Liquidity Premium in the Eye of the Beholder:
An Analysis of the Clientele Effect in the Corporate Bond Market∗
Jing-Zhi Huang, Zhenzhen Sun, Tong Yao, and Tong Yu†
September 2014
Abstract
This paper examines how liquidity and investors’ heterogeneous liquidity preferences
interact to affect asset pricing. We construct measures of liquidity preferences using data on insurer corporate bond holdings, and find that investors’ preferences
are highly persistent over time and related to investment horizons and funding constraints. We provide evidence that investors vary widely in their preferences and,
more importantly, evidence for liquidity clientele. Further, we find evidence that liquidity clienteles affect corporate bond prices—specifically, both the level and volatility
of liquidity premia are substantially attenuated among corporate bonds heavily held
by investors with a weak preference for liquidity.
Keywords: Corporate Bond Holdings, Liquidity Clientele, Corporate Bond Liquidity and Spreads
∗
We are very grateful to Yakov Amihud, Sandro Andrade (SFS Finance Cavalcade discussant), Jennie
Bai, Jack Bao (EFA discussant), Dan Bergstresser (BAFC discussant), Pierre Collin-Dufresne (AFA discussant), Jens Dick-Nielsen (MFA discussant), Song Han (CICF discussant), Jean Helwege, Jennifer Huang,
Igor Kozhanov (FMA discussant), Marco Rossi, and Adam Zawadowski (FIRS discussant) for helpful and
detailed comments and suggestions. We also thank seminar participants at Baruch College, City University
of Hong Kong, Nanjing University, SAIF, Shanghai University of Finance and Economics, University of
Iowa, and Washington State University; and conference participants at the 2013 SFS Finance Cavalcade,
2013 European Finance Association Meetings, 2013 Midwest Finance Association Meetings, 2013 China
International Conference in Finance, 2013 Boston Area Finance Conference, 2013 Financial Management
Association meetings, 2014 American Finance Association meetings, and 2014 Financial Intermediation Research Society meetings for valuable comments and suggestions.
†
Huang is at the Smeal College of Business, Pennsylvania State University. Email: jxh56@psu.edu. Sun is
at School of Business, Siena College. Email: zsun@siena.edu. Yao is at Henry B. Tippie College of Business,
University of Iowa. Email: tong-yao@uiowa.edu. Yu is at College of Business and Administration, University
of Rhode Island. Email: tongyu@uri.edu.
1
Introduction
Liquidity plays an important role in asset pricing. For example, liquidity premium—the
compensation demanded by investors for holding illiquid assets—has been documented in
various sectors of the financial market (e.g., Amihud, Mendelson, and Pedersen (2012) and
references therein). More recently, a growing literature on the credit market has argued
that liquidity may help explain the substantial unexplained component in corporate bond
yield spread changes (Collin-Dufresne, Goldstein, and Martin (2001)) and the “credit spread
puzzle” (Huang and Huang (2012)). Indeed, empirical studies such as Longstaff, Mithal, and
Neis (2005), Chen, Lesmond, and Wei (2007), Bao, Pan, and Wang (2011), Dick-Nielsen,
Feldhütter, and Lando (2012), and Friewald, Jankowitsch, and Subrahmanyam (2012), have
reported a significant liquidity component in corporate bond yield spreads.
In this study we examine the related phenomenon of “liquidity clientele”—that is, due
perhaps to heterogeneous investment horizons, some investors may require less compensation
for holding illiquid securities and prefer holding more illiquid securities given the same level
of compensation per extra unit of illiquidity, while other investors may prefer the opposite.
When illiquid securities predominantly attract investors with low liquidity preference, the
liquidity premium on these securities may be attenuated.
The idea of liquidity clientele can be traced to Amihud and Mendelson (1986), who
show that when investors with longer (exogenous) investment horizons tend to hold more
illiquid securities. In their model, the attenuating effect of liquidity clientele on liquidity
premium results in an unconditionally concave relation between trading cost and liquidity
premium. Subsequent theoretical studies (reviewed in Section II) have also concluded on the
importance of liquidity clientele when it comes to understanding the overall liquidity effect
on asset pricing. Despite such prominent predictions, however, so far there is little direct
empirical evidence on the liquidity clientele effect.
This study examines liquidity clientele and its asset pricing implications in the corporate
bond market—where liquidity presumably matters more than it does for equities or Treasury
securities. We analyze corporate bond holdings of insurance companies, which are by far
1
the largest group of corporate bond investors (e.g., Campbell and Taksler (2003) and Ellul,
Jotikasthira, and Lundblad (2011)).1 Our data sample covers corporate bond holdings of
3,413 U.S. insurers during the period of 2003-2011.
To detect the presence of liquidity clientele, we quantify the illiquidity of an insurer’s
corporate bond portfolio (ILP ) by the weighted average illiquidity of corporate bonds it
holds, where the bond-level illiquidity is based on five different measures from the existing
literature. We find that portfolio illiquidity is widely dispersed across insurers and highly
persistent over time. More importantly, insurers’ portfolio illiquidity can be linked to firm
characteristics indicative of their investment horizons. For example, insurers with higher
ILP s (i.e., holding more illiquid bonds) tend to have lower trading turnover and hold bonds
longer in their portfolios, and are more likely to be life insurers whose liability maturities are
typically longer than those of property and casualty insurers. These patterns are consistent
with the notion of the “liquidity clientele effect” introduced by Amihud and Mendelson
(1986). Going beyond the Amihud and Mendelson (1986) model, we find that investors’
funding constraints also affect their portfolio illiquidity. Insurers with higher ILP s tend to
be older, affiliated with an insurance group or a parent holding company, and more likely to
use re-insurance to outsource the risk in their insurance operations. Such evidence suggests
that access to external funding has a substitutive effect on insurers’ preference for portfolio
liquidity.
To detect the impact of liquidity clientele on bond pricing, we quantify the illiquidity
clientele (ILC ) for a corporate bond by the weighted average of its holders’ illiquidity preference (proxied by the portfolio illiquidity measure ILP ). We find that ILC interacts with
bond illiquidity to affect the yield spreads, consistent with the hypothesis that liquidity
clientele attenuates the liquidity premium effect. For example, consider the case with the
1
Based on insurer holdings and aggregate corporate bond outstanding provided by the National Association of Insurance Commissioners (NAIC) and Security Industry and Financial Market Association
(SIFMA), insurers collectively hold about 25% corporate bonds in the U.S. market from 2004 to 2012.
See www.naic.org/capital markets archive/140307.htm and www.sifma.org.
2
Amihud (2002) measure of bond-level illiquidity. Among investment-grade bonds2 in the
lowest ILC quintile (i.e., bonds held by insurers with strong preference for liquidity), the
average yield spread difference between bonds in the top illiquidity quintile and those in
the bottom quintile—a proxy for liquidity premium—is 0.94%. By contrast, among the
investment-grade bonds in the top ILC quintile (bonds held by insurers with weak preference for liquidity), the average yield spread difference between the top and bottom illiquidity
quintiles is only 0.59%. Thus, going from the lowest to the highest ILC quintile, the liquidity premium component in the yield spread is reduced by 0.35%. Similar results are
obtained when alternative bond-level liquidity measures are used, and after we control for
credit rating, maturity, and other bond characteristics in multivariate regressions.
Besides confirming the prediction on the level of liquidity premium, we find that clientele
also matters for the volatility of liquidity premium. Longer-horizon investors have lower
funding constraints since they demand less short-term funding. As a result, they are expected
to be more insulated from short-term market fluctuations. This conjecture is confirmed by
our data—liquidity premium is less volatile for bonds predominantly held by higher-ILP
insurers. The clientele effect on the liquidity premium volatility helps us understand the
recent data on liquidity premium. During and after the recent financial crisis, liquidity
premium in the corporate bond market has increased substantially; however, consistent with
the differential impact of market conditions on investor clienteles, the increase in liquidity
premium for high-ILC bonds is much modest relative to that for low-ILC bonds. As a result,
the clientele effect on bond pricing, measured by the difference in liquidity premium between
low-ILC bonds and high-ILC bonds, has become much larger in magnitude during recent
years.
We take advantage of rich information in the data to investigate several further implications of the liquidity clientele effect. First, if investment horizon matters for portfolio
liquidity and liquidity clientele, we expect the impact of liquidity clientele on liquidity premium to be stronger among longer-term bonds. This is because the effective holding horizon
2
Insurers mainly hold investment-grade bonds (e.g., Ellul et al. (2011)). Therefore, our main analysis
focuses such bonds. In later analysis we separately look at high-yield bonds.
3
on a short-term bond has to be short regardless of its holders’ investment horizon, and thus
long-term investors have no effective advantage amortizing the trading costs when holding
short-term bonds. Indeed, we find that the attenuating effect of liquidity clientele on liquidity
premium is strong among bonds with maturity beyond 5 years, but essentially non-existent
among bonds within 5 years of maturity.
Second, we investigate more directly the roles of both investment horizon and funding
constraint in the clientele effect on bond pricing. To examine the effect of funding constraint,
we construct an alternative illiquidity clientele measure by replacing portfolio illiquidity
(ILP ) in the original definition of ILC with insurer’ funding constraint characteristics. In
order to directly examine the effect of investment horizon, we construct another clientele
measure by replacing ILP with the inverse of insurers’ portfolio turnover. This turnoverbased ILC is also motivated by the notion of latent liquidity proposed in Mahanti et al.
(2008). We find that bond liquidity premium becomes lower when a bond is heavily held
by insurers with lower funding constraints and lower portfolio turnovers. Interestingly, the
two types of ILC effects are both significant in joint regressions, suggesting that investment
horizon and funding constraints both play a role in explaining the clientele effect of bond
pricing.
Third, motivated by existing studies on the correlation between credit risk and liquidity
(e.g., Ericsson and Renault (2006) and He and Milbradt (2014)), we study the clientele
effect in a subsample of corporate bonds that permits a cleaner identification of the liquidity
premium effect. The subsample consists of bonds issued by the same firm that essentially
have the same credit risk. We find evidence of a significant clientele effect on yield spread in
this subsample, which confirms the impact of clientele effect through the liquidity channel.
Finally, observing that insurers account for varying fractions of ownership across bonds,
we separately investigate the clientele effect among bonds with high and low insurer ownerships. We find that liquidity clientele has significant impact on the liquidity premium for
bonds with high insurer ownership, but insignificant impact among bonds with low insurer
ownership. In addition, the impact of the clientele measures on the liquidity premium of
4
high-yield bonds is rather weak. A possible explanation for this observation is that insurers
only hold a small fraction of the high-yield bonds and thus their liquidity preference does
not matter much for the pricing of these bonds. Combined, these findings highlight the
importance of relying on marginal investors’ portfolio holdings in order to detect the effect
of liquidity clientele on bond pricing.
The main contribution of our study is to provide direct evidence on a long-standing
conjecture in the asset pricing literature on liquidity, i.e., the liquidity clientele effect. We
show that investors with longer investment horizons and weaker funding constraints tend to
hold more illiquid bonds. Further, the liquidity preference of bond holders has economically
and significantly large impact on bond pricing. Ownership by investors who do not have a
strong demand for liquidity substantially reduces the level and volatility of liquidity premium
of the bonds. Several of our findings, including the role of funding constraints and the
clientele effect on liquidity premium volatility, go beyond the direct predictions of existing
studies and thus further enrich our understanding of the liquidity clientele effect.
Our study is related to Mahanti et al. (2008) and Nashikkar, Subrahmanyam, and Mahanti (2011). These studies introduce a measure of latent liquidity based on investors’
portfolio turnovers and holdings, in a way similar to how our liquidity clientele measure is
constructed. (See Section 3.2 for the differences and connections between the liquidity clientele measure and the latent liquidity measure.) However, our study is distinct in terms of
research questions addressed. Mahanti et al. (2008) examine the relation between the latent
liquidity measure and other liquidity measures. Nashikkar et al. (2011) focus on liquidity
premium reflected in the relation between latent liquidity and CDS-bond basis. They do
not investigate the heterogeneity in the level or volatility of liquidity premium caused by
different liquidity preferences of investors holding the securities.
The rest of the paper is organized as follows. Section 2 reviews the related literature.
Section 3 outlines the empirical implications of liquidity clientele and discusses how we
measure illiquidity clientele. Section 4 discusses the data and sample. Section 5 presents the
empirical findings. Section 6 concludes.
5
2
Related Literature
Amihud and Mendelson (1986) is the first to introduce the notion of liquidity clientele. In
their model, a security’s trading cost (or illiquidity) is the bid-ask spread, and an investor’s
liquidity preference is driven by her investment horizon. Both the bid-ask spread and the
investment horizon are exogenously specified. An investor’s net expected return per period
on a security is the gross expected return per period (before trading cost) minus the amortized
trading cost. In equilibrium, among securities with the same risk hence the same net expected
return, those with higher trading cost must have higher gross expected return. This is
generally known as the liquidity premium effect.
If investors’ horizons are heterogeneous, a separating equilibrium may exist where shorterhorizon (longer-horizon) investors prefer more (less) liquid securities. Intuitively, this is
because investors with longer horizon have lower amortized trading costs and thus have
competitive advantage (i.e., requiring a lower gross return) for holding illiquid securities.
Liquidity clientele refers to the tendency for investors with less demand for liquidity (i.e.,
longer-horizon investors) to hold more illiquid securities.
The liquidity clientele effect has an asset pricing implication: liquidity premium is lower
for securities held by investors with longer horizons because they require less compensation in
the gross expected return for per unit of trading cost. Amihud and Mendelson (1986) take
this effect further to derive a concave relation between the trading cost and the liquidity
premium: since illiquid securities tend to be owned by investors with a long horizon, after
integrating out the security ownership (i.e., the liquidity clientele), the liquidity premium
associated with per unit of trading cost decreases with trading cost.
Other theoretical studies have developed different versions of the liquidity clientele effect.
Using a model with endogenous trading horizons, Constantinides (1986) shows that investors
reduce their trading frequency in response to high trading cost and thus hold illiquid securities
longer than they hold liquid ones. Various extensions of the basic models have also reinforced
the notion of liquidity clientele. For instance, Acharya and Pedersen (2005) develop an asset
pricing model with liquidity risk and risk aversion. By incorporating these two features into
6
the Amihud and Mendelson (1986) model, Beber, Driessen, and Tuijp (2012) obtain a model
that can generate what they called liquidity risk clientele. Their calibration analysis shows
that liquidity risk clientele may substantially reduce the liquidity risk premium. Schuster,
Trapp, and Uhrig-Homburg (2013) propose an equilibrium model that can generate the
aging effect and a hump-shaped relation between trading volume and maturity, in addition
to liquidity clientele. In addition, Jang et al. (2007) extend Constantinides (1986) to allow
for time-varying investment opportunities. Trading in response to time-varying expected
returns essentially shortens investors’ holding horizon, resulting in a larger magnitude of
liquidity premium relative to the case of constant expected returns.
The aforementioned models generally take transaction costs as given. A recent development in the literature on liquidity, especially for securities traded in over-the-counter
markets, is to endogenize trading frictions using search models, an approach originated from
Duffie, Gârleanu, and Pedersen (2005). For example, Vayanos and Wang (2007) introduce a
model where investors with heterogeneous horizons can invest in two infinitely lived assets
with identical payoffs. They show that if investors can search for only one asset, then there
exists a clientele equilibrium. He and Milbradt (2014) develop a structural credit risk model
that explicitly incorporates endogenous illiquidity.
Relative to the active theoretic literature on liquidity clientele, the empirical literature is
rather sparse. In their seminal article, Amihud and Mendelson (1986) empirically document
a concave relation between quoted bid-ask spreads and stock returns, consistent with the
liquidity clientele effect without explicitly conditioning on the liquidity clientele. Using the
inverse of turnover as a proxy for the average holding period, Atkins and Dyl (1997) find
that among NYSE stocks, those with higher bid-ask spreads have longer holding periods.
However, efforts to find more direct evidence of liquidity clientele and its pricing impact
have been limited so far, in part due to data constraints to a large extent—typically we do
not know the identities of security holders and their liquidity preferences. As such, data on
insurance companies’ corporate bond holdings offer a unique opportunity to directly test the
liquidity clientele effect in the corporate bond market.
7
3
Liquidity Clientele: Implications and Measures
3.1
Empirical Implications
We consider the following three implications of liquidity clientele.
Determinants of liquidity preference/clientele: The basic premise of “liquidity clientele” is that in equilibrium, investors with stronger liquidity preference hold more liquid
stocks. In Amihud and Mendelson (1986), the driving factor for liquidity preference is investment horizon. In addition, we consider a feature important for the corporate bond
market – it is dominated by institutional investors. When an institution such as an insurer
needs cash, it can either sell securities or raise external financing. Therefore, access to external funding may have a substitutive effect on the preference for keeping a liquid investment
portfolio. Combined, we have:
H1: Insurers with longer investment horizons and weaker funding constraints tend to
hold more illiquid corporate bond portfolios.
Effect on level of liquidity premium: As discussed earlier, we expect liquidity clientele
to have an attenuating effect on the level of liquidity premium. That is,
H2: Liquidity premium is lower for bonds held by insurers with weaker preference for
liquidity.
Note that after integrating out liquidity clientele, Amihud and Mendelson (1986) obtain
that unconditionally, liquidity premium is a concave function of trading cost. This concave
relation is the result of combining the two hypotheses H1 and H2 above. By separately
examining the two hypotheses (in addition to documenting the unconditional concave relation), we can offer sharper evidence on the liquidity clientele effect.
Effect on volatility of liquidity premium: Besides the prediction in existing theoretical
studies on the first moment of liquidity premium, we are interested in the liquidity clientele
8
effect on its second moment as well. This is motivated by the following two observations.
First, longer-horizon investors may be less concerned with the short-term market conditions
when pricing the liquidity of securities. Second, for investors relying less on selling portfolios
to raise cash (i.e., those with easier access to financing), the liquidity premium they demand
may be more insulated from short-term market fluctuations.3 Both observations lead to the
following:
H3: Liquidity premium is more volatile for bonds primarily held by investors with
stronger liquidity preference.
3.2
Illiquidity Preference and Illiquidity Clientele Measures
To help understand what is to come, here we introduce the measure of insurers’ portfolio
illiquidity and the bond-level illiquidity clientele measure.
First, we quantify the illiquidity of an insurer’s corporate bond portfolio, ILP, by the
weighted-average illiquidity of all corporate bonds the insurer holds. That is,
PNi
Ni
X
j=1 Vi,j,t ILQj,t
ILPi,t =
wi,j,t ILQj,t =
PNi
j=1 Vi,j,t
j=1
(1)
where ILQ j,t is the time-t illiquidity measure for bond j (detailed in Section 4.3), wi,j,t is the
weight of bond j in insurer i ’s corporate bond portfolio, Vi,j,t is the dollar value of holding
by the insurer on bond j, and Ni is the number of corporate bonds held by the insurer.
Based on the principle of revealed preference, portfolio illiquidity ILP is an indication
of an insurer’s illiquidity preference. That is, insurers with higher ILP s exhibit stronger
preferences for illiquidity. Hence ILP can be understood interchangeably as illiquidity of
portfolio or illiquidity preference.
Next, we quantify each bond’s illiquidity clientele ILC as the weighted-average of illiquidity preferences (ILP s) across insurers holding the bond:
PM
Vi,j,t ILPi,t
ILCj,t = i=1
PM
i=1 Vi,j,t
3
(2)
The notion that investors relying on selling portfolios to raise cash may find themselves sensitive to
market funding conditions is related to the notion of funding liquidity by Brunnermeier and Pedersen (2008).
9
where M is the total number of insurers. By construction, corporate bonds held more by
insurers with high ILP s (i.e., with strong preference for illiquid bonds) have greater ILC s.
Two observations regarding the liquidity clientele measure are worth noting here. First,
in the Amihud and Mendelson (1986) world, there is a deterministic relation between ILQ
and ILC, because in equilibrium long-horizon (short-horizon) investors always hold illiquid
(liquid) securities. Thus, ILC can be viewed as an alternative measure of bond illiquidity
given the liquidity clientele effect. However, in reality the empirical measures ILQ and ILC
would not be perfectly correlated. One reason is that corporate bonds trade in the overthe-counter market with search frictions (e.g., Schultz (2001), Duffie et al. (2005), Vayanos
and Wang (2007), and Feldhütter (2012)). There is no guarantee that investors can always
locate bonds that perfectly fit their liquidity preferences. Another reason is that in reality
even a long-horizon investor may want to hold a certain amount of liquid securities. For
example, life insurers hold bonds to hedge the interest rate risk on the life insurance policies
they underwrite. While this may give life insurers a long investment horizon on average,
they still need to hold a certain amount of liquid investments to meet the claims that can
arrive at any given time.
Second, it is interesting to relate ILC to the latent liquidity measure introduced by
Mahanti et al. (2008). The latent liquidity of a bond (LLQit ) in their study is the weighted
average of portfolio turnover of investors holding the bond:
X
i
LLQit =
πj,t
T Oj,t ,
(3)
j
where
i
πj,t
is the fraction of the total outstanding amount of bond i held by investor j at t,
and T Oj,t is the turnover of investor j’s entire portfolio over the previous 12 months. Thus,
the main difference between ILC in (2) and LLQ in (3) is that the former uses portfolio
illiquidity (ILP ) as input while the latter relies on portfolio turnover (TO). In Section 5.6.2
we also consider and implement a turnover-based ILC, where insurer j’s portfolio illiquidity
ILP j is replaced by its the inverse of portfolio turnover. However, this turnover is based
on an insurer’s corporate bond portfolio (not its entire portfolio), whereas T Oj used in the
latent liquidity measure (LLQ) is the turnover at the fund level, i.e., based on an investor’s
10
entire portfolio (that may include many securities other than corporate bonds). As such,
our turnover-based ILC is also different from the latent liquidity measure.
On the other hand, a link between ILC and LLQ can be justified when there is a liquidity
clientele effect–that is, when investors with short horizons (and thus high turnovers) prefer
holding liquid securities, portfolio turnover is negatively related to the illiquidity of portfolio.4
Despite the correlation between liquidity clientele and liquidity (including latent liquidity), our study differs from Mahanti et al. (2008) in the research questions addressed.
Mahanti et al. (2008) (and Nashikkar et al. (2011)) use LLQ as an (advantageous) measure
of liquidity and establish an empirical relation between LLQ and expected return that is
consistent with the notion of liquidity premium. By contrast, we focus on the heterogeneity
of liquidity preferences and its impact on the magnitude and volatility of liquidity premium,
i.e., the attenuating role of ILC on liquidity premium.
4
Data
We use data from the National Association of Insurance Commissioners (NAIC), the Mergent
Fixed Investment Securities Database (FISD), and the Trade Reporting and Compliance
Engine (TRACE). While the NAIC and FISD data go back to the 1990s, a meaningful size
of corporate bond coverage by TRACE starts in 2003. Therefore, the sample period of this
study is from 2003Q1 to 2011Q4.
4.1
Insurers’ Corporate Bond Holdings
Insurers are required by state regulators to disclose their portfolio holdings and transactions
each year on stocks, bonds and other financial securities. Such information is collected in
4
Mahanti et al. (2008) motivates the latent liquidity measure from both the liquidity clientele effect
of Amihud and Mendelson (1986), and a reverse-causality effect of investors’ liquidity preference on bond
liquidity: bonds held by investors with active trading are likely to be more accessible in the market, and
thus more liquid. See also Vayanos and Wang (2007) for a theoretical model where liquidity of a security
is endogenous to investor horizon. In our empirical analysis, we treat the relation between bond liquidity
and bond investors’ liquidity preference as an equilibrium association, without differentiating the direction
of causality.
11
the form of Schedule D filings available from the NAIC.5
We start with all corporate bonds held and traded by insurers in the NAIC Schedule D
data during the period from 2003 to 2011. In order to obtain bond characteristics and bond
liquidity measures, we merge this data with FISD and TRACE, and keep all the plain-vanilla
bonds issued by the U.S. firms that satisfy certain standard filters (detailed in Section 4.2).
In order to measure insurers’ portfolio illiquidity and bond-level liquidity clientele at
the quarterly frequency, we infer insurers’ quarterly corporate bond holdings based on the
reported year-end holdings and reported bond trades. To obtain the par value of an insurer’s
holding on a bond in a specific quarter, we start with the par value of the insurer’s holding
of this bond at the beginning of the year, and then add the par value of the insurer’s net
purchases (buy minus sell) on this bond from the beginning of the year to the end of the
quarter. The resulting sample includes 9,846,975 insurer-bond-quarter observations.6
We use additional data filters to ensure the quality of the above procedure. We infer
an insurer’s year-end holdings by adding the net purchases during the entire year to the
holdings at the beginning of the year. If for a given bond, an insurer’s inferred year-end
par value is below 90% or above 110% of the reported year-end par value, we exclude that
year’s observations on that bond by that insurer from the sample. If more than 10% of
observations are excluded for an insurer during a given year for this reason, we exclude all
observations in that year for the insurer. These filters reduce the sample size to 9,454,512
insurer-bond-quarter observations. In this final sample, there are 7,873 unique bonds and
3,413 unique insurers, including 963 life insurers and 2,450 property-and-casualty insurers.
4.2
Data on Bond Characteristics and Bond Trading
FISD has detailed information for corporate debt securities, such as the issuer, seniority,
coupon, face value, issuance date, maturity date, credit rating, and redemption features. As
5
Studies that have used the NAIC corporate bond transaction data include Chakravarty and Sarkar
(1999), Hong and Warga (2000), Collin-Dufresne et al. (2001), Schultz (2001), Campbell and Taksler (2003),
among others. Chen et al. (2013) use the NAIC data on insurers’ Treasury bond holdings.
6
Note that the Schedule D data have bond holdings by both insurers and their holding companies. To
avoid double-counting, we exclude corporate bond holding of insurance holding companies from our sample.
12
mentioned earlier, we keep all the plain-vanilla corporate bonds issued by U.S. firms, and exclude bonds with optionality (e.g., callable and putable bonds, and bonds with sinking-fund,
convertibility, and exchangeability features), asset-backed securities, bonds with credit enhancements, floating-rate bonds, foreign-currency denominated bonds, and bonds with odd
frequency of coupon payments. We also exclude bonds with missing data on key characteristics such as issue date, maturity date, issue price, issuance size, coupon rate, and bonds with
missing credit ratings. Following the convention in the existing literature (e.g., Lin et al.
(2011)), we further exclude bonds that have less than six months to maturity by the end of
the year because such bonds are subject to high pricing errors and because our focus is on
relatively long-term bonds.
We measure bond-level liquidity using data from the TRACE, which provides information
on bond transactions, such as the date and time of execution, transaction price, and yield
to maturity at time of transaction. The TRACE reporting requirement is implemented in
three phases that progressively include more bonds: July 2002–February 2003, March 2003–
September 2004, and October 2004–present. Since only a limited number of corporate bonds
are included in phase I, we follow the existing literature (e.g., Edwards, Harris, and Piwowar
(2007) and Bao et al. (2011)) to start the analysis from Q1 2003. Note that changing the
sample starting date to either July 2002 (beginning of phase I) or October 2004 (beginning
of phase III) does not change any of our conclusions qualitatively.
Next, we apply two sets of data filters to alleviate potential reporting errors in TRACE.
The first set follows Dick-Nielsen (2009) and consists of the followings: (a) we delete duplicates identified by the message sequence number; (b) if a trade is subsequently reversed we
exclude both the original trade and the reversal; and (c) we exclude the following two types
of same-day corrections: if the correction is cancellation, both reports are deleted; otherwise
only the original is deleted. The second set of filters includes a median filter and a reversal
filter that help control for price errors (Edwards et al. (2007)). The former filter eliminates
any trade where the price deviates from the daily median or from a nine-trading-day median
centered at the trading day by more than 10%; the latter filter eliminates any trade with an
13
absolute price change deviating from the lead, lag, and average lead/lag price change by at
least 10%.
The resulting merged dataset from FISD and TRACE has 8,656 unique bonds during
the period from 2003 to 2011, including 6,839 investment-grade bonds and 1,717 speculative
bonds. Merging this sample with the Schedule D data then leads to our final sample that
covers 7,873 unique corporate bonds. Among them, 6,468 are investment-grade bonds and
1,405 are high-yield bonds.
Our sample size of unique corporate bonds is comparable to that of Dick-Nielsen et al.
(2012), which includes 5,376 bonds during the period from January 1, 2005 to June 30,
2009. When limited to their sample period, our sample has 6,749 bonds. Such difference
in sample size is likely because FISD, our data source, has more bond coverage relative to
Bloomberg, their data source. Our sample size is smaller than that of Friewald et al. (2012),
which consists of 23,703 bonds over the period from October 2004 to December 2008. This
is because in addition to plain-vanilla bonds, their sample also includes a large number of
bonds with embedded options and private bonds.
4.3
Yield Spreads and Bond Illiquidity
Following the existing literature, we look at the liquidity premium in corporate bond pricing
via the relation between bond illiquidity measures and bond yield spread.
At the end of a calendar quarter, we calculate the yield spread for a bond as the difference
between the bond’s yield to maturity and the fitted Treasury yield with matching maturity.
The Treasury yields for constant maturities of 1, 2, 3, 5, 7, 10, 20, and 30 years are obtained
from the Federal Reserve Bank of St. Louis.7 Following Duffee (1998) and Collin-Dufresne
et al. (2001), we use a linear interpolation scheme to fit the entire Treasury yield curve.
A well-known issue is that many corporate bonds are infrequently traded. We measure
quarter-end bond yields following the existing literature (e.g., Dick-Nielsen et al. (2012)). If
a bond is traded during the last month of a quarter, we take the average yield for all trades
7
The data are available at http://research.stlouisfed.org/fred2/categories/115.
14
on the last day it is traded. If a bond is not traded during the last month of the quarter but
traded during the first two months, we take the average yield over all trades on the bond
during the quarter.
We use the following five corporate bond illiquidity measures commonly in the literature.
The first is the Amihud (2002) measure of the price impact of per unit bond traded. The
second is the Roll’s (1984) effective bid-ask spread, based on the negative covariance between
returns of consecutive trades. Bao et al. (2011) consider a modified Roll’s measure. The third
is the LOT (Lesmond, Ogden, and Trzcinka (1999)) measure of round-trip transaction costs,
based on the frequency of zero-return days. The fourth is the imputed roundtrip cost (IRC )
proposed by Feldhütter (2012). Finally, we use the λ measure of Dick-Nielsen et al. (2012),
which takes the average of the normalized Amihud, IRC, the Amihud risk measure, and the
IRC risk measure. These measures are constructed for each bond in each quarter during
which the bond is traded. To alleviate the effect of outliers, we winsorize each illiquidity
measure at the top and bottom 1% across bonds in each quarter. More details on these
illiquidity measures are provided in the Appendix.
4.4
Summary Statistics
Table 1 provides summary statistics on corporate bond holdings by insurance companies in
our sample. As Panel A shows, the number of unique bonds in the combined FISD-TRACE
sample (reported in column 2) varies between 2,400 (in 2003) and 4,443 (in 2005), and the
number of unique bonds held by insurers (column 3) varies between 1,878 (in 2011) and 3,850
(in 2005). Overall, 91% (7,873 out of 8,656) of the bonds in the FISD-TRACE sample are
held by some insurers. Columns 4 through 8 report the numbers of bonds held by insurers
across five rating groups, respectively: AAA, AA (including AA+, AA, AA-), A (including
A+, A, A-), BBB (including BBB+, BBB, BBB-), and speculative bonds (Spec, including
all ratings below BBB-). Bond credit ratings are from S&P. If the S&P rating is missing,
we use the rating from Moody’s or Fitch, in this order; and bonds without credit ratings
are excluded. Most corporate bonds held by insurers are in the A and BBB groups, with a
15
relatively small number of junk bonds. Columns 9 through 12 report respectively the number
of bonds held across four maturity groups: below 2 years, 2-5 years, 5-10 years, and above
10 years. Insurers hold significant numbers of bonds in all the four maturity categories.
Panel B reports the cross-sectional distribution of insurers’ portfolio weights on various
types of bonds. Here, we divide bonds into groups using the same five credit rating categories
or the four maturity bins as described above. We first compute the portfolio weight (i.e., the
value of a specific type of bonds as a percentage of an insurer’s aggregate corporate bond
holding) in a given quarter, and then compute the cross-sectional statistics on such portfolio
weights across insurers. The cross-sectional statistics include the 5th, 25th, 50th, 75th, and
95th percentiles, as well as the mean and standard deviations. The numbers reported in the
table are the time-series averages of these cross-sectional statistics. Across the five rating
categories, A-rated bonds have the highest mean portfolio weight (35%), followed by the AA
category (25.88%). Speculative bonds have the lowest mean weight (7.41%). Across the four
maturity groups, bonds with 2 to 5 years of time to maturity have the highest mean portfolio
weight (34.15%), followed by bonds with less than 2 years of time to maturity (28.80%).
In Panel C, we further present the cross-sectional distribution of bonds held by insurers
as fractions of the total bonds outstanding. Again, bonds are classified into five credit rating
groups and four maturity groups. In each quarter for each bond, we compute the fraction
of total bond outstanding in a given category held by insurers collectively. We average
the fractions within each bond category and then compute the cross-sectional distribution
statistics of the fractional insurer holdings across various bond categories. The cross-sectional
statistics are averaged over time and reported here. For reference purpose we also report the
average number of unique bonds held by insurers in each category. Note that the average
number of speculative bonds (516) is much lower than that of investment-grade bonds (2,400).
In terms of the fraction of holdings by insurers, the mean and median for speculative bonds
are 12.66% and 8.30%, much lower than the corresponding statistics for bonds in any of
the four investment-grade categories. For example, the mean and median fractions of BBB
bonds held by insurers are 39.29% and 37.62%, respectively. Further, the panel shows
16
that insurance ownership on long-term bonds (bonds with maturity at or above 5 years) as
fractions of bonds outstanding are slightly higher than that on short-term bonds.8
These statistics show that insurers predominately hold investment-grade bonds. Therefore, in the main analysis we focus on such bonds (with analysis on speculative bonds in a
later part). In Panel D of Table 1, we additionally report the cross-sectional distribution of
insurers’ holdings of investment-grade (IG) bonds. There are 6,468 unique IG bonds in the
full sample. The number of these bonds ranges from 1,492 (in 2011) to 3,099 (in 2005), with
a time-series average of 2,400. The mean fraction of IG bonds outstanding held by insurers
is in the ranges of 34% to 42% over the sample period. This provides further evidence on
the importance of insurers in the IG bond market.
Overall, the bond ownership statistics presented in Table 1 are in line with those reported
by other studies. Hong and Warga (2000) report that insurance companies account for
roughly 25% of the market for high-yield debt, while their share of trading in the IG debt
market is around 40%. Schultz (2001) estimates that life insurance companies by themselves
hold about 40% of all corporate bonds. Further, Ellul et al. (2011) find that on average,
insurance companies hold about 34 percent of IG bonds and only 8 percent of high-yield
bonds. See also Campbell and Taksler (2003) and Hotchkiss and Jostova (2007).
We illustrate the concave relation between the illiquidity of investment grade bonds and
their yield spreads in Figure 1. The plots are the results of piecewise linear regressions. For
each of the five illiquidity measures, we first breakdown the full range of the value of a given
illiquidity measure into five groups. For instance, as the 5th and 95th percentiles of the
Amihud measure are 0.04% and 4.77%, we choose 0.25%, 0.75%, 1.25%, 1.75%, and 2.25%
8
It is interesting to observe that insurers hold a significant portion of short-term bonds, some of which can
be long bonds at the time of purchase and become short-term ones as time goes by. We have calculated some
further statistics to get a clear idea on the maturity of bonds when they are purchased by insurers. For newly
purchased bonds by property casualty insurers, the three types of maturities most often purchased are 10
years (27%), 5 years (21%) and 9 years (8%). In comparison, the most often purchased maturity categories
for life insurers are 10 years (35%), 30 years (11%), and 5 years (12%). The difference is consistent with
the differential liability structure across insurers: life insurers have more long-term liabilities than property
insurers, as a result life insurers may have longer investment horizons than property insurers.
17
as the breakpoints to form the five groups.9 Then, we perform piecewise linear regressions
within each group in each quarter, with the dependent variable being the yield spread and the
explanatory variables being the five piecewise functions of the illiquidity measure. We then
take the average coefficients for each group over time to re-construct the average piecewise
linear relation between yield spread and illiquidity. The plots across the five illiquidity
measures consistently reveal that yield spreads are an increasing and concave function of
bond illiquidity. These patterns resemble the concave relation between stock returns and
stock trading cost (the relative bid-ask spread) shown in Amihud and Mendelson (1986).
Note that the yield spreads are based on promised yields, not the expected yields to
investors. To more strictly follow the prediction of Amihud and Mendelson (1986), we
further obtain expected yield spreads by subtracting the expected default losses from the
promised yield spreads. Specifically, we take Moody’s estimates of credit loss rates for each
rating category in each year, based on their proprietary data starting in 1982. For example,
to obtain expected yield spreads of all BBB-rated bonds in 2003, we use Moody’s estimate
for Baa-rated bonds published in early 2003 that is based on the period 1982–2002. The
pattern (e.g., a concave relation between bond illiquidity and expected yield spread) is quite
similar to that revealed in Figure 1. To save space we do not plot them in the paper.
5
Empirical Results
In this section we present the findings from the empirical analysis. Section 5.1 investigates
liquidity preference of insurers and the persistence of such preference. In Section 5.2, we
present evidence on the existence of liquidity clientele. Sections 5.3 and 5.4 examine the
liquidity clientele effect in corporate bond yield spreads. Section 5.5 examines time variations
of liquidity premiums across different liquidity clientele groups. Section 5.6 provides a set of
extended analyses and robustness checks.
For the reason discussed earlier, most of the results reported in this section are for the
9
Additionally, the breakpoints we used are 1, 2, 3, 4, and 5 for Roll measure, 0.05, 0.20, 0.35, 0.50, and
0.65 for LOT measure, 0.15%, 0.35%, 0.55%, 0.75%, and 0.95% for IRC, and -0.5, 0, 0.5, 1, and 1.5 for λ.
18
investment-grade bonds. The results for high-yield bonds are presented in Section 5.6.4.
5.1
Bond Illiquidity, Portfolio Illiquidity, and Liquidity Clientele
Table 2 reports the cross-sectional statistics of the following four main variables used in our
empirical analysis: corporate bond yield spreads, ILQ, ILP, and ILC. The cross-sectional
statistics reported include the 5th, 25th, 50th, 75th, and 95th percentiles, as well as the mean,
and standard deviation of each variable. This provides an overall picture of the substantial
cross-sectional variation of each variable. These statistics are first computed cross-sectionally
in a given quarter (across bonds or across insurers) and then averaged over time.
Panel A illustrates the distribution of bond yield spreads, with a mean of 1.78%, a
median of 1.61%, and a standard deviation of 1.06%. These statistics are comparable to
those reported in other studies such as Friewald et al. (2012).
Panel B reports the distributions of the five bond illiquidity measures (ILQ). The Amihud
measure has a mean of 1.27%, a median of 0.61%, and a standard deviation of 2.01%. This
means that a trade of $1,000,000 in a bond, on average, has a price impact of 1.27%. The
variation in illiquidity (by the Amihud measure) across bonds is remarkably high and ranges
between 0.04% and 4.77% from the 5th to the 95th percentiles. This is consistent with the
findings in Dick-Nielsen et al. (2012) and Friewald et al. (2012). The Roll measure has a
mean of 1.69 and a standard deviation of 1.61, suggesting high liquidity variation across
bonds as well. The mean of LOT is 7.29%, and the median is 2.03%. The median imputed
roundtrip cost (IRC ) in percentage of the price is 0.43%. IRC is less than 0.10% for the
top 5% most liquid bonds. For the λ measure, we observe a mean of -0.03 and a median of
-0.15, consistent with Dick-Nielsen et al. (2012).
Panel C reports distributions of ILP Amihud , ILP Roll , ILP LOT , ILP IRC , and ILP λ —five
portfolio illiquidity measures with different underlying bond illiquidity measures. The mean
and median of ILPAmihud are 1.28% and 1.09%, respectively. The variation of this measure
is markedly large with the range between 0.73% at the 5th percentile and 3.03% at the
95th percentile. We observe similar patterns in the other four ILP measures. These results
19
suggest that corporate bond portfolios have very different levels of illiquidity across insurers.
Lastly, Panel D reports the distributions of the bond-level illiquidity clientele measures,
ILC. Based on the Amihud measure of bond illiquidity, the mean and median of ILC are
1.24% and 1.21%, and its 5th- and 95th-percentile values are 0.99% and 1.54%, respectively. Thus, compared with the mean or median, the dispersion of ILC is quite wide. The
distributions of other four ILC measures reveal a similar pattern.
Table 3 presents the correlation matrix of the five illiquidity proxies and the corresponding ILC s. The correlations across the illiquidity measures are all positive. For example,
the correlations among Amihud, Roll, and LOT range from 0.11 to 0.43. The correlations
between Amihud, IRC, and λ are between 0.40 and 0.79. This is consistent with the findings
in Dick-Nielsen et al. (2012) and Friewald et al. (2012). Similarly, correlations among the
five liquidity clientele measures (ILC s) are all positive, ranging from 0.35 to 0.88. Interestingly, correlations between each liquidity measure and the corresponding liquidity clientele
measure are all around 0.40, suggesting that the liquidity measures and the liquidity clientele
measures are positively correlated. This is consistent with our discussion in Section 3.2 on
the empirical relation between ILQ and ILC.
5.2
Evidence on Liquidity Preference/Clientele
An important issue is whether different levels of ILP across insurers indeed reflect their
differences in liquidity preferences, which is a key element of the clientele hypothesis. We
perform two sets of analysis on this issue.
First, we examine whether the constructed portfolio illiquidity measures persist. If portfolio illiquidity ILP captures an insurer’s stable illiquidity preference, its value must be
persistent over time. Figure 2 illustrates such persistence. In each quarter, we sort insurers
into quintiles based on a measure of ILP. We then calculate the average ILP of insurers in
each initial quintile in the ranking year and the subsequent three years. As the figure shows,
based on all five bond-level illiquidity measures, insurers initially ranked in the highest ILP
quintile continue to have high ILP s during the subsequent three years.
20
Next, we link ILP to firm characteristics that potentially reflect insurers’ illiquidity preferences. In Section 3, we hypothesize that investment horizon and funding constraint are
two key determinants of liquidity preference. Accordingly, here we look at six different firm
characteristics related to insurers’ investment horizon, and five other firm characteristics
related to their funding constraints.
The six characteristics related to investment horizon are the following. The first is the
annual portfolio turnover, TURN. Following the conventional portfolio turnover definition
(see, the CRSP Mutual Fund Database Guide), we compute TURN as the minimum of the
aggregate market value of bonds purchased by an insurer and the aggregate value of bonds
sold by the insurer in each quarter, scaled by the aggregate portfolio value at the end of the
quarter. Annual portfolio turnover is the quarterly measure multiplied by 4. A high portfolio
turnover rate indicates a short portfolio investment horizon. The next two characteristics,
STURN and LTURN, are variations of TURN. STURN is the annual turnover of an insurer’s
subportfolio that consists of bonds with maturity shorter than 5 years, and LTURN is the
annual turnover of the subportfolio of bonds with maturity at or above 5 years. We look at
turnover separately for the short-term and long-term bonds because the turnover on shortterm bonds is mechanically high, and the difference in investment horizon is more likely to
show up in the turnover for long-term bonds. The fourth characteristic is holding horizon
in years, HZ, which is the average time length a bond is held by an insurer since its initial
acquisition up to the current quarter. The NAIC’s Schedule D data report the acquisition
date of each bond by an insurer, which enables us to compute HZ.10 We also include MAT,
the average maturity of bonds purchased by insurers in years. If a long-horizon investor
engages in a buy-and-hold strategy, the bonds that the investor purchased should have long
maturities. The last characteristic, LIFE, equals to 1 for a life insurer and 0 otherwise. Life
insurance policies result in operating liabilities with much longer horizons relative to those
for property and casualty policies. Since insurers use bond portfolios to hedge the interest
10
Note that since HZ is computed on a bond that is still in an insurer’s portfolio and not sold yet, it is
therefore shorter than the true holding period of a bond.
21
rate risk of their operating liabilities, life insurers tend to buy and hold long-term bonds.11
The five characteristics related to funding constraints include total assets (TA), firm age
(AGE ), a dummy for affiliated insurers (AFF ), insurers that issue stocks (STOCK ), and the
reinsurance ratio (REINS ). TA is the total assets in billion dollars. AGE is the number of
years since the year of firm incorporation. Affiliated insurers are those affiliated with parent
insurer groups or insurance holding companies. STOCK equals to 1 for insurers owned by
stockholders, known as stock insurers, and 0 for non-stock insurers, such as mutual insurers
owned by policyholders. We expect larger insurers, older insurers, affiliated insurers, and
stock insurers are more resourceful in meeting liquidity needs (via either external financing
or internal capital markets) and therefore are less constrained when investing in illiquid
assets. REINS is the ratio of the insurance premiums that an insurer cedes to other insurers
through the reinsurance arrangement relative to the sum of insurance premiums it collects
and the insurance premium the insurer accepts from other insurers through the reinsurance
arrangement. A high REINS indicates that the insurer outsources a large part of its insurance
operating risk, suggesting a low capacity to bear operating risk. We hypothesize that such an
insurer similarly has a low external funding capacity. To sum up, larger and older insurers,
affiliated and stock insurers, and insurers with lower reinsurance ratio tend to have less
funding constraints. These characteristics are constructed using the NAIC data on annual
financial statements.
Table 4 presents these insurer characteristics across ILP -sorted insurer deciles. We rank
insurers into ILP deciles each quarter and compute the average characteristics for each decile,
and then take the averages over time. We also compute the differences in characteristics
between the top (D10) and bottom (D1) deciles and the corresponding t-statistics using the
Newey-West procedure with a four-quarter lag. In the discussion of Table 4 that follows
we focus on the case where bond illiquidity is based on the Amihud measure (Panel A), as
results based on the other illiquidity measures (Panels B to E) are qualitatively similar.
11
Portfolio turnover may be endogenous to the liquidity of securities in the portfolio. Thus, the relation
between ILP and portfolio turnover should be interpreted as an equilibrium association instead of a one-way
causality by portfolio turnover onto ILP, or vice versa. However, other insurer characteristics, such as LIFE
and those examined below (TA, AGE, AFF, STOCK, and REINS ), are likely exogenous to ILP.
22
Columns (1) through (6) are for investment-horizon characteristics. Note first that portfolio turnovers are lower for insurers with higher ILP decile ranks. Specifically, in Panel A,
the average turnover drops from 16% per year for the bottom ILP decile to 9% per year for
the top decile. The average turnovers of short-term bonds exhibit some variations across
ILP deciles, while larger variations are observed for the turnover of long-term bonds. The
average STURN for the D1 (D10) portfolio is 0.18 (0.14) while the average LTURN for
the D1 (D10) portfolio is 0.12 (0.06). The differences in STURN between the D10 and D1
deciles are all insignificant while the differences in LTURN are all significant regardless of
the illiquidity measure used.
Note also from Panel A that the average holding horizon (HZ) increases in the decile rank
of ILP. Under the Amihud illiquidity measure, the average holding horizon for D1 insurers
is 1.83 years and it is 3.36 years for D10 insurers. The difference is statistically significant at
the 1 percent level. The average maturity (M AT ) of insurers’ newly acquired bonds increases
in insurers’ ILP ranks, consistent with the notion of liquidity clientele. Additionally, note
that the fraction of life insurers is roughly 17% in the bottom ILP decile portfolio and 53%
for the top ILP decile.
The last five columns of Table 4 report the average funding-constraint characteristics
across ILP -sorted insurer deciles. ILP is positively correlated with firm size and firm age.
For instance, in Panel A, the average TA (AGE ) for the bottom ILP decile is $0.58 billion
(37.89 years) and that of the top ILP decile is $2.86 billion (49.16 years). That is, insurers
with higher ILP tend to be larger and older. Further, affiliated insurers, stock insurers, and
insurers relying more in reinsurance, tend to have higher ILP.
The evidence presented above supports the notion of liquidity clientele: insurers with
longer horizons and easier access to financing hold more illiquid bond portfolios.
5.3
Clientele Effect on Yield Spread: Two-way Sorted Portfolios
We now investigate the effect of liquidity clientele on corporate bond pricing. We first use
an intuitive double-sorted portfolio approach that helps highlight the difference between
23
the liquidity premium effect and the liquidity clientele effect. In each quarter, we sort all
the investment grade bonds on ILQ and ILC independently (i.e., sorting on ILC is not
conditional on ILQ). This results in 25 (5 by 5) groups with equal number of bonds in each
group. Across ILQs, ILQ1 and ILQ5 refer to the least illiquid (or most liquid) and the
most illiquid bonds, respectively. Across ILC s, ILC1 represents the group of bonds with
the lowest ILC (held by insurers with the lowest liquidity preference or equivalently, with
the highest liquidity demand), and ILC5 the group of bonds with the highest ILC (held by
insurers with the highest ILP, or the lowest liquidity demand).
Table 5 reports the average yield spreads for the 25 bond portfolios. In the lowest ILC
quintile (i.e., ILC1 ), yield spread monotonically increases in bond illiquidity, regardless of
the illiquidity measure used. For instance, under Amihud measure (Panel A), we find that,
for the lowest ILC group, the average yield spread for the most liquid bond group (ILQ1 )
is 1.28%, while that of the most illiquid bonds (ILQ5 is 2.22%. The liquidity premium,
proxied by the yield spread difference between the two groups, is 0.94% with a t-statistic
of 4.49. The liquidity premium remains significantly positive across all the ILC ranks. In
the highest ILC group (ILC5 ), the average yield spread of bonds in the top (bottom) ILQ
quintile is 2.39% (1.80%), resulting in a liquidity premium of 0.59%. The liquidity clientele
effect is measured by the difference in the liquidity premium between the top and bottom
ILC quintiles, which is -0.35% and significant at the 5% level in this case. Thus, going
from the bottom ILC quintile to the top ILC quintile, the liquidity clientele effect reduces
the liquidity premium by one third. The same pattern holds for all other bond illiquidity
measures—an increase in ILC reduces the liquidity premium component of corporate bond
yield spreads.
Also note that among bonds within the same ILQ quintile, there is a positive relation
between ILC and yield spreads. This is consistent with the notion of latent liquidity (Mahanti et al. (2008)) discussed in Section 3.2; that is, when there exists liquidity clientele,
ILC could be viewed as an alternative bond-level illiquidity measure and thus commands a
liquidity premium.
24
5.4
Panel Regressions on Yield Spreads
We now turn to a panel regression model to test the liquidity clientele effect while controlling
for various factors affecting yield spreads. We first classify all bonds into three groups
(terciles) based on a given bond liquidity clientele measure ILC (i.e., ILC Amihud , ILC Roll ,
ILC LOT , ILC IRC , and ILC λ ) in each quarter.12 Let T1 (T2, T3) be the indicator variable
that equals 1 if the bonds are in the first (second, third) tercile and zero otherwise. The
panel regression model has the following specification:
Spreadi,t = α0 + α1 ILQi,t + α2 T2i,t + α3 T3i,t + α4 ILQi,t ∗ T2i,t
+α5 ILQi,t ∗ T3i,t + Controli,t + εi,t ,
(4)
where Spreadi,t is the yield spread of bond i in quarter t; ILQ is a measure of bond illiquidity.
The error term εi,t includes both the time-fixed effects and the issuer-fixed effects.
Our main interest is on the interactions between ILQ and T2 as well as those between
ILQ and T3 in Eq. (4), as they represent the potential effect of liquidity clientele on liquidity
premium. We expect that α4 < 0 and α5 < 0. That is, liquidity clientele attenuates the
liquidity premium in yield spreads.
We include an extensive set of bond-specific and firm-specific control variables in Eq. (4).
The bond-specific control variables include bond age (the time since issuance, in years), a
bond’s time to maturity (in years), the logarithm of bond issue size (in million dollars),
annual coupon rates (in percentage), and credit rating dummies.13 Existing studies show
that bond age and issue size are positively related to bond yield spreads (e.g., Schultz (2001),
Campbell and Taksler (2003), and Dick-Nielsen et al. (2012)). In addition, Campbell and
Taksler (2003) argue that bonds with higher coupons are taxed more throughout the life of
the bond, making them less desirable than bonds with lower coupons, and thus implying a
12
We report the results based on ILC terciles to save space. Results based on ILC quintiles are similar.
Bond ratings are obtained from Standard & Poor’s. In cases where the S&P’s rating is missing, we use
Moody’s, and then Fitch’s, in that order. A dummy for a specific rating (e.g., AAA) equals 1 when a bond
has this rating and 0 otherwise. Altogether, there are 25 rating categories from AAA to D. We include
the top 24 rating dummies in the regressions and exclude that the D rating to void multi-colinearity in the
regression specification.
13
25
higher yield spread.
Firm-specific control variables include the ratio of operating income to sales, ratio of long
term debt to assets (LTD), total debt to capitalization (Leverage), equity volatility (EqVol ),
and four pretax interest coverage variables (Pretax1, Pretax2, Pretax3, and Pretax4 ).14 High
values of the ratio of operating income to sales and pretax interest coverage indicate financial
healthiness and are likely associated with low yield spreads (e.g., Blume et al. (1998), CollinDufresne et al. (2001), and Campbell and Taksler (2003)). In addition, we expect the equity
volatility to have a positive effect on yield spreads (e.g., Campbell and Taksler (2003)). The
accounting data are as of the end of the previous calendar year. The market value of equity
is at the end of the quarter. These control variables are similar to those used in Blume et al.
(1998), Collin-Dufresne et al. (2001), Campbell and Taksler (2003), Chen et al. (2007), and
Dick-Nielsen et al. (2012). For robust statistical inference in a panel regression setting (e.g.,
Petersen (2009)), we compute two-way clustered standard errors along the time and issuer
dimensions, in addition to the control for the issuer- and time-fixed effects.
Columns (1) through (5) in Table 6 present the baseline results from Eq. (4) in absence of
any control variables, for each of five bond illiquidity measures considered. First, consistent
with the literature, we find that the coefficients on ILQ are positive and highly significant
with a t-statistic ranging from 2 to 14 across the five bond illiquidity measures, indicating
that high illiquidity demands high premium. For instance, note from column (1) that the
yield spread would increase by 0.69% for a one-percentage increase in the Amihud illiquidity
measure. Next, the coefficients on the dummy variables T2 and T3 are both significantly
positive, consistent with the idea that the latent liquidity commands substantial liquidity
premium. Most importantly, the coefficients on the interactions between ILQ and T2 as
well as between ILQ and T3 are significantly negative. Further, the coefficients on the inter14
Following Blume et al. (1998), to control for the skewness of the distribution of pretax interest rate
coverage (PIRC, measured as EBIT divided by interest expenses), we construct four Pretax variables.
Pretax1 takes the value of PIRC if PIRC is less than 5, and 5 if it is above. Pretax2 is zero if PIRC is
below 5, takes the value of PIRC minus 5 if PIRC lies between 5 and 10, and 5 if PIRC lies above. Pretax3
is zero if PIRC is below 10, takes the value of PIRC minus 10 if it lies between 10 and 20, and 10 if it is
above. Pretax4 is zero if PIRC is below 20 and takes value of PIRC minus 20 if it is above 20 (we set the
maximum at 80 for observations with PIRC greater than 100).
26
actions involving T3 are more negative than those involving T2. This finding is consistent
with the hypothesis that liquidity clientele attenuates the liquidity premium.
Columns (6) through (10) report the results from regressions specified in Eq. (4) with
the full set of control variables. We find that illiquidity continues to be positively related to
yield spread after controlling for various bond-specific and firm-specific variables, regardless
of bond illiquidity measures used. Again, highly significant coefficients on the bond illiquidity
measures are consistent with the theoretical prior that liquidity is priced in the yield spread.
Next, note that the coefficient estimates on the interactions between ILQ and T2 as well
as those between ILQ and T3 are significantly negative across all five different illiquidity
measures used. For example, as shown in column (6) for the case of the Amihud liquidity
measure, the coefficient on ILQ*T2 is -0.10 (t-stat = -3.68) and that of ILQ and T3 is -0.20
(t-stat = -8.22), indicating that liquidity clientele reduces the liquidity premium of bonds.
Moreover, we note that the coefficients on control variables are largely consistent with
those reported in the literature. For instance, the coefficients of bond maturity are significantly positive, consistent with the evidence that longer term bonds have higher yield
spreads. Coefficient estimates on coupon rates are also significantly positive, suggesting that
high coupon bonds (normally high-yield bonds) have high yield spreads. The firm-specific
variables generally have expected signs when they are significant. As might be expected, the
coefficient on the ratio of income to sales is significantly negative while the coefficients on
LTD, Leverage, and equity volatility are significantly positive.
Overall, the results from panel regressions indicate that corporate bond yield spreads
are strongly correlated with the interaction between bond illiquidity and liquidity clientele.
This finding supports the hypothesis that the liquidity premium is attenuated when illiquid
securities predominantly attract investors with low liquidity preference.
5.5
Time Variation of Liquidity Premium
As discussed in Section 3 (i.e., hypothesis H3), we expect the liquidity premium for bonds
held by insurers with stronger liquidity preference to be be more sensitive to market condi-
27
tions and thus are more volatile. We investigate this hypothesis here. In each quarter we
sort sample bonds into terciles based on ILC. We then estimate the liquidity clientele effect
on yield spread using the following cross-sectional regression in each quarter for each ILC
tercile:
Spreadi,t = α0 + α1 ILQi,t + Controli,t + εi,t ,
(5)
where Spreadi,t is the yield spread of bond i in quarter t and ILQ is a measure of bond
illiquidity. We include the same set of control variables as those specified in Eq. (4).
To illustrate the time variation of liquidity premium, in Figure 3 we plot the time series
of the estimated coefficients for ILQ, i.e., the quarterly liquidity premium estimates. The
liquidity premium estimates for bonds in the lowest (T1 ) and highest (T3 ) ILC terciles are
plotted separately. The plot shows that the liquidity premium is much more volatile for the
T1 bonds than for the T3 bonds. According to our estimates (not tabulated in the paper),
based on the Amihud measure, the time-series standard deviation of the liquidity premium
estimates for the T1 bonds is 5.68%. By comparison, that for the T3 bonds is 2.69%. The
same pattern obtains under other bond illiquidity measures. This is consistent with the
implication of liquidity clientele on liquidity premium volatility.
The clientele effect on liquidity premium volatility can also help understand the behavior
of liquidity premium during the recent financial crisis. An eye-catching pattern in the plots
is that the liquidity premiums peaked in 2008Q3 or 2008Q4, when the financial crisis hit its
climax – when Lehman collapsed and several other financial institutions, including Merrill
Lynch, Citigroup, and AIG, were either acquired under duress or subject to government
takeover. The spike of liquidity premium is much more visible for the T1 bonds than for the
T3 bonds in the plots. As a result, when we measure the clientele effect by the difference in
liquidity premium between the two bond groups, the clientele effect is the strongest during
the crisis period.
The liquidity premium for the T1 bonds comes down after the crisis, however it remains
higher than the pre-crisis period until the end of our sample period. This is consistent with
the fact that during this subperiod, many investors including insurers struggle to obtain
28
financing or roll-over short-term financing, and liquidity remains scarce and the premium on
liquidity remains high (e.g., Dick-Nielsen et al. (2012) and Friewald et al. (2012)). However,
note that for the T3 bonds, i.e., those held by investors who are less subject to the funding
constraints, the liquidity premium remains relatively modest during the same period.
Overall, the findings here highlight the importance of liquidity clientele on the time
variation of liquidity premium.
5.6
Further Analysis
We conduct further analysis to test additional implications of liquidity clientele. We look at
the clientele effect among short-term vs. long-term bonds, two alternative liquidity clientele
measures that separately quantify the effect of investment horizon and funding constraints,
a subsample of bonds with relative clean control of credit risk, and the clientele effect among
speculative bonds as well as among bonds with varying degrees of insurer ownership. And
finally, we use expected yield spreads instead of promised yield spreads in analysis.
5.6.1
Short-term vs. Long-term Bonds
In contrast to the indefinite life of stocks typically considered in the theoretical models of
liquidity clientele, corporate bonds have finite maturities. This distinction offers an interesting opportunity to study the investment horizon effect. The effective holding horizon for
short-maturity bonds has to be short, regardless of how long an investor’s horizon is when
holding other securities. Consequently, for short-term bonds, long-horizon investors do not
have an advantage in amortizing trading costs. Thus, we expect the liquidity clientele effect
to be weaker among short-term bonds relative to long-term bonds.
To test this conjecture, we perform regressions specified by Eq. (4) for the short- and longterm bonds separately. The short-term bonds are those with less than five years to maturity,
and the long-term bonds with five or more years to maturity. Table 7 reports the regression
results. For short-term bonds, most of the coefficients on the interaction terms between
ILQ and the ILC tercile dummies are either insignificant or have wrong signs relative to
29
what the clientele effect suggests. For instance, under the Amihud illiquidity measure, across
short-term bonds, the coefficient on ILQ*T2 is -0.03 (t-stat = -0.75) and the coefficient on
ILQ*T3 is -0.11 (t-stat = -2.29). By contrast, across long-term bonds, the coefficients on
ILQ*T2 and ILQ*T3 are -0.14 (t-stat = -3.58) and -0.22 (t-stat = -6.28), respectively. This
confirms the notion that the effect of liquidity clientele on liquidity premium is stronger
among long-term bonds than among short-term bonds.
5.6.2
Alternative Liquidity Clientele Measures
In Table 4 we show that insurers’ liquidity preference is related to both investment horizon
and access to financing. Here, we more directly examine impact of these two types of insurer
characteristics on liquidity premium.
To investigate the investment horizon effect, we construct an alternative ILC measure
based on insurers’ portfolio turnover. Specifically, in the clientele measure definition of Eq.
(2), we replace ILP by the inverse of the 4-quarter rolling average of an insurer’s corporate
bond portfolio turnover (i.e., 1/TURN ). As noted earlier, this measure is also related to the
latent liquidity measure of Mahanti et al. (2008).
To investigate the effect of funding constraints, we construct a second alternative ILC
measure, which involves two steps. First, in each year, we combine five insurer characteristics
related to ease of financing into one combined measure. Specifically, we sort firms into
percentiles (with value from 0 to 1) based on each of the following three characteristics:
total assets (TA), firm age (AGE ), and the inverse of the reinsurance ratio (1/REINS ). For
the dummy variables AFF and STOCK, we keep their values of either 0 or 1. We then
take the average over the three percentile variables and the two dummy variables to obtain
the combined measure. Second, in the clientele measure definition of Eq.(2), we replace the
portfolio illiquidity ILP by the above combined measure for ease of financing.
We perform panel regressions following the specification in Eq. 4 but using the turnoverbased and funding constraint-based ILC as the main explanatory variables (separately and
jointly) instead of the original ILC. The regression results for the turnover-based ILC are
30
reported in the first five columns of Table 8, with each column involving one of the five bondlevel illiquidity measures ILQ. The pattern is consistent with those reported in Table 6 under
the original ILC measures. First, the coefficients on ILQ and the two ILC tercile dummies
(denoted as T2A and T3A) are all significantly positive regardless of bond illiquidity measures
used. For example, under the Amihud measure (column (1)), one percentage increase in ILQ
raises the yield spread by 0.16%. The coefficients on T2A and T3A are respectively 0.05
(t-stat = 2.29) and 0.14 (t-stat = 5.53), consistent with the notion of latent liquidity. The
coefficients on the interactions of ILQ with T2A and T3A are all significantly negative. This
is consistent with the finding in Table 6 although the magnitude of coefficients is slightly
smaller here. This suggests that liquidity clientele driven by differential investment horizons
across insurers attenuates liquidity premium. Again, the patterns of coefficients on control
variables are similar to those in Table 6.
The regression results for funding constraint-based ILC are reported in columns (6) to
(10) of Table 8. Across five different bond-level illiquidity measures ILQ, the coefficients
on ILQ and on the two ILC tercile dummies (denoted as T2B and T3B ) are significantly
positive. The coefficients on the interactions of ILQ with T2B and T3B are significantly
negative. The magnitudes of the coefficients for the interactions in columns (6) through (10)
are slightly lower than those reported in the first five columns and those reported in Table
6. But the clientele effects under these ILC measures are largely consistent with each other.
Finally, we include the two alternative ILC measures jointly in the regressions. The
results, reported in the last five columns of Table 8, show that both investment horizon and
funding constraints drive the liquidity clientele effect on liquidity premium. For instance,
using the Amihud bond illiquidity measure, we find that the coefficient on the interaction
of ILQ with T2A (based on turnover) is -0.04 (t-stat = -2.69) and the coefficient on the
interaction of ILQ with T2B (based on funding constraint) is -0.03 (t-stat = -1.82). Further,
the interaction coefficient involving the turnover-based T3A is -0.06 (t-stat = -4.69) and that
involving funding constraint-based T3B is -0.03 (t-stat = -1.98).
Taken together, the results suggest that both investment horizon and funding constraints
31
are important drivers of the liquidity clientele effect on liquidity premium.15
5.6.3
Analysis on Bond Pairs
The literature suggests that liquidity and credit risk are endogenous to each other and
interwined in affecting bond pricing (e.g., Ericsson and Renault (2006), He and Xiong (2012),
and He and Milbradt (2014)). This gives rise to an interesting possibility: ILC may affect
bond yield spreads via both the liquidity channel and the credit risk channel. In the regression
analysis reported in Table 6, we control for the effect of credit risk by including explanatory
variables such as the LTD, leverage, equity volatility, credit rating dummies as well as the
“catch-all” issuer-fixed effects. Here, we pursue an additional approach that has even stronger
control for credit risk and thus further highlights the liquidity channel of the clientele effect.
Specifically, we perform analysis on a sample of bond pairs by the same issuers. We
follow Helwege, Huang, and Wang (2014) to identify bond pairs which must have the same
issuer, same seniority, coupon type, interest frequency, and credit ratings. In addition, we
require the bond pairs to have sufficiently close maturity (no more than 1 year difference)
so that there is only minimal difference in the credit risk of the two bonds. When multiple
bond pairs are identified from the same issuer at the same time, we keep the pair with the
largest yield difference. In this way, we identify 963 unique bond pairs. Among each bond
pair, we define the base bond as the one with higher yield spread and the other as the paired
bond. By construction, the differences in yield spreads between the bond pairs are more
likely due to difference in liquidity rather difference in credit risk. Of course, because of the
correlation between credit risk and liquidity, by removing the credit risk effect, we may have
also removed part of the liquidity effect.
We perform panel regressions with the dependent variable being the difference in the
yield spreads of bond pairs (the yield spread of the base bond minus the yield spread of the
15
We have also examined the liquidity premium volatility effect using the two alternative IlC measures.
We separately estimate the liquidity premium in each quarter based on Eq. (5) for the top and bottom ILC
terciles using turnover-based ILC and funding constraint-based ILC. The patterns in the time variations of
liquidity premium using the alternative ILC s are consistent with those in Figure 3. That is, the liquidity
premium is more volatile for T1 bonds than for T3 bonds.
32
paired bond). The main independent variables are i) the difference in ILQ between the bond
pair, ii) the differences in T2 and T3, and iii) the difference in the interaction between ILQ
and T2, and the difference in the interaction between ILQ and T3. As the control variables,
we include the differences in bond characteristics including bond age, maturity, issue size
and coupon rate.
The results are reported in Table 9. We find a significant liquidity clientele effect on bond
pricing in the bond pair analysis. For example, using the Amihud illiquidity measure, we
find that the coefficient on the difference in the interaction between ILQ and T2 is -4.69%
(t-stat = -2.86), and the coefficient on the difference in the interaction between ILQ and
T3 is -9.76% (t-stat = -2.73), respectively. In addition, the coefficient on the difference in
ILQ is 6.34 with the 5% significant level. The coefficients on the differences in T2 and T3
are significantly positive, too. Moreover, the differences in bond age and the coupon rates
are significantly and positively correlated with the differences in yields. We find consistent
results under other bond-level illiquidity measures.
The results suggest a clientele effect on liquidity premium among bond pairs. This is
unlikely attributable to the credit risk channel, but rather to the liquidity channel.
5.6.4
Speculative Bonds and Bonds with Varying Degrees of Insurer Ownership
We now look into the importance of insurance ownership in detecting the clientele effect. As
observed in Panel C of Table 1, insurer ownership as a fraction of bonds outstanding varies
across bonds. For bonds with low insurer ownership, insurers may not be the marginal
investors and the clientele measures based on insurer holdings may not significantly affect
bond pricing.
To examine the effect of insurer ownership, we divide the investment-grade bond sample in
each quarter into two groups—those with insure ownership below 20% of bonds outstanding
and those on or above the 20% threshold. We perform panel regressions following Eq. (4)
within each subsample. As shown in Panels A and B of Table 10, the clientele effect on
liquidity premium, as measured by the coefficients on ILQ*T2 and ILQ*T3, are rarely
33
significant in the sample of bonds with low insurance ownership. However, the coefficients
on the interactions are pervasively significant in the sample of bonds with high insurance
ownership (i.e., insurers’ holding exceeds 20%). The coefficients and t-statistics also suggest a
weaker relation of T2 and T3 with yield spreads among bonds with lower insurer ownership.
However, not that the coefficients on ILQ (the construction of which does not depend on
insurer ownership) are comparable between the two subsamples. These results suggest that
it is important to rely on the holdings of marginal investors in detecting the clientele effect
on bond pricing.
Well known in existing literature (e.g., Campbell and Taksler (2003), Ellul et al. (2011),
Ambrose et al. (2012), and Becker and Ivashina (2013)) and confirmed by Panel C of Table
1, insurers have limited participation in the speculative bond market. If being marginal
investors is important for constructing effective liquidity clientele measures, then the ILC
based on insurer holdings is expected to have weak impact on the liquidity premium of
speculative bonds. This is indeed the case. We perform panel regressions following Eq. (4)
on the speculative bonds, and report the results in Panel C of Table 10. Most of the
coefficients on ILQ*T2 and ILQ*T3 are insignificant.16
5.6.5
Analysis based on Expected Yield Spreads
Lastly, we repeat the panel regressions following Eq. (4) with expected yield spreads as
the dependent variable. Recall from Section 4.4 that expected yield spreads are computed
by adjusting the (promised) yield spreads with expected default losses. Results from the
regressions on expected yield spreads are largely similar to those based on promised yield
spreads reported in Table 6. Thus, our main findings are robust to the use of expected yield
spreads. For brevity, these results are not tabulated.
16
Another possible reason for the insignificant clientele effect among speculative bonds is that for such
bonds, credit risk matters more than liquidity in bond pricing. This also helps explain the observation that
some of the ILQ measures (albeit not all) have weak or insignificant coefficients in Panel C.
34
6
Conclusions
Although the notion of “liquidity clientele,” first introduced by Amihud and Mendelson
(1986), is well known in the theoretical literature, to our knowledge it has not been formally
tested in the corporate bond market. In this study, we conduct such a test using a comprehensive dataset on corporate bond holdings of insurance firms, which are by far the largest
group of corporate bond investors. The dataset provides detailed information on these holders and thus allows us to quantify their liquidity preferences and link the preferences to
corporate bond yield spreads.
Our results provide evidence for the existence of liquidity clientele. We find substantial
heterogeneity in the liquidity preference across insurers. We also find that such liquidity
preference is persistent over time and correlated with characteristics indicative of insurers’
investment horizons and their funding constraints. Furthermore, we document that insurers’ liquidity preference interacts with bond liquidity to affect corporate bond yield spreads.
Bonds with higher illiquidity have higher yield spreads, consistent with the liquidity premium
effect. Moreover, liquidity clientele attenuates the liquidity premium. Additional implications of the clientele effect also find support in the data, such as the behavior of liquidity
premium volatility, the differential impact on short-term and long-term bonds, and the effect
of funding constraints on bond pricing.
35
Appendix: Corporate Bond Illiquidity Measures
This appendix describes the details of the five bond illiquidity measures.
1. Amihud
The daily Amihud measure is the average ratio of absolute return to the trade size (in $
million) of consecutive transactions during a day:
Ni,t Pi,j −Pi,j−1 1 X Pi,j−1 ,
Amihudi,t =
Ni,t j=1
Qi,j
(6)
where Ni,t is the number of trades of bond i on day t; Pi,j and Pi,j−1 are the prices for two
consecutive trades (j − 1th and j th ), for bond i on day t; Qi,j is the size of the j th trade
for bond i. As such, at least two transactions are required on a given day to calculate the
measure. Following Dick-Nielsen et al. (2012), the quarterly Amihud measure is the median
of daily measures within the quarter.
2. Roll
The Roll (1984) measure infers the effective bid-ask spread from negative serial dependence
of successive transaction price changes. Bao et al. (2011) show that this measure is positively related to corporate bond yields. Our procedure follows Dick-Nielsen et al. (2012).
Specifically, the daily Roll measure is:
Rolli,t
q
= 2 −cov(Ri,t , Ri,t−1 ),
(7)
where Ri,t and Ri,t−1 are returns to two consecutive trades, computed as price changes
scaled by the price of the first trade. The covariance is computed using a rolling window
of 21 trading days. The quarterly Roll measure is the median of daily measures within the
quarter.
36
3. LOT
The LOT measure of Lesmond et al. (1999) is based on the idea that given the same amount
of new information, more illiquid securities should have fewer trades, thus more zero-return
days. Specifically,
LOTi,t = α2,j − α1,j
(8)
where α1,j and α2,j are buy-side and sell-side costs of bond j that can be estimated using the
maximum likelihood method. We follow Chen et al. (2007) to specify the likelihood function:
LnL =
X
Ln
1
X 1
1
−
(Rj,t + α1,j − βj1 Durj,t ∗ ∆Rf t
(2πσj2 )1/2
2σj2
1
X
1
Ln
−βj2 Durj,t ∗ ∆S&Pt )2 +
(2πσj2 )1/2
2
X 1
−
(Rj,t + α2,j − βj1 Durj,t ∗ ∆Rf t
2
2σ
j
2
−βj2 Durj,t ∗ ∆S&Pt )2
X
+
Ln(Φ2,j − Φ1,j )
0
P
P
(region 2) refer to nonzero measured returns in negative and
P
positive market return regions, respectively. 0 (region 0) refers to the region of zero returns.
where
1
(region 1) and
2
∗
The return generating process is given as Rj,t
= βj1 Durj,t ∗ ∆Rf t + βj2 Durjt ∗ ∆S&Pt + j,t .
∗
Rj,t
is the unobserved “true” bond return for bond j that investors would bid given zero
liquidity costs; Durj,t is the bond’s duration; ∆Rf t is the daily change in the 10-year risk-free
interest rate; and ∆S&Pt is the daily return on the S&P 500 index. The liquidity effects on
∗
bond returns can be stated as Rj,t = Rj,t
− αi,j . The term Rj,t is the measured return; α1,j
is the effective sell-side cost for bond j and α2,j is the effective buy-side cost. Φ1,j and Φ2,j
are the distribution function of the standard normal distribution.
37
4. IRC
The imputed round-trip cost (IRC) follows Feldhütter (2012) and is based on the dispersion
of traded prices around the market-wide consensus valuation:
IRCi,t =
min
max
− Pi,t
Pi,t
min
Pi,t
(9)
where Pmax is the largest price in an imputed roundtrip transaction (IRT ) and Pmin is
the smallest price in the IRT. If two or three trades on a given bond with the same trade
size take place on the same day, they are likely the result of a dealer taking one side of a
trade and then taking an offsetting trade subsequently. They are considered as imputed
roundtrip transactions. The price differences among such trades likely reflect the bid-ask
spread charged by the bond dealers. The daily IRC measure is the average of roundtrip
costs on that day. A quarterly IRC measure is the average of the daily estimates.
5. λ
This measure, based on Dick-Nielsen et al. (2012), is an equally weighted sum of four variables
normalized to a common scale: Amihud measure, IRC, and the variability of each of these
two measures. To be specific, for each bond and quarter, we first calculate the four liquidity
measures: Amihud, IRC, and the standard deviations of the daily Amihud measure and IRC
measure over a quarter. Then we normalize each measure and compute λ as follows:
λi,t =
4
X
ILQji,t − µj
σj
j=1
,
(10)
where ILQji,t , j = 1, . . . , 4, denote the four illiquidity measures mentioned above, and µj and
σ j are the mean and standard deviation of each measure across bonds and quarters. See also
Han and Zhou (2008).
38
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41
Table 1: Statistics for Corporate Bonds Held by Insurers
This table reports summary statistics on sample bonds and insurers’ holdings of these bonds. Panel A
reports the statistics on the numbers of unique bonds in the entire sample and in various subsamples, at
the end of each year from 2003 to 2011. The “FISD-TRACE Sample” (Column 2) refers to plain-vanilla
bonds in the merged FISD and TRACE datasets. We require bonds to have non-missing yields, non-missing
credit rating, and maturity no less than six months. The “Bonds held by insurers” (Column 3) refers to
bonds in the FISD-TRACE sample that are held by insurers. Columns (4) to (8) report the numbers of
insurer-held bonds in five different credit rating categories, and Columns (9) to (12) for the numbers in four
maturity categories. The five rating groups are labeled AAA, AA (including AA+, AA, AA-), A (including
A+, A, A-), BBB (including BBB+, BBB, BBB-) and speculative bonds (with ratings below BBB-). The
four maturity categories include below 2 years, 2-5 years, 5-10 years, and above 10 years. The second to last
row captioned “All” reports the numbers of unique bonds throughout the entire period of 2003-2011. The
last row captioned “Average” reports the average number of unique bonds over the sample years. Panel B
reports the distributions of insurers’ portfolio weights on corporate bonds in five credit rating categories and
in four maturity categories. We first compute the portfolio weight of an insurer in a given bond category
in each quarter. We then compute the cross-sectional statistics on these weights across insurers in that
quarter. The distribution statistics include the 5th, 25th, 50th, 75th, and 95th percentiles, as well as the
mean and standard deviation. We then average these statistics over time and report the averages in this
panel. Panel C reports the distributions of insurer holdings as fractions of bonds outstanding in the five
credit rating categories and in the four maturity categories. The panel also reports (column captioned “N”)
the average number of bonds insurers hold in each category. Panel D reports statistics for the investmentgrade bonds held by insurers, for each year between 2003 and 2011. The statistics include the number of
unique bonds and the cross-sectional distributions of insurer holdings as fractions of bonds outstanding. The
last row captioned “All/Average” reports the time-series averages of the number of unique bonds and the
distributions of fractional insurer holdings, and the total number of unique bonds during the entire sample
period.
Panel A: Number of unique corporate bonds
(1)
(2)
(3)
(4)
(5)
(6)
FISDTRACE
Year
2003
2004
2005
2006
2007
2008
2009
2010
2011
All
Average
(8)
(9)
(10)
(11)
(12)
Bonds held by insurers
Total
Sample
2,400
3,607
4,443
4,439
4,310
4,047
4,167
4,122
4,054
8,656
3,954
(7)
2,252
3,192
3,850
3,724
3,469
3,054
2,599
2,250
1,878
7,873
2,916
by credit rating
by maturity
AAA
AA
A
BBB
Spec
<2y
2-5y
5-10y
>10y
72
81
84
89
97
69
14
25
13
166
60
310
355
386
405
426
182
208
183
103
757
284
1,284
1,276
1,328
1,309
1,199
1,062
860
763
727
2,954
1,089
422
1,103
1,301
1,213
1,144
1,154
940
784
649
2,591
967
164
377
751
708
603
587
577
495
386
1,405
516
446
724
895
929
842
663
655
642
557
2,058
705
724
1,059
1,218
1,129
1,095
1,121
919
660
469
2,018
932
627
966
1,145
1,046
918
747
620
574
532
2,066
797
455
443
592
620
614
523
405
374
320
1,731
482
42
Panel B: Insurers’ portfolio weights on corporate bonds (%)
Year
P5
P25
AAA
AA
A
BBB
Speculative
0.00
0.00
0.27
0.00
0.00
0.00
5.61
18.46
0.21
0.00
< 2 years
2-5 years
5-10 years
> 10 years
0.19
0.04
0.00
0.00
8.33
16.94
4.16
0.00
Mean
Median
i. by credit rating
10.75
0.78
25.88
24.67
35.00
30.32
20.97
18.13
7.41
0.00
ii. by maturity
28.80
26.47
34.15
31.83
25.54
25.01
11.51
2.38
P75
P95
Std Dev
18.37
38.94
45.19
31.94
8.23
39.35
65.17
96.40
60.71
36.93
15.95
22.31
25.31
21.69
15.89
41.68
47.58
39.05
20.11
80.75
94.59
73.05
49.78
24.65
24.99
23.64
19.47
Panel C: Insurers’ bond holdings as fractions of bonds outstanding (%)
Type
N
P5
AAA
AA
A
BBB
Speculative
60
284
1,089
967
516
3.81
3.51
6.95
8.25
0.44
<2 years
2-5 years
5-10 years
> 10 years
705
932
797
482
2.19
2.92
3.43
3.59
P25
Mean
Median
i. by credit rating
8.53
20.45
17.66
9.79
23.15
18.42
19.26
36.52
34.21
22.46
39.29
37.62
3.41
12.66
8.30
ii. by maturity
10.12
26.00
21.35
12.11
28.44
24.55
15.27
33.89
31.83
20.84
40.80
40.95
P75
P95
Std Dev
30.27
33.48
52.01
54.68
17.32
45.46
56.08
72.88
76.04
40.35
14.96
17.25
20.86
21.01
13.18
38.46
41.61
50.29
59.25
63.96
66.02
72.18
81.07
19.64
20.00
21.68
24.22
Panel D: Numbers and fractions of insurer holdings of investment-grade bonds (%)
Year
2003
2004
2005
2006
2007
2008
2009
2010
2011
All/Average
N
P5
P25
Mean
Median
P75
P95
Std Dev
2,088
2,815
3,099
3,016
2,866
2,467
2,022
1,755
1,492
6,468/2,400
5.00
6.11
5.39
7.10
5.81
5.35
4.85
5.10
4.75
5.50
16.76
21.98
20.92
22.64
20.40
19.93
17.40
17.70
16.57
19.37
34.13
40.69
40.89
41.77
38.56
38.00
35.55
37.05
35.54
38.02
31.19
39.18
39.79
39.78
36.24
35.19
32.47
34.22
31.97
35.56
49.67
57.98
58.99
58.95
55.36
54.56
51.75
54.49
51.89
54.85
72.41
79.88
81.44
83.59
78.80
79.07
77.12
78.38
76.10
78.53
21.14
23.09
23.81
23.56
22.64
22.90
22.46
22.91
22.45
22.77
43
Table 2: Cross-sectional Distributions of Yield Spreads, Liquidity, Liquidity
Preference, and Liquidity Clientele Measures
This table reports the cross-sectional distribution of yield spreads, bond illiquidity measures, insurer liquidity
preference, and bond clientele measures. Panel A reports the distribution of investment-grade corporate bond
yield spreads (in %), computed as the difference between the yield of a bond and the U.S. Treasury yield with
the same maturity. Panel B reports the distribution of bond illiquidity measures (ILQ) including the Amihud
measure (in %), Roll measure, LOT (in %), imputed roundtrip cost (IRC, in %), and the comprehensive
measure λ. Panel C reports the distributions of insurers’ liquidity preference measures (ILP ) and Panel D
reports the distributions of bond liquidity clientele measures (ILC ). The distributional attributes include the
5th, 25th, 50th, 75th and 95th percentiles, as well as the mean and standard deviation (“Std Dev”) of each
variable. We obtain each statistic in the fourth quarter of each year and then take the average over time.
The column captioned “N” shows the average numbers of investment-grade bonds or insurers (in Panel C)
included in the sample. The sample period is from 2003:Q1 to 2011:Q4.
Panel A: Yield spreads
spread (%)
N
P5
P25
Mean
Median
P75
P95
Std Dev
2,400
0.49
1.04
1.78
1.61
2.24
3.74
1.06
1.27
1.69
7.29
0.51
-0.03
0.61
1.29
2.03
0.43
-0.15
1.44
1.95
5.70
0.66
0.24
4.77
4.14
26.11
1.23
1.09
2.01
1.61
25.22
0.37
0.59
1.09
1.25
2.95
0.45
-0.09
1.44
1.54
4.03
0.53
0.05
3.03
2.47
8.22
0.75
0.62
0.65
0.44
1.79
0.10
0.24
1.21
1.70
6.22
0.53
-0.01
1.32
1.86
7.46
0.56
0.05
1.54
2.16
9.49
0.64
0.16
0.27
0.25
2.04
0.07
0.11
Panel B: Bond illiquidity measures (ILQ)
Amihud (%)
Roll
LOT (%)
IRC (%)
λ
2,034
2,166
2,201
2,115
1,847
0.04
0.46
0.05
0.10
-0.74
0.23
0.85
0.55
0.26
-0.44
Panel C: Insurers’ illiquidity preference measures (ILP )
ILPAmihud (%)
ILPRoll
ILPLOT (%)
ILPIRC (%)
ILPλ
3,410
3,411
3,413
3,410
3,392
0.73
0.97
1.55
0.38
-0.25
0.82
1.12
2.42
0.42
-0.19
1.28
1.40
3.43
0.49
-0.03
Panel D: Bond illiquidity clientele measures (ILC )
ILCAmihud (%)
ILCRoll
ILCLOT (%)
ILCIRC (%)
ILCλ
2,400
2,400
2,400
2,400
2,400
0.99
1.33
3.26
0.44
-0.12
1.12
1.56
5.05
0.49
-0.05
1.24
1.72
6.32
0.53
0.01
44
Table 3: Correlation of Liquidity and Liquidity Clientele Measures
This table reports the correlation matrix of five liquidity measures (Amihud, Roll, LOT, IRC, and λ) and
the corresponding liquidity clientele measures (ILC Amihud , ILC Roll , ILC LOT , ILC IRC , and ILC λ ). We
compute the correlations over investment grade bonds in each quarter and then take the averages over time.
The sample period is from 2003:Q1 to 2011:Q4.
Bond Illiquidity Measures
Amihud
Roll
LOT
IRC
λ
ILCAmihud
ILCRoll
ILCLOT
ILCIRC
ILCλ
Illiquidity Clientele Measures
Amihud
Roll
LOT
IRC
λ
ILCAmihud
ILCRoll
ILCLOT
ILCIRC
ILCλ
1.00
0.18
0.11
0.40
0.69
0.40
0.17
0.11
0.28
0.32
1.00
0.43
0.38
0.38
0.22
0.47
0.36
0.34
0.30
1.00
0.14
0.12
0.13
0.19
0.34
0.20
0.17
1.00
0.79
0.37
0.37
0.26
0.48
0.45
1.00
0.43
0.32
0.20
0.45
0.49
1.00
0.48
0.35
0.81
0.88
1.00
0.79
0.64
0.53
1.00
0.62
0.48
1.00
0.83
1.00
45
Table 4: Liquidity Preference and Insurer Characteristics
This table reports firm characteristics across insurer deciles sorted on liquidity preference (ILP ). The five panels are for ILP based on five
different bond illiquidity measures, i.e., Amihud, Roll, LOT, IRC, and λ. The six characteristics related to insurers’ investment horizons are
portfolio turnover (TURN ), turnover of short-term bonds (STURN ), turnover of long-term bonds (LTURN ), the average holding horizon
(HZ, in years) since initial acquisition of bonds, the maturity of bonds when purchased by insurers (MAT, in years), and the fraction of life
insurers within an ILP decile (LIFE, in %). The five characteristics related to insurers’ ease of financing are total assets (TA, in $billion),
firm age (AGE, in years), the percentage of affiliated firms (AFF ) in an ILP decile, the percentage of stock insurers (STOCK, in %), and
the fraction of reinsurance premiums in an insurer’s aggregate collected premiums (REINS, in %). Insurers are classified into ILP deciles in
each quarter. We first compute the average characteristics within each decile in each quarter and then take their time-series averages for each
decile. We also compute the difference between the top (D10) and bottom (D1) deciles and the associated t-statistics using the Newey-West
procedure with a four-quarter lag. *, **, and *** indicate statistical significance at the 10%, 5%, and 1% level, respectively. The sample
period is from 2003:Q1 to 2011:Q4.
Investment Horizon
TURN
(1)
STURN
(2)
LTURN
(3)
HZ
(4)
0.16
0.14
0.14
0.14
0.14
0.13
0.13
0.12
0.11
0.09
-0.07***
(-4.78)
0.18
0.18
0.18
0.18
0.18
0.17
0.16
0.15
0.15
0.14
-0.04
(-1.63)
0.12
0.10
0.08
0.09
0.09
0.08
0.09
0.08
0.07
0.06
-0.06***
(-4.28)
1.83
2.07
2.17
2.26
2.42
2.54
2.65
2.80
3.09
3.36
1.53***
(8.12)
Funding Constraints
MAT
(5)
LIFE
(6)
TA
(7)
AGE
(8)
AFF
(9)
STOCK
(10)
REINS
(11)
37.89
40.89
44.79
49.81
52.92
57.72
63.52
61.07
56.04
49.16
11.27***
(7.29)
0.62
0.69
0.68
0.71
0.72
0.69
0.70
0.70
0.71
0.72
0.10***
(3.27)
79.54
76.74
76.91
80.19
78.47
79.70
75.52
80.66
80.24
85.18
5.64***
(3.15)
39.08
32.67
31.89
29.69
29.13
29.18
28.67
31.08
27.81
25.04
-14.04***
(-11.62)
35.06
38.05
40.02
41.71
42.84
47.04
55.11
65.73
65.35
53.00
17.94***
(11.56)
0.57
0.60
0.65
0.66
0.68
0.70
0.72
0.72
0.71
0.70
0.13***
(4.55)
75.55
75.92
75.94
74.67
74.25
78.41
81.56
82.69
83.48
88.59
13.04***
(4.42)
35.47
34.16
33.68
33.73
31.10
27.94
28.90
27.38
26.71
25.35
-10.12***
(-7.19)
Panel A: Insurer deciles sorted by ILPAmihud
46
D1 (L)
D2
D3
D4
D5
D6
D7
D8
D9
D10 (H)
H-L
(t-stat)
7.44
7.77
8.09
9.43
8.50
8.43
9.46
9.71
10.17
10.34
2.90***
(5.29)
16.55
25.00
30.21
37.53
42.30
42.71
49.84
51.71
53.77
52.93
36.38***
(11.35)
0.58
1.09
1.79
2.38
3.28
3.12
4.34
2.76
2.92
2.86
2.28***
(4.07)
Panel B: Insurer deciles sorted by ILPRoll
D1 (L)
D2
D3
D4
D5
D6
D7
D8
D9
D10 (H)
H-L
(t-stat)
0.13
0.13
0.14
0.14
0.13
0.14
0.13
0.12
0.11
0.10
-0.03***
(-2.96)
0.17
0.17
0.17
0.18
0.18
0.18
0.17
0.17
0.16
0.16
-0.01
(-1.36)
0.09
0.08
0.09
0.09
0.09
0.08
0.09
0.09
0.07
0.06
-0.03***
(-3.25)
1.79
2.01
2.15
2.24
2.39
2.53
2.64
2.84
3.11
3.48
1.69***
(5.47)
6.12
7.10
7.61
8.87
7.96
9.26
9.52
10.24
11.03
11.61
5.49***
(5.55)
13.20
15.64
21.78
23.19
32.28
43.39
49.14
58.99
69.56
71.33
58.13***
(15.42)
0.36
0.45
0.71
0.95
1.46
2.62
3.94
4.64
4.48
2.90
2.54***
(4.36)
Investment Horizon
TURN
(1)
STURN
(2)
LTURN
(3)
HZ
(4)
Funding Constraints
MAT
(5)
LIFE
(6)
TA
(7)
AGE
(8)
AFF
(9)
STOCK
(10)
REINS
(11)
35.42
37.50
41.69
37.91
46.87
47.43
53.71
61.06
60.76
61.48
26.06***
(7.28)
0.53
0.64
0.69
0.70
0.72
0.75
0.77
0.77
0.82
0.77
0.24***
(4.84)
70.08
74.03
74.90
72.46
74.74
79.58
81.22
85.93
87.38
88.85
18.77***
(9.02)
35.44
34.20
32.39
30.09
32.33
31.89
28.27
29.14
25.34
25.37
-10.07***
(-5.62)
35.14
37.88
42.84
47.01
51.04
53.92
61.54
60.37
59.09
50.70
15.56***
(6.47)
0.64
0.66
0.67
0.69
0.70
0.70
0.73
0.71
0.67
0.74
0.10***
(3.54)
78.49
75.72
75.21
75.91
80.49
79.23
78.99
81.47
80.68
85.56
7.07***
(3.26)
37.26
33.62
34.13
31.05
29.73
29.28
27.88
29.76
28.63
23.04
-14.22***
(-9.50)
35.85
40.24
45.49
52.32
49.27
58.01
60.79
59.10
57.42
49.99
14.14***
(7.73)
0.60
0.64
0.67
0.70
0.71
0.71
0.72
0.73
0.72
0.73
0.13***
(4.49)
74.59
75.41
78.92
77.14
79.39
80.07
78.37
80.68
79.57
81.15
6.56***
(3.50)
38.38
33.74
32.69
31.36
28.68
27.87
29.38
30.26
27.56
24.36
-14.02***
(-7.55)
Panel C: Insurer deciles sorted by ILPLOT
D1 (L)
D2
D3
D4
D5
D6
D7
D8
D9
D10 (H)
H-L
(t-stat)
0.14
0.13
0.13
0.13
0.13
0.13
0.13
0.13
0.11
0.10
-0.04***
(-2.96)
0.18
0.18
0.18
0.17
0.18
0.18
0.17
0.17
0.16
0.16
-0.02
(-1.57)
0.08
0.07
0.07
0.07
0.06
0.06
0.06
0.06
0.05
0.05
-0.03***
(-3.60)
1.81
2.03
2.17
2.22
2.40
2.54
2.70
2.81
3.02
3.35
1.54***
(5.85)
D1 (L)
D2
D3
D4
D5
D6
D7
D8
D9
D10 (H)
H-L
(t-stat)
0.13
0.12
0.12
0.12
0.12
0.12
0.11
0.11
0.11
0.09
-0.04***
(-5.12)
0.17
0.17
0.18
0.17
0.18
0.17
0.17
0.16
0.16
0.16
-0.01
(-1.31)
0.10
0.08
0.09
0.09
0.09
0.07
0.07
0.06
0.05
0.04
-0.06***
(-4.36)
1.79
2.05
2.14
2.24
2.41
2.54
2.59
2.84
3.05
3.36
1.57***
(6.97)
7.54
7.13
7.73
8.40
8.58
8.60
9.57
9.71
11.15
10.97
3.43**
(2.43)
15.15
15.73
21.27
24.80
29.29
40.38
46.44
59.71
72.00
69.81
54.66***
(10.63)
0.30
0.45
0.55
0.69
0.93
1.67
2.75
4.37
6.25
4.11
3.81***
(4.25)
Panel D: Insurer deciles sorted by ILPIRC
47
6.72
7.09
7.81
8.43
8.32
9.69
10.05
9.10
10.94
11.17
4.45***
(4.36)
15.54
19.18
25.21
31.12
38.46
44.14
48.56
54.97
63.18
60.20
44.66***
(9.72)
0.38
0.60
1.03
1.83
3.22
3.09
3.79
3.93
2.99
2.25
1.87***
(5.41)
Panel E: Insurer deciles sorted by ILPλ
D1 (L)
D2
D3
D4
D5
D6
D7
D8
D9
D10 (H)
H-L
(t-stat)
0.12
0.14
0.14
0.14
0.14
0.13
0.12
0.12
0.10
0.09
-0.03***
(-5.21)
0.16
0.17
0.16
0.16
0.16
0.17
0.17
0.17
0.16
0.15
-0.01
(-1.44)
0.09
0.08
0.09
0.09
0.08
0.07
0.06
0.05
0.05
0.04
-0.05***
(-4.79)
1.80
2.07
2.20
2.28
2.44
2.52
2.63
2.75
2.95
3.39
1.59***
(6.79)
6.74
8.19
7.80
8.85
8.53
8.49
9.46
10.21
10.34
10.70
3.96***
(4.00)
14.28
20.64
30.26
37.31
38.44
42.55
49.20
54.31
58.14
56.30
42.02***
(10.80)
0.47
0.73
1.37
3.40
2.63
3.36
3.33
3.76
2.07
1.94
1.47***
(4.61)
Table 5: Yield Spreads for Bond Portfolios Sorted on ILQ and ILC
This table reports yield spreads of investment-grade bond portfolios sorted on ILQ and ILC. The five panels
are for five different bond illiquidity measures. Yield spread is expressed in percentage points. In each quarter
we sort bonds into 5x5 groups on a measure of ILQ and the corresponding measure of ILC independently.
We first calculate the average yield spreads in each group, and then average over time. Within each ILC
quintile, we also calculate the difference in yield spread between the top (ILQ5) and bottom (ILQ1) illiquidity
quintiles. The associated t-statistics are computed using the Newey-West procedure with a four-quarter lag.
*, **, and *** indicate statistical significance at the 10%, 5%, and 1% level, respectively. The sample period
is from 2003:Q1 to 2011:Q4.
ILC1
ILC2
ILC3
ILC4
ILC5
ILC5-ILC1
Panel A. Illiquidity Measure: Amihud
ILQ1
1.28
1.55
ILQ2
1.35
1.56
ILQ3
1.40
1.57
ILQ4
1.55
1.73
ILQ5
2.22
2.17
ILQ5-ILQ1
0.94***
0.62***
(t-stat)
(4.49)
(4.22)
1.73
1.72
1.74
1.82
2.26
0.53***
(3.15)
1.81
1.77
1.78
1.93
2.19
0.38***
(3.52)
1.80
1.82
1.86
1.92
2.39
0.59***
(5.95)
0.52
0.47
0.46
0.38
0.17
-0.35**
(-2.50)
Panel B. Illiquidity Measure: Roll
ILQ1
0.88
1.12
ILQ2
1.27
1.43
ILQ3
1.76
1.78
ILQ4
2.13
2.19
ILQ5
2.24
2.38
ILQ5-ILQ1
1.36***
1.26***
(t-stat)
(4.62)
(5.16)
1.37
1.62
2.04
2.34
2.37
1.00***
(6.17)
1.59
1.92
2.18
2.34
2.09
0.50***
(6.70)
1.73
1.76
1.79
1.82
1.96
0.23***
(2.56)
0.86
0.49
0.04
-0.30
-0.28
-1.14***
(-3.63)
Panel C. Illiquidity Measure: LOT
ILQ1
1.29
1.56
ILQ2
1.40
1.59
ILQ3
1.57
1.68
ILQ4
1.83
1.84
ILQ5
2.34
2.17
ILQ5-ILQ1
1.05***
0.61***
(t-stat)
(3.16)
(3.14)
1.82
1.73
1.83
1.93
2.17
0.35**
(2.48)
1.86
1.79
1.75
1.95
2.15
0.29**
(2.20)
1.99
1.85
1.84
1.97
2.17
0.18*
(1.79)
0.70
0.45
0.27
0.14
-0.17
-0.87***
(-3.51)
Panel D. Illiquidity Measure: IRC
ILQ1
0.83
1.10
ILQ2
1.08
1.30
ILQ3
1.45
1.68
ILQ4
1.99
2.10
ILQ5
2.50
2.47
ILQ5-ILQ1
1.67***
1.37***
(t-stat)
(4.26)
(5.02)
1.39
1.59
1.85
2.20
2.36
0.97***
(5.91)
1.68
1.78
2.07
2.20
2.07
0.39***
(4.21)
1.71
1.75
1.74
1.83
2.17
0.46***
(6.03)
0.88
0.67
0.29
-0.16
-0.33
-1.21***
(-3.40)
Panel E. Illiquidity Measure: λ
ILQ1
0.90
ILQ2
1.04
ILQ3
1.32
ILQ4
1.83
ILQ5
2.53
ILQ5-ILQ1
1.63***
(t-stat)
(4.38)
1.36
1.55
1.80
2.11
2.44
1.08***
(4.58)
1.65
1.86
1.94
2.07
2.18
0.53***
(4.26)
1.71
1.70
1.72
1.81
2.20
0.49***
(6.32)
0.80
0.65
0.40
-0.02
-0.33
-1.13***
(-3.53)
1.15
1.31
1.58
1.93
2.65
1.50***
(4.11)
48
Table 6: Panel Regressions of Yield Spreads
This table reports the results of panel regressions on yield spreads of investment grade bonds. The dependent variable, yield
spread, is expressed in percentage points. The main explanatory variables include bond illiquidity ILQ, two dummies T2 and T3
for the second and third terciles of the illiquidity clientele measure ILC (ranked each quarter), the interaction terms of ILQ with
T2 and T3. The control variables include the year since the bond was issued (Bond age), time to maturity (Maturity), issue
size (Issue size), annual coupon rates (Coupon), an issuer’s ratio of operating income to sales (Income to sales), an issuer’s ratio
of long term debt to assets (LTD), an issuer’s leverage ratio (Leverage), an issuer’s equity volatility (EqVol), and four pretax
interest coverage variables of an issuer (Pretax1, Pretax2, Pretax3, and Pretax4 ). The regressions additionally include credit
rating dummies, the issuer-fixed effects, and the time-fixed effects (not tabulated). The t-statistics reported in the parentheses
are based on two-way clustered (by time and by issuer) standard errors. *, **, and *** indicate statistical significance at the
10%, 5%, and 1% level, respectively. Columns (1) to (5) report results for regressions without control variables. Columns (6)
to (10) are results with control variables. The row under the column numbers indicates the bond illiquidity measure used. The
last two rows report the adjusted R-square and the number of observations used in the regression.
Intercept
ILQ
T2
T3
ILQ*T2
ILQ*T3
(1)
Amihud
(2)
Roll
(3)
LOT
(4)
IRC
(5)
λ
(6)
Amihud
(7)
Roll
(8)
LOT
(9)
IRC
(10)
λ
1.08***
(14.64)
0.69***
(13.92)
0.29***
(7.51)
0.58***
(9.28)
-0.23***
(-6.25)
-0.48***
(-11.18)
0.44***
(3.76)
1.13***
(10.69)
0.63***
(6.18)
1.00***
(8.48)
-0.52***
(-5.69)
-0.93***
(-8.93)
1.61***
(25.17)
0.04**
(2.27)
0.07**
(2.48)
0.15***
(3.19)
-0.01***
(-3.03)
-0.03***
(-3.77)
0.35***
(2.80)
3.59***
(11.38)
0.40***
(4.90)
0.78***
(7.56)
-1.04***
(-3.90)
-2.44***
(-9.01)
2.22***
(12.11)
2.29***
(14.22)
0.13***
(4.02)
0.51***
(11.94)
-0.31***
(-4.72)
-1.16***
(-9.50)
Yes
Yes
Yes
0.16
69,656
Yes
Yes
Yes
0.21
74,394
Yes
Yes
Yes
0.15
75,639
Yes
Yes
Yes
0.18
72,566
Yes
Yes
Yes
0.23
62,913
-4.67***
(-7.93)
0.29***
(11.28)
0.20***
(7.16)
0.30***
(7.72)
-0.10***
(-3.68)
-0.20***
(-8.22)
0.02**
(2.18)
0.68***
(3.31)
0.17***
(5.61)
0.08***
(5.27)
-0.22***
(-2.69)
2.79***
(4.41)
7.07***
(6.70)
0.98***
(9.26)
-1.24
(-1.50)
-1.19
(-0.11)
-3.24
(-1.01)
0.21
(1.32)
Yes
Yes
Yes
0.55
30,574
-5.99***
(-10.18)
0.59***
(10.77)
0.45***
(7.20)
0.84***
(11.08)
-0.25***
(-4.25)
-0.49***
(-8.34)
0.06**
(2.34)
1.55***
(6.37)
0.25***
(8.47)
0.02
(1.11)
-0.26***
(-3.14)
2.75***
(4.40)
7.08***
(6.93)
0.97***
(9.61)
-1.21
(-0.88)
-2.05
(-0.39)
-4.40
(-1.22)
0.23
(1.59)
Yes
Yes
Yes
0.57
32,073
-5.56***
(-8.55)
0.06***
(4.11)
0.17***
(6.11)
0.28***
(7.33)
-0.03***
(-2.99)
-0.05***
(-3.70)
0.03**
(2.35)
0.72***
(3.73)
0.24***
(7.30)
0.05***
(3.30)
-0.25***
(-2.86)
2.99***
(4.60)
7.82***
(7.23)
1.03***
(9.99)
-1.26
(-0.65)
-2.15
(-0.35)
-4.13
(-1.11)
0.21
(1.42)
Yes
Yes
Yes
0.54
32,422
-5.49***
(-9.74)
1.60***
(14.38)
0.34***
(7.42)
0.62***
(9.59)
-0.43***
(-3.95)
-1.12***
(-9.78)
0.04**
(2.07)
1.37***
(5.34)
0.19***
(6.29)
0.06***
(4.27)
-0.24***
(-2.97)
2.79***
(4.43)
7.15***
(6.83)
0.98***
(9.49)
-1.21
(-0.48)
-2.10
(-0.64)
-2.15
(-1.38)
0.23
(1.68)
Yes
Yes
Yes
0.57
31,550
-3.25***
(-6.04)
0.98***
(16.17)
0.15***
(5.18)
0.24***
(2.80)
-0.10**
(-2.11)
-0.55***
(-8.93)
0.02*
(1.90)
1.60***
(5.79)
0.15***
(5.18)
0.08***
(5.35)
-0.28***
(-3.43)
2.55***
(4.17)
6.22***
(6.52)
0.91***
(8.70)
-1.20
(-0.57)
-0.99
(-0.59)
-2.17
(-1.65)
0.24
(1.60)
Yes
Yes
Yes
0.58
28,342
Bond age
Maturity
Issue size
Coupon
Income to sales (%)
LTD (%)
Leverage (%)
EqVol
Pretax1 (%)
Pretax2 (%)
Pretax3 (%)
Pretax4 (%)
Rating dummies
Fixed effect - issuer
Fixed effect - quarter
Adj.R2
N
49
Table 7: Effects of Clientele on Liquidity Premium in Short-term and
Long-term Bonds
This table reports the results of panel regressions with the same specification as Table 6, but for shortterm bonds and long-term investment-grade bonds separately. Short-term bonds are those with maturity
below 5 years (Panel A) and long-term bonds are those with maturity on or above five years (Panel B).
The dependent variable is the yield spread expressed in percentage points. The main explanatory variables
include bond illiquidity ILQ, two dummies T2 and T3 for the second and third terciles of the illiquidity
clientele measure ILC (ranked each quarter), the interaction terms of ILQ with T2 and T3. The control
variables are the same as Table 6. The t-statistics reported in the parentheses are based on two-way clustered
(by time and by issuer) standard errors. *, **, and *** indicate statistical significance at the 10%, 5%, and
1% level, respectively. The first row indicates the bond illiquidity measure used. The last two rows report
the adjusted R-square and the number of observations used in the regression.
Amihud
Roll
LOT
IRC
λ
A. Short-term bonds
Amihud
Roll
LOT
IRC
λ
B. Long-term bonds
ILQ
0.21*** 0.36*** 0.06*** 1.00*** 0.69***
(6.50)
(6.00)
(3.01)
(6.27)
(6.91)
T2
-0.03
0.01
0.03
-0.10
-0.08
(-0.86)
(-0.08)
(0.75) (-1.34) (-1.45)
T3
-0.05
0.12
0.12** -0.34*
0.10
(-0.76)
(1.11)
(2.17) (-1.72) (0.46)
ILQ*T2
-0.03
0.01
-0.01
0.01
0.11
(-0.75)
(0.08)
(-0.64) (0.05)
(0.89)
ILQ*T3
-0.11** -0.20*** -0.05**
0.17
0.28
(-2.29)
(-2.63) (-2.45) (0.36)
(1.05)
Bond age
0.03*** 0.03*** 0.03*** 0.02*** 0.02**
(3.38)
(3.91)
(4.35)
(3.08)
(2.21)
Maturity
0.18*** 0.14*** 0.18*** 0.15*** 0.13***
(10.44)
(7.66)
(11.13) (7.00)
(5.74)
Issue size
0.06
0.08*** 0.09**
0.02
0.06
(0.17)
(2.62)
(2.06)
(0.52)
(0.19)
Coupon
0.02
0.03**
0.02
0.05
0.06
(0.09)
(2.32)
(1.47)
(0.04)
(0.52)
Income to sales (%)
-0.05
-0.05
-0.04
-0.04
-0.05
(-1.18)
(-1.07) (-0.91) (-0.85) (-0.98)
LTD (%)
1.07**
1.13** 1.23*** 1.32*
1.07**
(2.29)
(2.53)
(2.59)
(1.81)
(2.16)
Leverage (%)
6.10*** 6.22*** 6.80*** 6.48*** 5.91***
(4.58)
(5.12)
(5.19)
(5.07)
(4.81)
EqVol
0.14
0.13
0.18
0.15
0.07
(1.28)
(1.61)
(1.12)
(1.37)
(1.21)
Pretax1 (%)
-0.15
-0.18
-0.16
-0.10
-0.08
(-0.11)
(-0.24) (-0.26) (-0.34) (-0.18)
Pretax2 (%)
-0.22
0.14
-0.51
-0.27
-0.25
(-0.01)
(0.18)
(-0.40) (-0.21) (-0.25)
Pretax3 (%)
-0.15
-0.36
-0.50
-0.40
-0.22
(-0.28)
(-0.51) (-0.54) (-0.45) (-0.63)
Pretax4 (%)
0.10
0.12
0.14
0.13
0.10
(0.56)
(0.64)
(0.58)
(0.55)
(0.47)
Control variables
Yes
Yes
Yes
Yes
Yes
Fixed effect - issuer
Yes
Yes
Yes
Yes
Yes
Fixed effect - quarter
Yes
Yes
Yes
Yes
Yes
Adj.R2
0.57
0.58
0.58
0.58
0.59
N
12,054
12,583
12,682 12,433 11,289
50
0.29*** 0.41*** 0.03*** 1.09*** 0.80***
(7.93)
(5.04)
(3.41)
(7.70)
(10.43)
0.09**
0.20*
0.02**
0.10** 0.11***
(2.21)
(1.83)
(2.52)
(2.39)
(2.82)
0.19*** 0.53*** 0.14*** 0.32*** 0.13**
(3.61)
(4.43)
(2.98)
(3.89)
(2.16)
-0.14*** -0.15*** -0.02** -0.14*** -0.13**
(-3.58)
(-2.81)
(-2.37)
(-2.97)
(-2.46)
-0.22*** -0.33*** -0.03*** -0.69*** -0.45***
(-6.28)
(-3.91)
(-2.97)
(-5.04)
(-6.40)
0.02*** 0.03*** 0.03*** 0.04*** 0.02**
(3.16)
(4.81)
(5.48)
(4.14)
(2.22)
0.80*** 1.76*** 0.91*** 1.40*** 1.83***
(10.29)
(8.02)
(9.90)
(8.38)
(9.25)
0.22*** 0.29*** 0.28*** 0.24*** 0.20***
(6.00)
(7.51)
(7.04)
(6.36)
(5.25)
0.07***
0.03
0.04
0.08*** 0.10***
(3.09)
(1.29)
(1.61)
(3.32)
(4.35)
-0.28*** -0.27*** -0.22*** -0.26*** -0.25**
(-2.98)
(-3.34)
(-2.94)
(-3.10)
(-2.29)
2.35*** 2.32*** 2.44*** 2.36*** 2.18***
(3.67)
(3.57)
(3.66)
(3.65)
(3.46)
7.76*** 7.87*** 8.42*** 7.81*** 6.77***
(7.14)
(7.26)
(7.55)
(7.18)
(7.03)
0.88*** 0.89*** 0.92*** 0.88*** 0.82***
(9.92)
(10.13) (10.32)
(9.94)
(9.51)
-1.40
-1.45
-1.46
-1.31
-1.25
(-1.55)
(-0.97)
(-0.95)
(-1.10)
(-1.66)
-1.21
-2.43
-2.07
-2.02
-0.96
(-1.10)
(-0.37)
(-0.99)
(-1.14)
(-0.69)
-3.55
-4.20
-4.41
-3.15
-2.73
(-1.25)
(-1.21)
(-1.08)
(-1.25)
(-1.22)
0.25
0.23
0.24
0.25
0.22
(1.41)
(1.62)
(1.49)
(1.65)
(1.54)
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
0.60
0.60
0.59
0.61
0.62
18,520
19,490
19,740
19,117
17,053
Table 8: Panel Regressions of Yield Spreads using Alternative Illiquidity Clientele Measures
This table reports the results of panel regressions of yield spreads. The regression specification is the same as Table 6, but with two alternative
illiquidity clientele measures, one based on portfolio turnover and the other based on funding constraints. T2A and T3A are dummies for the
second and third turnover-based ILC, and T2B and T3B are dummies for the second and third funding constraint-based ILC. The dependent
variable is the yield spread expressed in percentage points. The main explanatory variables include bond illiquidity ILQ, the ILC tercile
dummies T2A and T3A (and/or T2B and T3B ), and the interactions of ILQ with the tercile dummies. The control variables are the same
as Table 6. The regressions additionally include dummies for each credit rating category, the issuer-fixed effects, and the time-fixed effects
(not tabulated). The t-statistics reported in the parentheses are based on two-way clustered (by time and by issuer) standard errors. *, **,
and *** indicate statistical significance at the 10%, 5%, and 1% level, respectively. The first row indicates the bond illiquidity measure used.
The last two rows report the adjusted R-square and the number of observations used in the regression.
Intercept
ILQ
T2A
51
T3A
ILQ*T2A
ILQ*T3A
(1)
Amihud
(2)
Roll
(3)
LOT
(4)
IRC
(5)
λ
(6)
Amihud
-4.76***
(-7.88)
0.16***
(10.93)
0.05**
(2.29)
0.14***
(5.53)
-0.04***
(-2.66)
-0.06***
(-4.62)
-5.80***
(-9.72)
0.20***
(9.44)
0.08**
(2.42)
0.18***
(4.59)
-0.04***
(-2.83)
-0.06***
(-2.69)
-8.13***
(-8.14)
0.02***
(3.95)
0.06**
(2.06)
0.12***
(4.53)
-0.01**
(-2.22)
-0.02**
(-2.05)
-5.55***
(-9.61)
0.92***
(14.28)
0.09***
(3.15)
0.14***
(3.97)
-0.16***
(-2.88)
-0.32**
(-2.25)
-3.58***
(-6.41)
0.72***
(16.15)
0.10**
(2.36)
0.08**
(2.43)
-0.08*
(-1.96)
-0.12***
(-2.77)
-4.55***
(-7.50)
0.13***
(11.59)
0.08**
(2.51)
0.08**
(2.30)
-0.01*
(-1.75)
-0.02*
(-1.94)
0.03
(1.49)
0.50***
(2.67)
0.18***
(5.45)
0.09***
(5.61)
T2B
T3B
ILQ*T2B
ILQ*T3B
Bond age
Maturity
Issue size
Coupon
0.02** 0.03** 0.03** 0.05**
(2.08)
(2.19)
(2.26)
(2.00)
0.45** 0.90*** 0.28*** 1.33***
(2.51)
(5.00)
(2.57)
(6.72)
0.18*** 0.25*** 0.22*** 0.20***
(5.70)
(8.30)
(6.78)
(6.52)
0.09*** 0.05*** 0.07*** 0.08***
(5.87)
(3.27)
(4.38)
(5.53)
0.02***
(2.88)
1.64***
(7.34)
0.16***
(5.50)
0.09***
(6.45)
(7)
Roll
(8)
LOT
(10)
λ
(11)
Amihud
(12)
Roll
-5.55*** -4.89*** -5.38***
(-9.29) (-7.74) (-9.25)
0.17*** 0.01*** 0.84***
(10.05) (4.58) (14.08)
-3.42***
(-6.11)
0.66***
(16.42)
0.13***
(2.92)
0.15***
(3.15)
-0.04**
(-2.35)
-0.04***
(-3.76)
0.04
(0.67)
0.93***
(4.91)
0.25***
(7.93)
0.05***
(3.05)
0.05*
(1.85)
0.05***
(2.74)
-0.04*
(-1.91)
-0.09*
(-1.99)
0.03***
(2.65)
1.68***
(7.32)
0.16***
(5.25)
0.08***
(6.19)
-4.73***
(-7.79)
0.17***
(10.85)
0.05**
(2.27)
0.14***
(5.44)
-0.04***
(-2.69)
-0.06***
(-4.69)
0.08**
(2.54)
0.09**
(2.52)
-0.03*
(-1.82)
-0.03*
(-1.98)
0.01*
(1.75)
0.49***
(2.63)
0.18***
(5.63)
0.09***
(5.73)
-5.79***
(-9.66)
0.21***
(9.87)
0.08**
(2.40)
0.18***
(4.73)
-0.04*
(-1.92)
-0.07***
(-2.83)
0.14***
(3.06)
0.17***
(3.24)
-0.05**
(-2.51)
-0.09***
(-3.85)
0.02
(0.39)
0.94***
(4.97)
0.25***
(8.19)
0.05***
(3.06)
0.06*
(1.99)
0.06*
(1.87)
-0.01*
(-1.90)
-0.02***
(-3.28)
0.04
(0.75)
0.28**
(2.26)
0.21***
(6.44)
0.07***
(4.20)
(9)
IRC
0.13***
(3.05)
0.14***
(3.59)
-0.13**
(-2.40)
-0.18***
(-3.34)
0.04
(0.67)
1.38***
(6.70)
0.20***
(6.37)
0.07***
(5.32)
(13)
LOT
(14)
IRC
(15)
λ
-5.11*** -5.52*** -3.52***
(-8.09) (-9.48) (-6.24)
0.02*** 0.96*** 0.74***
(3.59) (14.12) (16.11)
0.04** 0.09*** 0.02**
(2.29)
(3.24)
(2.18)
0.12*** 0.14*** 0.03**
(4.50)
(3.98)
(2.33)
-0.01** -0.18*** -0.10**
(-2.15) (-3.16) (-2.39)
-0.02** -0.16** -0.12***
(-2.08) (-2.30) (-2.80)
0.06* 0.14*** 0.04**
(1.98)
(3.07)
(2.27)
0.08** 0.16*** 0.06**
(2.17)
(3.67)
(2.26)
-0.01
-0.18**
-0.06
(-0.87) (-2.41) (-1.39)
-0.01*** -0.23*** -0.10*
(-3.29) (-3.42) (-2.10)
0.02
0.01
0.02***
(0.31)
(0.84)
(2.71)
0.30* 1.38*** 1.67***
(1.68)
(6.68)
(7.28)
0.22*** 0.20*** 0.16***
(6.74)
(6.49)
(5.39)
0.07*** 0.08*** 0.09***
(4.28)
(5.31)
(6.20)
Continued on next page
Table 8 – continued from previous page
(1)
Amihud
Income to sales (%)
52
-0.21**
(-2.52)
LTD (%)
2.87***
(4.47)
Leverage (%)
7.21***
(6.75)
EqVol
0.99***
(9.31)
Pretax1 (%)
-1.22
(-1.55)
Pretax2 (%)
-1.43
(-0.46)
Pretax3 (%)
-3.59
(-0.80)
Pretax4 (%)
0.80
(1.35)
Rating dummies
Yes
Fixed effect - issuer
Yes
Fixed effect - quarter
Yes
Adj.R2
0.49
N
30,574
(2)
Roll
(3)
LOT
(4)
IRC
(5)
λ
(6)
Amihud
(7)
Roll
(8)
LOT
(9)
IRC
(10)
λ
(11)
Amihud
(12)
Roll
(13)
LOT
(14)
IRC
(15)
λ
-0.25***
(-3.02)
2.84***
(4.41)
7.22***
(6.97)
1.02***
(9.87)
-1.30
(-0.78)
-1.21
(-0.69)
-4.13
(-1.18)
0.92
(1.44)
Yes
Yes
Yes
0.48
32,073
-0.23***
(-2.73)
3.02***
(4.61)
7.84***
(7.20)
1.04***
(10.04)
-1.44
(-1.25)
-1.22
(-0.43)
-4.17
(-1.15)
0.90
(1.40)
Yes
Yes
Yes
0.49
32,422
-0.23***
(-2.96)
2.85***
(4.50)
7.18***
(6.78)
0.98***
(9.63)
-1.39
(-1.33)
-1.23
(-0.73)
-4.15
(-1.42)
0.95
(1.60)
Yes
Yes
Yes
0.49
31,550
-0.26***
(-3.34)
2.65***
(4.32)
6.32***
(6.50)
0.91***
(8.76)
-1.21
(-0.50)
-1.21
(-0.70)
-3.79
(-1.67)
0.83
(1.64)
Yes
Yes
Yes
0.50
28,342
-0.21**
(-2.49)
2.92***
(4.50)
7.35***
(6.87)
0.98***
(9.35)
-0.92
(-1.58)
-1.45
(-0.32)
-3.30
(-0.85)
0.79
(1.34)
Yes
Yes
Yes
0.40
30,574
-0.26***
(-3.19)
2.88***
(4.45)
7.29***
(6.99)
0.99***
(9.88)
-1.15
(-0.71)
-1.24
(-0.62)
-4.16
(-1.16)
0.92
(1.44)
Yes
Yes
Yes
0.41
32,073
-0.25***
(-2.90)
3.05***
(4.62)
7.95***
(7.28)
1.03***
(10.06)
-1.42
(-1.23)
-1.16
(-0.38)
-4.12
(-1.13)
0.91
(1.41)
Yes
Yes
Yes
0.38
32,422
-0.24***
(-3.04)
2.88***
(4.50)
7.28***
(6.84)
0.97***
(9.63)
-1.36
(-1.31)
-1.25
(-0.70)
-4.10
(-1.41)
0.96
(1.61)
Yes
Yes
Yes
0.41
31,550
-0.27***
(-3.38)
2.69***
(4.32)
6.44***
(6.59)
0.90***
(8.75)
-1.17
(-0.55)
-1.22
(-0.67)
-3.82
(-1.66)
0.82
(1.68)
Yes
Yes
Yes
0.44
28,342
-0.22***
(-2.62)
2.92***
(4.51)
7.31***
(6.84)
0.97***
(9.32)
-1.26
(-1.58)
-1.06
(-0.35)
-3.31
(-0.85)
0.82
(1.32)
Yes
Yes
Yes
0.52
30,574
-0.26***
(-3.20)
2.88***
(4.46)
7.28***
(7.00)
0.99***
(9.91)
-1.14
(-0.82)
-1.20
(-0.32)
-4.12
(-1.14)
0.97
(1.43)
Yes
Yes
Yes
0.53
32,073
-0.25***
(-2.92)
3.04***
(4.63)
7.92***
(7.28)
1.02***
(10.06)
-1.39
(-1.21)
-1.21
(-0.38)
-3.83
(-1.12)
0.82
(1.35)
Yes
Yes
Yes
0.52
32,422
-0.24***
(-3.07)
2.89***
(4.53)
7.28***
(6.84)
0.97***
(9.64)
-1.42
(-1.30)
-1.22
(-0.71)
-3.59
(-1.41)
0.86
(1.61)
Yes
Yes
Yes
0.53
31,550
-0.27***
(-3.43)
2.70***
(4.35)
6.43***
(6.60)
0.90***
(8.78)
-1.10
(-0.58)
-1.18
(-0.67)
-3.78
(-1.62)
0.95
(1.65)
Yes
Yes
Yes
0.53
28,342
Table 9: Panel Regressions on Bond Pairs
This table reports the results of panel regressions of yield spreads on a sample of bond pairs that are
from the same issuers and thus have similar credit risks. The dependent variable is the difference in yield
spread (expressed in percentage points) between the bond pairs. The main explanatory variables include the
difference in ILQ between the bond pairs, the differences in the values of the ILC tercile dummies T2 and
T3 between the bond pairs, as well as the bond pairs’ differences in the interactions of ILQ with T2 and T3.
The control variables include the bond pair’s differences in the year since the bond was issued (∆Bondage),
the difference in time to maturity (∆M aturity), the difference in issue size (∆Issuesize), and the difference
in coupon rates (∆Coupon). The t-statistics reported in the parentheses are based on two-way clustered (by
time and by issuer) standard errors. *, **, and *** indicate statistical significance at the 10%, 5%, and 1%
level, respectively. The row under column numbers indicates the bond illiquidity measure used. The last
two rows report the adjusted R-square and the number of observations used in the regression.
Intercept
∆ILQ (x100)
∆T 2(x100)
∆T 3 (x100)
∆(ILQ ∗ T 2) (x100)
∆(ILQ ∗ T 3) (x100)
∆BondAge (x100)
∆M aturity (x100)
∆IssueSize (x100)
∆Coupon (x100)
Adj.R2
N
(1)
Amihud
(2)
Roll
(3)
LOT
(4)
IRC
(5)
λ
0.62***
(24.91)
6.34**
(2.47)
4.20*
(1.98)
7.15**
(2.21)
-4.69***
(-2.86)
-9.76***
(-2.73)
0.61***
(2.77)
2.14
(1.38)
-0.23
(-0.28)
1.34*
(1.88)
0.32
4,354
0.62***
(21.18)
7.89***
(4.21)
7.16**
(2.03)
13.31***
(3.07)
-5.92**
(-2.24)
-10.54***
(-3.45)
0.41**
(2.07)
2.16
(1.51)
-0.35
(-0.46)
1.17*
(1.70)
0.35
4,736
0.63***
(18.35)
2.26**
(2.21)
1.20*
(1.74)
2.15*
(1.93)
-0.65**
(-2.10)
-1.32**
(-2.22)
0.48**
(2.43)
2.16*
(1.73)
-0.52
(-0.65)
1.42**
(2.06)
0.32
4,751
0.73***
(22.55)
27.50***
(4.65)
6.33**
(2.25)
12.97***
(3.86)
-8.71**
(-2.11)
-16.70***
(-3.33)
0.52**
(2.52)
2.23**
(2.05)
-0.84
(-1.09)
1.38**
(2.04)
0.30
4,406
0.51***
(21.87)
9.17**
(2.32)
6.76***
(3.00)
6.17**
(2.01)
-0.82**
(-2.39)
-1.97***
(-2.61)
0.49**
(2.14)
2.16**
(2.14)
-0.45
(-0.51)
1.36*
(1.85)
0.30
4,269
53
Table 10: Panel Regressions on Bond Subsamples
This table reports the results of panel regressions on yield spreads among three subsamples of corporate bonds: investment-grade bonds
with insurer ownership below 20% of bonds outstanding (Panel A), investment-grade bonds with insurer ownership above 20% of bonds
outstanding (Panel B), and speculative bonds (Panel C). The regression specification is the same as Table 6. The dependent variable is
the yield spread expressed in percentage points. The main explanatory variables include bond illiquidity ILQ, two dummies T2 and T3 for
the second and third terciles of the illiquidity clientele measure ILC (ranked each quarter), the interaction terms of ILQ with T2 and T3.
The control variables are the same as Table 6. The regressions additionally include credit rating dummies, the issuer-fixed effects, and the
time-fixed effects (not indicated or tabulated). The t-statistics reported in the parentheses are based on two-way clustered (by time and by
issuer) standard errors. *, **, and *** indicate statistical significance at the 10%, 5%, and 1% level, respectively. The first row indicates the
bond illiquidity measure used. The last two rows report the adjusted R-square and the number of observations used in the regression.
Amihud
Roll
LOT
IRC
λ
A. IG bonds < 20% held by insurers
ILQ
54
0.38***
(6.04)
T2
0.08
(0.91)
T3
0.33***
(3.12)
ILQ*T2 -0.06
(-0.63)
ILQ*T3 -0.28
(-1.13)
2
Adj.R
0.20
N
4,235
0.57***
(6.83)
0.33**
(2.13)
0.90***
(5.01)
-0.11
(-0.88)
-0.48
(-1.22)
0.25
4,330
0.06***
(3.76)
0.16*
(1.98)
0.33***
(4.17)
-0.02
(-0.85)
-0.06
(-1.59)
0.26
4,354
1.77***
(6.60)
0.13
(0.84)
0.60***
(3.62)
-0.13
(-0.41)
-1.02
(-0.39)
0.21
4,289
Amihud
Roll
LOT
IRC
λ
B. IG bonds ≥ 20% held by insurers
1.06*** 0.27*** 0.58*** 0.04*** 1.52***
(7.23) (10.42) (9.67) (3.59) (14.10)
0.13
0.20*** 0.43*** 0.13*** 0.32***
(1.69)
(6.87) (7.05) (4.36) (7.03)
0.08
0.29*** 0.82*** 0.26*** 0.59***
(0.60)
(7.27) (10.56) (6.38) (9.69)
-0.21 -0.10*** -0.26*** -0.03** -0.42***
(-1.27) (-4.10) (-4.48) (-2.33) (-3.83)
-0.33 -0.19*** -0.47*** -0.04*** -1.09***
(-1.52) (-7.87) (-7.73) (-3.14) (-9.84)
0.20
0.54
0.56
0.53
0.56
4,110
26,339 27,743 28,068 27,261
Amihud Roll
LOT
IRC
λ
C. Speculative-grade bonds
0.95*** 0.18*** 0.30* 0.01
(15.53)
(4.57) (1.96) (1.59)
0.13***
0.04
0.12 -0.10
(4.51)
(0.32) (0.49) (-0.61)
0.21**
0.14
0.19
0.01
(2.47)
(0.75) (0.63) (0.02)
-0.13***
-0.07
-0.10 -0.01*
(-2.69)
(-0.81) (-0.85) (-1.99)
-0.58***
-0.18
-0.16 -0.01
(-10.61) (-1.24) (-0.91) (-1.09)
0.57
0.60
0.59
0.58
24,232
6,670 6,833 6,888
2.55***
(5.09)
0.37
(1.51)
0.02
(0.05)
-0.76
(-1.56)
-0.09
(-0.15)
0.61
6,756
1.92***
(4.98)
0.12
(0.76)
-0.10
(-0.53)
0.13
(0.32)
0.03
(0.08)
0.63
6,405
Figure 1. Yield Spreads and Bond Illiquidity Measures
The figure shows the piecewise-linear relation between yield spreads and bond illiquidity measures
based on piecewise-linear regressions. In each quarter we regress investment-grade bond yield
spreads onto the piecewise functions of a bond illiquidity measure. We average the time series
averages of the estimated coefficients and reconstruct the piecewise-linear relation based on the
average coefficients. The five panels are for the relation under five different bond illiquidity measures
Amihud, Roll, LOT, IRC, and λ.
Amihud
Roll
2%
Yield Spread
2%
1.5%
1.5%
1
0.25% 1.25% 2.25%
LOT
3
5

IRC
2%
2%
2%
1.5%
1.5%
1.5%
0.05
0.35
0.65
0.15% 0.55% 0.95%
55
-0.5
0.5
1.5
Figure 2. Persistence in Portfolio Illiquidity
This figure plots the average portfolio illiquidity measures ILP during the ranking year (Y) and
the subsequent three years (Y+1 to Y+3), across five insurer quintiles sorted by ILP. In the five
panels, ILP is constructed following Eq. (1) and based on the five different bond-level illiquidity
measures Amihud, Roll, LOT, IRC, and λ.
ILPAmihud
Q1
Q2
Q3
Q4
Q5
1%
0
-1%
Y
Y+1 Y+2 Y+3
ILPRoll
ILPLOT
1
0.5
0
-0.5
5%
0
Y
-5%
Y+1 Y+2 Y+3
Y
ILPIRC
ILP
0.4
0.2%
0
0
-0.2%
Y+1 Y+2 Y+3
Y
-0.4
Y+1 Y+2 Y+3
56
Y
Y+1 Y+2 Y+3
Figure 3. Liquidity Premium over Time in the Lowest and Highest ILC Terciles
The figure plots the time series of liquidity premium estimates among bonds in the lowest (T1 )
and highest (T3 ) terciles of illiquidity clientele (ILC ). The liquidity premium estimates are the
coefficients on bond illiquidity measures (ILQ) in the yield spread regressions specified by Eq. (5).
The five panels present the estimates under the five illiquidity measures Amihud, Roll, LOT, IRC,
and λ. The solid line is for the liquidity premium estimates of the lowest ILC tercile and the dash
line is for the highest ILC tercile.
Amihud
Roll
0.2
0
2003Q4
0.5
2007Q4
0
2003Q4
2011Q4
LOT
2007Q4
2011Q4
IRC
2
0.04
1
0
2003Q4
2007Q4
0
2003Q4
2011Q4

1
0.5
0
2003Q4
2007Q4
2011Q4
57
2007Q4
2011Q4