Three Essays on Corporate Bonds Yield Spreads, Credit Ratings and Liquidity

The objective of this research is to study the relationship between various aspects of corporate bonds liquidity , transaction costs and trading activity, and their perceived credit quality as measured by credit ratings. For debt securities, Credit quality and liquidity are perhaps the most important factors that affect the investors’ decisions whether to trade or hold these assets on their portfolio, as several theoretical and empirical studies identify these factors as key components of bonds yield spreads. However, the interaction and relationship between these two characteristics is not sufficiently addressed in the literature. From the investors’ perspective, it is beneficial to know whether they face a tradeoff between credit quality and liquidity or if both desirable features move in the same direction. We use more than twelve years of Enhanced TRACE data from 2002 to 2014 to analyze the liquidity of corporate bonds both cross-sectionally across credit ratings and intertemporally around credit rating changes. The first manuscript studies the relationship between corporate bonds’ credit risk and their market liquidity, and the dynamics of this relationship over the period from 2002 to 2014. Unlike the implication of theoretical models, our findings do not empirically support a monotonically positive relation between credit risk and transaction costs. Instead, we find an inverted U-shaped relationship where bonds with ratings near the Investment grade/ High yield boundary have the largest transaction costs (lowest liquidity) after controlling for other relevant factors. One explanation for this finding is that bond dealers behave more as brokers in speculative grade bonds and are reluctant to enter overnight positions in these risky securities, unless they find the other side of the trade. This kind of dealers behavior potentially reduces the transaction costs of lower rated bond, as captured by bid-ask spreads, to only reflect the cost of searching for counterparty rather than inventory or adverse selection risks, and may be even more pronounced during distressed market conditions due to more capital constrains and less funding liquidity. Consistent with this explanation, using a Markov Switching time series model, we find that while bid-ask spreads significantly increase for investment grade bonds during the crisis, they stay invariant for junk bonds. The second essay expands this investigation to examine the impact of rating changes on corporate bonds’ liquidity around the rating change announcements using an event study methodology. Many institutional investors such as insurance companies or pension funds are prohibited by regulations from investing substantial portion of their portfolios in risky bonds. Hence, the rating changes that move the bonds out of the investment grade category can elicit selling pressure or even fire sale of the fallen angels. Beyond just the investment grade issue, prudential regulators also have scoring algorithms that require more capital to be held as ratings fall. Our findings suggest an abnormal decrease in liquidity following the rating downgrades with more severe impact for downgrades that move the bond from investment grade to high yield category. Consistent with the prior findings, investment grade bonds liquidity is more sensitive to rating downgrades and for bonds that are already risky, further downgrades doesn’t seem to affect their liquidity and transaction costs significantly. We also find that bond and issuer characteristics like issue size and industry group affect the liquidity conditions around rating events. The third essay reviews the theoretical as well as empirical literature on the impact of liquidity on corporate bonds prices and yield spreads.

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Introduction
This paper studies the relationship between corporate bonds' trading costs and perceived credit quality as measured by their credit ratings. The nationally recognized statistical rating organizations (NRSRO's) such as Moody's and Standard and Poor's have been rating corporate bonds for over a century, and a broad array of contractual and regulatory requirements are tightly connected to the ratings they provide.
Although at times the incentives and ability of rating agencies to provide accurate and timely information have been called into question, credit ratings are widely used by investors and regulators alike as proxy for credit risk. In addition, different regulations use credit ratings to restrict investment or allocate risk: institutional investors such as insurance companies and pension funds are prohibited from investing significant proportion of their portfolio in high yield bonds, and risk based capital requirements for banks and other financial intermediaries are also determined based on credit ratings. As a result, the potential pool of investors, their trading frequency and strategy may vary across credit ratings. This variation may affect dealers' trading behavior, and ultimately liquidity and transaction costs for corporate bonds across different rating categories.
Traditional market microstructure models generally imply wider bid-ask spreads for lower rated bonds, conditional on certain assumptions. For example, inventory models relate bid-ask spreads to dealers' inventory risk which increases with the degree of asset price movements as well as the length of time the asset is kept in inventory (Stoll, 1978;Brunnermeier and Pedersen, 2008). Since lower rated bonds may experience higher price volatility and it may take longer time for the dealers to find a trading counterparty for risky bonds, this group of models suggest larger trading costs for low rated bonds.
Based on asymmetric information models such as Glosten and Milgrom (1985) and , bid-ask spreads are affected by the risk of trading against informed traders and increases with the degree of information asymmetry in the market and asset value uncertainty. Given the higher level of uncertainty regarding the future cash flows generated by riskier assets, dealers may charge wider spreads that compensate them for the risk. Moreover, although a significant proportion of investors in both investment grade and high yield bonds consist of large and sophisticated financial institutions, the type of institutions and their incentive to trade may vary for investment grade versus high yield bonds. For example insurance companies and pension funds are mainly buy-and-hold investors in investment grade bonds, whereas hedge funds and high yield mutual funds that trade lower rated bonds may follow more speculative strategies.
Recently the structural credit risk models with endogenous liquidity proposed by  and Chen, Cui, He and Milbradt (2015) also predict a positive relationship between corporate bonds credit risk and bid-ask spreads. 3 3  and Chen, Cui, He and Milbradt (2015) adapt the search and bargaining framework of Duffy, Gârleanu, and Pedersen (2005) to model the secondary market for corporate bonds. Two types of investors exist in their model: High type and Low type. High type investors are the ones that incur no cost for holding the asset. Low type investors are the ones affected by an exogenous liquidity shock and incur holding cost, so they search for a dealer to get rid of the bond. Chen, Cui, He and Milbradt (2015) model this holding cost in light of collateralized borrowing and assume that the bond is part of a large portfolio including leverage and can be used as collateral for these loans. Borrowing against the bond involves a haircut. A decline in a bonds credit quality pushes down its market price and increases the haircut. This in turn drives down the low type investor valuation of the bond and widens the valuation wedge between high type and low type investors. Since the bid-ask Empirically, the evidence is mixed. Hong and Warga (2000), Chakravarty and Sarkar (2003), Harris and Piwowar (2006), and Edwards, Harris and Piwowar (2007) find that lower rated bonds have larger transaction costs. On the other hand, Schultz (2001), Bao, Pan andHotchkiss (2017) find no significant relation between ratings and liquidity. In some of the previous studies, high yield bonds are either eliminated from the sample or are grouped in one or two big rating classes. Moreover, many of these studies predate the recent financial crisis which may have affected the relation between credit ratings and liquidity and the possible time variation in this relationship is often overlooked. 4 This study contributes to the literature by examining the dynamics and dimensions of bond market liquidity across the entire spectrum of credit ratings using more than twelve years of TRACE data from 2002 to 2014 and seven different liquidity measures: a price impact measure, three spread measures, and three trading activity measures. 5 As this period includes the financial crisis, this study also examines the effect of market distress and how liquidity varied across different rating categories, and whether the post-crisis regulations aiming to limit risk taking by spread in their model is a function of investors bargaining power and the valuation wedge between low type and high type investors, the above procedure results in a rise in the bid-ask spread.

4
The corporate bond market has changed dramatically since the recent financial crisis. Some new trends include huge amount of bond issuance, investors search for higher yield due to the nearly zero interest rates, great reduction in bond dealer's net inventory positions in corporate bond, changes in their risk management practices and improvements in electronic trading venues. These new trends have affected the trading behavior of both investors and market makers and it is reasonable to assume that they may affect the liquidity and transactions cost across different credit ratings.

5
Since Hamilton and Cantor (2004) note, the frequency of default increases non-linearly across ratings, credit rating is not treated as a continuous variable in this study. Hamilton and Cantor (2004) document three year default rates of 0.0%, 0.0%, 0.4%, 1.5%, 4.4%, 17.7% and 31% for Aaa, Aa, A, Baa, Ba, B and Caa bonds respectively. banking institutions, mainly the Volker Rule of Dodd-Frank Act, has adversely affected market liquidity of investment grade and high yield bonds.
The results show that the relation between credit rating and liquidity depends in part on how liquidity is defined. Not only are there differences by liquidity measure, but there are also notable non-linearities; for example, the Amihud price impact measure suggests that market resilience decreases for lower rated bonds. However, in contrast to the common wisdom and the implications of theoretical models, we don't find evidence of a monotonic increase in bid-ask spreads as we move to lower rated bonds. Instead, bid-ask spread measures suggest more of a step function, where spreads become notably higher just at the investment grade/high yield (BBB/BB) cutoff, and then decline. Trading activity across rating classes also show that high yield bonds are on average more actively traded in terms of both number of trades and volume after controlling for other relevant factors. There is also lower percentage of zero trading days for lower rated bonds. Piecewise panel regressions suggest similar results, implying a different relation between liquidity and credit quality within investment grade versus high yield bonds.
To examine the dynamic liquidity behavior of investment grade vs. high yield categories, the monthly aggregate liquidity and trading activity time series is modeled as Markov switching AR(k) processes. Our findings suggest that during the normal periods, the aggregate transaction cost for riskier bonds is higher compared to low risk bonds, but there is an abrupt regime change during the financial crisis period: spreads increase dramatically for investment grade bonds, but remain relatively constant for high-yield bonds. While the spreads for riskier bonds are quite low in dollar terms, as a percentage of price, these spreads are higher than the normal periods due to the sharp decline in junk bond prices during this period. Post-crisis and during the recent period of regulatory changes, the results suggest an increase in the aggregate market liquidity as measured by price impact and bid-ask spreads and higher aggregate trading activity.
The absolute bid-ask spreads for high yield bonds converge to a level above the spreads for investment grade bonds during post-crisis and regulatory periods.
To study further the time variation in the relationship between bonds liquidity and credit quality, we rerun the panel regressions with rating dummies and bond and issuer controls separately on three sub-periods: Pre-crisis which we define as the period from Jul. 2002to Nov. 2007, crisis which is the period from Dec. 2007 to June 2009 and post-crisis which we define as the period from July 2009 to Sep. 2014. Results show that during the pre-crisis period, although non-monotonically, trading costs increase for lower rated bonds, which is consistent with the findings of some previous studies that used the pre-crisis bond market data such as Hong and Warga (2000), Chacravarty and Sarkar (2003), Harris and Piwowar (2006), and Edwards, Harris and Piwowar (2007). However, the panel regressions show that consistent with the results from Markov-switching model time series analysis, after and particularly during the crisis, regression coefficients become larger as we move to lower rating dummies within the investment grade range, while they become insignificant or negative as we move to lower rated bonds within the high yield category.
A possible explanation for these findings is the heterogeneous trading behavior and market making activity of bond dealers for investment grade versus high yield bonds. We argue that dealers may be less willing to commit capital to hold riskier bonds in inventory and behave more as brokers in these types of securities, particularly during periods of market distress when they face more capital constraints.
As a result the observed bid-ask spreads may be more close to brokerage commission fees and reflect dealers search costs rather than their inventory risk.
This view is supported by a number of previous studies. An earlier evidence of this kind of behavior is documented by Bessembinder and Maxwell (2008) during the period following the initiation of TRACE as a side effect of increased transparency.
According to Bessembinder and Maxwell (2008), "(p)ost-TRACE, bond dealers no longer hold large inventories of bonds for some of the most active issues; for lessactive bonds they now serve only as brokers". Goldstein, Hotchkiss, and Sirri (2007) find that dealers perform a matching brokerage function in illiquid bonds. Feldhütter (2012), models OTC bond markets based on Duffie, Gârleanu, and Pedersen (2005) framework and assumes segmented markets by trading size during liquidity shocks.
He argues that during liquidity shocks risk limits often prohibit market makers from taking the bond on the book and splitting large trades. In this situation it is often the case that the sales person of the bank directly searches for a buyer and "typically, the bid-ask fee is collected by the sales person not the market maker". More recently Goldstein and Hotchkiss (2017) show that dealers are most likely to quickly offset trades rather than holding bonds in inventory overnight or longer for the least actively traded or riskier bonds.
This line of reasoning implies that the notion of bid-ask spreads as the price of "immediacy" services provided by dealers may not hold for riskier or less actively traded bonds, particularly during liquidity shocks. Therefore, caution should be taken interpreting narrower bid-ask spreads on riskier bonds as an indication of better liquidity condition. Instead, the risk of price movement may be shifted to investors, particularly during liquidity shocks when they need to wait longer for the opposite side of the trade to arrive.
The rest of the paper is organized as follows: Section 2 describes the data and summary statistics, Section 3 describes the liquidity measures used in this study and their summary statistics, Section 4 analyzes the illiquidity across credit ratings, Section 5 analyzes the time series behavior of (il)liquidity and trading activity measures, Section 6 discuss the robustness tests and Section 7 concludes the paper.  In summary the comparison between the original and final sample shows that the bonds analyzed in this study on average have larger issue size, higher rating and higher price and are issued by issuers with larger number of bonds outstanding compared to the original Enhanced TRACE-FISD sample.

Data and summary statistics
Panel C of Table 2 shows the number of bonds and summary statistics of the final sample by rating group. On average, higher rated bonds tend to have larger issue size, lower coupon rate, shorter age, shorter time to maturity and higher price. Also higher rated bonds are generally issued by firms with larger number of issues outstanding.

Liquidity measures
In this study, we examine different aspects of liquidity by using several measures calculated on a monthly basis. The first measure, Amihud is as price impact measure, Three bid -ask spread proxies: A round-trip cost measure proposed by the authors (RTC), Hong and Warga (HW) (Hong and Warga (2000) ;Chakravarty and Sarkar (2003)), Riskless principal trades markup (RPT) recently proposed by Harris (2015), and three trading activity measures including trading volume, number of trades and percentage of zero trading days in a month (Zero) (Lesmond, Ogden and Trzcinka(1999), Dick-Nielsen, Feldhütter and Lando (2012)). All these proxies, except volume and number of trades are in fact illiquidity measures.
A substantial proportion of the variation in percentage bid-ask spreads across ratings may be due to the price differences between high rated versus low rated bonds, which incorporates the credit risk associated with each rating. As a result, as we move from high rated to low rated bonds the average of bid and ask prices declines and naturally pushes up the relative measures of bid-ask spreads. To eliminate this effect and to focus on the dollar value of transaction costs, we calculate the bid-ask spread measures in the absolute form.
Having buy/sell side indicators in the Enhanced Trace sample allows us to compute a new roundtrip-cost measure (RTC) in the spirit of Feldhütter (2012)'s IRC, which was originally calculated without having buy/sell side information. As Feldhütter (2012) pointed out, calculating imputed roundtrip cost without having the order sign, results in underestimating the transactions costs. We incorporate order sign information in our proposed measure to remove this bias. We also include Riskless Principal Trade's markup (RPT) measure recently proposed by Harris (2015) in our analysis. The detailed explanation of the procedure for calculating liquidity measures and a thorough analysis of the behavior of the latter new measures are included in the Appendix.
Panel A of Table 3 shows the summary statistics for liquidity measures. The mean percentage of zero-trading days is 74% and the median is 90%, which demonstrate a high degree of illiquidity in our sample of corporate bonds. The median Amihud measure is 0.32 implying that a trade of $300,000 in an average bond, for example, moves price by roughly 9.6%, smaller than the 10.2% found by Han and Zhou (2008). In contrast the Amihud measure computed in Dick-Nielsen, Feldhütter and Lando (2012) imply that a trade of $300,000 in an average bond moves the price by roughly 0.13% which is much lower compared to Han and Zhou (2008) (2007)). Moreover, as mentioned earlier, the IRC measure calculated in Feldhütter (2012) tend to underestimate the transaction costs.
The RTC is only 1 cent for the 5% most liquid bonds. Other bid-ask proxies demonstrate comparable mean and median values. The mean and median RPT markup is 67 cents and 52 cents respectively. Generally, consistent with the findings in, Bessembinder, Maxwell, and Venkaraman (2006), Goldstein, Hotchkiss and Sirri (2007), Edwards, Harris and Piwowar (2007) and Feldhütter (2012), we find modest average transaction costs for our sample of corporate bonds.
Panel B of Table 3 shows the correlation among liquidity measures and their significance. There is 54% percent correlation between Amihud market depth measure and bid-ask spread as proxied by roundtrip cost (RTC). There is 32% percent correlation between Amihud and riskless principal trades (RTC) markup. Amihud is positively and significantly correlated with zero-trading days meaning that as the number of days in a month with at least one trade decrease, the price impact of trades will increase. This result is in contrast with Dick-Nielsen, Feldhutter and Lando (2012), as they found a negative correlation between quarterly Amihud measure and zero-trading days measure. There is nearly zero correlation between riskless principal trades' markup (RPT) and monthly volume as well as zero-trading days. Finally, we can observe negative and significant correlations among trading volume and Amihud, RTC and HW measures.
Panel C of Table 3 shows the mean liquidity measures by rating group. We can see that on average, the Amihud measure is higher for lower rated bonds. The average bid-ask measures increase for lower rated bonds and have the highest value for BB/Ba-B rating group and then decline for ratings equal or below CCC/Caa. The average volume is highest for AAA-AA/Aa bonds and for ratings equal or below CCC/Caa and the monthly number of trades has the highest value for AAA-AA/Aa bonds.

Panel regressions on entire sample
The goal of this study is to investigate how various aspects of liquidity vary across credit ratings. Previous studies such as Hong and Warga (2000), Chacravarty and Sarkar (2003), Harris and Piwowar (2006) and Edwards, Harris and Piwowar (2007) He and Xiong (2012),  and Chen, Cui, He and Milbradt (2015) models based on the structural credit risk models of Leland (1994) and Leland and Toft (1996) and search model of Duffie, Gârleanu, and Pedersen (2005) are consistent with the empirical findings of Bao, Pan and Wang (2011), Dick-Nielsen, Feldhütter and Lando (2012) and Friewald, Jankowitsch and Subrahmanyam (2012) (1) / 8 where k is the year indicator (k=1 for 2002,…,k=13 for 2014). By estimating the above model, we assume that each rating class has a different liquidity level (intercept), controlling for other factors and test how these levels vary across rating classes and whether they are significantly different from the liquidity level of the benchmark group (Aaa/AAA). We also assume that the effect of control variables on liquidity is not significantly different across rating classes.
represent the difference between the expected iliquidity, of each letter rating class with the expected iliquidity of the benchmark group. Each issuer in our sample may have multiple bonds outstanding with highly correlated characteristics.
Hence, we correct the standard errors by clustering observations at the issuer level and also control for heteroscedasticity using White-Huber robust standard errors. 11 Table 4 shows the results for the above regression analysis. Columns 2 to 8 of Table 4 show the regression coefficients and their significance levels for each liquidity and trading activity measure. To better see how the intercepts ( ) vary by credit ratings, Figure 1 shows the (il)liquidity intercept of each rating class for different (il)liquidity proxies and their 95% confidence intervals. Using monthly Amihud measure as dependent variable, we observe that the illiquidity levels for investment grade rating classes are not statistically different from that of Aaa rating.
However, the coefficient for Aa is negative and significant at 0.1 level implying that controlling for other relevant factors, Aa rated bonds have slightly lower Amihud measure. The coefficients for rating classes within the speculative grade range are positive and highly significant indicating that trading speculative grade bonds is

11
To save space the t-statistics are not reported and are available upon request. associated with significantly higher price impact. As Figure 1 shows, the mean Amihud is particularly high for bonds close to default (Ca/CC/C rated bonds). For example the 0.51 value for the coefficient of Ca/CC rated bonds tells us that holding other factors constant, a trade of $300,000 in a Ca/CC rated bond moves the price by 15.3% more than a trade of the same size in Aaa/AAA bonds.
The results for the bid-ask spreads as measured by three proxies: RTC, HW and RPT are quite different from what observed for the Amihud measure. The graph of coefficients in Figure 1 show a nearly inverted U-shaped relationship between the absolute bid-ask spreads and credit ratings using all three proxies. As we can see in Panel B of Figure 1, the maximum value for expected bid-ask spread belongs to Ba/BB rated bonds which is the rating class right below the investment grade boundary. The Expected spread for Aa/AA rated bonds (as proxied by RTC and HW) is significantly lower than that of Aaa/AAA bonds. The expected bid-ask spread increases as we move from Aa/AA rating to Investment grade boundary and then starts to decline for speculative grade bonds.
Analyzing the relationship between credit ratings and monthly trading activity variables also reveals interesting results. As we can see from both columns 6 to 8 of Table 4 and Figure 1, after controlling for bond and issuer level characteristics that affect trading activity, both monthly number of trades and monthly volume increase when we move from investment grade to speculative grade ratings. These results are consistent with the notion that the majority of the investors in investment grade bonds are large institutions with buy-and-hold strategy and after the investment grade bonds are placed in the portfolios of these institutional investors they are rarely traded. The average percentage of monthly zero trading days also declines significantly as we move from investment grade to non-investment grade category. These results are consistent with a recent evidence provided by Mizrach (2015). Dividing the corporate bond market to two segments based on trading activity (1000 most active issues and the rest), he finds that the percentage of investment grade bonds in the active trading group is less than their percentage in the less active trading group for their entire sample period from 2003 to 2015. In particular, he finds that on average 35% of the bonds in the less active category have A ratings.
Overall, the results from Table 4 and Figure 1 show that various dimensions of liquidity vary differently and non-linearly across ratings. The Amihud price impact measure increases as we move towards the lower rated bonds, whereas the transaction costs in the form of bid-ask spread seem to be highest for bonds with ratings close to investment grade boundary and declines for lower rated high yield bonds. Specifically, the results from Table 4 and Figure 1 appear to suggest two distinct liquidity regimes among Investment grade and high yield bonds. To further explore the non-linear nature of the relationship between ratings and liquidity and to quantify the liquidity differences among the three regimes, we examine a piecewise regression model in the following from: Where is one of the seven liquidity measures in each regression, is a dummy variable equal to 1 if the bond has rating below Baa3 and 0 otherwise, and  Table 5 reports the results of piecewise regressions for each liquidity measure. To save space we don't report the coefficients and t-statistics of control variables, as they are roughly similar to the values observed in Table 4. Column 2 shows the results for Amihud measure. The significant and positive coefficient for shows that the price impact is larger for lower rated bonds within the investment grade category. The positive and highly significant shows that within the high yield range, Amihud increases more as we move to lower rated bonds.

Controls
Figure 2 helps us better understand the results from Table 5. Panel A of Figure 2 illustrates the results for Amihud measure. The piecewise model allows us to quantify the magnitude of breaks among three regression lines for each measure. Columns 3 to 8 of Table 5 and Panel 2 of Figure 2 show the results for bid-ask spread and trading activity measures. We can see that the bid-ask spreads increase significantly as we move to lower rated bonds within the investment grade range. The regression slopes for high yield bonds is negative and significantly different from that of investment

Panel regression on sample sub-periods
In the previous section, we explored the relationship between various measures of liquidity and credit ratings over the entire sample period. However, our sample The results of these regressions are reported in Table 6 and Figure 3. Since our focus is the coefficients of the rating dummies, to save space the coefficients of the control variables are not reported in Table 6. Panel A shows the results for pre-crisis period. We can observe that during the pre-crisis period, although non-monotonically, the rating dummies' coefficients are positive and significant for ratings equal and below BBB/Baa and increase as we move to lower rated bonds. These results are in line with the findings of some previous studies that used the pre-crisis bond market data such as Hong and Warga (2000), Chacravarty and Sarkar (2003), Harris and Piwowar (2006), and Edwards, Harris and Piwowar (2007) and find larger trading costs for lower rated bonds.
Panel B and C of Table 6 show the results for crisis and post-crisis periods. For regressions with Amihud measure as the dependent variable, we can see that the coefficients for ratings equal or below BBB/Baa are positive, significant, and larger compared to the pre-crisis period but are mostly negative and insignificant during the post-crisis period. For bid-ask spread measures the coefficients are negative and significant for high yield bonds particularly for ratings equal or below Caa/CCC category during the crisis and mostly negative but insignificant for post-crisis period.
These results show an interesting phenomenon that during the financial crisis high yield bonds trade at lower bid-ask spread levels. To further examine the liquidity dynamics of investment grade versus high yield bonds, in the next section we conduct a time series regime switching analyses that enables us to identify the possible regime shifts in aggregate market liquidity as well as investment grade versus high yield categories.

Time series analysis
In this section, we explore the dynamic behavior of the liquidity and trading activity measures both at the aggregate market level and across rating categories using  Bessembinder et al. (2016) to capture "the implicit costs associated with trades that were desired but not completed". In particular, the riskless principal trades (RPTs) are considered as "effectively agency" trades that don't effectively influence the dealers' inventory. Hence a higher proportion of riskless principal trades (RPTs) in a month may imply dealers' reluctance to commit capital. Next, we consider the monthly percentage of block volume, to capture the difficulty of placing large orders.
Finally, we examine the monthly percentage of dealer-to-dealer trades as opposed to the customer trades to captures interdealer market activity. Higher block volume and interdealer percentage may imply better liquidity conditions.

Markov-switching model estimation and results
The aggregate monthly liquidity and trading activity measures, are modeled as non-linear processes that depend on their own past history, random shocks, and a discrete regime process, , The switching regimes affect the intercept, autocorrelation coefficients, and volatility, of the above process. The process governing the dynamics of the underlying regime follows a first-order Markov chain, where the transition matrix is: The Maximum Likelihood and EM algorithm of Gray (1996) are used to estimate the models' parameters and the regime probabilities. For model selection, AR(1) and AR(2) as well as simple Markov switching intercept models are considered as benchmarks and Markov switching AR(1) and AR (2) processes are examined based on their AIC and BIC criteria as well as their interpretability.  Panel A of Table 7  Panel B of Table 7 shows the results for the spread between the price impact and trading cost of high yield vs. investment grade bonds. While the Amihud measure is higher for the high yield bonds over the entire sample period, still a regime switching is observed with the wider spread regime dominating the crisis period and the narrower spread regime forming the major proportion of pre and post crisis periods and the entire regulatory period. These results imply that the price impact of investment grade and high yield bonds are converging more after the crisis and particularly during the regulatory period. Analyzing the bid-ask spread measures shows an interesting pattern. While the execution costs for investment grade bonds increases during the financial crisis, they actually decrease for the high yield bonds during the same period. For example, Figure 5 shows the regime changes for HW measure. As we can observe from Table7 and Figure 5, the regime with lower transaction costs for high yield bonds, forms 63% of the crisis period and the regime with higher positive mean mostly overlap with the pre-crisis and regulatory periods.
Similar results are observed for RTC and RPT measures. This finding is consistent with the search and bargaining model of bid-ask spreads. Higher selling pressure of riskier bonds during the crisis period and lack of enough buyers relative to sellers adversely affects the bargaining power of bond dealers and reduces the bid-ask spreads charged for these bonds.
The trading activity spreads show two distinct regimes for the number of trades, both with negative means, which indicates lower mean number of trades for HY bonds for both regimes. However the regime with wider spread (mean of -5.58) covers 86% of the pre-crisis period and the regime with narrower spread covers 97% of the postcrisis and 88%of the regulatory period which shows that the aggregate monthly number of HY bond trades is increasing with respect to the IG trades in recent periods.
The measures of dealers' capital commitment show the following patterns: The mean percentage of RPT trades is becoming larger for HY bonds compared to IG bonds during the regulatory period by around 5.2%. This result provides evidence of dealers becoming more reluctant to conduct principal transactions for riskier bonds during the regulatory period. However the findings from the other two measures do not show evidence of less liquidity provision for riskier bonds following the crisis, as the percentage of interdealer trades in HY bonds have become higher after the crisis and particularly during the regulatory period. %block volume for HY bonds for this period is comparable to pre-crisis and is smaller than the %block volume for the IG category.

Robustness tests
We test the robustness of the results on a subsample of top bonds for each issuer as they attract most of the trading activity. Ronen and Zhou (2013)  are the issuer's highest rated bonds. We use the above characteristics (except having embedded options 12 ) to identify the top bonds of each issuer on a monthly basis that 12 In the data filtering stage the bonds with embedded options like call and put options are removed from the sample so we didn't consider this characteristic in my procedure of estimating top bonds.
form around 73% of our sample of bonds. 13 We also construct a sample consisting of a single top bond for each issuer in the following way: for each issuer, we identify the bond that has been in the "top" role during a longer period (the bond that has the maximum number of months as a top bond). The unique top bonds estimated this way form around 32% of our sample. We repeated the regressions on these subsamples and the results are generally robust.
We also repeated the regressions on two subsample of retail size and institutional size trades and found qualitatively similar results. 14

Conclusion
In this paper, we use more than twelve years of bond transaction data from TRACE to conduct a comprehensive investigation of how liquidity and trading activity of corporate bonds vary with their credit ratings and how the dynamic behavior of this relationship changes over time.
Our main finding is that unlike the implications of traditional microstructure model, the trading costs as measured by bid-ask spreads do not increase monotonically with credit risk. Instead, we find and inverted U-shaped relationship over the entire sample where the bid-ask spreads increase with credit risk for investment grade bonds but decline gradually after we cross the investment grade / high yield boundary.
Moreover studying the dynamics of this relationship using panel regressions over three subsamples shows that trading costs become more negatively related to ratings as we move to riskier bonds following and particularly during the financial crisis.
Further, we examine the liquidity of investment grade vs. high yield categories by modeling the monthly aggregate liquidity and trading activity time series as Markov switching AR(k) processes. The results show that during the normal periods, the aggregate transaction costs for riskier bonds is higher compared to low risk bonds, however this relationship demonstrate an abrupt regime change during the crisis period: while the spreads increase dramatically for investment grade bonds, they stay relatively invariant for HY bonds.
These results can possibly be explained in light of a search based framework in which bond dealers actively search for trading counterparty to mitigate their holding period risk or even don't take inventory risk until they find the opposite side of the trade, particularly during liquidity shocks. Recent empirical evidence supports this explanation. This may undermine the informativeness of bid-ask spreads as an appropriate measure of liquidity for the most risky segments of the markets or during periods of market distress and highlight the importance of other measures that better reflect the cost of liquidity and dealers capital commitment. Narrowing our focus to bid-ask spreads to gauge market liquidity for some type of securities may be a case of being "penny wise and pound foolish".

Figure5:
Regime changes for HY vs. IG aggregate bid-ask spread (as proxied by HW) measure and the filtered probabilities for each regime      Rating is the numerical translation of Moody's rating: 1=Aaa, 21=C. Junk is a dummy variable equal to one if the Moody's rating for the bond is between 11=Ba to 19=Caa and equal to zero if the rating for the bond is investment grade.
denotes the year fixed effect. denotes the matrix of control variables. The t-statistics are calculated using heteroscedasticity and autocorrelation robust standard errors. *indicates significance at the 10% level, ** indicates significance at the 5% level, and *** indicates significance at the 1% level.

Price impact
Bid-ask spread Trading activity    Finally, trading activity as well as bond and issuer characteristics affect CAIL around the rating events.

Introduction
Credit rating agencies play a substantial role in financial markets by providing opinions about the creditworthiness of bond issuers as well as the default risk of particular issues. Several bond market regulations designed to restrict risk taking by financial institutions are based on credit ratings. Campbell and Taksler (2003) highlight that institutions subject to rating based restrictions on their holdings own While Kim and Verrecchia (1994) suggests that liquidity deteriorates around the time new information is released to the market and returns to normal a few days afterwards, the impact of rating changes on corporate bonds liquidity are likely to be larger and more persistent, so we use a variety of longer windows in our study. Hand et. al. 1992). Holthausen and Leftwich (1986) argue that rating agencies allocate more resources to revealing negative credit information than positive information because the loss of reputation is more severe when a false rating is too high than when it is too low. As a result downgrades represent information not yet known by the market, whereas upgrades confirm information that is already available.
Moreover, the downgrades may trigger forced selling or fire sales whereas the upgrades are not followed by forced buying. These heterogeneous trading patterns around downgrades and upgrades may cause different behavior of liquidity proxies in terms of their magnitude around downgrades and upgrades.
Interestingly, the mean CAIL is positive and significant prior to the downgrade announcement date, which suggests that downgrade events are at least partially anticipated by the market. This result, which is consistent with the previous literature, may either be due to advance notice of potential downgrades by inclusion in the watch list of credit rating agencies well before the actual downgrade date or a result of delayed rating changes by credit rating agencies based on their through-the-cycle approach, as in Altman and Rijken (2006).
The results also suggest a heterogeneous effect of rating changes across the investment grade and high yield boundary. Downgrades from investment grade to high yield have stronger and more persistent adverse impact on abnormal illiquidity both in terms of price impact and bid-ask spreads, whereas upgrades to investment grade have more muted and transitory impact. Downgrades to high yield category may impose a selling pressure on financial institutions such as insurance companies and pension funds, while providing an opportunity for less restricted investors such as hedge funds and high yield mutual funds to buy these securities at deep discounts (Fridson and Cherry, 1992, Fridson and Sterling, 2006and Dor and Xu, 2011. The selling pressure accompanied by the "slow moving capital" coming to the market by these new investors leads to a shallow market for fallen angels around the downgrade event. We also find that the positive impact of downgrades on abnormal illiquidity is more pronounced for downgrades within the investment grade category compared to the downgrades within the high yield category.
Analyzing the rating changes in normal versus crisis period shows that while the negative impact of downgrades is stronger during the financial crisis, no significant impact for upgrades are observed during this period; however, since the number of upgrades during the crisis is much lower compared to normal times, this result should be interpreted with caution.
The cross sectional determinants of abnormal illiquidity suggest that the adverse effect of downgrades on bond liquidity is more severe for downgrades of more than one step, and downgrades that simultaneously affect several bonds of the same firm.
Bonds with larger issue size experience significantly better liquidity around rating events. Sectors matter: bonds issued by financial and utility firms experience worse liquidity conditions in the event of a downgrade. The selling pressure around rating change events exacerbates the adverse impact of downgrades on liquidity , and higher trading volume around both downgrades and upgrades significantly improves the liquidity as defined by market depth and bid-ask spreads.
The rest of the paper is organized as follows: Section 2 describes the sample of rating changes and summary statistics, Section 3 describes the liquidity measures used in this study, Section 4 describes the event study methodology, Section 5 explains and discusses the event study results, Section 6 examines the cross sectional determinants of abnormal (il)liquidity around the rating events and section 7 concludes.

Sample of rating changes
To construct the event study sample, we use FISD to identify rating changes by Moody's, S&P and Fitch from July 2002 to September 2014. We exclude bonds that are denominated in a currency other than US dollar or have a foreign issuer, variable rate and zero coupon bonds, bonds that have credit enhancement, convertibles, assetbacked, callable, putable, exchangeable, fungible, preferred, tendered, and bonds that are part of a unit deal are excluded from the sample. Following May (2010), we also require bond's maturity date to be at least one year from its rating change date. In the event of multiple rating changes within five days interval, only the earliest rating change is included. If bonds of the same firm are downgraded (upgraded) on same day by more than one rating agency, only one agency's rating change is included according to the following priority: Moody's, S&P and Fitch. We also exclude the downgrades where the new rating is below Caa/CCC. Since these downgrades are very likely to be concurrent with the firm's default, there are more likely to be associated with other simultaneous events and information as pointed out by May (2010). We also exclude the upgrades where the old rating is below Caa/CCC to have symmetric downgrades and upgrades samples. Applying these filters result in a sample of 7,903 bond rating changes (5,373 downgrades and 2,530 upgrades). At the firm level, these represent 4,043 rating change events (2,613 downgrades and 1,430 upgrades).

Liquidity measures
In this study, the illiquidity is proxied by Amihud (2002)  Where is the mean customer buy price (Ask) and bid is the mean customer sell price and is the mean interdealer price. Finally the daily roundtrip cost for each bond is calculated as the average of all roundtrip costs for that bond during that day.
We examine the distribution of IRTs across various trade sizes to test the representativeness of the measure for the entire sample and identify the potential biases. Panel A of Table 9 shows the distribution of all transactions as well as transactions that are part of an IRT across different size groups. As we can see, more than 78% of all transactions in our sample are retail sized trades defined as trades below $100,000. Around 74% of retail sized transactions and around 51% of institutional sized trades are part of an IRT. Only 47% of trades above $1,000,000 are part of an IRT. These percentages imply that retail sized trades are more likely to be part of an IRT which may cause an upward bias in our measure of bid-ask spreads.
Panel B of

Methodology
The event study methodology used in this study is similar in spirit to the procedures used by Bessembinder et al. (2009) We use a matching portfolio model to calculate the abnormal bond illiquidity around rating changes. In order to control for market fluctuations in computing abnormal bond illiquidity, we use issues available in Enhanced TRACE data to construct illiquidity indices for each rating class that contain sufficient number of observations with non-missing illiquidity proxies.
The median numbers of bonds per issuer in our sample is 1. However around 43% of firms have more than one bond present in the sample with the maximum number being 26 bonds issued by General Electric Capital. This suggests a skewed distribution with a large number of firms having only one bond outstanding in the rating change sample, and a small number of firms with much more issues outstanding. This would cause the firms with larger number of bonds outstanding being over represented (Bessembinder et al., 2009). Moreover, usually several bonds of the same firm are downgraded on the same calendar date resulting in a clustered data with overlapping event windows. This clustering biases the standard errors downward because of the likely high correlation among bonds from the same firm, violating the assumption of independent observations and leading to inflated t-statistic (See Bernard 1987, Eberhart and Siddique, 2002 among others). To address these issues, we compute firm level abnormal illiquidity and treat each firm level rating change as a single observation. We compute the daily abnormal bond illiquidity as the raw illiquidity minus the contemporaneous illiquidity on an index of matched corporate bonds: Where on day t, is the abnormal bond illiquidity, is the bond illiquidity and is the illiquidity of a value-weighted index of matched corporate bonds that did not experience a rating change in the period between Day to Day .
The Enhanced TRACE is used to construct the matched corporate bond indices.
We use Dick-Nielsen (2014) Where N is the number of bond issues in the sample for firm j. For a multiple day window, cumulative abnormal illiquidity (CAILs) is computed as the sum of the firm's daily abnormal bond illiquidity over the window.

Event study results
In this section, we test the impact of credit rating changes on corporate bonds illiquidity over several windows around the announcement date. The illiquidity is proxied by a price impact measure (Amihud) and a bid-ask spread measure (RTC). We study the impact over two pre-event windows and three post event windows: , and .
Panel A of Table 10 shows the impact of downgrades using the entire sample. We compute both mean cumulative abnormal illiquidity (mean CAIL) and median cumulative abnormal illiquidity (median CAIL) for the events windows. The number of observations used to calculate mean and median CAIL for each window is also reported. To test the statistical significance, we use t-test and signed-rank test for mean CAIL and sign test for median CAIL.
The results in Table 10 show that the mean CAIL is positive and significant prior to the downgrade date for both Amihud and RTC measures which implies that the rating change is anticipated by the market. Some previous studies have shown that credit rating agencies are relatively delayed in their rating decisions and a number of explanations have been provided by the literature for this phenomenon, including the rating stability hypothesis, reputation hypothesis and through-the-cycle as opposed to point-in-time approach of the credit rating agencies (Cantor (2001), Löffler (2005) and Altman and Rijken (2006)). However the magnitudes of mean and median CAIL are greater for the windows following the downgrade. These results indicate that there is a significant increase in the abnormal illiquidity associated with credit rating downgrade.
Next, we investigate whether there is a heterogeneous effect of rating changes within investment grade (IG) as opposed to rating changes within high yield (HY) category. Panel B of These results may imply that downgrades of investment grade bonds are more consequential for the institutional investors holding them, as the downgrades may cause their portfolios to violate certain risk limits imposed by regulations or they may be indicative of the possibility that the bond will be soon downgraded to junk status.
While the investors in high yield bonds such as high yield mutual funds and hedge funds may not share similar concerns. However since the number of observations are also much lower for downgrades within high yield range, we should take caution when interpreting these results.
Panel D of Table 10 shows the impact of downgrades that moves the firm out of This situation also provides an opportunity for hedge funds and high yield mutual funds to buy the downgraded bonds at prices significantly below fundamental values (Fridson and Sterling, 2006). The selling pressure accompanied by the "slow moving capital" coming to the market by these new investors leads to a shallow market for fallen angels around the downgrade event. 19 Ellul et al. (2011) found that insurance companies that are relatively more constrained by regulations are more likely to sell downgraded bonds and those bonds subject to a high probability of regulatory induced selling show significant price declines and subsequent reversals, particularly when insurance companies as a group are relatively more distressed and when other potential buyers' capital is relatively scarce. In general, the results for upgrades are much smaller and less significant than those for downgrades. These results are in line with asymmetric market impact of downgrades and upgrades found in some prior studies (for example Holthausen and Leftwich (1986) and Hand, Holthausen and Leftwich (1992)). Similar to downgrade events, Panel B and C of Table 11 show that the impact of IG upgrades on bond liquidity is generally larger and more significant compared to that of HY upgrades except for window. Panel D of Table 11 shows that when the firm is upgraded from non-investment grade to investment grade we observe a negative abnormal illiquidity round the announcement date. For Amihud measure the impact is only significant for post-event windows of and .However, for the RTC measure the impact is not significant for any of the windows.
Panel A of Figure 6 compares the impact of IG downgrades, HY downgrades and fallen angel downgrades over days around the downgrade announcement date. This graph clearly demonstrates that fallen angel downgrades have more adverse impact on bond liquidity around the event compared to downgrades within either investment grade or high yield categories, emphasizing the role of restrictive regulations for holding high yield bonds by institutional investors. Panel B of Figure 6 shows similar results for upgrade events. In general the impact of upgrades on liquidity is much smaller; however the upgrades that move the bond from HY to IG category appear to have slightly larger impact.
Next, we study how the impact of rating changes on corporate bonds liquidity varies during normal economic conditions as opposed to crisis period. We split the sample to two subsample based on the economic conditions: Normal and Crisis. The   Figure 7 also shows the cumulative abnormal illiquidity (CAIL) using Amihud as illiquidity proxy, during [-20, +20] days around the rating change announcements, confirming the results obtained in Table 12.
We also examine the number of trades and volume. Figure 8 shows the trading activity over [-20, +20] days around downgrades and upgrades. First we can observe that the average number of trades per day is higher around downgrade announcements compared to upgrade announcements for all types of trade (buy, sell and interdealer).
Second, we can see that generally the number of trades doesn't appear to change much on the event date compared to the days prior to announcement which may imply that the rating event is anticipated by the market prior to actual announcement. However the average daily number of sell trades seems to increase during the window from downgrade announcement showing that the downgrades impose a selling pressure on the market to some extent. However, there is no evidence of fire sales following downgrades. Ambrose, Cai and Helwege (2012) also find that while the insurance companies are more active in selling fallen angels following rating downgrade but these increased sales only accounts for a small portion of their overall holdings of fallen angels. We can also observe that the average trading volume per day increases around 5 days prior to the event and starts to decline gradually after 6 days from the announcement date. However, similar results are not observed around upgrade announcements.

Determinants of bond abnormal illiquidity around rating events
The analysis presented in this section, identifies the determinants of corporate bond's abnormal illiquidity around rating change events. The dependent variable in all regressions is mean CAIL over window using Amihud (CAIL (Amihud)) and RTC (CAIL (RTC)) as illiquidity proxies. was stronger during the recent financial crisis. However, we observe no significant crisis effect when the RTC bid-ask spread measure is used as illiquidity measure. In other words, results imply that the abnormal bid-ask spreads around downgrades were not significantly affected during crisis period whereas abnormal price impact of trades around downgrades became significantly larger. These findings confirm the results obtained in Table 12.
We also define as a dummy variable equal to 1, if CAIL over window is positive and 0 otherwise, to control for bond abnormal iliquidity prior to the announcement date. The coefficients for this variable are highly significant indicating that bonds with positive CAIL prior to the event date have higher abnormal illiquidity over 10 days from the downgrade announcement. Table 13 also provides evidence that the size of downgrade affects the magnitude of CAIL around downgrade event. The effect is more significant for Amihud measure. Also consistent with our prior findings in Table 10, the adverse effect of downgrades on liquidity is more severe when they cross the investment grade boundary.
We further control for bond old rating prior to rating change, by including two dummy variables, namely:  have no significant impact on abnormal bid-ask spread around upgrade. The negative and significant coefficients of "Old rating: HY" in column 6 and 7 show that upgrades from high yield category are associated with lower abnormal transaction costs around the announcement. We can also observe that higher average trading volume is associated with lower abnormal illiquidity around upgrade events. The coefficients for bond and firm characteristics generally show similar signs as in Tanble9. In particular bonds with larger issue size enjoy better liquidity around upgrades and bonds with higher age experience lower liquidity (higher CAIL (Amihud)) during the ten days after the upgrade announcement.

Conclusion
This study examines the impact of rating changes on bond's liquidity around the announcement date. The results generally show positive and significant cumulative abnormal illiquidity (CAIL) around downgrades and negative CAIL around upgrades.
Consistent with prior literature, we find smaller and less significant impact for upgrades. We also find that the negative impact of downgrades on liquidity is more severe for fallen angel downgrades. Moreover, our findings suggest larger impact for downgrades and upgrades within investment grade category compared to rating changes within the high yield range. Analyzing the trading activity around rating changes show that downgrades elicit more trades (buy, sell and interdealer) compared to upgrades. There is a modest evidence of selling pressure after the downgrade date and an increase in trading volume around the downgrade announcements.
We also study the determinants of abnormal illiquidity around the rating change         * indicates significance at the 10% level, ** indicates significance at the 5% level, and *** indicates significance at the 1% level

Corporate Bond Pricing and Liquidity: A Review
By Elmira Shekari Namin 1 , Michael A. Goldstein 2

Introduction
There is a huge theoretical and empirical literature that explores the impact of corporate bonds' Credit risk on its' yield spread, the spread between the yield of a corporate bond and the yield of the risk free bond with comparable characteristics, which has its' origin in the structural credit risk models pioneered by the work of Black and Scholes (1963) and Merton (1974). However as empirically demonstrated by Jones, Mason, and Rosenfeld (1984), Black Scholes Merton model generates credit spreads that are smaller than actually observed. As such, many academics have tried to expand the original model by incorporating more realistic features of corporate debt.
Also, a growing body of literature has focused on the "non-default component" of yield spreads for explaining the "credit spread puzzle" that arises from Merton (1974) model. Their findings suggest that the "non-default component" is strongly associated with liquidity measures. Usually in these studies credit spread is treated as a combination of two parts: "default premium" and "liquidity premium" and the impact of each component on the cross sectional and time series variations of credit spread is empirically measured (e.g. Longstaff, Mithal, and Neis, 2005;Friewald, Jankowitsch and Subrahmanyam, 2009;by Bao, Pan and Wang, 2011;Dick-Nielsen, Feldhutter and Lando, 2012).
This paper reviews the literature related to the key theoretical and empirical researches that model and quantify the liquidity component of yield spreads including some recent studies that focus on the role of illiquidity during the recent financial crisis. First, we start by a brief background of the concept and theoretical models of liquidity in section 2. Section 3 gives an overview of the studies on the impact of liquidity on asset prices. In section 4, we turn our focus to corporate bond market and review structural credit risk models including the recent ones including liquidity either as an exogenous shock or an endogenous risk factor. Section 5 reviews the empirical studies on bond pricing and liquidity.

Models of liquidity
Liquidity is one of the key concepts in securities markets which is often a desirable feature and reflects a well-functioning market. At the same time it is not directly observable from the market data and is not easily measurable. Based on the intuitive but wage definition of Keynes, an asset is liquid if "it is more certainly realizable at short notice without loss." Market liquidity hinges in large part on whether market-makers respond to temporary imbalances in supply and demand by stepping in as buyers (or sellers) against trades sought by other market participants. The role of market makers as liquidity providers and price setting agents was originally studied in the traditional inventory based models of market microstructure. Researchers have typically followed three broad approaches to model liquidity and how prices are set by market makers.
One approach is inventory based modeling. The inventory based models view the trading process as a matching problem in which the market maker or price setting agent must use prices to balance supply and demand across time. There are several distinct modeling approaches in this area. For example Garman (1976) focus on the nature of order flow. Stoll (1978) examine the optimization problem facing dealers and Cohen, Maier, Schwartz and Whitcomb (1981) analyze the effect of multiple providers for immediacy. Common to all these models are uncertainties in order flow, which can result in inventory problems for market maker and execution problem for dealers. Amihud and Mendelson (1980), Stoll (1981, 1983), Mildenstein and Schleef (1983), and  examined the impact of inventories on liquidity provision. Based on , market liquidity is determined by the demand and supply of immediacy. In their setting, exogenous liquidity events and the risk of delayed trade create a demand for immediacy. Market makers supply immediacy by their presence and willingness to take inventory risk during the period between the arrival of final buyers and sellers. The number of market makers is adjusted in the long run to determine the equilibrium level of liquidity in the market. They show that the lower is the autocorrelation in rates of return, the higher is the equilibrium level of liquidity.
In general, inventory models without capital constraints predict that liquidity (the width of the bid-ask spread) is not affected by the market maker's inventory position, but there are exceptions (e.g. Amihud and Mendelson 1980;Shen and Starr (2002).
O' Hara and Oldfield (1986) show that spreads depend on inventories if market makers are risk-averse. Even models that do not predict a link between inventories and the width of the spread can generate time variation in liquidity, as a market maker's desire to supply liquidity is typically a function of an asset's fundamental volatility.
A second approach is related to the effect of asymmetric information on market prices. If some traders are better informed about the underlying value of an asset, their trades could reveal the information and affects the behavior of prices. This approach is followed by Kyle (1984, Glosten and Milgrom (1985) and Easley and O'Hara (1987) among others.
The third and more recent approach focuses on funding costs and financing constraints of market makers. In a model with margin constraints, Gromb and Vayanos (2002) show how arbitrageurs' liquidity provision benefits all investors. Coughenour and Deli (2002) examine the influence of the organizational form of the NYSE specialist firms on the nature of liquidity provision. They compare closely held firms whose specialists provide liquidity with their own capital to widely held firms whose specialists provide liquidity with diffusely owned capital. They argue that specialists using their own capital have a greater incentive and ability to reduce adverse selection costs, but face a greater cost of capital. Weill (2007) examines dynamic liquidity provision by market makers and shows that competitive market makers offer the socially optimal amount of liquidity, if they have access to sufficient capital. In his model, at time zero, outside investors receive an aggregate shock which lowers their marginal utility for holding assets relative to cash. This creates a sudden need for cash and induces a large selling pressure. Then, randomly over time, each investor recovers from the shock, implying that the initial selling pressure slowly disappears. The asset market can be illiquid in his model in the sense that investors make contact with market makers only after random delays. In this economic environment, market makers offer buyers and sellers "immediacy". Market makers anticipate that after the selling pressure subsides, they will achieve contact with more buyers than sellers, which will allow them then to transfer assets to buyers in two ways. Therefore, by accumulating inventories early, when the selling pressure is large, market makers mitigate the adverse impact on investors of execution delays.
The socially optimal asset allocation maximizes the sum of investors' and market makers' intertemporal utility, subject to the order-execution technology. He shows that if marketmakers maintain sufficient capital, the socially optimal allocation is implemented in a competitive equilibrium. However, If marketmakers do not maintain sufficient capital, then they are not able to purchase as many assets as prescribed by the socially optimal allocation.
Brunnermeier and Pedersen (2009) construct a model along the lines of  that also links an asset's market liquidity and traders' funding liquidity. The ability of market makers to provide liquidity depends on their access to funding. Conversely, dealers' funding and their capital and margin requirements, depends on the assets' market liquidity. They show that, under certain conditions, margins are destabilizing and market liquidity and funding liquidity are mutually reinforcing, leading to liquidity spirals. Furthermore they show that limited riskbearing capacity can have a differential impact on high and low fundamental volatility stocks. They use the term "flight to quality" to refer to the result that the liquidity differential between high and low volatility securities is greater when market makers have taken on larger positions or when market-maker wealth decreases. Flight-toquality evidence is also present in Pastor and Stambaugh (2003).

Liquidity and asset prices
Based on the discussion provided in the previous section, dealers' bid-ask spread (quoted or effective) which is defined as the difference in price between the highest price that a buyer is willing to pay and the lowest price for which a seller is willing to sell an asset, is commonly used as a measure of liquidity. Illiquidity can be measured by the cost of immediate execution. An investor willing to transact faces a tradeoff. He may either wait to transact at a favorable price or insist on immediate execution at the current bid or ask price. The quoted ask (offer) price includes a premium for immediate buying and the bid price similarly reflects a concession required for immediate sale. Thus the spread between the bid and ask prices can be a natural measure of illiquidity. Roll (1984) gives a measure of effective bid-ask spread assuming an efficient market ( ) in which is the first order serial covariance of successive price changes. This equation implies that the spread can be inferred from the sequence of price changes by computing and transforming serial covariance. Since collecting the bid-ask spreads from the market data is a costly procedure he validates this result indirectly by relating the measured implicit spread to firm size. Firm size is positively related to volume and volume is negatively related to spread. So there should be a strong negative cross sectional relation between measured spread and measured size which is confirmed by empirical results. Another interesting point in this paper is that using daily data, the average value of the implicit bid-ask spread across all stocks and time periods was only 0.298 percent. But the average implicit bid-ask spread estimated from weekly returns was 1.74 percent which is proved to be significantly different from 0.298. Since the spread inferred from any observation intervals must be equal when the market is informationally efficient, these results cast doubt on the efficiency of the New York and American Exchanges which are considered in this research. Amihud and Mendelson (1986) studied the effect of the bid-ask spread on asset pricing. They showed that market observed expected return is an increasing and concave function of the spread. Their model predicts that higher spread assets yield higher expected returns and that there is a clientele effect whereby investors with longer holding periods select assets with higher spreads. The prediction offered by their model can be tested by estimating the following regression for a portfolio j of assets: Where denotes the average monthly rate of return on a stock included in the portfolio j in excess of the 90-day return on Treasury bonds, is the beta coefficient for portfolio j, and is the average bid-ask spread. The empirical analysis based on estimates for (1) shows a high level of significance for all the arguments of the regression. Their research highlights the importance of securities market microstructure in determining asset returns and provides a link between this area and mainstream research on capital markets.
Also Mendelson (1988, 1991) show that average portfolio returns increase with the spread, and the spread effect persists if firm size is included in equation (1) as an additional variable.
In , time-series effect of liquidity on stock returns is considered as well as the cross sectional effect which had been previously explored by other researchers. This study suggested that over time, the ex-ante stock excess return is increasing in the expected illiquidity of the stock market, suggesting that expected stock excess return which is traditionally called risk premium and has been considered a compensation for risk, partly represents an illiquidity premium (a compensation for expected market illiquidity). He proposed the ILLIQ measure of illiquidity which is the daily ratio of absolute stock return to its dollar volume, averaged over some period In another study Huang (2002) shows that illiquidity can have large effects on asset returns when agents face liquidity shocks and borrowing constraints. Pastor and Stambaugh (2003) also investigated whether market wide liquidity is a state variable important for asset pricing. In order to construct their individual measure of illiquidity they focused on a dimension of liquidity associated with temporary price changes accompanying order flow. They obtained the measure of market liquidity in a given month as the equally weighted average of the liquidity measures of individual stocks in NYSE and AMEX, using daily data within the month.
The aggregate measure was then regressed on its lag as well as the lag of the scaled level series and the fitted residual of this regression is taken as the innovation in liquidity. They defined liquidity beta as the coefficient on liquidity innovation in a regression that also includes the three factors of Fama and French. The results suggest the following points: expected stock returns are related cross sectionally to the sensitivities of returns to fluctuations in aggregate liquidity. Stocks that are more sensitive to aggregate liquidity have substantially higher expected returns even after accounting for exposures to the market return, size, value and momentum factors and liquidity risk factor accounts for half of the profits to a momentum strategy over the period of 1966 to 1999. Acharya and Pedersen (2005) proposed a liquidity adjusted capital asset pricing model. Their model provides a unified theoretical framework that helps understand the various channels through which liquidity risk may affect asset pricing and can explain the previous empirical findings that :  Return sensitivity to market liquidity is priced. (Pastor and Stambaugh,2003)  Average liquidity is priced. (Amihud and Mendelson,1986)  Liquidity co-moves with return and predict future returns Chordia et al, 2001a;Jones, 2001;Bekaert et.al.2003).
In their asset pricing model, three liquidity betas are included based on three liquidity risk components: commonality in liquidity with market liquidity, return sensitivity to market liquidity and liquidity sensitivity to market returns. They use Amihud ILLIQ measure as liquidity proxy in their study. Their results show that liquidity adjusted CAPM explains the data better than the standard CAPM, while still exploiting the same degree of freedom. Positive shocks to illiquidity, if persistent, are associated with a low contemporaneous returns and high predicted future returns.
They also found a weak evidence that liquidity risk is important over and above the market risk and the level of liquidity. According to their findings, liquidity risk explains about 1.1 percent of cross sectional returns and about 80 percent of this effect is due to the liquidity sensitivity to the market return. Lou and Sadka (2010)

Structural credit risk models and credit spread puzzle
In Section 3, we discussed papers studying the impact of liquidity on securities prices. While the studies reviewed in previous section were mostly related to stock market, we now turn our focus to corporate bonds. The literature on corporate bond pricing and bonds' yield spread which is commonly referred to as 'credit spread' has its root in the pioneering work of Merton (1974) which utilized the Black and Scholes (1963) option pricing model to derive the value of firms' equity and debt. However it is widely recognized that the observed difference between the yield of a corporate bond and the yield of a risk free government bond with comparable maturities is wider than what is predicted by the structural credit risk model of Merton (1974) particularly for investment grade bonds. This difference between the actual credit spreads and the spreads predicted by the structural models gives rise to the 'credit spread puzzle' which has stimulated the academics to study the non-default component of credit spreads (eg. Longstaff and Schwartz, 1995a;Duffie and Singleton,1997;Goldstein, and Martin, 2001;Collin-Dufresne, Goldstein, and Helwege, 2003 among many others).
Recently, few studies have developed structural credit risk models incorporating secondary market illiquidity. The first paper along this line is He and Xiong (2012) which examines the effect of bond market liquidity deterioration on the firm's credit risk. Their model builds on the structural credit risk model of Leland (1994) and Leland and Toft (1996) which is based on the endogenous default notion of Black and Cox (1976). Briefly explained, the endogenous default concept is as follows: When a bond matures, the firm issues a new bond with the same face value and maturity to replace it at the market price, which can be higher or lower than the principal of the maturing bond. This rollover gain/loss is absorbed by the firm's equity holders. As a result, the equity price is determined by the firm's current fundamental (i.e., the firm's value when it is unlevered) and expected future rollover gains/losses. When the equity value drops to zero, the firm defaults endogenously and bond holders can only recover their debt by liquidating the firm's assets at a discount. Based on the above explanation, one can imagine a positive feedback loop between price and credit quality.
In He and Xiong (2012), an exogenous liquidity shock triggers the endogenous default: Bond holders are subject to Poisson liquidity shocks. Upon the arrival of a liquidity shock, a bond holder has to sell his holdings at a proportional cost. The trading cost multiplied by bond holders' liquidity shock intensity determines the liquidity premium in the firm's credit spread. The increased liquidity premium (i.e. Decreased secondary market price) feeds back to the primary market and suppresses the market price of the firm's newly issued bonds and increases equity Holders' rollover losses.
In another paper,  expand He and Xiong (2012) framework and introduce the concept of endogenous liquidity. Their rationale on how a decline in firms' credit quality affects bond liquidity is based on endogenous bid-ask spread notion of Duffie, Gârleanu, and Pedersen (2005). Two types of investors exist in their model: high type and low type. High type investors are the ones that incur no cost for holding the asset. Low type investors are the ones affected by an exogenous liquidity shock and incur holding cost, so they search for a dealer to get rid of the bond. Chen, Cui, He and Milbradt (2015) model this holding cost in light of collateralized borrowing and assume that the bond is part of a large portfolio including leverage and can be used as collateral for these loans. Borrowing against the bond involves haircut. The decline in bonds credit quality pushes down its market price and increases the haircut. This in turn drives down the low type investor valuation of the bond and widens the valuation wedge between high type and low type investors. Since the bid-ask spread in their model is a function of investors bargaining power and the valuation wedge between low type and high type investors, the above procedure results in a rise in the bid-ask spreads. They further propose a structural decomposition that nests the common additive default-liquidity decomposition to quantify the interaction between default and liquidity for corporate bonds. Similar to Longstaff et al. (2005), using CDS spread to proxy for default risk, they identify the "default" part by pricing a bond in a counterfactually perfectly liquid market but with the model implied default threshold. They identify the remaining credit spread after subtracting this "default" part as the "liquidity" part. Then they further decompose the "default" ("liquidity") part into a "pure default" ("pure liquidity") component and a "liquidity-driven-default" ("default-driven liquidity") component, where the "pure default" or "pure liquidity" part is the spread implied by a counterfactual model where either the bond market is perfectly liquid as in Leland and Toft (1996) hence equity holders default later, or only the over-the-counter search friction for risk free bonds is at work as in Duffie et al. (2005), respectively. The two interaction terms that emerge, i.e., the "liquidity-driven default" and the "default-driven liquidity" components, capture the endogenous positive spiral between default and liquidity. illiquidity, for each individual bond is constructed in this paper which is the negative of auto covariance in relative price changes (γ). The lack of liquidity in an asset gives rise to transitory components in its prices and thus the magnitude of such transitory price movements reflects the degree of illiquidity in the market. Because transitory price movements lead to negatively serially correlated price changes, γ gives a meaningful measure of illiquidity. As mentioned before, Roll (1984) first considered the simple case in which the transitory price movements arise from bid-ask bounce,

Empirical studies on bonds liquidity premium
where . But According to Bao et.al. (2011), in more general cases, γ captures the broader impact of illiquidity on prices above and beyond the effect of bid-ask spread.
Feldhütter (2012), uses the difference between prices paid by small traders and those paid by large traders as a measure to identify when the market price of an overthe-counter traded asset is below its fundamental value due to selling pressure.

Riskless principal trades markup (RPT)
Riskless principal trades (RPTs) are offsetting transactions that generate a riskless profit (markup) for the dealer. For example, suppose that a broker-dealer buys a bond at the best available quoted price of 100 on behalf of a client and then sells it to the client at 101, a markup of 1. In these transactions, the broker-dealer typically trades with another dealer first (who provided the quote), and then trades with the client.
Harris (2015) studies RPTs as a form of trade throughs when the broker fails to obtain the best available prices for their customers.
We identify RPTs in a similar way to Harris (2015) and Zitzowitz (2010). First, we identify potential RPTs as pairs of sequentially adjacent trades of the same size for which one trade is a customer trade. To find these trades in TRACE data, we need to identify all sequences of two or more trades of equal size. Next for each sequence, we identify potential RPTs if one trade of two adjacent trades within a size run is a dealer trade with a customer, or if both trades in an adjacent pair are customer trades and the dealer both buys and sells. We identify the first such pair as a potential RPT, and then continue searching the size run for any additional pairs that do not involve trades already defined as being a part of a potential RPT. Harris (2015) calls the potential RPTs with both trades in the pair being customer trades as "Crossing RPTs" and potential RPTs with one of the trades being interdealer trade as "Normal RPTs".
Finally, we identify RPTs as those potential RPTs for which the time between the two trades in the pair is one minute or less.
The difference between the two trade prices in a RPT pair is the markup. For crossing RPT trade pairs involving dealer trades with a customer buy and a customer sell, we identify the markup as the difference between the dealer's sales price to the buyer and the purchase price from the seller. For normal RPT pairs involving an interdealer trade and a sale to a customer, the markup is the customers purchase price minus the interdealer trade price, and vice versa for normal pars involving a dealer purchase from a customer.
To better understand this new measure and to test how it behaves in our data compared to Harris (2015), we replicate some of the analyses in Harris (2015). Panel A of  (2015) paper. This contrast may suggest that trading in the bond market is becoming more electronic.  (2015) who finds 45.4% of RPT pairs with trade reports within one minute of each other have zero markup). To some extent the decline in zero-markup trades with time between trades also may indicate that some trade pairs with non-zero markups are not RPTs since the longer the interval between any two non-RPT trades, the greater the probability that they will be arranged at different prices simply due to price volatility or because different dealers arrange he two trades. Among the potential RPTs 0.6% (3,718) have negative markups. The negative markups are unlikely to be RPTs. Note that the number of trades reported with negative markups rises with the length of the interval between the two trades.
Price volatility would explain this results if these trades were not RPTs. Following Harris (2015), we keep the negative-markup RPTs in the sample to ensure that results about mean markup are not upward biased (under the assumption that the distribution of computed markups from the non-RPTs in the set of potential RPTs is symmetric about zero). If indeed, the positive non-RPTs are 0.6% of all trades in the set of potential RPTs, the other positive mark-up RPTs represent 88% of the potential RPTs.
We also eliminated three types of potential RPTs (with time between trades of 1 minute or less) from my analysis: 1. RPTs that their markups exceed -5% and 5% of the average of the two trade prices for because many of them may be the result of trading or report errors that apparently were not corrected. 2. All zero-difference price pairs, because they most likely are agency trades. 3. Potential RPTs with Markups between -10 and 10 bp, because many of these markups may be a natural consequence of net trade pricing without commissions. The remaining sample has 463,706 potential RPT pairs. The average markup in the remaining sample is 77.6 bp of price for all trades and 72.6 bp for trades reported within 1 second of each other. The markup rises after 0 second. It is 71 bp for 0 second. It jumps to 88.5 bp at 1 second and remains above 90 bp for 2, 3 and 4 seconds time interval. It appears that RPT trades that are arranged automatically have smaller markups. The larger markups at the longer intervals may be due to price volatility affecting any non-RPTs in this sample, or to dealers pricing trades that may be costlier for them to arrange, and thus take longer.
The total value of these markups is around $141M. The markups occur on customer trades with a reported aggregate market trade volume of $25B. Results in Table 17 show that retail-size trades ($100,000 or less in par value) are a greater fraction of the potential RPTs (92.4%) than they are of all trades (78.56% from Table 2) and IRT trades (80.99%). Mean markups for these trades also are larger than for institutionalsize trades at 78.8 bp versus 63.8 bp. Retail traders probably pay markups more often and at higher values because they are less able to negotiate trades than can institutional buy-side traders. Among institutional-size trades, markups and markup values are highest for smaller trades. These results suggest that automated trade systems might   Table 4 using Tobit regression model for the liquidity proxies with left-censored distributions including Amihud, RTC, HW,RPT and Zero and OLS regression for Log (#Trades) and Log (Vol.). Aa/AA,…, C are dummy variables equal to one if Moody's rating class for the bond is Aa (Aa or Aa2 or Aa3),…C, and zero otherwise. If the bond is not rated by Moody's, S&P rating is used. Control variables are defined both in Table 2 and the text. Utility is a dummy variable equal to one, if the issuer belongs to utility industry group and zero otherwise. Finance is a dummy variable equal to one if the issuer is a financial firm and zero otherwise. For Tobit models, z-statistics are calculated using robust standard errors. For OLS regressions, t-statistics are calculated using firm level clustered robust standard errors.