasury Yields, Equity Returns, and Credit Spread Dynamics                          Yun Li


   Table 4 shows that not all of the credit spreads are cointegrated with their significant

explanatory variables. Trace test indicates one cointegrating equation at the 5% level for

rating A and one cointegrating equation at both 5% and 1% levels for ratings BB and B.

The cointegrating relation can be interpreted as an equilibrium expression for the

determinants of credit spreads. These findings are consistent with Joutz et al. (2001)

except that my analysis does not support cointegration between credit spreads of ratings

AA and BBB and Treasury yields. To confirm this result, I also test the presence of a

cointegrating vector in a pair of credit spreads of all the seven ratings and various proxies

for the Treasury market viz. two-year Treasury yield, ten-year Treasury yield, 30-year

Treasury yield,      and the short-end slope, using the Johansen maximum likelihood

procedure with two lags. However, there is no cointegration in any pairs.



5. Error Correction Models

Having detected the long-run relation between credit spreads of ratings A, BB, and B and

their significant explanatory variables, naturally, I start to estimate error correction

models (ECMs) to examine how these factors affect credit spreads in the short and long

run. ECMs combine the information from the short run dynamics of the credit spreads

while directly incorporating the long run relation revealed in the cointegration analysis.

Tables 5 and 6 provide the cointegrating vectors and estimation statistics of the error

correction models.

                                 Tables 5 and 6 about here

   Table 5 shows that almost all variables in the cointegrating vectors are significant

except ten-year Treasury yield for rating BB. In the long run, credit spread is positively


                                                12
Treasury Yields, Equity Returns, and Credit Spread Dynamics                       Yun Li


related to Equity market volatility, two-year Treasury yield, and 30-year Treasury yield;

and is negatively related to S&P 500 index level. However, the analysis suggests

different impacts of ten-year Treasury yield and the short-end slope of the Treasury yield

curve on credit spreads. For rating A, credit spread is negatively related to ten-year

Treasury yield and is positively related to the short-end slope, whereas it is positively

related to ten-year Treasury yield and is negatively related to the short-end slope for

rating BB.

   Table 6 shows that the error correction coefficient is negative and statistically

significant for all the ratings. The results from the cointegration analysis and from the

error correction models suggest that there is a long-run relationship for ratings A, BB,

and B. On the whole, changes in credit spread are positively related to changes in Equity

market volatility of lag one, changes in the two-year Treasury yield of lag one, and

changes in the 30-year Treasury yield of lag one; and are negatively related to changes in

the S&P 500 index level of lag one. The signs of the relations are consistent with those

from the cointegrating vectors, except that change in credit spread of rating BB is

positively related to change in the short-end slope of lag one. Amongst the significant

exogenous variables, changes in credit spread are negatively related to Treasury yields,

the long-end slope, and the Fama and French systematic risk factors.



6. Conclusion

This paper examines the relations between changes in corporate credit spreads and

changes in the Treasury market and the Equity market both in the short run and in the

long run. Based on daily data from 26 July 2001 through 31 December 2002, for a total


                                                13
Treasury Yields, Equity Returns, and Credit Spread Dynamics                         Yun Li


of 356 observations, I find that daily series of credit spreads of all the ratings are non-

stationary, but changes in credit spreads are stationary at the 1% level of significance. I

start the analysis by investigating how well economic variables suggested by literature

explain changes in credit spread of all the seven ratings. Then, the presence of stationary

cointegrating vectors between credit spreads and their significant explanatory variables is

examined to discover their equilibrium relations.

   The results suggest that changes in credit spread of different ratings behave in

different ways, and each has its own set of explanatory factors. Various proxies of

Treasury market and Equity market affect daily credit spread changes differently. As

credit quality deteriorates, changes in credit spread become dependent on the short-end

slope of the Treasury yield curve. The Fama and French systematic risk factors are

significant and negative as expected most of the time.

   Credit spreads of ratings A, BB, and B are cointegrated with their significant

explanatory variables. In the long run, credit spread is positively related to Equity market

volatility, two-year Treasury yield, and 30-year Treasury yield; and is negatively related

to S&P 500 index level. The analysis suggests different impacts of ten-year Treasury

yield and the short-end slope of the Treasury yield curve on credit spreads. However, my

analysis does not support cointegration in any pair of credit spreads of all the seven

ratings and various proxies for the Treasury market viz. two-year Treasury yield, ten-year

Treasury yield, 30-year Treasury yield, and the short-end slope.




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Treasury Yields, Equity Returns, and Credit Spread Dynamics                      Yun Li


References

Bielecki, Tomasz R., and Marek Rutkowski, 2000, Multiple Ratings Model of

      Defaultable Term Structure, Mathematical Finance 10, 125-139.

Briys, E., and F. de Varenne, 1997, Valuing Risky Fixed Rate Debt: An Extension,

      Journal of Financial and Quantitative Analysis 32, 239-248.

Collin-Dufresne, P., R. Goldstein, and J. Martin, 2001, The Determinants of Credit

      Spread Changes, Journal of Finance 56, 2177-2207.

Delianedis, G. and R. Geske, 2001, The Components of Corporate Credit Spreads:

      Default, Recovery, Tax, Jumps, Liquidity, and Market Factors, Working Paper,

      UCLA.

Duffie, Darrell, and Kenneth J. Singleton, 1999, Modeling the Term Structures of

      Defaultable Bonds, Review of Financial Studies 12, 687-720.

Duffee, Gregory R., 1998, The Relation Between Treasury Yields and Corporate Bond

      Yield Spreads, Journal of Finance 53, 2225-2241.

Elton, Edwin J., Martin J. Gruber, Deepak Agrawal, and Christopher Mann, 2001,

      Explaining the Rate Spread on Corporate Bonds, Journal of Finance 56, 247-277.

Fama, E. F. and K. R. French, 1993, Common risk factors in the returns on stocks and

      bonds, Journal of Financial Economics 33, 3-56.

Jarrow, R., and S. Turnbull, 1995, Pricing Derivatives on Financial Securities Subject to

      Credit Risk, Journal of Finance 50, 53-85.

Jarrow, R., D. Lando, and S. Turnbull, 1997, A Markov Model for the Term Structure of

      Credit Risk Spreads, Review of Financial Studies 10, 481-523.




                                                15
Treasury Yields, Equity Returns, and Credit Spread Dynamics                   Yun Li


Joutz, Fred, Sattar A. Mansi, and William F. Maxwell, 2001, The Dynamics of Corporate

      Credit Spreads, Working Paper, George Washington University and Texas Tech

      University.

Leland, Hayne E., 1994, Corporate Debt Value, Bond Covenants, and Optimal Capital

      Structure, Journal of Finance 49, 1213-1252.

Longstaff, Francis A., and Eduardo S. Schwartz, 1995, A Simple Approach to Valuing

      Risky Fixed and Floating Rate Debt, Journal of Finance 50, 789-819.

Madan, Dilip and Haluk Unal, 2000, A Two-Factor Hazard Rate Model for Pricing Risky

      Debt and the Term Structure of Credit Spreads, Journal of Financial and

      Quantitative Analysis 35, 43-65.

Merton, Robert C., 1974, On the Pricing of Corporate Debt: The Risk Structure of

      Interest Rates, Journal of Finance 29, 449-470.

Neal, Robert, Doug Rolph, and Charles Morris, 2000, Interest Rates and Credit Spread

      Dynamics, Working Paper, Indiana University, University of Washington, and

      Federal Reserve Bank of Kansas City.

Pedrosa, M. and R. Roll, 1998, Systematic risk in corporate bond spreads, Journal of

      Fixed Income 8, 7-26.




                                                16
Treasury Yields, Equity Returns, and Credit Spread Dynamics                        Yun Li


                   Table 1 Descriptive Statistics for Credit Spreads

This table reports descriptive statistics for Goldman Scachs’ daily spreads of corporate
bond index to Treasuries of seven different ratings (AAA, AA, A, BBB, BB, B, and
CCC) for the period 26 July 2001 through 31 December 2002, for a total of 356
observations, retrieved from Bloomberg. Reported statistics are the mean, standard
deviation, median, skewness, and kurtosis for all the ratings.



                   Mean           Std. Dev.       Median   Skewness     Kurtosis
     AAA          70.7574           8.7780        70.0000    0.3274     -0.5299
     AA           96.6226          16.2367        96.0000   -0.1491      0.0130
     A           141.2393         19.9098        135.7600    0.6545     -0.6696
     BBB          259.6967         53.1581       237.3550    1.2727      0.4503
     BB          541.6288          99.9084       515.5150    0.4506     -1.1278
     B           904.8617         136.5213       934.6800   -0.1760     -1.4001
     CCC         2384.6317        317.9022       2365.0800   0.0526     -0.9649




                                                17
Treasury Yields, Equity Returns, and Credit Spread Dynamics                        Yun Li


                     Table 2 Augmented Dickey-Fuller Test Statistic

This table presents ADF test statistic for credit spreads of seven ratings and their
explanatory variables. The Augmented Dickey-Fuller test equation includes an intercept
and tests for unit root in level with two lagged differences. MacKinnon critical values for
rejection of null hypothesis of a unit root are -3.4508 for 1% significance, -2.8699 for
5% significance, and -2.5712 for 10% significance. Significance at 1% is denoted by ***,
at 5% by **, and at 10% by *.


         Variable                       Level                 First Difference
         aaa                           -1.9618                  -10.1283***
         aa                            -1.3596                  -10.7808***
         a                             -1.6411                  -10.2909***
         bbb                           -1.6141                  -10.6485***
         bb                            -1.2222                  -9.9683***
         b                             -1.0992                  -10.5892***
         ccc                           -1.1026                  -10.5307***
         vxn                           -2.4136                  -11.1981***
         vix                           -2.123                   -12.2451***
         tb1m                         -2.8883**                 -9.2324***
         tb3m                         -3.149**                  -8.9927***
         tb6m                         -2.7809*                  -9.7663***
         tb2y                          -1.0666                  -11.9804***
         tb10y                         -0.9989                  -11.8599***
         tb30y                         -1.4658                  -11.4286***
         slope                        -2.7649*                  -9.7697***
         slope1                        -1.6319                  -12.1076***
         prime                         -2.768*                  -11.1273***
         excretmkt                   -11.3156***                -20.0559***
         smb                         -9.7333***                 -18.0641***
         hml                         -10.5748***                -18.9087***
         vwretd                      -11.615***                 -20.1505***
         spindx                        -1.1399                  -12.2427***



                                                  18
Treasury Yields, Equity Returns, and Credit Spread Dynamics                                                Yun Li




                                           Table 3 Estimation Statistics for the Best Economic Models

This table reports the estimation statistics of the “best” economic models. AD1(-1) represents change in credit spread of lag one for
rating A. C represents the constant term. MA(1) denotes the moving average term.


   AAA
   Variable   AAAD1(-1)    TB1M       TB6M       SLOPE       EXCRET       HML       VWRETD SPIDXD1          MA(1)                                                 Adj. R2
   Coef        -0.4588     -2.6684    2.8825     -0.1925      -2.6313    -0.2892     298.2073 -0.0720       0.4159                                                0.0905
   p-value     0.0007      0.0066     0.0077      0.0778      0.0004     0.0967      0.0001      0.0012     0.0044
   AA
   Variable   AAD1(-1)     VXND1      TB1M        TB3M       TB2YD1     TB10YD1 TB30YD1         SLOPE      PRIME       HML      VWRETD       MA(1)                Adj. R2
   Coef        0.8484      -0.1066    3.2371      -2.7090     5.0033     -10.2256 6.1702        0.2743     -0.4016    -0.4377    -59.2349    -0.9899              0.2274
   p-value     0.0000      0.0218     0.0000      0.0000      0.0012     0.0016      0.0457      0.0000     0.0000    0.0002     0.0000      0.0000
   A
   Variable    AD1(-1)     TB3M       TB6M       TB10YD1 TB30YD1         SLOPE      SLP1D1      PRIME      EXCRET      HML      SPIDXD1      MA(1)                Adj. R2
   Coef        0.5374      5.1225     -3.2458     -16.7574 20.8281       0.7282     -4.1869     -1.1742     -1.6802   -0.6656    0.0908      -0.5450              0.2767
   p-value     0.0000      0.0275     0.0562      0.0040      0.0007     0.0233      0.0477      0.0144     0.0001    0.0114     0.0224      0.0000
   BBB
   Variable   BBBD1(-1)     TB1M      TB3M        TB6M       TB2YD1     TB10YD1 TB30YD1         SLP1D1 EXCRET          SMB      VWRETD       MA(1)                Adj. R2
   Coef        0.5256      -8.3622    13.0164     -4.5263    19.9108     -34.2913 25.6832       -21.6765 -21.3227     3.7408    1973.6970    -0.3965              0.2802
   p-value     0.0000      0.0561     0.0453      0.0848      0.0143     0.0274      0.0629      0.0000     0.0000    0.0000     0.0000      0.0000
   BB
   Variable       C       BBD1(-1)     TB1M      TB3M        TB2YD1     TB10YD1     SLP1D1      EXCRET       SMB       HML      SPIDXD1      MA(1)                Adj. R2
   Coef        -2.2812     0.1467     -18.5883   20.0475     -42.7745    -41.3989   -15.3362     -3.9467    -1.3443   -1.9338    0.2583      -0.1603              0.6406
   p-value     0.0393      0.0003     0.0003      0.0003      0.0000     0.0000      0.0074      0.0000     0.0190    0.0049     0.0042      0.0179
   B
   Variable    VIXD1        TB1M      TB3M       TB2YD1      EXCRET       HML                                                                                     Adj. R2
   Coef        -1.4304     -29.6873   29.6188    -122.5973    -3.8311    -4.0810                                                                                  0.4441
   p-value     0.0159      0.0046     0.0052      0.0000      0.0001     0.0041
   CCC
   Variable       C       CCCD1(-1)   VIXD1       TB1M       TB3M        TB6M       TB30YD1     SLOPE      SLP1D1 EXCRET          SMB       VWRETD      MA(1)     Adj. R2
   Coef        -21.3209    0.8805     2.6959     -18.2836    44.3972    -22.5786     -91.5299   4.5138     55.4148 -33.7243      6.3570     3484.9530   -0.9899   0.0800
   p-value     0.0009      0.0000     0.0723      0.0987      0.0108     0.0020      0.0027      0.0017     0.0098    0.0299     0.0186      0.0264     0.0000




                                                               19
Treasury Yields, Equity Returns, and Credit Spread Dynamics                                     Yun Li


                                Table 4 Cointegration Results

This table reports cointegraiton test between credit spread and its significant explanatory
variables suggested by the “best” economic model using the Johansen maximum likelihood
procedure with two lags for each rating. * (**) denotes rejection of the hypothesis at the 5% (1%)
level.

                                         Panel A: AAA SPINDX
       Hypothesized         Eigenvalue        Trace             5 Percent        1 Percent
       No. of CE(s)                          Statistic        Critical Value   Critical Value
       None                  0.013641        7.297472             12.53            16.31
       At most 1             0.006913        2.448899              3.84            6.51
                              Panel B: AA VXN TB2Y TB10Y TB30Y
       Hypothesized         Eigenvalue        Trace             5 Percent        1 Percent
       No. of CE(s)                          Statistic        Critical Value   Critical Value
       None                  0.050144         42.5568             59.46            66.52
       At most 1             0.035659        24.39674             39.89            45.58
                            Panel C: A TB10Y TB30Y SLOPE1 SPINDX
       Hypothesized         Eigenvalue        Trace             5 Percent        1 Percent
       No. of CE(s)                          Statistic        Critical Value   Critical Value
       None *                0.080441        59.59388             59.46            66.52
       At most 1             0.048505        29.99076             39.89            45.58
                            Panel D: BBB TB2Y TB10Y TB30Y SLOPE1
       Hypothesized         Eigenvalue        Trace             5 Percent        1 Percent
       No. of CE(s)                          Statistic        Critical Value   Critical Value
       None                  0.042383        37.56424             59.46            66.52
       At most 1             0.035275        22.27674             39.89            45.58
                      Panel E: BB TB2Y TB10Y SLOPE1 SPINDX (with constant)
       Hypothesized         Eigenvalue        Trace             5 Percent        1 Percent
       No. of CE(s)                          Statistic        Critical Value   Critical Value
       None **               0.092241        85.85112             76.07            84.45
       At most 1             0.072675        51.68898             53.12            60.16
                                         Panel F: B VIX TB2Y
       Hypothesized         Eigenvalue        Trace             5 Percent        1 Percent
       No. of CE(s)                          Statistic        Critical Value   Critical Value
       None **               0.068027        32.14594             24.31            29.75
       At most 1             0.01191         7.276502             12.53            16.31
                         Panel G: CCC VIX TB30Y SLOPE1 (with constant)
       Hypothesized         Eigenvalue        Trace             5 Percent        1 Percent
       No. of CE(s)                          Statistic        Critical Value   Critical Value
       None                  0.047045         35.594              53.12            60.16
       At most 1             0.029443        18.58393             34.91            41.07


                                                         20
Treasury Yields, Equity Returns, and Credit Spread Dynamics                         Yun Li




                                                Table 5 Estimates of Cointegrating Vectors

This table reports estimates of the cointegrating vector for credit spreads and their significant explanatory variables suggested by the
“best” economic model using the Johansen maximum likelihood procedure with two lags for ratings A, BB, and B. Other stationary
variables suggested by the “best” economic model are included as exogenous variables. CS(-1) represents credit spread with lag one.
t-statistics are reported in [ ].


                      CS(-1)        VIX(-1)         TB2Y(-1)     TB10Y(-1)    TB30Y(-1)      SLOPE1(-1)    SPINDX(-1)        C
     A(-1)             1.00                                       1547.26      -4797.04        -1441.91        0.80
                                                                 [ 9.72949]   [-28.4933]      [-14.9803]    [ 3.50516]
     BB(-1)            1.00                         -11135.82       -9.84                      10103.37        4.59       -3989.68
                                                    [-17.4468]   [-0.02543]                   [ 19.6180]    [ 5.99082]   [-3.71892]
     B(-1)             1.00          -26.41           -108.86
                                   [-14.1845]       [-2.72309]




                                                     21
Treasury Yields, Equity Returns, and Credit Spread Dynamics                          Yun Li


              Table 6 Estimation Statistics for the Error Correction Models

This table reports the estimation statistics of the error correction models. CointEq1 is the
error correction term. D(A(-1)) represents change in credit spread of lag one for rating A.
t-statistics are reported in [ ].


  Variables            D(A)      Variables          D(BB)      Variables           D(B)
  CointEq1           -0.00101    CointEq1         -0.003155    CointEq1         -0.033527
                    [-2.02636]                    [-4.43446]                    [-4.53416]
  D(A(-1))           0.037498    D(BB(-1))         0.090411    D(B(-1))          0.027603
                    [ 0.69100]                    [ 1.22803]                    [ 0.44221]
  D(A(-2))           0.076574    D(BB(-2))         0.119773    D(B(-2))          0.03327
                    [ 1.57625]                    [ 1.67567]                    [ 0.53260]
  D(TB10Y(-1))       -31.9722    D(TB2Y(-1))       15.42868    D(VIX(-1))        0.583227
                    [-4.99387]                    [ 1.12489]                    [ 1.26830]
  D(TB10Y(-2))       6.266938    D(TB2Y(-2))      -1.124405    D(VIX(-2))       -0.303699
                    [ 0.93399]                    [-0.08044]                    [-0.66395]
  D(TB30Y(-1))       37.70905    D(TB10Y(-1))     -8.327254    D(TB2Y(-1))       4.848829
                    [ 5.57200]                    [-0.63614]                    [ 0.36878]
  D(TB30Y(-2))      -8.717922    D(TB10Y(-2))      26.73789    D(TB2Y(-2))       7.221947
                    [-1.21062]                    [ 2.01815]                    [ 0.55145]
  D(SLOPE1(-1))      4.880017    D(SLOPE1(-1))     5.02273     TB1M              27.84399
                    [ 2.03913]                    [ 0.57137]                    [ 2.20123]
  D(SLOPE1(-2))     -1.190087    D(SLOPE1(-2))     0.708825    TB3M             -31.42589
                    [-0.51384]                    [ 0.08653]                    [-2.40894]
  D(SPINDX(-1))     -0.051819    D(SPINDX(-1))    -0.123694    EXCRETMKT        -5.281871
                    [-4.30724]                    [-3.45773]                    [-7.92908]
  D(SPINDX(-2))     -0.016913    D(SPINDX(-2))    -0.085798    HML              -3.256012
                    [-1.38408]                    [-2.37411]                    [-1.89570]
  TB3M               6.309436    TB3M              -34.8391
                    [ 1.45910]                    [-4.40957]
  TB6M              -6.969492    EXCRETMKT        -3.487449
                    [-2.12244]                    [-8.40989]
  SLOPE             -2.800481    SMB              -1.264027
                    [-1.42896]                    [-1.50493]
  PRIME             -1.548646    HML               -1.95766
                    [-1.78372]                    [-1.95086]
  EXCRETMKT         -0.820487
                    [-6.21228]
  HML               -0.677155
                    [-2.08735]
  Adj. R-squared     0.280335    Adj. R-squared    0.289296    Adj. R-squared   0.210993




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