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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 1 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 branchesthe 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- 7 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 8 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 11 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. 14 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 22