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Corporate Yield Spreads and Bond Liquidity

Long Chen

Department of Finance

Michigan State University

chen@bus.msu.edu

(517) 353-2955

David A. Lesmond

A.B. Freeman School of Business

Tulane University

dlesmond@tulane.edu

(504) 865-5665

Jason Wei

Rotman School of Management

University of Toronto

wei@Rotman.Utoronto.Ca

(416) 287-7332

April 21, 2005

This paper is based on an earlier version entitled “An Indirect Estimate of Transaction Costs for

Corporate Bonds.” We thank conference participants at the 2001 FMA and 2003 AFA meetings, and the 14th

Annual Conference on Finance and Accounting at Indiana University. We also thank seminar participants

at Beijing University, Louisiana State University, Michigan State University, the University of New Orleans,

and York University for their helpful comments. Sincere thanks go to (especially) Yakov Amihud, Laurence

Booth, Kirt Butler, Melanie Cao, John Hull, Raymond Kan, Madhu Kalimipalli, Tom McMcurdy, Gordon

Roberts, Chester Spatt, Yisong Tian, Alan White, and Xiaoyun Yu for their constructive comments. We

wish to thank Andre Haris, Lozan Bakayatov, and Davron Yakubov for their excellent data collection eﬀorts.

In addition, we thank the ﬁnancial assistance of the Social Sciences and Humanities Research Council of

Canada. All errors remain the responsibility of the authors.

Corporate Yield Spreads and Bond Liquidity

Abstract

We examine whether liquidity is priced in corporate yield spreads. Using a battery

of liquidity measures covering over 4000 corporate bonds and spanning investment grade

and speculative categories, we ﬁnd that more illiquid bonds earn higher yield spreads; and

that an improvement of liquidity causes a signiﬁcant reduction in yield spreads. These

results hold after controlling for common bond-speciﬁc, ﬁrm-speciﬁc, and macroeconomic

variables, and are robust to issuers’ ﬁxed eﬀect and potential endogeneity bias. Our ﬁnding

mitigates the concern in the default risk literature that neither the level nor the dynamic

of yield spreads can be fully explained by default risk determinants, and suggests that

liquidity plays an important role in corporate bond valuation.

Introduction

A number of recent studies (Collin-Dufresne, Goldstein, and Martin, 2001, and Huang and

Huang, 2003) indicate that neither levels nor changes in the yield spread of corporate bonds

over treasury bonds can be fully explained by credit risk determinants proposed by structural

form models. Illiquidity is acknowledged as a possible explanation for the failure of these models

to more properly capture the yield spread variation (Longstaﬀ, Mithal, and Neis, 2004). Yet

much of the current literature abstracts from liquidity’s inﬂuence (Elton, Gruber, Agrawal,

and Mann, 2001), focuses on aggregate liquidity proxies (Grinblatt, 1995, Duﬃe and Singleton,

1997, Collin-Dufresne et al., 2001, and Campbell and Taksler, 2003) or simply assumes that the

unexplained portion of the yield spread is liquidity based (Duﬀee, 1999). This paper attempts

to ﬁll this void by comprehensively assessing bond-speciﬁc liquidity for a broad spectrum of

corporate investment grade and speculative grade bonds and by examining the association

between bond-speciﬁc liquidity estimates and corporate bond yield spreads.

The notion that investors demand a liquidity premium for illiquid securities dates back to

Amihud and Mendelson (1986). Lo, Mamaysky, and Wang (2004) further argue that liquidity

costs inhibit the frequency of trading. Because investors cannot continuously hedge their risk,

they demand an ex-ante risk premium by lowering security prices. Therefore, for the same

promised cash ﬂows, less liquid bonds will be traded less frequently, have lower prices, and

exhibit higher yield spreads. Thus, the theoretical prior is that liquidity is expected to be

priced in yield spreads. We investigate bond-speciﬁc liquidity eﬀects on the yield spread using

three separate liquidity measures. These include the bid-ask spread, the liquidity proxy of zero

1

returns, and a liquidity estimator based on a model variant of Lesmond, Ogden, and Trzcinka

(1999). We ﬁnd that liquidity is indeed priced in both levels and changes of the yield spread.

Contemporaneous studies by Longstaﬀ et al. (2004) and Ericsson and Renault (2002) also

relate corporate bond liquidity to yield spreads. However, Longstaﬀ et al. (2004) focus only on

68 issuers that have liquid default-swap trading data, leaving some doubt as to the generality

of the results for the larger universe of corporate bonds. Ericsson and Renault (2002) focus on

a theoretical model and they simply use a new issue dummy as their empirical bond-speciﬁc

liquidity measure. However, this liquidity proxy will not shed light on the liquidity diﬀerence

spanning corporate bonds, nor provide liquidity measures for more mature bonds. We provide

extensive bond-speciﬁc liquidity measures for over 4000 corporate bonds spanning investment

and speculative grade categories over a nine year period allowing for a more comprehensive

assessment of the relation between liquidity and yield spreads.

Historically, the lack of credible information on spread prices1or bond quotes has been

a major impediment in the analysis of liquidity (Goodhart and O’Hara, 1997) and liquidity’s

impact on yield spreads. We employ Bloomberg and Datastream to provide our three liquidity

estimates. Among them, the bid-ask spread is arguably the most demonstrable measure of

liquidity costs, while the percentage of zero returns is increasingly used as a liquidity proxy in

1Liquidity’s importance is well recognized by academics, regulators, and bond traders. Arthur Levitt, as the

Chairman of the Securities and Exchange Commission, notes that “the sad truth is that investors in the corporate

bond market do not enjoy the same access to information as a car buyer or a home buyer or, I dare say, a fruit

buyer. Improving transparency is a top priority for us” (Wall Street Journal, 9/10/1998). Greg Ip of the Wall

Street Journal notes that “the bond market’s biggest worry these days isn’t default or interest rates. It’s illiquidity

that is crippling the very workings of the market” (Wall Street Journal, 10/19/1998). Reﬂecting on bond liquidity

concerns, the NASD has recently instituted TRACE (Trade Reporting and Compliance Engine) which provides

real-time quote estimates for 4200 corporate bond issues (Wall Street Journal, 3/14/2003).

2

a host of empirical studies.2Despite the clear intuition surrounding the zero return proxy, it is

a noisy measure of liquidity, since it is the combination of a zero return and the simultaneous

movement of bond price determinants that more properly estimates liquidity costs, not the lack

of price changes per se.

To more properly capture this notion, we employ the limited dependent variable model

proposed by Lesmond, Ogden, and Trzcinka (1999) (hereafter, LOT) to obtain an alternative

liquidity estimate.3The premise of the LOT model is that, while the true value of the bond

is driven by many stochastic factors, measured prices will reﬂect new information only if the

information value of the marginal trader exceeds the total liquidity costs. This implies that a

liquidity cost threshold exists for each bond, which is equivalent to the minimum information

value for a trade. Within the liquidity cost threshold, the probability of observing a zero return

is higher than outside the liquidity cost threshold. We use a maximum likelihood method to

jointly estimate the risk factors related to market-wide information and the upper and lower

liquidity thresholds that, taken as a whole, represent round-trip liquidity costs.

We ﬁnd a signiﬁcant association between corporate bond liquidity and the yield spread with

each of the three liquidity measures. Depending on the liquidity measure, liquidity alone can

explain as much as 7% of the cross-sectional variation in bond yields for investment grade bonds,

2Theoretically, it is well known that in the presence of transaction costs, investors will trade infrequently

(Constantinides, 1986), and thus the magnitude of the proportion of zero returns is representative of illiquidity.

Empirically, this measure has been found to be an eﬀective liquidity measure in the U.S. equity market (e.g.,

Lesmond, Schill, and Zhou, 2004) and in the emerging market for equities where the lack of liquidity-related

information remains a challenge (e.g., Bekaert, Lundblad, and Campbell, 2003.)

3Lesmond et al. (1999) and Lesmond (2004) ﬁnd that this method works well for equity markets, as evidenced

by an 80% correlation between the LOT liquidity estimate and the bid-ask spread plus commissions. The proposed

LOT model does not rely on the use of bid-ask spread prices; instead, it uses only daily closing returns to estimate

liquidity costs. This method is also a natural extension of Glosten and Milgrom (1985), who illustrate that trades

will occur when the information value exceeds the transaction costs deﬁned by the bid-ask spread.

3

and 22% for speculative grade bonds. Using the bid-ask spread as the measure, we ﬁnd that

one basis point increase in bid-ask spread is related to 0.42 basis point increase in the yield

spread for investment grade bonds, and 2.30 basis point increase for speculative grade bonds.

Using either the bid-ask spread or the LOT estimate, the liquidity eﬀect remains signiﬁcant

even after we control for general yield spread factors such as credit rating, maturity, and the

amount outstanding; the tax eﬀect (Elton et al., 2001); the equity volatility (Merton, 1974,

and Campbell and Taksler, 2003); the accounting variables of Campbell and Taksler; and the

macroeconomic variables of Collin-Dufresne et al. (2001). The results are robust to issuer ﬁxed

eﬀects and potential endogeneity in yield spreads, liquidity, and credit ratings. The results

extend to the zero return liquidity proxy, but are most robust for investment grade bonds.

Extending the study to changes in yield spreads, we again ﬁnd a liquidity inﬂuence. Under all

three liquidity measures, an increase in illiquidity is signiﬁcantly and positively associated with

an increase in yield spreads regardless of controlling for changes in credit rating, macro-economic

inﬂuences, or ﬁrm-speciﬁc factors.

This paper contributes to the growing debate over bond market liquidity and corporate

yields. First, in the credit risk literature, it is common to assume that the yield spread, as

a whole, represents default risk. Practitioners frequently draw conclusions regarding default

probability from yield spreads. Our ﬁndings imply that this approach is inappropriate, as the

liquidity component in the yield spread is not directly related to default risk. Our results also

mitigate the concern that the yield spread overstates the default probability (e.g., Elton et al.,

2001, and Huang and Huang, 2003). Additionally, the high consistency between the traditional

4

model-independent measure, the bid-ask spread, and the model-dependent measure, the LOT

estimate, suggests that the latter, making use of return data only, can be an eﬀective tool

in bond liquidity studies. This is particularly meaningful for illiquid bonds where the lack of

liquidity-related information is common.

The paper is organized as follows. Section 1 introduces the liquidity measures and their

summary statistics. Section 2 presents model validation tests, the consistency among the

liquidity measures, and initial tests on the relation between liquidity and the yield spread.

Section 3 studies the relation between liquidity levels and yield spread levels. Section 4 presents

test results of changes in liquidity and changes in the yield spread. Section 5 concludes.

1. Liquidity Measures

The literature provides a menu of measures for estimating liquidity. The most demonstrable

measure is the bid-ask spread, but the spread is not always available for all bonds or for all

time periods. This is especially true for thinly traded bonds or oﬀ-the-run bonds. Additionally,

because our data is hand-collected, our quote information is gathered only on a quarterly basis

resulting in a less precise measure of liquidity. This is especially true if only a single quarterly

quote is available for the bond over an annual trading period.

Lesmond et al. (1999) introduce an alternative indirect method for estimating liquidity based

on the occurrence of zero returns. Bekaert et al. (2004) show that zero returns themselves are

a reasonable liquidity proxy. The LOT measure is a comprehensive estimate of liquidity by

including the spread and other costs that may impinge on informed trade, such as commission

costs, opportunity costs, and price impact costs. The maintained hypothesis is that the marginal

5

trader will trade only if the value of the information exceeds the marginal costs. If trading costs

are sizeable, Lesmond et al. (1999) argue that zero return days will occur more frequently

because new information must accumulate longer, on average, before informed trade aﬀects

price. They show that the LOT estimate is a more accurate measure of the underlying liquidity

costs than is the percentage of zero returns because the LOT measure extracts more information

from the return generating process.

A potential theoretical drawback of the LOT model is that it requires a return generating

model for bonds which the literature has yet to deﬁnitively prescribe. A practical limitation

is that the LOT model requires some zero returns to estimate liquidity’s eﬀect on the price.

For on-the-run bonds or bonds oﬀered mid-year, the sequence of prices may not reveal any zero

returns invalidating the LOT estimate. Conversely, too many zero returns (i.e. greater than

85% over the estimation period) also makes this measure inestimable. However, both the zero

return liquidity proxy and the LOT liquidity measure are presumed to be positively related to

the bid-ask spread.

Because of the strengths and weaknesses of each measure, we employ all three estimators to

determine the relation between corporate bond yield spreads and liquidity. This will not only

increase robustness, but also shed light on the relative power of each liquidity measure. If we

ﬁnd that all three liquidity measures lead to consistent inferences, then we can take comfort in

using the other two measures in situations where the bid-ask spread is not available. Bekaert et

al. (2003) is a case in point when they study the equity liquidity in emerging markets.

6

1.1 The bid-ask spread

Data on the quarterly bid-ask quotes are hand-collected from the Bloomberg Terminals. Most

quotes are available only from 2000 to 2003. For each quarter, we calculate the proportional

spread as the ask minus the bid divided by the average bid and ask price. The bond-year’s

proportional bid-ask spread is then calculated as the average of the quarterly proportional

spreads. To include as many bonds as possible, we compute the annual proportional spread as

long as there is at least one quarterly quote for the year. The bid-ask quotes recorded are the

Bloomberg Generic Quote which reﬂects the consensus quotes among market participants.

1.2 The percentage zeros and the LOT model

The LOT measure of informed trading utilizes only daily bond returns to estimate bond-level

liquidity costs. The eﬀect of liquidity is observable through the incidence of zero returns.

Datastream is used to provide prices, which, in turn, uses Merrill Lynch as the data source

for the price across all market makers for the bond. This feature will underestimate the number

of zero returns for each bond issue as the probability of observing a zero return is decreasing

with increasing numbers of market makers. Given that our model is predicated on days with no

price changes, we will understate our estimate of bond-speciﬁc liquidity costs, biasing against

our liquidity hypothesis. We choose the start date of 1995 since daily prices are more regularly

available through Datastream only after 1995. The data span a nine-year period ending in 2003.

We record the clean, non-matrix price of each bond on a daily basis, deleting prices that

deviate more than 50% from the prior day’s price. We separate the data into bond-years; that is,

7

using daily data for each bond within each year, we jointly estimate the bond’s return generating

function and liquidity costs applicable to that year. This allows time-series variations in the

bond liquidity estimates to be adequately represented.

To price corporate bonds, we extend the Lesmond et al. (1999) methodology to a two-factor

model. (Appendix A shows the theoretical basis for this approach.) The two factors are the

interest rate and the equity market return, reﬂecting the fact that a corporate bond is a hybrid

between a risk free bond and equity. Following Jarrow (1978), we scale all risk coeﬃcients by

duration to obtain stable estimation coeﬃcients. The return generating process is then given

as:

R∗

j,t =βj1Durationj,t ∗∆Rft +βj2Durationj,t ∗∆S&P Indext+j,t.(1)

The term R∗

j,t represents the unobserved “true” bond return for bond j and day t that investors

would bid given zero transaction costs. ∆Rft is the daily change in the ten-year, risk-free interest

rate. Following Cornell and Green (1991), ∆S&P Index is the daily return in the Standard &

Poor’s 500 index.4

Amihud and Mendelson (1986, 1987) develop a framework in which the intrinsic value of a

ﬁrm diﬀers from its observed value. Amihud and Mendelson (1986) attribute this diﬀerence to a

liquidity premium that requires higher cost assets to be priced lower to compensate investors for

liquidity costs. Extending Amihud and Mendelson (1986) to ﬁxed income securities, liquidity

eﬀects on bond returns can be stated as:

Rj,t =R∗

j,t −αi,j,(2)

4We also estimated the model using the Fama-French (1993) bond factors in the objective function. The results

are largely invariant to this speciﬁcation.

8

where Rj,t is the measured return, α2,j is the eﬀective buy side cost, and α1,j is the eﬀective

sell side cost for bond j. Thus, the desired return and the measured return are related, but

only after taking transaction costs into account. The eﬀect of liquidity on bond prices is then

modeled by combining the objective function with the liquidity constraint as:

R∗

j,t =βj1Durationj,t ∗∆Rft +βj2Durationj,t ∗∆S&P Indext+j,t.(3)

where:

Rj,t =R∗

j,t −α1,j if R∗

j,t <α

1,j and α1,j <0

Rj,t =0 if α1,j ≤R∗

j,t ≤α2,j

Rj,t =R∗

j,t −α2jif R∗

j,t >α

2,j and α2,j >0

The resulting log-likelihood function is stated as:

LnL =

X

1

Ln 1

(2πσ2

j)1/2−X

1

1

2σ2

j

(Rj+α1,j −βj1Durationj,t ∗∆Rft −βj2Durationj,t ∗∆S&P Indext)2

+X

2

Ln 1

(2πσ2

j)1/2−X

2

1

2σ2

j

(Rj+α2,j −βj1Durationj,t ∗∆Rft −βj2Durationj,t ∗∆S&P Indext)2

+X

0

Ln(Φ2,j −Φ1,j),(4)

where Φi,j represents the cumulative distribution function for each bond-year evaluated at (αi,j −

βj1Durationj,t ∗∆Rft −βj2Durationj,t ∗∆S&P Indext)/σj.P1(region 1) represents the negative

nonzero measured returns, P2(region 2) represents the positive nonzero measured returns, and

P0(region 0) represents the zero measured returns. Maddala (1983) and Lesmond et al. (1999)

outline the estimation procedure.

For purposes of liquidity estimation, we focus only on the α2,j and α1,j estimates. Taken in

diﬀerence form, α2,j −α1,j, represents the liquidity eﬀects on bond returns related to round-trip

transaction costs.

9

Implicitly, our model assumes that information motivates trade in bonds and that

information is eﬃciently impounded into bond prices. This assumption ﬁnds support from

Hotchkiss and Ronen (2002) who conclude that the informational eﬃciency of bond prices is

similar to that of the underlying equity. The marginal trader is assumed to assess the value

of information before deciding to trade relative to the expected liquidity costs. The marginal

trader with the highest net diﬀerence between the value of information and transaction costs will

drive price movements.5We do not impose any particular assumptions on whether the marginal

investor possesses public or private information; rather, we assume that prices should rationally

reﬂect the costs of trade relative to the information value of the trade. Unanticipated public

information, noise trades, or trades of idiosyncratic nature will not be priced in a rational asset

pricing framework and will only be captured, on average, in the error term.

1.3 Yield spreads and corporate information

We examine over 4000 U.S. corporate bonds. Datastream is used to provide yield spreads and

bond characteristics. We use the Fixed Income Securities Database to provide up-to-date credit

ratings for each bond, and when unavailable we use Standard and Poor’s rating on Datastream.

We delete bonds not rated by either S&P or the Fixed Income Securities Database. Finally, we

use the Compustat Annual Industrial database to collect all ﬁrm-level data for both active and

inactive ﬁrms to minimize any survivorship bias in the liquidity determinant and yield spread

regressions.6Each variable is collected in the year prior to the yield spread measurement. The

5The LOT model is consistent with the Kyle (1985) model. Speciﬁcally, Kyle assumes that the market maker is

risk neutral and allows for the market being composed of three trader types: informed, uninformed, and the market

maker. The LOT model is predicated on trades made by the marginal trader who could be informed, uninformed,

or even the market maker.

6We collect the operating income after depreciation (item 178) and the interest expense (item 15) to determine

10

equity volatility is estimated using 252 daily returns (from the CRSP ﬁle) for the year prior to

the bond liquidity estimate. The bond volatility is estimated similarly using bond prices.

2. Preliminary Findings

2.1 Summary statistics

Table 1 contains the summary statistics segregated by maturity levels and credit ratings.

Within each panel there are two sets. The ﬁrst set relates all the bond information for a

matching sample of zero returns and the LOT estimate, while the second presents information

for a matching sample of zero returns, the LOT estimate and the bid-ask spread. Several

observations are apparent. First, liquidity costs are demonstrably higher for speculative grade

bonds than for investment grade bonds. In particular, we observe a signiﬁcant increase in

the percentage of zero returns and the size of the LOT estimate of liquidity while moving

from investment grade to speculative grade bonds. This is matched with a similar increase in

the bid-ask spread.7Not surprisingly, yield spreads also increase markedly across these bond

categories. For the matched sample of all three liquidity measures, the trend of each liquidity

measure appears to match the underlying credit rating. Namely, for investment grade bonds,

moving from AA bonds to BBB bonds we observe increasing transaction costs. However, for

speculative grade bonds, the trend of increasing liquidity costs with decreasing credit worthiness,

the pre-tax interest coverage. For the operating income to sales we collect the ﬁrm’s operating income before

depreciation (item 13) divided by the net sales (item 12). We use two deﬁnitions for debt: total long-term debt

(item 9) divided by total assets (item 6), and total long-term debt plus debt in current liabilities (item 34) plus

short-term borrowings (item 104) divided by total liabilities (item 181) plus market capitalization.

7We emphasize that, while the general trends are similar, the LOT liquidity costs do not necessarily need to

agree with the bid-ask spread in magnitude. The LOT estimates are derived from the investors’ trading decision,

which incorporates all relevant liquidity related costs. The marginal traders’ reservation price will then reﬂect all

these relevant costs which could include commission costs, credit spread costs, and search costs, in addition to the

bid-ask spread.

11

is only observed for the LOT measure and the bid-ask spread. The percentage of zero returns

appears to be a weaker proxy for liquidity.

Second, liquidity costs increase moving from short to long maturity bonds, consistent with an

investment horizon argument oﬀered by Amihud and Mendelson (1991) or the return volatility

arguments of Chakravarty and Sarkar (1999).

Finally, yield spreads generally increase (decrease) with maturity for investment

(speculative) grade bonds. Merton (1974) shows that corporate yield spreads can either increase

or decrease with maturity depending on the risk of the ﬁrm. Investmentgrade issuers face upward

sloping yield spreads while speculative grade issuers face ﬂat or downward sloping yield spreads.

Helwege and Turner (1999) ﬁnd that within the same speculative credit rating category, the

safer ﬁrms tend to issue longer term bonds, which causes the average yield spread to decline

with maturity.

2.2 Model validation

Even though the proportion of zero returns and the LOT estimate both stem from the

premise that liquidity costs inhibit trade, the LOT estimate is a less noisy measure because

it incorporates the covariation between the zero returns and the market movement of the

bond price determinants. To verify this point, we ﬁrst perform a model speciﬁcation check,

by investigating whether the LOT model helps to recover intuitive beta coeﬃcients on the

systematic risk factors. These coeﬃcients are then compared to a naive asset pricing model

without liquidity cost considerations.

12

If the model is correctly speciﬁed, we would expect several patterns to appear. First, the

interest rate coeﬃcient should be negative. However, moving from high-grade to low-grade

bonds, this relationship is expected to become weaker (Schultz, 2001). Second, the equity

return coeﬃcient should be positive for low-grade bonds (Cornell and Green, 1991). Intuitively,

a positive equity return, signaling an improvement in the ﬁrm’s business operation, will have a

positive eﬀect on the bond return. However, the eﬀect of the equity return on high-grade bonds

is not clear. On the one hand, a positive equity return might increase bond prices, as in the

low-grade bond case. On the other hand, the positive equity return might be caused by capital

ﬂows from the corporate bond market into the equity market, in which case a negative return

on corporate bonds is expected.8

The estimation results are summarized in Panel A of Table 2. A comparison of the LOT

results with those of the naive OLS model provides a clear indication of the inﬂuence that zero

returns have on the estimation results. The LOT model’s interest rate estimates are mostly

negative and signiﬁcant, while the interest rate inﬂuence is decreasing with decreasing bond

ratings, all as expected. In sharp contrast, the naive OLS model produces interest rate estimates

that are largely insigniﬁcant from zero. In addition, the interest rate eﬀect has no apparent trend

with bond rating, contrary to common beliefs.

The falloﬀ in interest rate inﬂuence for the LOT model is oﬀset by a concomitant increase

in the S&P500 equity return inﬂuence, especially for speculative grade bonds. Also evident is

8Kwan (1996) ﬁnds a positive equity return coeﬃcient for investment grade bonds. Cornell and Green (1991)

ﬁnd that, when both the interest rate and the S&P500 equity return are considered, the sign of equity return

coeﬃcient changes from positive to negative for the period 1977 to 1989.

13

the switch in sign for the S&P500 coeﬃcient from investment grade to speculative grade bonds.

This would indicate that signaling eﬀects prevail in the case of speculative grade bonds, while

substitution eﬀects prevail for investment grade bonds. Similar, but more muted patterns are

apparent for the naive OLS model’s estimates.

2.3 Bid-ask spread tests

We provide further evidence on the consistency of the three liquidity measures. In particular,

we regress the bid-ask spread separately on the other two liquidity measures controlling for other

liquidity determinants as follows:

Bid-Askit =η0+η1Liquidityit +η2Maturityit +η3Ageit +η4Amount Outstandingit

+η5Bond Ratingit +η6Bond Volatilityi+η7Bond Rating Dummy + t

The subscript “it” refers to bond i and year t. Liquidity refers to either the proportion of

zero returns or the LOT estimate. The liquidity determinants are chosen according to Garbade

and Silber (1979), Sarig and Warga (1989), Chakravarty and Sarkar (1999), Stoll (2000), Schultz

(2001), and Brandt and Kavajecz (2003). Bond rating proxies for default risk. For the overall

regressions, bond ratings are assigned a cardinal scale ranging from one for AAA rated bonds

to seven for CCC to D rated bonds. Panel B of Table 2 presents the results.

For investment grade bonds, the LOT liquidity estimate alone explains 6.39% of the

cross-sectional variation in the bid-ask spread, while the percentage of zero returns explains

6.82% of the cross-sectional variation in the bid-ask spread. In comparison, Schultz (2001)

reports an R2of 3.43% in regressions on all microstructure trading cost determinants for

investment grade bonds. Both the LOT estimate and the percentage of zero returns remain

14

positively and signiﬁcantly related to the bid-ask spread when other variables are included.9

Similar results can be seen for speculative bonds, but only for the LOT model estimate. In

particular, the proportion of zeros is insigniﬁcant without the control variables, but becomes

signiﬁcant after including them in the regression. The percentage of zero returns appears to

suﬀer more from speciﬁcation error bias than does the LOT measure. This is to be expected

given that the LOT measure extracts more information than is provided by the percentage of

zero returns.

2.4 Initial yield spread and liquidity tests

We now test the relation between the yield spread and the three liquidity estimates. To

provide a consistent comparison we match the bid-ask spread sample to the available liquidity

estimates. As shown in Panel C of Table 2, for investment grade bonds all three liquidity

estimates are positively and signiﬁcantly associated with the underlying yield spread. The LOT

measure and the bid-ask spread provide almost identical power in explaining the cross-sectional

variation in the yield spread, with a reported R2of approximately 7.3%. The percentage of zero

returns explains almost 6% of the cross-sectional variation in the yield spread.

For speculative bonds, only the bid-ask spread and the LOT measure are signiﬁcantly

associated with the underlying yield spread. The LOT measure explains 7.39% of the

cross-sectional variation in the yield spread, while the bid-ask spread explains only 0.86% of

the cross-sectional variation in the yield spread.

9Although not reported, we also include the log scaled equity volatility in the regression and ﬁnd it to be

insigniﬁcantly associated with the bid-ask spread.

15

3. Liquidity Eﬀects on Yield Spread Levels

Many theoretical models (e.g., Amihud and Mendelson, 1986) predict that investors demand

higher expected returns for less liquid assets to compensate for the liquidity risk. This implies

that, for the same cash ﬂows in the future, less liquid assets will have lower prices. Because bond

yield is a promised yield given known cash ﬂows, the lower prices of less liquid bonds lead to

higher bond yields and higher yield spreads, ceteris paribus. We test this theoretical prediction

by investigating whether various liquidity proxies can explain yield spread levels.

3.1 Regression tests of liquidity estimates and other yield spread determinants

The following regression is speciﬁed with the yield spread as the dependent variable and the

various yield spread determinants as independent variables:

Yield Spreadit =η0+η1Liquidityit +η2Maturityit +η3Amount Outstandingit

+η4Couponit +η5Treasury Ratet+η610Yr-2Yr Treasury Ratet+η7EuroDollart+η8Volatilityit

+η9Bond Ratingt+η10PreTax Coverage Dummyit +η11Operating Income/Salesit

+η12Debt/Assetsit +η13Debt/Capitalizationit +t

The subscript “it” refers to bond i and year t. Liquidity refers to the bid-ask spread, the

proportion of zero returns, or the LOT estimate. The choice of yield spread determinants is

largely based on Elton et al. (2001) and Campbell and Taksler (2003).10 We measure the

incremental inﬂuence of the pretax coverage using the procedure outlined in Blume, Lim, and

MacKinlay (1998). In addition, we include three macroeconomic variables associated with the

yield spread. These are the one-year Treasury rate, the diﬀerence between the 10-year and

10 We exclude the additional equity market index considered by Campbell and Taksler (2003) because of potential

endogeneity problems given that the LOT estimate includes the market return from the S&P500 index.

16

2-year Treasury rates that describes the slope of the yield curve, and the diﬀerence between

the 30-day Eurodollar and 3-month Treasury bill rate that controls for other potential liquidity

eﬀects on corporate bonds relative to Treasury bonds.

We present two separate regressions for each liquidity estimate. The ﬁrst uses only the

bond-speciﬁc information yielding a larger sample, while the second incorporates the corporate

and market information yielding a smaller sample. The sample for each liquidity measure diﬀers

due to the estimation limitations for each measure. The percentage of zero returns is the most

comprehensive sample because it only requires the daily bond prices. As a practical matter,

The LOT sample comprises more oﬀ-the-run bonds than does the bid-ask spread sample, but

the bid-ask spread sample comprises more on-the-run bonds than does the LOT sample.

The most telling ﬁnding is the consistent signiﬁcance of the liquidity variable regardless

of the speciﬁcation used to deﬁne liquidity, regardless of the speciﬁcation used for the yield

spread determinants, or regardless of investment grade or speculative grade categories. All

these liquidity measures are positively related to the yield spread in all scenarios, for both

investment grade and speculative grade bonds, even after we control for extensive bond-speciﬁc,

ﬁrm-speciﬁc, and macroeconomic variables. The liquidity coeﬃcients are highly signiﬁcant (at

1%) in every scenario, supporting our theoretical prior that liquidity is priced in the yield

spreads.

The interpretation of the magnitude of the liquidity inﬂuence varies depending on the

liquidity measure. For investment grade bonds, the LOT measure would predict an incremental

0.21 basis point increase in the yield spread for a one basis point increase in liquidity costs,

17

while the bid-ask spread would predict an incremental 0.42 basis point increase in the yield

spread for a one basis point increase in the bid-ask spread. The coeﬃcient for bond rating is

20 basis points, regardless of the LOT measure or the bid-ask spread liquidity measure, which

means that for each grade drop in bond rating (e.g., from BBB+ to BBB), the yield spread will

increase by 20 basis points. The incremental eﬀect of maturity on the yield spread is signiﬁcant,

but only one basis point.

For speculative grade bonds, focusing on the full accounting variable regressions, the LOT

measure would predict an incremental 0.82 basis point increase in the yield spread for a one

basis point increase in liquidity costs, while the bid-ask spread would predict an incremental

2.29 basis point increase in the yield spread for a one basis point increase in the bid-ask spread.

It may be noted that the maturity coeﬃcient is generally positive for investment grade

bonds and negative for speculative grade bonds. For investment grade bonds, longer maturities

are often noted to be associated with increased yield spreads (Campbell and Taksler, 2003),

consistent with the positive sign for maturity. For speculative grade bonds, Helwege and Turner

(1999) argue that better quality ﬁrms are able to issue bonds with longer maturity, causing a

negative relation between the yield spread and maturity for these bonds.

At the bottom of Table 3 we report the regression of yield spread on each liquidity measure

alone using the full sample whenever the measure is available. For each measure, we also

regress the yield spread on bond rating alone for that sample as a comparison. For investment

grade bonds, liquidity alone explains from 2.12%, for the bid-ask spread, to 7.57%, for the LOT

estimate, of the cross-sectional variation in the yield spread. In comparison, for the same sample,

18

bond rating alone explains 15.20% of the cross-sectional variation of yield spread for the LOT

sample and 20.12% for the bid-ask spread sample. For speculative bonds, the bid-ask spread

alone explains 7.49% of the yield spread variation while the LOT liquidity measure explains

21.83% of the yield spread variation.

3.2 Issuer ﬁxed-eﬀects regressions

We perform an issuer ﬁxed-eﬀects regression to control for issuer inﬂuences on yields because

a small set of companies may dominate the bond market. For instance, Ford Motor Company’s

bonds comprise almost 10% of the entire bond market. As in the levels regression tests, we

use separate samples for each liquidity measure to allow for diﬀerent bond characteristics. This

results in approximately 1100 issuers for investment grade bonds and 220 issuers for speculative

grade bonds. However, approximately only 300 issuers have complete accounting information for

investment grade bonds and approximately only 90 issuers have complete accounting information

for speculative grade bonds. Table 4 presents the results.

We observe the same, consistent result using either the bid-ask spread or the LOT liquidity

estimate. Liquidity is positively and signiﬁcantly associated with the yield spread regardless of

bond grade, even after controlling for bond-speciﬁc, ﬁrm-speciﬁc, and macroeconomic variables.

The coeﬃcients are highly signiﬁcant at 1%. Note that the proportion of zero returns is

signiﬁcantly positive (at 1%) for both investment grade bonds and for speculative grade bonds

when the accounting variables are not included, but is only signiﬁcant at 10% when the ﬁrm-level

variables are included. In other words, while all liquidity measures lead to the same conclusion,

the case for the proportion of zero returns is slightly weaker, consistent with the notion that the

19

proportion of zero returns is a relatively noisy measure of liquidity.

3.3 Simultaneous equation regressions

Every liquidity measure, whether based on observable bid-ask spreads or new estimable

measures, could contain information about the credit quality of a bond, and thus could aﬀect

the yield through the credit-risk channel. This would make it diﬃcult to interpret the main

results purely in terms of liquidity costs. Much of the liquidity costs are due to adverse selection

under asymmetric information. For a typical corporate bond, asymmetric information on its

credit quality (rather than on interest rate) is the main reason for adverse selection costs.

Intuitively, one expects that bonds with lower credit quality should have a more severe adverse

selection problem, ceteris paribus. So higher liquidity costs could mean a lower credit quality,

which should lead to higher yield spreads. In addition, Campbell and Taksler (2003) note

that bond ratings may be contemporaneously incorporating the observed ﬁrm-level accounting

characteristics. Rating agencies may also absorb market information through the observed yield

spread as well as macro-economic information when assigning a credit rating.

To control for the potential endogeneity problems arising from the contemporaneous

measurement of the yield spread, liquidity costs, and the credit rating, we perform a simultaneous

regression using three equations representing each of the potentially endogenous variables. The

system of equations is stated as follows:

20

Yield Spreadit =η0+η1Liquidityit +η2Maturityit +η3Couponit

+η4Treasury Ratet+η510Yr -2Yr Treasury Ratet+η6EuroDollart+η7Volatilityit

+η8Credit Ratingt+η9PreTax Coverage Dummyit +η10Operating Income/Salesit

+η11Debt/Assetsit +η12Debt/Capitalizationit +t

Liquidityit =η0+η1Maturityit +η2Ageit +η3Amount Outstandingit

+η4Credit Ratingit +η5Bond Volatilityit +η6Yield Spreadit +t

Credit Ratingit =η0+η1Treasury Rateit +η210Yr -2Yr Treasury Ratet

+η3PreTax Coverage Dummyit +η4Operating Income/Salesit +η5Debt/Assetsit

+η6Debt/Capitalizationit +η7Yield Spreadit +t

The results are presented in Table 5. As is shown, the potential endogeneity bias does

not aﬀect the relation between liquidity and the yield spread for either investment grade or

speculative grade bonds. The LOT liquidity estimate and the bid-ask spread liquidity measure

remain signiﬁcant at the 1% level for investment grade bonds, and they remain signiﬁcant at

the 5% level for speculative grade bonds. The percentage of zero returns is signiﬁcant at the 5%

level for investment grade bonds, but is insigniﬁcant for speculative grade bonds. We conclude

that liquidity is priced in yield spreads even after the potential endogeneity bias is controlled;

and that, again, the proportion of zero returns appears to be a less powerful liquidity measure.

4. Liquidity Eﬀects on the Yield Spread Changes

We conduct regression tests to study whether issue-speciﬁc liquidity changes are a

determinant of yield spread changes. This test oﬀers a glimpse into how the dynamics of liquidity

are incorporated into yield spread changes. Econometrically, diﬀerencing the time-series removes

autocorrelative inﬂuences that may cause spurious results due to time-series trends.

21

4.1 Regression tests of changes in liquidity and yield spread determinants

We include a list of independent variables used in Collin-Dufresne et al. (2001) and Campbell

and Taksler (2003). Unlike the levels speciﬁcation, we use the unscaled pretax coverage because

of the diﬀerencing operation. In addition, unlike Collin-Dufresne et al., we directly control for

the default probability by using the changes experienced each year in the credit ratings for each

bond. We believe this is a better control than using the change in the forward jump rate in the

option market. The regression is stated as:

∆(Yield Spread)i=γ0+γ1∆(Liquidity)i+γ2∆(S&P Rating)i+γ3∆(σE)i+γ4∆(Treasury Rate)i

+γ5∆(10 yr - 2 yr Treasure Rate)i+γ6∆(30 Day EuroDollar Rate)i

+γ7∆(PreTax Interest Coverage)i+γ8∆(Operating Income/Sales)i

+γ9∆(LT Debt/Assets)i+γ10∆(Total Debt/Market Cap)i+

where, ∆ represents the ﬁrst diﬀerence in each variable, for each bond i. The results are presented

in Table 6.

As expected, a deterioration of bond quality (rating) is related to a signiﬁcant increase in the

yield spread. Similarly, a rise in interest rates leads to a reduction in the yield spread, especially

for investment grade bonds (Duﬀee, 1998, and Longstaﬀ and Schwartz, 1995). However, even

after controlling for this and other factors, changes in liquidity are highly associated with changes

in the yield spread, especially for the bid-ask spread and the LOT estimate. This is the case for

both investment grade and speculative grade bond categories.

Adding the macro-variables and ﬁrm-speciﬁc accounting variables increases the explanatory

power, but not at the expense of the liquidity variable which remains signiﬁcant. The

22

conclusive result in Table 6 is the positive, signiﬁcant coeﬃcient for the liquidity change

variable. Liquidity changes remain signiﬁcantly associated with yield spread changes regardless

of including bond-speciﬁc, ﬁrm-speciﬁc, or macro-level variables.

Economically, for investment grade bonds, a one basis point increase in LOT liquidity costs

over time results in a 0.12 basis point increase in the yield spread, while a one basis point increase

in the bid-ask spread over time results in a 0.29 basis point increase in the yield spread. The

corresponding impact for speculative grade bonds are 0.61 basis points (LOT liquidity costs)

and 2.46 basis points (bid-ask spread). Note that the coeﬃcients for the liquidity variables are

broadly consistent with those of Table 3.

At the bottom of Table 6 we report the regression of the change in the yield spread on

the change in each liquidity measure alone using the full sample whenever the measure is

available. For each measure, we also regress the change in the yield spread on the change

in bond rating alone for that sample as a comparison. For investment grade bonds, the changes

in the percentage of zero returns and the LOT liquidity measure explain more than 2.0% of the

cross-sectional variation in the change of yield spread. For speculative bonds, changes in the

LOT liquidity measure alone explains 16.89% of changes in the yield spread, while changes in

the percentage zeros alone explains 5.97% of changes in the yield spread. Changes in the bid-ask

spread alone have a relatively lower explanatory power for both categories of bonds.

23

4.2 Simultaneous regression tests

To control for the potential endogeneity bias, we run a simultaneous system regression

with the yield spread change and the change in each of the liquidity measure (respectively) as

the endogenous variables. Unlike the levels test, we do not endogenize bond rating changes

because changes in the credit rating are infrequent within the sample period, causing a limited

dependent variable problem in the simultaneous system regression. Additionally, the equations

for the bid-ask spread sample for speculative grade bonds were unidentiﬁed because of linear

dependence between the macroeconomic variables. We therefore remove the Eurodollar variable

to allow for system identiﬁcation. Moreover, changes in maturity, age, and coupon are also

excluded. The resulting simultaneous regression for yield spread changes is speciﬁed as:

∆(Yield Spread)i=η0+η1∆(Liquidity)i+η2∆(Treasury Rate)i+η3∆(10Yr -2Yr Treasury Rate)i

+η4∆(EuroDollar)i+η5∆(Volatility)i+η6∆(Credit Rating)i+η7∆(PreTax Coverage)i

+η8∆(Operating Income/Sales)i+η9∆(Debt/Assetsi)+η10∆(Debt/Capitalization)i+

∆(Liquidity)it =η0+η1∆(Credit Rating)i+η2∆(Bond Volatility)i+η3∆(Yield Spread)i+

The results, presented in Table 7, can be summarized as follows. For the bid-ask spread or

the LOT estimates, an increase of liquidity costs causes a signiﬁcantly positive increase in yield

spreads, for both the investment grade and the speculative grade bonds. For the proportion

of zero returns, an increase of liquidity costs causes a signiﬁcant increase in yield spreads for

investment grade bonds, but not for speculative bonds. The results concerning the percentage of

zero returns for the speculative grade bonds are consistent with the levels tests. On the whole,

Table 7 indicates that our tests on changes in liquidity are robust to potential endogeneity bias.

24

5. Conclusions

We examine the association between corporate bond liquidity and yield spreads. To ensure

robustness, we adopt two model-independent liquidity measures (the bid-ask spread and the

proportion of zero returns) and a liquidity estimate from a model developed by Lesmond et

al. (1999). We provide additional robustness checks to ensure that our liquidity measures are

intuitively consistent and empirically sound.

We ﬁnd that liquidity is a key determinant in yield spreads. This is found both in yield

spread levels and changes over time. Liquidity is priced in yield spreads regardless of controlling

for issuer ﬁxed eﬀects, potential simultaneity bias between credit ratings, liquidity, and yield

spreads, or the commonly used yield spread determinants adopted by Campbell and Taksler

(2003) and yield spread change determinants of Collin-Dufresne et al. (2001). The liquidity

eﬀects are apparent for both the investment grade and speculative grade bonds.

Our study adds to the literature in the following sense. Many prior studies simply assume

that liquidity is a second order eﬀect, or totally neglect its impact given the diﬃculties in

estimating liquidity costs. The observation that bond yields exhibit signiﬁcant liquidity eﬀects

alters our view of bond pricing and risk estimation. It mitigates the concern that the yield spread

is “too high” to be explained by default risk alone (Elton et al., 2001 and Huang and Huang,

2003). Our results imply that the liquidity-related component must be taken into account when

examining yield spreads.

25

Bibliography

1. Amihud, Y., and H. Mendelson, 1986, “Asset pricing and the bid-ask spread,” Journal of

Financial Economics, 17, 223-249.

2. Amihud, Y., and H. Mendelson, 1987, “Trading mechanisms and stock returns: An empirical

investigation,” Journal of Finance, 42, 533-553.

3. Amihud, Y., and H. Mendelson, 1991, “Liquidity, maturity, and the yields on U.S. treasury

securities,” Journal of Finance, 46, 1411-1425.

4. Bekaert, G., H. Campbell, and C. Lundblad, 2003, “Liquidity and expected returns: Lessons

from emerging markets,” Working Paper, Duke University.

5. Blume, M. F. Lim, and C. MacKinlay, 1998, “The declining credit quality of U.S. corporate

debt: Myth or Reality,” Journal of Finance, 53, 1389-1413.

6. Brandt, M., and K. Kavajecz, 2003, “Price discovery in the U.S. treasury market: The

impact on order ﬂow and liquidity on the yield curve,” Working Paper, Duke University

7. Campbell, J., and G. Taksler, 2003, “Equity volatility and corporate bond yields,” Journal

of Finance, 58, 2321-2349.

8. Chakravarty, S., and A. Sarkar, 1999, “Liquidity in ﬁxed income markets: A comparison of

the bid-ask spread in corporate, government, and municipal bond markets,” Working Paper,

Federal Reserve Bank of New York.

9. Collin-Dufresne, P., R. Goldstein, and S. Martin, 2001, “The determinants of credit spread

changes,” Journal of Finance, 56, 2177-2207.

10. Constantinides, G. 1986, “Capital market equilibrium with transactions costs,” Journal of

Political Economy, 94, 842-862.

11. Cornell, B., and K. Green, 1991, “The investment performance of low-grade bond funds,”

26

Journal of Finance, 46, 29-48.

12. Duﬀee, G., 1998, “The relation between treasury yields and corporate bond yield spreads,”

Journal of Finance, 53, 2225-2241.

13. Duﬀee, G., 1999, “Estimating the price of default risk,” Review of Financial Studies, 12,

197-266.

14. Duﬃe, D., and K. Singleton, 1997, “An econometric model of the term structure of

interest-rate swap yields,” Journal of Finance, 53, 2225-2241.

15. Elton, E., M. Gruber, D. Agrawal, and D. Mann, 2001, “Explaining the rate spread on

corporate bonds,” Journal of Finance, 56, 247-277.

16. Ericsson, J., and O. Renault, 2002, “Liquidity and Credit Risk,” Working Paper, McGill

University.

17. Fama, E., and K. French, 1993, “Common risk factors in the returns on stocks and bonds,”

Journal of Financial Economics, 33, 3-56.

18. Garbade, D., and W. Silber, 1979, “Structural organization of secondary markets: Clearing

frequency, dealing activity, and liquidity risk,” Journal of Finance, 34, 577-593.

19. Glosten, L., and P. Milgrom, 1985, “Bid, ask, and transaction prices in a specialist market

with heterogeneously informed traders,” Journal of Financial Economics, 2, 24-38.

20. Goodhart, C., and M. O’Hara, 1997, “High frequency data in ﬁnancial markets: Issues and

applications,” Journal of Empirical Finance, 4, 73-114.

21. Grinblatt, M., 1995, “An analytical solution for interest-rate swap spreads,” Working Paper,

UCLA, Anderson Graduate School of Management.

22. Helwege, J., and C. Turner, 1999, “The slope of the credit yield curve for speculative-grade

issuers,” Journal of Finance, 54, 1869-1884.

27

23. Hotchkiss, E., and T. Ronen, 2002, “The informational eﬃciency of the corporate bond

market: An intraday analysis,” Review of Financial Studies, 15, 1326-1354.

24. Huang, J., and M. Huang, 2003, “How much of the Corporate-Treasury yield spread is due

to credit risk,” Working Paper, Stanford University.

25. Jarrow, R., 1978, “The relationship between yield, risk, and the return on corporate bonds,”

Journal of Finance, 33, 1235-1240.

26. Kwan, S., 1996, “Firm-speciﬁc information and the correlation between individual stocks

and bonds,” Journal of Financial Economics, 40, 63-80.

27. Kyle, A., “Continuous auctions and insider trading,” Econometrica, 53, 1315-1335.

28. Lesmond, D., J. Ogden, and C. Trzcinka, 1999, “A new estimate of transaction costs,”

Review of Financial Studies, 12, 1113-1141.

29. Lesmond, D., M. Schill, and C. Zhou, 2004, “The illusory nature of momentum proﬁts,”

Journal of Financial Economics, 71, 349-380.

30. Lesmond, D., 2004, “Liquidity of emerging markets,” Journal of Financial Economics,

Forthcoming.

31. Lo, A., H. Mamaysky, and J. Wang, 2001, “Asset prices and trading volume under ﬁxed

transaction costs,” Working Paper, MIT.

32. Longstaﬀ, F., S. Mithal, and E. Neis, 2004, “Corporate yield spreads: Default risk or

liquidity? New evidence from the credit-default swap market,” Forthcoming, Journal of

Finance

33. Longstaﬀ, F., and E. Schwartz, 1995, “A simple approach to valuing risky ﬁxed and ﬂoating

rate debt,” Journal of Finance, 50, 789-820.

34. Maddala, G., 1983, “Limited dependent and quantitative variables in econometrics,”

28

Cambridge University Press, Cambridge, Mass.

35. Merton, R., 1974, “On the pricing of corporate debt: The risk structure of interest rates,”

Journal of Finance, 29, 449-470.

36. Sarig, O., and A. Warga, 1989, “Bond price data and bond market liquidity,” Journal of

Financial and Quantitative Analysis, 24, 367-378.

37. Schultz, P., 2001, “Corporate bond trading costs: A peek behind the curtain,” Journal of

Finance, 56, 677-698.

38. Scruggs, H., 1998, “Resolving the puzzling intertemporal relation between the market risk

premium and conditional market variance: A two-factor approach,” Journal of Finance, 53,

575-603.

39. Stoll, H., 2000, “Friction,” Journal of Finance, 46, 1479-1514.

40. White, H., 1980, “A heteroskedasticity-consistent covariance matrix estimator and a direct

test for heteroskedasticity,” Econometrica, 48, 817-838.

29

Appendix A: The Return Generating Function

The bond price, Bt, by deﬁnition, is:

Bt=

T−t

X

n=T−t−k

Ce−rn +Ae−r(T−t),

where T is the maturity, k+1 is the number of coupon payments remaining, C is the half-year

coupon payment rate, A is the face value of debt, and r is the yield to maturity for k+1 coupon

payments remaining. We assume that rtfollows some unspeciﬁed stochastic process. By Ito’s

lemma we have:

dBt=∂B

∂r dr +∂B

∂t dt +1

2

∂2B

∂r2Λtdt, (A1)

where Λtis the square of the diﬀusion coeﬃcients of rtprocess. If rtis a multivariate process,

then Λtshould also include the covariance terms. Therefore, from Equation (A1):

∂B

∂r =−DtBt,(A2)

where Dtis the bond’s duration. We can rewrite Equation (A2) as:

dBt

Bt=−Dtdr +∂B

∂t +1

2∂2B

∂r2Λt

Btdt. (A3)

Barring arbitrage, there exists some state price density process, Λt, such that:

dΛt=µΛ,tdt +σT

Λtdωt.

In equilibrium, the risky bond return should satisfy:

EtdBt

Bt−rtdt =−covtdBt

Bt,dΛt

Λt=Dtcovtrt,dΛt

Λt,(A4)

where covt(dPt/Pt,dΛt/Λt) is the instantaneous conditional covariance, and rt=−µΛ,t/Λtis the

risk-free rate. We obtain the second equality above by using Equation (A3). Following the

discrete time empirical literature, we further assume that the state price density is a linear

function of both market equity return and long-term risk free bond return (e.g., Scruggs, 1998).

This implies that:

EtdBt

Bt=rtdt +Dt×γ1×covtrt,dBl,t

Bl,t +Dt×γ2×covt(rt,dMt

Mt),(A5)

30

where, γi,i=1,2 is the price of risk associated with the respective state variable, dBl,t/Bl,t is

long-term bond return, and dMt/Mtis market equity return. In the empirical implementation,

we will make the two adjustments. First, we only measure the proportional daily price change

in dBt/Btand we will not consider daily accrued interest. The last condition means we will

consider only clean prices. In summary, bond price changes will only be driven by long-term risk

free bond returns and equity returns. We also assume the conditional covariances are constant.11

This leads to the following speciﬁcation for equation (1) in the text:

R∗

j,t =βj1×Durationj,t ×∆Rl,t +βj2×Durationj,t ×∆S&P Indext+j,t ,(1)

where Rj,t is the daily return for bond jthat investors would bid given zero transaction costs,

Durationj,t is the bond’s duration, and ∆S&P Indextis daily S&P equity return. Durationj,t ×

∆Rl,t is the proportional bond return of a long-term risk free bond adjusted by the duration of

the risky bond. The scaling of the market sensitivities by duration is consistent with Jarrow

(1978).

11 This can be justiﬁed for two reasons. First, for each bond we split daily bond prices into separate years and

estimate beta coeﬃcients within the year. The coeﬃcients can thus be treated as conditionally constant. Second,

we assume that changes in duration for each bond within the year will capture some of the variation in beta

coeﬃcients.

31

Table 1

Corporate Bond Summary Statistics

We present liquidity and yield spread statistics for non-callable corporate bonds from 1995 to 2003 by three

maturity categories. %Zeros is the percentage of zero returns for a given year adjusted for missing prices. LOT refers

to the modiﬁed Lesmond et al. (1999) model’s liquidity estimate. The bid-ask is the proportional spread derived

from quarterly quotes from Bloomberg. To assign bond ratings, we use the Fixed Income Securities Database, and,

when unavailable, the Standard & Poor’s credit rating from Datastream. The yield spread is the diﬀerence between

the bond yield and the yield of a comparable maturity treasury bond as determined from Datastream. Two separate

samples for each maturity classiﬁcation are presented. The ﬁrst sample is restricted to only bonds with available

LOT estimates, while the second sample is restricted to only bonds with available bid-ask spreads. bp stands for

basis points and N stands for the sample size.

Short Maturity (1-7 years)

Liquidity & S&P Credit Ranking

Yield Spreads AAA AA A BBB BB B CCC to D

Zeros (%) 5.93 4.10 3.88 8.43 40.63 44.71 46.31

LOT (bp) 7.88 9.63 10.51 34.99 201.45 458.86 933.06

Yield Spread (bp) 84.06 96.91 129.34 252.09 575.58 1213.43 3949.55

N 87 336 1162 1234 333 167 119

Zeros (%) 3.20 3.35 3.33 7.80 42.77 44.00 51.09

LOT (bp) 5.83 8.18 9.82 34.40 191.23 335.63 868.59

Bid-Ask (bp) 24.51 26.02 25.82 31.01 54.26 58.76 77.00

Yield Spread (bp) 71.43 95.05 118.92 235.41 549.88 1247.23 3559.09

N 56 285 972 775 178 72 22

Medium Maturity (7-15 years)

Liquidity & S&P Credit Ranking

Yield Spreads AAA AA A BBB BB B CCC to D

Zeros (%) 9.79 12.59 10.61 11.94 36.99 38.71 34.96

LOT (bp) 24.28 47.26 57.74 70.29 259.34 342.50 941.84

Yield Spread (bp) 82.44 146.24 177.68 277.45 566.53 947.14 2887.47

N 49 120 539 730 152 78 44

Zeros (%) 10.36 8.34 6.62 8.91 42.40 38.96 18.04

LOT (bp) 25.00 36.17 36.82 51.45 266.11 272.96 282.84

Bid-Ask (bp) 49.52 36.57 38.20 44.22 54.65 60.44 180.35

Yield Spread (bp) 70.65 129.02 154.19 251.68 497.45 863.71 1619.04

N 37 67 386 394 76 32 9

Long Maturity (15-40 years)

Liquidity & S&P Credit Ranking

Yield Spreads AAA AA A BBB BB B CCC to D

Zeros (%) 7.53 9.75 10.39 8.68 29.13 31.67 41.00

LOT (bp) 59.34 83.65 79.40 66.57 252.14 284.81 1023.18

Yield Spread (bp) 133.81 152.25 183.76 242.16 437.69 681.44 2047.11

N 49 189 674 929 112 48 48

Zeros (%) 7.28 8.27 7.79 8.00 32.36 37.25 35.14

LOT (bp) 76.81 75.60 56.97 58.57 281.56 245.78 328.25

Bid-Ask (bp) 51.65 52.68 54.76 58.62 73.56 82.47 86.75

Yield Spread (bp) 113.65 142.83 172.21 236.89 457.97 623.45 2192.41

N 27 110 410 494 62 14 8

Table 2

Liquidity Measure Tests

Panel A reports coeﬃcients on the risk free rate factor, βT−Bond , and the equity market return factor, βEquity , from, respectively,

a nave OLS model and the modiﬁed Lesmond et al. (1999) model (LOT). The interest rate factor is expected to be negative for all

bonds while the equity factor can be either positive or negative for investment grade bonds but positive for speculative grade bonds. N is

the sample size for each bond rating. %Zeros is the percentage of zero returns for a given year adjusted for missing prices. LOT is the

liquidity estimate from the Lesmond et al. (1999) model. Panel B reports the regression of the bid-ask spread on the other two liquidity

measures, the percentage of zero returns, and the LOT estimate, and control for other liquidity determinants. Age and maturity are in

years referenced from the year the bond was issued or its maturity date relative to the year being analyzed. The amount outstanding

is the dollar amount of the bond that has not been redeemed and is log scaled. The bond volatility is log scaled. The bond ratings are

numbered from one to 10 for investment grade bonds (S&P ratings, AAA to BBB-) and from one to 12 for speculative grade bonds (S&P

ratings, BB+ to D). Panel C reports an OLS regression of the yield spread on each liquidity measure for a matched sample using the

bid-ask as a basis. White’s (1980) t-statistics are in parentheses. An * denotes signiﬁcance at the 1% level, while a †denotes signiﬁcance

at the 5% level.

Panel A: LOT Model and the Naive Model Coeﬃcient Estimates

S&P Limited Dependent Variable Model Naive Model

Rating N % Zeros LOT βT−Bond βEquity βT−Bond βEquity

Investment AAA 185 7.37* 0.0026* -0.9077* -0.0072* -0.0515 -0.0055*

Grade AA 645 7.34* 0.0038* -0.9127* -0.0084* 0.0068* -0.0064*

A 2395 7.29* 0.0041* -0.9395* -0.0090* -0.0223 -0.0068*

BBB 2893 9.40* 0.0054* -0.9047* -0.0069* -0.0487 -0.0040†

Speculative BB 597 37.55* 0.0225* -0.5332* -0.0001 -0.0450 -0.0019

Grade B 293 40.97* 0.0399* 0.4424 0.0171†-0.1261 0.0127*

CCC to D 211 42.74* 0.0955* -0.1976 0.0885* -0.0662 0.0341†

Panel B: Regression of the Bid-Ask Spread on Liquidity Measures

Variable Investment Grade Bonds Speculative Grade Bonds

Intercept 0.0112* 0.0059* 0.0032* 0.0051* 0.0049* 0.0043 0.0054* 0.0069

(103.18) (5.31) (129.10) (6.50) (26.06) (0.99) (26.96) (1.74)

LOT 0.0442* 0.0233* 0.0440* 0.0297*

(9.81) (5.65) (5.16) (3.50)

% Zeros 0.0037* 0.0027* 0.0007 0.0017*

(15.03) (11.73) (1.81) (3.80)

Maturity 0.0001* 0.0001* 0.0001* 0.0001*

(10.59) (12.92) (4.02) (5.46)

Age -0.0000 0.0000 0.0001 0.0001

(0.34) (1.25) (1.67) (0.89)

Ln(Amt. Outstanding) 0.0001 0.0001†-0.0000 -0.0001

(0.60) (2.34) (0.14) (0.16)

Ln(Bond Volatility) 0.0004* 0.0003* 0.0001 0.0002*

(12.15) (14.61) (1.47) (3.05)

Bond Rating 0.0001 0.0001 0.0002†0.0003*

(1.38) (1.49) (2.30) (2.81)

Sample Size 3970 6040 421 525

% Adjusted R26.39 25.34 6.82 25.23 6.45 15.02 0.35 15.03

Panel C: Regression of the Yield Spread on Liquidity Measures

Investment Grade Bonds Speculative Grade Bonds

Variable Bid-Ask LOT % Zero Bid-Ask LOT % Zero

Coeﬃcient 1.8246* 0.3181* 0.0239* 1.7396†0.7804* 0.0014

(17.70) (17.65) (15.76) (2.16) (5.88) (1.87)

N3970 421

% Adjusted R27.29 7.26 5.87 0.86 7.39 1.72

Table 3

Yield Spread Determinants and Liquidity Tests

The yield spread determinants are based on bond-speciﬁc eﬀects (bond rating, amount outstanding, and maturity in years), macroe-

conomic variables (One-year Treasury note rate (T-Note), the diﬀerence between the 10-year and 2-year Treasury rates (Term Slope),

and the 30-day Eurodollar rate minus the 3-month T-Bill Rate (Eurodollar)), and ﬁrm-speciﬁc operating characteristics (pre-tax interest

coverage, operating income to sales, long-term debt to assets, and total debt to capitalization). The pretax interest coverage is further

grouped into one of four categories according to Blume et al. (1998). σEis the equity volatility for each issuer. Investment grade bonds

are numbered from one (AAA rated bonds) to 10 (BBB- rated bonds) Speculative grade bonds are numbered from one (BB+ rated bonds)

to 12 (D rated bonds). The liquidity cost estimates are based on the modiﬁed LOT model, the percent zero returns, and the bid-ask

spread. White’s (1980) t-statistics are presented in parentheses. The last partition is a univariate regression of the yield spread on either

liquidity or credit rating alone using only the bond-speciﬁc sample for each liquidity measure. An * or a †signiﬁes signiﬁcance at the 1%

or 5% level, respectively.

Variable Investment Grade Bonds Speculative Grade Bonds

Intercept 0.1573* 0.1251 0.0696* 0.0902* 0.1737* 0.1408†0.5696†0.5397†0.3232* 0.2784* 0.9056* 0.8242*

(15.03) (11.52) (9.97) (8.76) (12.25) (14.08) (2.00) (1.98) (2.81) (3.23) (2.99) (2.88)

LOT 0.5122* 0.2166* 1.6757* 0.8213*

(10.71) (10.03) (7.82) (2.95)

Bid-Ask 0.4362* 0.4200* 2.7266* 2.2957*

(5.65) (5.20) (4.99) (4.69)

% Zeros 0.0255* 0.0138* 0.0600* 0.0521*

(12.94) (8.84) (5.25) (3.10)

Maturity 0.0001 0.0001* 0.0001* 0.0001* 0.0001* 0.0001* -0.0024* -0.0021* -0.0009* -0.0106* -0.0027* -0.0032*

(1.57) (5.28) (5.40) (5.89) (7.25) (7.44) (4.62) (3.92) (5.75) (4.03) (5.61) (4.93)

Amount 0.0001 -0.0005 0.0003 -0.0008†-0.0001 -0.0007* -0.0071* 0.0005 -0.0004 0.0011 -0.0064†0.0023

(0.34) (1.33) (0.92) (2.48) (0.75) (2.66) (3.08) (0.34) (0.17) (0.28) (2.25) (0.78)

Coupon 0.2074* 0.1141* 0.0013* 0.0009* 0.1828* 0.1078* 0.4895 0.4441†0.0034* 0.0027* 1.3981* 1.2975†

(10.30) (6.28) (11.09) (5.48) (12.45) (7.36) (1.52) (2.13) (3.69) (3.67) (3.42) (2.24)

T-Note -2.4595* -1.5603* -1.1035* -0.9273* -2.5467* -1.7185* -9.5597†-9.4014†-4.0206* -3.3823* -14.0365* -13.771*

(17.84) (15.68) (13.09) (9.83) (22.00) (15.20) (2.40) (2.43) (2.72) (4.26) (3.18) (4.43)

Term Slope -5.5080* -3.8658* -2.9417* -2.6337* -5.9552* -4.3546* -14.0822 -19.6601†-10.0332* -10.7150* -28.8487* -34.342*

(18.01) (15.71) (14.92) (11.25) (23.43) (16.71) (1.58) (2.21) (2.99) (5.25) (2.97) (3.69)

EuroDollar -0.0774* -0.0677* -0.0560* -0.0541* -0.0889* -0.0751* 0.0328 -0.1369 -0.2440* -0.3370* -0.4291* -0.3924†

(16.42) (15.31) (14.02) (13.92) (23.61) (19.13) (0.25) (0.98) (4.11) (5.15) (3.01) (2.45)

Credit 0.0021* 0.0020* 0.0023* 0.0023* 0.0021* 0.0021* 0.0247* 0.0249* 0.0092* 0.0091* 0.0372* 0.0366*

Rating (26.96) (20.14) (32.54) (24.35) (34.62) (22.55) (9.61) (6.45) (8.67) (6.85) (13.25) (9.29)

σE3.4437* 5.2107* 4.1768* 4.2847 2.8546†16.8334*

(4.99) (6.85) (5.32) (1.92) (2.27) (3.86)

PreTax D1 -0.0012* -0.0015* -0.0010* 0.0091* -0.0014 0.0037

(5.93) (6.85) (5.32) (2.79) (0.93) (0.73)

PreTax D2 0.0005* 0.0006* 0.0005* -0.0103 0.0043†-0.0051

(3.56) (4.83) (4.33) (1.46) (2.12) (0.85)

PreTax D3 0.0001 0.0002†0.0001 0.0060 0.0047 0.0138*

(1.21) (2.24) (1.59) (0.75) (1.78) (2.66)

PreTax D4 -0.0001* -0.0001* -0.0001 0.0014 -0.0067†0.0273

(2.57) (4.52) (1.65) (0.12) (2.52) (1.16)

Oper. Inc. -0.0069* -0.0080* -0.0079* -0.0185 -0.0277* -0.0900

to Sales (4.80) (6.34) (5.29) (1.38) (2.81) (1.10)

LT Debt -0.0057* -0.0061* -0.0047†0.0165 -0.0147 -0.0295

to Assets (3.22) (3.83) (2.56) (0.48) (0.90) (0.32)

Total Debt 0.0049†0.0036†0.0073* 0.0519 0.0748* 0.0185*

to Cap. (2.53) (2.19) (4.29) (0.78) (4.24) (4.29)

N5838 2176 6035 2374 8802 3257 1041 461 583 288 1413 606

% Adj. R229.19 41.84 25.44 47.91 25.47 46.02 37.04 44.30 32.04 58.36 33.40 44.09

LOT Rating Bid-Ask Rating % Zeros Rating LOT Rating Bid-Ask Rating % Zeros Rating

Coeﬃcient 0.4233* 0.0028* 0.5536* 0.0025* 0.0183* 0.0026* 2.4233* 0.0318* 3.3941* 0.0106* 0.1158* 0.0379*

(9.67) (29.82) (6.36) (32.67) (10.96) (35.00) (9.07) (9.89) (4.77) (10.17) (7.14) (12.35)

% Adj. R27.57 15.20 2.12 20.12 3.95 15.08 21.83 24.00 7.49 25.12 3.02 28.21

Table 4

Fixed Eﬀects: Yield Spread Determinant Tests

The yield spread determinants are based on bond-speciﬁc eﬀects (bond rating, amount outstanding, and maturity in years), macroe-

conomic variables (one-year Treasury note rate (T-note), the diﬀerence between the 10-year and 2-year Treasury rates (Term Slope),

and the 30-day Eurodollar rate minus the 3-month T-Bill Rate (Eurodollar)), and ﬁrm-speciﬁc operating characteristics (pre-tax interest

coverage, operating income to sale, long-term debt to assets, and total debt to capitalization). The pretax interest coverage is further

grouped into one of four categories according to Blume et al. (1998). σEis the equity volatility for each issuer. Investment grade bonds

are numbered from one (AAA rated bonds) to 10 (BBB- rated bonds) Speculative grade bonds are numbered from one (BB+ rated bonds)

to 12 (D rated bonds). The liquidity cost proxies include the LOT estimate, the percentage of zero returns, and the bid-ask spread. The

issuer is the ﬁxed eﬀect. The issuer ﬁxed eﬀects test is reported by the F-test. An * or a †signiﬁes signiﬁcance at the 1% or 5% level,

respectively.

Variable Investment Grade Bonds Speculative Grade Bonds

Intercept 0.1111* 0.1194* 0.1086* 0.0932* 0.1219* 0.1053* 0.7743†0.2208 0.3588* 0.4188* 1.0571* 0.0360

(12.15) (14.11) (14.93) (10.25) (10.98) (13.78) (2.55) (0.61) (2.87) (3.78) (3.47) (0.85)

LOT 0.2118* 0.1078* 2.2897* 0.8764*

(13.12) (9.73) (13.80) (4.31)

Bid-Ask 0.1703* 0.2019* 1.4963* 1.5890*

(5.72) (5.15) (4.75) (4.17)

% Zeros 0.0119* 0.0044* 0.0981* 0.0482

(13.01) (5.75) (5.01) (1.72)

Maturity 0.0001* 0.0001* 0.0002* 0.0001* 0.0001* 0.0002* -0.0029* -0.0029* -0.0011* -0.0011* -0.0022* -0.0028*

(5.60) (12.15) (12.51) (12.45) (9.98) (14.75) (4.84) (4.22) (7.85) (7.18) (3.94) (3.73)

Amount -0.0006†-0.0004 -0.0001 -0.0002 -0.0005* -0.0003 -0.0058 -0.0026 -0.0064* -0.0041†0.0038 0.0087†

(2.26) (1.86) (0.60) (0.84) (2.72) (1.63) (1.48) (0.79) (2.93) (1.95) (1.00) (2.20)

Coupon 0.0658* 0.0705* 0.0005* 0.0005* 0.0629* 0.0667* 0.6891 1.6274* 0.0013 0.0002 0.6689 1.5849*

(3.84) (5.32) (5.10) (3.84) (4.83) (6.03) (1.28) (3.09) (1.00) (0.17) (1.31) (2.62)

T-Note Rate -1.5298* -1.2470* -1.1839* -0.9141* -1.6169* -1.1972* -13.6442* -5.8177 -2.4538 -5.3023* -19.0025* -10.352

(17.02) (18.48) (15.85) (10.96) (19.69) (17.02) (3.48) (1.18) (1.35) (3.29) (4.24) (1.78)

Term Slope -3.6526* -3.3459* -3.2950* -2.6766* -3.9435* -3.2680* -20.8069†-13.1133 -7.5091†-13.7416* -39.3252* -24.667

(17.60) (21.05) (19.81) (14.15) (21.16) (20.08) (2.42) (1.20) (2.04) (4.18) (4.59) (1.92)

Eurodollar -0.0570* -0.0602* -0.0685* -0.0545* -0.0637* -0.0591* -0.2086 -0.2031 -0.2571* -0.2533* -0.6623* -0.3158

(15.95) (20.94) (25.95) (17.22) (21.74) (21.90) (1.57) (1.20) (7.64) (6.39) (5.37) (1.62)

Credit 0.0035* 0.0008* 0.0009* 0.0008* 0.0031* 0.0012* 0.0048 0.0250* 0.0123* 0.0123* 0.0300* 0.0423*

Rating (16.98) (3.87) (5.92) (3.75) (19.03) (6.28) (1.25) (6.52) (10.37) (9.80) (8.36) (9.67)

σE1.1266* 2.2140* 1.8186* -1.5774 -2.9956* 6.8704

(3.89) (5.40) (6.80) (0.44) (3.21) (1.72)

Pre-Tax D1 -0.0013* -0.0010* -0.0009* 0.0098 0.0035†0.0007

(7.67) (5.42) (5.82) (1.52) (2.34) (0.10)

Pre-Tax D2 0.0003†0.0005* 0.0004* -0.0045 0.0007 0.0028

(1.96) (3.55) (3.70) (0.29) (0.26) (0.23)

Pre-Tax D3 0.0001 0.0000 0.0001 0.0336 0.0076 0.0057

(0.47) (0.27) (1.11) (0.66) (1.26) (0.30)

Pre-Tax D4 -0.0000 0.0000 -0.0000 -0.0578 -0.0077 -0.0099

(0.15) (0.42) (0.37) (0.62) (1.26) (0.36)

Oper. Inc. -0.0022 -0.0068* -0.0039 -0.0274 -0.0713* 0.0024

to Sales (1.00) (3.10) (1.92) (0.69) (3.42) (0.46)

LT Debt -0.0004 -0.0047 0.0005 0.0618†0.0812* 0.0037

to Assets (0.15) (1.42) (0.19) (2.02) (2.73) (0.09)

Total Debt 0.0187* 0.0182* 0.0186* 0.1041 0.0732* -0.0094

to Cap. (6.79) (6.33) (7.60) (1.25) (2.79) (0.12)

Sample Size 5838 2176 6035 2374 8802 3257 1041 461 583 288 1413 606

Issuers 1124 336 1019 306 1235 367 263 96 179 76 294 106

F-Statistic 6.67* 14.01* 14.06* 14.12* 8.74* 15.80 3.06* 2.10* 11.11* 9.65* 3.67* 2.90*

Table 5

Simultaneous Regressions

Simultaneous regressions are presented using three liquidity measures, the LOT estimate, the percentage of zero returns, and the

bid-ask spread. The liquidity instrumental variablesare the bond return volatility, the amount outstanding, the age and maturity in years,

and bond rating. σBand σE, refer to bond volatility and equity volatility, respectively. The amount outstanding and bond volatility are

log scaled. The instrumental variables of the yield spread include bond-speciﬁc eﬀects (bond rating, amount outstanding, and maturity

in years), macroeconomic variables (one-year T-note rate, the diﬀerence between the 10-year and two-year Treasury rates, and the 30-day

Eurodollar rate over 3-month T-bill rate), and ﬁrm-speciﬁc accounting variables (pre-tax interest coverage, operating income to sales,

long-term debt to assets, and total debt to capitalization), and equity market eﬀects (equity volatility). The instrumental variables of

bond rating are the bond age and ﬁrm-speciﬁc accounting variables. An * denotes 1% signiﬁcance while a †denotes 5% signiﬁcance.

Investment Grade

Instrumental Yield Credit Yield Credit Yield Credit

Variable Spread Bid-Ask Rating Spread LOT Rating Spread %Zeros Rating

Intercept 0.1661* 0.0150* 8.4213* 0.2398* 0.1476* 8.1414* 0.7819 1.1697* 7.9553*

(2.77) (5.05) (6.52) (5.10) (13.84) (8.39) (1.87) (10.46) (9.12)

Liquidity 7.0442* 0.9975* 0.2126†

(4.23) (7.44) (1.96)

Maturity -0.0003 0.0001†0.0001 -0.0004* 0.0001 -0.0028*

(1.94) (2.19) (1.29) (9.23) (1.72) (5.88)

Coupon -0.0009 -0.0504 -0.1899

(1.14) (0.66) (1.93)

T-Note -2.5455* -49.4529†-3.9712* -35.4179†-11.8048†-34.8361†

(3.41) (2.35) (6.55) (2.32) (1.96) (2.50)

Term Slope -6.7878* -86.3815†-8.6125* -61.5634†-26.2885†-60.4370†

(3.82) (2.08) (6.93) (0.31) (2.00) (2.17)

Eurodollar -0.1121* -0.0810* -0.2727†

(4.36) (6.79) (2.19)

σE2.0849 1.6004 -5.2688

(0.92) (1.88) (1.43)

Credit Rating 0.0057†0.0003* 0.0056* 0.0018* 0.0038* 0.0396*

(2.34) (3.18) (2.65) (4.90) (3.94) (9.54)

PreTax D1 -0.0001 0.0414 -0.0003 0.0140 0.0016 0.0382

(1.44) (1.15) (0.81) (0.39) (1.10) (1.29)

PreTax D2 0.0015 -0.2862* 0.0015†-0.2921* 0.0012 -0.2964*

(1.66) (9.67) (2.19) (9.52) (1.03) (11.98)

PreTax D3 0.0005 -0.1152* 0.0004 -0.1012* 0.0001 -0.1031*

(1.02) (5.48) (1.51) (4.20) (1.03) (5.56)

PreTax D4 -0.0002 0.0337* -0.0001 0.0298* 0.0001 0.0226*

(0.81) (3.67) (0.99) (2.82) (0.31) (2.88)

Operating Income 0.0002 -1.4810* 0.0051 -1.7060* 0.0079 -1.4883*

(0.03) (5.84) (1.02) (6.41) (1.21) (6.93)

Long Term Debt -0.0282†3.9493* -0.0189 4.0813 -0.0188 3.6651*

to Assets (2.40) (12.85) (1.90) (12.76) (1.28) (14.21)

Total Debt 0.0026 -0.1889 0.0077†-0.4549 0.0202†-0.4472

to Cap. (0.44) (0.58) (2.17) (1.34) (2.53) (1.59)

Ln(σB) 0.0008* 0.0080* 0.0633*

(5.44) (17.22) (12.76)

Ln(Amt. Outstanding) -0.0002 -0.0026* -0.0250*

(1.80) (5.79) (5.53)

Bond Age 0.0001†-0.0001 -0.0001

(2.45) (0.58) (0.04)

Yield Spread -0.0784* 63.4919* -0.7430* 50.2688* -9.9378* 56.7310*

(3.24) (11.34) (9.11) (8.78) (10.83) (12.14)

Sample Size 2374 2176 3257

Adjusted R25.23 5.48 40.05 17.77 13.80 36.88 3.45 5.88 36.45

Table 5: Continued

Simultaneous Regressions

Speculative Grade

Instrumental Yield Credit Yield Credit Yield Credit

Variable Spread Bid-Ask Rating Spread LOT Rating Spread %Zeros Rating

Intercept 0.0139 0.0077 4.9369 0.1265 0.0568* -8.1870 0.4540* -0.7170* -2.8820

(0.04) (0.78) (0.75) (0.30) (1.06) (1.64) (0.66) (3.02) (0.51)

Liquidity 12.1308†1.8432†-0.1944

(1.95) (1.96) (0.83)

Maturity -0.0027†0.0001* -0.0024* 0.0008 -0.0039* 0.0041†

(2.14) (2.72) (3.89) (1.85) (3.37) (2.07)

Coupon 0.0064†0.2784 1.5665*

(2.35) (1.24) (2.76)

T-Note 0.4380 -49.1239 -4.5914 192.8104†-4.3845 80.9381

(0.08) (0.45) (0.82) (2.35) (0.58) (0.87)

Term Slope -5.7854 -66.7110 -5.8488 375.1280†-16.1279 165.3930

(0.51) (0.31) (0.39) (2.29) (1.00) (0.89)

Eurodollar -0.5536†0.0981 -0.5329†

(2.65) (0.36) (2.11)

σE5.9458 -0.4133 17.8417†

(1.32) (0.17) (1.97)

Credit Rating 0.0321* 0.0018* 0.0211†-0.0024 0.0397* 0.0657*

(3.68) (4.70) (2.04) (0.79) (3.85) (3.10)

PreTax D1 0.0090†-0.3952* 0.0081 -0.3802* -0.0017 -0.1887†

(2.14) (6.20) (1.80) (4.38) (0.20) (1.98)

PreTax D2 0.0073 0.0611 0.0078 -0.0868* -0.0170 -0.0784

(1.06) (0.49) (0.73) (0.36) (0.85) (0.41)

PreTax D3 -0.0067 -0.1693 -0.0192 -0.0994 0.0194 -0.0460

(0.64) (0.92) (0.81) (0.21) (0.97) (0.17)

PreTax D4 -0.0031 0.2538 0.0345 0.1380 -0.0190 0.1594

(0.26) (1.11) (0.88) (0.18) (0.80) (1.79)

Operating Income 0.1101 -0.5159 -0.0045 -0.8189 0.0410 -1.3637

(1.90) (0.97) (0.15) (1.45) (0.69) (1.79)

Long Term Debt -0.1915* 2.4873* 0.0490 -0.1068 -0.2921* 3.2336*

to Assets (2.84) (3.17) (1.50) (0.20) (3.81) (2.89)

Total Debt 0.1994* -3.1155* -0.0372 -1.2718 0.1443†-1.4239

to Cap. (3.77) (4.00) (0.59) (1.47) (1.96) (1.45)

Ln(σB) 0.0004 0.0024 -0.0992*

(1.30) (0.65) (6.38)

Ln(Amt. Outstanding) -0.0001 -0.0012 -0.0006

(0.11) (1.06) (0.09)

Bond Age -0.0002†-0.0004 -0.0057

(2.28) (1.03) (1.56)

Yield Spread -0.0312 24.3250* 0.3014* 22.3214* 0.1582 15.5033*

(1.59) (9.38) (3.45) (16.65) (0.56) (14.32)

Sample Size 288 461 606

Adjusted R228.81 22.17 58.57 46.46 22.84 47.82 35.31 6.08 36.87

Table 6

Yield Spread Change Determinants and Liquidity Tests

The yield spread change determinants are based on bond-speciﬁc eﬀects, macroeconomic eﬀects, and ﬁrm-speciﬁc operating charac-

teristics. Annual changes in all variables are examined for the 1995-2003 period. The liquidity cost proxies include the LOT estimate,

the percentage of zero returns, and the bid-ask spread. We use a cardinal scale for all bonds, regardless of whether they are investment

grade or speculative grade bonds, ranging from one for AAA bonds to 22 for D rated bonds. The ﬁrm-speciﬁc operating characteristics

are pre-tax interest coverage, operating income to sales, long-term debt to assets, and total debt to capitalization. σEis equity volatility.

T-Note Rate is the one-year Treasury rate. Term-Slope is the diﬀerence between the 10 year and 2-year Treasury rates. Eurodollar refers

to the diﬀerence between the 30-day Eurodollar rate and the 3-month T-Bill rate. The last partition is a univariate regression of the yield

spread on either liquidity or credit rating alone using only the available bond-speciﬁc sample for each liquidity measure. White’s (1980)

t-statistics are presented in parentheses. An * denotes 1% signiﬁcance while a †denotes 5% signiﬁcance.

Variable Investment Grade Bonds Speculative Grade Bonds

Intercept -0.0001 -0.0004 -0.0005* -0.0006* -0.0014* -0.0006 0.0327 0.0213 0.0003 0.0080 -0.0103* -0.0006

(0.49) (1.34) (2.81) (2.80) (5.49) (1.83) (2.55) (1.31) (0.08) (1.06) (10.21) (0.39)

∆(LOT) 0.1885* 0.1239* 1.5153* 0.6068*

(5.92) (4.01) (3.56) (4.17)

∆(%Zero) 0.0286* 0.0134†0.0172 0.0369†

(6.02) (3.51) (1.81) (2.11)

∆(Bid-Ask) 0.1873†0.2909†2.1636†2.4613†

(2.22) (2.34) (2.44) (2.57)

∆(Credit 0.0015* 0.0011* 0.0018* 0.0015* 0.0007* 0.0014* 0.0123 0.0293* 0.0098* 0.0089* 0.0181* 0.0197*

Rating) (2.64) (2.91) (4.48) (5.10) (4.25) (4.33) (1.90) (4.99) (5.75) (3.03) (6.72) (6.17)

∆(T-Note) -0.9791* -0.7426* -1.1166* -0.6589* -0.9203* -0.4271* -8.9819 -6.9540 -4.2911†-2.6598 -0.2080 0.4007

(13.04) (9.69) (11.04) (7.48) (12.31) (4.18) (2.29) (1.65) (2.43) (0.56) (0.46) (0.56)

∆(Term -2.6012* -2.2579* -2.7856* -1.9930* -2.5691* -1.5795* -18.153†-20.057†-10.728* 9.8818 -1.1486 -3.3099

Slope) (15.60) (13.90) (13.24) (11.41) (16.15) (7.72) (2.22) (2.40) (3.12) (0.99) (1.17) (1.69)

∆(Euro- -0.0538* -0.0473* -0.0504* -0.0397* -0.0601* -0.0385* -0.2534 -0.2927†-0.1999* -0.2396* -0.2001* -0.2808*

Dollar) (16.93) (12.62) (9.40) (15.28) (23.95) (11.13) (2.41) (2.30) (7.18) (3.37) (3.96) (4.87)

∆(σE) -0.3013 -0.5490 -1.7774 -3.0106 -2.1667†2.2830

(0.36) (0.73) (1.77) (1.79) (1.94) (1.21)

∆(PreTax 0.0000 0.0001 0.0001 -0.0001 -0.0005 -0.0000

Interest) (0.08) (1.02) (1.75) (0.10) (1.08) (0.02)

∆(Operating -0.0107* -0.0115* -0.0181* 0.0044 -0.0192 -0.0393

Income) (2.57) (4.01) (3.12) (0.16) (1.55) (0.75)

∆(LT Debt 0.0094 0.0037 0.0189* 0.0437 0.0027 0.0709

to Assets) (1.80) (0.97) (3.02) (1.25) (0.09) (0.97)

∆(Debt to 0.0083 0.0075†-0.0057 0.0674 0.0407 0.0349

Capit.) (1.67) (2.08) (0.92) (1.38) (1.54) (0.90)

Sample Size 2646 985 5170 1842 2914 1164 451 198 477 195 188 103

Adj R2(%) 11.93 21.19 9.10 17.32 16.06 18.34 17.49 63.26 18.98 33.05 34.17 50.43

Liquidity 0.1847 0.0276* 0.2270* 1.7739* 0.0527* 0.9534†

Alone (6.19) (5.95) (2.57) (4.74) (5.57) (2.00)

% Adj. R22.80 2.32 0.19 16.89 5.97 0.75

Credit Risk 0.0018†0.0023* 0.0007* 0.0250* 0.0095* 0.0178*

Alone (2.53) (4.36) (3.13) (3.56) (4.67) (6.84)

% Adj. R21.03 1.19 0.34 4.30 5.39 19.65

Table 7

Simultaneous Regressions: Yield Spread Changes

Simultaneous regressions are presented using three liquidity measures: the LOT estimate, the percentage of zero returns, and the

bid-ask spread. The liquidity instrumental variables are the bond return volatility and bond rating. σBand σE, refer to bond volatility

and equity volatility, respectively. The instrumental variables of the yield spread are bond rating, macroeconomic variables (one-year

Treasury note rate, the diﬀerence between the 10-year and two-year Treasury rates, and the 30-day Eurodollar rate over the 3-month

T-bill rate), ﬁrm-speciﬁc accounting variables (pre-tax interest coverage, operating income to sales, long-term debt to assets, and total

debt to capitalization), and equity market eﬀects (equity volatility). An * denotes 1% signiﬁcance while a †denotes 5% signiﬁcance.

Investment Grade Speculative Grade

Instrumental Yield Yield Yield Yield Yield Yield

Variable Spread LOT Spread %Zeros Spread Bid-Ask Spread LOT Spread %Zeros Spread Bid-Ask

Intercept 0.0006 -0.0005†0.0001 -0.0080* -0.0027 -0.0001†0.0169 -0.0119* 0.1634 -0.0090 -0.2785†0.0002

(1.33) (2.32) (0.10) (4.77) (1.16) (2.45) (0.80) (4.71) (0.43) (1.06) (2.55) (0.43)

∆(LOT) 0.7608* 1.6039†

(8.03) (2.55)

∆(%Zero) 0.2785* 2.2042

(5.20) (0.44)

∆(Bid-Ask) 19.0803†12.4693*

(2.51) (2.90)

∆(T-Note) -0.5787* -3.6513* -241.617 -9.5024 71.448 1.1050

(3.97) (5.48) (1.90) (1.24) (0.42) (1.74)

∆(Term -1.8475* -7.7999* -2.3671 -16.522 131.721 -428.795

Slope) (5.92) (5.95) (1.44) (1.08) (0.39) (1.68)

∆(Euro- -0.0299* -0.0575* 0.0230 0.1190 1.3221

Dollar) (5.76) (6.99) (0.71) (0.59) (0.36)

∆(σE) -0.1831 0.2952 3.3901 -5.9277* -39.873 -2.7684

(0.44) (0.38) (0.93) (3.49) (0.45) (0.99)

∆(Credit 0.0013* -0.0004 0.0021* -0.0008 0.0005 -0.0000 -0.0022 0.0053†-0.0231 0.0248†0.0183* 0.0000

Rating) (3.16) (1.10) (3.39) (0.33) (0.34) (0.38) (0.39) (2.02) (0.31) (2.12) (3.35) (1.24)

∆(PreTax 0.0000 -0.0000 -0.0001 0.0033†0.0042 -0.0015

Interest) (0.09) (0.23) (0.28) (2.24) (0.36) (1.44)

∆(Operating -0.0165* -0.0102 -0.0068 0.1287†0.1280 0.1304

Income) (4.79) (1.79) (0.49) (2.45) (0.35) (1.51)

∆(Debt to 0.0115†-0.0107 0.0123 0.1187 0.1484 -0.0291

Assets) (2.34) (1.29) (0.54) (1.91) (0.36) (0.30)

∆(Debt to 0.0050 0.0057 0.0029 -0.0067 -0.1256 0.0139

Capit.) (1.06) (0.77) (0.14) (0.11) (0.28) (0.22)

∆(Ln(σB)) 27.3013* 138.250* -0.0816 5.4303 -22.2797 2.1237

(8.33) (5.38) (0.08) (0.97) (0.88) (1.03)

∆(Yield 0.1109 -1.0143 0.0596* 0.1847 0.3965 -0.0205

Spread) (1.35) (1.65) (3.06) (1.28) (0.55) (0.68)

Sample Size 985 1842 1164 198 195 103

Adjusted R218.92 12.20 3.63 1.83 0.60 1.46 20.36 11.33 -4.98 3.17 26.59 -0.22