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Liquidity effects on the corporate bond pricing in China
Abstract
The paper explores the effects of bond-specific liquidity level and liquidity risk on the expected return of Chinese corporate bonds over the period from February 2009 and March 2017. The Amihud liquidity measure is adopted for calculating the bond illiquidity level and constructing the market liquidity factor. Using the Fama and MacBeth two-pass cross-sectional regression tests, results suggest that the effect of bond-specific liquidity level is insignificant on the pricing of corporate bonds, while liquidity risk has significant positive effects on the expected returns of corporate bonds. Corporate bonds with higher exposures to market liquidity shocks offer higher compensation to investors. Furthermore, the significant impacts of liquidity risk on corporate bond pricing is robust to the effects of bond characteristics and different test methods.
Name Yichun Zheng Student number 10621806 Programme MSc Finance Specialization Asset Management Supervisor Jeroen Ligterink Date June 2017
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Statement of Originality
This document is written by Student Yichun Zheng who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
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1. Introduction
Liquidity refers to the extent to which an asset or security can be traded quickly without losing its value. Some asset pricing theories predict the effects of liquidity factors on the cross-section of asset returns and a number of studies have been conducted to examine these theories. Empirical research shows that security-specific liquidity level, in addition to traditional risk factors and other security characteristics, plays an important role in the pricing of securities (Amihud and Mendelson (1986) and Chen et al. (2007)). Harder-to-trade assets tend to have a lower price as investors require more returns to compensate for the higher transaction costs associated with illiquidity (Amihud et al., 2006). Besides the asset-specific liquidity level, another liquidity factor that affects asset pricing is the liquidity risk, which is the exposure of an asset’s value to the market-wide liquidity shocks (Bongaerts et al. (2011) and Lin et al. (2011)). The existing asset pricing models suggest that the expected returns of assets increase with their exposure to systematic risk in equilibrium. As the aggregate liquidity condition are varying over time, assets with higher exposure to aggregate liquidity shocks may offer larger risk premia to investors.
Unlike stocks, corporate bonds are highly heterogenous and thus they are mostly traded in decentralized OTC markets, where it is more difficult to locate a willing trading counterparty. As a result, corporate bond markets have lower trading frequency and are more illiquid as compared to equity markets. Not only the scholars in this field, but also the market participants are interested in how liquidity factors can affect the pricing of corporate bonds. For investors, they should consider the costs of illiquidity and the larger liquidity risk in the bond market when they design their investment strategies. For companies, they are also concerned with how liquidity factors are priced in the required returns of corporate bonds as this affects their costs of financing and thus issuance decisions.
In recent years, the Chinese bond market has grown to be the third largest in the world following the United States and Japan due to supportive policies and firms’ pursuit of lower funding costs (Borst, 2016). With its comparatively stable high yields and the
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loosening of China’s capital controls, the bond market in China is increasingly attractive to international investors (Fan et al., 2014). Despite these great strides made, the Chinese corporate bond market is still confronted with a problem of infrequent trading and low liquidity, with a turnover of only around 7% of that in the U.S. (Bloomberg, 2017). As a result, the effects of liquidity factors may be more noteworthy than that in the developed markets.
This paper focuses on examining the effects of liquidity on the pricing of corporate bonds in China. As mentioned earlier, the liquidity effects on the asset pricing involve both the effects of the asset-specific liquidity level and the effects of liquidity risk. The existing literature, which is mostly based on the U.S. market, has indicated that both factors are important determinants of expected bond returns or yield spreads (Houweling et al. (2005), Chen et al. (2007) and Bongaerts et al. (2011) and Lin et al. (2011)). Hence, the main research objective is to investigate how the bond-specific liquidity level and liquidity risk affect the expected returns of Chinese corporate bonds. This paper can complement the existing research in several aspects. First, it takes into account both the effect of bond liquidity level and the effect of liquidity risk, while most previous studies only consider the effect of liquidity as a bond-specific characteristic. Furthermore, it fills the gap in studying the liquidity effects on asset prices based on the Chinese corporate bond market. As almost all existing literature focuses on the U.S corporate bond market, this paper can provide insights into the role of liquidity factors in a fast-developing, immature and illiquid bond market. Furthermore, most research is based on the period up to 2008, whereas this study covers a more recent period to test the liquidity effects after the onset of the global financial crisis, when the aggregate liquidity deteriorate.
Using the Fama-MacBeth (1973) cross-sectional regressions, the results show that for the two liquidity factors examined, liquidity risk has significant and robust effects on the expected returns of corporate bonds, while the effect of bond liquidity level on corporate bond pricing is statistically insignificant and economically negligible. The liquidity risk premium is positive, indicating that corporate bonds which are more sensitive to market liquidity shocks have higher expected returns.
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The remainder of this paper is organized as follows. Section 2 reviews the existing literature on liquidity and asset pricing and derives the hypotheses of the study. Section 3 introduces the research methodology, estimation procedures and liquidity measures construction. Section 4 provides details about Chinese corporate bond market and describes the data used. The main results are presented in section 5, followed by some robustness tests in section 6. Then in section 7 the final conclusions are reached.
2. Literature and hypotheses
In this section, the first two parts summarize the existing studies about the effects on asset pricing of the two liquidity factors: bond liquidity level and liquidity risk, respectively. Then the connections between this paper and the previous literature are discussed. The hypotheses are derived in the last subsection.
2.1 Liquidity level and asset pricing
Theoretically, liquidity level of an asset will affect the prices of assets because for assets with lower liquidity levels, the sellers should incur higher searching costs to locate a willing buyer. Moreover, even if they successfully find a trading partner, they may compromise in the price negotiations as there are no alternative buyers for the assets. As a result, investors will require cheaper asset prices and thus higher compensation for bearing these illiquidity costs.
Empirical evidence of the effects of asset liquidity level on the asset price is mostly found in the equity market. Amihud and Mendelson (1986) are the first to study the relationship between liquidity and asset pricing. Their study uses the bid-ask spreads as a measure of stock illiquidity and derive a hypothesis that the expected asset return is a concave increasing function of illiquidity costs of stocks. And their empirical results show consistency with the hypothesis. In 1989, Amihud and Mendelson (1989) conducted a further study on the return-bid ask spread relationship with an extended model with also accounts for the effects of the portfolio’s beta, unsystematic risk and size. Controlling for these additional factors, the results indicate that the effect of the bid-ask spread on stock
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returns remain positive and significant. Brennan and Subrahmanyam (1996) also investigate the stock returns-illiquidity relationship, but they use an illiquidity measure which is the slope coefficient estimated by regressing the trade-by-trade price change on the signed transaction size. This coefficient indicates the effect of a unit trading size on the stock price, which is smaller for more liquid stock. Besides the illiquidity variables, they also include the three Fama-French factors in the cross-sectional regression and account for the impacts of the stock price level. The results suggest a significant positive relation between illiquidity and required rates of return. The research of Amihud (2002), based on the stocks traded in the NYSE over the period 1963-1996, employs the ratio of absolute daily return to dollar trading volume as illiquidity measure, which reflects the price change brought by a given trading volume. Their findings also support a positive link between illiquidity and expected stock returns and show that contemporaneous unexpected illiquidity negatively affects stock returns.
As government bonds are risk-free and there is no need to separate the default premium from the illiquidity premium, they provide a fertile ground for the study of liquidity effects on asset pricing. The study of Elton and Green (1998) tests the liquidity effects on government bond using the trading volume as the liquidity measure. They find low-trading volume bonds have lower prices and higher yields compared to high-volume bonds with similar maturity after controlling for the tax effects. However, the liquidity effects are very limited and have been diminishing over time. Longstaff (2004) examines liquidity impacts on Treasury bond yields by comparing their prices with the prices of Refcorp bonds, which are also default risk-free but are more illiquid than the Treasury bonds. Longstaff finds a significant premium on the yield of Refcorp bonds and this liquidity premium is associated with varying market conditions including changes in consumer confidence and credit spread and Treasury buybacks.
While the most literature focus on the equity and government bond markets, some more recent studies provide insights into the impacts of liquidity level on the expected returns or yield spreads of corporate bonds. Houweling et al. (2005) employ nine proxies to measure liquidity of corporate bonds and control for the differences in
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maturity, rating, credit risk and interest rate risk between bond portfolios. For eight out of the nine liquidity measures, they find significant liquidity premia, indicating that liquidity is an important determinant of corporate bond pricing. The study of Chen et al. (2007) covers more than 4000 U.S. corporate bonds and tests the association between corporate bond liquidity and yield spreads and between changes in liquidity and changes in yield spread levels. The results show that corporate yield spreads are negatively related to bond liquidity and thus proof that the liquidity can explain partially the large corporate yield spreads, which cannot be fully explained by default risk factors. The research of Helwege et al. (2013) forms a sample of bond pairs, in which the two bonds are issued by the same firm and trade on the same day, to separate out the credit risk effects and examine the liquidity effects on the corporate bond spreads. They find that the liquidity proxies have poor explanatory power for the differences in the corporate bond spreads and even when liquidity proxies incorporate prices on other bonds, a significant portion of the cross-sectional variation in the yield spreads remains unexplained. The study of Longstaff (2005) explores the default and nondefault components in corporate spreads and suggests that the default risk explains the majority of the corporate spread, but the individual corporate bond and aggregate liquidity are also important components of the spread.
2.2 Liquidity risk and asset pricing
Investors bear liquidity risk as liquidity changes over time and thus investors are uncertain about the transaction costs they need to pay when they sell the assets. Furthermore, as liquidity level affects asset prices, variations in liquidity results in larger price volatility of the assets. Investors will also require higher returns for assets with higher exposure to liquidity risk.
The impacts of liquidity risk on the expected returns are supported by studies based on different kinds of assets. The research of Pastor and Stambaugh (2003) explores whether systematic liquidity is a determinant of stock pricing and the results suggest that stocks which are more sensitive to aggregate liquidity shocks have higher expected
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returns. Their measure for liquidity is the return reversal in response to order flow, which is greater when liquidity is lower. Acharya and Pedersen (2005) constructs an asset pricing model which incorporates an expected illiquidity variable and three liquidity-related betas into the ordinary Capital Asset Pricing Model. The estimation results show that both the stock portfolio’s illiquidity level and its liquidity betas, which are the measures for exposure to liquidity risk, have significant and positive impacts on its excess return. Furthermore, they find that illiquid stocks have greater exposure to liquidity risk, which is in line with the concept of flight to liquidity. Kamara (1994) investigate the yield differences of Treasury notes and bills with same maturities and find that they are induced by the differences in liquidity risk and taxes. In addition, the yield differences are negatively affected by dealers’ inventories of notes, which are the less liquid asset. Sadka (2010) investigates the effect of liquidity risk, measured by the covariation of fund returns with market liquidity shocks, on the expected hedge fund returns and finds that liquidity risk significantly determines the cross-section of hedge fund returns, while the liquidity level of a fund have no impacts on the hedge fund returns.
There are also several studies contributing to exploring the effects of liquidity risk on corporate bond pricing. De Jong and Driessen (2012) investigates the effects of liquidity risk on corporate bond and they find that liquidity risk is priced in the expected corporate bond returns and bonds with higher exposures to liquidity factors have higher liquidity risk premium. The study of Lin et al. (2011) adopts an augmented Fama-French three-factor model, in which the default premium, term premium and a liquidity factor are incorporated, to examine how the sensitivities of corporate bonds to aggregate liquidity shocks determine the expected corporate bond returns. Their results suggest that a positive relationship exists between the expected corporate bond returns and liquidity beta and that the exposure to aggregate liquidity risk is a significant factor in determining the expected corporate bond returns. Bongaerts et al. (2011) investigates the impacts of expected liquidity and liquidity risk on expected returns of U.S. corporate bonds using an asset pricing approach. They use a Bayesian estimation of Roll’s effective cost model to measure corporate bond liquidity and find that expected bond returns are
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substantially affected by expected liquidity level of the bond and equity market liquidity risk and are hardly affected by the exposure to corporate bond liquidity innovations.
2.3 Connections with existing research
Like the existing literature, this paper posits that the bond liquidity level and liquidity risk are priced in the expected returns of corporate bonds. This paper is related to previous studies primarily in two aspects: liquidity measures and estimation procedures. The selection of liquidity measures is one of the key issues in studying the liquidity effects. As corporate bonds are traded mostly on the over-counter market and infrequently, it is hard to obtain reliable data for direct liquidity measures like the bid-ask spreads. Further, since this paper is based on the China’s corporate bond market, the data on corporate bond transactions are more limited compared to the U.S. market. This paper uses the Amihud (2002) illiquidity measure to define the bond illiquidity variable and to construct the liquidity risk variable because it can capture the price impacts of trades, which is a good indicator the bond liquidity level and the data for calculating this measure is easy to access. Moreover, results from the research of Brennan and Subrahmanyam (1996) and of Lin et al. (2011) indicates that it has good explanatory power for the cross section of corporate bond returns. And many studies use some bond characteristics such as bond age and issue size as indirect liquidity proxies and the results show significant liquidity premia. Therefore, this paper includes these bond characteristics in the cross-sectional regressions for robustness checks. As for the estimation procedures, the paper uses a two-pass regression model following the studies of Lin et al. (2011) and of Bongaerts et al. (2011) so that both the impacts of bond liquidity level and liquidity risk can be investigated. The first step is time-series regressions to get the liquidity betas, which are the exposures to market liquidity risk of individual corporate bonds. The second step is cross-sectional regressions of bond returns on the liquidity betas and the bond-specific illiquidity levels to examine the effects of these two liquidity factors, controlling for other risk factors.
10 2.4 Hypotheses
The research objective is to test how the bond-specific liquidity level and liquidity risk affect the expected corporate bond returns in China.
In theory, higher liquidity level of the bond means lower transaction costs incurred, which increases the cash flow and the price of the bond and thus decreases the expected bond returns. Most existing literature also supports the negative relationship between bond liquidity level and the expected bond returns. Thus, the first hypothesis is expressed as:
Hypothesis 1: Bond-specific liquidity level has a significant negative effect on the expected corporate bond returns in China.
And many studies demonstrate that bonds with higher sensitivity to market liquidity shocks, which means higher liquidity risk, have higher expected returns. Therefore, the second hypothesis is stated as:
Hypothesis 2: Liquidity risk has a significant positive effect on the expected corporate bond returns in China.
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3. Research Method
As the effects of liquidity risk on the expected corporate bond returns are explored in this paper, the research method includes two steps. In the first step, the liquidity risk of each corporate bond, which is the exposure of a bond’s return to the liquidity innovations in the market, is estimated through a multi-factor model. Then, using liquidity risk estimates and bond-specific illiquidity levels, the Fama-Macbeth cross-sectional regression is conducted in the second step to test the influence of liquidity risk and bond illiquidity level on the expected corporate bond returns. The section first explains the construction of the two liquidity measures: bond illiquidity level 𝐵𝑖𝑙𝑙𝑖𝑞𝑖 and market liquidity factor
M𝐿𝑖𝑞𝑡. Then the models used in the two steps of the research method are specified.
3.1 Measures for bond illiquidity level (𝑩𝒊𝒍𝒍𝒊𝒒𝒊) and market liquidity factor (𝐌𝑳𝒊𝒒𝒕)
The Amihud (2002) illiquidity measure is adopted to measure the bond-specific illiquidity level 𝐵𝑖𝑙𝑙𝑖𝑞𝑖 and to estimate the market liquidity factor M𝐿𝑖𝑞𝑡. This measure captures the
price impact of a given trading volume. If a bond has a higher liquidity level, the effect on price of a given trading volume will be smaller. The formula for the Amihud illiquidity measure is expressed as:
𝐼𝐿𝐿𝐼𝑄𝑖𝑡 = 1 𝐷𝐴𝑌𝑖𝑡 ∑ |𝑟𝑖,𝑗,𝑡| 𝑉𝑜𝑙𝑖,𝑗,𝑡 𝐷𝑎𝑦𝑖𝑡 𝑗=1 , (1)
where 𝐼𝐿𝐿𝐼𝑄𝑖𝑡 measures illiquidity of the bond i in month t, the 𝑟𝑖,𝑗,𝑡 is bond i’ s return
on day j in month t, 𝐷𝐴𝑌𝑖𝑡 is the number of days for which there are transaction records
for bond i in month t and 𝑉𝑜𝑙𝑖,𝑗,𝑡 is the trading volume of bond i on day j in month t (in
millions, RMB). The higher the measure, the larger the price impact of trades, which indicates higher illiquidity of the bond. This measure is calculated for every bond in the sample in each month and it is used as the value for the variable bond illiquidity level 𝐵𝑖𝑙𝑙𝑖𝑞𝑖 in the cross-sectional regressions.
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To obtain the market liquidity factor M𝐿𝑖𝑞𝑡, the first step is to calculate the market wide
illiquidity in each month by averaging the illiquidity measures of individual bonds in the sample. The formula for the market-wide illiquidity in month t is:
𝐼𝐿𝐿𝐼𝑄𝑀𝑡 = 1
𝑛𝑡∑ 𝐼𝐿𝐿𝐼𝑄𝑖𝑡
𝑛𝑡
𝑖=1 , (2)
where n is the number of bonds in the sample.
Additionally, to eliminate the huge influence of outliers, the individual 𝐼𝐿𝐿𝐼𝑄𝑖𝑡
values for each month are first winsorized using the 2nd and 98th percentiles of the
distribution and then used in the calculation of 𝐼𝐿𝐿𝐼𝑄𝑀𝑡. The monthly difference of the market-wide illiquidity is calculated as: ∆𝐼𝐿𝐿𝐼𝑄𝑀𝑡= 𝐼𝐿𝐿𝐼𝑄𝑀𝑡− 𝐼𝐿𝐿𝐼𝑄𝑀𝑡−1. Then, the
innovations in market-wide illiquidity in month t can be derived from an Autoregressive Integrated Moving Average (Arima) regression:
∆𝐼𝐿𝐿𝐼𝑄𝑀𝑡= 𝛼0+ 𝜑1Δ𝐼𝐿𝐿𝐼𝑄𝑀𝑡−1+ 𝜑2Δ𝐼𝐿𝐿𝐼𝑄𝑀𝑡−2+ 𝜑3𝐼𝐿𝐿𝐼𝑄𝑀𝑡−1+ 𝜀𝑡+ 𝜉1𝜀𝑡−1. (3)
The term 𝜀𝑡 denotes the innovations of market illiquidity in month t. And 𝜀𝑡−1 is the
moving average component included to remove the serial correlation in the residuals. And the Bayesian Information Criterion (BIC) is used to decide the order of the moving average component and autoregressive terms. As 𝜀𝑡 represents the innovations of
market illiquidity, its converted form −𝜀𝑡 means innovations in market liquidity.
Therefore, the estimate for the converted innovation series ( −𝜀̂ ) measures the 𝑡
innovations of market liquidity and is used as the Market liquidity factor M𝐿𝑖𝑞𝑡. As the
market liquidity factor represents market liquidity innovations, the time series of the market liquidity factor is normalized to have a unit standard deviation and a zero mean for the remaining analysis following the study of Acharya and Pedersen (2005).
3.2 First step: Time-series regressions using a multi-factor model
For the first step, the time series of monthly excess returns of each corporate bond are regressed against a series of risk factors to obtain the exposures of each corporate bond to those factors. A multi-factor model, which is the Fama-French three-factor model
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incorporated with a term premium, a default premium and a market liquidity factor, is employed for the time-series regressions. Fama and French (1993) investigate the common risk factors in the stock and bond returns and they find that the two bond-market factors, which are related to term and default risks respectively, capture the variation in corporate bond returns. Therefore, the term premium and default premium factors are included in this multifactor model for corporate bond returns. They also find that stock returns are captured by three stock-market factors: an overall market factor, a factor related to book-to-market equity and a factor related to firm size. As both bond and stock are the claims on the same underlying assets of the firm, stock market factors affect bond returns to some extents. Furthermore, the default risk of corporate bonds decreases with the appreciation of stock value and thus the stock value has influence on corporate bond returns (Lin et al., 2011). Hence, the three stock market factors in the study of Fama and French (1993) are also included this multifactor model for time series regressions. The research of Elton et al. (2001) provides empirical evidence that stock market factors can indeed explain corporate bond returns. As a result, this multifactor model can be expressed as the following equation:
𝑟𝑖𝑡− 𝑟𝑓𝑡 = 𝛽0𝑖+ 𝛽𝑖𝐸𝑅𝑀𝐸𝑅𝑀𝑡+ 𝛽𝑖𝑆𝑀𝐵𝑆𝑀𝐵𝑡+ 𝛽𝑖𝐻𝑀𝐿𝐻𝑀𝐿𝑡+ 𝛽𝑖𝐿𝑀𝐿𝑖𝑞𝑡+ 𝛽𝑖𝑇𝑒𝑟𝑚𝑇𝑒𝑟𝑚𝑡+ 𝛽𝑖𝐷𝑒𝑓𝐷𝑒𝑓𝑡+ 𝜀𝑖𝑡. (4)
The dependent variable (𝑟𝑖𝑡− 𝑟𝑓𝑡) is the return 𝑟𝑖𝑡 of corporate bond i in excess of the
risk-free return 𝑟𝑓𝑡 in month t. The monthly return of the three-month central bank bill is used as the proxy for the monthly risk-free rate. 𝐸𝑅𝑀𝑡, 𝑆𝑀𝐵𝑡 and 𝐻𝑀𝐿𝑡 are the Fama
and French (1993) three stock market factors. 𝐸𝑅𝑀𝑡 denotes stock market excess return.
𝑆𝑀𝐵𝑡 is the Fama-French size factor and 𝐻𝑀𝐿𝑡 is the book-to-market equity factor.
𝑇𝑒𝑟𝑚𝑡 is the term premium and it is calculated as the difference between the monthly
returns of the long-term government bond index and the three-month central bank bill. 𝐷𝑒𝑓𝑡 is the default premium factor and it is measured by the difference between the
monthly returns of the corporate bond index and the government bond index. M𝐿𝑖𝑞𝑡 is
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capture the exposures of individual corporate bond returns to different risk factors. Among them, 𝛽𝑖𝐿 captures the sensitivity of excess returns of bond i to market liquidity
shocks and represents the liquidity risk of bond i, which is one of the liquidity factors examined in this paper.
3.3 Second step: Cross-sectional regressions based on the beta estimates
In the second step, the Fama and MacBeth (1973) cross sectional regressions are used to test the effects of both liquidity risk and bond-specific illiquidity level on the expected bond returns. The model is presented by an equation:
𝑟𝑖𝑡− 𝑟𝑓𝑡 = 𝛼𝑖 + 𝜆𝐸𝑅𝑀𝛽𝑖𝐸𝑅𝑀+ 𝜆𝑆𝑀𝐵𝛽𝑖𝑆𝑀𝐵+ 𝜆𝐻𝑀𝐿𝛽𝑖𝐻𝑀𝐿+ 𝜆𝑙𝛽𝑖𝐿 + 𝜆𝑇𝑒𝑟𝑚𝛽𝑖𝑇𝑒𝑟𝑚+ 𝜆𝐷𝑒𝑓𝛽𝑖𝐷𝑒𝑓+ 𝜆𝐵𝑖𝑙𝐵𝑖𝑙𝑙𝑖𝑞𝑖+ 𝜆𝑒𝑛𝑡𝑒𝑛𝑡𝑒𝑟𝑝𝑟𝑖𝑠𝑒𝑖 + 𝑢𝑖, (5)
where the dependent variable is the excess return of each bonds in month t. The term 𝐵𝑖𝑙𝑙𝑖𝑞𝑖 is the bond-specific illiquidity level of each bond in month t and its calculation is elaborated in the subsection 3.1. The variable 𝑒𝑛𝑡𝑒𝑟𝑝𝑟𝑖𝑠𝑒𝑖 is a dummy variable, for which
the value is 1 if the bond is an enterprise bond and 0 if the bond is a listed-company bond. Both types of bonds are classified as corporate bonds, so this variable is used to control for the effect of the bond type. For each bond, betas are estimated from the time series regression in the first step over the rolling past 3-year periods and then used in the cross-sectional regression for the following month. The lambdas 𝜆′𝑠 capture the risk premiums for different factors. For each month, all corporate bond excess returns are regressed against the estimated betas for all corporate bonds in the sample to determine the risk premium 𝜆 for each risk factor. For example, 𝜆𝑙 is the risk premium for the liquidity risk
𝛽𝑖𝐿 in a given month and it measures how the liquidity risk is priced in the expected
corporate bond returns. Since a cross-sectional regression is conducted for each point in time, there will be T regressions if there are T months in the sample period. Then for each risk factor, the risk premium λ can be calculated by averaging the 𝜆𝑡 across T regressions.
And the t-statistics for λ is calculated as: λ
(𝜎λ /√𝑇), which is then used for the statistical
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liquidity risk 𝛽𝑖𝐿 and the bond-specific illiquidity level 𝐵𝑖𝑙𝑙𝑖𝑞𝑖. The betas of market 𝛽𝑖𝐸𝑅𝑀,
size 𝛽𝑖𝑆𝑀𝐵, book-to-market 𝛽𝑖𝐻𝑀𝐿 , term 𝛽𝑖𝑇𝑒𝑟𝑚 and default factors 𝛽𝑖𝐷𝑒𝑓 and the
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4. Chinese corporate bond sector and data
This section first introduces the Chinses corporate bonds in detail and then specify the sample and data sources and in the last subsection, a table of summary statistics and correlations is presented.
4.1 Chinese corporate bonds
There are mainly four types of corporate bonds in the Chinese market: convertible bonds, short-term corporate financing bills, enterprise bonds and listed-company bonds (Chen et al., 2011). Convertible bonds are traded on the exchanges and they encompass both the features of bonds and equity since they are convertible into firms’ shares at predetermined prices. To avoid the complexity brought by its embedded options, convertible bonds are excluded from the analysis in this paper. Shor-term corporate financing bills are the most liquid corporate bonds which are traded only in the interbank market and commonly have a maturity shorter than 1 year. They are also eliminated from the sample because they are hardly subject to liquidity risk and their transaction records are too short for time series regression. Enterprise bonds are issued by state-owned enterprise and are intended for financing infrastructure construction or other projects that can facilitate public welfare and national development. They are traded in both the exchanges and the interbank market and are commonly rated as AAA bonds by the rating agencies in China because their issuance is approved by the National Development and Reform Commission (NDRC) and guaranteed by state-owned banks. Listed-company bonds, introduced in 2007, are issued by companies listed on the Shanghai or Shenzhen Stock Exchange and regulated by the China Securities Regulatory Commission (CSRC). Compared to enterprise bonds, they are traded only in exchange markets and are exposed to higher default risk as they are not guaranteed by state banks and their issuance are less restricted. The sample consists of the transaction data for both types of corporate bonds and a dummy variable are used in the cross-sectional regressions to control for the effect of bond type on the expected bond returns.
17 4.2 Data and sample
The data of the paper are all from the databases of the RESSET Financial Research platform. The RESSET database platform is co-established and designed by many well-known experts in finance database and financial modeling research from Tsinghua University and Peking University in China. It provides extensive and high-quality economic and financial data on the Chinese markets, which cover multiple industries and various asset markets including the equity, funds, fixed-income, derivatives and foreign exchange markets.
The monthly data for the Fama and French three stock market factors 𝐸𝑅𝑀𝑡, 𝑆𝑀𝐵𝑡 and 𝐻𝑀𝐿𝑡 are obtained from the RESSET Stock database. The daily transaction data including prices, trading volumes and accrued interests for the corporate bonds, three-month central bank bill, long-term government bond index, corporate bond index and the government bond index are obtained from RESSET Bond database. Bond characteristics data including coupon rate, age, credit rating, issue size and bond type are also available from this database. Monthly returns of the three-month central bank bill are available directly. And for those indices, monthly returns can be calculated from their close prices at the end of each month by the formula: 𝑟𝑡 =
𝑃𝑡−𝑃𝑡−1
𝑃𝑡−1 . The monthly return of a corporate
bond is calculated through the formula: 𝑟𝑡=
𝑃𝑡−𝑃𝑡−1+𝐴𝐼𝑡−𝐴𝐼𝑡−1+𝐶𝑡 𝑃𝑡−1+𝐴𝐼𝑡−1 , (6)
in which 𝑃𝑡 is the last transaction price at the end of month t and 𝐴𝐼𝑡 is the accrued
interest on the same day. 𝑃𝑡−1 is the last transaction price in month t-1 and 𝐴𝐼𝑡−1 is the
accrued interest on that day. 𝐶𝑡 is the annual coupon payment, if applicable, in month t.
The sample period for the rolling time series regressions in the first step is from February 2006 to March 2017. Therefore, the full sample includes the transaction data of corporate bonds in the 134 months of this period. The cross-sectional regressions in the second step use betas estimated from the first-step time series regressions over the rolling past three years. For instance, the betas estimated over the period February 2006 to January 2009 are used in the cross-sectional regression for February 2009 and the betas estimated over
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the period from March 2006 to February 2009 are used in the cross-sectional regression for March 2009. As the sample period for rolling regressions is from February 2006 to March 2017 and the rolling window is 3 years, the cross-sectional regression test is conducted for each month within the period from February 2009 to March 2017, in which there are in total 98 months. And for the rolling time-series regressions in step 1, each corporate bond is required to have at least 15 monthly returns over the rolling 3-year windows for beta estimations. As a result, the final sample includes 1337 bonds in total: 1008 enterprise bonds and 329 listed company bonds. If the bonds are categorized by the ratings assigned by Chinese credit rating agencies, there are 306 AAA bonds, 387 AA+ bonds, 620 AA bonds, 22 AA- bonds and 2 A+ bonds. Under the credit rating standards set by the People's Bank of China, there are totally 9 grades ranging from AAA to C for the Chinese long-term credit rating system and the plus ‘+’ and minus ‘– ‘sign indicate upward and downward adjustment respectively. The corporate bonds in the final sample generally have high credit ratings since all of them are graded above A and the vast majority of them are graded at or above AA.
4.3 Descriptive statistics
Table 1 presents the descriptive statistics for the dependent variable and the risk factors in the first-step time series regressions using the multi-factor model in equation (4). The sample period is from February 2006 to March 2017.
As the Panel A shows, for the three stock market factors, the mean monthly stock market excess return over the sample period is 1.32% with a standard deviation of 0.45%. The monthly average returns of the size factor SMB and the book-to-market factor HML are 1.34% and -0.12% respectively. For the two bond market factors, the mean monthly default premium and term premium are 0.13% and 0.08% respectively. The market liquidity factor has a mean at around 0 as it represents the market liquidity innovations. Panel B shows the correlations among the risk factors used for time series regressions. It is noticeable that the market liquidity factor has low correlations with all the other standard risk factors. This implies that it is reasonable to incorporate the liquidity factor
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into the bond pricing model to account for the variation in return which is not explained by the standard risk factors.
Table 1. Descriptive statistics
Panel A presents the summary statistics for the dependent variable and the six risk factors used in the time series regression in step 1, equation (4): the Fama-French market factor 𝐸𝑅𝑀, size factor 𝑆𝑀𝐵, book-to-market equity factor 𝐻𝑀𝐿, default premium, term premium and the market liquidity factor. The data for all variables are monthly and are expressed in percentage. The market liquidity factor is normalized by standard deviation. The sample period is from February 2006 to March 2017 and thus there are 134 months. For the dependent variable bond’s excess return, the average excess return over the sample period for each bond is first calculated and the summary statistics is based on the distribution of the mean returns of individual bonds. There are 1337 bonds in the sample. Panel B presents the correlations among the six risk factors.
Mean Median Minimum Maximum Standard deviation Number of Obs.
Excess return 0.37 0.26 -4.22 2.12 0.45 1337 ERM 1.32 2.03 -26.85 29.49 9.46 134 SMB 1.34 1.66 -17.31 19.15 4.71 134 HML -0.12 -0.07 -15.82 14.83 3.52 134 Default premium 0.13 0.17 -2.21 2.43 0.54 134 Term premium 0.08 0.11 -4.89 6.91 1.88 134
Market liquidity -3.72E-09 0.02 -2.29 3.99 1.00 134
ERM SMB HML Default premium Term premium Market liquidity ERM SMB 0.17 HML 0.08 -0.46 Default premium -0.20 0.15 -0.02 Term premium -0.26 0.08 -0.08 0.36 Market liquidity -0.06 -0.08 0.07 -0.08 0.06 Panel A: Summary staticstics for risk factors
Panel B: Factor correlations
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5. Results
The section provides the results and interpretations for each estimation procedure in the research method. As introduced in the section 3, the estimation procedures include the construction of market liquidity factor, the first-step time series regressions and the second-step cross-sectional regressions.
5.1 Estimation result of the market liquidity factor 𝐌𝑳𝒊𝒒𝒕
The market liquidity factor M𝐿𝑖𝑞𝑡 measures the market liquidity innovations and it is
estimated from the Autoregressive Integrated Moving Average (Arima) regression in equation (3): ∆𝐼𝐿𝐿𝐼𝑄𝑀𝑡= 𝛼0+ 𝜑1Δ𝐼𝐿𝐿𝐼𝑄𝑀𝑡−1+ 𝜑2Δ𝐼𝐿𝐿𝐼𝑄𝑀𝑡−2+ 𝜑3𝐼𝐿𝐿𝐼𝑄𝑀𝑡−1+ 𝜀𝑡+
𝜉1𝜀𝑡−1. The 𝜀𝑡 represents the innovations in market illiquidity and thus its converted
series (−𝜀𝑡) is used to measure the innovations in market liquidity. The estimation result
of the Arima regression is reported in Table 2. The result shows that the lagged change in aggregate illiquidity Δ𝐼𝐿𝐿𝐼𝑄𝑀𝑡−1 has a good explanatory power for the change in
aggregate illiquidity, with a coefficient estimate significant at 1% level. The coefficient for the moving average term 𝜀𝑡−1 is also significant at 1% level, while the coefficients for the
lagged value of market illiquidity level and the second-order lagged term of the market illiquidity change are insignificant. Then, by using these parameter estimates, the series of illiquidity innovations 𝜀𝑡 can be predicted and its converted form (−𝜀𝑡) is used as the market liquidity factor. The market liquidity factor is normalized to have a zero mean and a unit standard deviation since it measures market liquidity innovations.
Figure 1 depicts the series of the market liquidity factor over the sample period from February 2006 to March 2017. As shown in the figure, from 2007 to 2008, the market liquidity innovations in the Chinese corporate bond market are generally positive. This can be explained by the considerable increase in the trading volume following the key reform in 2007 to allow listed companies to issue corporate bonds without bank guarantees and the subsequent regulatory changes which have streamlined the approval process for issuing listed-company bonds (Chen et al., 2011). After the onset of the 2008
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global financial crisis, the liquidity shocks are mostly negative. However, the positive shocks in late 2011, 2014 and 2015 are notably large. These positive liquidity innovations may be associated with the great expansion and prosperity of Chinese bond market in late 2011 and 2012, the easing of monetary policy in 2014 and the favorable reform by the CSRC on the administration of corporate bond issuance and trading in early 2015, respectively.
Table 2. Estimation of Market illiquidity innovations.
This table presents the estimation of the Amihud market illiquidity innovations by equation (3): ∆𝐼𝐿𝐿𝐼𝑄𝑀𝑡= 𝛼0+
𝜑1Δ𝐼𝐿𝐿𝐼𝑄𝑀𝑡−1+ 𝜑2Δ𝐼𝐿𝐿𝐼𝑄𝑀𝑡−2+ 𝜑3𝐼𝐿𝐿𝐼𝑄𝑀𝑡−1+ 𝜀𝑡+ 𝜉1𝜀𝑡−1 , where the dependent variable ∆𝐼𝐿𝐿𝐼𝑄𝑀𝑡=
𝐼𝐿𝐿𝐼𝑄𝑀𝑡− 𝐼𝐿𝐿𝐼𝑄𝑀𝑡−1 is the monthly difference in the market-wide illiquidity measure. The 𝜀𝑡 is the error term and
measures the innovations in market-wide illiquidity. The model includes the lagged term of the level series and two lagged terms of the difference series and a moving average term, which is intended for removing the autocorrelation in the residuals. The orders for the auto-regression and the moving average term are selected by Bayesian Information Criterion. The sample period is from February 2006 to March 2017.
Sample period 2006m2-2017m3
Adj.
0.259Dependent variable
Parameters Coefficients Standard error t-value P>|t|
0.978 0.174 5.63 0.000
-0.239 0.170 -1.41 0.160
-0.247 0.169 -1.46 0.144
-1.000 0.081 -12.39 0.000
Intercept 0.555 0.200 2.78 0.005
22 Figure 1. Market Liquidity Innovations
This figure plots the Chinese corporate bond market liquidity innovations (market liquidity factor) over the period from February 2006 to March 2017.
5.2 Summary of the time series regressions
In the first step of the research method, rolling time series regressions are performed for each corporate bond to get the time-varying betas for the cross-sectional regressions in the second step. As the 3-year rolling regressions yield a series of beta for each bond, it is hard to present the overall estimation results for the full sample. To summarize the time series estimation results, a full-period time series regression is conducted for each bond using the model in Equation (4): 𝑟𝑖𝑡− 𝑟𝑓𝑡 = 𝛽0𝑖+ 𝛽𝑖𝐸𝑅𝑀𝐸𝑅𝑀𝑡+ 𝛽𝑖𝑆𝑀𝐵𝑆𝑀𝐵𝑡+ 𝛽𝑖𝐻𝑀𝐿𝐻𝑀𝐿𝑡+ 𝛽𝑖𝐿𝑀𝐿𝑖𝑞𝑡+ 𝛽𝑖𝑇𝑒𝑟𝑚𝑇𝑒𝑟𝑚𝑡+ 𝛽𝑖𝐷𝑒𝑓𝐷𝑒𝑓𝑡+ 𝜀𝑖𝑡.
Table 3 reports the summary statistics of the time series regressions results for all corporate bonds over the sample period from February 2006 to March 2017. The mean t and median t refer to the average t-value and median t-value across the regressions for all corporate bonds in the sample. As shown in the table, the mean betas for the three stock market factors ERM, SMB and HML are 0.045, -0.044 and 0.081 respectively and on average they are insignificant with small t-values. For the bond market risk factors default
-2 0 2 4 Ma rke t L iq u id it y F a ct o r 2006m1 2008m1 2010m1 2012m1 2014m1 2016m1 2018m1 month
23
premium and term premium, their average betas are 0.039 and 0.2 respectively and have larger average t-values than the betas for the stock market factors. However, the default beta and term beta are still not significant on average. The liquidity beta has an average value of 0.017 and its mean t statistics is 2.063, indicating that it is on average significant at the 5% level. These results suggest that on average, the corporate bond returns are more sensitive to bond market risk factors than stock market factors. And among the risk factors, the market liquidity factor has on average the most significant effects on the excess returns of corporate bonds.
Table 3. Summary statistics of the full-period time series regressions
This table reports the summary statistics of the full-period time series regressions conducted on the full sample. The sample period is from February 2006 to March 2017. Beta are estimated from the model: 𝑟𝑖𝑡− 𝑟𝑓𝑡= 𝛽0𝑖+
𝛽𝑖𝐸𝑅𝑀𝐸𝑅𝑀𝑡+ 𝛽𝑖𝑆𝑀𝐵𝑆𝑀𝐵𝑡+ 𝛽𝑖𝐻𝑀𝐿𝐻𝑀𝐿𝑡+ 𝛽𝑖𝐿𝑀𝐿𝑖𝑞𝑡+ 𝛽𝑖𝑇𝑒𝑟𝑚𝑇𝑒𝑟𝑚𝑡+ 𝛽𝑖𝐷𝑒𝑓𝐷𝑒𝑓𝑡+ 𝜀𝑖𝑡 , where the dependent
variable is a bond’s monthly excess return and the explanatory variables are, in turn, the Fama-French stock market factor 𝐸𝑅𝑀, size factor 𝑆𝑀𝐵, book-to-market equity factor 𝐻𝑀𝐿, market liquidity factor M𝐿𝑖𝑞, term premium 𝑇𝑒𝑟𝑚 and default premium 𝐷𝑒𝑓. The mean t and Median t is the average t- value and median t-value across all corporate bonds in the sample.
5.3 Cross-sectional regression results
In the second step, the Fama-MacBeth (1973) cross-sectional regressions are conducted for each month to test whether the liquidity risk (liquidity beta) and bond illiquidity level are priced in the expected excess return of corporate bonds using the model in equation (5): 𝑟𝑖𝑡− 𝑟𝑓𝑡 = 𝛼𝑖 + 𝜆𝐸𝑅𝑀𝛽𝑖𝐸𝑅𝑀+ 𝜆𝑆𝑀𝐵𝛽𝑖𝑆𝑀𝐵 + 𝜆𝐻𝑀𝐿𝛽𝑖𝐻𝑀𝐿+ 𝜆𝑙𝛽𝑖𝐿+ 𝜆𝑇𝑒𝑟𝑚𝛽𝑖𝑇𝑒𝑟𝑚+
𝜆𝐷𝑒𝑓𝛽𝑖𝐷𝑒𝑓+ 𝜆𝐵𝑖𝑙𝐵𝑖𝑙𝑙𝑖𝑞𝑖+ 𝜆𝑒𝑛𝑡𝑒𝑛𝑡𝑒𝑟𝑝𝑟𝑖𝑠𝑒𝑖 + 𝑢𝑖.
For each bond, the betas of the six risk factors used in the cross-sectional regression for a given month are estimated from rolling regressions over past 3-year
Variable Mean Standard deviation Minimum Maximum Mean t Median t
0.0447 0.1308 -0.7432 0.9927 0.5243 0.5259 -0.0444 0.3001 -2.2449 1.9556 -0.2980 -0.3255 0.0813 0.4222 -4.0751 3.0551 0.3549 0.3842 0.0392 2.7854 -14.2210 13.4016 1.1846 0.8872 0.2006 0.5264 -4.3476 4.0639 1.4887 1.1162 0.0166 0.5553 -6.1137 4.2026 2.0631 1.7937 Adj. 0.1873 0.1119 0.0003 0.6679
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periods. As the full period for all 3-year rolling regressions are from February 2006 to March 2017, the cross-sectional regression is performed for each month over the period from February 2009 to March 2017.
Table 4 presents the results of the Fama-MacBeth cross-sectional regressions. The coefficient of each beta is the mean coefficient across all cross-sectional regressions conducted. To better compare the risk premia of different factors and interpret the results, all dependent variables are scaled by their cross-sectional standard deviations each month. As a result, the coefficients show the effects of per unit standard deviation of each dependent variable on the excess bond returns.
Generally, the results show that the expected excess returns of corporate bonds are significantly associated with the liquidity betas and the dummy variable 𝑒𝑛𝑡𝑒𝑟𝑝𝑟𝑖𝑠𝑒. Liquidity risk 𝛽𝐿 has a statistically significant positive effect on bond excess returns at the
5% level with its parameter estimate of 0.182 and a t-statistics of 2.08. This indicates that a unit standard deviation above the cross-sectional mean of liquidity beta 𝛽𝐿 is related to
a rise of 0.182 percentage points in the monthly excess return of corporate bonds. And this change makes up around 40% of the standard deviation of monthly excess returns of corporate bonds (0.45% shown in Panel A, Table 1), implying that the impact of liquidity risk on the expected corporate bond returns is also economically important and meaningful. These results support the hypothesis 2 of this paper: liquidity risk has a significant positive effect on the expected returns of Chinese corporate bonds. Hence, controlling for other risk factors, corporate bonds with higher exposures to the market liquidity shocks tend to have higher expected returns.
As for bond illiquidity level 𝐵𝑖𝑙𝑙𝑖𝑞𝑖, it has a positive coefficient estimate and this is
consistent with the hypothesis 1 that expected corporate bond returns is negatively associated with the bond liquidity level. Nevertheless, the effect of bond illiquidity level is not statistically significant with a t-value of 0.28. The parameter estimate of 0.015 means that a one standard deviation above the cross-sectional mean of bond illiquidity level results in an increase of 0.015 percentage points in the monthly bond excess return,
25
which makes up only 3% of the standard deviation of monthly bond excess returns. This suggests that bond-specific liquidity level is also not an economically significant determinant of corporate bonds’ expected returns.
The results also indicate that betas of standard risk factors have poor explanatory power for the cross-sectional variation in expected bond returns. However, the dummy variable 𝑒𝑛𝑡𝑒𝑟𝑝𝑟𝑖𝑠𝑒, which equals 1 when the bond is an enterprise bond and 0 if it is a listed company bond, significantly affects the expected bond returns. It coefficient estimate of -0.222 indicates that enterprise bonds have lower expected excess returns relative to listed-company bonds. This coincides with the fact that enterprise bonds has relatively lower credit risk since they are guaranteed by state banks, which implies that they may have higher prices and lower expected returns.
Table 4. Fama-MacBeth cross-sectional regression results
This table reports the results of the Fama-MacBeth cross-sectional regressions of individual bonds over the period from February 2009 to March 2017 using the model in equation (5): 𝑟𝑖𝑡− 𝑟𝑓𝑡= 𝛼𝑖+ 𝜆𝐸𝑅𝑀𝛽𝑖𝐸𝑅𝑀+ 𝜆𝑆𝑀𝐵𝛽𝑖𝑆𝑀𝐵+
𝜆𝐻𝑀𝐿𝛽𝑖𝐻𝑀𝐿+ 𝜆𝑙𝛽𝑖𝐿+ 𝜆𝑇𝑒𝑟𝑚𝛽𝑖𝑇𝑒𝑟𝑚+ 𝜆𝐷𝑒𝑓𝛽𝑖𝐷𝑒𝑓+ 𝜆𝐵𝑖𝑙𝐵𝑖𝑙𝑙𝑖𝑞𝑖+ 𝜆𝑒𝑛𝑡𝑒𝑛𝑡𝑒𝑟𝑝𝑟𝑖𝑠𝑒𝑖+ 𝑢𝑖. The betas for each bond are
estimated from rolling regressions over past 3-year periods. The dependent variable is the monthly excess return of a bond (in percentage) and the explanatory variables are betas of the Fama-French stock market factor, size factor, book-to-market equity factor, market liquidity factor, term premium, default premium and bond illiquidity level and a dummy variable whose value is 1 for enterprise bonds and 0 for listed-company bonds. All explanatory variables are normalized by their cross-sectional standard deviations each month for easier interpretations.
Sample period: 2009m2-2017m3 Num. time periods: 98
F( 8, 97) 1.27 Prob > F 0.2682 avg. R-squared 0.1656 Dependent variable
Independent variables Coefficients Standard error t-value P>|t|
0.037 0.086 0.43 0.666 -0.133 0.207 -0.019 0.096 -0.19 0.848 -0.210 0.173 0.030 0.098 0.31 0.759 -0.165 0.226 0.056 0.065 0.86 0.390 -0.073 0.186 -0.046 0.080 -0.58 0.562 -0.205 0.112 0.182 0.087 2.08 0.040 0.009 0.355 0.015 0.053 0.28 0.778 -0.091 0.121 -0.222 0.118 -1.89 0.061 -0.456 0.011 Intercept 0.450 0.180 2.51 0.014 0.094 0.807
Fama-MacBeth cross-sectional regression
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6. Robustness checks
Results in Section 5 indicate that liquidity risk is a statistically and economically significant determinant of corporate bond expected returns, while bond illiquidity level has no significant effects on corporate bond pricing. This section presents the results of additional tests for robustness.
6.1 Cross-sectional regression test with an extended model
To check the robustness of the results, the cross-sectional regression model in equation (5) is extended by incorporating four variables of bond characteristics: years to maturity (𝑌𝑟𝑠𝑇𝑜𝑀𝑎𝑡), coupon rate, issue size and credit rating.
𝑌𝑟𝑠𝑇𝑜𝑀𝑎𝑡 is widely used as a proxy for liquidity because bonds are less likely to trade and become more illiquid when they get older and thus a higher proportion of its issued amount get into the buy and hold portfolios of investors. Issue size is also a popular liquidity proxy based on the logic that a larger issue size means more investors own the bond and thus the information and searching costs are lower. Since the cross-sectional tests in section 5 show that bond illiquidity level, calculated using the Amihud illiquidity measure, has no significant effects on the corporate bond expected returns, these two liquidity proxies are included to examine whether the poor result is due to an inappropriate liquidity measure and whether the effect will become significant when alternative liquidity measures are used. Credit rating is used as an extra variable to control for the effects of default risk in addition to the default premium beta and coupon rate is added as it is closely related to the market prices of corporate bonds.
The cross-sectional regression results using the new extended model are reported in Table 5. As it shows, after controlling for the impacts of bond characteristics, the coefficient of liquidity beta 𝛽𝐿 remains significant at the 5% level with an even higher
t-value of 2.59. This result again provides evidence for the important role of liquidity risk in the pricing of corporate bonds. Also, the coefficient of the dummy variable 𝑒𝑛𝑡𝑒𝑟𝑝𝑟𝑖𝑠𝑒 remains negative and significant at the 10% level. However, the coefficients for all the
27
other variables are not significant. And the results of the two liquidity proxies 𝑌𝑟𝑠𝑇𝑜𝑀𝑎𝑡 and 𝐼𝑠𝑠𝑢𝑒 𝑆𝑖𝑧𝑒 indicate that when alternative liquidity measures are involved, the impact of bond liquidity level on expected bond returns is still insignificant.
Table 5 Cross-sectional regression with an extended model
This table reports the results of the Fama-MacBeth cross-sectional regressions of individual bonds over the period from February 2009 to March 2017 using an extended model based on the model in equation (5) incorporated with four bond characteristics: 𝑟𝑖𝑡− 𝑟𝑓𝑡= 𝛼𝑖+ 𝜆𝐸𝑅𝑀𝛽𝑖𝐸𝑅𝑀+ 𝜆𝑆𝑀𝐵𝛽𝑖𝑆𝑀𝐵+ 𝜆𝐻𝑀𝐿𝛽𝑖𝐻𝑀𝐿+ 𝜆𝑙𝛽𝑖𝐿+ 𝜆𝑇𝑒𝑟𝑚𝛽𝑖𝑇𝑒𝑟𝑚+ 𝜆𝐷𝑒𝑓𝛽𝑖𝐷𝑒𝑓+
𝜆𝐵𝑖𝑙𝐵𝑖𝑙𝑙𝑖𝑞𝑖+ 𝜆𝑒𝑛𝑡𝑒𝑛𝑡𝑒𝑟𝑝𝑟𝑖𝑠𝑒𝑖+ 𝜆𝑌𝑇𝑀𝑌𝑟𝑠𝑇𝑜𝑀𝑎𝑡𝑖+ 𝜆𝑐𝑜𝑢𝑝𝑜𝑛𝐶𝑜𝑢𝑝𝑜𝑛𝑖+ 𝜆𝑠𝑖𝑧𝑒𝐼𝑠𝑠𝑢𝑒 𝑆𝑖𝑧𝑒𝑖+ 𝜆𝑟𝑎𝑡𝑖𝑛𝑔𝑅𝑎𝑡𝑖𝑛𝑔𝑖+ 𝑢𝑖. The
betas for each bond are estimated from rolling regressions over past 3-year periods. The dependent variable is the monthly excess return of a bond (in percentage). Besides the original explanatory variables in equation (5), four bond characteristic variables are included: years to maturity, coupon rate, issue size and credit rating. The rating variable is measured by assigning values, in a way that 1 being assigned to AAA, 1.5 to AA+, 2 to AA, 2.5 to AA- and 3 to A+. All explanatory variables are normalized by their cross-sectional standard deviations each month for easier interpretations.
6.2 Portfolio sorts
In the section, the importance of liquidity risk and bond illiquidity level in the cross-section variation in bond excess returns are explored using analyses based on portfolio sorts.
To examine the role of liquidity risk in corporate bond pricing, individual bonds are sorted into 10 portfolios with an equal number of bonds in each month based on their
Sample period: 2009m2-2017m3 Num. time periods: 98
F( 12, 97) 1.1
Prob > F 0.3666
avg. R-squared 0.2371 Dependent variable
Independent variables Coefficients Standard error t-value P>|t|
0.016 0.092 0.17 0.866 -0.168 0.199 -0.034 0.104 -0.32 0.747 -0.240 0.173 -0.005 0.104 -0.05 0.963 -0.211 0.201 -0.007 0.095 -0.07 0.942 -0.195 0.181 -0.074 0.092 -0.81 0.421 -0.256 0.108 0.254 0.098 2.59 0.011 0.059 0.448 0.010 0.054 0.19 0.851 -0.097 0.118 -0.206 0.109 -1.89 0.062 -0.423 0.011 0.043 0.040 1.07 0.288 -0.037 0.122 0.015 0.081 0.18 0.854 -0.145 0.175 -0.029 0.044 -0.65 0.516 -0.116 0.058 0.118 0.193 0.61 0.541 -0.265 0.501 Intercept 0.207 0.470 0.44 0.661 -0.726 1.140
Fama-MacBeth cross-sectional regression
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liquidity betas, which are estimated from their rolling regressions over the past three-year periods. Table 6 reports the average values for different variables of each portfolio. It is obvious from the results that liquidity beta is positively associated with default beta and negatively related to term beta. The positive relation between liquidity beta and bond excess returns appears to be strong. The high liquidity-beta portfolio has an average excess return of about 0.6% per month, which is 0.53% higher than the average excess return of the low liquidity beta portfolio and this difference is significantly at the 10% level with a t-value of 1.71. This result suggests that liquidity risk has a positive premium and investors require higher return for corporate bonds with higher exposures to market liquidity innovations, implying the important effects of liquidity risk on expected returns of corporate bonds. In addition, the differences in credit rating among various portfolios are not evident as the divergence in credit ratings among all bonds in the sample is small, implying that the rating is not a good proxy for default risk in the Chinese bond market. Similarly, to further investigate the effects of bond liquidity level, individual bonds are sorted in each month into 10 portfolios with an equal number of bonds based on their illiquidity measures, which are calculated from the Amihud illiquidity measure. Table 7 presents the results for different variables of portfolios sorted on bond illiquidity level. It shows that the relation between bond illiquidity level and monthly bond excess returns is not monotonously negative or positive, although the portfolio with highest illiquidity level earns a higher return than the one with lowest illiquidity level. There is no certain links between bond excess returns and bond illiquidity level as can be seen in the table. And bond illiquidity level shows no significant associations with other variables either.
The results from the robustness checks shows that the positive impacts of liquidity risk on the expected returns of corporate bonds is significant and robust and the effects of bond-specific liquidity level are insignificant.
29 Table 6. Portfolio sorts based on Liquidity betas
This table presents the values for different variables of portfolios sorted based on the market liquidity betas of individual bonds. Each month, bonds are sorted into 10 portfolios with an equal number of bonds by their liquidity betas, which are estimated from rolling regressions over past 3-year periods for each bond. The sample period for portfolio sorts is from February 2009 to March 2017. For each portfolio, the average values over the sample period for the variables including excess return, default beta, term beta, liquidity beta, bond illiquidity level, enterprise, years to maturity, coupon rate, issue size and credit rating are calculated. The rating variable is measured by assigning values, in a way that 1 being assigned to AAA, 1.5 to AA+, 2 to AA, 2.5 to AA- and 3 to A+. The excess return variable is in percentage. To obtain the average excess return for each portfolio, portfolio excess return in each month is first calculated as the mean excess return of individual bonds in the portfolio and then the portfolio excess return can be calculated by taking the average of portfolio excess returns across the full period. The difference in average excess returns between the highest and lowest liquidity-beta portfolios and its t-value is reported.
Variables Low 2 3 4 5 6 7 8 9 High Difference t
Excess return 0.08 0.13 0.20 0.20 0.21 0.21 0.32 0.35 0.38 0.60 0.53 1.71 0.14 0.50 0.62 0.75 0.73 0.84 0.77 0.90 1.16 1.77 0.29 0.28 0.25 0.23 0.22 0.14 0.13 0.12 0.08 -0.07 -0.13 -0.06 -0.04 -0.03 -0.01 0.00 0.01 0.02 0.05 0.14 Bond illiquidity 149.14 150.02 145.31 146.42 102.12 97.33 96.24 130.88 129.65 216.72 enterprise 0.85 0.81 0.80 0.82 0.79 0.79 0.75 0.75 0.83 0.91 YrsToMat 6.22 4.63 4.20 4.03 4.10 3.72 3.40 3.41 4.01 4.85 Coupon 5.78 5.71 5.68 5.74 5.62 5.60 5.57 5.58 5.70 5.57 Issue Size 18.83 19.82 18.69 16.96 17.97 18.40 19.12 19.30 19.44 22.66 Credit rating 1.40 1.41 1.38 1.41 1.37 1.37 1.38 1.37 1.38 1.38
30 Table 7. Portfolio sorts based on bond illiquidity levels
In this table, bonds are sorted into 10 portfolios with an equal number of bonds by their illiquidity levels in each month. The sample period for portfolio sorts is from February 2009 to March 2017. For each portfolio, the average values over the sample period for the variables including excess return, default beta, term beta, liquidity beta, bond illiquidity level, enterprise, years to maturity, coupon rate, issue size and credit rating are calculated. The rating variable is measured by assigning values, in a way that 1 being assigned to AAA, 1.5 to AA+, 2 to AA, 2.5 to AA- and 3 to A+. The excess return variable is in percentage. The average bond illiquidity level for each portfolio is calculated by first calculating the portfolio illiquidity level in each month as the mean illiquidity level of individual bonds in the portfolio and then taking the average of portfolio illiquidity levels across the whole period.
Low 2 3 4 5 6 7 8 9 High Excess return 0.26 0.38 0.23 0.18 0.04 0.22 0.27 0.18 0.10 0.39 0.57 0.69 0.86 0.90 0.83 0.77 0.72 0.76 0.71 0.66 0.20 0.24 0.23 0.22 0.24 0.25 0.24 0.25 0.25 0.27 -0.01 0.00 -0.01 -0.01 -0.01 -0.02 -0.01 -0.01 -0.01 -0.01 Bond illiquidity 0.36 1.02 2.13 4.03 7.45 13.59 27.72 56.50 143.06 846.40 enterprise 0.87 0.84 0.80 0.82 0.83 0.82 0.84 0.85 0.85 0.85 YrsToMat 4.17 4.17 3.48 3.55 3.76 3.90 4.16 4.40 4.52 5.24 Coupon 5.37 5.56 5.58 5.52 5.46 5.40 5.33 5.34 5.34 5.34 Issue Size 26.77 22.60 20.12 19.77 20.09 20.27 20.11 20.21 20.29 20.09 Credit rating 1.32 1.36 1.36 1.34 1.32 1.29 1.27 1.26 1.26 1.25
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7. Conclusion
This paper investigates the role of liquidity factors on the pricing of corporate bonds in China. The main research objective is to explore how the two liquidity factors: bond-specific liquidity level and liquidity risk influence the expected returns of Chinese corporate bonds. Based on the broad literature and theories about liquidity effects on asset pricing, two hypotheses are made for this paper. Hypothesis 1 is that bond-specific liquidity level has a significant negative impact on the expected corporate bond returns in China and hypothesis 2 states that liquidity risk significantly positively affects the expected returns of Chinese corporate bonds.
In terms of liquidity measures, the paper adopts the Amihud (2002) illiquidity measure to calculate the bond specific illiquidity level and to construct market liquidity factor. The Autoregressive Integrated Moving Average (Arima) regression is employed to estimate the market liquidity factor as the moving average terms can eliminate the autocorrelation in the residuals of Amihud illiquidity measure. As for the methodology, a two-pass regression method is applied, in which the first step is to estimate the liquidity betas along with betas of other risk factors of individual bonds through rolling time series regressions over past three-year periods for each bond and the second step is to perform a Fama-MacBeth (1973) cross-sectional regression test for each month based on the liquidity beta estimates and bond illiquidity levels to examine the effects of liquidity factors. The sample period for the rolling time series regressions is from February 2006 to March 2017. The data used includes all transaction records and bond characteristics of corporate bonds over this period. As there is a three-year window for the rolling regressions, the sample period for cross-sectional regression tests is from February 2009 to March 2017.
The cross-sectional regression results indicate that firstly, bond-specific liquidity level has no significant effects, economically or statistically, on the expected returns of corporate bonds. Hence, the first hypothesis of the paper is rejected. Secondly, the liquidity beta (liquidity risk) is a statistically and economically important determinant of
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the expected bond excess returns in China. And the liquidity premium is positive, implying that corporate bonds with higher exposures to market liquidity innovations offer higher returns. This means that the second hypothesis is strongly supported by the empirical evidence.
Robustness checks include cross-sectional regressions using an extended model incorporated with four bond characteristic variables and portfolio sorts based on liquidity betas and bond illiquidity levels. Results show that the significant positive impact of liquidity risk on the expected returns of corporate bonds is robust to effects of bond characteristic variables and to different test methods, while the effect of bond illiquidity level on corporate bond pricing remains insignificant when other liquidity proxies are involved.
The findings of this paper offer strong support for the notion that market liquidity shocks are considered as undesirable by investors and thus they require higher compensations for investing in bonds with greater sensitivity to liquidity innovations and above all, they provide empirical evidence for the significant role of liquidity risk in the Chinese corporate bond pricing. Therefore, it is of great importance for the central bank and securities regulatory authorities to make and implement effective plans to stimulate the trading in the corporate bond market and improve and sustain good liquidity conditions, which reduce the liquidity risk of corporate bonds and thus the costs of bond financing.
However, there are still some limitations in this study with respect to data and the research model employed. Firstly, the transaction data of many Chinses corporate bonds is not completely and continuously available, which results in a small final sample after removing all noisy data. This may lead to some bias in the estimation results. Secondly, as shown in the time series regressions and cross-sectional regression results, the model based on the Fama-French stock market factors, term premium and default premium appears to have a poor explanatory power for the cross-section of the expected excess returns of Chinese corporate bonds. It would be interesting if future studies can use other
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risk factors and theoretical models to see whether they perform better in explaining the variation in the bond excess returns. And for the liquidity proxies used in this paper, results show that bond-specific liquidity level has no significant influence on the Chinese corporate bond pricing. Future studies can use more liquidity proxies to check whether this is still the case.
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