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Realized Volatility, Liquidity, and Corporate Yield Spreads Marco Rossi * April 6, 2012 Abstract I propose a bond-specific, time-varying friction measure of round-trip liquidity costs. The measure is robust to outliers in daily bond returns and accounts for the idiosyn- cratic information behind bond trading decisions. Using transactions from January 2004 to December 2010, I find that liquidity costs display a strong correlation with credit conditions and peaked during the sub-prime crisis. The proposed measure also captures a smaller spike in liquidity costs for speculative-grade bonds during the Ford/GM crisis of 2005. High-frequency measures of volatility alone explain about 50% of the variation of yield spreads. After controlling for equity volatility, liquidity costs still explain a substantial fraction of the variation in the yield spreads of highly rated bonds. The properties of the proposed model are valuable in dealing with the credit risk puzzle, which pertains mainly to the investment-grade universe. Keywords: credit risk, liquidity, corporate bonds, realized volatility. * Mendoza College of Business, University of Notre Dame. Email: [email protected]; Phone: +1-574- 631-4943. This paper is the main chapter of my dissertation and has benefited enormously from discussions with Jingzhi Huang (chair) and Jean Helwege. I would also like to thank the other members of my committee (Joel Vanden, William Kracaw, and John Liechty), as well as Jack Bao, Peter Ilev, Berardino Palazzo, Lukas Roth, Robert Dittmar, Asher Curtis, Lubomir Petrasek, Xuemin (Sterling) Yan, Chunchi Wu, Kingsley Fong, and seminar participants at Penn State, the University of Missouri, the University of Kansas, the Bank of Canada, Seattle University, HEC Montreal, Northeastern University, the University of New South Wales, the University of Notre Dame, the Board of the Federal Reserve (DC), the University of Western Ontario, Washington University, and the University of Washington for their helpful comments and suggestions. This paper has benefited also from comments received at the FMA (2009) and NFA(2009) conferences and at the FMA (2009) doctoral consortium.

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Page 1: RealizedVolatility,Liquidity,andCorporate YieldSpreads...RealizedVolatility,Liquidity,andCorporate YieldSpreads Marco Rossi∗ April 6, 2012 Abstract I propose a bond-specific, time-varying

Realized Volatility, Liquidity, and Corporate

Yield Spreads

Marco Rossi∗

April 6, 2012

Abstract

I propose a bond-specific, time-varying friction measure of round-trip liquidity costs.The measure is robust to outliers in daily bond returns and accounts for the idiosyn-cratic information behind bond trading decisions. Using transactions from January2004 to December 2010, I find that liquidity costs display a strong correlation withcredit conditions and peaked during the sub-prime crisis. The proposed measurealso captures a smaller spike in liquidity costs for speculative-grade bonds during theFord/GM crisis of 2005. High-frequency measures of volatility alone explain about 50%of the variation of yield spreads. After controlling for equity volatility, liquidity costsstill explain a substantial fraction of the variation in the yield spreads of highly ratedbonds. The properties of the proposed model are valuable in dealing with the creditrisk puzzle, which pertains mainly to the investment-grade universe.

Keywords: credit risk, liquidity, corporate bonds, realized volatility.

∗Mendoza College of Business, University of Notre Dame. Email: [email protected]; Phone: +1-574-631-4943. This paper is the main chapter of my dissertation and has benefited enormously from discussionswith Jingzhi Huang (chair) and Jean Helwege. I would also like to thank the other members of my committee(Joel Vanden, William Kracaw, and John Liechty), as well as Jack Bao, Peter Ilev, Berardino Palazzo, LukasRoth, Robert Dittmar, Asher Curtis, Lubomir Petrasek, Xuemin (Sterling) Yan, Chunchi Wu, Kingsley Fong,and seminar participants at Penn State, the University of Missouri, the University of Kansas, the Bank ofCanada, Seattle University, HEC Montreal, Northeastern University, the University of New South Wales,the University of Notre Dame, the Board of the Federal Reserve (DC), the University of Western Ontario,Washington University, and the University of Washington for their helpful comments and suggestions. Thispaper has benefited also from comments received at the FMA (2009) and NFA(2009) conferences and at theFMA (2009) doctoral consortium.

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1 Introduction

Structural credit risk models explain credit spreads, the difference between corporate bond

yields and the yield offered by benchmark treasury bonds, with variables and actions that

predict the likelihood of the issuer’s default, and the loss rsulting from this credit event. The

inability of structural models to fully explain credit spread levels, credit spread changes,

and observed defaults has prompted interest in illiquidity as an additional determinant of

corporate bond prices.1 Given its potential correlation with credit risk, teasing out illiquidity

from the data is a challenging task. Even the difference between corporate bond yields and

credit default swap spreads (Longstaff, Mithal, and Neis (2005)), which should depend purely

on credit risk, could result in a contaminated illquidity measure (Das and Hanouna (2009)).

One of the most prominent attempts to derive a liquidity measure addressing the in-

teraction of credit risk and liquidity costs was recently presented by Chen, Lesmond, and

Wei (2007). Building on the informational efficiency of the U.S. corporate bond market

(Hotchkiss and Ronen (2002) and Ronen and Zhou (2008)), the authors use Datastream

data to estimate a modified version of the friction model of Lesmond, Ogden, and Trzcinka

(1999, henceforth LOT). They find that round-trip liquidity costs can explain credit spreads,

especially in the speculative-grade universe.

The idea behind friction models is that, while true returns depend on several stochastic

factors, observed returns will reflect changes in the underlying factors only if the information

value of the marginal trader is sufficient to cover the liquidity cost of trading. The factors

used in the modified LOT model are systematic: the returns on the S&P500 index represent

the equity market factor; the changes in the 10-year treasury rate represent the bond market

factor. Moreover, the LOT measure assumes that daily bond returns are homoscedastic and

that liquidity costs are constant.

1See Eom, Helwege, and Huang (2004) on spread levels, Collin-Dufresne, Goldstein, and Martin (2001)on spread changes, and Huang and Huang (2003) on the credit spread puzzle, stating that credit risk modelcannot simultaneously explain observed defaults and average corporate yield spreads.

2

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While the assumptions of the LOT measure might be appropriate with the well behaved

Datastream data (which are not necessarily based on transactions or firm quotes), these as-

sumptions are certainly not met in the transaction data available through the Trade Report-

ing and Compliance Engine (TRACE). In particular, I show that outliers in the distribution

of bond returns computed from TRACE data are more likely to appear in low rated bonds.

Unable to account for either idiosyncratic risk or heteroscedasticity, the LOT measure is

very sensitive to outliers and likely attributes some credit risk to illiquidity. It is, therefore,

important to have a liquidity measure that, while preserving the economic intuition of the

LOT model, overcomes its shortcomings.

I propose a stochastic friction model in which both systematic and idiosyncratic vari-

ables affect bond returns. The proposed model is robust to the presence of outliers in the

distribution of bond returns and can be applied to bonds that trade very infrequently. After

obtaining several liquidity measures, I conduct a panel regression analysis to assess the rela-

tive importance of illiquidity and credit risk variables in explaining corporate yield spreads.

In addition to the usual determinants of credit spreads, I propose high frequency measures

of firm equity return volatility that are able to distinguish between diffusion and jump risk.

I validate both the LOT and proposed friction measures using TRACE data. Although

correlated with credit spreads, the LOT measure produces estimates of liquidity costs that

are implausibly high. Furthermore, the risk factor loadings implied by the model are not

consistent with economic intuition. For instance, the equity factor loadings are not increasing

with credit risk and they are often negative, even for low-rated bonds. The friction measure

produces meaningful estimates of liquidity cost that are more in line with other estimates

of trading costs (e.g. Schultz (2001)). The friction measure has very desirable time series

properties showing that liquidity costs spiked during the sub-prime crisis and came back

down to normal levels toward the end of the sample period. Interestingly, the friction model

shows that only the liquidity cost of speculative-grade bonds spiked during the Ford/GM

crisis of 2005. This finding is consistent with the fact that the 2005 crisis was mainly a fallen

3

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angel one.

Univariate regressions of credit spreads on several illiquidity measures (Friction, LOT,

Zero, Roll, Amihud, and IRC)2 show that the friction measure explains the most variation

in credit spreads. They also show that this success is due mainly to investment-grade bonds.

Univariate regressions involving high-frequency measures of equity return volatility show that

these variables alone can explain approximately 50% of the variation in credit spreads. In

particular, disentangling jumps from diffusion provides extra explanatory power and reveals

that both sources of risk are important.

I also carry out several multivariate regressions on different sub-samples. I find that equity

volatility (both diffusion and jumps) has a large economic impact in all the specifications. In

general, credit risk variables such as realized volatility and market leverage tend to mitigate

the contribution of the liquidity measures in explaining the variation of credit spreads and

their economic impact is higher for speculative-grade bonds. Running the regression on the

data from the crisis period in isolation makes many liquidity variables lose their statistical

significance. This loss of significance implies that illiquidity is more relevant in the time

domain that in the cross-section. Specifically, the credit crisis is the fundamental driver of

the time-series properties of the illiquidity measures considered.

The literature on the link between liquidity and credit spreads using TRACE data is

growing rapidly. Papers showing that liquidity proxies can explain credit spreads include

Bao, Pan, and Wang (2010), Dick-Nielsen, Feldhutter, and Lando (2012), Helwege, Huang,

and Wang (2009), Friewald, Jankowitsch, and Subrahmanyam (2012), and Longstaff, Mithal,

and Neis (2005). This paper represents a further contribution to the literature because it

derives a liquidity measure that addresses the peculiarities of bond transaction data. This

approach produces a liquidity measure with remarkable time-series properties that is able to

capture not just the credit crisis, but also the Ford/GM crisis. Cross-sectionally, the measure

works especially well in the investment-grade universe, which is exactly what is needed to

2See Dick-Nielsen, Feldhutter, and Lando (2012) for a detailed definition of the last 4 measures.

4

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tackle the credit spread puzzle.

The remainder of the paper is structured as follows. Section 2 presents a literature

review. Section 3 present the friction model. Section 4 presents the data. Section 5 present

the liquidity cost estimates. In section 6, I conduct a regression analysis of the determinants

of credit spreads. Section 7 concludes the study.

2 Related Literature

The limited dependent variable approach (LDV) of LOT and Chen, Lesmond, and Wei (2007)

was first proposed by Rosett (1959) to study central bank interventions. Using this approach,

Chen, Lesmond, and Wei (2007) derive a bond-specific measure of liquidity which explains

7% of the cross-sectional variation in yield spreads in investment-grade bonds, and up to

22% of the variation in speculative-grade bonds. The proposed methodology improves on

the LDV approach in several ways.3 First, I model bond returns as a function of systematic

and firm-specific factors. The relation between firm bond and equity returns is convenient

because it allows for a hedging interpretation (Schaefer and Strebulaev (2008)). Next, I use

a panel data approach to model liquidity as a function of bond characteristics such as issue

size. Lastly, my model is robust to the presence of outliers, which are typical of tic-by-tic

transaction data (Brownlees and Gallo (2006)). The use of actual transaction data from

TRACE is yet another improvement on studies using Datastream or matrix price data.4

This paper is also closely related to the studies by Campbell and Taksler (2003) and

Zhang, Zhou, and Zhu (2009) who use equity volatility measures to explain credit and CDS

spreads. Campbell and Taksler (2003) find that the correlation between equity volatility

and the spread of an index of A-rated bonds over treasuries is 0.7 in the sample period

3In a recent paper, Omori and Miyawaki (2009) independently derive a tobit model with covariate-dependent thresholds and homoscedastic errors. However, their thresholds are linear functions of the covari-ates, which complicates and slows down their sampling scheme in order to attain non-negative thresholds,and depend on individuals only, but not on time.

4See Warga and Welch (1993) on the problems of using matrix-based data for studies involving corporatebonds.

5

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from 1965 to 1999. Zhang, Zhou, and Zhu (2009) use high-frequency volatility measures as

explanatory variables in CDS spread regressions. They find that volatility alone explains

roughly 50% of the variation in CDS spreads. Similarly to Zhang, Zhou, and Zhu (2009), I

extract equity jumps from equity realized variance and use both jumps and diffusive volatility

to study how these two components of equity volatility affect credit spreads. Tauchen and

Zhou (2010) show that the volatility of realized market jumps explains more than 60% of the

variation of Moody’s AAA and BAA credit spread monthly indices. Using equity options,

Cremers, Driessen, and Maenhout (2008) also highlight the importance of firm-specific jumps

in explaining credit spreads.

More generally, my study is related to a series of papers dealing with liquidity, credit

risk, and their interaction. Longstaff, Mithal, and Neis (2005) use CDS data to extract the

default component of credit spreads and suggest that taxes and illiquidity in the bond mar-

ket explain the non-default component. Bao and Pan (2008) relate excess bond volatility (at

short horizons) to corporate bond liquidity. Bao, Pan, and Wang (2010) use the negative

of the auto-covariance of bond prices as a measure of liquidity. They document substan-

tial commonality across individual measures and correlation with market volatility (VIX).

Mahanti, Nashikkar, Subrahmanyam, Chacko, and Mallik (2008) propose a measure of liq-

uidity defined as the “weighted average turnover of investors who hold a particular bond,

where the weights are the fractional holdings of the amount outstanding of the bond”. The

intuition behind this measure is that investors with high turnover prefer to hold bonds with

lower transaction costs, and they further improve the liquidity of these bonds by trading

them. Ambrose, Cai, and Helwege (2008, 2009) analyze the confounding effects of credit

risk and selling pressure for fallen angels and conclude that the latter is over-stated. Finally,

Dick-Nielsen, Feldhutter, and Lando (2012) and Friewald, Jankowitsch, and Subrahmanyam

(2012) provide a detailed analysis of the behavior of several liquidity measures before, during,

and after the credit crisis. See also Driessen (2005), Houweling, Mentink, and Vorst (2003),

and Kalimipalli and Nayak (2009) for more notable work in this area.

6

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3 Model

The empirical model that I propose allows for liquidity costs to vary over time as a function

of bond characteristics and potentially macro variables. In order to generate time variation,

Chen, Lesmond, and Wei (2007) estimate their model once a year for every bond. I follow

the same approach to preserve comparability with their original work. However, I do allow

time-variation within the year obtaining roundtrip liquidity costs on a monthly basis.

3.1 Model Specification and Prior Probabilities

True and unobserved bond returns R∗it, sell-side (Ls

it) and buy-side (Lbit) liquidity costs are

modeled as

R∗it = β ′

ixit + εit, εit ∼ N(0, σ2it) (1)

Lsit = αs

i × exp{γ′zit}, αsi < 0 (2)

Lbit = αb

i × exp{γ′zit}, αbi > 0, (3)

where xit is a vector of risk factors and zit is a vector of time varying variables. The

exponentials in Equations (2) and (3) ensure liquidity costs are positive. The bond-specific

liquidity effects are log normally distributed:

−αsi |αs, zi, σ

2s ∼ LogN(α′

szi, σ2s) (4)

αbi |αb, zi, σ

2b ∼ LogN(α′

bzi, σ2b ), (5)

where zi is a vector of time-invariant bond characteristics.

In order to reduce noise and preserve heterogeneity across bonds (see Tsionas (2002)),

I shrink the factor loadings toward a common beta, βi|β,∆ ∼ N(β,∆). Following Geweke

(1993), I simplify the variance structure of the error term in Equation (1) with the decom-

7

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position σ2it = σ2 × vit, where σ2 ∼ IG(sh, sc) and r/vit ∼ χ2(r). The degrees-of-freedom

parameter r captures the extent of heteroscedasticity in the data. Low values of r reflect

the prior beliefs that the data might contain several large outliers, while large values of r

are consistent with homoscedastic error terms. To complete the model, I impose flat pri-

ors for the parameters β, αs, αb, and γ, and diffuse priors for the remaining parameters:

∆ ∼ IW (∆0, N0) and σ2s , σ

2b ∼ IG(sh, sc).

3.2 Observed Returns and Transaction Costs

Returns are observed only when they are large enough to justify transaction costs. The

observation rule of bond returns that I propose is a generalization of the friction model

originally proposed by Rosett (1959):

Rit =

R∗it − Ls

it, R∗it < Ls

it

0, Lsit ≤ R∗

it ≤ Lbit

R∗it − Lb

it, R∗it > Lb

it

(6)

With this observation rule, the likelihood function for every observation is given by

p(Rit|Lsit, L

bit, βi, σ

2it, xit) =

[

1

σit

φ

(

Rit + Lsit − β ′

ixit

σit

)]

1{Rit

<0}

×

[

1

σit

φ

(

Rit + Lbit − β ′

ixit

σit

)]1{Rit

>0}

×

[

Φ

(

Lbit − β ′

ixit

σit

)

− Φ

(

Lsit − β ′

ixit

σit

)]1{Rit

=0}

. (7)

Round trip liquidity costs are obtained as

Costit ≡ Lbit − Ls

it = (αbi − αs

i )× exp{γ′zit}, (8)

which reduce to the LOT measure when zi = 1 and zit = ∅.

8

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4 Data

The data in this study cover the period from January 2004 to Decemebr 2010 and come from

five sources. The fixed investment securities data base (FISD) provides bond characteristics;

the trades reporting and compliance engine (TRACE) contains the actual bond transaction

data; CRSP contains stock price data; COMPUSTAT contains balance sheet data; the Dow

Jones trades and quotes (TAQ) database is used to construct realized volatility, and its

diffusive and jump components. In Appendix C, I provide details on these databases, and

on the filters used to determine the final sample.

4.1 Corporate Bond Data

Under the pressure from several government bodies and buy-side traders, on July 1, 2002,

the National Association of Securities Dealers (NASD) started a three-phase dissemination

process of corporate bond transactions through its trades reporting and compliance engine

(TRACE).5 This process progressively increased the pool of bonds subject to dissemination

resulting in over 95% coverage of U.S. corporate bonds after October 2004. The only bond

transactions not reported to TRACE are those that take place in exchanges, e.g. NYSE’s

automated bond system (ABS). Although the role of TRACE is to increase transparency

in the corporate bond market (see Bessembinder, Maxwell, and Venkataraman (2006) and

Edwards, Harris, and Piwowar (2007)), not all information is released after each transaction.

For instance, until recently, the side of the transaction was unknown and volume is top-coded.

I obtain bond characteristics from the fixed investment securities database (FISD) com-

piled by Mergent Inc. I consider only senior unsecured bonds (medium term notes and

debentures) with no optionality and issued by industrial firms. Next, I merge the FISD data

with TRACE to obtain the bond transactions. Details of the filter used for TRACE are

available in the appendix. After imposing these filters, and merging the resulting bond data

5The body that oversees TRACE now is the Financial Industry Regulatory Authority (FINRA)

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with CRSP, COMPUSTAT, and TAQ, I obtain a final sample of 1056 bonds issued by 358

issuers.

Table 1 reports descriptive statistics, grouped by year, on bond characteristics and trans-

actions. As can be seen, the time to maturity at issuance has increased over time, while the

average coupon rate and bond age have remained quite stable. The price and size percentiles

of the distribution show that approximately half of the trade prices are within 5% of par, and

that a significant proportion of trade sizes (50%) is below $25,000 indicating an active pres-

ence of retail investors in the corporate bond market, even though the market is dominated

by institutional invertors.

Table 2 reports the number of bond transactions grouped by issue size (in one dimension)

and by two measures of bond seasoning (in the other dimension): Panel A considers a

classification by age; Panel B considers a classification by time to maturity. The number

in parenthesis represent the number of bonds in each category. This table shows that large

issues trade much more frequently. Bonds with an issue size smaller than $50 million trade

25,285 times, while bonds with an issue size in excess of $500 million trade almost 868,444

times during the same period. Note that the difference is not accounted by the varying

number of bonds. There is also substantial variation in trading volume depending on age

and time maturity, with large issues trading less frequently as they age, and smaller issues

doing just the opposite. Finally, trading activity declines rapidly when bonds approach

maturity.

4.2 Bond Returns and Credit Spreads

Bond returns are defined as

Rt =Pt + AIt + Ct

Pt−1 + AIt−1,

where Pt is the clean price of the bond, AIt is the accrued interest over one period, and Ct

is the coupon payment whenever it is paid (in which case AIt = 0). I set Rt = 0 if there is

10

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no trading. Care must be taken on the first day of trading after a period of stale prices, as

two consecutive genuine price observations are not available. To compute this return, I use

two alternative approaches and conduct separate analysis. The first approach assumes stale

prices, while the second approach assumes the price grows linearly during the no-trading

period. For example, suppose there is a trade at t = 0 for $100, no trade at t = 1, and a

trade at t = 2 for $102. With interpolation, the return for t = 1 is 0 and the return for t =

2 is 0.99% (102/101-1). In the case of stale prices the return at t=2 would be equal to 2%.

The two approaches do not affect the results significantly. In the interest of space, I only

report results for the interpolation case.

Figure 1 presents the distribution of corporate bond returns. Figure 1a presents box plots

of bond returns grouped by rating and reveals that outliers are more likely to occur with

bonds having a lower credit rating. This type of heteroschedasticity is likely to affect the LOT

measure because outliers have a big impact on the estimation of the intercepts (thresholds)

of the model. Given that outliers are related to credit risk, the model’s lack of robustness

might mechanically generate liquidity costs that explain the cross section of credit spreads.

As can be seen, outliers are present regardless of whether I use stale prices or interpolated

prices, but interpolation mitigates their size. By presenting results for interpolated prices, I

am giving the standard LOT measure a better chance of success. Although, the data present

substantial outliers, the empirical cumulative distribution function of bond returns (Figure

1b) reveals the most of the data is well behaved, with well over 90% of the returns falling in

the plus/minus 5% range.

Table 3 presents average credit spreads categorized by rating in one dimension and by

time to maturity (Panel A) or by year (Panel B) in the other dimension. As can be seen,

credit spreads are generally increasing in time to maturity and decreasing with credit ratings.

The break down by year (Panel B) reveals the effect of the credit crisis which started in 2007.

11

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4.3 High-Frequency Data (TAQ)

Given the documented importance of equity volatility, I use high-frequency data from the

NYSE trades and quotes (TAQ) database to compute equity realized volatility and to dis-

entangle its diffusive and jump components. To screen out jumps, I use a nonparametric

approach developed by Barndorff-Nielsen and Shephard (2004) which relies on the concepts

of realized variance and bipower variation.6 In Appendix D, I explain the methodology to

recover jumps from high frequency data, and provide references for its exact implementation.

Following Tauchen and Zhou (2011), it is possible to identify jumps from the jump variation

of equity returns. I follow their approach and compute the volatility of jumps (jump risk),

which I use as a an explanatory variable in the yield spread regressions.

5 Estimation of Liquidity Costs

Bayesian estimation of the model parameters and latent variables requires the combination

of the likelihood of the model, and the use of prior information on the parameters. To

simplify notation, collect the parameters of the data generating process into ΘR, and those

of the liquidity processes into Θl, and define Θ ≡ [ΘR,Θl]. The prior over these parameters

if p(Θ). We obtain the posterior distribution of the parameters and the latent variables,

given the data, as

p(Θ, Ls, Lb|R,X, Z, Z) ∝ p(R|Ls, Lb, X,ΘR)× p(Ls, Lb|Z, Z,Θl)× p(Θ). (9)

Sampling directly from the joint posterior distribution of the parameters is not feasible.

However, the parameters can be estimated using a Markov Chain Monte Carlo (MCMC)

algorithm (see Appendix E), which is an iterative scheme to draw from the conditional

distributions of blocks of parameters of the vector Θ. Conditional posterior distributions of

6See Huang and Tauchen (2005), Barndorff-Nielsen and Shephard (2006) and Huang (2007) for an appli-cation of this approach.

12

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these blocks of parameters are derived in Appendix B.

5.1 LOT Measure with TRACE Data

I use the same return generating process of Chen, Lesmond, and Wei (2007). In particular,

I use the changes in the long-term default-free rate (systematic bond factor), and market

equity returns (systematic equity factor). In order to stabilize the slope coefficients, I interact

the factors with bond duration.

Table 4 reports average estimates of factor loadings and liquidity costs grouped by time

to maturity and rating. The results reported in the table are somewhat consistent with those

reported in Chen, Lesmond, and Wei (2007, p. 127) in the sense that they are characterized

by a generally negative relation between liquidity costs and credit quality. In terms of size,

Table 4 shows that, using TRACE data, estimates of liquidity cost are implausibly high,

even higher than those reported in Chen, Lesmond, and Wei (2007). With regard to the

factor loadings, it can be seen that the loadings on the bond factors are mostly negative.

However, the loadings on the equity factor are inconsistent with theory, given that they do

not increase with credit risk and are often negative.

5.2 Friction Model

The return generating process depends on three factors: a bond market factors; a firm equity

factor; and a firm realized volatility factor. These factors are interacted with bond duration.

The liquidity covariates in the threshold component of the model (Equations (4) and (5)) are

the issue size (in log) and the coupon rate. Consistently with the LOT measure, I estimate

liquidity costs every year. To capture intra-year variation in liquidity, I use monthly effects

(dummies) as explanatory variables in (2) and (3).

Table 5 presents average estimates of the parameters in Equation (1) grouped by rating

and time to maturity. As can be seen, bond factor loadings are on average negative for every

group. The average firm-specific equity factor loading is always positive, which means that

13

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good news for equity holders are typically good news for bond holders given that both debt

and equity are positive claims on firms’ assets. As expected, the equity factor loading is

increasing in credit risk. Due to noise in daily realized volatility, it is hard to see a definite

pattern, but it should be noted that all the results of this paper go through even without

including volatility in the return generating process.

Contrary to what I find for the LOT measure, estimates of round-trip liquidity costs are

economically meaningful with group averages which do not exceed 5%. While liquidity costs

are relatively higher for junk bonds, no clear pattern can be detected with respect to ratings.

Only within the investment grade universe, a relation between liquidity and rating seems to

exist. This finding is consistent with the credit risk puzzle which is particularly relevant for

investment-grade bonds, given that credit risk models do quite well in explaining the credit

spreads of speculative-grade bonds (Huang and Huang (2003)).

Overall, these findings suggest that, with TRACE data, the modeling approach of this

paper generates estimates that are more reliable and economically meaningful than the LOT

measure. These results are achieved thanks to the statistical robustness of the proposed

friction model and the use of firm equity returns, which are better able to capture credit-

relevant information that might influence trading decisions.

5.3 Time Series Variation of Liquidity Costs

Figure 2 shows the average behavior of estimated liquidity costs over time and by rating

category. Although a monotonic relation is not present in the cross-section, Figure 2a shows

that the friction model produces liquidity estimates that covary strongly with the state of

the economy. Liquidity costs spike during the crisis and have come down to normal levels in

2010, which is consistent with the findings of Dick-Nielsen, Feldhutter, and Lando (2012).

Figure 2a also shows that the friction model is able to detect the smaller spike in liquidity

costs taking place during 2005 following the downgrades of Ford and GM (see Friewald,

Jankowitsch, and Subrahmanyam (2012)). Interestingly, only junk bonds experienced a

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spike, which is consistent with the fact that this was a fallen angel crisis. Figure 2b shows

a qualitatively similar (but somewhat less sharp) relation with the state of the economy.

However, the LOT measure does not respond to the Ford/GM crisis and liquidity costs

seem to peak in 2009 rather than 2008. Again, comparing the scales in the two graphs, one

can immediately see that the LOT measure applied to TRACE data produces liquidity cost

estimates that are economically impossible.

6 Credit Spreads Determinants

The general specification of the regressions mimics those of Campbell and Taksler (2003)

and Chen, Lesmond, and Wei (2007) and is given by

Y ield Spreadit = αj + β ′1Illiquidityit + β ′

2V olatiltiyit

+β ′3Bond Characteristicsit + β ′

4Accounting V ariablesit

+β ′5Macro V ariablest + εit,

where t, i, and j index months, bonds, and firms respectively.

I consider a total of six illiquidity measures: the friction measure proposed in this paper;

the LOT measure; the percentage of zero trading days (in a month); the Roll measure

(Bao, Pan, and Wang (2010)); the Amihud measure; and the imputed round-trip cost (IRC)

measure proposed by Feldhutter (2011). A description of these measures can be found in

Dick-Nielsen, Feldhutter, and Lando (2012). In the interest of space, and because the focus

of the paper is on the proposed friction measure, I do not repeat the descriptions here.

Volatility is either total realized volatility (I try both a one-week and a one-month average

of daily volatilities), or its two components (diffusion risk and jump risk). Table 6 reports

descriptive statistics of the variable included in the regressions.

The focus of these regressions will be to compare the explanatory power and economic

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significance of liquidity and volatility. To account for the dependence induced by issuer-

specific effects, I compute standard errors clustered by issuer (see Petersen (2009) and Gow,

Ormazabal, and Taylor (2009)).

6.1 Liquidity and Credit Spreads

Table 7 reports estimates (grouped by rating) and robust t-statistics of univariate regressions

of credit spreads on six different liquidity measures. Consistent with the previous section,

Friction explains a substantial portion of credit spreads, especially among investment grade

bonds. Referring to Figure 2a, it is safe to conclude that a substantial fraction of the

explanatory power of Friction comes from its time series variation. In terms of R2, the

LOT measure performs comparably in both sub-samples and its slope almost doubles in the

sample of junk bonds. With the exception of Zero, all the other measures of illiquidity are

significant at the one percent level in both samples and seem to be more relevant for junk

bonds.

6.2 Volatility and Credit Spreads

Table 8 presents regression estimates of credit spreads on several volatility measures. For

comparison purposes, I also include historical volatility based on daily return data (based

on the previous six months). These regressions show a remarkable explanatory power of all

liquidly measures. The 5-day (1w) average of realized volatility is too noisy and results in

both lower R2 and coefficients , relative to the 21-day (1m) average. The table also reveals

that both components of volatility seem to be important in explaining the variation of credit

spreads.

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6.3 Multivariate Analysis

Table 9 reports several regression models similar to those estimated by Campbell and Taksler

(2003) and Chen, Lesmond, and Wei (2007). The estimation is done by rating group and only

one liquidity measure is included in each regression. The first thing worth noting from Table 9

is that the coefficients on the liquidity measures experience a substantial decline in their size.

Furthermore, some measures lose their statistical significance. On the other hand, realized

volatility is strongly significant in all models and both sub-samples. Even controlling for

bond liquidity and other factors affecting bond yields, realized volatility has a large economic

impact on credit spreads. In particular, a standard deviation change in average daily realized

volatility over the previous month is associated with an 80 (≈ 1×0.008) basis point increase

in credit spreads for investment-grade bonds and a staggering 120 (≈ 1.5×0.008) basis point

increase for speculative grade bonds.

The behavior of the volatility and liquidity measures across sub-sample is informative.

As expected, volatility and the other credit risk measures, e.g. leverage, have a bigger

impact on the credit spreads of junk bonds in every estimated model. With the exception

of Friction (which is strongly significant in the full sample as well), this pattern is true for

the other liquidity measure. However, in order to solve the credit risk puzzle (Huang and

Huang (2003)), liquidity measures should work better in the sample of investment-grade

bonds because that is where structural credit risk models do not do as well.

The ability of realized volatility to explain credit spreads so well relatively to traditional

volatility measures based on six months of data is that realized volatility incorporates in-

formation as it becomes available and quickly forgets it when it is no longer relevant. This

feature of the data makes realized volatility more informative than traditional volatility

measures.

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6.3.1 Credit Spreads and Jump Risk

Table 10 reports regression estimates similar to those of Table 9, with the exception that

the two components of realized volatility (diffusion and jump risk) are included as separate

variables. This table shows that both components of volatility play an important role in

explaining credit spreads, with an economic significance of 17 and 55 basis points for the

investment-grade and junk bond respectively. Note also that jump risk does not substitute

diffusion risk. Taken together, the two components of volatility have more economic signifi-

cance than realized volatility alone. The joint impact is roughly 97 (17+80) basis points for

investment-grade bonds and 155 (100+55) basis points for speculative-grade bonds. Lastly,

having the two components of volatility separate of each other does not further discount the

contribution of the liquidity measures.

6.3.2 Normal Times vs Crisis

Table 11 reports regression estimates grouped by sub-periods, with the crisis period going

from July 2007 to July 2009. Again, credit risk variables such as volatility and market

leverage continue to have a large impact on credit spreads. With the exception of IRC,

the impact of liquidity measures is greatly reduced. This partition of the data shows that

the time series variation of the liquidity measures is probably more important than the

cross-sectional variation. Moreover, the within-period time series variation of the liquidity

measures is also not very effective in explaining credit spreads and is driven out by volatility.

7 Conclusion

This paper resurrects the friction approach to modeling liquidity costs with bond data from

TRACE. Considering both liquidity and credit risk, the friction model is able to make sharper

predictions. In the time series domain, the model shows that liquidity costs covary strongly

with credit conditions. Liquidity costs increased substantially during the credit crisis and,

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to a lesser extent, during the Ford/GM crisis. While the recent crisis was quite systemic,

the Ford/GM crisis affected mainly speculative-grade bonds. Looking at subsets of the data

separately reveals that realized volatility always plays a fundamental role in explaining credit

spreads. On the other hand, the sub-prime crisis is indispensable in generating the kind of

variation required by illiquidity to play an economically important role in the time series

domain.

The credit risk puzzle is a cross-sectional puzzle. While structural credit risk models can

explain most of the observed credit spreads of speculative-grade bonds, they fail in matching

the data when it comes to investment-grade bonds (Huang and Huang (2003)). The puzzle

is not due the 500-basis point-spread required to hold B-rated bonds, but rather to the 50-

basis point-spread on a AAA rated bond. There are simply not enough defaults in the AAA

category to justify the 50 basis points, but there are enough defaults in the B category to

justify the 500 basis points. If illiquidity is to be of any help in solving the credit spread

puzzle, then (cross-sectionally) it should manifest its importance in the investment-grade

space. Particularly effective with highly rate bonds, the friction measure that I propose does

just that.

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Appendix

A Augmented Likelihood

For purpose of estimation of the parameters entering Equation 1, it is better to work with

the augmented likelihood function (see e.g. Chib (1992))

p(R∗it|Rit, L

sit, L

bit, βi, σ

2, xit) =1

σitφ

(

R∗it − β ′

ixit

σit

)

, (10)

where the rule for obtaining the latent variable R∗it is given by

p(R∗it|Rit, L

sit, L

bit, βi, σ

2it, xit) =

Rit + Lsit, Rit < 0

∼ TN(Lsit,Lb

it)(β

′ixit, σ

2it), Rit = 0

Rit + Lbit, Rit > 0

(11)

B Conditional Posterior Distributions

B.1 Conditional Distribution of βi and σ2it

To the derive the conditional posterior distribution of βi and σ2it, it is more convenient to

work with the augmented likelihood in (10). To see this, notice that, once we augment

that data with the auxiliary variable R∗it, the likelihood function is the standard likelihood

function of a linear regression model, and the standard conditional distributions apply.

Using vector notation on the time observations, and defining Vi = diag(vi1, vi2 . . . , viTi),

we can multiply the likelihood in (10) and the prior distribution for β to obtain

p(βi|β,∆, σ2, Vi, R∗i , Xi) ∼ N(Bi, Vi), i = 1, . . . , N (12)

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where Bi = Vi ×(

X ′iV

−1i R∗

i /σ2 +∆−1β

)

and Vi =(

X ′iV

−1i Xi/σ

2 +∆−1)−1

.

The posterior distribution for σ2 is given by

p(σ2|{β}Ni=1,∆, R∗i , Xi) ∼ IG(

N∑

i=1

Ti/2 + sh,

N∑

i=1

SSRi/2 + sc), (13)

where SSRi ≡ (R∗i − Xiβi)

′V −1i (R∗

i − Xiβi) and Ti is equal to the number of censored and

uncensored observations available for bond i.

Finally, the distribution of the time-varying component of the variance has been shown

by Geweke (1993) to be implicitly given by

e2it/σ2 + r

vit|βi, σ

2 ∼ χ2(r + 1), (14)

where e2it is the squared residual of observation it.

B.2 Conditional Distribution of αsi and αb

i

To obtain the posterior distribution for this parameter, I need to combine the observed

likelihood in (7) with the expressions in (2), and (3). Defining l = log(L), The posterior

distribution of αsi is given by

p(αsi |βi, σ

2it, Rit, xit, L

sit, L

bit) ∼ p(Rit|L

sit, L

bit, βi, σ2, xit)× p(lsit|γsi, σ

2s , zit)

∝ exp

{

−1

2

(

Rit + Lsit − β ′

ixit

σit

)2}

1{Rit

<0}

×

[

Φ

(

Lbit − β ′

ixit

σit

)

− Φ

(

Lsit − β ′

ixit

σit

)]1{Rit

=0}

×

exp

{

−1

2

(

αsi − α′

sziσs

)2}

. (15)

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The posterior distribution of the buy-side liquidity costs is given by

p(αbi |βi, σ

2it, Rit, xit, L

sit, L

bit) ∝ exp

{

−1

2

(

Rit + Lbit − β ′

ixit

σit

)2}

1{Rit

>0}

×

[

Φ

(

Lbit − β ′

ixit

σit

)

− Φ

(

Lsit − β ′

ixit

σit

)]1{Rit

=0}

×

exp

{

−1

2

(

αbi − α′

bziσb

)2}

. (16)

The expressions in (15) and (16) do not resemble the kernels of any well known distribution.

Therefore, I implement a Metropolis-Hastings algorithm to sample from these unknown

target distributions.

B.3 Conditional Distribution of αs and αb

Given the flat prior, the distribution of αs is given by

p(αs|{αsi}

Ni=1, σ

2s , zi) ∼ N(α, V ), (17)

where α = V × (z′αs/σ2s) and Vi = σ2

s (z′z)−1. Note that the posterior parameters of the dis-

tribution are just the OLS slope and its covariance matrix. A similar posterior distributions

can be obtained for αb.

B.4 Conditional Distribution of β and ∆

Combining the distributions in which it appears, β can be shown to have the following

posterior conditional distribution:

p(β|{β}Ni=1,∆) ∼N∏

i=1

N(βi,∆)

∼ N

(

N∑

i=1

βi/N,∆/N

)

. (18)

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Using the the linearity and cyclic property of the trace operator, the posterior conditional

distribution for ∆ is given by

p(β|{β}Ni=1,∆) ∼ IW (∆0, N0)×N∏

i=1

N(βi,∆)

∝ |∆|−N+N0+K+1

2 exp{−tr(∆−1(∆0 +∆1))}

∼ IW (∆0 +∆1, N +N0), (19)

where ∆1 ≡∑N

i=1(βi − β)(βi − β)′.

B.5 Conditional Distribution of γ

To obtain the posterior distribution for this parameter, I need to combine the observed

likelihood in (7) with the expressions in (2), and (3). The posterior distribution of γ is given

by

p(αsi |βi, σ

2it, Rit, xit, L

sit, L

bit) ∼ p(Rit|L

sit, L

bit, βi, σ2, xit)× p(lsit|γsi, σ

2s , zit)

∝ exp

{

−1

2

(

Rit + Lsit − β ′

ixit

σit

)2}

1{Rit

<0}

×

[

Φ

(

Lbit − β ′

ixit

σit

)

− Φ

(

Lsit − β ′

ixit

σit

)]1{Rit

=0}

×

exp

{

−1

2

(

Rit + Lbit − β ′

ixit

σit

)2}

1{Rit

>0}

. (20)

The expressions in (20) does not resemble the kernel of any well known distribution. There-

fore, I implement a Metropolis-Hastings algorithm to sample from this unknown target

distribution.

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B.6 Conditional Distribution of σ2s and σ2

b

The derivation of the posterior conditional distribution for σ2j , j = {s, b} is given by

p(σ2j |{α

ji , zi}

Ni=1) ∼ IG (N/2 + sh, SSR/2 + sc) , j = {s, b} (21)

where SSRi ≡ (αj − zαj)′(αj − zαj) and N is equal to the number of bonds.

C Databases and Merging

To conduct my analysis, I use 5 databases. Below, I briefly describe the databases and the

filters used for the sample selection.

1. FISD is used to obtain bond characteristics and identify the sample of bonds to include

in the study; the unique identifier for each issue in this database are the merge issue-id

variable and the bond 9-letter cusip; before the merge with TRACE by cusip, I impose

several filters to define the initial sample:

• exclude bonds that are convertible, putable, callable, and exchangeable

• keeps bonds that are either corporate debentures or medium term notes

• keep bonds denominated in US dollars

• exclude variable-rate bonds

2. TRACE is used to obtain transaction prices; the unique identifier for each issue in

this database is the bond 9-letter cusip; I use regular trades end exclude commission

trade; I then impose the following filters in the order listed below:

• filter the data following Dick-Nielsen (2010);

• eliminate 50% return reversal, i.e. eliminate a bond price if it is preceded and

followed by a price increase or drop of more than 50%;

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• to further minimize the impact of unusual observations, I keep price observations

that pass the following screening:7

|p−med(p, k)| ≤ 5 ∗MAD(p, k) + g, (22)

where g is a granularity parameter which I set equal to $1, and med(p, k), and

MAD(p, k) are respectively the centered rolling median, and median absolute

deviations of the price p using k observations (I set k = 20).8

• I keep bonds that are traded on at least 20 distinct days.

3. CRSP to obtain stock returns of the company currently backing a given bond; the

unique identifier for each firm and securitiy in this database are the PERMCO and

PERMNO numbers respectively;

4. COMPUSTAT to obtain balance sheet information on the company backing a given

bond; firms are identified by their GVKEY number;

5. TAQ to obtain 5-minute returns to construct the realized variance measures used in

the specification of the bond return generating process; securities are identified by their

TICKER symbol (which varies over time and is not a unique identifier). In order to

the impact of bid-ask bounce, I use mid-quotes instead of actual transactions in the

calculation of returns.

The link between these databases is straightforward in some cases and quite complicated in

others. FISD and TRACE are easily linked through the 9-letter cusip. Once a preliminary

sample of bonds is formed, to see whether a firm with public equity is backing them, I match

the six-letter cusip (which identifies the firm at issuance in the FISD database) with the

historical cusip (NCUSIP) in the CRSP “stocknames” table. During this merge I obtain the

7Brownlees and Gallo (2006) propose a similar algorithm, based on rolling trimmed statistics, to filterTAQ data.

8I also try to eliminate smaller return reversals as in Bessembinder, Maxwell, and Venkataraman (2006)but this procedure leaves several observations that are clearly outliers.

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historical tickers, and PERMCO and PERMNO numbers associated with firms’ CUSIPs,

which I then use to get data from COMPUSTAT and TAQ. Lastly, I keep track of delistings

and merge activity to make sure that bonds are always matched with the right permno.

D Extracting Jumps from Realized Variance

To screen out jumps, I use a nonparametric approach developed by Barndorff-Nielsen and

Shephard (2004) which relies on the concepts of realized variance and bipower variation.9

The idea is that, as we sample price data at very high frequency, the limiting behaviors of

the return realized variance and bipower variation capture different aspects of the return

process. More formally, given a log asset price p(t), we can define the instantaneous return

of the associated jump-diffusion process as

dp(t) = µ(t)dt+ σ(t)dW (t) + k(t)dq(t), 0 ≤ t ≤ T, (23)

where µ(t) and σ(t) are the drift and the diffusion of the process, W (t) is a standard Brownian

motion, q(t) is a counting process which controls the arrival of jumps, and k(t) is the size

of the jumps upon arrival. I refer to Andersen, Bollerslev, and Diebold (2007) for a precise

description of the parameters of the process and their properties. Given a sample of high-

frequency price data in a given day, one can create ∆-period returns, where ∆ is a fraction

of the day, as rt,∆ ≡ p(t)− p(t−∆). Setting the time interval to unity, we get 1/∆ intervals

in a day, and we also have rt+1 ≡ rt+1,1. It can be shown that the realized variance converges

uniformly in probability to the quadratic variation of the process:

RVt+1(∆) ≡

1/∆∑

j=1

r2t+j∆,∆ −→

∫ t+1

t

σ2(s)ds+∑

t<s≤t+1

k2(s), (24)

9See Huang and Tauchen (2005), Barndorff-Nielsen and Shephard (2006) and Huang (2007) for an appli-cation of this approach.

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for ∆ −→ 0. The other object of interest, the bipower variation, converges to just the

diffusive component of the quadratic variation of the process:

BVt+1(∆) ≡ µ−1

1/∆∑

j=2

|rt+j∆,∆||rt+(j−1)∆,∆| −→

∫ t+1

t

σ2(s)ds, (25)

for ∆ −→ 0, where µ−1 ≡√

2/π.

It can be shown (see Barndorff-Nielsen and Shephard (2004) and Andersen, Bollerslev,

and Diebold (2007)) that the difference between the quantities in expressions (24) and (25)

converges to∑

t<s≤t+1 k2(s). In most applications (e.g. Andersen, Bollerslev, Diebold, and

Ebens (2001)), including mine, 5-minute returns are typically used to obtain daily measures

of realized variance and bipower variation, i.e. ∆ is small but not zero, so this difference is

not even guarantied to be positive. To deal with this issue, Barndorff-Nielsen and Shephard

(2004) propose a statistical procedure to determine whether price variation is due to jumps

or diffusive movements based on the test statistics RJit ≡RVit−BVit

RVit, which, appropriately

scaled, converges to a standard normal distribution. I implement this methodology exactly

as in Zhang, Zhou, and Zhu (2009, Appendix, p. 35).

E Estimation Algorithm

Given the conditional posterior densities derived in the previous section, I implement the

Gibs sampler, and Hasting-Metropolis algorithm it, as follows.

1. Initialize the chain by assigning {R∗i , β1, . . . , βN , α1, . . . , αN , σ, Vi, β,∆, σs, σb, γ, αs, αb}

0;

2. Move the Markov chain one step forward by drawing parameters from the posterior

densities derived in the previous sections. In particular, we obtain updated values (not

necessarily in this order), for j > 0, as follows:

• R∗ij |Ri, L

sij−1, Lb

ij−1

, i = 1, . . . , N : use equation (11);

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• βji |σ

j−1, V j−1i , βj−1,∆j−1, i = 1, . . . , N : use equation (12);

• σj |{β1 . . . βN}j, {V1 . . . VN}

j−1: use equation (13);

• V ji |β

ji , σ

j , i = 1, . . . , N : use equation (14);

• βj |{β1 . . . βN}j,∆j−1: use equation (18);

• ∆j−1|βj, {β1 . . . βN}j : use equation (19);

• σjs |{L

s1 . . . L

sN}

j−1: use equation (21); similarly for σb;

• αjs|{L

s1 . . . L

sN}

j−1, {Lb1 . . . L

bN}

j−1: use equation (17); similarly for αjb;

• αsi , α

bi , γ

j: the posterior densities of interest are proportional to the expressions

in (15) , (16), and (20) respectively, and a Metropolis-Hastings (within-Gibbs-

sampler) algorithm is required to sample from this non-standard distributions.

The procedure for generating a generic sample θ from one of these distributions

works as follows:

– given the current sample previously drawn, θc, generate a new sample θp from

the proposal distribution q(θp|θc); the proposal and target density should have

the same support;

– evaluate the acceptance probability as

α(θp|θc) = min

(

1,p(θp)q(θc|θn)

p(θc)q(θp|θc)

)

– accept the proposed value θp with probability α(θp|θc), i.e.

{θ}j+1 =

θp, with prob α(θp|θc)

θc, with prob 1− α(θp|θc)

The proposal density for αs and αb is a truncated normal, i.e. q(θp|θc) ∼ TN(0, ν2),

where ν2 is a perturbation parameter; the proposal for γ is a normal distribution;

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3. Repeat step 2 J times, where J is large enough to ensure convergence of the chain;

4. Discard the first K

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References

Ambrose, B. W., N. Cai, and J. Helwege, 2008, “Forced Selling of Fallen Angels,” The

Journal of Fixed Income, 18(1), 72 – 85.

, 2009, “Fallen Angels and Price Pressure,” Penn State Working Paper.

Amihud, Y., 2002, “Illiquidity and stock returns: cross-section and time-series effects,”

Journal of Financial Markets, 5(1), 31–56.

Andersen, T. G., T. Bollerslev, and F. X. Diebold, 2007, “Roughing It Up: Including Jump

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Table 1: Summary Statistics of Corporate Bond Transactions

This table presents summary statistics, categorized by year, of bond characteristics and bond transactions. To enter the final sample, the bondsmust have data on FISD, TRACE, CRSP, COMPUSTAT, and TAQ. Moreover, bonds that trade on less than 20 trading days are excluded from thesample. Issues is the number of bonds. Issuers is the number of issuers (issuer id variable in FISD). Issue Size is the average issue size. Coupon isthe average fixed coupon rate. Maturity is the time to maturity at issuance. Bond Age is age measured in years at the time of trade. Trade Price isthe price, as a percentage of par, of the bond (several percentiles are provided). Trade Size is the par value size of the transaction (several percentilesare provided).

2004 2005 2006 2007 2008 2009 2010 2004-2010

Issues 875 969 848 743 639 545 515 1,056Issuers 306 346 318 291 257 238 222 358Issue Size (millions) 292.80 274.69 271.99 276.75 278.14 292.45 301.13 297.93Coupon 7.13 7.24 7.31 7.36 7.43 7.62 7.57 7.13Maturity (years) 17.69 17.86 19.15 20.52 22.08 24.28 25.41 17.28Bond Age (years) 9.85 9.44 9.08 9.44 8.16 8.59 10.36 9.29Trade Price

Minimum 19.00 10.00 18.95 10.50 0.01 0.01 0.01 0.01First Quartile 100.54 92.83 91.78 96.80 93.88 93.73 99.50 96.44Median 104.42 100.57 99.64 100.00 99.96 100.71 105.21 100.87

Third Quartile 109.12 104.41 102.00 103.38 102.91 105.69 109.95 105.83Maximum 153.42 159.85 148.66 144.45 151.47 146.77 152.95 159.85

Trade Size (× $1,000)First Quartile 10 10 10 10 10 10 10 10Median 25 25 25 25 20 20 20 25

Third Quartile 130 100 100 90 50 50 50 75

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Table 2: Trading Activity by Bond Characteristics

This table presents summary statistics of corporate bond transactions categorized by age and issue size(Panel A), and time to maturity and issue size (Panel B). The numbers in the table represent the tradeoccurrences with a given size-age or size-TTM bin. The number in parenthesis represent the number ofbonds falling in each category. Notice that for the number in parentheses the marginal distribution is notobtained by summing numbers in the joint table as a given bond might be in more than one category duringits life.

Issue Size (×$1,000,000)

≤ 50 (50− 100] (100− 250] (250− 500] > 500

PANEL A: by Age (in years)

≤ 2 1,859 1,552 36,404 210,659 447,677 698,151( 620) ( 103) ( 520) ( 1915) ( 5890)

(2 − 7] 12,484 30,342 202,503 323,079 317,058 885,466( 240) ( 330) ( 750) ( 2168) ( 6746)

(7 − 10] 6,783 23,390 191,254 191,293 70,854 483,574( 126) ( 320) ( 736) ( 2014) ( 2443)

(10− 15] 4,159 19,863 97,972 72,211 32,855 227,060( 154) ( 389) ( 715) ( 1536) ( 2738)

PANEL B: by Time to Maturity (in years)

≤ 2 11,264 29,324 160,706 291,682 201,561 694,537( 179) ( 299) ( 600) ( 1620) ( 2761)

(2 − 7] 7,859 16,996 117,664 175,958 239,809 558,286( 148) ( 283) ( 726) ( 1543) ( 5329)

(7 − 10] 3,870 13,972 106,159 143,874 205,486 473,361( 184) ( 291) ( 742) ( 2116) ( 7611)

(10− 15] 2,292 14,855 143,604 185,728 221,588 568,067( 164) ( 381) ( 964) ( 3202) ( 8864)

Total Issue Size 25,285 75,147 528,133 797,242 868,444 2,294,251

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Table 3: Average Corporate Credit Spreads

This table presents average end-of-month credit spreads grouped by credit rating, and subsequently by timeto maturity (Panel A), and by year (Panel B). Credit spreads are defined as the difference between corporatebond yields (obtained by volume-averaging the available yields on a given day and taking the observationclosest to the end of the month, provided it is within three business days of the end of the month) and theyields on the treasury benchmark with the same time to maturity. The constant maturity benchmark yieldsare from Datastream and are for the following yearly maturities: 1/12, 1/4, 1/2, 1, 2, 3, 5, 7, 10, 20, 30.I use linear interpolation to get the yield of intermediate maturities. Transactions for which the spread isnegative are not included in the sample. The top and bottom one percent of the distribution is trimmed.

AAA AA A BBB BB B CCC-D

Panel A: Breakdown by Time to Maturity (in years)

Short (0-4) 77 67 103 158 343 429 931Medium [4-10) 77 80 111 235 412 558 942Long (≥ 10) 82 127 163 256 400 537 859

Panel B: Breakdown by Year

2004-2010 79 85 126 214 379 502 8962004 53 54 80 125 293 348 11852005 57 62 86 128 276 397 6962006 77 83 115 166 266 407 5442007 149 168 265 404 699 798 11152008 130 156 234 465 721 814 11322009 149 168 265 404 699 798 11152010 130 156 234 465 721 814 1132

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Table 4: LOT Measure with TRACE Data

This table presents estimation results for the parameters of the modified LOT model of Chen, Lesmond, andWei (2007). The model is estimated bond by bond on a yearly basis. To be included in the estimation, abond must trade at least 10 times in a given year. The betas are the average estimated factor loadings. Thealphas are the average estimates of the positive and negative thresholds. The lot measure is the differencebetween the two thresholds, i.e. the sum of the buy-side and sell-side transaction costs. The table alsoreports the number of bonds in each rating-maturity category.

AAA AA A BBB BB B CCC-D

Panel A: Short Maturity (1-7 years)

Bond Factor (β1) -0.2770 -0.5891 -0.6046 -0.7533 0.2402 -0.0738 -0.1849Equity Factor (β2) 0.1446 -0.0294 0.0203 0.0120 0.0689 -0.0402 -0.0325LOT = αb − αs 642 330 650 1258 1546 1149 2723N (Bond-Years) 51 196 828 735 195 102 82

Panel B: Medium Maturity (7-15 years)

Bond Factor (β1) -0.7260 -0.5243 -0.8250 -0.8254 0.0881 -0.8001 0.3438Equity Factor (β2) 0.0093 -0.0039 0.0052 0.0034 0.0120 0.0196 0.0460LOT = αb − αs 741 1757 1860 1720 1508 1803 2802N (Bond-Years) 30 43 223 314 73 48 58

Panel C: Long Maturity (more than 15 years)

Bond Factor (β1) -0.6385 -0.7452 -0.7056 -0.7045 -0.2319 -0.3226 0.2224Equity Factor (β2) 0.0069 -0.0015 -0.0029 -0.0011 0.0099 0.0323 0.0463LOT = αb − αs 1041 1979 1916 2191 2129 1425 1578N (Bond-Years) 33 71 428 455 91 51 67

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Table 5: Friction Model

This table presents average estimation results for the factor loadings and round-trip liquidity costs of thefriction model. The results are grouped by rating and time to maturity as of the beginning of the year. Themodel is estimated a yearly basis on two groups of bonds: investment-grade and speculative-grade. To beincluded in the estimation, a bond must trade at least 10 times in a given year. “LOT”, is the estimatedround-trip liquidity cost as of the end of the year.

AAA AA A BBB BB B CCC-D

Short Maturity (1-7 years)

Bond Market -0.2478 -0.2653 -0.2569 -0.2395 -0.0556 -0.0619 -0.0480Firm Equity 0.0007 0.0007 0.0007 0.0009 0.0079 0.0104 0.0164Realized Volatility 0.0001 0.0002 0.0001 0.0001 0.0022 0.0020 0.0023“LOT” = αb − αs 109 117 153 195 440 322 385

N (Bond-Years) 51 196 828 735 195 102 82

Medium Maturity (7-15 years)

Bond Market -0.3033 -0.2357 -0.2141 -0.2231 -0.0660 -0.0385 -0.0122Firm Equity 0.0009 0.0010 0.0007 0.0009 0.0055 0.0075 0.0098Realized Volatility 0.0007 0.0000 -0.0002 -0.0000 0.0039 0.0026 0.0043“LOT” = αb − αs 105 217 239 222 376 395 402

N (Bond-Years) 30 43 223 314 73 48 58

Long Maturity (more than 15 years)

Bond Market -0.2153 -0.2013 -0.1917 -0.1793 -0.0618 -0.0324 -0.0179Firm Equity 0.0008 0.0010 0.0004 0.0015 0.0036 0.0060 0.0142Realized Volatility -0.0006 -0.0005 -0.0001 -0.0001 0.0019 0.0021 0.0040“LOT” = αb − αs 152 215 213 223 427 373 244

N (Bond-Years) 33 71 428 455 91 51 67

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Table 6: Regression Variables

This table reports summary statistics of the variables used in the regression analysis of the paper. CreditSpreads are end-of-month credit spreads; Friction is the monthly round-trip liquidity cost measure from theproposed friction model; LOT is the yearly round-trip liquidity most from the modified LOT model; Roll isdefined as twice the square root of the negative autocovariance of log bond price changes; Amihud is a priceimpact measure (Amihud (2002)); IRC is a TRACE-based measure of round-trip trading costs (Feldhutter(2011)); Realized Volatility is monthly average of daily realized volatility defines at the sum of 5-minutesquared returns (returns are obtained from 5-minute mid quotes); Diffusion Risk and Jump Risk are thetwo components of realized volatility; Age, Maturity, Issue Size, and Coupon are self-explanatory; Rating isvariable going from 1 (AAA) to 22 (D), which is transformed to Rating-10 in the regressions for the speculativegrade sample; Pretax Interest Coverage is defined as (income before depreciation+interest)/interest; Incometo Sale is equal to (income after depreciation)/sales; LT Debt/Assets is self-explanatory; Market Leverage isequal to (total long-term debt + debt in current liabilities +average short-term borrowing)/(total liabilities+market value of equity (from CRSP)); Treasury (1y) is the one-year constant maturity treasury rate; TermSp. is the difference between the 10-year and 2-year constant-maturity treasury rates; TED Sp. is thedifference between the 30-day Eurodollar and treasury rates.

Variables Mean St. Dev. P5 P25 P50 P75 P95

Credit Spreads 0.022 0.025 0.003 0.007 0.014 0.026 0.068Friction 0.019 0.018 0.003 0.007 0.015 0.024 0.05LOT 0.09 0.127 0.002 0.009 0.032 0.09 0.376Zero 0.489 0.303 0 0.227 0.524 0.762 0.909Roll 0.901 0.753 0.105 0.355 0.692 1.243 2.368Amihud 0.467 0.743 0.001 0.061 0.218 0.577 1.693IRC 0.006 0.006 0 0.002 0.005 0.009 0.017Realized Volatiltiy 0.014 0.008 0.007 0.009 0.011 0.016 0.03Diffusion Risk 0.014 0.008 0.007 0.009 0.011 0.015 0.03Jump Risk 0.008 0.005 0.004 0.005 0.007 0.009 0.018Age 0.808 0.386 0.158 0.556 0.784 1.084 1.465Maturity 0.718 0.639 0.036 0.167 0.466 1.285 1.884Issue Size (log) 12.41 0.82 11.48 11.918 12.429 12.835 13.816Coupon 0.071 0.015 0.044 0.064 0.071 0.08 0.095Credit Rating 7.927 3.555 3 6 8 10 15Pretax Interest Coverage 9.897 21.041 1.58 3.877 6.218 10.616 28.222Income to Sale 0.199 0.124 0.05 0.113 0.172 0.276 0.403LT Debt/Assets 0.247 0.124 0.084 0.166 0.228 0.307 0.456Market Leverage 0.22 0.137 0.057 0.124 0.19 0.287 0.494Treaury (1y) 0.029 0.017 0.003 0.016 0.033 0.047 0.051Term Sp. (10y-2y) 0.01 0.01 -0.001 0.001 0.008 0.019 0.026TED Sp. (30-day) 0.006 0.007 0.001 0.002 0.003 0.006 0.018

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Table 7: Liquidity and Credit Spreads

This table presents uni-variate regressions of credit spreads on six different liquidity measures. The regres-sions are estimated on two groups of bonds (investment- and speculative-grade bonds). Variables definitionsare in Table 6. Robust t-stats, clustered by issuer, are in parenthesis.

Model(1) (2) (3) (4) (5) (6)

PANEL A: Investment Grade Bonds

Friction 0.4270*(12.30)

LOT 0.0290*(8.16)

Zero 0.0050*(3.33)

Roll 0.0060*(10.92)

Amihud 0.0050*(10.80)

IRC 0.8300*(10.43)

R2 0.132 0.054 0.01 0.083 0.053 0.087N 27357 27357 27371 19794 25842 25260

PANEL B: Speculative Grade Bonds

Friction 0.1990†

(2.09)LOT 0.0500†

(2.52)Zero -.0100

(-1.20)Roll 0.0090*

(3.55)Amihud 0.0110*

(4.36)IRC 1.7770*

(6.92)R2 0.027 0.042 0.008 0.029 0.052 0.101N 5734 5734 5831 4419 5549 5403

† significant at 5%; * significant at 1%

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Table 8: Volatility and Credit Spreads

This table presents uni-variate regressions of credit spreads on several equity volatility measures. Theregressions are estimated on two groups of bonds (investment- and speculative-grade bonds). Variablesdefinitions are in Table 6. Robust t-stats, clustered by issuer, are in parenthesis.

Model(1) (2) (3) (4)

Panel A: Investment Grade Bonds

Historical Volatility 1.15*17.44

Realized Volatility (1w) 1.37*( 18.17)

Realized Volatility (1m) 1.47*( 19.92)

Diffusion Risk (1m) 1.23*( 15.00)

Jump Risk (6m) 0.71*( 5.89)

R2 0.49 0.42 0.49 0.51N 27764 27764 27764 27764

Panel B: Speculative Grade Bonds

Historical Volatility 1.58*7.72

Realized Volatility (1w) 2.25*( 16.97)

Realized Volatility (1m) 2.46*( 17.55)

Diffusion Risk (1m) 1.52*( 5.42)

Jump Risk (6m) 1.80*( 3.60)

R2 0.45 0.43 0.51 0.51N 5810 5810 5810 5810

† significant at 5%; * significant at 1%

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Table 9: Credit Spreads Determinants

This table presents multi-variate regressions of credit spreads on liquidity measure, volatility, and other controls. The regressions are estimated on two groups of bonds(investment- and speculative-grade bonds). Variables definitions are in Table 6. Robust t-stats, clustered by issuer, are in parenthesis.

Investment Grade Speculative Grade

Friction LOT Zero Roll Amihud IRC Friction LOT Zero Roll Amihud IRC

Liquidity 0.069* 0.002 0.001 0.000* 0.001* 0.119* 0.001 0.013 0.001 0.003* 0.003* 0.496*(2.86) (1.08) (0.90) (3.65) (4.61) (6.26) (0.04) (1.45) (0.26) (3.27) (3.71) (3.20)

Real. Volatiltiy 1.031* 1.043* 1.041* 1.072* 1.040* 1.040* 1.503* 1.483* 1.507* 1.591* 1.509* 1.484*(14.21) (14.71) (14.95) (14.10) (14.80) (14.84) (7.70) (7.68) (7.86) (6.79) (7.90) (7.57)

Bond CharacteristicsAge 0.005* 0.005* 0.005* 0.005* 0.005* 0.005* 0.010† 0.010† 0.010† 0.007 0.008 0.008

(7.92) (7.96) (8.25) (6.50) (7.68) (7.29) (2.01) (1.99) (1.99) (1.45) (1.93) (1.79)Maturity 0.003* 0.003* 0.003* 0.003* 0.003* 0.002* 0.006* 0.006* 0.006* 0.005* 0.005* 0.004*

(10.46) (10.74) (10.66) (10.83) (10.92) (10.51) (5.90) (4.55) (5.65) (4.15) (4.76) (3.38)Issue Size (log) 0.000 -0.001† 0.000 -0.001† -0.001* -0.001† -0.001 0.000 0.000 0.000 0.000 -0.001

(-0.69) (-2.30) (-1.94) (-2.55) (-2.66) (-2.45) (-0.73) (0.10) (-0.33) (-0.36) (-0.40) (-0.87)Coupon -0.013 -0.010 -0.012 -0.007 -0.005 -0.001 0.065 0.039 0.076 0.157 0.127 0.139

(-0.84) (-0.62) (-0.73) (-0.39) (-0.33) (-0.08) (0.64) (0.37) (0.78) (1.68) (1.45) (1.51)Credit Rating 0.002* 0.002* 0.002* 0.002* 0.002* 0.002* 0.002 0.002 0.001 0.001 0.001 0.001

(4.77) (4.96) (4.99) (4.93) (4.94) (4.96) (1.44) (1.50) (1.38) (1.16) (1.41) (1.37)

Firm Accounting VariablesInt Cov < 5) -0.003 -0.003 -0.004† -0.004 -0.004 -0.004 -0.011† -0.009 -0.008 -0.022* -0.009 -0.009

(-1.68) (-1.86) (-1.97) (-1.94) (-1.87) (-1.90) (-2.12) (-1.70) (-1.05) (-3.59) (-1.32) (-1.48)Int Cov [5,10) -0.001 -0.001 -0.001 -0.001 -0.001 -0.001 -0.008 -0.006 -0.005 -0.019* -0.006 -0.007

(-0.74) (-0.85) (-0.94) (-0.87) (-0.84) (-0.88) (-1.80) (-1.27) (-0.67) (-3.18) (-0.97) (-1.10)Int Cov [10,20) -0.001 -0.001 -0.001 -0.002 -0.001 -0.001 -0.006 -0.003 -0.002 -0.016† -0.004 -0.005

(-1.02) (-1.07) (-1.03) (-1.11) (-1.02) (-1.09) (-1.15) (-0.63) (-0.29) (-2.20) (-0.66) (-0.82)Inc to Sale -0.021 -0.020 -0.020† -0.020† -0.020† -0.021† -0.031 -0.028 -0.029 -0.030 -0.027 -0.029

(-1.92) (-1.88) (-2.01) (-2.14) (-2.03) (-2.06) (-1.13) (-1.05) (-1.04) (-1.02) (-1.05) (-1.12)LT Debt/Assets -0.023* -0.023* -0.024* -0.020† -0.024* -0.023* -0.089* -0.089* -0.085* -0.080† -0.084* -0.079*

(-3.13) (-3.21) (-3.26) (-2.60) (-3.18) (-3.10) (-3.15) (-3.07) (-2.85) (-2.44) (-2.90) (-2.73)Market Leverage 0.055* 0.055* 0.054* 0.054* 0.054* 0.054* 0.115* 0.115* 0.111* 0.105* 0.110* 0.101*

(6.35) (6.43) (6.33) (5.89) (6.29) (6.29) (5.22) (5.16) (4.95) (4.04) (4.95) (4.25)

Macroeconomic VariablesTreaury (1y) -0.382* -0.405* -0.416* -0.406* -0.419* -0.416* -0.816* -0.820* -0.786* -0.647† -0.746* -0.746*

(-9.12) (-10.33) (-10.60) (-9.76) (-10.62) (-10.67) (-3.52) (-3.42) (-3.19) (-2.59) (-3.05) (-3.17)Term Sp. (10y-2y) -0.514* -0.536* -0.549* -0.552* -0.559* -0.558* -0.775† -0.803† -0.707† -0.467 -0.661 -0.624

(-8.19) (-8.97) (-9.21) (-8.92) (-9.41) (-9.57) (-2.28) (-2.29) (-2.00) (-1.19) (-1.79) (-1.76)TED Sp. (30-day) 0.155* 0.172* 0.171* 0.169* 0.172* 0.175* 0.199 0.186 0.199 0.238 0.205 0.228

(4.58) (5.00) (4.93) (4.39) (4.92) (4.94) (1.57) (1.48) (1.58) (1.77) (1.73) (1.92)

R2 0.716 0.715 0.711 0.736 0.714 0.716 0.737 0.738 0.731 0.737 0.735 0.741N 27054 27054 27268 19743 25754 25177 5661 5661 5666 4321 5395 5253

† significant at 5%; * significant at 1%

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Table 10: Jump Risk and Yield Spreads

This table presents multi-variate regressions of credit spreads on liquidity measure, volatility, and other controls. The regressions are estimated on twogroups of bonds (investment- and speculative-grade bonds). Variables definitions are in Table 6. Robust t-stats, clustered by issuer, are in parenthesis.

Investment Grade Speculative GradeFriction LOT Zero Roll Amihud IRC Friction LOT Zero Roll Amihud IRC

Liquidity 0.059† 0.001 0.001 0.000* 0.001* 0.111* -0.019 0.010 0.001 0.003* 0.003* 0.485*(2.53) (1.08) (0.93) (3.57) (4.39) (5.81) (-0.47) (0.93) (0.29) (3.28) (3.76) (3.11)

DIffusion Risk 0.959* 0.965* 0.960* 0.999* 0.960* 0.962* 0.988* 0.978* 0.983* 1.028* 0.994* 0.975*(11.81) (11.98) (12.19) (11.82) (12.09) (12.11) (4.36) (4.34) (4.31) (3.92) (4.36) (4.16)

Jump Risk 0.331* 0.347* 0.358* 0.327* 0.358* 0.351* 1.103* 1.067* 1.089* 1.129* 1.059* 1.039*(3.28) (3.44) (3.58) (3.13) (3.43) (3.35) (4.90) (4.79) (5.11) (4.72) (4.79) (4.51)

Bond CharacteristicsAge 0.004* 0.005* 0.005* 0.004* 0.005* 0.004* 0.010† 0.010† 0.010† 0.007 0.009 0.008

(7.67) (7.65) (7.97) (6.16) (7.37) (7.00) (2.05) (2.04) (2.01) (1.47) (1.97) (1.80)Maturity 0.003* 0.003* 0.003* 0.003* 0.003* 0.002* 0.006* 0.006* 0.006* 0.005* 0.005* 0.004*

(11.05) (11.25) (11.06) (11.08) (11.21) (10.61) (6.18) (4.76) (5.80) (4.28) (4.93) (3.52)Issue Size (log) 0.000 -0.001† 0.000† -0.001* -0.001* -0.001* -0.002 -0.001 -0.001 -0.001 -0.001 -0.001

(-1.03) (-2.49) (-2.05) (-2.78) (-2.93) (-2.75) (-1.35) (-0.47) (-0.68) (-0.83) (-0.89) (-1.47)Coupon -0.008 -0.005 -0.007 -0.002 0.000 0.003 0.067 0.041 0.070 0.156 0.123 0.134

(-0.50) (-0.31) (-0.42) (-0.12) (-0.03) (0.22) (0.65) (0.39) (0.70) (1.65) (1.38) (1.44)Credit Rating 0.002* 0.002* 0.002* 0.002* 0.002* 0.002* 0.001 0.001 0.001 0.000 0.001 0.001

(4.91) (5.07) (5.07) (5.05) (5.03) (5.06) (0.72) (0.80) (0.67) (0.42) (0.68) (0.65)

Firm Accounting VariablesInt Cov < 5) -0.003 -0.003 -0.003 -0.004 -0.003 -0.003 -0.008 -0.005 -0.004 -0.018* -0.005 -0.005

(-1.57) (-1.69) (-1.75) (-1.76) (-1.65) (-1.69) (-1.53) (-1.03) (-0.46) (-3.57) (-0.74) (-0.94)Int Cov [5,10) -0.001 -0.001 -0.001 -0.001 -0.001 -0.001 -0.004 -0.001 0.000 -0.015* -0.001 -0.002

(-0.66) (-0.73) (-0.77) (-0.73) (-0.68) (-0.71) (-0.80) (-0.28) (0.05) (-2.70) (-0.19) (-0.37)Int Cov [10,20) -0.001 -0.001 -0.001 -0.002 -0.001 -0.001 -0.002 0.000 0.003 -0.013† -0.001 -0.002

(-1.07) (-1.08) (-1.01) (-1.11) (-1.00) (-1.06) (-0.40) (0.08) (0.34) (-2.03) (-0.08) (-0.29)Inc to Sale -0.021 -0.021 -0.020† -0.021† -0.021† -0.021† -0.025 -0.023 -0.024 -0.030 -0.024 -0.025

(-1.93) (-1.89) (-2.00) (-2.11) (-2.02) (-2.03) (-1.06) (-0.96) (-1.01) (-1.19) (-1.05) (-1.13)LT Debt/Assets -0.022* -0.023* -0.023* -0.020* -0.023* -0.022* -0.088* -0.088* -0.084* -0.083* -0.084* -0.080*

(-3.09) (-3.16) (-3.20) (-2.60) (-3.12) (-3.05) (-3.24) (-3.08) (-2.94) (-2.71) (-3.04) (-2.88)Market Leverage 0.052* 0.052* 0.051* 0.050* 0.050* 0.050* 0.114* 0.113* 0.110* 0.108* 0.110* 0.101*

(5.90) (5.94) (5.83) (5.42) (5.80) (5.81) (5.36) (5.18) (5.10) (4.38) (5.11) (4.43)

Macroeconomic VariablesTreaury (1y) -0.331* -0.348* -0.358* -0.354* -0.361* -0.360* -0.774* -0.772* -0.737* -0.603† -0.704† -0.705*

(-7.31) (-8.02) (-8.24) (-7.84) (-8.20) (-8.21) (-3.02) (-2.91) (-2.74) (-2.20) (-2.61) (-2.71)Term Sp. (10y-2y) -0.445* -0.461* -0.473* -0.482* -0.482* -0.483* -0.741† -0.769† -0.677 -0.448 -0.644 -0.604

(-6.52) (-6.96) (-7.14) (-7.17) (-7.24) (-7.32) (-1.99) (-2.01) (-1.76) (-1.07) (-1.61) (-1.57)TED Sp. (30-day) 0.167* 0.181* 0.179* 0.175* 0.180* 0.183* 0.369† 0.347† 0.363† 0.425* 0.366† 0.387*

(4.64) (4.96) (4.88) (4.33) (4.86) (4.88) (2.42) (2.30) (2.43) (2.73) (2.57) (2.72)

R2 0.721 0.72 0.715 0.74 0.718 0.72 0.739 0.74 0.733 0.739 0.737 0.742N 26893 26893 27109 19629 25607 25037 5628 5628 5635 4297 5365 5223

† significant at 5%; * significant at 1%

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Table 11: Yield Spreads And the Crisis

This table presents multi-variate regressions of credit spreads on liquidity measure, volatility, and other controls. The regressions are estimated ontwo sub-samples (normal Vs crisis times). Variables definitions are in Table 6. Robust t-stats, clustered by issuer, are in parenthesis.

Normal Times CrisisFriction LOT Zero Roll Amihud IRC Friction LOT Zero Roll Amihud IRC

Liquidity 0.067 0.007 -0.001 0.001* 0.001* 0.197* 0.002 0.002 0.001 0.000 0.001* 0.209*(1.47) (1.64) (-0.68) (3.48) (5.02) (3.96) (0.04) (0.29) (0.60) (0.75) (2.99) (2.89)

DIffusion Risk 0.622* 0.624* 0.617* 0.625* 0.610* 0.591* 0.873* 0.872* 0.877* 0.947* 0.882* 0.882*(4.14) (4.15) (4.10) (3.48) (4.00) (3.86) (10.39) (10.30) (10.52) (9.61) (10.53) (10.65)

Jump Risk 0.650* 0.662* 0.677* 0.712* 0.687* 0.673* 0.607† 0.607† 0.604† 0.559† 0.570† 0.558†

(4.32) (4.56) (4.84) (4.29) (4.65) (4.57) (2.38) (2.39) (2.38) (2.24) (2.33) (2.27)

Bond CharacteristicsAge 0.006* 0.006* 0.006* 0.005* 0.005* 0.005* 0.004† 0.004 0.004† 0.003 0.004 0.003

(5.04) (5.37) (5.57) (4.91) (5.80) (5.49) (2.03) (1.95) (2.03) (1.36) (1.97) (1.62)Maturity 0.004* 0.004* 0.004* 0.004* 0.004* 0.003* 0.000 0.000 0.000 0.000 -0.001 -0.002†

(11.63) (8.94) (12.26) (11.04) (12.17) (9.93) (-0.03) (-0.15) (-0.60) (-0.48) (-1.32) (-2.03)Issue Size (log) 0.000 0.000 -0.001 0.000 0.000 0.000 -0.002 -0.002 -0.001 -0.002 -0.002 -0.002

(-0.50) (-0.46) (-1.88) (-1.64) (-1.90) (-1.68) (-1.25) (-1.35) (-1.09) (-1.53) (-1.51) (-1.81)Coupon -0.026 -0.028 -0.012 0.000 -0.007 -0.005 0.045 0.042 0.040 0.085 0.050 0.078

(-0.96) (-1.01) (-0.43) (0.02) (-0.29) (-0.19) (0.77) (0.71) (0.74) (1.30) (0.97) (1.59)Credit Rating 0.002* 0.002* 0.002* 0.002* 0.002* 0.002* 0.004* 0.004* 0.004* 0.005* 0.004* 0.004*

(6.18) (6.24) (5.95) (5.30) (5.82) (5.97) (2.75) (2.74) (3.37) (4.74) (3.75) (4.19)

Firm Accounting VariablesInt Cov < 5) -0.004 -0.004† -0.004† -0.003 -0.004 -0.004 -0.001 -0.001 0.000 0.001 0.001 0.000

(-1.90) (-1.98) (-2.00) (-1.61) (-1.86) (-1.87) (-0.09) (-0.09) (0.04) (0.18) (0.12) (0.08)Int Cov [5,10) -0.001 -0.001 -0.001 -0.001 -0.001 -0.001 0.001 0.001 0.001 0.003 0.002 0.002

(-0.97) (-1.10) (-1.10) (-0.65) (-0.92) (-0.92) (0.15) (0.16) (0.29) (0.53) (0.34) (0.31)Int Cov [10,20) -0.001 -0.001 -0.001 -0.001 -0.001 -0.001 -0.002 -0.002 -0.001 -0.002 -0.002 -0.002

(-0.70) (-0.76) (-0.82) (-0.65) (-0.72) (-0.77) (-0.59) (-0.59) (-0.33) (-0.56) (-0.53) (-0.55)Inc to Sale -0.021† -0.022† -0.023* -0.023* -0.023* -0.023* -0.048 -0.048 -0.046 -0.038 -0.044 -0.046

(-2.45) (-2.47) (-2.78) (-2.68) (-2.77) (-2.69) (-1.65) (-1.65) (-1.61) (-1.40) (-1.56) (-1.59)LT Debt/Assets -0.038† -0.039† -0.036† -0.035† -0.036† -0.036† -0.074* -0.074* -0.075* -0.071* -0.075* -0.072*

(-2.40) (-2.40) (-2.28) (-1.98) (-2.31) (-2.27) (-3.14) (-3.11) (-3.03) (-2.77) (-3.03) (-2.87)Market Leverage 0.059* 0.060* 0.058* 0.059* 0.058* 0.057* 0.126* 0.126* 0.122* 0.125* 0.121* 0.118*

(5.62) (5.61) (5.60) (5.20) (5.52) (5.57) (4.68) (4.65) (4.47) (4.27) (4.38) (4.21)

Macroeconomic VariablesTreaury (1y) -0.235* -0.253* -0.247* -0.246* -0.250* -0.250* -0.549* -0.548* -0.570* -0.512* -0.567* -0.570*

(-4.55) (-4.28) (-4.21) (-4.35) (-4.37) (-4.55) (-5.47) (-5.67) (-5.89) (-5.00) (-5.87) (-5.93)Term Sp. (10y-2y) -0.234* -0.252* -0.242* -0.255* -0.249* -0.249* -0.799* -0.799* -0.812* -0.765* -0.816* -0.817*

(-2.93) (-2.96) (-2.93) (-3.12) (-3.03) (-3.18) (-4.97) (-4.89) (-4.78) (-4.24) (-4.77) (-4.77)TED Sp. (30-day) 0.136* 0.155* 0.174* 0.153* 0.171* 0.173* 0.126* 0.126* 0.117* 0.127* 0.122* 0.127*

(3.10) (3.70) (3.95) (2.93) (3.99) (3.97) (3.53) (3.50) (3.26) (3.32) (3.39) (3.51)

R2 0.791 0.791 0.788 0.806 0.793 0.795 0.778 0.778 0.769 0.786 0.772 0.776N 25166 25166 25272 18574 23863 23269 7355 7355 7472 5352 7109 6991

† significant at 5%; * significant at 1%

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−100

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(b) Empirical CDF

Figure 1: Distribution of Corporate Bond ReturnsThis figure presents the distribution of corporate bond returns by rating (left) and their empirical cumulative distribution function. The Figurepresents two ways of computing daily returns. Following a period of no trading, the top panel assumes that all the returns is realized on the lastday of no trading. The bottom panels assume that the returns are realized uniformly over the no-trading period. Returns computed on consecutivetrading days are not affected by this assumption.

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2004 2005 2006 2007 2008 2009 20100.01

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Figure 2: Timeseries Variation of Liquidity CostsThis figure presents average estimated liquidity cost by rating. The top panel presents results for the Frictionmodel; the bottom panel presents results for the LOT model.

47