Determinants of Credit Default Swap Spread: Evidence from the Japanese Credit Derivative Market

Transcription

1 Determinants of Cred Default Swap Spread: Evidence from the Japanese Cred Derivative Market Keng-Yu Ho Department of Finance, National Taiwan Universy, Taipei, Taiwan Yu-Jen Hsiao Department of Finance, National Central Universy, Taoyuan, Taiwan Wen-Chi Lo Department of Finance, National Central Universy, Taoyuan, Taiwan This Draft: August 30, 2008 Preliminary version: Please do not quote whout permission.

2 Determinants of Cred Default Swap Spread: Evidence from the Japanese Cred Derivative Market Abstract In this paper, we investigate the determinants of cred default swap (CDS) spread for the Japanese market. Although the Japanese CDS market is one of the major markets in the world, to the best of our knowledge, there has been no related study so far. We thus contribute the lerature by focusing on the Japanese market. The empirical results show that the theoretical determinants perform well in explaining cross-sectional variation in the level of CDS spread. However, the model has rather limed explanatory power on the difference in the level of CDS spread. We also find that the effect of leverage, historical volatily, and risk-free rate are larger for lower cred rating firms than for higher cred rating firms in the level of CDS spread. In addion, on the difference in the level of CDS spread, the empirical results indicate that the lower the cred rating, the more sensive the changes in CDS spread are to the changes in the historical volatily and risk-free rate. Finally, our findings remain robust for different sub-sample periods and non-financial industry firms. JEL Classification: G00; G19 Keywords: Cred Default Swap Spread; Cred Risk; Structure Model 1

3 1. Introduction Cred derivative market, which emerged at the beginning of the 1990 s, has grown rapidly. The cred derivative instruments enable market participants to manage cred risk in much the same way as market risk. Among various types of cred derivative, cred default swap (CDS) is one of the most popular types. It provides a payoff equal to the loss-given default on bonds or loans of a reference enty (obligor), triggered by cred-related events such as default, bankruptcy, failure to pay, and restructuring. The buyer pays a premium as a percentage of the notional value of the bonds or loans each quarter, denoted as an annualized spread in basis points and receives the payoff from the seller should a cred-related event occur prior to the expiration of the contract. There are two major models for cred spread dynamics: (i) structural model and (ii) reduced-form model. Structure model derives from Black and Scholes (1973) and Merton (1974). This model assumes that a firm s value follows a stochastic process and the default occurs when the firm value falls below a certain threshold, such as the nominal value of debt. Therefore, the model s link wh a firm s economic fundamentals is explic. Collin-Dufresne, Goldstein, and Martin (2001) and Ericsson, Jacobs, and Oviedo (2005) suggest certain theoretical determinants of cred spread. First, leverage is the center of the model. The higher leverage of a firm, the higher the probabily of default. Second, the structural model implies that the debt claim has features similar to short posion in a put option. Increasing in volatily leads to higher option value and lower value of debt claim, resulting in higher cred spread. This prediction is intuive since increase volatily increase the probabily of default. Third, the level of the risk-free rate also affects the value of option. The risk-free rate determines the risk-adjusted drift of firm value and thus an increase in the risk-free rate tends to decrease risk-adjusted default 2

4 probabilies and also spread. The same argument has been shown in models in Longstaff and Schwartz (1995). Consequently there is a negative relationship between risk-free rate and cred spread. On the other hand, a reduced-form model (see Lterman and Iben (1991)); Jarrow and Turnbull (1995)) assumes that the mechanism governing a default process is unobservable and a latent factor known as default intensy determines the probabily of default. In this paper, we apply the structure model to the empirical examination of the Japanese CDS market, because explicly describes the default mechanism and enables us to analyze the relationship between cred spread and financial and macroeconomic variables. Several papers have studied theoretical determinants of corporate cred spread based on structural models. Collin-Dufresne, Goldstein and Martin (2001) investigate the determinants of cred spread changes. They use monthly data of U.S. industrial bonds July 1988 to December In the first model, they test the explanatory power of theoretical determinants on cred spread changes. The findings show that the effects of changes in leverage and implied volatily are posive on cred spread changes. The sign of the estimated coefficients of changes in a risk-free rate is significantly negative. However, the residuals in the above regression are highly cross-correlated, and they are mostly driven by a single common factor. Therefore, Collin-Dufresne, Goldstein and Martin (2001) further consider several financial and economic variables as candidate proxies for this factor. The results of the second model have slightly higher explanatory power, and the main results still hold. They also suggest that cred spread differences in the corporate bond market are mainly driven by local supply/demand shocks. 3

5 Unlike Collin-Dufresne, Goldstein and Martin (2001), Campell and Taksler (2003) and Cremers, Driessen, Maenhout, and Weinbaum (2006) study the effect of volatily on corporate bond spreads using different measures of volatily. Both studies confirm that volatily is an important determinant of cred spread. Zhang, Zhou and Zhu (2005) explore the determinants of cred spread from the CDS market. In contrast to Collin-Dufresne, Goldstein and Martin (2001) they use level of CDS spreads on 307 reference enties from 2001 to The results show that volatily and jump variables alone explain 54% of cred spreads. In addion, they find that the sensivy of volatily and jump is clearly higher among lower rated enties. Overall, their results are consistent wh the implications from structural models which incorporate stochastic volatily and jumps. These studies use corporate bond data to estimate cred spreads. Although there is a close relation between corporate bond and CDS spreads (see Duffie (1999)), the latter are preferable from several perspectives when analyzing the determinants of the shape of the cred curve (see Hull, Predescu, and Whe (2004); Blanco, Brennan, and Marsh (2005); Longstaff, Mhal, and Neis (2005); Ericsson, Jacobs, and Oviedo (2005)). Ericsson, Jacobs, and Oviedo (2005) examine the relationship between theoretical determinants of cred risk and actual CDS spreads. They use daily data on the U.S. companies from year The empirical results show that there is a posive relationship between CDS spread and leverage and volatily. In addion, there is a negative relation between CDS spread and risk-free rate. Overall, the results are robust across various specifications. There are also some previous studies using non-u.s. data. Cossin, Hricko, Aunon-Nerin, and Hyang (2002) use international data. However, their analysis is based 4

6 on 392 CDS quotes, majory of which are U.S. companies. They find that all of the theoretical factors have a significant influence and that taken together these factors drive much of the variation in the pricing of Cred Default Swaps. Jakovlev (2007) contributes the lerature by focusing on 50 European companies. Their empirical results concerning theoretical determinants are mixed, but mainly in line wh the previous studies. Although there are many empirical studies on the determinants of CDS spread in the U.S and Europe, to the best of our knowledge, there is no empirical study on CDS spread in Japan. Japan is one of the important cred derivative markets in the world. The CDS market in Japan has grown tremendously during the past years. Remolona and Shim (2008) shows that Asia-Pacific single-name CDS contracts comprise almost 25% of all those traded around the world. Most of the CDS contracts are traded in Japan. Since Japan plays an important role in the Asia-Pacific region, is of interest to study cred spread determinants using Japanese data and to fill the gap in the related lerature. We carry out a linear regression analysis on the relationship between CDS spread and the key variables suggested by economic theory of the structure model. Our findings show that the level in leverage and implied volatily are posively related to CDS spread. The sign of the estimated coefficients of level in the risk-free rate is negative. The above relations are consistent wh the theory wh statistical significance. Overall, we find that the CDS spread in Japan shares the same characteristics as those in the U.S. and Europe (see Ericsson, Jacobs and Oviedo (2005); Jakovlev (2007)). By separating our sample based on cred rating, we find that the effect of leverage, historical volatily, and risk-free rate are larger for lower cred rating firms than for higher cred rating firms in the level of CDS spread. In addion, on the difference in the level of CDS spread, the 5

7 empirical results indicate that the lower the cred rating, the more sensive the changes in CDS spread are to the changes in the historical volatily and risk-free rate. These results are also consistent wh the U.S. and Europe evidence. Finally, our findings remain robust after controlling different sub-sample period and non-financial industry firms. The rest of this paper is organized as follows. In section 2, we describe the data used in this study. In section 3, we present the regression models and analyze the empirical results. We report the results on robustness check in Section 4, and finally. Section 5 concludes the paper. 2. Data 2.1 Cred Default Swap For our analysis, we use the weekly compose spread of Japanese Yen-denominated five-year single-name CDS (Spread ), which is the most liquid and most common cred derivative in recent years (see Benkert (2004); Ericsson, Jacobs, and Oviedo (2005), Jakovlev (2007)). We obtain the data from a comprehensive database from the Mark Group. This database provides international daily CDS compose spreads on more than 3,000 individual obligors starting from The daily compose spreads are computed form quotes contributed by more than 30 banks and are undergone a statistical procedure where outliers and stale quotes are removed. In addion, three or more contributors are needed before a daily compose spread is calculated, ensuring a reasonable qualy of the data. 2.2 Firm-Level and Market Level Variables The data for the theoretical determinants of the CDS spread and other variables in the regression model are constructed as follows. 6

8 Leverage (leverage ): The leverage ratio is defined as Book Value of Debt Market Value of Equy + Book Value of Debt The market value of equy and book value of total liabilies are obtained from PACAP database. Historical Volatily (vol ): The time series of equy volatily is compute for each company using a shifting window of 180 daily returns obtained from PACAP database for every week. In the empirical lerature on the determinants of CDS spread, our approach is similar to that of Campbell and Taksler (2003), Cremers, Driessen, Maenhout, and Weinbaum (2006) and Jakovlev (2007). Benkert (2004), on the other hand, use implied volatily backed out from option data as well as historical volatily. Risk-Free Rate (r 2-year t ): Weekly data on 2-year Japan government bond yields are collected from Datastream database. Square of Treasury Bond Yield ( 2 year r t 2 ): To capture potential nonlinear effects due to convexy, we also include the squared level of the term structure for treasury bond. Slope of Yield Cure (slope t ): In order to measure the slope of the yield curve, we calculate the difference between 10-year and 2-year Japanese government bond yields also obtained from Datastream database. We interpret the economic influence of the yield curve as conveying information on business condions. For example in Longstaff and Schwartz (1995) model wh stochastic interest rate, short-term interest rates are in the long run expected to converge to long-term interest rate. Hence, an increase in the slope should lead to an increase in the expected future spot rate and lower CDS spread. On the other hand, an increase in yield curve slope may also imply an improving economy and thus lead to lower CDS spread. 7

9 Market Return (mrktret t ): We use weekly return on NIKKEI 225 index obtained form PACAP database as a proxy for the overall business climate. 2.3 Summary statistics To be included in the final sample, we require the obligors have at least 252 observations of the CDS spread, the 180-day historical volatily, and the leverage ratio. These requirement ensure that each obligor have at least one year of weekly data for the firm-level time-series regression analysis. This leaves us wh a final sample of 106 firms from January 2001 to December Panel A of Table 1 presents the cross-sectional summary statistics of the time-series mean of the variables. We observe that mean CDS spread is basis points, and the standard deviation is basis points, indicating that there are firms wh very high levels of CDS spreads. Panel B of Table 1 reports the correlation among variables. The preliminary results show that financial leverage, firm specific volatily, and the risk-free rate, suggested by economic theory, seem to be more related to the CDS spread. 3. Regression Analysis 3.1 Regression Models Most of previous studies on the determinants of cred spread use eher level or difference of cred spread. Here we conduct empirical analysis using both level and difference data for completeness. Since our data contain both cross-sectional and time-series dimensions, we apply a panel data regression framework wh fixed effect (see Campbell and Taksler (2003); Cremers, Driessen, Maenhout, and Weinbaum (2006); Jakovlev (2007)). First, we run univariate regressions for the CDS spread on each of the 8

10 explanatory variables based on the theory of the main determinants of cred spread, i.e., leverage, historical volatily, and risk-free rate. The univariate regressions for level data of CDS spread are as follows. Spread l i l i = α + β leverage + ε ; (1) Spread v i v i = α + β vol + ε ; (2) Spread r i r 2 year i r = α + β + ε. (3) Next, we run a multivariate regression for the CDS spread on all the three variables, as shown in Equation (4). Finally, we include other market-level explanatory variables, such as including, square of Treasury bond yield, slope of yield curve, and market return, for completeness. The model is shown as Equation (5). Spread 2 year 0 + α1leverage + α 2vol + α 3r ε ; (4) = α year 2 year = α0 + α1 + α2 + α3 + α4 Spread leverage vol r r + α slope + α mrktret + ε 5 6 (5) Similar regressions are run for the difference data of CDS spread. The analogues of the above five equations are shown as Spread l i l i = α + β leverage + ε ; (6) Spread v i v i = α + β vol + ε ; (7) Spread r i r i 2 year = α + β r + ε ; (8) Spread 2 year 0 + α1 leverage + α 2 vol + α 3 r ε ; (9) = α + Spread = α + α leverage 0 + α slope α vol + α mrktret ε + α r 3 2 year + α r year (10) 9

11 3.2 Regression Analysis on the Whole Sample We report the empirical results for the whole sample in Table 2. Panel A of Table 2 presents the results of level regressions: Models (1) to (5). A number of important findings are obtained. First, we find that the coefficients on leverage are significant and posive. Second, the coefficients on historical volatily are also posively significant. Third, the results on the risk-free rate confirm the theoretical expectation, because there is a significant negative relation between CDS spread level and risk-free rate. Our results are consistent wh the implications of structure model and wh prior lerature in the U.S. and Europe (see Ericsson, Jacobs and Oviedo (2005); Jakovlev (2007)). Furthermore, for the multivariate regression, we show that the coefficients on the slope of the yield curve and market return in Model (5) are negative, being consistent wh the theoretical predictions, for example in Longstaff and Schwartz (1995) model wh stochastic interest rate, short-term interest rate are in the long run expected to converge to long-term interest rate. Hence, an increase in the slope should lead to an increase in the expected future spot rate and lower CDS spread. Panel B of Table 2 presents the results of difference regressions, Models (6) to (10). The coefficients on historical volatily are posively significant and are consistent wh the theory. Although less significant, the results are consistent wh previous studies for risk-free rate. A rather surprising result is from Models (6) and (9), where we find that there is a negative relation between the difference in CDS spread and that in leverage ratio. However, the results are the same as Jakovlev (2007) s finding which are not significant at all. From the coefficient estimates, models using level data yields similar results as those 10

12 using differences data. We note that the explanatory power of the level regressions is much higher than that of the difference regressions. For the level regressions, the theoretical variables explain approximately 56% of the variation in CDS spread. For the difference regressions in the Japanese market, the theoretical variables explain difference in CDS spread much poorer than previous studies in the U.S. and European CDS markets (see Ericsson, Jacobs and Oviedo (2005); Jakovlev (2007)). 3.3 Regression Analysis Based on Cred Rating We observe a broad spectrum of different cred qualy, rating from AAA (investment-grade) to B (speculative-grade), among our sample firms. An important question is whether the determinants of cred spread would vary across firms wh different cred ratings. Since the cred rating is related to the overall level of cred risk of a firm, firm wh lower cred ratings are expected to have higher CDS spreads and to experience more abrupt changes in CDS spreads over time (see Cao, Yu and, Zhong (2006)). This intuion motivates us to divide our sample firms by cred rating. We partion our sample into two subgroups: A and above, and BBB and below. Panel A of Table 3 reports level panel data regression results partioned by cred rating. We find some differences across firms wh different cred ratings. For lower cred rating firms, leverage and historical volatily are more sensive to CDS spread than higher cred rating firms. These effects are intuive and consistent wh the predictions of the structural cred risk model. In addion, similar results are found for risk-free rate. Our evidence shows that the CDS spread for lower cred rating firms are more sensive to risk-free rate than higher cred rating firms. This is consistent wh the empirical findings in Duffie (1998) for the corporate bond yield spread and in Ericsson, 11

13 Jacobs, and Oviedo (2005) for the U.S. CDS spread. Panel B of Table 3 reports difference panel data regression results partioned by cred rating. The results are similar to those from level data regressions. The CDS spread for lower cred rating firms are more sensive to risk-free rate. The results are intuive since firms wh lower cred rating are closer to default boundary and thus they should be more sensive to risk-free rate. The Argument is also support by Cao, Yu and, Zhong (2006) and Jakovlev (2007). 3.4 Regression Analysis Based on Sub-Sample Period In this section, we spl our sample on two sub-sample periods evenly through our whole sample period. Panel A of Table 4 report regression results for level data. We find that, in general, the results for the sub-sample periods are very similar to each other and to the whole sample period results. The coefficient estimates on leverage and historical volatily are posively significant, and the coefficient estimates on the risk-free rate are negatively significant. The empirical findings are in line wh the theoretical expectations. Panel B of Table 4 presents the regression results for difference data. We find slightly different results between the two sub-sample periods. Specifically, risk-free rate plays a more significant role during 2001 to 2002 than during 2003 to On the other hand, the coefficient on the slope of yield curve is negatively significant for the second half of the sample period, while is not so for the first half. We suggest that the main reason behind these differences results may be due to different stages of the economy and the pattern in CDS market. In general, our results in Table 4 suggest that the theoretical explanatory variables remain robust to explain the CDS spread for different time periods in Japan. 12

14 3.5 Regression Analysis Based on Industry Previous related studies normally eliminate obligors in the financial sectors from the sample because of the difficulty in interpreting their capal structure variables (see Ericsson, Jacobs, and Oviedo (2005); Cao, Yu, and Zhong (2006)). Our study, however, include financial firms for completeness. In order to compare our results from the Japanese CDS market to those from the U.S. and European cred markets, we separate our sample into two sub-samples by industry: financial and non-financial industries. As can be seen from the regression results for non-financial industry in Table 5, the theoretical variables, such as leverage; historical volatily, and risk-free rate show similar results as the whole sample in Table 2. Regressions for level data again have higher explanatory power over regressions based on difference data. Specifically, the coefficient estimates on leverage is significant for level data regression, but not for difference data regression. Interestingly, the results for financial industry show different pattern, compared to non-financial industry. We find that, for level data regression, the coefficient on historical volatily is negatively significantly. That means higher firm risk would lead to lower CDS spread for that obligor. Such finding is not consistent wh the structure model s expectation and is not intuive. However, might be due to the characteristic of financial firms. 4. Robustness Check We mention earlier that our data are cross-sectional as well as time-series data. Therefore, in the previous section, we apply a panel data regression framework wh fixed effect on coefficient estimation following Campbell and Taksler (2003), Cremers, Driessen, Maenhout, and Weinbaum (2006), and Jakovlev (2007). In this section, we 13

15 conduct a robustness check using an alternative approach. Following Collin-Dufresne, Goldstein, and Martin (2001) and Ericsson, Jacobs, and Oviedo (2005), we estimate the coefficients by first running the time-series regressions for each firm and then calculate the cross-sectional mean of the estimated coefficients. Panel A of Table 6 presents the results of level data regressions. It is clear that the results from this alternative estimating approach are similar to those in the previous section. Leverage, historical volatily, and the risk-free rate are all significant, and the signs of the coefficient estimates are consistent wh the theory. The percentage for leverage wh t-statistic greater than 1.96 is around 62%, the percentage for historical volatily wh t-statistic greater than 1.96 is about 73%, and the percentage for risk-free rate wh t-statistic smaller than is lower at 49%. In other words, the level data regression results hold regardless of the estimation method. Panel B of Table 6 presents the results of difference data regression. However, none of the variable yields significant results from the alternative approach. 5. Conclusion This study investigates the determinants of CDS spread for the Japanese market. Japanese CDS market is one of the major markets in the world. While there are many prior studies on the determinants of CDS spread in the U.S and Europe, to the best of our knowledge, there is no empirical study on CDS spread in Japan. Our study contributes the lerature by filling the above gap and by studying the role of financial and macroeconomic variables in determining the dynamics of CDS spreads in Japan. We use the Japanese CDS data from 2001 to 2004 and apply a panel data regression approach wh fixed effect. We also examine both level and difference data on CDS spread for completeness. Our univariate regression analysis focuses on the three 14

16 theoretical determinants on CDS spread: a firm s leverage, a firm s historical volatily, and the risky-free rate. We further take into account other explanatory variables in the multivariate regression analysis. Our findings show that the effects of level in leverage and implied volatily on CDS spread are posively significant. On the other hand, there is a negative relation between risk-free rate and CDS spread. The empirical results show that the theoretical determinants perform well in explaining cross-sectional variation in the level of CDS spread. However, the model has rather limed explanatory power on the difference in the level of CDS spread. In general, our findings are consistent wh the theory wh statistical significance. We further separate the whole sample into sub-samples by various creria. By separating our sample based on cred rating, we find that the effect of leverage, historical volatily, and risk-free rate are larger for lower cred rating firms than for higher cred rating firms. In addion, the empirical results indicate that the lower the cred rating, the more sensive the changes in CDS spread are to the changes in the historical volatily and risk-free rate. These results are also consistent wh the U.S. and Europe evidence. Next, we spl our sample into two sub-sample periods evenly through our whole sample period. We find that, in general, the results for the sub-sample periods are very similar to each other and to the whole sample period results. The coefficient estimates on leverage and historical volatily are posively significant, and the coefficient estimates on the risk-free rate are negatively significant. Finally, taking into account of industrial effect, we separate our sample into two sub-samples based on financial and non-financial industries and find the theoretical variables, such as leverage; historical volatily, and risk-free rate, in regression results for 15

17 non-financial industry show similar results as the whole sample. However, the results for financial industry show different pattern, compared to non-financial industry, which may be due to unique characteristics of financial firms. In general, our findings remain robust after controlling different sub-sample period and non-financial industry firms. 16

18 Reference Benkert C., 2004, Explaining cred default swap premia, Journal of Futures Markets 24, Black, F. and Scholes, M., 1973, The pricing of options and corporate liabilies, Journal of Polical Economy 81, Blanco, R., Brennan, S., and Marsh, I.W., 2004, An empirical analysis of the dynamic relationship between investment grade bonds and cred default swap, Working Paper, Bank of England. Campbell, J.Y. and Taksler G.B., 2003, Equy volatily and corporate bond yields, Journal of Finance 58, Cao, C., Yu, F., and Zhong Z., 2007, The information content of option-implied volatily for cred default swap valuation, Working Paper, FDIC Center for Financial Research. Collin-Dufresne, P., Goldstein, R.S., and Martin, J.S., 2001, The determinants of cred spread changes, Journal of Finance 56, Cossin, D., Hricko, T., Aunon-Nerin, D., and Huang Z., 2002, Exploring for the determinants of cred risk in cred default swap transaction data: Is fixed-income markets information sufficient to evaluate cred risk? Working Paper, HEC. Cremers, M., Driessen, J., Maenhout, P.J., and Weinbaum, D., 2006, Individual stock-option prices and cred spreads, Working Paper, Yale Universy. Duffie, G.R., 1999, Estimating the price of default risk, Reviews of Financial Studies 12, Ericsson, J., Jacobs, K., and Oviedo, R., 2005, The determinants of cred default swap premia, forthcoming at Journal of Financial and Quantative Analysis. Hull, J.C., Predescu, M., and Whe, A., 2004, The relationship between cred default swap spread, bond yield, and cred rating announcement, Journal of Banking and Finance 28,

19 Jakovlev, M., 2007, Determiants of cred default swap spread: Evidence from European cred derivatives market, Working paper, Lappeenranta Universy of Technology. Jarrow, R.A., and Turnbull, S.M., 1995, Pricing derivatives wh cred risk, Journal of Finance 50, Lterman, R. and Iben, T., 1991, Corporate bond valuation and the term structure of cred spreads, Journal of Portfolio Management 17, Issue 3, Longstaff, F.A., Mhal, S., and Neis, E., 2005, Corporate yields spreads: Default risk or liquidy? New evidence from the cred default swap market, Journal of Finance 60, Longstaff, F. and Schwartz, E., 1995, A simple approach to valuing risky fixed and floating rate debt, Journal of Finance 50, Merton, R., 1974, On the pricing of corporate debt: The risk structure of interest rate, Journal of Finance 29, Remolona, E.M., and Shim, I., 2008, Cred derivatives and structured cred: The nascent markets of Asia and the Pacific, BIS Quarterly Review, Zhang, B.Y., Zhou, H., and Zhu, H., 2005, Explaining cred default swap spreads wh equy volatily and jump risks of individual firms, Working Paper, Bank of International Settlements. 18

20 Table 1 Summary Statistics for the Variables This table reports summary statistics for the variables used in this study. Variables definions are detailed in Sections 2.1 and 2.2. Panel A reports the mean, Q1 (25 th percentile), median, Q3 (75 th percentile) and standard deviation for each variable. We first obtain the time-series average of the variables for each firm and then average across firms during January 2001 to December Panel B reports average (across firms) correlation among variables. Panel A Cross-sectional statistics for time-series means Variables Mean Q1 Median Q3 Standard Deviation CDS Spread (basis point) Leverage Historical Volatily (%) Risk-Free Rate (%) Slope of Yield Curve (%) Market Return (%) Panel B Cross-sectional means of time series correlation between variable pairs Spread leverage vol 2-year r t Spread 1 leverage vol slope mrktret r t 2-year slope mrktret

21 Table 2 Regressions Results for Whole Sample The table reports the regression results of weekly data for the 106 firms over the period from January 2001 to December Variables definions are detailed in Section 2.1 and 2.2. Standard errors are reported in parentheses. ***, **, and * indicate significance at the 1, 5, and 10 percent levels, respectively. The regression coefficients are estimated under a panel data regression framework wh fixed effect. Variables Panel A: Regressions for Level Data (1) (2) (3) (4) (5) Intercept (0.0007)*** (0.0005)*** (0.0005)*** (0.0008)*** (0.0009)*** Leverage (0.0013)*** (0.0013)*** (0.0014)*** Historical Volatily (0.0001)*** (0.0001)*** (0.0001)*** Risk-Free Rate (0.1248)*** (0.1264)*** (0.4418)*** Square of Treasury Bond Yield (154.80)*** Slope of Yield Curve (0.0306)*** Market Return (0.0018) Adjusted R % 53.19% 51.09% 56.18% 56.76% Variables Panel B: Regressions for Difference Data (6) (7) (8) (9) (10) Intercept ( 10 4 ) (1.7200) (1.7100) (1.7100) (1.7200) (1.7200) Leverage (0.0017) (0.0017) (0.0018) Historical Volatily (0.0004)*** (0.0004)*** (0.0004)*** Risk-Free Rate (0.0933)* (0.0943)* (0.3041)** Square of Treasury Bond Yield (99.30) Slope of Yield Curve (0.0344)*** Market Return (0.0004) Adjusted R % 0.15% 0.11% 0.17% 0.31% 20

22 Table 3 Regressions Results by Cred Rating The table reports the regression results of weekly data for the 106 firms over the period from January 2001 to December We separate our whole sample into two sub-groups based on cred rating: A and above and BBB and below. Variables definions are detailed in Section 2.1 and 2.2. Standard errors are reported in parentheses. ***, **, and * indicate significance at the 1, 5, and 10 percent levels, respectively. The regression coefficients are estimated under a panel data regression framework wh fixed effect. Variables Panel A: Regressions for Level Data A and above (investment-grade) BBB and below (speculative-grade) Intercept (0.0003)*** (0.0027)*** Leverage (0.0006)*** (0.0029)*** Historical Volatily (0.0001)*** (0.0003)*** Risk-Free Rate (0.1623)*** (1.1134)*** Square of Treasury Bond Yield (56.44)*** (393.70)*** Slope of Yield Curve (0.0113)*** (0.0768)*** Market return (0.0007) (0.0042) Number of firms Adjusted R % 55.59% Variables Panel B: Regressions for Difference Data A and above (investment-grade) BBB and below (speculative-grade) Intercept ( 10 4 ) (0.5400) (2.6200) Leverage (0.0009)*** (0.0035) Historical Volatily (0.0002)*** (0.0009) Risk-Free Rate (0.1188) (0.7806)*** Square of Treasury Bond Yield ( ) (256.50)* Slope of Yield Curve (0.0141) (0.0813)*** Market Return (0.0002) (0.0011) Number of firms Adjusted R % 0.53% 21

23 Table 4 Regression Results by Sub-Sample Period The table reports the regression results of weekly data for the 106 firms over the period from January 2001 to December We separate our whole sample into two sub-groups based on sample period: 2001 to 2002 and 2003 to Variables definions are detailed in Section 2.1 and 2.2. Standard errors are reported in parentheses. ***, **, and * indicate significance at the 1, 5, and 10 percent levels, respectively. The regression coefficients are estimated under a panel data regression framework wh fixed effect. Variables Panel A: Regression for Level Data 2001~ ~2004 Intercept (0.0024)*** (0.0007)*** Leverage (0.0035)*** (0.0011)*** Historical Volatily (0.0005)*** (0.0001)*** Risk-Free Rate (0.8180)*** (0.4750)*** Square of Treasury Bond Yield (260.20)*** (165.00)*** Slope of Yield Curve (0.1155)* (0.0245)*** Market return (0.0103) (0.0010) Adjusted R % 80.96% Variables Panel B: Regression for Difference Data 2001~ ~2004 Intercept ( 10 4 ) (3.0000) (2.1700) Leverage (0.0026) (0.0025) Historical Volatily (0.0008)*** (0.0005)** Risk-Free Rate (0.4290)** (0.4902) Square of Treasury Bond Yield (136.60) (160.30) Slope of Yield Curve (0.0780) (0.0398)*** Market Return (0.0023) (0.0005) Adjusted R % 1.19% 22

24 Table 5 Regressions Results by Industry The table reports the regression results of weekly data for the 106 firms over the period from January 2001 to December We separate our whole sample into two sub-groups based on industry: financial industry and non-financial industry. Variables definions are detailed in Section 2.1 and 2.2. Standard errors are reported in parentheses. ***, **, and * indicate significance at the 1, 5, and 10 percent levels, respectively. The regression coefficients are estimated under a panel data regression framework wh fixed effect. Variables Panel A: Regression for Level Data Financial Industry Non-Financial Industry Intercept (0.0025)*** (0.0010)*** Leverage (0.0025)*** (0.0016)*** Historical Volatily (0.0003)*** (0.0001)*** Risk-Free Rate (1.0540)*** (0.4766)*** Square of Treasury Bond Yield (440.80)*** (164.30)*** Slope of Yield Curve (0.0644)*** (0.0330)*** Market Return (0.0034) (0.0020) Number of firms Adjusted R % 57.02% Variables Panel B: Regression for Difference Data Financial Industry Non-Financial Industry Intercept ( 10 4 ) (1.8000) (1.7800) Leverage (0.0033) (0.0019) Historical Volatily (0.0007) (0.0005)*** Risk-Free Rate (0.7135) (0.3290)*** Square of Treasury Bond Yield (254.10) (106.40) Slope of Yield Curve (0.0630) (0.0378)*** Market Return (0.0009) (.0005) Number of firms Adjusted R % 0.35% 23

25 Table 6 Robustness Check for Regression Analysis The table reports the regression results of weekly data for the 106 firms over the period from January 2001 to December Variables definions are detailed in Section 2.1 and 2.2. Standard errors are reported in parentheses. ***, **, and * indicate significance at the 1, 5, and 10 percent levels, respectively. The regression coefficients are obtained first by running the time-series regressions for each firm and then calculate the cross-sectional mean of the estimated coefficients. Adjusted R 2 is the mean of the adjusted R 2 s for each firm regression. The entries under t (explanatory variables)>1.96 (<-1.96) is the percentage of explanatory variables wh t-statistics greater (less) than 1.96 (-1.96). Variables Panel A Level Data Regressions Regression Panel B Difference Data Regressions Intercept (0.0042)*** (0.0052) ** ( ) ( ) Leverage (0.0060)*** (0.0065)*** ( ) ( ) Historical Volatily (0.0006)*** (0.0007) *** ( ) ( ) Risk-free Rate (0.4177)*** (1.7372) *** ( ) ( ) Square of treasury bond yield (1.7372) ( ) Slope of yield curve (680.21)** ( ) Market return (0.0061) ( ) Percentage of t (leverage) % 61.32% 15.09% 15.09% Percentage of t (leverage) % 9.43% 6.60% 6.60% Percentage of t (Vol) % 69.81% 8.49% 7.54% Percentage of t (Vol) % 12.26% 6.60% 7.54% Percentage of t (r 2-year t ) % 6.60% 2.83% 3.77% Percentage of t (r 2-yea t ) % 50.94% 3.77% 4.72% Adjusted R % 68.07% 3.68% 3.98% 24