# Liquidity, Credit Risk, and Their Interaction on the Spreads in China’s Corporate Bond Market

Authors: Zijian Wu; Baochen Yang; Yunpeng Su
Journal: Discrete Dynamics in Nature and Society
 (2022)

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## Abstract

This paper investigates the impact of multidimension liquidity, credit risk, and the interaction between liquidity and credit risk on corporate bond spreads based on a large transaction data set from July, 2006 to June, 2016, including the monthly data of 3716 bonds in China. Our main findings reveal that liquidity premiums are the main parts of corporate bond spreads. The interaction between liquidity and credit risk plays a significant role in determining corporate bond spreads. In addition, the differences between the interbank market and the exchange market have a significant impact on corporate bond spreads in normal period, and the interaction between liquidity and credit risk has an enhanced impact on corporate bond spreads during financial crisis. We also find that the interaction between liquidity and credit risk will increase with the increase of liquidity risk and credit risk and it is a time-varying dynamic process.


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## Body

## 1. Introduction

Several literature studies investigate the determinants of corporate yield spreads and link them to credit risk and liquidity [1–3]. Huang and Huang [4] use structural bond pricing models and find that credit risk accounts for only a small fraction of bond spreads. Collin-Dufresn et al. [5] document a large unexplained portion of bond spreads which are driven mainly by factors that are independent of credit risk. Consequently, many researchers focus on the potential for liquidity to explain a large portion of bond yield spreads [6–8]. Lin et al. [9] and Acharya et al. [10] find that liquidity risk is priced in corporate bonds returns. The relevant literature can also refer to Zou et al. [11]; Dick-Nielsen et al. [12]; and Helwege et al. [13]. In addition, by proposing a new illiquidity measure, Longstaff et al. [7] discover that credit risk is the main determinant of corporate yield spreads. Covitz and Downing [14] report similar findings with Longstaff et al. [7] through investigating very short-term commercial paper issued by nonfinancial U.S. corporations.The impact of the two types of risk on the spreads has been discussed in several literature studies. Longstaff and Schwartz [15] find that the correlation between default risk and the interest rate has a significant impact on the properties of the credit spreads. Several literature studies have discussed the impact of liquidity and credit risk on spreads [16–20]. Ericsson and Renault [16] analyze the interaction between liquidity and credit risk in theory. Studies by Chen et al. [8]; Covitz and Downing [14]; Rossi [21]; and Kalimipalli and Nayak [22] provide evidence that liquidity impacts are mingled with credit risk impacts on bond yield spreads. Wang and Wu [23] find strong evidence of a significant interactive impact of liquidity and credit risk, magnifying during the financial crisis period. Sperna Weiland et al. [24] propose a novel way of modeling credit-liquidity interactions through mutually exciting processes. Chen et al. [25] develop a structural credit risk model to examine how the interactions of liquidity and default risk affect corporate bond pricing. Li et al. [26] propose a generalized bond pricing model, accounting for all the impacts of credit risk, liquidity risk, and their correlation, and they extend the traditional bond pricing model with only credit risk by incorporating liquidity risk into the framework in which the probabilities of the two risk events are estimated by a joint distribution.In fact, previous literature regarding the above tends to focus on how liquidity or credit component contributed to the yield spreads independently in China’s corporate bond market. Ai et al. [27] discuss the impact of the interaction term on corporate bond spreads by using a single dimensional liquidity measure. Different from previous literature, this paper investigates liquidity in different dimensions from the perspective of speculative trading and investment trading and introduces dynamic credit risk and static credit risk. And the paper also studies different types of the interaction between liquidity and credit risk on corporate bond spreads and explains their affecting mechanism and market transmission channels. For example, dynamic credit risk represents the credit risk level of a firm over time, and it changes in resonance with the dynamic change of liquidity risk. When liquidity affects asset prices, dynamic credit risk usually interacts with liquidity risk in a dynamic spiral, forming the resonance enhancement interaction between liquidity and credit risk to dynamically affect asset prices. This study aims to provide a deeper understanding of the impact of multidimension liquidity, credit risk, and the interaction between liquidity and credit risk on the spreads in China. This paper uses a large transaction data set from July 2006 to June 2016, including the monthly data of 3716 bonds in China’s bond market.Our research contributes to the literature in four ways. First, we select multidimension liquidity measures from the Chinese corporate bond market, which can measure liquidity more comprehensively. We select bonds in China’s interbank market and exchange market and construct many liquidity measures from three dimensions of trading activity, price shock and bond life time. Many scholars construct the liquidity measure of corporate bonds from a single dimension or several dimensions, which only reflects a certain dimension or several dimensions of liquidity. Our method of multidimension liquidity measures is more accurate and reliable than those used in the existing literature.Second, we introduce the interaction between liquidity and credit risk into the spread model. Our results demonstrate that the interaction between liquidity and credit risk plays a significant role in determining yield spreads in China's bond market, and such findings are robust to the alternative proxies for liquidity and credit risk with various model specifications. It shows that the impact of the interaction between liquidity and credit risk on bond spreads is significant in China’s bond market. Therefore, we note that liquidity and credit risk alone does not explain the entire yield-spread behavior. This study provides evidence regarding the significant impact of the interaction between liquidity and credit risk on the spreads.Third, we investigates liquidity premiums from multiple dimensions and find that liquidity premiums are the main parts of corporate bond spreads in China’s corporate bond market. This finding is consistent with Collin-Dufresn et al. [5] and Huang and Huang [4].Finally, dummy variables are introduced to eliminate the impact of the differences in the structure of the interbank market and the exchange market on the results, because the differences between the two markets are taken into account. The research shows that the results are consistent when the characteristics of the two markets are taken into account, and the interaction between liquidity and credit risk has a significant impact on corporate bond spreads, and the impact is greater during financial crisis.Our main findings are as follows. First, liquidity premiums are the main parts of corporate bond spreads in China’s corporate bond market. Second, the interaction between liquidity and credit risk on bond spreads plays a significant role in determining corporate bond spreads and liquidity and credit risk alone does not explain the entire yield-spread behavior. The interaction between liquidity and credit risk will increase with the increase of liquidity risk and credit risk, and it is a time-varying dynamic process. Related research can also refer to Sperna Weiland et al. [24] and Chen et al. [25]. Third, the interaction between liquidity and credit risk has an enhanced impact on corporate bond spreads during financial crisis than normal period. And the differences between the interbank market and the exchange market have a significant impact on corporate bond spreads in normal period than financial crisis. Finally, dynamic credit risk changes in resonance with the dynamic change of liquidity risk, while the static credit risk does not change with the dynamic change of liquidity risk.The rest of this paper is organized as follows. Section2 describes the selected variables and the hypothesis; Section 3 elaborates on the empirical results; Section 4 gives the results of robustness test; and Section 5 presents our conclusions.


## 2. Data and Sample

### 2.1. Data and Sample Description

We use a sample of corporate bonds in WIND database during the period July, 2006 to June, 2016. We collect data on bond liquidity and credit risk from WIND database, no transaction of bonds is removed. When bonds are less than a year’s remaining trading time, we drop the corresponding observations from the sample as these bonds are rarely traded. Finally, we have 47436 observations, a total of 3716 bonds, including 2281 interbank bonds and 1435 exchange bonds. In addition, we collect data for issuer characteristics and the trading volume, trading days, the yield to maturity, the highest price, the lowest price, the average price, the remaining life, age, credit rating, coupon rate and historical price, and the proxies of liquidity and credit risk are calculated based on the above data. In many cases, bonds with time-to-maturity of less than 12 months are especially unlikely to trade, so we exclude such bonds with time-to-maturity of less than 12 months from the sample [28].


### 2.2. Selected Variables and Hypothesis

#### 2.2.1. Spread

The Spread is the difference between the yield-to-maturity on the corporate bond and the corresponding Treasury rate. When calculating the spread sequence, we selected corporate bonds and treasury bonds with the same maturity yield period to calculate spread by subtraction. We primarily use existing treasury data, but where unavailable we use estimated data from WIND database. Our analysis employs the spread of each bond as a dependent variable in the regression model.


#### 2.2.2. Liquidity Measures

There is no consensus on how to measure the liquidity of an asset so we examine a number of liquidity-related measures for corporate bonds. The following describes the measures and their implementation in more detail. In this study, we select multidimension liquidity measures, which can measure liquidity more comprehensively. The liquidity proxies used in this analysis include the following seven liquidity measures: turnover, trade vol, day, amihud, range, time-to-maturity and age.Turnover is the frequency of market assets trading hands in a certain period. In general, therefore, this proxy is expected to be negatively related to yield spreads. The second liquidity measure is Vol, it is obtained by dividing the total trading volume with the number of months during which the issue is traded. The common expectation is that this variable is expected to have an inverse relation with the yield spreads. Day is defined as the number of trading days in the corresponding month. This variable is expected to be negatively related to yield spreads. Following the amihud measure [29], we construct a monthly liquidity measure proxy to describe the liquidity. We construct a monthly liquidity measure proxy of Range based on Han and Zhou [30]. The disadvantage of this measure is that it should be sensitive to outliers. Time-to-Maturity is the time left until maturity from the issuance date of a security and is a liquidity measure proxy [7, 14, 31]. Age is defined as the age of bond transactions since the issue in the corresponding month. Researchers frequently proxy for the liquidity of a corporate bond with its age [32–35]. A number of problems with studying liquidity in corporate bonds arise from the fact that corporate bonds trade only infrequently [33, 36]. Therefore, the liquidity is closely related to age.


#### 2.2.3. Credit Risk Measures

This study considers three credit risk variables as explanatory variables. They are rating, coupon and volatility.Rating is the credit rating assigned to each security that a firm issues [14, 37]. Our study adopts the coding method of Covitz and Downing [14] and Shin and Kim [37] for credit ratings: AAA = 1, AA+ = 2, …, and C = 14. We assign the lower credit rating to 15. Obviously, a positive relationship is expected between yield spreads and credit ratings. Coupon refers to the coupon rate of bonds [7, 38]. Longstaff et al. [7] and Bharath and Shumway [38] show that coupon rates have significantly positive correlation with yield spreads. See also Chen et al. [39] or Lin et al. [9]. As expected, the coupon of bond issued by firm with higher default risk is significantly high, other things being constant. Thus, we expect the coefficient of the coupon rate to be positive. Hull [40] uses the historical price volatility of corporate bonds as a measure of the bond's credit. Volatility is the historical price volatility of corporate bonds, and it is estimated from the past historical prices of 125 days. It is well known that as a firm approaches default, the risk associated with its debt also increases, and such risk is correlated to the bond volatility. Accordingly, we expect the Volatility to have a positive correlation with bond spreads.


#### 2.2.4. Hypothesis

Turnover, Vol, Day are the proxies of trading activity [3, 12, 37]. The greater the values is, more active the bond transaction is, which shows that the bond liquidity risk is smaller, and the spreads are smaller. Therefore, Turnover, Vol, Day have negative relation with spreads in the corporate bond market. Time-to-Maturity represents the remaining life of the bond. These bonds close to maturity are rarely traded, and the bond holders often choose to hold them until maturity, and they will not be traded, so the coefficient of Time-to-Maturity is negative [14, 31]. New bonds are not more liquid than older ones. Because of information asymmetry, when new bonds are issued, investors will not buy and trade. Over time, for more than two years, investors will choose to buy the bonds. Then the bond transactions become active, and the spreads begin to become small. Therefore, Age and spreads are negative correlation [33, 34]. Based on the above analysis, we propose hypothesis H1.H1: turnover, vol, day, age and time-to-maturity have negative relation with spreads in the corporate bond market.Range and Amihud are the liquidity proxies of price impact [29, 30, 37]. When trading a certain amount of bonds, the greater the bond price changes caused by the transaction, which indicates that the liquidity is poorer, so the bond spreads are also larger. Therefore, Amihud and Range have positive correlation with the bond spreads. Rating, Coupon, and Volatility are the proxies of credit risk [14, 38–40]. The greater the value is, the worse credit is, and the greater the spreads are. So Rating, Coupon, and Volatility have positive relation with spreads in the corporate bond market. Based on the above analysis, we propose hypothesis H2.H2: range, amihud, rating, coupon, and volatility have positive relation with spreads in the corporate bond market.Ericsson and Renault [16] prove theoretically that the liquidity and credit risk are correlated, and the interaction of liquidity and credit risk is present. When liquidity is low, default risk of bonds tends to be high, suggesting the possibility of an interactive impact of liquidity and default risk. It directly draws on the implications that the interaction of liquidity and credit risk is present. See also Chen et al. [25] or Li et al. [26]. We test this hypothesis using data of bonds with different liquidity and credit characteristics such as Age, Vol, Day, Amihud and Coupon. We now turn to empirical tests. Based on the above analysis, we propose hypothesis H3.H3: the interaction between liquidity and credit risk has a significant impact on corporate bond spreads.


## 2.1. Data and Sample Description

We use a sample of corporate bonds in WIND database during the period July, 2006 to June, 2016. We collect data on bond liquidity and credit risk from WIND database, no transaction of bonds is removed. When bonds are less than a year’s remaining trading time, we drop the corresponding observations from the sample as these bonds are rarely traded. Finally, we have 47436 observations, a total of 3716 bonds, including 2281 interbank bonds and 1435 exchange bonds. In addition, we collect data for issuer characteristics and the trading volume, trading days, the yield to maturity, the highest price, the lowest price, the average price, the remaining life, age, credit rating, coupon rate and historical price, and the proxies of liquidity and credit risk are calculated based on the above data. In many cases, bonds with time-to-maturity of less than 12 months are especially unlikely to trade, so we exclude such bonds with time-to-maturity of less than 12 months from the sample [28].


## 2.2. Selected Variables and Hypothesis

### 2.2.1. Spread

The Spread is the difference between the yield-to-maturity on the corporate bond and the corresponding Treasury rate. When calculating the spread sequence, we selected corporate bonds and treasury bonds with the same maturity yield period to calculate spread by subtraction. We primarily use existing treasury data, but where unavailable we use estimated data from WIND database. Our analysis employs the spread of each bond as a dependent variable in the regression model.


### 2.2.2. Liquidity Measures

There is no consensus on how to measure the liquidity of an asset so we examine a number of liquidity-related measures for corporate bonds. The following describes the measures and their implementation in more detail. In this study, we select multidimension liquidity measures, which can measure liquidity more comprehensively. The liquidity proxies used in this analysis include the following seven liquidity measures: turnover, trade vol, day, amihud, range, time-to-maturity and age.Turnover is the frequency of market assets trading hands in a certain period. In general, therefore, this proxy is expected to be negatively related to yield spreads. The second liquidity measure is Vol, it is obtained by dividing the total trading volume with the number of months during which the issue is traded. The common expectation is that this variable is expected to have an inverse relation with the yield spreads. Day is defined as the number of trading days in the corresponding month. This variable is expected to be negatively related to yield spreads. Following the amihud measure [29], we construct a monthly liquidity measure proxy to describe the liquidity. We construct a monthly liquidity measure proxy of Range based on Han and Zhou [30]. The disadvantage of this measure is that it should be sensitive to outliers. Time-to-Maturity is the time left until maturity from the issuance date of a security and is a liquidity measure proxy [7, 14, 31]. Age is defined as the age of bond transactions since the issue in the corresponding month. Researchers frequently proxy for the liquidity of a corporate bond with its age [32–35]. A number of problems with studying liquidity in corporate bonds arise from the fact that corporate bonds trade only infrequently [33, 36]. Therefore, the liquidity is closely related to age.


### 2.2.3. Credit Risk Measures

This study considers three credit risk variables as explanatory variables. They are rating, coupon and volatility.Rating is the credit rating assigned to each security that a firm issues [14, 37]. Our study adopts the coding method of Covitz and Downing [14] and Shin and Kim [37] for credit ratings: AAA = 1, AA+ = 2, …, and C = 14. We assign the lower credit rating to 15. Obviously, a positive relationship is expected between yield spreads and credit ratings. Coupon refers to the coupon rate of bonds [7, 38]. Longstaff et al. [7] and Bharath and Shumway [38] show that coupon rates have significantly positive correlation with yield spreads. See also Chen et al. [39] or Lin et al. [9]. As expected, the coupon of bond issued by firm with higher default risk is significantly high, other things being constant. Thus, we expect the coefficient of the coupon rate to be positive. Hull [40] uses the historical price volatility of corporate bonds as a measure of the bond's credit. Volatility is the historical price volatility of corporate bonds, and it is estimated from the past historical prices of 125 days. It is well known that as a firm approaches default, the risk associated with its debt also increases, and such risk is correlated to the bond volatility. Accordingly, we expect the Volatility to have a positive correlation with bond spreads.


### 2.2.4. Hypothesis

Turnover, Vol, Day are the proxies of trading activity [3, 12, 37]. The greater the values is, more active the bond transaction is, which shows that the bond liquidity risk is smaller, and the spreads are smaller. Therefore, Turnover, Vol, Day have negative relation with spreads in the corporate bond market. Time-to-Maturity represents the remaining life of the bond. These bonds close to maturity are rarely traded, and the bond holders often choose to hold them until maturity, and they will not be traded, so the coefficient of Time-to-Maturity is negative [14, 31]. New bonds are not more liquid than older ones. Because of information asymmetry, when new bonds are issued, investors will not buy and trade. Over time, for more than two years, investors will choose to buy the bonds. Then the bond transactions become active, and the spreads begin to become small. Therefore, Age and spreads are negative correlation [33, 34]. Based on the above analysis, we propose hypothesis H1.H1: turnover, vol, day, age and time-to-maturity have negative relation with spreads in the corporate bond market.Range and Amihud are the liquidity proxies of price impact [29, 30, 37]. When trading a certain amount of bonds, the greater the bond price changes caused by the transaction, which indicates that the liquidity is poorer, so the bond spreads are also larger. Therefore, Amihud and Range have positive correlation with the bond spreads. Rating, Coupon, and Volatility are the proxies of credit risk [14, 38–40]. The greater the value is, the worse credit is, and the greater the spreads are. So Rating, Coupon, and Volatility have positive relation with spreads in the corporate bond market. Based on the above analysis, we propose hypothesis H2.H2: range, amihud, rating, coupon, and volatility have positive relation with spreads in the corporate bond market.Ericsson and Renault [16] prove theoretically that the liquidity and credit risk are correlated, and the interaction of liquidity and credit risk is present. When liquidity is low, default risk of bonds tends to be high, suggesting the possibility of an interactive impact of liquidity and default risk. It directly draws on the implications that the interaction of liquidity and credit risk is present. See also Chen et al. [25] or Li et al. [26]. We test this hypothesis using data of bonds with different liquidity and credit characteristics such as Age, Vol, Day, Amihud and Coupon. We now turn to empirical tests. Based on the above analysis, we propose hypothesis H3.H3: the interaction between liquidity and credit risk has a significant impact on corporate bond spreads.


## 2.2.1. Spread

The Spread is the difference between the yield-to-maturity on the corporate bond and the corresponding Treasury rate. When calculating the spread sequence, we selected corporate bonds and treasury bonds with the same maturity yield period to calculate spread by subtraction. We primarily use existing treasury data, but where unavailable we use estimated data from WIND database. Our analysis employs the spread of each bond as a dependent variable in the regression model.


## 2.2.2. Liquidity Measures

There is no consensus on how to measure the liquidity of an asset so we examine a number of liquidity-related measures for corporate bonds. The following describes the measures and their implementation in more detail. In this study, we select multidimension liquidity measures, which can measure liquidity more comprehensively. The liquidity proxies used in this analysis include the following seven liquidity measures: turnover, trade vol, day, amihud, range, time-to-maturity and age.Turnover is the frequency of market assets trading hands in a certain period. In general, therefore, this proxy is expected to be negatively related to yield spreads. The second liquidity measure is Vol, it is obtained by dividing the total trading volume with the number of months during which the issue is traded. The common expectation is that this variable is expected to have an inverse relation with the yield spreads. Day is defined as the number of trading days in the corresponding month. This variable is expected to be negatively related to yield spreads. Following the amihud measure [29], we construct a monthly liquidity measure proxy to describe the liquidity. We construct a monthly liquidity measure proxy of Range based on Han and Zhou [30]. The disadvantage of this measure is that it should be sensitive to outliers. Time-to-Maturity is the time left until maturity from the issuance date of a security and is a liquidity measure proxy [7, 14, 31]. Age is defined as the age of bond transactions since the issue in the corresponding month. Researchers frequently proxy for the liquidity of a corporate bond with its age [32–35]. A number of problems with studying liquidity in corporate bonds arise from the fact that corporate bonds trade only infrequently [33, 36]. Therefore, the liquidity is closely related to age.


## 2.2.3. Credit Risk Measures

This study considers three credit risk variables as explanatory variables. They are rating, coupon and volatility.Rating is the credit rating assigned to each security that a firm issues [14, 37]. Our study adopts the coding method of Covitz and Downing [14] and Shin and Kim [37] for credit ratings: AAA = 1, AA+ = 2, …, and C = 14. We assign the lower credit rating to 15. Obviously, a positive relationship is expected between yield spreads and credit ratings. Coupon refers to the coupon rate of bonds [7, 38]. Longstaff et al. [7] and Bharath and Shumway [38] show that coupon rates have significantly positive correlation with yield spreads. See also Chen et al. [39] or Lin et al. [9]. As expected, the coupon of bond issued by firm with higher default risk is significantly high, other things being constant. Thus, we expect the coefficient of the coupon rate to be positive. Hull [40] uses the historical price volatility of corporate bonds as a measure of the bond's credit. Volatility is the historical price volatility of corporate bonds, and it is estimated from the past historical prices of 125 days. It is well known that as a firm approaches default, the risk associated with its debt also increases, and such risk is correlated to the bond volatility. Accordingly, we expect the Volatility to have a positive correlation with bond spreads.


## 2.2.4. Hypothesis

Turnover, Vol, Day are the proxies of trading activity [3, 12, 37]. The greater the values is, more active the bond transaction is, which shows that the bond liquidity risk is smaller, and the spreads are smaller. Therefore, Turnover, Vol, Day have negative relation with spreads in the corporate bond market. Time-to-Maturity represents the remaining life of the bond. These bonds close to maturity are rarely traded, and the bond holders often choose to hold them until maturity, and they will not be traded, so the coefficient of Time-to-Maturity is negative [14, 31]. New bonds are not more liquid than older ones. Because of information asymmetry, when new bonds are issued, investors will not buy and trade. Over time, for more than two years, investors will choose to buy the bonds. Then the bond transactions become active, and the spreads begin to become small. Therefore, Age and spreads are negative correlation [33, 34]. Based on the above analysis, we propose hypothesis H1.H1: turnover, vol, day, age and time-to-maturity have negative relation with spreads in the corporate bond market.Range and Amihud are the liquidity proxies of price impact [29, 30, 37]. When trading a certain amount of bonds, the greater the bond price changes caused by the transaction, which indicates that the liquidity is poorer, so the bond spreads are also larger. Therefore, Amihud and Range have positive correlation with the bond spreads. Rating, Coupon, and Volatility are the proxies of credit risk [14, 38–40]. The greater the value is, the worse credit is, and the greater the spreads are. So Rating, Coupon, and Volatility have positive relation with spreads in the corporate bond market. Based on the above analysis, we propose hypothesis H2.H2: range, amihud, rating, coupon, and volatility have positive relation with spreads in the corporate bond market.Ericsson and Renault [16] prove theoretically that the liquidity and credit risk are correlated, and the interaction of liquidity and credit risk is present. When liquidity is low, default risk of bonds tends to be high, suggesting the possibility of an interactive impact of liquidity and default risk. It directly draws on the implications that the interaction of liquidity and credit risk is present. See also Chen et al. [25] or Li et al. [26]. We test this hypothesis using data of bonds with different liquidity and credit characteristics such as Age, Vol, Day, Amihud and Coupon. We now turn to empirical tests. Based on the above analysis, we propose hypothesis H3.H3: the interaction between liquidity and credit risk has a significant impact on corporate bond spreads.


## 3. Empirical Analysis

### 3.1. Summary Statistics

#### 3.1.1. Description

Table1 provides summary statistics for the variables used in empirical analysis. It summarizes trading data and bond characteristics of the sample used in our study. Mean, median, maximum, minimum, standard deviation, Jarque-Bera, probability, and observations for each variable are reported for the whole sample in Table 1.Table 1
Summary statistics for the whole sample. The table shows the summary statistics for variables used in the regression analysis for the whole sample.
VariableMeanMedianMaximumMinimumStd. dev.Jarque-BeraProbabilityObservationsSpread2.54632.494035.58900.00821.12754558494.00000.000147436.0000Turnover0.08280.03622.84760.00010.13322378552.00000.000147436.0000Vol87.503442.39493072.23000.0102133.59003004256.00000.000147436.0000Day4.65382.000023.00001.00005.366738023.83000.000147436.0000Amihud0.01220.00033.52100.00010.0798667000000.00000.000147436.0000Range0.02380.00058.40910.00010.1410685000000.00000.000147436.0000Time-to-maturity5.40855.293227.00271.00272.2759334283.60000.000147436.0000Age2.26541.912313.97810.02471.7405105440.70000.000147436.0000Volatility0.50040.414314.45790.00020.36176590932.00000.000147436.0000Coupon6.79526.90009.30003.17001.05301311.12800.000147436.0000Rating3.33234.000015.00001.00001.5065734923.60000.000147436.0000We report mean, median, maximum, minimum, standard deviation, Jarque-Bera, probability, and observations. Spread is the difference between the yield-to-maturity on the corporate bond and the corresponding treasury rate. Turnover is the frequency of market assets trading hands in a certain period of time. Vol is the average of the total trading volume in the corresponding month. Day is defined as the number of trading days in the corresponding month. Amihud and range are illiquidity measures and describe the liquidity measure of the bond price impact dimension. Time-to-maturity is the remaining years of the bond. Age denotes years since issuance. Volatility is a standard deviation of historical bond price. Coupon is the annual coupon interest. Rating is the credit rating assigned to each security, coded so that AAA = 1. The sample period is July 2006 to June 2016. The whole sample includes 3716 bond issues and 47436 observations.From the whole sample, as seen from Table1, the observation is 47436. The average of the spread is 2.5463%, with a standard deviation of 1.1275%. As seen from the median, the distribution of the spread has a long right tail, indicating that some of the very wide yield spreads skew the distribution to the right. Turnover registers a value of 0.0828 every month per issue, reflecting some large values in the right tail of the distribution, while vol averages 87.5034, again with a long right tail. Day averages 4.6538, with a standard deviation of 5.3667. Amihud registers a value of 0.0122 every month, reflecting some large values in the right tail of the distribution, while range averages 0.0238, again with a long right tail. The average of time-to-maturity is 5.4085 years, and the median is 5.2932 years, while age averages 2.2654 years, and the median is 1.9123 years. The mean value of coupon is 6.7952, with a standard deviation 1.0530, while volatility averages 0.5004, with a standard deviation of 0.3617, where the lowest value is 0.0002 and the highest is 14.4579. Finally, The average credit rating score is 3.3323 (between AA− and AA), with a standard deviation of 1.5065.


#### 3.1.2. Pairwise Correlation Test

Table2 shows the pairwise correlation coefficients among the independent variables respectively in the whole sample. As confirmed from Table 2, turnover and vol are positively high correlated with each other, with a correlation coefficient of 0.8683, while turnover and day seem to be quite weakly correlated and vol and day are also like this; amihud is also positively correlated with range, with a correlation coefficient of 0.7673. Coupon, volatility, and rating are positively correlated with one another; the coefficient value between coupon and rating is relatively high, with a correlation coefficient of 0.3228, while volatility and coupon exhibit weaker correlation, with a correlation coefficient of 0.0234. On the other hand, liquidity and credit risk proxies also have correlation. Age is negatively correlated with Coupon, with a correlation coefficient of −0.2927.Table 2
Pairwise correlations between independent variables for the whole sample.
TurnoverVolDayAmihudRangeTime-to-maturityAgeVolatilityCouponRatingTurnover1Vol0.8683∗∗∗1Day−0.0293∗∗∗−0.0268∗∗∗1Amihud−0.0926∗∗∗−0.0976∗∗∗−0.0201∗∗∗1Range−0.1030∗∗∗−0.1085∗∗∗0.0064∗∗∗0.7673∗∗∗1Time-to-maturity0.0113∗∗∗0.0437∗∗∗0.1396∗∗∗0.03030.07101Age−0.1541∗∗∗−0.1232∗∗∗0.0741∗∗∗0.02740.0423−0.2945∗∗∗1Volatility0.0490∗∗∗0.0798∗∗∗0.0900∗∗∗0.06400.1036∗∗∗0.1158∗∗∗0.0583∗∗∗1Coupon0.09850.0357∗∗∗0.0921∗∗∗−0.0026−0.0315−0.2345∗∗∗−0.2927∗∗∗0.0234∗∗∗1Rating0.1040∗∗∗0.0198∗∗∗0.0655∗∗∗0.00630.0090−0.1691∗∗∗−0.1786∗∗∗0.0404∗∗∗0.3228∗∗∗1The table shows the pairwise correlation coefficients for the variables used in the regression analysis for the whole sample. The meanings of the variables are given in Table1. The sample period is July 2006 to June 2016. The whole sample includes 3716 bond issues and 47436 observations. “∗∗∗” indicates significance at the 1% level.


#### 3.1.3. Unit Root Test

In order to avoid spurious regressions, we first make unit root tests for the sample data. From the results of ADF test of Table3, all variables are significant at the level of 1%, and the original hypothesis of unit root is rejected. That is to say, all the variables are stationary sequence, and the sample data can be analyzed by regression analysis. Then we will study the impact factors of the spreads, especially the interaction between liquidity and credit risk. The stable variable sequence can ensure the validity of the regression results.Table 3
ADF unit root test.
SpreadTurnoverVolDayAmihudRangeTime-to-maturityAgeVolatilityCouponRatingPanel A. The interbank markett-statistic−9.9746∗∗∗−31.5022∗∗∗−27.1805∗∗∗−22.0632∗∗∗−157.0229∗∗∗−156.2083∗∗∗−9.7004∗∗∗−14.8666∗∗∗−13.1248∗∗∗−18.5285∗∗∗−33.6873∗∗∗1% level−3.4304−3.4304−3.4304−3.4304−3.4304−3.4304−3.4304−3.4304−3.4304−3.4304−3.4304Prob.∗0.00010.00010.00010.00010.00010.00010.00010.00010.00010.00010.0001Panel B. The exchange markett-statistic−9.9574∗∗∗−31.6225∗∗∗−33.1601∗∗∗−10.9301∗∗∗−53.5030∗∗∗−53.5321∗∗∗−6.8669∗∗∗−22.4293∗∗∗−8.6634∗∗∗−22.5326∗∗∗−75.8180∗∗∗1% level−3.4305−3.4305−3.4305−3.4305−3.4305−3.4305−3.4305−3.4305−3.4305−3.4305−3.4305Prob.∗0.00010.00010.00010.00010.00010.00010.00010.00010.00010.00010.0001Panel C. The whole samplet-statistic−11.5249∗∗∗−18.8832∗∗∗−20.0654∗∗∗−15.9010∗∗∗−43.0203∗∗∗−41.7255∗∗∗−10.0992∗∗∗−22.1840∗∗∗−15.6788∗∗∗−21.7887∗∗∗−58.7438∗∗∗1% level−3.4303−3.4303−3.4303−3.4303−3.4303−3.4303−3.4303−3.4303−3.4303−3.4303−3.4303Prob.∗0.00010.00010.00010.00010.00010.00010.00010.00010.00010.00010.0001The table shows the ADF unit root test results for the variables used in the regression analysis. The test results include the test of thet statistic, the 1% significance level, and the probability of receiving the original hypothesis. The meanings of the variables are given in Table 1. The sample period is July 2006 to June 2016. The subsample (panel A) includes 2281 bond issues and 25648 observations. The subsample (panel B) includes 1435 bond issues and 21788 observations. The whole sample (panel C) includes 3716 bond issues and 47436 observations. “∗,” “∗∗,” and “∗∗∗’ indicate significance at the 10%, 5%, and 1% levels, respectively.


### 3.2. The Impact of the Interaction between Liquidity and Credit Risk on Spreads

Some scholars study liquidity and explain why it affects asset prices [41–44]. Bagehot [43] proposes that due to the impact of information asymmetry, liquidity refers to the impact of a transaction on the market price. [44] believe that illiquidity is the risk that assets cannot be sold at a reasonable price within a given time. The above literature shows that liquidity is a potential cost of asset transaction, and investors with illiquid assets need liquidity risk compensation, namely liquidity risk premiums. Information asymmetry is an important factor affecting asset liquidity. The reason why liquidity affects asset price is that investors’ information asymmetry leads to speculative transaction, investment transaction and investors’ compensation for different liquidity risk.Acharya and Pedersen [45] explain the affecting mechanism of liquidity on asset prices. They establish a theoretical model of Liquidity Capital Asset Pricing Model and identify two channels of risk transmission. The first channel is direct compensation for the transaction costs of assets. This is a premium for liquidity level. The second channel is the compensation of asset returns for systemic liquidity. This is a premium for liquidity risk. Bongaerts et al. [46] use an asset pricing approach to compare the impacts of liquidity level and liquidity risk on expected U.S. corporate bond returns and analyze which of these two channels is more important. Liu [47] and Bervas [48] find that a liquid market presents many different dimensions. Díaz and Escribano [49] classify and describe the variety of the existing liquidity measures with the different characteristics and dimensions of liquidity. Previous literature suggests that liquidity has many dimensions. We divide liquidity into three dimensions based on the economic significance of liquidity, including trading activity, price shock, and bond survival time. Liquidity of different dimension has a different impact on corporate bond spreads. Liquidity of transaction activity dimension is the common result of speculative trading and investment trading, while liquidity of price shock dimension is mostly due to investors’ speculative trading. In addition, liquidity of bond survival time dimension mainly represents investors’ investment transaction. Different dimension liquidity premiums have different economic significance. Therefore, liquidity should be measured across the different dimensions in order to have a global view of liquidity. We study the mechanism and channels of liquidity’s impact on asset price from the perspective of multidimension liquidity.Bond credit risk is the risk of loss to investors due to bond default. Investors need some compensation for risk when holding defaultable assets, which is why credit risk affects asset prices. Referring to the existing literature, we select three credit risk indicators, including price volatility, coupon rate, and credit rating. We divide credit risk into two dimensions according to the economic significance, including dynamic credit risk and static credit risk. Relevant literature can also be referred to Li and Song [50]. Different dimension credit risk have different impacts on corporate bond spreads. Dynamic credit risk is mostly caused by investors' speculative trading of liquidity risk, so it often interacts with liquidity, while static credit risk is mainly determined by the default probability of credit bonds themselves, and it is often not linked with liquidity risk. Therefore, credit risk premium of different dimension has a different economic significance. Credit rating and coupon rate are static credit risk measures, while price volatility is a dynamic credit risk measure. The static credit risk represents the credit risk level of an firm in this period of time, and it does not change with the dynamic change of liquidity risk. When liquidity affects asset prices, static credit risk generally does not interact with liquidity risk in a dynamic spiral. Dynamic credit risk represents the credit risk level of an firm over time, and it changes in resonance with the dynamic change of liquidity risk. When liquidity affects asset prices, dynamic credit risk usually interacts with liquidity risk in a dynamic spiral, forming the resonance enhancement interaction between liquidity and credit risk to dynamically affect asset prices. This may be affecting mechanism of the interaction between liquidity and credit risk for asset prices.From the perspective of the market transmission mechanism of risk, if investors hold assets with high credit risk, some informed traders will take the lead in selling assets when adverse information comes out. Massive asset sales can cause asset prices to fall rapidly and make some investors panic. In the case of information asymmetry, some investors will follow to sell assets at lower prices and suffer liquidity losses. Further decline of asset prices will increase liquidity risk. Information outflow and information asymmetry become the spiral transmission path of the interaction between liquidity and credit risk on asset prices.From an economic point of view, investors holding illiquid assets need liquidity risk compensation, similarly, investors holding defaultable assets need credit risk compensation. Default risk and liquidity are linked through investors’ transaction based on information asymmetry, which will inevitably lead to a series of dynamic economic transmission impacts of liquidity and credit risk, and then affect asset prices spirally. Therefore, we introduce interaction between liquidity and credit risk into corporate bond spread model to study their affecting mechanism on asset prices and risk transmission channels.Based on the above analysis, the impact of the interaction between liquidity and credit risk on corporate bond spreads is discussed in this part. The premium regression equation that contains the interaction is as follows(1)Spreadit=α+β1×liquidity risk factorsit+β2×credit risk factorsit+β3×interaction functionliquidity risk factors, credit risk factorsit+εt.To investigate whether the impact of interaction on the spreads is present, the following assumption is given(2)Spreadit=α+β1×liquidity risk factorsit+β2×credit risk factorsit+β3×liquidity risk factorsit×credit risk factorsit+εt.Ifβ3 is significantly different from zero, the impact of the interaction on the spreads is present. For estimating the impact of the interaction, we run a pooled regression of bond spreads in the interbank market, exchange market and the whole sample. The term “Liquidity risk factors” represents a set of possible proxies for liquidity risk from three dimensions, including transaction activity (turnover, vol, and day), price impact (amihud and range), and bond survival time (time-to-maturity, age). Similarly, the term “credit risk factors” represents a set of possible proxies for the default risk, including coupon and volatility. The cross terms of the proxies of liquidity and credit risk represent their interaction. If the regression coefficient of the cross term is significantly different from zero, the interaction has a significant impact on the bond spreads. In order to guarantee the reliability of the research results, we have made empirical tests from many perspectives.


#### 3.2.1. The Empirical Results Based on Liquidity Proxies of Transaction Activity

China’s bond market is the second largest in the world after the America. According to the People’s Bank of China, by the end of December 2021, the stock of bonds in China’s bond market is about $21 trillion, while that in the US is about $50 trillion. In 2021, China’s bond issuance reach about $9.6 trillion, accounting for about 54% of China’s GDP ($17.7 trillion) and 11% of global GDP ($90 trillion). It shows that China’s bond market has become an important factor affecting China’s economy and global economy. According to the People’s Bank of China, the stock of corporate debenture bonds is about $5 trillion by the end of December 2021. Corporate Bonds are important parts of China’s bond market. Therefore, it is of great significance to study the impact factors of Chinese corporate bond prices.China’s corporate bond market consists of interbank market and exchange market. In the interbank market, commercial banks, insurance companies, securities firms and other financial institutions buy and sell bonds, and participants ask selected counterparties to complete the transaction. The exchange bond market is dominated by nonbank financial institutions and individuals. China has two types of corporate bonds. One is issued by central government departments or state-owned enterprises, and the other is issued by listed companies. The former can be traded on the exchange market and the interbank market, while the latter can only be traded on the exchange market. This shows that both of markets are important trading places for corporate bonds in China, but the types of corporate bonds traded in the two markets are different, and the structures of investors are different. Therefore, it is necessary to study the impact factors of corporate bond spreads in the two markets. In order to explore the impact of the two markets on the test results, we, respectively, analyze the sample of whole market and subsamples of the interbank market and exchange market. In the whole sample, the dummy variable is introduced to test the significance of the impact of the interbank market and the exchange market on the test results. Where, the dummy variable of the interbank market is set to 1, and the dummy variable of the exchange market is set to 0. The basic proxies of credit risk and liquidity are given, including Vol, Day, Range, Age, Coupon and Volatility. The empirical results are shown in Tables4 and 5.Table 4
The impact of interaction between liquidity and credit risk on spreads based on transaction activity in the whole sample.
123456C2.5912∗∗∗0.7928∗∗∗0.3340∗∗∗0.2715∗∗∗0.3530∗∗∗0.3298∗∗∗(111.7038)(11.0667)(6.96)(5.78)(8.66)(6.87)Dummy0.4812∗∗∗0.4367∗∗∗0.2687∗∗∗0.2065∗∗∗−0.1371∗∗∗0.2494∗∗∗(20.8164)(19.3486)(22.38)(17.42)(−13.11)(20.73)Turnover1.9158∗∗∗1.5967∗∗∗−0.07252.2141∗∗∗1.7381∗∗∗(12.7908)(10.8800)(−0.30)(5.24)(4.28)Vol−0.0020∗∗∗−0.0018∗∗∗−0.0013∗∗∗−0.0018∗∗∗−0.0020∗∗∗(−13.6127)(−12.4066)(−5.38)(−4.49)(−5.01)Day0.0737∗∗∗0.0650∗∗∗−0.0108∗∗−0.0122∗∗−0.0132∗∗(37.6845)(33.6513)(−1.96)(−2.22)(−2.42)Amihud0.3513∗∗∗0.2517∗∗∗0.2506∗∗∗0.2480∗∗∗−0.1368∗∗0.2487∗∗∗(4.0216)(2.9561)(4.41)(4.36)(−2.34)(4.39)Age−0.2030∗∗∗−0.1739∗∗∗−0.1349∗∗∗−0.1314∗∗∗−0.1254∗∗∗−0.1313∗∗∗(−32.1614)(−27.7859)(−49.35)(−47.86)(−44.52)(−47.99)Volatility0.2141∗∗∗−0.2482∗∗∗−0.2266∗∗∗0.1438∗∗∗−0.2437∗∗∗(8.8111)(−13.70)(−12.54)(9.78)(−13.42)Coupon0.2422∗∗∗0.3315∗∗∗0.3391∗∗∗0.3606∗∗∗0.3310∗∗∗(25.0131)(49.42)(51.69)(66.47)(49.26)Turnover × volatility0.2046∗∗−0.3269∗∗−0.2896∗(2.28)(−1.97)(−1.81)Turnover × coupon0.0081−0.1077∗−0.0624(0.24)(−1.84)(−1.11)Vol × volatility0.0005∗∗∗0.0005∗∗∗0.0008∗∗∗(6.33)(3.69)(6.05)Vol × coupon0.0001∗∗∗0.0001∗0.0000(2.93)(1.72)(0.57)Day × volatility0.0614∗∗∗0.0615∗∗∗0.0611∗∗∗(26.65)(26.65)(26.58)Day × coupon0.0052∗∗∗0.0050∗∗∗0.0055∗∗∗(7.18)(6.94)(7.60)aj−R20.17520.21840.26820.26690.21170.2723To investigate whether the impact of interaction on the spreads is present, the following regression equations are given. Spreadit = α + β1 × (liquidity risk factors)it + β2 × (credit risk factors)it + β3 × (transaction activity liquidity risk factors)it × (credit risk factors)it + єt. The meanings of the variables are given in Table 1. The sample period is July 2006 to June 2016. The whole sample includes 3716 bond issues and 47436 observations. The t-statistics are shown in parentheses below each coefficient estimate, and “∗,” “∗∗,’ and “∗∗∗’ indicate significance at the 10%, 5%, and 1% levels, respectively.Table 5
The impact of interaction between liquidity and credit risk on spreads based on transaction activity in interbank market and exchange market.
The inter bank marketThe exchange market12341234C0.3490∗∗∗0.2341∗∗∗0.2655∗∗∗0.3312∗∗∗0.8091∗∗∗0.6666∗∗∗0.4069∗∗∗0.7630∗∗∗(5.63)(3.83)(4.80)(5.32)(10.59(8.83)(6.91)(10.16)Turnover0.8623∗∗∗1.7225∗∗∗1.5566∗∗∗−1.876818.8014∗∗∗24.2606∗∗∗(3.14)(4.34)(3.93)(−1.39)(6.97)(9.39)Vol0.0003−0.0012∗∗∗−0.0004−0.0114∗∗∗−0.0246∗∗∗−0.0252∗∗∗(1.15)(−2.93)(−0.99)(−9.98)(−10.86)(−11.62)Day−0.0676∗∗∗−0.0324−0.0766∗∗∗−0.0022−0.0070−0.0018(−3.08)(−1.54)(−3.47)(−0.31)(−1.00)(−0.26)Amihud12.8027∗∗∗13.4242∗∗∗13.4778∗∗∗12.9596∗∗∗0.2895∗∗∗0.3265∗∗∗0.00280.2956∗∗∗(8.80)(9.22)(9.36)(8.93)(4.96)(5.65)(0.05)(5.16)Age−0.1474∗∗∗−0.1443∗∗∗−0.1417∗∗∗−0.1420∗∗∗−0.1309∗∗∗−0.1248∗∗∗−0.1087∗∗∗−0.1252∗∗∗(−37.34)(−36.25)(−35.89)(−35.79)(−34.87)(−33.47)(−28.39)(−33.83)Volatility−0.1971∗∗∗−0.1899∗∗∗−0.1939∗∗∗−0.1967∗∗∗−0.1253∗∗∗−0.0750∗∗0.1765∗∗∗−0.0762∗∗(−8.06)(−7.76)(−9.88)(−8.06)(−3.83)(−2.31)(8.00)(−2.37)Coupon0.3678∗∗∗0.3822∗∗∗0.3882∗∗∗0.3672∗∗∗0.2522∗∗∗0.2659∗∗∗0.3301∗∗∗0.2543∗∗∗(41.14)(43.26)(49.53)(40.86)(23.62)(25.18)(43.42)(24.23)Turnover × volatility0.2945∗∗−0.2244−0.3161∗∗16.3455∗∗∗13.1480∗∗∗12.1640∗∗∗(2.50)(−1.43)(−1.97)(34.04)(12.99)(12.49)Turnover × coupon−0.1400∗∗∗−0.1075∗−0.0821−0.4313∗∗−2.2377∗∗∗−3.2118∗∗∗(−3.69)(−1.96)(−1.50)(−2.38)(−6.08)(−9.09)Vol × volatility0.0007∗∗∗0.0009∗∗∗0.0010∗∗∗0.0138∗∗∗0.0042∗∗∗0.0046∗∗∗(6.86)(6.69)(7.19)(31.82)(4.56)(5.25)Vol × coupon−0.0002∗∗∗0.0001−0.0002∗∗∗0.0008∗∗∗0.0026∗∗∗0.0026∗∗∗(−4.15)(−0.13)(−3.10)(5.40)(8.55)(8.73)Day × volatility−0.01240.0110−0.00960.0215∗∗∗0.0181∗∗∗0.0144∗∗∗(−1.09)(0.99)(−0.83)(6.62)(5.59)(4.48)Day × coupon0.0207∗∗∗0.0094∗∗∗0.0215∗∗∗0.0065∗∗∗0.0068∗∗∗0.0065∗∗∗(6.27)(3.03)(6.50)(6.70)(7.13)(6.84)aj−R20.22760.22470.22630.23180.34260.35460.30450.3649To investigate whether the impact of interaction on the spreads is present, the following regression equations are given. Spreadit = α +β1 × (liquidity risk factors)it + β2 × (credit risk factors)it + β3 × (transaction activity liquidity risk factors)it × (credit risk factors)it + єt. The meanings of the variables are given in Table 1. The sample period is July 2006 to June 2016. The subsample of the interbank market includes 2281 bond issues and 25648 observations. The subsample of the exchange market includes 1435 bond issues and 21788 observations. The t-statistics are shown in parentheses below each coefficient estimate, and “∗,” “∗∗,” and “∗∗∗” indicate significance at the 10%, 5%, and 1% levels, respectively.In Table4, Model 1 gives the regression results that include liquidity, and Model 2 gives the regression results including credit risk and liquidity. Compared with Model 2, the results of Model 1 show that the liquidity premiums are the main components of corporate bond spreads. Corporate bonds are rarely traded in China’s bond market, which results in poor liquidity. In Model 1 and Model 2, the regression coefficients of Vol are −0.0020 and −0.0018, respectively, and they are significant at the level of 1%, which is consistent with the hypothesis. The greater the values is, more active the bond transaction is. It shows that the bond liquidity risk is smaller, and the spreads are smaller [3, 12, 37]. The regression coefficients of Turnover and Day are positive, and they are inconsistent with the hypothesis. China’s corporate bond market trades infrequently, and the increase of turnover rates and trading days may be due to speculative trading. In Model 1 and Model 2, the regression coefficients of Amihud are 0.3513 and 0.2517, respectively, and they are significant at the level of 1%, which is consistent with the hypothesis. The results of model 1 show that for every 1 unit increase in liquidity risk of price shock dimension, corporate bond spreads increase by 0.3513 unit. See also Shin and Kim [37] and Han and Zhou [30]. In Model 1 and Model 2, the regression coefficients of Age are −0.2030 and −0.1739, respectively, and they are significant at the level of 1%, which is consistent with the hypothesis. Because of information asymmetry, investors will not buy and trade new bonds. Over time, investors will choose to buy the bonds. Then the transactions become active, and the spreads begin to become small. Goldstein et al. [33] and Hotchkiss and Jostova [34] find similar results. In Model 2, the regression coefficients of Volatility and Coupon are 0.2141 and 0.2422, respectively, and they are significant at the level of 1%, which is consistent with the hypothesis. Volatility and Coupon are the proxies of credit risk. The greater the value is, the worse credit is, and the greater the spreads are. So Volatility and Coupon have positive relation with spreads [37, 39, 40].The regression results containing interaction terms are given in Model 3. Model 4 and Model 5 gives the robustness analysis results. In addition, the regression analysis results of the all transaction activity dimension are given in Model 6. Cross term represents the corresponding interaction proxy. If the coefficient of cross term is significantly different from zero, the impact of the interaction on the spreads is significant. According to the test results of Table4, the coefficient of dummy variable is significant at the level of 1%, which indicates that the differences between the interbank market and the exchange market cannot be ignored.In Table4, regression results of Model 3 show that the coefficient of vol is significant at the level of 1%, and the sign is in line with the hypothesis, while the regression coefficient of coupon is very significant. Meanwhile, the coefficient of the cross term of vol and coupon is very significant. The coefficient of the cross term of vol and coupon is significantly different from zero, which indicates that the interaction has impacts on the spreads. In Model 3, the regression coefficient of volatility is significant, but the sign is not in line with the hypothesis. It shows that when the trading volume of high-credit risk assets increases, the panic selling of some investors due to asymmetric information leads to increase asset price volatility. The increase of the volatility leads to the increase of speculative liquidity risk. And the spiral increase of speculative liquidity risk and static credit risk leads to the impact of the interaction between liquidity and credit risk on asset prices. The coefficients of day, coupon and day × coupon have similar characteristics.In Model 4, the coefficients of day, coupon and day × coupon are significant, which shows that the interaction between day and coupon has a significant impact on corporate bond spreads. The reason is that static credit risk does not weaken when investment liquidity increases, and the interaction between liquidity and credit risk affects asset prices in the same direction as static credit risk.In Model 5, the coefficient of the interaction between vol and volatility is greater than one of the interaction between vol and coupon. And they have enhanced impacts on bond spreads. It shows that dynamic credit risk changes in resonance with the dynamic change of liquidity risk, while the static credit risk does not change with the dynamic change of liquidity risk. When liquidity affects asset prices, dynamic credit risk interacts with liquidity risk in a dynamic spiral, forming a bigger resonance enhancement interaction between liquidity and credit risk to dynamically affect asset prices than static credit risk. Li and Song [50] study the pricing of China’s convertible bonds and find that the dynamic credit risk is important in convertible bond pricing.Regression analysis results are given in Model 6, which contains all the liquidity risk proxies of the transaction activity. The coefficients of vol × volatility, day × volatility and day × coupon are significant, which shows that the interaction between liquidity and credit risk has a significant impact on spreads. The coefficients of turnover × coupon and vol × coupon are not significant, and the reason is that when liquidity affects asset prices, static credit risk generally does not interact with liquidity risk in a dynamic spiral. From Model 1 to Model 6, the coefficients of age are all significant at the level of 1%, and the signs are negative. Chinese investors tend to be cautious about newly listed bonds due to information asymmetry, so they prefer to buy corporate bonds that trade for many years, which causes bond liquidity to increase over time. Therefore, the high age bonds have lower bond spreads in China’s corporate bond market. Relevant literature can also be referred to Zhu [51].In Table5, the empirical results of the interbank market and the exchange market are given. Regression results of Model 1 show that the regression coefficient of vol is significant at the level of 1% and the sign is in line with the hypothesis on the exchange market, while the regression coefficient of day is significant at the level of 1% and the sign is in line with the hypothesis in the interbank market. The reason is that exchange market is dominated by individual investors with many trading days but few trading volumes, so trading volume is a good proxy for liquidity in the exchange market. On the other hand, interbank market is dominated by institutional investors with few trading days and high trading volumes, so trading day is a better proxy for liquidity in the interbank market. In the interbank market, the assumption that the coefficient of day × coupon is equal to zero is rejected, which indicates that the interaction between liquidity and credit risk has a significant impact on the spreads in Model 1. When investors hold high credit risk bond, with the increase of trading days, some investors panic sell-off due to asymmetric information, that is to say, they are worried about potential default risk to sudden frequent trading bonds, which leads to spiral interaction between liquidity and credit risk, resulting in corporate bond spreads widen. The regression coefficient of vol × coupon has similar conclusion on the exchange market.Robustness analysis are done in Model 2 and Model 3. The empirical results show that the regression coefficients of the interaction between liquidity and credit risk are all significant in the exchange market, while some of these coefficients are not significant in the interbank market. The reason is that the interbank market is mainly composed of institutional investors with infrequent transactions, leading to the discontinuous linkage between liquidity and credit risk and the failure to form continuous transmission and feedback of information. This shows that the establishment of a continuous market trading mechanism, which makes information flow and reduces information asymmetry, is conducive to price discovery.Regression analysis results are given in Model 4, which contains all the liquidity risk proxies of the transaction activity. The regression coefficients of interaction between liquidity and credit risk are all significant in the exchange market, while the regression coefficients of Turnover × Coupon and Day × Volatility are not significant in the interbank market. The reason is that investor structure and transaction characteristic are different in the interbank market and the exchange market.Through the above analysis, interaction between liquidity and credit risk cannot be ignored and liquidity premiums are the main components of corporate bond spreads in China’s bond market. Dynamic credit risk changes in resonance with the dynamic change of liquidity risk, while the static credit risk does not change with the dynamic change of liquidity risk. When liquidity affects asset prices, dynamic credit risk interacts with liquidity risk in a dynamic spiral, forming a bigger resonance enhancement interaction between liquidity and credit risk to dynamically affect asset prices than static credit risk.


#### 3.2.2. Subsample Results

In this part, we give sub samples regression analysis, and the liquidity and credit risk proxies are divided into high, medium and low in order to explore the impact of the interaction between liquidity and credit risk on the spreads.In Table6, there are nine subsamples. The regression results of the three subsamples are given according to the trading volume in the panel A. In the high-vol subsample, the regression coefficients of amihud × volatility, amihud × coupon, age × volatility and age × coupon are significant, while the regression coefficients of vol × volatility and vol × coupon are not significant. It suggests that the interactions between liquidity and credit risk in high-vol bonds are mainly the interaction between speculative liquidity of price shock dimension and credit risk and the interaction between investment liquidity and credit risk. In the low-vol subsample, the regression coefficient of amihud × volatility is not significant, suggesting that the spiral interaction between speculative liquidity of price shock dimension and dynamic credit risk requires high trading volume as the basic condition.Table 6
The impact of interaction between liquidity and credit risk on spreads in subsample results.
Panel A: volPanel B: amihudPanel C: ageHightMiddleLowHightMiddleLowHightMiddleLowc−1.0268∗∗∗−0.4000∗∗∗−0.6494∗∗∗−0.6142∗∗∗−0.4396∗−0.6475∗∗∗0.24710.0498−2.0406∗∗∗(−5.84)(−3.56)(−6.10)(−3.92)(−1.84)(−8.50)(1.16)(0.33)(−19.95)Dummy0.3600∗∗∗0.3715∗∗∗0.3015∗∗∗0.4950∗∗∗0.3671∗∗∗0.3201∗∗∗0.1926∗∗∗0.2973∗∗∗0.2909∗∗∗(5.80)(21.04)(6.43)(4.70)(8.28)(20.60)(5.90)(19.01)(17.81)Vol0.0003−0.0101∗∗∗0.0110−0.0652−0.0091−0.0010∗∗∗−0.0010−0.0008∗∗0.0001(0.76)(−6.49)(0.52)(−1.54)(−1.24)(−3.60)(−1.46)(−2.47)(0.49)Day0.0947∗∗∗0.0616∗∗∗0.0341∗∗∗0.0259∗∗∗0.0466∗∗∗0.0621∗∗∗0.0583∗∗∗0.0608∗∗∗0.0373∗∗∗(23.33)(42.81)(20.30)(7.42)(19.39)(50.00)(22.49)(46.14)(26.67)Amihud−1940.6200∗∗∗−83.3530∗∗0.8493∗∗0.6793−12.5975−280.7775∗∗∗1.7829∗∗−0.0439−0.9569(−5.15)(−2.24)(2.27)(1.58)(−0.37)(−3.86)(2.03)(−0.09)(−1.16)Age0.2520∗∗∗0.2224∗∗∗0.2046∗∗∗0.2015∗∗∗0.1688∗∗∗0.1779∗∗∗−0.0557−0.08411.0736∗∗∗(6.72)(10.34)(9.73)(5.75)(5.18)(10.33)(−1.30)(−1.18)(6.90)Volatility0.09090.05580.1072∗∗0.1180∗0.1472−0.0227−0.4399∗∗∗0.8224∗∗∗−0.2797∗∗∗(1.32)(1.16)(2.38)(1.85)(1.52)(−0.62)(−4.82)(12.72)(−6.19)Coupon0.4754∗∗∗0.4229∗∗∗0.4915∗∗∗0.4886∗∗∗0.4350∗∗∗0.4604∗∗∗0.3421∗∗∗0.3014∗∗∗0.7048∗∗∗(20.58)(25.74)(32.98)(22.75)(12.88)(41.73)(9.34)(14.22)(48.18)Vol × volatility−0.00010.0039∗∗∗0.0248∗∗∗0.0188∗∗0.00030.0006∗∗∗0.0007∗∗∗0.0006∗∗∗0.0000(−1.06)(5.90)(2.95)(2.34)(0.17)(7.15)(3.51)(6.76)(−0.02)Vol × coupon−0.00010.0011∗∗∗−0.0054∗0.00150.00050.00000.00020.0000−0.0001∗∗−1.44(5.02)(−1.82)(0.26)(0.54)(1.02)(1.51(−0.26)(−2.47)Amihud × volatility400.6426∗∗∗15.0529∗−0.0999−0.102819.2996317.0865∗∗∗−0.3220−0.3831∗∗0.0986(4.79)(1.94(−0.82)(−0.74)(1.30)(10.76)(−1.04)(−2.21)(0.63)Amihud × coupon238.7952∗∗∗9.6909∗−0.0996∗∗−0.08541.552623.8625∗∗−0.2105∗0.07820.1160(4.60)(1.89)(−1.96)(−1.47)(0.32)(2.28)(−1.83)(1.13)(1.10)Age × volatility0.0498∗∗−0.0736∗∗∗−0.0321∗∗∗−0.0301∗−0.0702∗∗∗−0.0186∗∗0.0840∗∗∗−0.2944∗∗∗0.7791∗∗∗(2.50)(−6.77)(−3.11)(−1.85)(−4.14)(−2.02)(4.37)(−10.13)(10.95)Age × coupon−0.0648∗∗∗−0.0552∗∗∗−0.0563∗∗∗−0.0522∗∗∗−0.0478∗∗∗−0.0511∗∗∗−0.0175∗∗0.0096−0.2350∗∗∗(−11.01)(−16.27)(−16.63)(−9.31)(−9.00)(−18.76)(−2.19)(0.95)(−10.66)aj−R20.25120.27890.29840.25180.31230.26790.13490.21780.4787To investigate whether the impact of interaction on the spreads is present, the following regression equations are given. Spreadit = α + β1 × (liquidity risk factors)it + β2 × (credit risk factors)it + β3 × (different dimension liquidity risk factors)it × (credit risk factors)it + єt. The meanings of the variables are given in Table 1. The sample period is July 2006 to June 2016. The whole sample includes 3716 bond issues and 47436 observations. The t-statistics are shown in parentheses below each coefficient estimate, and “∗,” “∗∗,” and “∗∗∗” indicate significance at the 10%, 5%, and 1% levels.In the high-amihud subsample of panel B, the regression coefficients of vol × volatility, age × volatility and age × coupon are significant, while the regression coefficients of vol × coupon, amihud × volatility, and amihud × coupon are not significant. It shows that high price shock is usually caused by a huge amount of investors’ sudden trading. Generally, prices will recover calm immediately after a huge impact, which makes it difficult to form risk transmission and interaction between liquidity and credit risk in a very short period of time. In the subsamples of panel B, the regression coefficients of vol × coupon are all not significant. Coupon is static credit risk measure. The static credit risk represents the credit risk level of an firm in this period of time, and it does not change with the dynamic change of liquidity risk. When liquidity affects asset prices, static credit risk generally does not interact with liquidity risk in a dynamic spiral.In the high-age subsample of panel C, the regression coefficients of vol × volatility, amihud × coupon, age × volatility and age × coupon are significant, while the regression coefficients of vol × coupon and amihud × volatility are not significant. It shows that high age bonds are actively traded, and sufficient trading volume forms the spiral interaction between speculative liquidity and dynamic credit risk and the interaction between liquidity of price shock dimension and static credit risk, thus affecting asset prices. In the low-age subsample of panel C, the regression coefficients of vol × coupon, age × volatility and age × coupon are significant, while the regression coefficients of vol × volatility, amihud × volatility, and amihud × coupon are not significant. The reason is that low age bonds are not actively traded, and the lack of trading volume only forms the interaction between investment liquidity and static credit risk, which indicates that the interaction between liquidity of price shock dimension and credit risk requires sufficient trading volume as the basic condition.To sum up, the interaction between liquidity and credit risk will increase with the increase of liquidity risk and credit risk and it is a time-varying dynamic process. When market liquidity risk increases, some investors will take the lead in selling corporate bonds with high default risk, which causes the price of corporate bonds with high credit risk to fluctuate greatly. These behaviors of investors further cause more investors to sell these corporate bonds with high credit risk, so the investors who hold these high credit risk bonds have to bear the gradually increasing liquidity risk. With the increase of market liquidity risk, firms with high default risk are affected due to the depletion of operating cash flow, and the probability of default will also increase. Because of information asymmetry, investors sell their bonds more quickly, creating a spiral interaction between liquidity and credit risk that affects asset prices. If market liquidity risk continues to increase, corporate bonds with low credit risk will gradually be affected by the interaction between liquidity and credit risk, and eventually more corporate bond prices will be affected by risk contagion.


## 3.1. Summary Statistics

### 3.1.1. Description

Table1 provides summary statistics for the variables used in empirical analysis. It summarizes trading data and bond characteristics of the sample used in our study. Mean, median, maximum, minimum, standard deviation, Jarque-Bera, probability, and observations for each variable are reported for the whole sample in Table 1.Table 1
Summary statistics for the whole sample. The table shows the summary statistics for variables used in the regression analysis for the whole sample.
VariableMeanMedianMaximumMinimumStd. dev.Jarque-BeraProbabilityObservationsSpread2.54632.494035.58900.00821.12754558494.00000.000147436.0000Turnover0.08280.03622.84760.00010.13322378552.00000.000147436.0000Vol87.503442.39493072.23000.0102133.59003004256.00000.000147436.0000Day4.65382.000023.00001.00005.366738023.83000.000147436.0000Amihud0.01220.00033.52100.00010.0798667000000.00000.000147436.0000Range0.02380.00058.40910.00010.1410685000000.00000.000147436.0000Time-to-maturity5.40855.293227.00271.00272.2759334283.60000.000147436.0000Age2.26541.912313.97810.02471.7405105440.70000.000147436.0000Volatility0.50040.414314.45790.00020.36176590932.00000.000147436.0000Coupon6.79526.90009.30003.17001.05301311.12800.000147436.0000Rating3.33234.000015.00001.00001.5065734923.60000.000147436.0000We report mean, median, maximum, minimum, standard deviation, Jarque-Bera, probability, and observations. Spread is the difference between the yield-to-maturity on the corporate bond and the corresponding treasury rate. Turnover is the frequency of market assets trading hands in a certain period of time. Vol is the average of the total trading volume in the corresponding month. Day is defined as the number of trading days in the corresponding month. Amihud and range are illiquidity measures and describe the liquidity measure of the bond price impact dimension. Time-to-maturity is the remaining years of the bond. Age denotes years since issuance. Volatility is a standard deviation of historical bond price. Coupon is the annual coupon interest. Rating is the credit rating assigned to each security, coded so that AAA = 1. The sample period is July 2006 to June 2016. The whole sample includes 3716 bond issues and 47436 observations.From the whole sample, as seen from Table1, the observation is 47436. The average of the spread is 2.5463%, with a standard deviation of 1.1275%. As seen from the median, the distribution of the spread has a long right tail, indicating that some of the very wide yield spreads skew the distribution to the right. Turnover registers a value of 0.0828 every month per issue, reflecting some large values in the right tail of the distribution, while vol averages 87.5034, again with a long right tail. Day averages 4.6538, with a standard deviation of 5.3667. Amihud registers a value of 0.0122 every month, reflecting some large values in the right tail of the distribution, while range averages 0.0238, again with a long right tail. The average of time-to-maturity is 5.4085 years, and the median is 5.2932 years, while age averages 2.2654 years, and the median is 1.9123 years. The mean value of coupon is 6.7952, with a standard deviation 1.0530, while volatility averages 0.5004, with a standard deviation of 0.3617, where the lowest value is 0.0002 and the highest is 14.4579. Finally, The average credit rating score is 3.3323 (between AA− and AA), with a standard deviation of 1.5065.


### 3.1.2. Pairwise Correlation Test

Table2 shows the pairwise correlation coefficients among the independent variables respectively in the whole sample. As confirmed from Table 2, turnover and vol are positively high correlated with each other, with a correlation coefficient of 0.8683, while turnover and day seem to be quite weakly correlated and vol and day are also like this; amihud is also positively correlated with range, with a correlation coefficient of 0.7673. Coupon, volatility, and rating are positively correlated with one another; the coefficient value between coupon and rating is relatively high, with a correlation coefficient of 0.3228, while volatility and coupon exhibit weaker correlation, with a correlation coefficient of 0.0234. On the other hand, liquidity and credit risk proxies also have correlation. Age is negatively correlated with Coupon, with a correlation coefficient of −0.2927.Table 2
Pairwise correlations between independent variables for the whole sample.
TurnoverVolDayAmihudRangeTime-to-maturityAgeVolatilityCouponRatingTurnover1Vol0.8683∗∗∗1Day−0.0293∗∗∗−0.0268∗∗∗1Amihud−0.0926∗∗∗−0.0976∗∗∗−0.0201∗∗∗1Range−0.1030∗∗∗−0.1085∗∗∗0.0064∗∗∗0.7673∗∗∗1Time-to-maturity0.0113∗∗∗0.0437∗∗∗0.1396∗∗∗0.03030.07101Age−0.1541∗∗∗−0.1232∗∗∗0.0741∗∗∗0.02740.0423−0.2945∗∗∗1Volatility0.0490∗∗∗0.0798∗∗∗0.0900∗∗∗0.06400.1036∗∗∗0.1158∗∗∗0.0583∗∗∗1Coupon0.09850.0357∗∗∗0.0921∗∗∗−0.0026−0.0315−0.2345∗∗∗−0.2927∗∗∗0.0234∗∗∗1Rating0.1040∗∗∗0.0198∗∗∗0.0655∗∗∗0.00630.0090−0.1691∗∗∗−0.1786∗∗∗0.0404∗∗∗0.3228∗∗∗1The table shows the pairwise correlation coefficients for the variables used in the regression analysis for the whole sample. The meanings of the variables are given in Table1. The sample period is July 2006 to June 2016. The whole sample includes 3716 bond issues and 47436 observations. “∗∗∗” indicates significance at the 1% level.


### 3.1.3. Unit Root Test

In order to avoid spurious regressions, we first make unit root tests for the sample data. From the results of ADF test of Table3, all variables are significant at the level of 1%, and the original hypothesis of unit root is rejected. That is to say, all the variables are stationary sequence, and the sample data can be analyzed by regression analysis. Then we will study the impact factors of the spreads, especially the interaction between liquidity and credit risk. The stable variable sequence can ensure the validity of the regression results.Table 3
ADF unit root test.
SpreadTurnoverVolDayAmihudRangeTime-to-maturityAgeVolatilityCouponRatingPanel A. The interbank markett-statistic−9.9746∗∗∗−31.5022∗∗∗−27.1805∗∗∗−22.0632∗∗∗−157.0229∗∗∗−156.2083∗∗∗−9.7004∗∗∗−14.8666∗∗∗−13.1248∗∗∗−18.5285∗∗∗−33.6873∗∗∗1% level−3.4304−3.4304−3.4304−3.4304−3.4304−3.4304−3.4304−3.4304−3.4304−3.4304−3.4304Prob.∗0.00010.00010.00010.00010.00010.00010.00010.00010.00010.00010.0001Panel B. The exchange markett-statistic−9.9574∗∗∗−31.6225∗∗∗−33.1601∗∗∗−10.9301∗∗∗−53.5030∗∗∗−53.5321∗∗∗−6.8669∗∗∗−22.4293∗∗∗−8.6634∗∗∗−22.5326∗∗∗−75.8180∗∗∗1% level−3.4305−3.4305−3.4305−3.4305−3.4305−3.4305−3.4305−3.4305−3.4305−3.4305−3.4305Prob.∗0.00010.00010.00010.00010.00010.00010.00010.00010.00010.00010.0001Panel C. The whole samplet-statistic−11.5249∗∗∗−18.8832∗∗∗−20.0654∗∗∗−15.9010∗∗∗−43.0203∗∗∗−41.7255∗∗∗−10.0992∗∗∗−22.1840∗∗∗−15.6788∗∗∗−21.7887∗∗∗−58.7438∗∗∗1% level−3.4303−3.4303−3.4303−3.4303−3.4303−3.4303−3.4303−3.4303−3.4303−3.4303−3.4303Prob.∗0.00010.00010.00010.00010.00010.00010.00010.00010.00010.00010.0001The table shows the ADF unit root test results for the variables used in the regression analysis. The test results include the test of thet statistic, the 1% significance level, and the probability of receiving the original hypothesis. The meanings of the variables are given in Table 1. The sample period is July 2006 to June 2016. The subsample (panel A) includes 2281 bond issues and 25648 observations. The subsample (panel B) includes 1435 bond issues and 21788 observations. The whole sample (panel C) includes 3716 bond issues and 47436 observations. “∗,” “∗∗,” and “∗∗∗’ indicate significance at the 10%, 5%, and 1% levels, respectively.


## 3.1.1. Description

Table1 provides summary statistics for the variables used in empirical analysis. It summarizes trading data and bond characteristics of the sample used in our study. Mean, median, maximum, minimum, standard deviation, Jarque-Bera, probability, and observations for each variable are reported for the whole sample in Table 1.Table 1
Summary statistics for the whole sample. The table shows the summary statistics for variables used in the regression analysis for the whole sample.
VariableMeanMedianMaximumMinimumStd. dev.Jarque-BeraProbabilityObservationsSpread2.54632.494035.58900.00821.12754558494.00000.000147436.0000Turnover0.08280.03622.84760.00010.13322378552.00000.000147436.0000Vol87.503442.39493072.23000.0102133.59003004256.00000.000147436.0000Day4.65382.000023.00001.00005.366738023.83000.000147436.0000Amihud0.01220.00033.52100.00010.0798667000000.00000.000147436.0000Range0.02380.00058.40910.00010.1410685000000.00000.000147436.0000Time-to-maturity5.40855.293227.00271.00272.2759334283.60000.000147436.0000Age2.26541.912313.97810.02471.7405105440.70000.000147436.0000Volatility0.50040.414314.45790.00020.36176590932.00000.000147436.0000Coupon6.79526.90009.30003.17001.05301311.12800.000147436.0000Rating3.33234.000015.00001.00001.5065734923.60000.000147436.0000We report mean, median, maximum, minimum, standard deviation, Jarque-Bera, probability, and observations. Spread is the difference between the yield-to-maturity on the corporate bond and the corresponding treasury rate. Turnover is the frequency of market assets trading hands in a certain period of time. Vol is the average of the total trading volume in the corresponding month. Day is defined as the number of trading days in the corresponding month. Amihud and range are illiquidity measures and describe the liquidity measure of the bond price impact dimension. Time-to-maturity is the remaining years of the bond. Age denotes years since issuance. Volatility is a standard deviation of historical bond price. Coupon is the annual coupon interest. Rating is the credit rating assigned to each security, coded so that AAA = 1. The sample period is July 2006 to June 2016. The whole sample includes 3716 bond issues and 47436 observations.From the whole sample, as seen from Table1, the observation is 47436. The average of the spread is 2.5463%, with a standard deviation of 1.1275%. As seen from the median, the distribution of the spread has a long right tail, indicating that some of the very wide yield spreads skew the distribution to the right. Turnover registers a value of 0.0828 every month per issue, reflecting some large values in the right tail of the distribution, while vol averages 87.5034, again with a long right tail. Day averages 4.6538, with a standard deviation of 5.3667. Amihud registers a value of 0.0122 every month, reflecting some large values in the right tail of the distribution, while range averages 0.0238, again with a long right tail. The average of time-to-maturity is 5.4085 years, and the median is 5.2932 years, while age averages 2.2654 years, and the median is 1.9123 years. The mean value of coupon is 6.7952, with a standard deviation 1.0530, while volatility averages 0.5004, with a standard deviation of 0.3617, where the lowest value is 0.0002 and the highest is 14.4579. Finally, The average credit rating score is 3.3323 (between AA− and AA), with a standard deviation of 1.5065.


## 3.1.2. Pairwise Correlation Test

Table2 shows the pairwise correlation coefficients among the independent variables respectively in the whole sample. As confirmed from Table 2, turnover and vol are positively high correlated with each other, with a correlation coefficient of 0.8683, while turnover and day seem to be quite weakly correlated and vol and day are also like this; amihud is also positively correlated with range, with a correlation coefficient of 0.7673. Coupon, volatility, and rating are positively correlated with one another; the coefficient value between coupon and rating is relatively high, with a correlation coefficient of 0.3228, while volatility and coupon exhibit weaker correlation, with a correlation coefficient of 0.0234. On the other hand, liquidity and credit risk proxies also have correlation. Age is negatively correlated with Coupon, with a correlation coefficient of −0.2927.Table 2
Pairwise correlations between independent variables for the whole sample.
TurnoverVolDayAmihudRangeTime-to-maturityAgeVolatilityCouponRatingTurnover1Vol0.8683∗∗∗1Day−0.0293∗∗∗−0.0268∗∗∗1Amihud−0.0926∗∗∗−0.0976∗∗∗−0.0201∗∗∗1Range−0.1030∗∗∗−0.1085∗∗∗0.0064∗∗∗0.7673∗∗∗1Time-to-maturity0.0113∗∗∗0.0437∗∗∗0.1396∗∗∗0.03030.07101Age−0.1541∗∗∗−0.1232∗∗∗0.0741∗∗∗0.02740.0423−0.2945∗∗∗1Volatility0.0490∗∗∗0.0798∗∗∗0.0900∗∗∗0.06400.1036∗∗∗0.1158∗∗∗0.0583∗∗∗1Coupon0.09850.0357∗∗∗0.0921∗∗∗−0.0026−0.0315−0.2345∗∗∗−0.2927∗∗∗0.0234∗∗∗1Rating0.1040∗∗∗0.0198∗∗∗0.0655∗∗∗0.00630.0090−0.1691∗∗∗−0.1786∗∗∗0.0404∗∗∗0.3228∗∗∗1The table shows the pairwise correlation coefficients for the variables used in the regression analysis for the whole sample. The meanings of the variables are given in Table1. The sample period is July 2006 to June 2016. The whole sample includes 3716 bond issues and 47436 observations. “∗∗∗” indicates significance at the 1% level.


## 3.1.3. Unit Root Test

In order to avoid spurious regressions, we first make unit root tests for the sample data. From the results of ADF test of Table3, all variables are significant at the level of 1%, and the original hypothesis of unit root is rejected. That is to say, all the variables are stationary sequence, and the sample data can be analyzed by regression analysis. Then we will study the impact factors of the spreads, especially the interaction between liquidity and credit risk. The stable variable sequence can ensure the validity of the regression results.Table 3
ADF unit root test.
SpreadTurnoverVolDayAmihudRangeTime-to-maturityAgeVolatilityCouponRatingPanel A. The interbank markett-statistic−9.9746∗∗∗−31.5022∗∗∗−27.1805∗∗∗−22.0632∗∗∗−157.0229∗∗∗−156.2083∗∗∗−9.7004∗∗∗−14.8666∗∗∗−13.1248∗∗∗−18.5285∗∗∗−33.6873∗∗∗1% level−3.4304−3.4304−3.4304−3.4304−3.4304−3.4304−3.4304−3.4304−3.4304−3.4304−3.4304Prob.∗0.00010.00010.00010.00010.00010.00010.00010.00010.00010.00010.0001Panel B. The exchange markett-statistic−9.9574∗∗∗−31.6225∗∗∗−33.1601∗∗∗−10.9301∗∗∗−53.5030∗∗∗−53.5321∗∗∗−6.8669∗∗∗−22.4293∗∗∗−8.6634∗∗∗−22.5326∗∗∗−75.8180∗∗∗1% level−3.4305−3.4305−3.4305−3.4305−3.4305−3.4305−3.4305−3.4305−3.4305−3.4305−3.4305Prob.∗0.00010.00010.00010.00010.00010.00010.00010.00010.00010.00010.0001Panel C. The whole samplet-statistic−11.5249∗∗∗−18.8832∗∗∗−20.0654∗∗∗−15.9010∗∗∗−43.0203∗∗∗−41.7255∗∗∗−10.0992∗∗∗−22.1840∗∗∗−15.6788∗∗∗−21.7887∗∗∗−58.7438∗∗∗1% level−3.4303−3.4303−3.4303−3.4303−3.4303−3.4303−3.4303−3.4303−3.4303−3.4303−3.4303Prob.∗0.00010.00010.00010.00010.00010.00010.00010.00010.00010.00010.0001The table shows the ADF unit root test results for the variables used in the regression analysis. The test results include the test of thet statistic, the 1% significance level, and the probability of receiving the original hypothesis. The meanings of the variables are given in Table 1. The sample period is July 2006 to June 2016. The subsample (panel A) includes 2281 bond issues and 25648 observations. The subsample (panel B) includes 1435 bond issues and 21788 observations. The whole sample (panel C) includes 3716 bond issues and 47436 observations. “∗,” “∗∗,” and “∗∗∗’ indicate significance at the 10%, 5%, and 1% levels, respectively.


## 3.2. The Impact of the Interaction between Liquidity and Credit Risk on Spreads

Some scholars study liquidity and explain why it affects asset prices [41–44]. Bagehot [43] proposes that due to the impact of information asymmetry, liquidity refers to the impact of a transaction on the market price. [44] believe that illiquidity is the risk that assets cannot be sold at a reasonable price within a given time. The above literature shows that liquidity is a potential cost of asset transaction, and investors with illiquid assets need liquidity risk compensation, namely liquidity risk premiums. Information asymmetry is an important factor affecting asset liquidity. The reason why liquidity affects asset price is that investors’ information asymmetry leads to speculative transaction, investment transaction and investors’ compensation for different liquidity risk.Acharya and Pedersen [45] explain the affecting mechanism of liquidity on asset prices. They establish a theoretical model of Liquidity Capital Asset Pricing Model and identify two channels of risk transmission. The first channel is direct compensation for the transaction costs of assets. This is a premium for liquidity level. The second channel is the compensation of asset returns for systemic liquidity. This is a premium for liquidity risk. Bongaerts et al. [46] use an asset pricing approach to compare the impacts of liquidity level and liquidity risk on expected U.S. corporate bond returns and analyze which of these two channels is more important. Liu [47] and Bervas [48] find that a liquid market presents many different dimensions. Díaz and Escribano [49] classify and describe the variety of the existing liquidity measures with the different characteristics and dimensions of liquidity. Previous literature suggests that liquidity has many dimensions. We divide liquidity into three dimensions based on the economic significance of liquidity, including trading activity, price shock, and bond survival time. Liquidity of different dimension has a different impact on corporate bond spreads. Liquidity of transaction activity dimension is the common result of speculative trading and investment trading, while liquidity of price shock dimension is mostly due to investors’ speculative trading. In addition, liquidity of bond survival time dimension mainly represents investors’ investment transaction. Different dimension liquidity premiums have different economic significance. Therefore, liquidity should be measured across the different dimensions in order to have a global view of liquidity. We study the mechanism and channels of liquidity’s impact on asset price from the perspective of multidimension liquidity.Bond credit risk is the risk of loss to investors due to bond default. Investors need some compensation for risk when holding defaultable assets, which is why credit risk affects asset prices. Referring to the existing literature, we select three credit risk indicators, including price volatility, coupon rate, and credit rating. We divide credit risk into two dimensions according to the economic significance, including dynamic credit risk and static credit risk. Relevant literature can also be referred to Li and Song [50]. Different dimension credit risk have different impacts on corporate bond spreads. Dynamic credit risk is mostly caused by investors' speculative trading of liquidity risk, so it often interacts with liquidity, while static credit risk is mainly determined by the default probability of credit bonds themselves, and it is often not linked with liquidity risk. Therefore, credit risk premium of different dimension has a different economic significance. Credit rating and coupon rate are static credit risk measures, while price volatility is a dynamic credit risk measure. The static credit risk represents the credit risk level of an firm in this period of time, and it does not change with the dynamic change of liquidity risk. When liquidity affects asset prices, static credit risk generally does not interact with liquidity risk in a dynamic spiral. Dynamic credit risk represents the credit risk level of an firm over time, and it changes in resonance with the dynamic change of liquidity risk. When liquidity affects asset prices, dynamic credit risk usually interacts with liquidity risk in a dynamic spiral, forming the resonance enhancement interaction between liquidity and credit risk to dynamically affect asset prices. This may be affecting mechanism of the interaction between liquidity and credit risk for asset prices.From the perspective of the market transmission mechanism of risk, if investors hold assets with high credit risk, some informed traders will take the lead in selling assets when adverse information comes out. Massive asset sales can cause asset prices to fall rapidly and make some investors panic. In the case of information asymmetry, some investors will follow to sell assets at lower prices and suffer liquidity losses. Further decline of asset prices will increase liquidity risk. Information outflow and information asymmetry become the spiral transmission path of the interaction between liquidity and credit risk on asset prices.From an economic point of view, investors holding illiquid assets need liquidity risk compensation, similarly, investors holding defaultable assets need credit risk compensation. Default risk and liquidity are linked through investors’ transaction based on information asymmetry, which will inevitably lead to a series of dynamic economic transmission impacts of liquidity and credit risk, and then affect asset prices spirally. Therefore, we introduce interaction between liquidity and credit risk into corporate bond spread model to study their affecting mechanism on asset prices and risk transmission channels.Based on the above analysis, the impact of the interaction between liquidity and credit risk on corporate bond spreads is discussed in this part. The premium regression equation that contains the interaction is as follows(1)Spreadit=α+β1×liquidity risk factorsit+β2×credit risk factorsit+β3×interaction functionliquidity risk factors, credit risk factorsit+εt.To investigate whether the impact of interaction on the spreads is present, the following assumption is given(2)Spreadit=α+β1×liquidity risk factorsit+β2×credit risk factorsit+β3×liquidity risk factorsit×credit risk factorsit+εt.Ifβ3 is significantly different from zero, the impact of the interaction on the spreads is present. For estimating the impact of the interaction, we run a pooled regression of bond spreads in the interbank market, exchange market and the whole sample. The term “Liquidity risk factors” represents a set of possible proxies for liquidity risk from three dimensions, including transaction activity (turnover, vol, and day), price impact (amihud and range), and bond survival time (time-to-maturity, age). Similarly, the term “credit risk factors” represents a set of possible proxies for the default risk, including coupon and volatility. The cross terms of the proxies of liquidity and credit risk represent their interaction. If the regression coefficient of the cross term is significantly different from zero, the interaction has a significant impact on the bond spreads. In order to guarantee the reliability of the research results, we have made empirical tests from many perspectives.


### 3.2.1. The Empirical Results Based on Liquidity Proxies of Transaction Activity

China’s bond market is the second largest in the world after the America. According to the People’s Bank of China, by the end of December 2021, the stock of bonds in China’s bond market is about $21 trillion, while that in the US is about $50 trillion. In 2021, China’s bond issuance reach about $9.6 trillion, accounting for about 54% of China’s GDP ($17.7 trillion) and 11% of global GDP ($90 trillion). It shows that China’s bond market has become an important factor affecting China’s economy and global economy. According to the People’s Bank of China, the stock of corporate debenture bonds is about $5 trillion by the end of December 2021. Corporate Bonds are important parts of China’s bond market. Therefore, it is of great significance to study the impact factors of Chinese corporate bond prices.China’s corporate bond market consists of interbank market and exchange market. In the interbank market, commercial banks, insurance companies, securities firms and other financial institutions buy and sell bonds, and participants ask selected counterparties to complete the transaction. The exchange bond market is dominated by nonbank financial institutions and individuals. China has two types of corporate bonds. One is issued by central government departments or state-owned enterprises, and the other is issued by listed companies. The former can be traded on the exchange market and the interbank market, while the latter can only be traded on the exchange market. This shows that both of markets are important trading places for corporate bonds in China, but the types of corporate bonds traded in the two markets are different, and the structures of investors are different. Therefore, it is necessary to study the impact factors of corporate bond spreads in the two markets. In order to explore the impact of the two markets on the test results, we, respectively, analyze the sample of whole market and subsamples of the interbank market and exchange market. In the whole sample, the dummy variable is introduced to test the significance of the impact of the interbank market and the exchange market on the test results. Where, the dummy variable of the interbank market is set to 1, and the dummy variable of the exchange market is set to 0. The basic proxies of credit risk and liquidity are given, including Vol, Day, Range, Age, Coupon and Volatility. The empirical results are shown in Tables4 and 5.Table 4
The impact of interaction between liquidity and credit risk on spreads based on transaction activity in the whole sample.
123456C2.5912∗∗∗0.7928∗∗∗0.3340∗∗∗0.2715∗∗∗0.3530∗∗∗0.3298∗∗∗(111.7038)(11.0667)(6.96)(5.78)(8.66)(6.87)Dummy0.4812∗∗∗0.4367∗∗∗0.2687∗∗∗0.2065∗∗∗−0.1371∗∗∗0.2494∗∗∗(20.8164)(19.3486)(22.38)(17.42)(−13.11)(20.73)Turnover1.9158∗∗∗1.5967∗∗∗−0.07252.2141∗∗∗1.7381∗∗∗(12.7908)(10.8800)(−0.30)(5.24)(4.28)Vol−0.0020∗∗∗−0.0018∗∗∗−0.0013∗∗∗−0.0018∗∗∗−0.0020∗∗∗(−13.6127)(−12.4066)(−5.38)(−4.49)(−5.01)Day0.0737∗∗∗0.0650∗∗∗−0.0108∗∗−0.0122∗∗−0.0132∗∗(37.6845)(33.6513)(−1.96)(−2.22)(−2.42)Amihud0.3513∗∗∗0.2517∗∗∗0.2506∗∗∗0.2480∗∗∗−0.1368∗∗0.2487∗∗∗(4.0216)(2.9561)(4.41)(4.36)(−2.34)(4.39)Age−0.2030∗∗∗−0.1739∗∗∗−0.1349∗∗∗−0.1314∗∗∗−0.1254∗∗∗−0.1313∗∗∗(−32.1614)(−27.7859)(−49.35)(−47.86)(−44.52)(−47.99)Volatility0.2141∗∗∗−0.2482∗∗∗−0.2266∗∗∗0.1438∗∗∗−0.2437∗∗∗(8.8111)(−13.70)(−12.54)(9.78)(−13.42)Coupon0.2422∗∗∗0.3315∗∗∗0.3391∗∗∗0.3606∗∗∗0.3310∗∗∗(25.0131)(49.42)(51.69)(66.47)(49.26)Turnover × volatility0.2046∗∗−0.3269∗∗−0.2896∗(2.28)(−1.97)(−1.81)Turnover × coupon0.0081−0.1077∗−0.0624(0.24)(−1.84)(−1.11)Vol × volatility0.0005∗∗∗0.0005∗∗∗0.0008∗∗∗(6.33)(3.69)(6.05)Vol × coupon0.0001∗∗∗0.0001∗0.0000(2.93)(1.72)(0.57)Day × volatility0.0614∗∗∗0.0615∗∗∗0.0611∗∗∗(26.65)(26.65)(26.58)Day × coupon0.0052∗∗∗0.0050∗∗∗0.0055∗∗∗(7.18)(6.94)(7.60)aj−R20.17520.21840.26820.26690.21170.2723To investigate whether the impact of interaction on the spreads is present, the following regression equations are given. Spreadit = α + β1 × (liquidity risk factors)it + β2 × (credit risk factors)it + β3 × (transaction activity liquidity risk factors)it × (credit risk factors)it + єt. The meanings of the variables are given in Table 1. The sample period is July 2006 to June 2016. The whole sample includes 3716 bond issues and 47436 observations. The t-statistics are shown in parentheses below each coefficient estimate, and “∗,” “∗∗,’ and “∗∗∗’ indicate significance at the 10%, 5%, and 1% levels, respectively.Table 5
The impact of interaction between liquidity and credit risk on spreads based on transaction activity in interbank market and exchange market.
The inter bank marketThe exchange market12341234C0.3490∗∗∗0.2341∗∗∗0.2655∗∗∗0.3312∗∗∗0.8091∗∗∗0.6666∗∗∗0.4069∗∗∗0.7630∗∗∗(5.63)(3.83)(4.80)(5.32)(10.59(8.83)(6.91)(10.16)Turnover0.8623∗∗∗1.7225∗∗∗1.5566∗∗∗−1.876818.8014∗∗∗24.2606∗∗∗(3.14)(4.34)(3.93)(−1.39)(6.97)(9.39)Vol0.0003−0.0012∗∗∗−0.0004−0.0114∗∗∗−0.0246∗∗∗−0.0252∗∗∗(1.15)(−2.93)(−0.99)(−9.98)(−10.86)(−11.62)Day−0.0676∗∗∗−0.0324−0.0766∗∗∗−0.0022−0.0070−0.0018(−3.08)(−1.54)(−3.47)(−0.31)(−1.00)(−0.26)Amihud12.8027∗∗∗13.4242∗∗∗13.4778∗∗∗12.9596∗∗∗0.2895∗∗∗0.3265∗∗∗0.00280.2956∗∗∗(8.80)(9.22)(9.36)(8.93)(4.96)(5.65)(0.05)(5.16)Age−0.1474∗∗∗−0.1443∗∗∗−0.1417∗∗∗−0.1420∗∗∗−0.1309∗∗∗−0.1248∗∗∗−0.1087∗∗∗−0.1252∗∗∗(−37.34)(−36.25)(−35.89)(−35.79)(−34.87)(−33.47)(−28.39)(−33.83)Volatility−0.1971∗∗∗−0.1899∗∗∗−0.1939∗∗∗−0.1967∗∗∗−0.1253∗∗∗−0.0750∗∗0.1765∗∗∗−0.0762∗∗(−8.06)(−7.76)(−9.88)(−8.06)(−3.83)(−2.31)(8.00)(−2.37)Coupon0.3678∗∗∗0.3822∗∗∗0.3882∗∗∗0.3672∗∗∗0.2522∗∗∗0.2659∗∗∗0.3301∗∗∗0.2543∗∗∗(41.14)(43.26)(49.53)(40.86)(23.62)(25.18)(43.42)(24.23)Turnover × volatility0.2945∗∗−0.2244−0.3161∗∗16.3455∗∗∗13.1480∗∗∗12.1640∗∗∗(2.50)(−1.43)(−1.97)(34.04)(12.99)(12.49)Turnover × coupon−0.1400∗∗∗−0.1075∗−0.0821−0.4313∗∗−2.2377∗∗∗−3.2118∗∗∗(−3.69)(−1.96)(−1.50)(−2.38)(−6.08)(−9.09)Vol × volatility0.0007∗∗∗0.0009∗∗∗0.0010∗∗∗0.0138∗∗∗0.0042∗∗∗0.0046∗∗∗(6.86)(6.69)(7.19)(31.82)(4.56)(5.25)Vol × coupon−0.0002∗∗∗0.0001−0.0002∗∗∗0.0008∗∗∗0.0026∗∗∗0.0026∗∗∗(−4.15)(−0.13)(−3.10)(5.40)(8.55)(8.73)Day × volatility−0.01240.0110−0.00960.0215∗∗∗0.0181∗∗∗0.0144∗∗∗(−1.09)(0.99)(−0.83)(6.62)(5.59)(4.48)Day × coupon0.0207∗∗∗0.0094∗∗∗0.0215∗∗∗0.0065∗∗∗0.0068∗∗∗0.0065∗∗∗(6.27)(3.03)(6.50)(6.70)(7.13)(6.84)aj−R20.22760.22470.22630.23180.34260.35460.30450.3649To investigate whether the impact of interaction on the spreads is present, the following regression equations are given. Spreadit = α +β1 × (liquidity risk factors)it + β2 × (credit risk factors)it + β3 × (transaction activity liquidity risk factors)it × (credit risk factors)it + єt. The meanings of the variables are given in Table 1. The sample period is July 2006 to June 2016. The subsample of the interbank market includes 2281 bond issues and 25648 observations. The subsample of the exchange market includes 1435 bond issues and 21788 observations. The t-statistics are shown in parentheses below each coefficient estimate, and “∗,” “∗∗,” and “∗∗∗” indicate significance at the 10%, 5%, and 1% levels, respectively.In Table4, Model 1 gives the regression results that include liquidity, and Model 2 gives the regression results including credit risk and liquidity. Compared with Model 2, the results of Model 1 show that the liquidity premiums are the main components of corporate bond spreads. Corporate bonds are rarely traded in China’s bond market, which results in poor liquidity. In Model 1 and Model 2, the regression coefficients of Vol are −0.0020 and −0.0018, respectively, and they are significant at the level of 1%, which is consistent with the hypothesis. The greater the values is, more active the bond transaction is. It shows that the bond liquidity risk is smaller, and the spreads are smaller [3, 12, 37]. The regression coefficients of Turnover and Day are positive, and they are inconsistent with the hypothesis. China’s corporate bond market trades infrequently, and the increase of turnover rates and trading days may be due to speculative trading. In Model 1 and Model 2, the regression coefficients of Amihud are 0.3513 and 0.2517, respectively, and they are significant at the level of 1%, which is consistent with the hypothesis. The results of model 1 show that for every 1 unit increase in liquidity risk of price shock dimension, corporate bond spreads increase by 0.3513 unit. See also Shin and Kim [37] and Han and Zhou [30]. In Model 1 and Model 2, the regression coefficients of Age are −0.2030 and −0.1739, respectively, and they are significant at the level of 1%, which is consistent with the hypothesis. Because of information asymmetry, investors will not buy and trade new bonds. Over time, investors will choose to buy the bonds. Then the transactions become active, and the spreads begin to become small. Goldstein et al. [33] and Hotchkiss and Jostova [34] find similar results. In Model 2, the regression coefficients of Volatility and Coupon are 0.2141 and 0.2422, respectively, and they are significant at the level of 1%, which is consistent with the hypothesis. Volatility and Coupon are the proxies of credit risk. The greater the value is, the worse credit is, and the greater the spreads are. So Volatility and Coupon have positive relation with spreads [37, 39, 40].The regression results containing interaction terms are given in Model 3. Model 4 and Model 5 gives the robustness analysis results. In addition, the regression analysis results of the all transaction activity dimension are given in Model 6. Cross term represents the corresponding interaction proxy. If the coefficient of cross term is significantly different from zero, the impact of the interaction on the spreads is significant. According to the test results of Table4, the coefficient of dummy variable is significant at the level of 1%, which indicates that the differences between the interbank market and the exchange market cannot be ignored.In Table4, regression results of Model 3 show that the coefficient of vol is significant at the level of 1%, and the sign is in line with the hypothesis, while the regression coefficient of coupon is very significant. Meanwhile, the coefficient of the cross term of vol and coupon is very significant. The coefficient of the cross term of vol and coupon is significantly different from zero, which indicates that the interaction has impacts on the spreads. In Model 3, the regression coefficient of volatility is significant, but the sign is not in line with the hypothesis. It shows that when the trading volume of high-credit risk assets increases, the panic selling of some investors due to asymmetric information leads to increase asset price volatility. The increase of the volatility leads to the increase of speculative liquidity risk. And the spiral increase of speculative liquidity risk and static credit risk leads to the impact of the interaction between liquidity and credit risk on asset prices. The coefficients of day, coupon and day × coupon have similar characteristics.In Model 4, the coefficients of day, coupon and day × coupon are significant, which shows that the interaction between day and coupon has a significant impact on corporate bond spreads. The reason is that static credit risk does not weaken when investment liquidity increases, and the interaction between liquidity and credit risk affects asset prices in the same direction as static credit risk.In Model 5, the coefficient of the interaction between vol and volatility is greater than one of the interaction between vol and coupon. And they have enhanced impacts on bond spreads. It shows that dynamic credit risk changes in resonance with the dynamic change of liquidity risk, while the static credit risk does not change with the dynamic change of liquidity risk. When liquidity affects asset prices, dynamic credit risk interacts with liquidity risk in a dynamic spiral, forming a bigger resonance enhancement interaction between liquidity and credit risk to dynamically affect asset prices than static credit risk. Li and Song [50] study the pricing of China’s convertible bonds and find that the dynamic credit risk is important in convertible bond pricing.Regression analysis results are given in Model 6, which contains all the liquidity risk proxies of the transaction activity. The coefficients of vol × volatility, day × volatility and day × coupon are significant, which shows that the interaction between liquidity and credit risk has a significant impact on spreads. The coefficients of turnover × coupon and vol × coupon are not significant, and the reason is that when liquidity affects asset prices, static credit risk generally does not interact with liquidity risk in a dynamic spiral. From Model 1 to Model 6, the coefficients of age are all significant at the level of 1%, and the signs are negative. Chinese investors tend to be cautious about newly listed bonds due to information asymmetry, so they prefer to buy corporate bonds that trade for many years, which causes bond liquidity to increase over time. Therefore, the high age bonds have lower bond spreads in China’s corporate bond market. Relevant literature can also be referred to Zhu [51].In Table5, the empirical results of the interbank market and the exchange market are given. Regression results of Model 1 show that the regression coefficient of vol is significant at the level of 1% and the sign is in line with the hypothesis on the exchange market, while the regression coefficient of day is significant at the level of 1% and the sign is in line with the hypothesis in the interbank market. The reason is that exchange market is dominated by individual investors with many trading days but few trading volumes, so trading volume is a good proxy for liquidity in the exchange market. On the other hand, interbank market is dominated by institutional investors with few trading days and high trading volumes, so trading day is a better proxy for liquidity in the interbank market. In the interbank market, the assumption that the coefficient of day × coupon is equal to zero is rejected, which indicates that the interaction between liquidity and credit risk has a significant impact on the spreads in Model 1. When investors hold high credit risk bond, with the increase of trading days, some investors panic sell-off due to asymmetric information, that is to say, they are worried about potential default risk to sudden frequent trading bonds, which leads to spiral interaction between liquidity and credit risk, resulting in corporate bond spreads widen. The regression coefficient of vol × coupon has similar conclusion on the exchange market.Robustness analysis are done in Model 2 and Model 3. The empirical results show that the regression coefficients of the interaction between liquidity and credit risk are all significant in the exchange market, while some of these coefficients are not significant in the interbank market. The reason is that the interbank market is mainly composed of institutional investors with infrequent transactions, leading to the discontinuous linkage between liquidity and credit risk and the failure to form continuous transmission and feedback of information. This shows that the establishment of a continuous market trading mechanism, which makes information flow and reduces information asymmetry, is conducive to price discovery.Regression analysis results are given in Model 4, which contains all the liquidity risk proxies of the transaction activity. The regression coefficients of interaction between liquidity and credit risk are all significant in the exchange market, while the regression coefficients of Turnover × Coupon and Day × Volatility are not significant in the interbank market. The reason is that investor structure and transaction characteristic are different in the interbank market and the exchange market.Through the above analysis, interaction between liquidity and credit risk cannot be ignored and liquidity premiums are the main components of corporate bond spreads in China’s bond market. Dynamic credit risk changes in resonance with the dynamic change of liquidity risk, while the static credit risk does not change with the dynamic change of liquidity risk. When liquidity affects asset prices, dynamic credit risk interacts with liquidity risk in a dynamic spiral, forming a bigger resonance enhancement interaction between liquidity and credit risk to dynamically affect asset prices than static credit risk.


### 3.2.2. Subsample Results

In this part, we give sub samples regression analysis, and the liquidity and credit risk proxies are divided into high, medium and low in order to explore the impact of the interaction between liquidity and credit risk on the spreads.In Table6, there are nine subsamples. The regression results of the three subsamples are given according to the trading volume in the panel A. In the high-vol subsample, the regression coefficients of amihud × volatility, amihud × coupon, age × volatility and age × coupon are significant, while the regression coefficients of vol × volatility and vol × coupon are not significant. It suggests that the interactions between liquidity and credit risk in high-vol bonds are mainly the interaction between speculative liquidity of price shock dimension and credit risk and the interaction between investment liquidity and credit risk. In the low-vol subsample, the regression coefficient of amihud × volatility is not significant, suggesting that the spiral interaction between speculative liquidity of price shock dimension and dynamic credit risk requires high trading volume as the basic condition.Table 6
The impact of interaction between liquidity and credit risk on spreads in subsample results.
Panel A: volPanel B: amihudPanel C: ageHightMiddleLowHightMiddleLowHightMiddleLowc−1.0268∗∗∗−0.4000∗∗∗−0.6494∗∗∗−0.6142∗∗∗−0.4396∗−0.6475∗∗∗0.24710.0498−2.0406∗∗∗(−5.84)(−3.56)(−6.10)(−3.92)(−1.84)(−8.50)(1.16)(0.33)(−19.95)Dummy0.3600∗∗∗0.3715∗∗∗0.3015∗∗∗0.4950∗∗∗0.3671∗∗∗0.3201∗∗∗0.1926∗∗∗0.2973∗∗∗0.2909∗∗∗(5.80)(21.04)(6.43)(4.70)(8.28)(20.60)(5.90)(19.01)(17.81)Vol0.0003−0.0101∗∗∗0.0110−0.0652−0.0091−0.0010∗∗∗−0.0010−0.0008∗∗0.0001(0.76)(−6.49)(0.52)(−1.54)(−1.24)(−3.60)(−1.46)(−2.47)(0.49)Day0.0947∗∗∗0.0616∗∗∗0.0341∗∗∗0.0259∗∗∗0.0466∗∗∗0.0621∗∗∗0.0583∗∗∗0.0608∗∗∗0.0373∗∗∗(23.33)(42.81)(20.30)(7.42)(19.39)(50.00)(22.49)(46.14)(26.67)Amihud−1940.6200∗∗∗−83.3530∗∗0.8493∗∗0.6793−12.5975−280.7775∗∗∗1.7829∗∗−0.0439−0.9569(−5.15)(−2.24)(2.27)(1.58)(−0.37)(−3.86)(2.03)(−0.09)(−1.16)Age0.2520∗∗∗0.2224∗∗∗0.2046∗∗∗0.2015∗∗∗0.1688∗∗∗0.1779∗∗∗−0.0557−0.08411.0736∗∗∗(6.72)(10.34)(9.73)(5.75)(5.18)(10.33)(−1.30)(−1.18)(6.90)Volatility0.09090.05580.1072∗∗0.1180∗0.1472−0.0227−0.4399∗∗∗0.8224∗∗∗−0.2797∗∗∗(1.32)(1.16)(2.38)(1.85)(1.52)(−0.62)(−4.82)(12.72)(−6.19)Coupon0.4754∗∗∗0.4229∗∗∗0.4915∗∗∗0.4886∗∗∗0.4350∗∗∗0.4604∗∗∗0.3421∗∗∗0.3014∗∗∗0.7048∗∗∗(20.58)(25.74)(32.98)(22.75)(12.88)(41.73)(9.34)(14.22)(48.18)Vol × volatility−0.00010.0039∗∗∗0.0248∗∗∗0.0188∗∗0.00030.0006∗∗∗0.0007∗∗∗0.0006∗∗∗0.0000(−1.06)(5.90)(2.95)(2.34)(0.17)(7.15)(3.51)(6.76)(−0.02)Vol × coupon−0.00010.0011∗∗∗−0.0054∗0.00150.00050.00000.00020.0000−0.0001∗∗−1.44(5.02)(−1.82)(0.26)(0.54)(1.02)(1.51(−0.26)(−2.47)Amihud × volatility400.6426∗∗∗15.0529∗−0.0999−0.102819.2996317.0865∗∗∗−0.3220−0.3831∗∗0.0986(4.79)(1.94(−0.82)(−0.74)(1.30)(10.76)(−1.04)(−2.21)(0.63)Amihud × coupon238.7952∗∗∗9.6909∗−0.0996∗∗−0.08541.552623.8625∗∗−0.2105∗0.07820.1160(4.60)(1.89)(−1.96)(−1.47)(0.32)(2.28)(−1.83)(1.13)(1.10)Age × volatility0.0498∗∗−0.0736∗∗∗−0.0321∗∗∗−0.0301∗−0.0702∗∗∗−0.0186∗∗0.0840∗∗∗−0.2944∗∗∗0.7791∗∗∗(2.50)(−6.77)(−3.11)(−1.85)(−4.14)(−2.02)(4.37)(−10.13)(10.95)Age × coupon−0.0648∗∗∗−0.0552∗∗∗−0.0563∗∗∗−0.0522∗∗∗−0.0478∗∗∗−0.0511∗∗∗−0.0175∗∗0.0096−0.2350∗∗∗(−11.01)(−16.27)(−16.63)(−9.31)(−9.00)(−18.76)(−2.19)(0.95)(−10.66)aj−R20.25120.27890.29840.25180.31230.26790.13490.21780.4787To investigate whether the impact of interaction on the spreads is present, the following regression equations are given. Spreadit = α + β1 × (liquidity risk factors)it + β2 × (credit risk factors)it + β3 × (different dimension liquidity risk factors)it × (credit risk factors)it + єt. The meanings of the variables are given in Table 1. The sample period is July 2006 to June 2016. The whole sample includes 3716 bond issues and 47436 observations. The t-statistics are shown in parentheses below each coefficient estimate, and “∗,” “∗∗,” and “∗∗∗” indicate significance at the 10%, 5%, and 1% levels.In the high-amihud subsample of panel B, the regression coefficients of vol × volatility, age × volatility and age × coupon are significant, while the regression coefficients of vol × coupon, amihud × volatility, and amihud × coupon are not significant. It shows that high price shock is usually caused by a huge amount of investors’ sudden trading. Generally, prices will recover calm immediately after a huge impact, which makes it difficult to form risk transmission and interaction between liquidity and credit risk in a very short period of time. In the subsamples of panel B, the regression coefficients of vol × coupon are all not significant. Coupon is static credit risk measure. The static credit risk represents the credit risk level of an firm in this period of time, and it does not change with the dynamic change of liquidity risk. When liquidity affects asset prices, static credit risk generally does not interact with liquidity risk in a dynamic spiral.In the high-age subsample of panel C, the regression coefficients of vol × volatility, amihud × coupon, age × volatility and age × coupon are significant, while the regression coefficients of vol × coupon and amihud × volatility are not significant. It shows that high age bonds are actively traded, and sufficient trading volume forms the spiral interaction between speculative liquidity and dynamic credit risk and the interaction between liquidity of price shock dimension and static credit risk, thus affecting asset prices. In the low-age subsample of panel C, the regression coefficients of vol × coupon, age × volatility and age × coupon are significant, while the regression coefficients of vol × volatility, amihud × volatility, and amihud × coupon are not significant. The reason is that low age bonds are not actively traded, and the lack of trading volume only forms the interaction between investment liquidity and static credit risk, which indicates that the interaction between liquidity of price shock dimension and credit risk requires sufficient trading volume as the basic condition.To sum up, the interaction between liquidity and credit risk will increase with the increase of liquidity risk and credit risk and it is a time-varying dynamic process. When market liquidity risk increases, some investors will take the lead in selling corporate bonds with high default risk, which causes the price of corporate bonds with high credit risk to fluctuate greatly. These behaviors of investors further cause more investors to sell these corporate bonds with high credit risk, so the investors who hold these high credit risk bonds have to bear the gradually increasing liquidity risk. With the increase of market liquidity risk, firms with high default risk are affected due to the depletion of operating cash flow, and the probability of default will also increase. Because of information asymmetry, investors sell their bonds more quickly, creating a spiral interaction between liquidity and credit risk that affects asset prices. If market liquidity risk continues to increase, corporate bonds with low credit risk will gradually be affected by the interaction between liquidity and credit risk, and eventually more corporate bond prices will be affected by risk contagion.


## 3.2.1. The Empirical Results Based on Liquidity Proxies of Transaction Activity

China’s bond market is the second largest in the world after the America. According to the People’s Bank of China, by the end of December 2021, the stock of bonds in China’s bond market is about $21 trillion, while that in the US is about $50 trillion. In 2021, China’s bond issuance reach about $9.6 trillion, accounting for about 54% of China’s GDP ($17.7 trillion) and 11% of global GDP ($90 trillion). It shows that China’s bond market has become an important factor affecting China’s economy and global economy. According to the People’s Bank of China, the stock of corporate debenture bonds is about $5 trillion by the end of December 2021. Corporate Bonds are important parts of China’s bond market. Therefore, it is of great significance to study the impact factors of Chinese corporate bond prices.China’s corporate bond market consists of interbank market and exchange market. In the interbank market, commercial banks, insurance companies, securities firms and other financial institutions buy and sell bonds, and participants ask selected counterparties to complete the transaction. The exchange bond market is dominated by nonbank financial institutions and individuals. China has two types of corporate bonds. One is issued by central government departments or state-owned enterprises, and the other is issued by listed companies. The former can be traded on the exchange market and the interbank market, while the latter can only be traded on the exchange market. This shows that both of markets are important trading places for corporate bonds in China, but the types of corporate bonds traded in the two markets are different, and the structures of investors are different. Therefore, it is necessary to study the impact factors of corporate bond spreads in the two markets. In order to explore the impact of the two markets on the test results, we, respectively, analyze the sample of whole market and subsamples of the interbank market and exchange market. In the whole sample, the dummy variable is introduced to test the significance of the impact of the interbank market and the exchange market on the test results. Where, the dummy variable of the interbank market is set to 1, and the dummy variable of the exchange market is set to 0. The basic proxies of credit risk and liquidity are given, including Vol, Day, Range, Age, Coupon and Volatility. The empirical results are shown in Tables4 and 5.Table 4
The impact of interaction between liquidity and credit risk on spreads based on transaction activity in the whole sample.
123456C2.5912∗∗∗0.7928∗∗∗0.3340∗∗∗0.2715∗∗∗0.3530∗∗∗0.3298∗∗∗(111.7038)(11.0667)(6.96)(5.78)(8.66)(6.87)Dummy0.4812∗∗∗0.4367∗∗∗0.2687∗∗∗0.2065∗∗∗−0.1371∗∗∗0.2494∗∗∗(20.8164)(19.3486)(22.38)(17.42)(−13.11)(20.73)Turnover1.9158∗∗∗1.5967∗∗∗−0.07252.2141∗∗∗1.7381∗∗∗(12.7908)(10.8800)(−0.30)(5.24)(4.28)Vol−0.0020∗∗∗−0.0018∗∗∗−0.0013∗∗∗−0.0018∗∗∗−0.0020∗∗∗(−13.6127)(−12.4066)(−5.38)(−4.49)(−5.01)Day0.0737∗∗∗0.0650∗∗∗−0.0108∗∗−0.0122∗∗−0.0132∗∗(37.6845)(33.6513)(−1.96)(−2.22)(−2.42)Amihud0.3513∗∗∗0.2517∗∗∗0.2506∗∗∗0.2480∗∗∗−0.1368∗∗0.2487∗∗∗(4.0216)(2.9561)(4.41)(4.36)(−2.34)(4.39)Age−0.2030∗∗∗−0.1739∗∗∗−0.1349∗∗∗−0.1314∗∗∗−0.1254∗∗∗−0.1313∗∗∗(−32.1614)(−27.7859)(−49.35)(−47.86)(−44.52)(−47.99)Volatility0.2141∗∗∗−0.2482∗∗∗−0.2266∗∗∗0.1438∗∗∗−0.2437∗∗∗(8.8111)(−13.70)(−12.54)(9.78)(−13.42)Coupon0.2422∗∗∗0.3315∗∗∗0.3391∗∗∗0.3606∗∗∗0.3310∗∗∗(25.0131)(49.42)(51.69)(66.47)(49.26)Turnover × volatility0.2046∗∗−0.3269∗∗−0.2896∗(2.28)(−1.97)(−1.81)Turnover × coupon0.0081−0.1077∗−0.0624(0.24)(−1.84)(−1.11)Vol × volatility0.0005∗∗∗0.0005∗∗∗0.0008∗∗∗(6.33)(3.69)(6.05)Vol × coupon0.0001∗∗∗0.0001∗0.0000(2.93)(1.72)(0.57)Day × volatility0.0614∗∗∗0.0615∗∗∗0.0611∗∗∗(26.65)(26.65)(26.58)Day × coupon0.0052∗∗∗0.0050∗∗∗0.0055∗∗∗(7.18)(6.94)(7.60)aj−R20.17520.21840.26820.26690.21170.2723To investigate whether the impact of interaction on the spreads is present, the following regression equations are given. Spreadit = α + β1 × (liquidity risk factors)it + β2 × (credit risk factors)it + β3 × (transaction activity liquidity risk factors)it × (credit risk factors)it + єt. The meanings of the variables are given in Table 1. The sample period is July 2006 to June 2016. The whole sample includes 3716 bond issues and 47436 observations. The t-statistics are shown in parentheses below each coefficient estimate, and “∗,” “∗∗,’ and “∗∗∗’ indicate significance at the 10%, 5%, and 1% levels, respectively.Table 5
The impact of interaction between liquidity and credit risk on spreads based on transaction activity in interbank market and exchange market.
The inter bank marketThe exchange market12341234C0.3490∗∗∗0.2341∗∗∗0.2655∗∗∗0.3312∗∗∗0.8091∗∗∗0.6666∗∗∗0.4069∗∗∗0.7630∗∗∗(5.63)(3.83)(4.80)(5.32)(10.59(8.83)(6.91)(10.16)Turnover0.8623∗∗∗1.7225∗∗∗1.5566∗∗∗−1.876818.8014∗∗∗24.2606∗∗∗(3.14)(4.34)(3.93)(−1.39)(6.97)(9.39)Vol0.0003−0.0012∗∗∗−0.0004−0.0114∗∗∗−0.0246∗∗∗−0.0252∗∗∗(1.15)(−2.93)(−0.99)(−9.98)(−10.86)(−11.62)Day−0.0676∗∗∗−0.0324−0.0766∗∗∗−0.0022−0.0070−0.0018(−3.08)(−1.54)(−3.47)(−0.31)(−1.00)(−0.26)Amihud12.8027∗∗∗13.4242∗∗∗13.4778∗∗∗12.9596∗∗∗0.2895∗∗∗0.3265∗∗∗0.00280.2956∗∗∗(8.80)(9.22)(9.36)(8.93)(4.96)(5.65)(0.05)(5.16)Age−0.1474∗∗∗−0.1443∗∗∗−0.1417∗∗∗−0.1420∗∗∗−0.1309∗∗∗−0.1248∗∗∗−0.1087∗∗∗−0.1252∗∗∗(−37.34)(−36.25)(−35.89)(−35.79)(−34.87)(−33.47)(−28.39)(−33.83)Volatility−0.1971∗∗∗−0.1899∗∗∗−0.1939∗∗∗−0.1967∗∗∗−0.1253∗∗∗−0.0750∗∗0.1765∗∗∗−0.0762∗∗(−8.06)(−7.76)(−9.88)(−8.06)(−3.83)(−2.31)(8.00)(−2.37)Coupon0.3678∗∗∗0.3822∗∗∗0.3882∗∗∗0.3672∗∗∗0.2522∗∗∗0.2659∗∗∗0.3301∗∗∗0.2543∗∗∗(41.14)(43.26)(49.53)(40.86)(23.62)(25.18)(43.42)(24.23)Turnover × volatility0.2945∗∗−0.2244−0.3161∗∗16.3455∗∗∗13.1480∗∗∗12.1640∗∗∗(2.50)(−1.43)(−1.97)(34.04)(12.99)(12.49)Turnover × coupon−0.1400∗∗∗−0.1075∗−0.0821−0.4313∗∗−2.2377∗∗∗−3.2118∗∗∗(−3.69)(−1.96)(−1.50)(−2.38)(−6.08)(−9.09)Vol × volatility0.0007∗∗∗0.0009∗∗∗0.0010∗∗∗0.0138∗∗∗0.0042∗∗∗0.0046∗∗∗(6.86)(6.69)(7.19)(31.82)(4.56)(5.25)Vol × coupon−0.0002∗∗∗0.0001−0.0002∗∗∗0.0008∗∗∗0.0026∗∗∗0.0026∗∗∗(−4.15)(−0.13)(−3.10)(5.40)(8.55)(8.73)Day × volatility−0.01240.0110−0.00960.0215∗∗∗0.0181∗∗∗0.0144∗∗∗(−1.09)(0.99)(−0.83)(6.62)(5.59)(4.48)Day × coupon0.0207∗∗∗0.0094∗∗∗0.0215∗∗∗0.0065∗∗∗0.0068∗∗∗0.0065∗∗∗(6.27)(3.03)(6.50)(6.70)(7.13)(6.84)aj−R20.22760.22470.22630.23180.34260.35460.30450.3649To investigate whether the impact of interaction on the spreads is present, the following regression equations are given. Spreadit = α +β1 × (liquidity risk factors)it + β2 × (credit risk factors)it + β3 × (transaction activity liquidity risk factors)it × (credit risk factors)it + єt. The meanings of the variables are given in Table 1. The sample period is July 2006 to June 2016. The subsample of the interbank market includes 2281 bond issues and 25648 observations. The subsample of the exchange market includes 1435 bond issues and 21788 observations. The t-statistics are shown in parentheses below each coefficient estimate, and “∗,” “∗∗,” and “∗∗∗” indicate significance at the 10%, 5%, and 1% levels, respectively.In Table4, Model 1 gives the regression results that include liquidity, and Model 2 gives the regression results including credit risk and liquidity. Compared with Model 2, the results of Model 1 show that the liquidity premiums are the main components of corporate bond spreads. Corporate bonds are rarely traded in China’s bond market, which results in poor liquidity. In Model 1 and Model 2, the regression coefficients of Vol are −0.0020 and −0.0018, respectively, and they are significant at the level of 1%, which is consistent with the hypothesis. The greater the values is, more active the bond transaction is. It shows that the bond liquidity risk is smaller, and the spreads are smaller [3, 12, 37]. The regression coefficients of Turnover and Day are positive, and they are inconsistent with the hypothesis. China’s corporate bond market trades infrequently, and the increase of turnover rates and trading days may be due to speculative trading. In Model 1 and Model 2, the regression coefficients of Amihud are 0.3513 and 0.2517, respectively, and they are significant at the level of 1%, which is consistent with the hypothesis. The results of model 1 show that for every 1 unit increase in liquidity risk of price shock dimension, corporate bond spreads increase by 0.3513 unit. See also Shin and Kim [37] and Han and Zhou [30]. In Model 1 and Model 2, the regression coefficients of Age are −0.2030 and −0.1739, respectively, and they are significant at the level of 1%, which is consistent with the hypothesis. Because of information asymmetry, investors will not buy and trade new bonds. Over time, investors will choose to buy the bonds. Then the transactions become active, and the spreads begin to become small. Goldstein et al. [33] and Hotchkiss and Jostova [34] find similar results. In Model 2, the regression coefficients of Volatility and Coupon are 0.2141 and 0.2422, respectively, and they are significant at the level of 1%, which is consistent with the hypothesis. Volatility and Coupon are the proxies of credit risk. The greater the value is, the worse credit is, and the greater the spreads are. So Volatility and Coupon have positive relation with spreads [37, 39, 40].The regression results containing interaction terms are given in Model 3. Model 4 and Model 5 gives the robustness analysis results. In addition, the regression analysis results of the all transaction activity dimension are given in Model 6. Cross term represents the corresponding interaction proxy. If the coefficient of cross term is significantly different from zero, the impact of the interaction on the spreads is significant. According to the test results of Table4, the coefficient of dummy variable is significant at the level of 1%, which indicates that the differences between the interbank market and the exchange market cannot be ignored.In Table4, regression results of Model 3 show that the coefficient of vol is significant at the level of 1%, and the sign is in line with the hypothesis, while the regression coefficient of coupon is very significant. Meanwhile, the coefficient of the cross term of vol and coupon is very significant. The coefficient of the cross term of vol and coupon is significantly different from zero, which indicates that the interaction has impacts on the spreads. In Model 3, the regression coefficient of volatility is significant, but the sign is not in line with the hypothesis. It shows that when the trading volume of high-credit risk assets increases, the panic selling of some investors due to asymmetric information leads to increase asset price volatility. The increase of the volatility leads to the increase of speculative liquidity risk. And the spiral increase of speculative liquidity risk and static credit risk leads to the impact of the interaction between liquidity and credit risk on asset prices. The coefficients of day, coupon and day × coupon have similar characteristics.In Model 4, the coefficients of day, coupon and day × coupon are significant, which shows that the interaction between day and coupon has a significant impact on corporate bond spreads. The reason is that static credit risk does not weaken when investment liquidity increases, and the interaction between liquidity and credit risk affects asset prices in the same direction as static credit risk.In Model 5, the coefficient of the interaction between vol and volatility is greater than one of the interaction between vol and coupon. And they have enhanced impacts on bond spreads. It shows that dynamic credit risk changes in resonance with the dynamic change of liquidity risk, while the static credit risk does not change with the dynamic change of liquidity risk. When liquidity affects asset prices, dynamic credit risk interacts with liquidity risk in a dynamic spiral, forming a bigger resonance enhancement interaction between liquidity and credit risk to dynamically affect asset prices than static credit risk. Li and Song [50] study the pricing of China’s convertible bonds and find that the dynamic credit risk is important in convertible bond pricing.Regression analysis results are given in Model 6, which contains all the liquidity risk proxies of the transaction activity. The coefficients of vol × volatility, day × volatility and day × coupon are significant, which shows that the interaction between liquidity and credit risk has a significant impact on spreads. The coefficients of turnover × coupon and vol × coupon are not significant, and the reason is that when liquidity affects asset prices, static credit risk generally does not interact with liquidity risk in a dynamic spiral. From Model 1 to Model 6, the coefficients of age are all significant at the level of 1%, and the signs are negative. Chinese investors tend to be cautious about newly listed bonds due to information asymmetry, so they prefer to buy corporate bonds that trade for many years, which causes bond liquidity to increase over time. Therefore, the high age bonds have lower bond spreads in China’s corporate bond market. Relevant literature can also be referred to Zhu [51].In Table5, the empirical results of the interbank market and the exchange market are given. Regression results of Model 1 show that the regression coefficient of vol is significant at the level of 1% and the sign is in line with the hypothesis on the exchange market, while the regression coefficient of day is significant at the level of 1% and the sign is in line with the hypothesis in the interbank market. The reason is that exchange market is dominated by individual investors with many trading days but few trading volumes, so trading volume is a good proxy for liquidity in the exchange market. On the other hand, interbank market is dominated by institutional investors with few trading days and high trading volumes, so trading day is a better proxy for liquidity in the interbank market. In the interbank market, the assumption that the coefficient of day × coupon is equal to zero is rejected, which indicates that the interaction between liquidity and credit risk has a significant impact on the spreads in Model 1. When investors hold high credit risk bond, with the increase of trading days, some investors panic sell-off due to asymmetric information, that is to say, they are worried about potential default risk to sudden frequent trading bonds, which leads to spiral interaction between liquidity and credit risk, resulting in corporate bond spreads widen. The regression coefficient of vol × coupon has similar conclusion on the exchange market.Robustness analysis are done in Model 2 and Model 3. The empirical results show that the regression coefficients of the interaction between liquidity and credit risk are all significant in the exchange market, while some of these coefficients are not significant in the interbank market. The reason is that the interbank market is mainly composed of institutional investors with infrequent transactions, leading to the discontinuous linkage between liquidity and credit risk and the failure to form continuous transmission and feedback of information. This shows that the establishment of a continuous market trading mechanism, which makes information flow and reduces information asymmetry, is conducive to price discovery.Regression analysis results are given in Model 4, which contains all the liquidity risk proxies of the transaction activity. The regression coefficients of interaction between liquidity and credit risk are all significant in the exchange market, while the regression coefficients of Turnover × Coupon and Day × Volatility are not significant in the interbank market. The reason is that investor structure and transaction characteristic are different in the interbank market and the exchange market.Through the above analysis, interaction between liquidity and credit risk cannot be ignored and liquidity premiums are the main components of corporate bond spreads in China’s bond market. Dynamic credit risk changes in resonance with the dynamic change of liquidity risk, while the static credit risk does not change with the dynamic change of liquidity risk. When liquidity affects asset prices, dynamic credit risk interacts with liquidity risk in a dynamic spiral, forming a bigger resonance enhancement interaction between liquidity and credit risk to dynamically affect asset prices than static credit risk.


## 3.2.2. Subsample Results

In this part, we give sub samples regression analysis, and the liquidity and credit risk proxies are divided into high, medium and low in order to explore the impact of the interaction between liquidity and credit risk on the spreads.In Table6, there are nine subsamples. The regression results of the three subsamples are given according to the trading volume in the panel A. In the high-vol subsample, the regression coefficients of amihud × volatility, amihud × coupon, age × volatility and age × coupon are significant, while the regression coefficients of vol × volatility and vol × coupon are not significant. It suggests that the interactions between liquidity and credit risk in high-vol bonds are mainly the interaction between speculative liquidity of price shock dimension and credit risk and the interaction between investment liquidity and credit risk. In the low-vol subsample, the regression coefficient of amihud × volatility is not significant, suggesting that the spiral interaction between speculative liquidity of price shock dimension and dynamic credit risk requires high trading volume as the basic condition.Table 6
The impact of interaction between liquidity and credit risk on spreads in subsample results.
Panel A: volPanel B: amihudPanel C: ageHightMiddleLowHightMiddleLowHightMiddleLowc−1.0268∗∗∗−0.4000∗∗∗−0.6494∗∗∗−0.6142∗∗∗−0.4396∗−0.6475∗∗∗0.24710.0498−2.0406∗∗∗(−5.84)(−3.56)(−6.10)(−3.92)(−1.84)(−8.50)(1.16)(0.33)(−19.95)Dummy0.3600∗∗∗0.3715∗∗∗0.3015∗∗∗0.4950∗∗∗0.3671∗∗∗0.3201∗∗∗0.1926∗∗∗0.2973∗∗∗0.2909∗∗∗(5.80)(21.04)(6.43)(4.70)(8.28)(20.60)(5.90)(19.01)(17.81)Vol0.0003−0.0101∗∗∗0.0110−0.0652−0.0091−0.0010∗∗∗−0.0010−0.0008∗∗0.0001(0.76)(−6.49)(0.52)(−1.54)(−1.24)(−3.60)(−1.46)(−2.47)(0.49)Day0.0947∗∗∗0.0616∗∗∗0.0341∗∗∗0.0259∗∗∗0.0466∗∗∗0.0621∗∗∗0.0583∗∗∗0.0608∗∗∗0.0373∗∗∗(23.33)(42.81)(20.30)(7.42)(19.39)(50.00)(22.49)(46.14)(26.67)Amihud−1940.6200∗∗∗−83.3530∗∗0.8493∗∗0.6793−12.5975−280.7775∗∗∗1.7829∗∗−0.0439−0.9569(−5.15)(−2.24)(2.27)(1.58)(−0.37)(−3.86)(2.03)(−0.09)(−1.16)Age0.2520∗∗∗0.2224∗∗∗0.2046∗∗∗0.2015∗∗∗0.1688∗∗∗0.1779∗∗∗−0.0557−0.08411.0736∗∗∗(6.72)(10.34)(9.73)(5.75)(5.18)(10.33)(−1.30)(−1.18)(6.90)Volatility0.09090.05580.1072∗∗0.1180∗0.1472−0.0227−0.4399∗∗∗0.8224∗∗∗−0.2797∗∗∗(1.32)(1.16)(2.38)(1.85)(1.52)(−0.62)(−4.82)(12.72)(−6.19)Coupon0.4754∗∗∗0.4229∗∗∗0.4915∗∗∗0.4886∗∗∗0.4350∗∗∗0.4604∗∗∗0.3421∗∗∗0.3014∗∗∗0.7048∗∗∗(20.58)(25.74)(32.98)(22.75)(12.88)(41.73)(9.34)(14.22)(48.18)Vol × volatility−0.00010.0039∗∗∗0.0248∗∗∗0.0188∗∗0.00030.0006∗∗∗0.0007∗∗∗0.0006∗∗∗0.0000(−1.06)(5.90)(2.95)(2.34)(0.17)(7.15)(3.51)(6.76)(−0.02)Vol × coupon−0.00010.0011∗∗∗−0.0054∗0.00150.00050.00000.00020.0000−0.0001∗∗−1.44(5.02)(−1.82)(0.26)(0.54)(1.02)(1.51(−0.26)(−2.47)Amihud × volatility400.6426∗∗∗15.0529∗−0.0999−0.102819.2996317.0865∗∗∗−0.3220−0.3831∗∗0.0986(4.79)(1.94(−0.82)(−0.74)(1.30)(10.76)(−1.04)(−2.21)(0.63)Amihud × coupon238.7952∗∗∗9.6909∗−0.0996∗∗−0.08541.552623.8625∗∗−0.2105∗0.07820.1160(4.60)(1.89)(−1.96)(−1.47)(0.32)(2.28)(−1.83)(1.13)(1.10)Age × volatility0.0498∗∗−0.0736∗∗∗−0.0321∗∗∗−0.0301∗−0.0702∗∗∗−0.0186∗∗0.0840∗∗∗−0.2944∗∗∗0.7791∗∗∗(2.50)(−6.77)(−3.11)(−1.85)(−4.14)(−2.02)(4.37)(−10.13)(10.95)Age × coupon−0.0648∗∗∗−0.0552∗∗∗−0.0563∗∗∗−0.0522∗∗∗−0.0478∗∗∗−0.0511∗∗∗−0.0175∗∗0.0096−0.2350∗∗∗(−11.01)(−16.27)(−16.63)(−9.31)(−9.00)(−18.76)(−2.19)(0.95)(−10.66)aj−R20.25120.27890.29840.25180.31230.26790.13490.21780.4787To investigate whether the impact of interaction on the spreads is present, the following regression equations are given. Spreadit = α + β1 × (liquidity risk factors)it + β2 × (credit risk factors)it + β3 × (different dimension liquidity risk factors)it × (credit risk factors)it + єt. The meanings of the variables are given in Table 1. The sample period is July 2006 to June 2016. The whole sample includes 3716 bond issues and 47436 observations. The t-statistics are shown in parentheses below each coefficient estimate, and “∗,” “∗∗,” and “∗∗∗” indicate significance at the 10%, 5%, and 1% levels.In the high-amihud subsample of panel B, the regression coefficients of vol × volatility, age × volatility and age × coupon are significant, while the regression coefficients of vol × coupon, amihud × volatility, and amihud × coupon are not significant. It shows that high price shock is usually caused by a huge amount of investors’ sudden trading. Generally, prices will recover calm immediately after a huge impact, which makes it difficult to form risk transmission and interaction between liquidity and credit risk in a very short period of time. In the subsamples of panel B, the regression coefficients of vol × coupon are all not significant. Coupon is static credit risk measure. The static credit risk represents the credit risk level of an firm in this period of time, and it does not change with the dynamic change of liquidity risk. When liquidity affects asset prices, static credit risk generally does not interact with liquidity risk in a dynamic spiral.In the high-age subsample of panel C, the regression coefficients of vol × volatility, amihud × coupon, age × volatility and age × coupon are significant, while the regression coefficients of vol × coupon and amihud × volatility are not significant. It shows that high age bonds are actively traded, and sufficient trading volume forms the spiral interaction between speculative liquidity and dynamic credit risk and the interaction between liquidity of price shock dimension and static credit risk, thus affecting asset prices. In the low-age subsample of panel C, the regression coefficients of vol × coupon, age × volatility and age × coupon are significant, while the regression coefficients of vol × volatility, amihud × volatility, and amihud × coupon are not significant. The reason is that low age bonds are not actively traded, and the lack of trading volume only forms the interaction between investment liquidity and static credit risk, which indicates that the interaction between liquidity of price shock dimension and credit risk requires sufficient trading volume as the basic condition.To sum up, the interaction between liquidity and credit risk will increase with the increase of liquidity risk and credit risk and it is a time-varying dynamic process. When market liquidity risk increases, some investors will take the lead in selling corporate bonds with high default risk, which causes the price of corporate bonds with high credit risk to fluctuate greatly. These behaviors of investors further cause more investors to sell these corporate bonds with high credit risk, so the investors who hold these high credit risk bonds have to bear the gradually increasing liquidity risk. With the increase of market liquidity risk, firms with high default risk are affected due to the depletion of operating cash flow, and the probability of default will also increase. Because of information asymmetry, investors sell their bonds more quickly, creating a spiral interaction between liquidity and credit risk that affects asset prices. If market liquidity risk continues to increase, corporate bonds with low credit risk will gradually be affected by the interaction between liquidity and credit risk, and eventually more corporate bond prices will be affected by risk contagion.


## 4. Robustness Test

### 4.1. Robustness Test Based on Liquidity

Liquidity has many dimensions, and price impact is one of the most important dimensions of liquidity. Famous measures are amihud and range [29, 30, 37]. Controlling other liquidity and credit risk measure proxies, we use the measures of the liquidity of the price impact dimension to discuss the robustness of impact of the interaction between liquidity and credit risk on the spreads. The basic proxies of liquidity and credit risk are given, including vol, day, amihud, age, coupon and volatility. Amihud measure reflects the impact of a unit of trading volume on the price, while Range measure is the impact of a unit of trading volume on the highest and lowest price, and both of which represent the liquidity measure of the price shock dimension [20, 30]. Therefore, robustness analysis is done by range to replace amihud, and coupon and volatility are proxies of credit risk. The cross terms are the proxies of the interaction between liquidity and credit risk.To investigate the robustness of impact of interaction between liquidity and credit risk on the spreads, the following regression equation is given(3)Spreadit=α+β1×liquidity risk factorsit+β2×credit risk factorsit+β3×price impact liquidity risk factorsit×credit risk factorsit+εit.Ifβ3 is significantly different from zero, the impact of the interaction on the spreads is present, and the result is robust. The term “liquidity risk factors” represents a set of basic proxies for liquidity from three dimensions, including transaction activity (vol, day), price impact (range) and bond survival time (age). The term “price impact Liquidity risk factors” represents price impact, including amihud or range or both. The term “credit risk factors” represents the proxies for the default risk, including coupon and volatility. In Table 7, the regression results of the interaction between liquidity and credit risk are given in the whole sample and subsamples.Table 7
The impact of interaction between liquidity and credit risk on spreads in the dimension of price impact.
The whole sampleThe interbank marketThe exchange market123123123C0.05550.0571∗0.05330.1860∗∗∗0.1894∗∗∗0.1768∗∗∗0.02730.02510.0246(1.61)(1.65)(1.54)(4.40)(4.49)(4.19)(0.50)(0.46)(0.45)Dummy0.2474∗∗∗0.2502∗∗∗0.2505∗∗∗(20.64)(20.83)(20.84)Vol−0.0003∗∗∗−0.0003∗∗∗−0.0003∗∗∗−0.0003∗∗∗−0.0003∗∗∗−0.0003∗∗∗0.0013∗∗∗0.0013∗∗∗0.0013∗∗∗(−6.79)(−6.78)(−6.77)(−5.89)(−5.97)(−5.65)(7.84)(8.01)(8.01)Day0.0569∗∗∗0.0570∗∗∗0.0570∗∗∗0.0479∗∗∗0.0478∗∗∗0.0468∗∗∗0.0523∗∗∗0.0524∗∗∗0.0524∗∗∗(56.54)(56.70)(56.63)(12.34)(12.29)(12.02)(45.24)(45.39)(45.29)Amihud1.1900∗∗∗0.9831∗51.1388∗∗∗41.3188∗∗∗0.9672∗∗0.6071(3.14)(1.70)(6.45)(3.33)(2.41)(1.00)Range0.5741∗∗∗0.226034.0069∗∗∗19.6406∗∗0.7470∗∗∗0.4286(2.81)(0.71)(7.06)(2.50)(3.44)(1.28)Age−0.1399∗∗∗−0.1399∗∗∗−0.1399∗∗∗−0.1500∗∗∗−0.1494∗∗∗−0.1495∗∗∗−0.1293∗∗∗−0.1297∗∗∗−0.1295∗∗∗(−51.33)(−51.33)(−51.32)(−38.31)(−38.18)(−38.23)(−33.62)(−33.73)(−33.68)Volatility0.0891∗∗∗0.0918∗∗∗0.0903∗∗∗−0.1565∗∗∗−0.1581∗∗∗−0.1550∗∗∗0.4001∗∗∗0.4092∗∗∗0.4119∗∗∗(7.00)(7.19)(7.05)(−9.78)(−9.92)(−9.71)(19.07)(19.34)(19.36)Coupon0.3508∗∗∗0.3500∗∗∗0.3506∗∗∗0.3938∗∗∗0.3936∗∗∗0.3949∗∗∗0.3286∗∗∗0.3278∗∗∗0.3277∗∗∗(77.25)(76.96)(76.92)(67.41)(67.62)(67.66)(45.77)(45.50)(45.32)Amihud × volatility−0.2631∗∗0.039638.8328∗∗∗−23.1397∗∗∗−0.8894∗∗∗−0.3006(−2.17)(0.22)(17.27)(−3.87)(−6.90)(−1.60)Amihud × coupon−0.1123∗∗−0.1464∗−14.1722∗∗∗−2.2058−0.0304−0.0677(−2.20)(−1.90)(−10.47)(−0.98)(−0.56)(−0.84)Range × volatility−0.2660∗∗∗−0.2518∗∗36.2733∗∗∗52.1587∗∗∗−0.5962∗∗∗−0.4727∗∗∗(−3.86)(−2.40)(19.31)(11.11)(−8.12)(−4.29)Range × coupon−0.03110.0197−11.6695∗∗∗−11.8540∗∗∗−0.02640.0111(−1.20)(0.49)(−10.64)(−6.35)(−0.95)(0.26)aj−R20.25640.25650.25660.23340.23640.23710.30040.30130.3013To investigate whether the impact of interaction on the spreads is present, the following regression equations are given. Spreadit = α+β1 × (liquidity risk factors)it + β2 × (credit risk factors)it + β3 × (price impact liquidity risk factors)it × (credit risk factors)it + єt. The meanings of the variables are given in Table 1. The sample period is July 2006 to June 2016. The subsample (the interbank bond market) includes 2281 bond issues and 25648 observations. The subsample (the exchange market) includes 1435 bond issues and 21788 observations. The whole sample includes 3716 bond issues and 47436 observations. The t-statistics are shown in parentheses below each coefficient estimate, and “∗,” “∗∗,” and “∗∗∗” indicate significance at the 10%, 5%, and 1% levels, respectively.In the whole sample, the dummy variable is introduced to test the significance of the impact of the interbank market and the exchange market on the test results, where the dummy variable of the interbank market is set to 1, and the one of the exchange market is set to 0. As shown in the Model 1 to Model 3, the regression coefficients of the dummy variables are all significant. In order to ensure the robustness of the test results, we do regression analysis of the interbank market and the exchange market independently in Table7.In the whole sample, the regression results of Model 1 show that the regression coefficients of amihud, volatility and coupon are significant at the level of 1%, and the coefficients of amihud × volatility and amihud × coupon are significant at the level of 5%. This shows that the liquidity of price shock dimension interacts with both dynamic credit risk and static credit risk, thus affecting asset prices. In Model 2, amihud is replaced by range to test the robustness of the results. The regression coefficients of range, volatility, coupon and range × volatility are significant at the level of 1%, while the regression coefficient of range × coupon is not significant. The reason is that the static credit risk represents the credit risk level of an firm in this period of time, and it does not easily interact with liquidity risk. In Model 3, amihud and range are introduced into the regression equation. The regression coefficients of volatility and coupon are very significant, while the coefficients of amihud and amihud × coupon are significant at the level of 10% and the coefficient of range is not significant. The reason may be the high correlation between amihud and range. In spite of this, the results still prove that the impact of the interaction between liquidity and credit risk on the spreads is not negligible, and the results are robust in the Chinese corporate bond market.In the interbank market, the regression results of Model 1 show that the regression coefficients of amihud, coupon and amihud × coupon are significant at the level of 1%, and the signs are in line with expectation. It shows that the impact of the interaction between liquidity and credit risk on the spreads is present. In Model 1, the regression coefficient of amihud × volatility is greater than one of amihud × coupon. It shows that the liquidity of price shock dimension has a greater interaction with dynamic credit risk than static credit risk. Dynamic credit risk represents the credit risk level of an firm over time, and it changes in resonance with the dynamic change of liquidity risk. When liquidity affects asset prices, dynamic credit risk interacts with liquidity risk in a dynamic spiral, forming the resonance enhancement interaction between liquidity and credit risk to dynamically affect asset prices. In Model 2, amihud is replaced by range to test the robustness of the results. The regression coefficient of range × volatility is also greater than one of Range × Coupon, and this result is consistent with Model 1. In Model 3, amihud and range are introduced into the regression equation. The regression coefficients of amihud × volatility and range × volatility are greater than ones of amihud × coupon and amihud × coupon, respectively. The results prove that the liquidity of price shock dimension has a greater interaction with dynamic credit risk than static credit risk, and the impact of the interaction between liquidity and credit risk on the spreads is present in the interbank bond market.Empirical studies show that similar results are found in the exchange market. In the exchange market, the regression coefficients of coupon, and volatility are significant at the level of 1%, and the signs are in line with the hypothesis. In Model 1, the regression coefficient of amihud × volatility is significant at the level of 1%, while the regression coefficient of amihud × coupon is not significant. It shows that the liquidity of price shock dimension has a greater interaction with dynamic credit risk than static credit risk. In Model 2, amihud is replaced by range to test the robustness of the results, and the similar results are found. This shows that the results are robust. In Model 3, the coefficients of amihud and range are not significant. Because the correlation between amihud and range is high.The above analysis shows that the liquidity of price shock dimension has a greater interaction with dynamic credit risk than static credit risk, and the impact of the interaction between liquidity and credit risk on the spreads is not negligible in the interbank market and the exchange market. And the results are robust. This suggests that similar results are found in the two markets. When investors encounter liquidity risk, they panic to sell assets with high credit risks due to information asymmetry, and the behaviors of investors are consistent in the two markets. Because the behaviors of investors are determined by human egoism.


### 4.2. Robustness Test Based on Credit Risk and Macrofactors

In order to investigate whether the results are stable, we perform robustness analysis based on credit risk and macrofactors. We have carried out a lot of robustness tests of liquidity risk, and the results are stable. Rating is the credit rating assigned to each security that a firm issues [14, 37]. The higher the credit rating, the lower the credit risk. Coupon refers to the coupon rate of bonds [20, 38]. The lower the coupon, the less credit risk. It shows that rating and coupon are proxy variables of credit risk. So we use rating to replace coupon as the proxy of credit risk, in order to explore whether the interaction between liquidity and credit risk is present on the spreads. We choose the basic liquidity and credit risk proxies, and use their cross terms to represent the interaction. The empirical tests of the whole period, the financial crisis and the normal period are done in Panel A, Panel B and Panel C of Table 8. And the empirical tests of macro factors are done in Panel D of Table 8.Table 8
Robustness test of impact of interaction between liquidity and credit risk on spreads based on credit risk and macrofactors.
CDummyVolDayAmihudAgeVolatilityRatingVol × volatilityVol × ratingAmihud × volatilityAmihud × ratingAge × volatilityAge × ratingaj-R2Panel A: the whole period1.8930∗∗∗0.2326∗∗∗−0.0010∗∗∗0.0596∗∗∗1.8066∗∗∗−0.1658∗∗∗0.0823∗∗∗0.1884∗∗∗0.0006∗∗∗0.0001∗∗∗−0.5708∗∗∗−0.3607∗∗∗−0.0145∗∗−0.00020.2262(76.10)(18.85)(−9.22)(57.82)(10.05)(−28.17)(3.20)(32.61)(7.37)(4.59)(−4.64)(−8.63)(−2.03)(−0.15)Panel B: during the financial crisis1.8560∗∗∗0.0122−0.0010∗∗∗0.0042−0.3237−0.1141∗∗∗−0.4597∗∗∗0.0459∗∗∗0.0004∗∗∗0.0008∗∗∗0.02180.09250.1181∗∗∗−0.0351∗∗∗0.2031(22.04)(0.20)(−3.47)(1.02)(−0.59)(−5.09)(−7.99)(3.07)(2.86)(8.12)(0.08)(1.29)(5.44)(−3.79)Panel C: normal period1.7215∗∗∗0.2609∗∗∗−0.0009∗∗∗0.0652∗∗∗1.3577∗∗∗−0.1362∗∗∗0.3131∗∗∗0.2076∗∗∗0.0006∗∗∗0.0001−0.3170∗∗−0.2607∗∗∗−0.0473∗∗∗−0.0059∗∗∗0.2419(66.63)(21.14)(−7.83)(62.26)(7.14)(−22.73)(11.54)(33.83)(7.18)(1.16)(−2.38)(−5.78)(−6.45)(−4.06)Panel D: macrofactorsCVolTurnoverAmihudBML_VolBML_AmihudYear102S10 yearCPIGDPM0Vol × CouponTurnover × CouponDay × CouponAdj−R2(%)1.2203∗∗∗−0.0015∗∗∗0.1846∗∗∗−0.0078∗∗∗1.0654∗0.1760∗∗∗0.1487∗∗∗0.1081∗∗∗−0.0969∗∗∗−0.0205∗∗∗0.0002∗∗∗0.0004∗∗2.9413(7.51)(−3.78)(2.74)(−6.23)(1.90)(4.91)(6.37)(6.23)(−3.54)(−3.90)(3.23)(2.09)1.2328∗∗∗−1.8679∗∗∗0.1659∗∗−0.0079∗∗∗1.0650∗0.1738∗∗∗0.1495∗∗∗0.1079∗∗∗−0.0978∗∗∗−0.0208∗∗∗0.2129∗∗∗0.0005∗∗3.0494(7.59)(−4.35)(2.45)(−6.31)(1.90)(4.85)(6.41)(6.22)(−3.58)(−3.95)(3.76)(2.17)To investigate the robustness of impact of interaction on the spreads, the following regression equation is given. Spreadit = α+β1 × (liquidity risk factors)it + β2 × (credit risk factors)it+β3 × (different dimension liquidity risk factors)it × (credit risk factors)it + єt. In panel A, panel B and panel C, the meanings of the variables are given in Table 1. In panel D, BML_Vol is the monthly trading volume of the corporate bond market. BML_Amihud is illiquidity measures of the corporate bond market based on amihud. Year102 is the difference between the 10-year treasury rate and the 2-year treasury rate. S10 year is the spread between the bond market index yield and the 10-year treasury rate. CPI is the consumer price index, and GDP is gross domestic product. M0 is an increase in cash in circulation. In panel D, vol, turnover and amihud are liquidity measures of matched pairs of bonds. The cross-term is the interaction between liquidity and credit risk. The whole period is July 2006 to June 2016. The sample period of the financial crisis is May 2007 to December 2009. The sample period of normal period is from July 2006 to April 2007 and from January 2010 to June 2016. The t-statistics are shown in parentheses below each coefficient estimate, and “∗,” “∗∗,” and “∗∗∗” indicate significance at the 10%, 5%, and 1% levels, respectively.In Panel A, Panel B and Panel C of Table8, the dummy variable is introduced to test the significance of the impact of the interbank market and the exchange market on the test results. Where, the dummy variable of the interbank market is set to 1, and the one of the exchange market is set to 0. As shown in Table 8, the regression coefficients of the dummy variables are significant in normal period, which indicates that the impact of the differences between the two markets on the spreads is significant in normal period. However, the coefficient of dummy variable is not significant during the financial crisis. The reason may be that liquidity and credit risk have major impact on the spreads during the financial crisis than the differences between the two markets. In the whole period, the regression coefficients of vol, amihud, volatility, rating, vol × volatility, vol × rating, amihud × volatility and amihud × rating are significant at the level of 1%, and the signs are in line with expectation, which shows that the interaction between liquidity and credit risk is present on the spreads and the results are robust in the Chinese corporate bond market.As shown in Table8, the coefficient of Vol is increased from −0.0009 to −0.0010 from the normal period to the financial crisis, while the coefficient of age is dropped from −0.1362 to −0.1141 from the normal period to the financial crisis. This shows that compared with normal period, speculative liquidity risk premiums are increased and investment liquidity risk premiums are reduced during the financial crisis. During the financial crisis, many investors have no confidence in the future and become less willing to hold assets for the long term. Some investors begin to implement the short-term investment strategy of quick entry and quick exit, which leads to the increase of the impact of speculative liquidity and the decrease of the impact of investment liquidity on asset prices. The coefficient of Volatility is increased from 0.3131 to −0.4597 from the normal period to the financial crisis, while the coefficient of Rating is dropped from −0.2076 to −0.0459 from the normal period to the financial crisis. This shows that compared with normal period, dynamic credit risk premiums are increased and static credit risk premiums are reduced during the financial crisis. During the financial crisis, some investors sell assets in a panic. In the case of insufficient liquidity, the price fluctuation of assets with high default risk will increase, and the increase of price fluctuation will lead more investors to sell the assets with high default risk. Therefore, during the financial crisis, the impact of dynamic credit risk on asset price will gradually increase compared with static credit risk.During the financial crisis, the regression coefficients of vol, rating and vol × rating are significant at the level of 1%, and the signs are in line with expectation, while the regression coefficients of vol, amihud, volatility, rating, vol × volatility, and amihud × rating are significant at the level of 1%, and the signs are in line with expectation in normal period. This shows that the impact of the interaction between liquidity and credit risk cannot be ignored. In addition, the coefficients of age × volatility and age × rating are increased from −0.0473 and −0.0059 to 0.1181 and −0.0351 from the normal period to the financial crisis, respectively. It shows that the interaction between liquidity and credit risk has greater impact on the spreads during the financial crisis. And the results are robust. During financial crises, some investors prefer to sell assets with high default risk, which leads to large price swings. Due to information asymmetry, this will cause more investors to continue to sell assets with high default risk, further forming a bigger liquidity crisis. Finally, it leads to the incrementally increasing spiral interaction between liquidity and credit risk during financial crises.In Panel D of Table8, we perform robustness analysis based on macro factors. Some scholars find that macro factors affect corporate bond spreads. Han and Zhou [30] focus on the linkage between the corporate bond spreads and the macroeconomic conditions. See also Yang et al. [20]. In order to study macro factors, we construct matched pairs of bonds by stripping out credit risk. Relevant studies refer to Dick-Nielsen et al. [12] and Helwege et al. [13]. We study the impact of the interaction between liquidity and credit risk on corporate bond spreads under macro factors. BML_Vol is the monthly trading volume of the corporate bond market. BML_Amihud is illiquidity measures of the corporate bond market based on Amihud. Year102 is the difference between the 10-year treasury rate and the 2-year Treasury rate. S10 year is the spread between the bond market index yield and the 10-year Treasury rate. CPI is the consumer price index, and GDP is gross domestic product. M0 is an increase in cash in circulation. In Panel D of Table 8, vol, turnover and amihud are liquidity measures of matched pairs of bonds. The cross-term is the interaction between liquidity and credit risk. The regression coefficients of Vol and Turnover are significant at the level of 1%, and the signs are in line with expectation, while the regression coefficients of vol × coupon and turnover × rating are significant at the level of 1%. This shows that under the condition of controlling macrofactors, the interaction between liquidity and credit risk has a significant impact on corporate bond spreads. In Panel D of Table 8, the regression coefficients of BML_Vol, Year102, S10 year, CPI, GDP, and M0 are significant at the level of 1%. Macrofactors affect corporate bond spreads by common liquidity factors in China's corporate bond market. During the financial crisis, the impact of the interaction between liquidity and credit risk on corporate bond spreads is closely related to macro factors.


### 4.3. Robustness Test Based on Credit and Liquidity Levels

In Table9, we divide the sample into six subsamples to investigate the robustness based on credit and liquidity levels. The sample is divided into three subsamples according to the three levels of coupon, and then each subsample is divided into two subsamples according to the two levels of Vol. The cross terms of vol, amihud, age and coupon are used as measures of the interaction between liquidity and credit risk, and the regression results are shown in Table 9. These cross terms are vol × coupon, amihud × coupon and age × coupon.Table 9
The impact of interaction between liquidity and credit risk on spreads in subsample results.
CouponVolCDummyVolDayAmihudAgeVolatilityCouponVol × couponAmihud × couponAge × couponaj-R2HighHigh−2.0665∗∗∗0.4177∗∗∗−0.00120.0793∗∗∗−832.90940.9520∗∗∗0.7036∗∗∗0.5790∗∗∗0.0001109.0945−0.1525∗∗∗0.1360(−3.58)(5.94)(−0.77)(17.58)(−1.34)(4.32)(15.89)(7.95)(0.36)(1.40)(−5.45)Low−0.13270.4796∗∗∗−0.0576∗∗∗0.0532∗∗∗−0.54201.3198∗∗∗0.1143∗∗∗0.4020∗∗∗0.0071∗∗∗0.0987−0.2061∗∗∗0.2191(−0.33)(13.71)(−4.10)(25.81)(−0.37)(8.64)(3.58)(7.84)(3.99)(0.52)(−10.63)MiddleHigh−2.2082∗∗∗0.3998∗∗∗−0.00170.0794∗∗∗−561.02670.9547∗∗∗0.7029∗∗∗0.5978∗∗∗0.000175.9640−0.1528∗∗∗0.1386(−3.80)(5.66)(−1.11)(17.52)(−0.90)(4.33)(15.85)(8.15)(0.70)(0.97)(−5.46)Low−0.17950.4800∗∗∗−0.0585∗∗∗0.0538∗∗∗−0.53471.3125∗∗∗0.1103∗∗∗0.4073∗∗∗0.0072∗∗∗0.0984−0.2052∗∗∗0.2211(−0.44)(13.69)(−4.15)(26.14)(−0.36)(8.63)(3.46)(7.92)(4.03)(0.52)(−10.63)LowHigh−1.9248∗∗∗0.3986∗∗∗0.00060.0728∗∗∗184.31720.2139∗∗∗−0.01100.6444∗∗∗−0.0001−41.4980−0.0524∗∗∗0.2195(−10.75)(11.30)(0.96)(21.44)(0.76)(5.65)(−0.45)(21.10)(−1.37)(−0.99)(−7.53)Low−2.6984∗∗∗0.2102∗∗∗0.0353∗∗∗0.0292∗∗∗−0.46410.2063∗∗∗0.1488∗∗∗0.8341∗∗∗−0.0068∗∗∗0.1374−0.0509∗∗∗0.2321(−15.46)(7.75)(4.92)(13.58)(−0.63)(6.71)(5.81)(27.52)(−5.36)(1.05)(−8.53)To investigate whether the impact of interaction on the spreads is present, the following regression equations are given. Spreadit = α + β1 × (liquidity risk factors)it+ β2 × (credit risk factors)it+β3 × (different dimension liquidity risk factors)it × (representative credit risk factor)it +єt. The meanings of the variables are given in Table 2. The sample period is July 2006 to June 2016. The whole sample includes 3716 bond issues and 47436 observations. The t-statistics are shown in parentheses below each coefficient estimate, and “∗,” “∗∗,” and “∗∗∗” indicate significance at the 10%, 5%, and 1% levels, respectively.In the high-coupon subsample, the regression coefficient of vol × coupon in the low-vol sample is significant at the level of 1%, while the regression coefficient of vol × coupon in the high-vol sample is not significant. In middle-coupon and low-coupon sub sample, the regression coefficient of vol × coupon also have similar results. When trading volume is relatively high, liquidity risk is small, and small liquidity risk does not interact with credit risk. Liquidity risks are rising as trading volumes fall. When liquidity risk increases to a certain extent, it begins to interact spirally with credit risk, affecting asset prices. This shows that the interaction between liquidity and credit risk will start from scratch with the increase of liquidity risk and it is a time-varying dynamic process.In high-coupon, middle-coupon and low-coupon subsamples, the regression coefficient of age × coupon in the low-vol sample is greater than one of age × coupon in the high-vol sample. For example, in the high-coupon sub sample, the regression coefficient of age × coupon in the low-vol sample is −0.2061, while the regression coefficient of age × coupon in the high-vol sample is −0.1525. It shows that when credit risk is controlled, the interaction between liquidity and credit risk will increase with the increase of liquidity risk. In low-vol sample, the regression coefficients of age × coupon in the low-coupon sample, the middle-coupon sample and the high-coupon sample are −0.0509, −0.2052, and −0.2061, respectively. It suggests that when liquidity risk is controlled, the interaction between liquidity and credit risk will increase with the increase of credit risk.The above analysis shows that the interaction between liquidity and credit risk will increase with the increase of liquidity risk and credit risk and it is a time-varying dynamic process. The impact of the interaction between liquidity and credit risk on the spreads is not negligible in China’s corporate bond market. And, the results are robust.


## 4.1. Robustness Test Based on Liquidity

Liquidity has many dimensions, and price impact is one of the most important dimensions of liquidity. Famous measures are amihud and range [29, 30, 37]. Controlling other liquidity and credit risk measure proxies, we use the measures of the liquidity of the price impact dimension to discuss the robustness of impact of the interaction between liquidity and credit risk on the spreads. The basic proxies of liquidity and credit risk are given, including vol, day, amihud, age, coupon and volatility. Amihud measure reflects the impact of a unit of trading volume on the price, while Range measure is the impact of a unit of trading volume on the highest and lowest price, and both of which represent the liquidity measure of the price shock dimension [20, 30]. Therefore, robustness analysis is done by range to replace amihud, and coupon and volatility are proxies of credit risk. The cross terms are the proxies of the interaction between liquidity and credit risk.To investigate the robustness of impact of interaction between liquidity and credit risk on the spreads, the following regression equation is given(3)Spreadit=α+β1×liquidity risk factorsit+β2×credit risk factorsit+β3×price impact liquidity risk factorsit×credit risk factorsit+εit.Ifβ3 is significantly different from zero, the impact of the interaction on the spreads is present, and the result is robust. The term “liquidity risk factors” represents a set of basic proxies for liquidity from three dimensions, including transaction activity (vol, day), price impact (range) and bond survival time (age). The term “price impact Liquidity risk factors” represents price impact, including amihud or range or both. The term “credit risk factors” represents the proxies for the default risk, including coupon and volatility. In Table 7, the regression results of the interaction between liquidity and credit risk are given in the whole sample and subsamples.Table 7
The impact of interaction between liquidity and credit risk on spreads in the dimension of price impact.
The whole sampleThe interbank marketThe exchange market123123123C0.05550.0571∗0.05330.1860∗∗∗0.1894∗∗∗0.1768∗∗∗0.02730.02510.0246(1.61)(1.65)(1.54)(4.40)(4.49)(4.19)(0.50)(0.46)(0.45)Dummy0.2474∗∗∗0.2502∗∗∗0.2505∗∗∗(20.64)(20.83)(20.84)Vol−0.0003∗∗∗−0.0003∗∗∗−0.0003∗∗∗−0.0003∗∗∗−0.0003∗∗∗−0.0003∗∗∗0.0013∗∗∗0.0013∗∗∗0.0013∗∗∗(−6.79)(−6.78)(−6.77)(−5.89)(−5.97)(−5.65)(7.84)(8.01)(8.01)Day0.0569∗∗∗0.0570∗∗∗0.0570∗∗∗0.0479∗∗∗0.0478∗∗∗0.0468∗∗∗0.0523∗∗∗0.0524∗∗∗0.0524∗∗∗(56.54)(56.70)(56.63)(12.34)(12.29)(12.02)(45.24)(45.39)(45.29)Amihud1.1900∗∗∗0.9831∗51.1388∗∗∗41.3188∗∗∗0.9672∗∗0.6071(3.14)(1.70)(6.45)(3.33)(2.41)(1.00)Range0.5741∗∗∗0.226034.0069∗∗∗19.6406∗∗0.7470∗∗∗0.4286(2.81)(0.71)(7.06)(2.50)(3.44)(1.28)Age−0.1399∗∗∗−0.1399∗∗∗−0.1399∗∗∗−0.1500∗∗∗−0.1494∗∗∗−0.1495∗∗∗−0.1293∗∗∗−0.1297∗∗∗−0.1295∗∗∗(−51.33)(−51.33)(−51.32)(−38.31)(−38.18)(−38.23)(−33.62)(−33.73)(−33.68)Volatility0.0891∗∗∗0.0918∗∗∗0.0903∗∗∗−0.1565∗∗∗−0.1581∗∗∗−0.1550∗∗∗0.4001∗∗∗0.4092∗∗∗0.4119∗∗∗(7.00)(7.19)(7.05)(−9.78)(−9.92)(−9.71)(19.07)(19.34)(19.36)Coupon0.3508∗∗∗0.3500∗∗∗0.3506∗∗∗0.3938∗∗∗0.3936∗∗∗0.3949∗∗∗0.3286∗∗∗0.3278∗∗∗0.3277∗∗∗(77.25)(76.96)(76.92)(67.41)(67.62)(67.66)(45.77)(45.50)(45.32)Amihud × volatility−0.2631∗∗0.039638.8328∗∗∗−23.1397∗∗∗−0.8894∗∗∗−0.3006(−2.17)(0.22)(17.27)(−3.87)(−6.90)(−1.60)Amihud × coupon−0.1123∗∗−0.1464∗−14.1722∗∗∗−2.2058−0.0304−0.0677(−2.20)(−1.90)(−10.47)(−0.98)(−0.56)(−0.84)Range × volatility−0.2660∗∗∗−0.2518∗∗36.2733∗∗∗52.1587∗∗∗−0.5962∗∗∗−0.4727∗∗∗(−3.86)(−2.40)(19.31)(11.11)(−8.12)(−4.29)Range × coupon−0.03110.0197−11.6695∗∗∗−11.8540∗∗∗−0.02640.0111(−1.20)(0.49)(−10.64)(−6.35)(−0.95)(0.26)aj−R20.25640.25650.25660.23340.23640.23710.30040.30130.3013To investigate whether the impact of interaction on the spreads is present, the following regression equations are given. Spreadit = α+β1 × (liquidity risk factors)it + β2 × (credit risk factors)it + β3 × (price impact liquidity risk factors)it × (credit risk factors)it + єt. The meanings of the variables are given in Table 1. The sample period is July 2006 to June 2016. The subsample (the interbank bond market) includes 2281 bond issues and 25648 observations. The subsample (the exchange market) includes 1435 bond issues and 21788 observations. The whole sample includes 3716 bond issues and 47436 observations. The t-statistics are shown in parentheses below each coefficient estimate, and “∗,” “∗∗,” and “∗∗∗” indicate significance at the 10%, 5%, and 1% levels, respectively.In the whole sample, the dummy variable is introduced to test the significance of the impact of the interbank market and the exchange market on the test results, where the dummy variable of the interbank market is set to 1, and the one of the exchange market is set to 0. As shown in the Model 1 to Model 3, the regression coefficients of the dummy variables are all significant. In order to ensure the robustness of the test results, we do regression analysis of the interbank market and the exchange market independently in Table7.In the whole sample, the regression results of Model 1 show that the regression coefficients of amihud, volatility and coupon are significant at the level of 1%, and the coefficients of amihud × volatility and amihud × coupon are significant at the level of 5%. This shows that the liquidity of price shock dimension interacts with both dynamic credit risk and static credit risk, thus affecting asset prices. In Model 2, amihud is replaced by range to test the robustness of the results. The regression coefficients of range, volatility, coupon and range × volatility are significant at the level of 1%, while the regression coefficient of range × coupon is not significant. The reason is that the static credit risk represents the credit risk level of an firm in this period of time, and it does not easily interact with liquidity risk. In Model 3, amihud and range are introduced into the regression equation. The regression coefficients of volatility and coupon are very significant, while the coefficients of amihud and amihud × coupon are significant at the level of 10% and the coefficient of range is not significant. The reason may be the high correlation between amihud and range. In spite of this, the results still prove that the impact of the interaction between liquidity and credit risk on the spreads is not negligible, and the results are robust in the Chinese corporate bond market.In the interbank market, the regression results of Model 1 show that the regression coefficients of amihud, coupon and amihud × coupon are significant at the level of 1%, and the signs are in line with expectation. It shows that the impact of the interaction between liquidity and credit risk on the spreads is present. In Model 1, the regression coefficient of amihud × volatility is greater than one of amihud × coupon. It shows that the liquidity of price shock dimension has a greater interaction with dynamic credit risk than static credit risk. Dynamic credit risk represents the credit risk level of an firm over time, and it changes in resonance with the dynamic change of liquidity risk. When liquidity affects asset prices, dynamic credit risk interacts with liquidity risk in a dynamic spiral, forming the resonance enhancement interaction between liquidity and credit risk to dynamically affect asset prices. In Model 2, amihud is replaced by range to test the robustness of the results. The regression coefficient of range × volatility is also greater than one of Range × Coupon, and this result is consistent with Model 1. In Model 3, amihud and range are introduced into the regression equation. The regression coefficients of amihud × volatility and range × volatility are greater than ones of amihud × coupon and amihud × coupon, respectively. The results prove that the liquidity of price shock dimension has a greater interaction with dynamic credit risk than static credit risk, and the impact of the interaction between liquidity and credit risk on the spreads is present in the interbank bond market.Empirical studies show that similar results are found in the exchange market. In the exchange market, the regression coefficients of coupon, and volatility are significant at the level of 1%, and the signs are in line with the hypothesis. In Model 1, the regression coefficient of amihud × volatility is significant at the level of 1%, while the regression coefficient of amihud × coupon is not significant. It shows that the liquidity of price shock dimension has a greater interaction with dynamic credit risk than static credit risk. In Model 2, amihud is replaced by range to test the robustness of the results, and the similar results are found. This shows that the results are robust. In Model 3, the coefficients of amihud and range are not significant. Because the correlation between amihud and range is high.The above analysis shows that the liquidity of price shock dimension has a greater interaction with dynamic credit risk than static credit risk, and the impact of the interaction between liquidity and credit risk on the spreads is not negligible in the interbank market and the exchange market. And the results are robust. This suggests that similar results are found in the two markets. When investors encounter liquidity risk, they panic to sell assets with high credit risks due to information asymmetry, and the behaviors of investors are consistent in the two markets. Because the behaviors of investors are determined by human egoism.


## 4.2. Robustness Test Based on Credit Risk and Macrofactors

In order to investigate whether the results are stable, we perform robustness analysis based on credit risk and macrofactors. We have carried out a lot of robustness tests of liquidity risk, and the results are stable. Rating is the credit rating assigned to each security that a firm issues [14, 37]. The higher the credit rating, the lower the credit risk. Coupon refers to the coupon rate of bonds [20, 38]. The lower the coupon, the less credit risk. It shows that rating and coupon are proxy variables of credit risk. So we use rating to replace coupon as the proxy of credit risk, in order to explore whether the interaction between liquidity and credit risk is present on the spreads. We choose the basic liquidity and credit risk proxies, and use their cross terms to represent the interaction. The empirical tests of the whole period, the financial crisis and the normal period are done in Panel A, Panel B and Panel C of Table 8. And the empirical tests of macro factors are done in Panel D of Table 8.Table 8
Robustness test of impact of interaction between liquidity and credit risk on spreads based on credit risk and macrofactors.
CDummyVolDayAmihudAgeVolatilityRatingVol × volatilityVol × ratingAmihud × volatilityAmihud × ratingAge × volatilityAge × ratingaj-R2Panel A: the whole period1.8930∗∗∗0.2326∗∗∗−0.0010∗∗∗0.0596∗∗∗1.8066∗∗∗−0.1658∗∗∗0.0823∗∗∗0.1884∗∗∗0.0006∗∗∗0.0001∗∗∗−0.5708∗∗∗−0.3607∗∗∗−0.0145∗∗−0.00020.2262(76.10)(18.85)(−9.22)(57.82)(10.05)(−28.17)(3.20)(32.61)(7.37)(4.59)(−4.64)(−8.63)(−2.03)(−0.15)Panel B: during the financial crisis1.8560∗∗∗0.0122−0.0010∗∗∗0.0042−0.3237−0.1141∗∗∗−0.4597∗∗∗0.0459∗∗∗0.0004∗∗∗0.0008∗∗∗0.02180.09250.1181∗∗∗−0.0351∗∗∗0.2031(22.04)(0.20)(−3.47)(1.02)(−0.59)(−5.09)(−7.99)(3.07)(2.86)(8.12)(0.08)(1.29)(5.44)(−3.79)Panel C: normal period1.7215∗∗∗0.2609∗∗∗−0.0009∗∗∗0.0652∗∗∗1.3577∗∗∗−0.1362∗∗∗0.3131∗∗∗0.2076∗∗∗0.0006∗∗∗0.0001−0.3170∗∗−0.2607∗∗∗−0.0473∗∗∗−0.0059∗∗∗0.2419(66.63)(21.14)(−7.83)(62.26)(7.14)(−22.73)(11.54)(33.83)(7.18)(1.16)(−2.38)(−5.78)(−6.45)(−4.06)Panel D: macrofactorsCVolTurnoverAmihudBML_VolBML_AmihudYear102S10 yearCPIGDPM0Vol × CouponTurnover × CouponDay × CouponAdj−R2(%)1.2203∗∗∗−0.0015∗∗∗0.1846∗∗∗−0.0078∗∗∗1.0654∗0.1760∗∗∗0.1487∗∗∗0.1081∗∗∗−0.0969∗∗∗−0.0205∗∗∗0.0002∗∗∗0.0004∗∗2.9413(7.51)(−3.78)(2.74)(−6.23)(1.90)(4.91)(6.37)(6.23)(−3.54)(−3.90)(3.23)(2.09)1.2328∗∗∗−1.8679∗∗∗0.1659∗∗−0.0079∗∗∗1.0650∗0.1738∗∗∗0.1495∗∗∗0.1079∗∗∗−0.0978∗∗∗−0.0208∗∗∗0.2129∗∗∗0.0005∗∗3.0494(7.59)(−4.35)(2.45)(−6.31)(1.90)(4.85)(6.41)(6.22)(−3.58)(−3.95)(3.76)(2.17)To investigate the robustness of impact of interaction on the spreads, the following regression equation is given. Spreadit = α+β1 × (liquidity risk factors)it + β2 × (credit risk factors)it+β3 × (different dimension liquidity risk factors)it × (credit risk factors)it + єt. In panel A, panel B and panel C, the meanings of the variables are given in Table 1. In panel D, BML_Vol is the monthly trading volume of the corporate bond market. BML_Amihud is illiquidity measures of the corporate bond market based on amihud. Year102 is the difference between the 10-year treasury rate and the 2-year treasury rate. S10 year is the spread between the bond market index yield and the 10-year treasury rate. CPI is the consumer price index, and GDP is gross domestic product. M0 is an increase in cash in circulation. In panel D, vol, turnover and amihud are liquidity measures of matched pairs of bonds. The cross-term is the interaction between liquidity and credit risk. The whole period is July 2006 to June 2016. The sample period of the financial crisis is May 2007 to December 2009. The sample period of normal period is from July 2006 to April 2007 and from January 2010 to June 2016. The t-statistics are shown in parentheses below each coefficient estimate, and “∗,” “∗∗,” and “∗∗∗” indicate significance at the 10%, 5%, and 1% levels, respectively.In Panel A, Panel B and Panel C of Table8, the dummy variable is introduced to test the significance of the impact of the interbank market and the exchange market on the test results. Where, the dummy variable of the interbank market is set to 1, and the one of the exchange market is set to 0. As shown in Table 8, the regression coefficients of the dummy variables are significant in normal period, which indicates that the impact of the differences between the two markets on the spreads is significant in normal period. However, the coefficient of dummy variable is not significant during the financial crisis. The reason may be that liquidity and credit risk have major impact on the spreads during the financial crisis than the differences between the two markets. In the whole period, the regression coefficients of vol, amihud, volatility, rating, vol × volatility, vol × rating, amihud × volatility and amihud × rating are significant at the level of 1%, and the signs are in line with expectation, which shows that the interaction between liquidity and credit risk is present on the spreads and the results are robust in the Chinese corporate bond market.As shown in Table8, the coefficient of Vol is increased from −0.0009 to −0.0010 from the normal period to the financial crisis, while the coefficient of age is dropped from −0.1362 to −0.1141 from the normal period to the financial crisis. This shows that compared with normal period, speculative liquidity risk premiums are increased and investment liquidity risk premiums are reduced during the financial crisis. During the financial crisis, many investors have no confidence in the future and become less willing to hold assets for the long term. Some investors begin to implement the short-term investment strategy of quick entry and quick exit, which leads to the increase of the impact of speculative liquidity and the decrease of the impact of investment liquidity on asset prices. The coefficient of Volatility is increased from 0.3131 to −0.4597 from the normal period to the financial crisis, while the coefficient of Rating is dropped from −0.2076 to −0.0459 from the normal period to the financial crisis. This shows that compared with normal period, dynamic credit risk premiums are increased and static credit risk premiums are reduced during the financial crisis. During the financial crisis, some investors sell assets in a panic. In the case of insufficient liquidity, the price fluctuation of assets with high default risk will increase, and the increase of price fluctuation will lead more investors to sell the assets with high default risk. Therefore, during the financial crisis, the impact of dynamic credit risk on asset price will gradually increase compared with static credit risk.During the financial crisis, the regression coefficients of vol, rating and vol × rating are significant at the level of 1%, and the signs are in line with expectation, while the regression coefficients of vol, amihud, volatility, rating, vol × volatility, and amihud × rating are significant at the level of 1%, and the signs are in line with expectation in normal period. This shows that the impact of the interaction between liquidity and credit risk cannot be ignored. In addition, the coefficients of age × volatility and age × rating are increased from −0.0473 and −0.0059 to 0.1181 and −0.0351 from the normal period to the financial crisis, respectively. It shows that the interaction between liquidity and credit risk has greater impact on the spreads during the financial crisis. And the results are robust. During financial crises, some investors prefer to sell assets with high default risk, which leads to large price swings. Due to information asymmetry, this will cause more investors to continue to sell assets with high default risk, further forming a bigger liquidity crisis. Finally, it leads to the incrementally increasing spiral interaction between liquidity and credit risk during financial crises.In Panel D of Table8, we perform robustness analysis based on macro factors. Some scholars find that macro factors affect corporate bond spreads. Han and Zhou [30] focus on the linkage between the corporate bond spreads and the macroeconomic conditions. See also Yang et al. [20]. In order to study macro factors, we construct matched pairs of bonds by stripping out credit risk. Relevant studies refer to Dick-Nielsen et al. [12] and Helwege et al. [13]. We study the impact of the interaction between liquidity and credit risk on corporate bond spreads under macro factors. BML_Vol is the monthly trading volume of the corporate bond market. BML_Amihud is illiquidity measures of the corporate bond market based on Amihud. Year102 is the difference between the 10-year treasury rate and the 2-year Treasury rate. S10 year is the spread between the bond market index yield and the 10-year Treasury rate. CPI is the consumer price index, and GDP is gross domestic product. M0 is an increase in cash in circulation. In Panel D of Table 8, vol, turnover and amihud are liquidity measures of matched pairs of bonds. The cross-term is the interaction between liquidity and credit risk. The regression coefficients of Vol and Turnover are significant at the level of 1%, and the signs are in line with expectation, while the regression coefficients of vol × coupon and turnover × rating are significant at the level of 1%. This shows that under the condition of controlling macrofactors, the interaction between liquidity and credit risk has a significant impact on corporate bond spreads. In Panel D of Table 8, the regression coefficients of BML_Vol, Year102, S10 year, CPI, GDP, and M0 are significant at the level of 1%. Macrofactors affect corporate bond spreads by common liquidity factors in China's corporate bond market. During the financial crisis, the impact of the interaction between liquidity and credit risk on corporate bond spreads is closely related to macro factors.


## 4.3. Robustness Test Based on Credit and Liquidity Levels

In Table9, we divide the sample into six subsamples to investigate the robustness based on credit and liquidity levels. The sample is divided into three subsamples according to the three levels of coupon, and then each subsample is divided into two subsamples according to the two levels of Vol. The cross terms of vol, amihud, age and coupon are used as measures of the interaction between liquidity and credit risk, and the regression results are shown in Table 9. These cross terms are vol × coupon, amihud × coupon and age × coupon.Table 9
The impact of interaction between liquidity and credit risk on spreads in subsample results.
CouponVolCDummyVolDayAmihudAgeVolatilityCouponVol × couponAmihud × couponAge × couponaj-R2HighHigh−2.0665∗∗∗0.4177∗∗∗−0.00120.0793∗∗∗−832.90940.9520∗∗∗0.7036∗∗∗0.5790∗∗∗0.0001109.0945−0.1525∗∗∗0.1360(−3.58)(5.94)(−0.77)(17.58)(−1.34)(4.32)(15.89)(7.95)(0.36)(1.40)(−5.45)Low−0.13270.4796∗∗∗−0.0576∗∗∗0.0532∗∗∗−0.54201.3198∗∗∗0.1143∗∗∗0.4020∗∗∗0.0071∗∗∗0.0987−0.2061∗∗∗0.2191(−0.33)(13.71)(−4.10)(25.81)(−0.37)(8.64)(3.58)(7.84)(3.99)(0.52)(−10.63)MiddleHigh−2.2082∗∗∗0.3998∗∗∗−0.00170.0794∗∗∗−561.02670.9547∗∗∗0.7029∗∗∗0.5978∗∗∗0.000175.9640−0.1528∗∗∗0.1386(−3.80)(5.66)(−1.11)(17.52)(−0.90)(4.33)(15.85)(8.15)(0.70)(0.97)(−5.46)Low−0.17950.4800∗∗∗−0.0585∗∗∗0.0538∗∗∗−0.53471.3125∗∗∗0.1103∗∗∗0.4073∗∗∗0.0072∗∗∗0.0984−0.2052∗∗∗0.2211(−0.44)(13.69)(−4.15)(26.14)(−0.36)(8.63)(3.46)(7.92)(4.03)(0.52)(−10.63)LowHigh−1.9248∗∗∗0.3986∗∗∗0.00060.0728∗∗∗184.31720.2139∗∗∗−0.01100.6444∗∗∗−0.0001−41.4980−0.0524∗∗∗0.2195(−10.75)(11.30)(0.96)(21.44)(0.76)(5.65)(−0.45)(21.10)(−1.37)(−0.99)(−7.53)Low−2.6984∗∗∗0.2102∗∗∗0.0353∗∗∗0.0292∗∗∗−0.46410.2063∗∗∗0.1488∗∗∗0.8341∗∗∗−0.0068∗∗∗0.1374−0.0509∗∗∗0.2321(−15.46)(7.75)(4.92)(13.58)(−0.63)(6.71)(5.81)(27.52)(−5.36)(1.05)(−8.53)To investigate whether the impact of interaction on the spreads is present, the following regression equations are given. Spreadit = α + β1 × (liquidity risk factors)it+ β2 × (credit risk factors)it+β3 × (different dimension liquidity risk factors)it × (representative credit risk factor)it +єt. The meanings of the variables are given in Table 2. The sample period is July 2006 to June 2016. The whole sample includes 3716 bond issues and 47436 observations. The t-statistics are shown in parentheses below each coefficient estimate, and “∗,” “∗∗,” and “∗∗∗” indicate significance at the 10%, 5%, and 1% levels, respectively.In the high-coupon subsample, the regression coefficient of vol × coupon in the low-vol sample is significant at the level of 1%, while the regression coefficient of vol × coupon in the high-vol sample is not significant. In middle-coupon and low-coupon sub sample, the regression coefficient of vol × coupon also have similar results. When trading volume is relatively high, liquidity risk is small, and small liquidity risk does not interact with credit risk. Liquidity risks are rising as trading volumes fall. When liquidity risk increases to a certain extent, it begins to interact spirally with credit risk, affecting asset prices. This shows that the interaction between liquidity and credit risk will start from scratch with the increase of liquidity risk and it is a time-varying dynamic process.In high-coupon, middle-coupon and low-coupon subsamples, the regression coefficient of age × coupon in the low-vol sample is greater than one of age × coupon in the high-vol sample. For example, in the high-coupon sub sample, the regression coefficient of age × coupon in the low-vol sample is −0.2061, while the regression coefficient of age × coupon in the high-vol sample is −0.1525. It shows that when credit risk is controlled, the interaction between liquidity and credit risk will increase with the increase of liquidity risk. In low-vol sample, the regression coefficients of age × coupon in the low-coupon sample, the middle-coupon sample and the high-coupon sample are −0.0509, −0.2052, and −0.2061, respectively. It suggests that when liquidity risk is controlled, the interaction between liquidity and credit risk will increase with the increase of credit risk.The above analysis shows that the interaction between liquidity and credit risk will increase with the increase of liquidity risk and credit risk and it is a time-varying dynamic process. The impact of the interaction between liquidity and credit risk on the spreads is not negligible in China’s corporate bond market. And, the results are robust.


## 5. Conclusion

This paper investigates the impact of multidimension liquidity, credit risk, and the interaction between liquidity and credit risk on corporate bond spreads based on a large transaction data set from July 2006 to June 2016, including the monthly data of 3716 bonds in China. Our main conclusions are as follows.First, liquidity premiums are the main parts of corporate bond spreads in China's corporate bond market. We select multidimension liquidity measures from the Chinese corporate bond market, and construct many liquidity measures from three dimensions of trading activity, price shock and bond life time. This study shows that the results are robust. Related research can also refer to Longstaff et al. [7]. Our method of multidimension liquidity measures is more accurate and reliable than those used in the existing literature.Second, the interaction between liquidity and credit risk on bond spreads plays a significant role in determining corporate bond spreads and liquidity and credit risk alone does not explain the entire yield-spread behavior. Related research can also refer to Sperna Weiland et al. [24] and Chen et al. [25]. The interaction between liquidity and credit risk will increase with the increase of liquidity risk and credit risk and it is a time-varying dynamic process. When credit risk is controlled, the interaction between liquidity and credit risk will increase with the increase of liquidity risk. When liquidity risk is controlled, the interaction between liquidity and credit risk will increase with the increase of credit risk.The liquidity of price shock dimension has a greater interaction with dynamic credit risk than static credit risk. And, these results are robust.Third, we find that the interaction between liquidity and credit risk has an enhanced impact on corporate bond spreads during financial crisis than normal period. The reason is that liquidity and credit risk interact during financial crisis. We also find that the differences between the interbank market and the exchange market have impacts on corporate bond spreads in normal period than financial crisis. The reason may be that liquidity and credit risk have major impact on the spreads during the financial crisis than the differences between the two markets. In addition, compared with normal period, speculative liquidity risk premiums are increased and investment liquidity risk premiums are reduced, while dynamic credit risk premiums are increased and static credit risk premiums are reduced during the financial crisis.Finally, dynamic credit risk changes in resonance with the dynamic change of liquidity risk, while the static credit risk does not change with the dynamics change of liquidity risk. When liquidity affects asset prices, dynamic credit risk interacts with liquidity risk in a dynamic spiral, forming a bigger resonance enhancement interaction between liquidity and credit risk to dynamically affect asset prices than static credit risk.This study provides new interpretation channels for corporate bond pricing. These findings are robust. Investor structure differences between the interbank market and the exchange market may be a direction for further research.



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