Liquidity Patterns in the U.S. Corporate Bond Market
Stephanie Heck∗1 , Dimitri Margaritis2 and Aline Muller3
1,3
HEC Liège, Management School-University of Liège
2
University of Auckland, Business School
April 6, 2016
Abstract
Liquidity level and liquidity risk are priced in the cross-section of corporate bond yields
and returns. In the first case the focus is on the individual liquidity level, while in the
second case it is on the exposure to a common liquidity factor. In this paper we focus
on the impact of the liquidity level on yield spreads by acknowledging that liquidity is a
latent variable with an important fraction of commonality. We first document the extent
of this commonality in liquidity in the US corporate bond market. Second we assess
whether the relation to yield spreads is driven by this commonality or by the remaining
idiosyncratic part. We find that a large fraction of the liquidity effect in yield spreads
stems from liquidity commonality. The impact of the bond-specific idiosyncratic liquidity
level is minor overall, but increases in the post-crisis period and for some bond categories.
Keywords : Idiosyncratic liquidity, Liquidity commonality, Yield spreads, Global Financial
Crisis
The authors thank Jan Annaert, Alain Durré, Helen Lu, Matthias Saerens and seminar participants at HEC Montréal and conference participants at the 2014 Belgian Financial Research
Forum, the 2014 Worldfinance and Banking Symposium, the Winter 2014 and 2015 Conference
of the Multinational Finance Society, the 6th Annual Financial Market Liquidity Conference,
the 28th Australasian Finance and Banking Conference for useful comments and suggestions.
Stephanie Heck gratefully acknowledges financial support from the FRS-FNRS.
∗
Corresponding author: [email protected]
1
1
Introduction
The recent global financial crisis has seen a deterioration of market-wide liquidity across all
assets classes, which has been especially detrimental to markets for fixed-income securities and
their derivatives, such as the corporate bond market. Many studies have thus been devoted
to the impact of liquidity shocks on corporate bond yields and returns. Two approaches are
usually adopted. When looking at the pricing implications of liquidity and liquidity risk, most
studies focus on the total level of liquidity or on the sensitivity to a common liquidity factor,
respectively. When studying yield spreads, a strong cross-sectional relation is established
between yield spreads and an individual bond’s liquidity level. When returns are considered, it
is usually the exposure to a market wide liquidity factor which is priced in expected corporate
bond returns. The theoretical model of Acharya and Pedersen (2005) shows that both liquidity
channels should be considered. In the corporate bond market literature, a first attempt to
reconcile both effects is provided by Bongaerts et al. (2012). The authors integrate liquidity
as a bond characteristic as well as various forms of liquidity risk, finding that the liquidity
level is priced but that there is no corporate bond liquidity risk premium. In the stock market
literature, Chordia et al. (2015) find that firm characteristics usually explain a much larger
fraction of variation in expected returns, than exposure to a common factor.
In light of these recent findings, this chapter considers the relationship between yield spreads
and an individual bond’s liquidity level. In fact, liquidity is a latent variable and whatever
proxy of liquidity is used, individual liquidity levels exbibit an important part of commonality
(Chordia et al., 2000, Hasbrouck and Seppi, 2001, Kamara et al., 2008). We complement the
existing literature on liquidity commonality in stock markets, by first describing the extent
of liquidity commonality in the corporate bond market. We calculate the fraction of common
and idiosyncratic liquidity in individual liquidity levels and assess their evolution over time.
Second, we evaluate the relation of these two components to yield spreads. We find that the
liquidity premium contained in yield spreads almost entirely stems from commonality, that is,
the liquidity fraction shared by all bonds. There is thus no discernable relation to the bond’s
idiosyncratic or specific level of liquidity and it all comes down to the pricing of a common
liquidity factor, exactly like what is found when considering exposure to a common liquidity
factor in corporate bond returns.
The assessment of liquidity in the corporate bond market is important. Despite the large
volumes traded in this market, the demand for corporate bonds in the secondary market,
especially for those of shorter maturities, remains scarce.1 Managing this illiquidity and its
1
Stricter post-crisis regulations on banks as well as increases in their risk aversion in conjunction with
ongoing bouts of market volatility have put further pressure on bond market liquidity with dealers’ inventories
shrinking by more than 75% since mid-2007, according to data published by the Federal Reserve Bank of New
York. Asset managers now hold more than 99% of corporate bond inventory and while dealers continue to
play an important role in the price discovery process the balance is starting to tilt with big buy-side players
having more pricing information and influence than before.
2
related risk constitutes a big challenge for investors, as the ease with which they will be able
to trade and at what cost, is a centrepiece of the investment decision.
The specific institutional settings of the corporate bond market contribute to the existence
of, at times, poor liquidity conditions. Corporate bonds trade over-the-counter, where little
price transparency exists. Investors moreover face search costs as brokers must be approached
sequentially to obtain the quotes and prices (Duffie et al., 2005, 2007). Trading in the corporate bond market is generally dominated by a small group of institutional investors and the
market remains opaque to the general public. Unlike equities, there is a large diversity in the
securities provided. Corporate bonds trade infrequently and there is rarely a constant supply
of buyers and sellers looking to trade sufficiently to sustain a central pool of investor provided
liquidity. In this specific setting, we argue that an important part of the bond’s liquidity may
remain idiosyncratic. We therefore study the fractions of common liquidity and bond-specific
or idiosyncratic liquidity.
Second, we use this decomposition to provide a deeper understanding on the interactions
between liquidity and bond yield spreads. In particular, we focus in this chapter, on the
relation between corporate bonds yield spreads and a bond’s common and idiosyncratic level
of liquidity. There is large empirical evidence for the existence of a premium for systematic
liquidity risk (Pastor and Stambaugh, 2003, Sadka, 2006) in the equity market, and similarly
in the corporate bond market (Lin et al., 2011, Acharya et al., 2013). In these studies, the
exposure of individual returns to a common market liquidity factor requires a risk premium in
the security’s returns. In addition, other studies support the view that individidual liquidity
levels are priced in yield spreads (Bao et al., 2011, Dick-Nielsen et al., 2012). Further, Rösch
and Kaserer (2013) provide evidence that commonality is time-varying and that it peaks
during major crisis events.
Liquidity has many facets and generally encompasses the time, cost and volume of a trade. It
can be defined as the ability to trade large quantities of an asset and at a low cost. Therefore
it is reflected in trading costs, which are arguably well proxied by bid-ask spreads or in the
impact of a single trade on prices. In our study we use several liquidity measures to capture
the different dimensions. We use Amihud’s (2002) measure to capture the price impact of a
trade, the imputed roundtrip cost introduced by Feldhütter (2012), Roll’s (1984) measure as
a proxy of trading costs as well as the ratio of a bond’s zero trading days within a period of
time to capture trading activity in the spirit of Lesmond et al. (1999).
Using US corporate bonds transaction data from TRACE, we aim to make a contribution to
the literature in the following way. We decompose a bond’s individual liquidity into a common
and an idiosyncratic component and study how these two components interact in driving bond
yields. We start by measuring the magnitude of liquidity commonality of this market and
define the residual as the idiosyncratic bond liquidity. The commonality in liquidity can
be seen as the part that is driven by the market and which is common to all bonds. The
3
idiosyncratic liquidity is the residual bond-specific liquidity after controlling for those common
factors. We use a factor decomposition to derive the common liquidity fraction in each bond.
The common part based on 3 factors accounts for between 25% and 67% of the liquidity
variation on average, which leaves and important part of liquidity defined as the idiosyncratic
component.
We then test whether commonality only exhibits a relation to yield spreads, whether idiosyncratic liquidity can have some explanatory power, and how the prevalence between both varies
over time. We use Fama and MacBeth (1973) type regressions to measure the extent of the
sensitivity of yield spreads to common and idiosyncratic liquidity shocks and consider the time
series behavior of the coefficients on these measures. We find that the relationship between
yield spreads and illiquidity levels is driven essentially by the common fraction in liquidity
and disentangling this component increases the importance of liquidity in yield spreads. The
bond specific, idiosyncratic illiquidity of the bond is only weakly significant, but has an in
impact on yield spreads during the recent post-financial-crisis period.
The remainder of the chapter is organised as follows. In section 2 we present a survey of the
relevant literature. In section 3 we describe our dataset and the methodology. In section 4
we discuss the empirical results. Section 5 concludes.
2
Literature review
Since Amihud and Mendelson (1986) liquidity has been considered as an important element
in asset pricing. A number of studies, especially on stock markets, investigate the pricing
implications and provide evidence of a premium for systematic liquidity risk (Amihud, 2002,
Pastor and Stambaugh, 2003, Acharya and Pedersen, 2005, Sadka, 2006). Pastor and Stambaugh (2003) consider market liquidity as a state variable. They find that expected stock
returns are related cross-sectionally to the sensitivities of returns to fluctuations in aggregate
liquidity.
Liquidity has many dimensions and there is not one single measure that has been accepted
unanimously. Several proxies have emerged in the literature and are usually considered as
reliable measures of transaction costs. Roll’s (1984) measure essentially relates transaction
costs to bid-ask spreads. The idea behind is that the price bounces back and forth between
bid and ask prices and higher percentage bid-ask spreads lead to higher negative covariance
between consecutive returns. The measure is indeed able to capture liquidity dynamics above
and beyond the effect of bid-ask bounce as shown in Bao et al. (2011). Amihud (2002)
develops a measure relating the price impact of a trade to the trade volume. Pastor and
Stambaugh (2003) build an illiquidity measure as the temporary price changes induced by
trading volume. Mahanti et al. (2008) derive a ’latent liquidity’ measure from custodian
4
banks’ turnover, defined as the weighted average turnover of investors who hold a bond, in
which the weights are the fractional investor holdings. Jankowitsch et al. (2011) propose a
price dispersion measure, based on the dispersion of market transaction prices of an asset
around their consensus valuation by market participants.
A number of studies demonstrate that liquidity exhibits a systematic common component and
that this commonality is time-varying and especially strong during crisis periods. Chordia
et al. (2000) are the first ones in showing that individual liquidity measures of stocks comove.
Hasbrouck and Seppi (2001) provide evidence of common factors in returns and order flows.
Kamara et al. (2008) consider the cross-sectional variation of liquidity commonality and show
how it has increased over time and how it depends on institutional ownership.
Recent papers in the finance literature show that both liquidity as a characteristic and liquidity
risk are important components in explaining the credit spread puzzle exhibited in corporate
bond returns. Bao et al. (2011) use a modified version of Roll’s measure as a proxy for
liquidity and show it is an important factor in explaining the time variation in bond indices
and the cross-section of individual yield spreads. Further the measure relates to other bond
characteristics that are commonly used as liquidity proxies and exhibits commonality across
bonds, which tends to go up during periods of market crisis. Dick-Nielsen et al. (2012) use
a principal component analysis of eight liquidity measures to define a factor, which is used
as a new liquidity proxy. The authors find that illiquidity contributes to spreads and does
so even more for speculative bonds. The contribution is only small before the crisis but
increases strongly at the onset of the crisis for all bonds except AAA-rated bonds. This
finding underscores the flight-to-quality effect that occurred in AAA bonds. Friewald et al.
(2012) study the pricing of liquidity in the US corporate bond market in periods of financial
crisis. The liquidity measures are derived from standard liquidity measures such as Roll and
Amihud, bond characteristics, trading activity variables and price dispersion. Liquidity is
found to account for 14% of the explained time-series variation in corporate bond yields and
its economic impact is almost doubled in crisis periods.
Liquidity risk implications are analyzed in De Jong and Driessen (2012), Lin et al. (2011),
Acharya et al. (2013). De Jong and Driessen (2012) use a linear factor models in which
corporate bond returns are exposed to market risk factors and a liquidity risk factor. Returns
are measured at the index level and liquidity risk factors are derived from shocks to equity
market and government bond market liquidity, respectively. Expected corporate bond returns
are exposed to fluctuations in both Treasury market and equity market liquidity. Similarly
Acharya et al. (2013) study the exposure of US corporate bond returns to liquidity shocks
in the stock market and the Treasury bond market over more than 30 years. They find a
conditional impact of liquidity shocks on bond prices defined over two regimes. In the first
regime, characterized by normal times, liquidity shocks do not affect bond prices. However in
the second regime, which is characterized by macroeconomic and financial distress, there is a
5
differential impact of liquidity on investment grade bonds versus speculative bonds. Junk bond
returns respond negatively to illiquidity shocks, while investment grade bond returns respond
in a positive and significant way. Lin et al. (2011) focus instead on liquidity risk obtained
in the corporate bond market itself. Using the Fama and French (1993) five factor model
for bond returns, augmented by this liquidity factor, they find that liquidity risk is priced in
expected corporate bond returns and this result is robust to the inclusion of default, term and
stock market risk factors, bond characteristics, the level of liquidity and the rating.
The literature thus highlights the existence of commonality in liquidity, the pricing of the
bond’s liquidity level in yield spreads and the exposure to a liquidity risk factor in returns.
The presence of commonality in liquidity involves that part of a security’s liquidity remains
idiosyncratic or unexplained by the market. In a very opaque market such as the corporate
bond market, with a large number of different securities and a large number of small dealers,
this idiosyncratic component may even be quite important. Further it remains unclear whether
the liquidity effect found in yield spreads is indeed related to the bond’s specific individual
liquidity level or if it is merely the result of an exposure to a common factor, following the
interpretation typically obtained in a risk premium approach.
The present study can therefore be distinguished from prior research in the following way.
We focus on the pricing of individual liquidity levels in yields spreads and decompose this
individual level. We consider the relative magnitude of common and idiosyncratic components
over time and in bond groups. We also study the pricing implications of these two measures
over time and in bond groups. No study so far has carried out this decomposition nor studied
the differential pricing effects. The large diversity of products confronted to a large number of
dealers with small market shares does not offer an optimal transparency on all bonds that may
be available to the investors. In this context, we conjecture that some bonds exhibit a stronger
idiosyncratic illiquidity because they are not broadly available or known to all investors. On
the other hand, liquidity is a market variable, which argues in favor of important shared
fraction in the liquidity of individual securities and the pricing of this common fraction. Our
sample allows us to conduct a thorough analysis of the relation pre- and post- financial crisis
as we have equal-length periods of data before and after the crisis at our disposal.
3
3.1
Data and methodology
Liquidity measures
We build weekly series of four liquidity measures which have been used in recent studies,
among others in Dionne and Maalaoui Chun (2013), Dick-Nielsen et al. (2012). Our weekly
measures are computed over weeks starting on Wednesday and ending on Tuesday, to avoid
weekend effects.
6
1. Amihud price impact: Amihud (2002) measures the price impact of a trade by
taking the absolute value of the return over the trading volume. We follow Dionne and
Maalaoui Chun (2013) by constructing this measure on all days, when at least three
transactions of the bond are observed. For each individual bond i, we construct a daily
Amihud measure, which is then aggregated weekly by taking the mean:
Amii,t =
N
1 X |returnij,t |
N
volumeij,t
j=1
(1)
where N is the number of returns during each day t, returnij,t is the return on the
j-th transaction during day t and volumeij,t is the volume of this j-th transaction. The
measure thus reflects how much the price moves in response to a given volume of trade.
2. Imputed roundtrip cost: The measure is developed by Feldhütter (2012) and is based
on the observation that bonds might trade two or three times within a short interval,
after a long interval without any trade. This is likely to occur because a dealer matches
a buyer and a seller and collects the bid-ask spread as a fee. The dealer buys the bond
from a seller, and further sells it to the buyer. The price difference can be seen as the
transaction fee or the bid-ask spread. The imputed roundtrip cost (IRC) is therefore
defined as:
IRCi,t =
max − P min
Pi,t
i,t
max
Pi,t
(2)
max and P min are the largest and smallest prices in the set of transactions with
where Pi,t
i,t
the same size, within a day. For each bond we obtain the daily IRC as the average of
all roundtrip costs on that day for different sizes and we then take averages of daily
estimates to obtain weekly estimates.
3. Roll bid-ask spread: Roll (1984) shows that the bid-ask spread on bond i and on day
t can be approximated as follows:
p
Rolli,t = − cov(∆pt , ∆pt−1 )
(3)
The idea behind this measure is that adjacent price movements can be interpreted
as bid-ask bounces and this results in a negative correlation between transitory price
movements. A higher negative covariance therefore indicates higher bid-ask spreads and
hence higher transaction costs. We compute this measure daily for each bond, using a
rolling window of 21 days in which we require at least four transactions.
4. Zero trading days of the bond: Our last liquidity indicator reflects the frequency
at which the bond trades. Following the suggestions in Lesmond et al. (1999), many
studies compute the ratio of the number of zero trading days over the total number of
trading days during a period. Less trading days indicate less liquidity of the bond. We
7
compute this ratio rolling over every day for each bond, using a period of 21 trading
days:
ZT Di,t =
number of days without trading of the bond in the rolling window
(4)
number of days in the rolling window
All liquidity measures are designed in such a way that higher positive values reflect higher
illiquidity. In the remainder of the chapter, we will thus stick to this interpretation of an
increasing measure -be it the measure of price impact, of transaction costs or trade frequencyas higher illiquidity or equivalently as lower liquidity.
3.2
Sample construction
In a view to increase transparency in the US corporate bond market FINRA (Financial Industry Regulatory Authority) has, since 2002, been gradually releasing transaction data of
secondary corporate bond market trades. Since 2005 almost 99% of all transactions must be
reported to TRACE (Trade Reporting and Compliance Engine). The availability of this data
has created a new avenue for research investigating the effects of illiquidity in the cross-section
of bond yields and returns.
The database contains detailed trade-by-trade records with the timestamp of the transaction,
the clean price and the par value traded, although the par value traded is truncated at $1
million for speculative grade bonds and at $5 million for investment grade bonds. All FINRA
members are responsible for reporting all OTC corporate bond transactions in the secondary
market to this system. The information is disseminated in TRACE and makes it a most
valuable tool for microstructure research of bond market liquidity. Even if the reporting requirements are well specified, the database nevertheless contains many erroneous and cancelled
reports. We follow Dick-Nielsen et al. (2012) to manually filter out error reports, cancelations,
reversals and agency transactions. For our analysis we require the bonds to have frequent
enough trading to be able to construct a liquidity measure at a weekly frequency.
We operate our selection in two steps. First, we include only bonds which are present in the
sample for more than a year and are traded on at least 30 business days each year. Second,
once liquidity measures are computed, we operate a further selection of bonds to be able to
obtain a time series of liquidity measures for a specific bond. Since Amihud’s measure requires
most transaction to be built it is the most restrictive one and has fewest observations. By
selecting on this measure we make sure that we have more frequent observations of other
liquidity measures. We require that Amihud’s liquidity measure be observed for an individual
bond on a least 20% of the weeks of its presence in the sample.2 This selection criterion
2
We admit that our selection is arbitrary but it is the choice we make to face the tradeoff between obtaining
a large cross-section of bonds and being able to compute liquidity measures, since some bonds have very few
trades.
8
leaves us with a sample of 9,670 bonds and still allows for large heterogeneity across bonds,
despite the fact of being slightly biased towards ‘the most observed’ and hence more liquid
bonds. We use this bond list to retrieve bond characteristics from Bloomberg. Based on
this information we retain only dollar denominated bonds with a bullet or callable repayment
structure, without any other option features. We also require having information available on
bond characteristics such as its issue size and date, its rating and its coupon. We end up with
a selection of 7,535 bonds for which we obtain the complete transaction data in TRACE and
construct weekly liquidity measures. In table 1 we report summary statistics on the bonds
in our final sample and provide information about their trading activity. In our sample we
have 519 weeks, starting on 21 January 2004 and ending on 31 December 2013. Since the
number of bonds in the sample is not fixed, we obtain an unbalanced panel for each of the
illiquidity measures, depending on the weeks and the bonds for which a liquidity measure can
be calculated.
While the total sample consists of 7,535 bonds, the number of bonds in the sample gradually
increases over the years, from 1,251 in 2004 to 5,635 in 2013 as displayed in table 1. Average
issue size of the bonds increases slightly over the years. In all years, average maturity is close
to 15 years. The gradual decrease in maturity can be explained by our sample selection, as
a bond usually stays in the sample once it is selected. We can see from the table that these
bonds trade very little. Median number of trades a week ranges from 11 to 20, while the mean
lies between 20 and 40. Both values are highest in 2009. Overall the mean and the median
number of trades increases considerably towards the end of the sample. Turnover, measured
as the total monthly trading volume over issue size has been decreasing between 2004 and
2008, where it attains 4.7%. It was higher in 2009 but then experienced a steady decrease
until the end of the sample, which might also be related to the fact that the average issue size
has been increasing. The number of trading days is higher in the second half of the sample,
which comes along with a higher activity on this market and with the fact that over the years
more and more bonds have become subject to reporting. Average daily and weekly returns
have alternated from positive to negative. The strongest negative values have been observed
in 2008, which corresponds to the onset of the financial crisis in the US.
3.3
Liquidity decomposition
We would like to gain a deeper insight into liquidity dynamics and their pricing implications.
We are interested in the extent of commonality in liquidity and the remaining idiosyncratic
part. Since the focus of this chapter is on the liquidity level, we propose to decompose
our liquidity measures into a common part and an idiosyncratic part. The common part is
assumed to reflect shocks in liquidity that are common to all bonds, while the idiosyncratic
part is assumed to reflect shocks that are specific to the individual bond. To identify those
distinct components, one option is to extract common factors in liquidity series and to treat the
9
10
Bonds
Issue size
Maturity
Coupon
Rating
Turnover
Weekly trades
Trading days
Price
Daily returns
Weekly returns
Bonds
Issue size
Maturity
Coupon
Rating
Turnover
Weekly trades
Trading days
Price
Daily returns
Weekly returns
500
10
6.12
8.33
4.90
20.2
181
99.40
0.06
0.24
2009
Median
Mean
3874
661
14.1
6.19
8.79
6.80
39.7
170.9
94.20
0.13
0.44
322
15
6.38
9
5.5
11.9
64
101.3
0.01
0.02
2004
Median
1251
489
16.87
6.24
9.25
8.2
24.8
110
103.3
0.02
0.05
Mean
712
9.02
1.73
3.61
6.60
59.1
64.5
16.10
0.29
0.69
SD
583
8.6
1.35
3.55
9.1
43.8
82
8.8
0.16
0.32
SD
4938
672
13.24
6.08
8.77
6.70
35
183
103.90
0.02
0.05
Mean
1619
496
16.3
6.16
9.22
7.4
19.6
162.9
100
-0.04
-0.12
Mean
500
10
6
8.33
4.50
19.3
197
104.20
0.02
0.05
2010
Median
350
14
6.2
9
5.1
11.5
168
100.1
-0.02
-0.05
2005
Median
714
8.85
1.92
3.65
6.70
49.3
63.1
10.70
0.08
0.28
SD
566
8.6
1.5
3.67
7.8
30.7
65.4
11.4
0.12
0.3
SD
5708
680
12.98
5.88
8.73
4.20
26.5
199.1
105.60
-0.04
-0.04
Mean
1930
537
16.11
6.15
9.2
7.3
18.7
158.6
97.5
0.01
0.05
Mean
500
10
5.9
8.33
3.60
15.2
207
105.70
0.00
0.01
2011
Median
400
12
6.15
9
4.9
11.1
166
97.8
0.00
0.00
2006
Median
705
8.74
2.04
3.65
2.90
32.5
46.3
10.70
2.28
2.29
SD
577
8.7
1.56
3.6
7.2
23.5
64.9
8.7
0.10
0.23
SD
5905
661
13.55
5.7
8.76
3.50
25.4
188.3
108.50
0.01
0.07
Mean
2607
586
15.82
6.12
9.12
6.2
19.2
144.1
98
-0.03
-0.08
Mean
500
10
5.75
8
2.90
13.3
196
107.40
0.01
0.06
2012
Median
400
11.5
6.12
9
4.3
10.2
151
98.6
-0.01
-0.04
2007
Median
686
8.86
2.15
3.65
2.50
35.3
51.2
14.00
0.42
0.51
SD
637
8.95
1.64
3.61
5.9
28.4
70.4
7.4
0.11
0.29
SD
5635
654
14
5.57
9
3.30
22.9
179.3
108.90
-0.02
-0.07
Mean
3071
625
15.27
6.13
8.92
4.7
25
154.8
89.5
-0.22
-0.52
Mean
500
10
5.65
8
2.70
13
191
107.90
-0.02
-0.07
2013
Median
450
10
6.1
8.5
3.6
11.3
155
93.5
-0.06
-0.21
2008
Median
685
9
2.14
4
2.80
30.3
63.1
12.10
0.60
0.83
SD
684
9.08
1.63
3.6
4.2
42.8
63.6
14
1.1
1.48
SD
Table 1: The table provides summary statistics on the bonds used in the empirical analysis. To be included in the sample a bond must
trade on a least 30 business days of the year and remain in the sample for at least one year. The sample is from January 2004 to December
2013. Bonds gives the number of unique bonds in the sample in a given year. Issue size is the average issuance of bonds in the sample in
$ millions. Maturity is measured in years and gives the number of years to maturity. Rating is an average of ratings provided by the three
rating agencies, measured on a scale from 1 (high rated) to 21 (low rated). Coupon is the coupon payment in percentage. Turnover is
the total volume traded during one month over issue size, measured in percentage. Weekly trades provides the average number of trades
over the week. Trading days is the average number of days on which a bond was traded during the year. Return is the mean of the daily
or weekly return series obtained in a given year, measured in percentage. Price is the average price of the bond during the year.
remaining part as idiosyncratic. We follow the approach used in Korajczyk and Sadka (2008)
to identify the common liquidity component. To avoid any problems of different measurement
units across the four liquidity series and to facilitate the comparison, we standardize each
individual series using its the sample mean and standard deviation. We then assume that
liquidity is explained by an approximate factor model in the following way:
Lk = β k F k + k
(5)
where Lk is the n × T matrix of liquidity observations of measure k, with k = 1, ..., 4 on the n
assets over T time periods, F k is the s × T matrix of common liquidity factors and β k is the
n × s matrix of exposure to those s factors for all individual assets n. Connor and Korajczyk
(1986) show that for a balanced panel, the s latent factors of this approximate factor model
can be obtained by calculating the eigenvectors corresponding to the s largest eigenvalues
of
0
Lk Lk
Ω =
.
n
k
(6)
The authors show that the eigenvector analysis of the T × T covariance matrix in the case
of asset returns is asymptotically equivalent to a traditional factor analysis. The estimates of
those factors are referred to as asymptotic principal components. The main advantage of the
asymptotic principal component analysis is that it overcomes the problems that are inherent
to factor estimations in large cross-sections. The matrix Ωk has dimension T × T and allows
for a much easier factor decomposition than an n × n matrix, when n is large. Connor and
Korajczyk (1987) further show how this estimation procedure can be extended to unbalanced
panels. Elements of Ωk are obtained by averaging over observed data only. To this end, let
Lk be the matrix with liquidity measures where missing values are replaced by 0 and let N k
be an n × T matrix where N kj,t is equal to one if liquidity measure k of bond j at time t
is observed and zero otherwise. The matrix Ω that accommodates missing data is built as
follows:
0
Ωk,u
t,τ
(Lk Lk )t,τ
=
(N k0 N k )t,τ
(7)
Element (t, τ ) of matrix Ω(T × T ) is defined over the cross-sectional averages of the observed
liquidity values only. The factors used for the approximate factor model are then obtained by
calculating the eigenvectors for the s largest eigenvalues of Ωk,u .
We apply this asymptotic principal component analysis to our set of liquidity measures. We
do this for the four individual liquidity measures and we extract common factors across all
four measures as well. We obtain the factor estimations for each liquidity measure k and
we run time series regressions of individual liquidity series on the identified common factors,
alternatively using one, two or three factors. The choice of stopping after three factors follows
Korajczyk and Sadka (2008). Furthermore, adding more factors increases the amount of
variance captured by 1% only for each factor. Table 2 reports the average adjusted R2 , the
11
Table 2: This table reports distribution statistics of time-series regressions of individual
liquidity series on three common factors. The factors are extracted separately for each measure
using the asymptotic principal component method. The table presents averages of the adjusted
R2 obtained with one, two or three factors. The columns Factor 1 to Factor 3 show the
percentage of bonds for which the extracted factor is statistically significant at a 5% level in
it’s time series regression.
Amihud
IRC
Roll
ZTD
Adj. R2
Factor 1
Factor 2
Factor 3
1 factor
2 factors
3 factors
40.08
46.96
51.98
84.81
72.53
64.86
72.69
59.23
70.35
1 factor
2 factors
3 factors
19.74
23.22
25.68
63.17
52.78
52.65
30.04
25.16
22.46
1 factor
2 factors
3 factors
35.83
49.36
50.59
88.01
71.32
70.76
81.37
76.02
44.82
1 factor
2 factors
3 factors
52.96
59.72
62.79
92.74
78.55
78.59
73.75
73.92
56.00
percentage of explained variance obtained from the APCA and the percentage of significant tstatistics obtained by fitting our weekly illiquidity measures to one, two or three latent factors.
Next we define the fitted and residual values obtained from regressions on the 3 factors as our
common and idiosyncratic illiquidity measures. Hence for each bond we obtain weekly time
series of common and idiosyncratic illiquidity over the time period a bond is present in the
sample.
Results in table 2 indicate that there is evidence of commonality within individual bond
liquidity measures. Most of the commonality seems to be captured by the first factor, as
evidenced by the percentage of significant t-statistics of factor 1. The three first factors are
able to capture between 26% and 63% of the variance in the data, as evidenced by the adjusted
R2 values of the regressions. This leaves an important part attributable to the idiosyncratic
components.
In table 3 we provide the results of the regressions on a within-measure factor and an acrossmeasure factor. The common across measure factors are obtained by stacking all liquidity
variables together. Before entering the regression, the within-measure factor is projected
on the across measure factor in order to keep only the measure specific variation. Results
indicate that the across measure factor is significant for 40% to 67% of the individual bonds,
according to which liquidity measure is considered. The measure-specific factor is significant
12
Table 3: This table reports distribution statistics of time-series regressions of individual liquidity series on the factors extracted using the asymptotic principal component method. The
two regressors are a within-measure factor and an across-measure factor. Within measure
common factors are extracted separately for each of the liquidity measures. Across-measure
common factors are extracted for all liquidity measures jointly. Then for each liquidity measure and each bond a time-series regression is run on those two factors. The two factors are
first orthogonalized by projecting the within-measure common factor on the across-measure
common factor. The table reports the percentage of bonds in the sample that exhibit significant coefficients at the 1% and 5% significance levels as well as the joint significance
(F-statistic). Average R2 and adjusted R2 are also reported.
Liquidity measure
Stat.
Significance
Amihud
5%
1%
5%
1%
5%
1%
5%
1%
IRC
Roll
ZTD
Intercept Measure
specific
64.55
59.52
69.95
65.44
73.11
68.9
75.96
71.53
19.89
14.29
28.98
22.16
41.87
34.1
62.75
56.54
Across
factor
F-stat
40.70
34.60
56.64
51.04
60.66
55.55
66.82
61.74
45.04
35.04
62.87
53.61
68.63
59.3
85.52
79.64
Average Average
R2
Adj.
R2
7.84
5.22
10.84
9.08
13.02
11.23
20.01
18.61
in fewer instances, once this across measure factor has been accounted for. Overall with these
two factors, between 8% and 20% of the variation in individual liquidity time series can be
explained, leaving an important idiosyncratic component.
By standardizing illiquidity measures and by running regressions on common factors, we
necessarily obtain some negative values for the liquidity components. This opposition in signs
poses a challenge, since illiquidity is by construction a positive variable. A negative value
is by itself hard to interpret. The variables are constructed in a way such that increasing
positive values reflect higher illiquidity. As a result of the sandardization, negative values
can still be interpreted in relative terms, as indicating lower illiquidity than if the value
is positive. For example a bond with a negative value would have an illiquidity level that
is lower than the average illiquidity level. We thus leave the signs unchanged in order to
best reflect the relative magnitudes between common and idiosyncratic values as well as
to maintain the relative magnitudes in the cross-section of bonds. The reasoning can be
extended to the decomposition, where a regression on factors is used. For instance if a bond
has a negative commonality value, its exposure to common factors is negative, suggesting
that the individual bond’s illiquidity decreases as the market illiquidity increases. Instead
if the individidual bond’s illiquidity level has a strong commonality, larger than the market
illiquidity, its idiosyncratic illiquidity might be negative, thereby reducing the bond’s total
illiquidity.
13
Table 4 reports descriptive information on total liquidity measures and the two components.
The magnitudes of the liquidity components are aggregated cross-sectionnally in bond groups
and in the time series. We know from previous research that illiquidity contributed to the
widening of credit spreads during the financial crisis (Friewald et al., 2012, Dick-Nielsen et al.,
2012). To disentangle the behavior of liquidity in crisis periods, we decompose the sample
period into three parts pre-, during and post-crisis. We focus on the most tormented period
of the crisis in the US market, which is usually assumed to be the period around the fall of
Lehman Brothers. We therefore define the crisis period as starting in June 2008 and lasting
until May 2009.
We further consider our illiquidity measures in different subgroups of bonds, designed according to the maturity, the rating, the issuance size and the industry of the bond. Most groups
and sub-periods contain a few hundred bonds on which means and standard deviations of
weekly liquidity measures are computed. For ratings AAA and C and for maturities around
2Y however, we obtain only a few observations, at least at the beginning of the sample, and
results should therefore be interpreted with care.
As expected, illiquidity and in particular commonality, is highest during the crisis and postcrisis it falls below its pre-crisis level. This relation is verified throughout all liquidity proxies.
Rösch and Kaserer (2013) among others also show that liquidity commonality increases during
market downturns and peaks in periods of major crisis events. Better liquidity conditions
after the crisis might be the result of the stimulus program initiated by the Fed starting in
May 2009. Note that this pattern appears for our aggregate liquidity measure and for the
commonality measure but not for idiosyncratic illiquidity. Idiosyncratic illiquidity instead has
been increasing over time starting from negative values and increasing towards positive values
in the last period. There is thus an important fraction of common variation in individual
liquidity levels over all periods, and this commonality is strongest during the crisis. In the
two first periods, the idiosyncratic fraction of illiquidity reduces this commonality but in the
post-crisis period, both commonality and idiosyncratic part add up to the total illiquidity
measure.
Considering this decomposition for bonds classified based on their rating, we surprisingly
find that in the pre-crisis period, the lowest illiquidity levels are exhibited by junk bonds
(rating C or below). This finding is confirmed by all measures except the zero trading days
measure, where it is the other way round. Despite having the highest fraction of zero trading
days per bond, these junk bonds display lower illiquidity on other dimensions. During the
crisis, we observe that illiquidity increases as the credit quality deteriorates (from AAA to
B). This is valid for the total illiquidity measure as well as for the commonality fraction.
The idiosyncratic fraction instead steadily increases when credit quality lowers and is highest
for the C rated bonds. Hence these bonds exhibit lower levels of commonality but this is
compensated by higher idiosyncratic illiquidity values. In the post crisis period, the relation
14
15
0.37
4.60
0.16
5.20
1.12
5.89
-1.19
2.23
-1.56
1.06
Rating AAA
Other
Industrial
Financial
Issuance large -small
Issuance Large
Issuance Medium
1.05
6.18
-0.64
3.55
0.60
5.34
0.76
6.25
-0.77
3.03
-0.71
2.33
-1.46
0.46
Issuance Small
Maturity 30Y-5Y
Maturity 30Y
Maturity 10Y
Maturity 5Y
-0.35
2.41
-0.49
3.31
0.16
4.97
1.39
6.73
2.00
0.91
Maturity 2Y
Rating C-AAA
Rating C
Rating B
Rating A
0.37
5.47
Overall
Pre-crisis
4.12
10.52
1.23
7.97
2.59
8.45
2.91
10.23
1.89
8.17
1.51
5.88
-1.39
0.74
1.74
3.67
1.47
7.83
2.72
9.03
4.57
10.73
3.10
0.67
1.47
5.33
2.92
9.51
3.50
11.50
1.26
7.50
-0.21
2.34
2.63
9.37
-0.08
4.24
-1.06
2.72
-0.56
3.44
-0.18
4.20
-1.06
2.53
-1.20
1.91
-1.03
0.41
-1.19
2.42
-1.00
2.71
-0.39
3.75
0.46
4.63
1.45
0.96
-0.85
2.84
-0.59
3.41
-0.46
3.81
-0.26
3.89
0.59
0.81
-0.59
3.59
Amihud
Crisis Post-crisis
1.19
2.39
-0.42
1.69
0.75
2.61
0.84
2.67
-0.48
1.46
-0.44
1.58
-1.28
0.35
-0.47
0.77
-0.35
1.59
0.34
2.16
1.58
2.77
2.11
0.60
0.28
2.03
0.40
2.43
1.25
2.30
-0.55
1.14
-0.85
0.48
0.54
2.37
4.34
5.34
1.27
3.72
2.55
4.94
3.13
5.17
1.87
4.06
1.53
3.76
-1.60
0.41
1.57
2.16
1.52
4.23
2.77
4.72
4.74
5.27
3.23
0.58
1.76
3.14
2.94
4.91
3.60
5.97
1.36
3.32
-0.40
1.26
2.73
4.86
-0.13
1.95
-1.10
1.27
-0.59
1.83
-0.21
2.01
-1.12
1.18
-1.23
1.13
-1.02
0.33
-1.20
1.13
-1.06
1.28
-0.42
1.75
0.38
2.23
1.44
0.85
-0.83
1.50
-0.64
1.77
-0.55
1.59
-0.44
1.42
0.39
0.48
-0.64
1.73
Amihud Commonality
Pre-crisis Crisis Post-crisis
-0.13
5.65
-0.22
3.19
-0.15
4.54
-0.08
5.55
-0.29
2.71
-0.26
1.98
-0.18
0.42
0.12
2.24
-0.14
2.90
-0.18
4.47
-0.19
6.00
-0.11
0.55
0.09
4.06
-0.24
4.55
-0.12
5.45
-0.64
2.25
-0.71
1.08
-0.17
4.87
-0.22
8.93
-0.04
6.73
0.05
6.69
-0.22
8.67
0.01
6.72
-0.01
4.21
0.21
0.78
0.17
3.08
-0.05
6.16
-0.05
7.48
-0.18
9.38
-0.13
0.67
-0.29
4.40
-0.02
7.82
-0.10
9.64
-0.09
6.98
0.20
2.62
-0.10
7.80
0.05
3.85
0.05
2.39
0.04
2.95
0.03
3.74
0.06
2.24
0.03
1.52
0.00
0.21
0.02
2.22
0.06
2.42
0.03
3.35
0.08
4.12
0.02
0.38
-0.01
2.54
0.05
2.95
0.08
3.81
0.18
3.61
0.20
0.80
0.05
3.18
Amihud Idiosyncratic
Pre-crisis Crisis Post-crisis
145
300
365
100
201
382
212
421
215
1
24
181
396
47
819
258
589
550
292
416
598
312
432
567
2
34
191
794
105
1375
492
1167
1011
614
829
1267
477
689
1071
557
72
466
1718
277
2836
Number of obs
Pre-crisis Crisis Post-crisis
Table 4: This table provides average values and standard deviations (in italics) of our total illiquidity measures and their decomposition
into a common and idiosyncratic component. We consider different subgroups and subperiods. The bonds are classified according to their
rating, maturity, issuance and industry. The average rating of a bond is converted on a numerical scale from 1 to 21. Rating AAA, A, B
and C refer to bonds with a numerical rating below 4.5, between 4.5 and 10.5, between 10.5 and 16.5, above 16.5 respectively. Maturity
groups are formed with bonds of maturity between 1 and 2 years, between 2 and 7 years, between 7 and 17 years and of more than 17
years. Issuance small, medium and large refer to issue sizes below 500Mln, between 500Mln and 1Bln, and above 1Bln respectively. We
also provide the number of observation of each measure on which the statistics are obtained.
16
0.04
4.17
-0.15
4.39
0.83
4.69
-0.60
2.73
-0.64
0.95
Rating AAA
Other
Industrial
Financial
Issuance large -small
Issuance Large
Issuance Medium
0.87
5.15
-0.85
2.97
-0.04
4.35
0.40
5.07
-1.20
2.09
-0.92
1.96
-1.32
0.49
Issuance Small
Maturity 30Y-5Y
Maturity 30Y
Maturity 10Y
Maturity 5Y
-0.45
2.75
-0.62
2.91
-0.13
3.92
1.07
5.73
1.84
0.76
Maturity 2Y
Rating C-AAA
Rating C
Rating B
Rating A
0.11
4.52
Overall
Pre-crisis
4.53
11.93
0.91
5.03
1.11
5.36
2.32
7.92
0.86
4.75
1.62
4.32
-0.70
0.74
4.30
7.02
1.31
5.94
3.15
10.49
3.05
8.19
1.75
0.70
2.22
6.21
1.75
6.46
4.74
13.72
3.89
8.66
1.67
1.17
2.44
8.82
IRC
Crisis
0.38
4.02
-0.91
2.52
-0.66
2.94
0.05
3.87
-1.02
2.20
-0.89
1.95
-0.94
0.40
-1.13
2.22
-0.68
2.64
-0.05
3.52
0.36
4.17
1.04
0.75
-0.44
3.12
-0.51
3.04
-0.05
3.60
0.89
4.49
1.33
0.79
-0.36
3.33
Post-crisis
0.95
2.32
-0.77
1.26
-0.10
2.24
0.35
2.30
-1.06
1.09
-0.84
1.21
-1.20
0.35
-0.07
1.22
-0.54
1.63
0.00
1.84
1.00
2.68
1.78
0.69
-0.07
1.70
-0.17
2.18
1.10
1.99
0.21
1.47
0.27
0.47
0.16
2.20
4.35
4.66
0.92
2.17
1.12
2.66
2.44
3.55
0.82
2.13
1.39
2.36
-1.05
0.31
4.37
4.59
1.24
2.46
3.01
4.29
3.03
4.08
1.79
0.56
2.22
2.86
1.83
3.09
4.25
5.34
3.02
3.92
0.80
0.25
2.36
3.87
0.35
1.99
-0.94
1.25
-0.68
1.72
0.05
2.05
-1.06
1.16
-0.90
1.25
-0.95
0.32
-1.09
1.11
-0.75
1.26
-0.07
1.77
0.39
2.44
1.14
0.73
-0.42
1.58
-0.51
1.80
-0.17
1.54
0.61
1.93
1.03
0.25
-0.39
1.78
IRC Commonality
Pre-crisis Crisis Post-crisis
Table 4 con’t
-0.07
4.54
-0.08
2.76
0.06
3.62
0.04
4.36
-0.14
1.98
-0.08
1.67
-0.12
0.31
-0.38
2.63
-0.08
2.59
-0.13
3.53
0.08
4.83
0.06
0.55
0.10
3.74
0.01
3.67
-0.26
4.35
-0.81
2.80
-0.91
0.92
-0.05
3.91
0.18
10.58
-0.01
4.50
-0.01
4.79
-0.12
7.11
0.04
4.23
0.23
3.47
0.35
0.74
-0.07
6.69
0.06
5.29
0.14
9.02
0.02
7.29
-0.04
0.49
0.00
5.52
-0.08
5.74
0.49
11.94
0.86
7.72
0.87
1.19
0.07
7.67
0.03
3.57
0.02
2.14
0.02
2.39
0.00
3.33
0.04
1.79
0.01
1.48
0.01
0.19
-0.04
1.91
0.08
2.30
0.02
3.05
-0.03
3.49
-0.11
0.24
-0.02
2.72
0.00
2.50
0.12
3.24
0.28
4.03
0.30
0.82
0.03
2.84
IRC Idiosyncratic
Pre-crisis Crisis Post-crisis
203
415
564
108
253
641
305
597
293
2
33
244
585
71
1180
358
818
826
316
531
1015
459
618
757
3
55
311
1112
136
2009
654
1545
1350
660
1000
1738
598
839
1324
665
86
571
2132
345
3534
Number of obs
Pre-crisis Crisis Post-crisis
17
0.23
2.78
-0.12
2.71
0.81
3.24
-0.48
2.22
-0.71
0.84
Rating AAA
Other
Industrial
Financial
Issuance large -small
Issuance Large
Issuance Medium
0.56
3.09
-0.34
2.48
-0.22
2.64
0.51
3.02
-0.91
1.82
-1.51
1.51
-2.02
0.33
Issuance Small
Maturity 30Y-5Y
Maturity 30Y
Maturity 10Y
Maturity 5Y
-0.54
2.40
-0.67
2.15
0.03
2.80
0.63
3.06
1.36
0.44
Maturity 2Y
Rating C-AAA
Rating C
Rating B
Rating A
0.10
2.86
Overall
Pre-crisis
3.76
6.80
2.12
5.46
2.46
5.33
3.72
6.64
2.27
5.32
0.31
3.89
-3.41
0.82
3.43
5.08
1.92
5.44
2.89
6.09
3.82
6.26
1.90
0.47
1.54
4.86
2.98
6.12
3.44
6.44
2.63
6.08
1.09
0.57
2.84
6.10
Roll
Crisis
-0.19
2.71
-0.88
2.17
-0.65
2.26
-0.08
2.67
-1.02
1.93
-1.70
1.45
-1.62
0.70
-1.26
1.78
-0.90
2.07
-0.33
2.60
0.25
2.79
1.15
0.48
-0.67
2.52
-0.68
2.32
-0.32
2.48
-0.13
2.68
0.54
0.50
-0.57
2.45
Post-crisis
0.64
1.69
-0.24
1.32
-0.12
1.42
0.54
1.46
-0.77
0.97
-1.35
0.95
-1.89
0.39
-0.69
1.19
-0.53
1.27
0.10
1.60
0.78
1.41
1.33
0.28
0.31
1.62
-0.04
1.45
0.84
1.64
-0.13
1.08
-0.45
0.33
0.20
1.60
4.00
3.75
2.23
3.10
2.53
3.08
3.86
3.43
2.35
3.06
0.50
2.49
-3.36
0.55
2.01
3.01
2.09
3.24
2.92
3.37
4.13
3.34
2.04
0.28
1.81
3.15
3.07
3.40
3.62
3.68
3.06
3.08
1.26
1.00
2.99
3.48
-0.22
1.59
-0.90
1.23
-0.68
1.30
-0.10
1.43
-1.05
1.04
-1.72
0.91
-1.62
0.66
-1.31
1.12
-0.95
1.19
-0.32
1.53
0.20
1.36
1.15
0.42
-0.70
1.64
-0.69
1.35
-0.37
1.37
-0.25
1.35
0.45
0.26
-0.60
1.43
Roll Commonality
Pre-crisis Crisis Post-crisis
Table 4 con’t
-0.08
2.62
-0.10
2.12
-0.10
2.21
-0.03
2.66
-0.14
1.62
-0.16
1.27
-0.13
0.33
0.15
2.21
-0.14
1.78
-0.07
2.30
-0.15
2.70
0.03
0.42
-0.08
2.32
-0.08
2.29
-0.03
2.74
-0.34
2.07
-0.26
0.73
-0.09
2.40
-0.24
5.53
-0.11
4.23
-0.08
4.19
-0.14
5.43
-0.09
4.12
-0.19
2.83
-0.06
0.67
1.43
4.60
-0.17
4.17
-0.03
4.83
-0.31
5.19
-0.14
0.55
-0.27
3.75
-0.09
4.82
-0.18
5.13
-0.44
5.23
-0.17
1.01
-0.15
4.81
0.03
2.19
0.02
1.80
0.03
1.86
0.02
2.26
0.02
1.63
0.02
1.14
-0.01
0.17
0.05
1.41
0.05
1.69
-0.01
2.10
0.05
2.46
0.00
0.24
0.03
1.88
0.01
1.90
0.05
2.06
0.12
2.31
0.08
0.43
0.03
1.99
Roll Idiosyncratic
Pre-crisis Crisis Post-crisis
200
400
541
109
249
603
295
588
286
2
32
241
561
69
1141
343
773
749
312
522
902
434
588
736
3
44
289
1040
130
1849
647
1530
1334
658
995
1714
594
838
1316
662
85
564
2109
341
3519
Number of obs
Pre-crisis Crisis Post-crisis
18
-0.08
3.84
-0.04
3.93
0.45
3.67
1.00
3.86
1.08
2.65
Rating AAA
Other
Industrial
Financial
Issuance large -small
Issuance Large
Issuance Medium
0.27
3.97
-0.03
3.82
-0.41
3.85
1.30
3.64
-1.64
3.30
-3.48
2.85
-4.78
0.40
Issuance Small
Maturity 30Y-5Y
Maturity 30Y
Maturity 10Y
Maturity 5Y
1.82
2.44
-0.82
3.47
-0.51
3.52
-0.05
3.60
1.02
0.61
Maturity 2Y
Rating C-AAA
Rating C
Rating B
Rating A
0.04
3.91
Overall
Pre-crisis
1.11
4.15
0.24
3.98
0.31
3.91
2.09
3.65
-0.96
3.55
-3.19
2.90
-5.28
0.17
0.06
3.39
-0.53
3.84
0.24
3.82
0.77
3.72
1.30
0.30
-0.32
4.27
0.21
4.06
1.61
3.64
2.27
3.86
2.60
0.78
0.61
4.06
ZTD
Crisis
-1.01
3.62
-1.69
3.23
-1.43
3.36
-0.24
3.40
-2.35
2.84
-3.81
2.35
-3.56
0.53
-1.94
3.19
-1.76
3.28
-1.43
3.34
-1.07
3.22
0.70
0.49
-1.44
3.63
-1.79
3.22
-1.14
3.36
-0.93
3.51
0.50
0.91
-1.38
3.43
Post-crisis
0.36
3.33
0.08
3.08
-0.30
3.19
1.35
2.77
-1.49
2.70
-3.21
2.63
-4.56
0.53
1.33
1.35
-0.69
2.87
-0.34
2.93
0.25
2.94
1.19
0.35
-0.06
3.19
0.06
3.25
0.57
2.94
1.12
2.90
1.18
2.65
0.14
3.23
1.05
3.75
0.01
3.33
-0.04
3.19
1.97
2.84
-1.31
2.82
-3.42
2.49
-5.39
0.21
0.99
1.63
-0.49
3.43
0.18
3.36
0.58
3.32
1.08
0.14
-0.08
3.83
-0.05
3.45
1.54
3.19
1.85
3.45
1.93
0.29
0.44
3.52
-1.01
3.08
-1.67
2.62
-1.40
2.79
-0.23
2.59
-2.30
2.34
-3.80
2.09
-3.57
0.52
-2.06
2.71
-1.65
2.79
-1.27
2.85
-1.01
2.68
0.64
0.21
-1.41
3.14
-1.74
2.67
-1.15
2.72
-1.02
2.59
0.39
0.57
-1.36
2.86
ZTD Commonality
Pre-crisis Crisis Post-crisis
Table 4 con’t
-0.10
2.02
-0.11
2.15
-0.11
2.07
-0.05
2.29
-0.16
1.85
-0.28
1.26
-0.23
0.34
0.49
2.32
-0.13
2.04
-0.17
1.99
-0.30
2.13
-0.17
0.46
-0.02
2.03
-0.09
2.09
-0.12
2.04
-0.12
2.45
-0.10
0.79
-0.10
2.09
0.06
2.09
0.22
2.12
0.35
2.15
0.12
2.35
0.35
2.00
0.23
1.39
0.11
0.21
-0.92
2.49
-0.03
2.02
0.06
2.06
0.19
2.20
0.22
0.31
-0.24
2.01
0.26
2.18
0.07
2.00
0.42
2.17
0.67
0.71
0.18
2.12
0.00
1.93
-0.02
1.92
-0.03
1.92
-0.01
2.21
-0.04
1.71
0.00
1.17
0.00
0.15
0.13
1.77
-0.12
1.87
-0.16
1.88
-0.06
1.93
0.06
0.34
-0.03
1.80
-0.04
1.85
0.01
2.00
0.09
2.34
0.12
0.58
-0.01
1.93
ZTD Idiosyncratic
Pre-crisis Crisis Post-crisis
213
438
595
110
258
695
325
628
300
2
35
253
623
75
1246
393
894
938
322
560
1161
508
668
819
3
63
360
1219
148
2218
676
1581
1399
665
1023
1828
618
865
1357
677
88
583
2180
355
3641
Number of obs
Pre-crisis Crisis Post-crisis
between liquidity deterioration and credit quality is uniform and highest values are observed
for junk bonds. Hence idiosyncratic illiquidity is positive essentially for lower graded bonds,
which might have undergone the strongest selling pressure during the crisis, as investors start
by selling the least credit-worthy assets.
We then group bonds according to their maturity, where we distinguish between bonds with
time to maturity between 1 and 2 years (2Y), between 2 and 7 years (5Y), between 7 and 17
years (10Y) and above 17 years (30Y). All measures indicate lower liquidity for bonds with a
longer time to maturity. As time to maturity increases the bonds experience higher illiquidity
in terms of the four liquidity dimensions that we measure. This is in line with the buy-andhold phenomenon of many long-term bonds. Once they are detained in a portfolio and no
trade occurs, they are more likely to exhibit commonality. The relation is verified throughout
the three sub-periods and illiquidity levels after the crisis fall below their pre-crisis levels.
Idiosyncratic components are quite volatile in the sample but overall idiosyncratic illiquidity
is positive in the post-crisis sample and it generally increases as the time to maturity of the
bond increases.
We further sort bonds into three categories based on their issuance size: the bonds with an
issue size below 500 Million (small issuance), an issue size between 500 Million and 1 Billion
(medium issuance) and an issue size above 1 Billion (large issuance). We find that liquidity
usually increases with the issue size or is lowest for small issue sizes. Indeed large issues are
usually expected to be more liquid. Again, the illiquidity levels post-crisis are below their precrisis levels. Idiosyncratic illiquidity generally decreases with the issue size in the pre-crisis
period and remains around the same level for all categories in the post-crisis period.
Finally, we show that financial bonds exhibit highest illiquidity and the magnitude is again
higher during the crisis period. The commonality part follows this same patter, while the
idiosyncratic part increases over time.
3.4
Relative magnitudes of liquidity components
From table 4 it appears that the value of liquidity commonality is often larger than the value of
idiosyncratic liquidity. It results from the fact that values are averaged cross-sectionnally each
week and there may be compensating effects between positive and negative values. However
it also appears from this table that idiosyncratic liquidity values exhibit a much larger crosssectional deviation, which points to some very high or low values. We therefore assess the
relative magnitudes of common and idiosyncratic fractions in the total liquidity level. To
deal with negative values we distinguish the cases in which one or two of the components are
negative. We thus have four cases, the first when both quantities are positive, the second
when both are negative, the third when commonality is positive and idiosyncratic illliquidity
negative and the fourth when it is the other way round. In each case we consider the bonds
19
that satisfy this criteria and we consider the average proportions across all bonds during a
given week. We then aggregate these values in the time series by considering the evolution in
years.
1.0
0.8
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
Figure 1: The figures display the relative proportions of common and idiosyncratic fraction
in the total illiquidity level, using several liquidity measures. The four measures are the
Amihud price impact ratio, the imputed roundtrip cost (IRC), Roll’s bid-ask spread and the
ratio of zero trading days (ZTD). For each liquidity measure we distinguish four types of
proportions. (a) is when common and idiosyncratic values are both positive, (b) is when
common and idiosyncratic values are negative, (c) is when the common value is positive and
the idiosyncratic one negative, (d) when the common value is negative and the idiosyncratic
one positive. The dark part of the bars reflects the proportion of commonality, the light grey
part of the bars reflects the proportion of idiosyncratic liquidity.
2004
2006
2008
2010
2012
2004
2006
2010
2012
2010
2012
0.8
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
(b)
1.0
(a)
2008
2004
2006
2008
2010
2012
2004
(c)
2006
2008
(d)
Amihud
The most standard case is when both quantities are positive. For each liquidity measure, the
relative proportions are represented in panels a) of figure 1. The figure shows that the fraction
20
1.0
0.0
0.2
0.4
0.6
0.8
1.0
0.8
0.6
0.4
0.2
0.0
2004
2006
2008
2010
2012
2004
2006
2010
2012
2010
2012
0.8
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
(b)
1.0
(a)
2008
2004
2006
2008
2010
2012
2004
(c)
2006
2008
(d)
IRC
of commonality in total illiquidity is relatively low for the first three measures (around 30%).
Further it remains more or less constant over the years. Instead the ratio of zero trading
days exhibits strong commonality across bonds (around 60%). It reflects on the fact that
the number of trades per bond can be low and this is usually shared by most bonds in the
market. The second case is when both values are negative and the relative magnitudes are
displayed in panels b) of figure 1. In this case the fraction of commonality is much higher and
always above 50%. It is also slightly increasing over time. When both values are negative,
we are in the presence of bonds that are essentially more liquid than the average bond in the
market. In this case the fraction of shared variation in their individual liquidity levels is also
higher. In the third case commonality is positive and idiosyncratic illiquidity is negative. We
measure the proportions relative to the absolute range between the two values. The fraction
of commonality is around 40% and it is higher in the case of the ZTD measure. Finally when
only commonality is negative this proportion is slightly higher and the fraction of idiosyncratic
21
1.0
0.0
0.2
0.4
0.6
0.8
1.0
0.8
0.6
0.4
0.2
0.0
2004
2006
2008
2010
2012
2004
2006
2010
2012
2010
2012
0.8
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
(b)
1.0
(a)
2008
2004
2006
2008
2010
2012
2004
2006
(c)
2008
(d)
Roll
illiquidity increases over time. Overall if the individual bond liquidity level is decomposed, less
than 50 % of this level is due to common market variations, leaving an important idiosyncratic
component.
4
4.1
Yield spreads and liquidity components
Regression analysis
In this section, we investigate how a bond’s yield spread is related the bond’s liquidity level
and in particular whether the relation stems from the common or the idiosyncratic part. We
then study how this relation evolves over time and across different bond portfolios. We follow
the Fama and MacBeth (1973) methodology applied to panel data and perform weekly cross-
22
1.0
0.0
0.2
0.4
0.6
0.8
1.0
0.8
0.6
0.4
0.2
0.0
2004
2006
2008
2010
2012
2004
2006
2010
2012
2010
2012
0.8
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
(b)
1.0
(a)
2008
2004
2006
2008
2010
2012
2004
2006
(c)
2008
(d)
ZTD
sectional regressions of individual yield spreads on a bond’s illiquidity measure - common
and idiosyncratic- and some control variables. A bond’s yield spread is defined with respect
to Treasury yields, matched according to their respective maturities.3 More specifically, we
adopt the following cross-sectional regression:
Y Si,t = α + βLi,t + γZi,t + i,t
(8)
where i refers to a bond, Li,t is the individual illiquidity measure at time t - either aggregate or
decomposed - and Zi,t contains the control variables. In all specifications, we systematically
include a bond’s credit rating to control for credit risk, a callable dummy, which is one if
the bond is callable and zero if not, the average transaction volume during the week and
3
At each point in time we compute the bond’s remaining time to maturity and we choose the Treasury
yield series closest to this time to maturity. We use Treasury Notes and Bills series with maturities of 3 and 6
months, 1, 2, 3, 5, 7, 10 and 20 years
23
the bond’s remaining time to maturity. Most of these variables have been used in previous
literature, like for instance in Dick-Nielsen et al. (2012), Houweling et al. (2005), Bao et al.
(2011), as proxies for a bond’s liquidity. A bond that is traded more frequently or that has
lower trading costs is expected to be more liquid and have lower yield spreads. While there is
some overlapping of different measures, we expect that they are not mutually exclusive and
that they capture different aspects of liquidity. In our first set of regressions we consider a
bond’s aggregate liquidity measure only, while in the second set we consider the two liquidity
components to see whether the relation stems from commonality in liquidity only or whether
idiosyncratic illiquidity matters as well.
4.2
Correlations
Before turning to the regression analysis we report the correlations between explanatory variables and between liquidity components in table 5. The correlations between two variables
are computed first for each week using pairwise complete observations and then averaged over
the sample. As expected there is some correlation across the different measure. Amihud and
IRC and ZTD and Roll are most strongly correlated. The Roll measure is also somewhat correlated to Amihud and IRC measures but to a lower extent. We also find that the correlation
with other explanatory variables is moderate, which will allow us to include these variables
in the same cross-sectional regression.
We further consider the correlations between the two liquidity components. The correlation
between the commonality series of the different liquidity measures is usually much stronger
than the one between idiosyncratic liquidity series. This correlation across commonality series
is also higher than the one observed across the total measures. We essentially find the same
trends than above, with usually higher coefficients. Commonality in Amihud and IRC and
in ZTD and Roll exhibit the strongest correlations, with values of 69% and 54% respectively.
The common part in Roll’s measure is also strongly related to commonality in Amihud and
IRC (53% and 47% respectively). Idiosyncratic liquidity series are weakly correlated to each
other. The decomposition thus highlights the large common dimension observed through
all liquidity measures that becomes apparent with this decomposition. These measures are
subject to common dynamics captured in their commonality component but each of them
exhibits some noise that is specific to the measure and to the individual bond.
4.3
Aggregate results
Table 6 reports the results of alternative specifications of the regression model. We report
time-series averages of the coefficients and their Fama-MacBeth t-statistics. The latter are
obtained with standard errors with serial correlation corrected with Newey and West (1987).
In a first step we analyze each liquidity measure individually along with other explanatory
24
Table 5: Panel A of this table reports the correlations observed between aggregate series
of the variables of interest. Every week we compute pairwise correlations on the observed
variables and present their average in the table. We consider four liquidity measures, Amihud,
IRC, Roll and the ratio of zero trading days. Rating is the average rating of the bond
measured on a numerical scale from 1 (high-rated) to 21 (low rated). Maturity is a bond’s
time remaining to maturity, measured in years. Volume is the average trade size of a bond
in the week in thousands of $. Call dummy is one if the bond is callable. In Panel B of this
table we report the correlations observed between the the liquidity components following their
decomposition with the APC method. Liquidity commonality series are denoted with upper
com and idiosyncratic liquidity series are denoted with upper idi.
Amihud
IRC
Roll
ZTD
Maturity
Rating
Volume
Call dummy
Amihud
IRC
Roll
1
0.32
1
0.19
0.16
1
Amihudcom
Amihudcom
Amihudidi
IRCcom
IRCidi
Rollcom
Rollidi
ZTDcom
ZTDidi
1.00
Amihudidi
-0.01
1.00
Panel A
ZTD
Maturity
0.03
0.01
0.31
1
IRCcom
0.69
0.02
1.00
0.15
0.14
0.19
0.09
1
Panel B
IRCidi Rollcom
0.02
0.17
0.00
1.00
0.53
0.01
0.47
0.01
1.00
Rating
Volume
Call
dummy
0.04
0.09
0.08
0.06
-0.12
1
-0.19
-0.2
-0.17
0.00
0.12
-0.05
1
0.04
0.02
0.00
0.00
0.08
0.22
0.02
1
Rollidi
ZTDcom ZTDidi
0.01
0.05
0.01
0.01
-0.01
1.00
0.08
-0.01
0.07
-0.01
0.54
0.01
1.00
0.01
0.00
-0.02
-0.02
-0.05
0.09
0.01
1.00
variables. The table presents five different specifications. In model 1, we use a specification
without liquidity measures, our baseline model, where individual bond yields are regressed on
a bond’s rating, its time to maturity, its average trading volume per day and a maturity type
dummy. Rating is measured on a numerical scale from 1 to 21, where higher values represent
less creditworthy bonds. The baseline model is already able to explain a substantial part of
variation in yield spreads, as the adjusted R2 attains a value of 39%. The coefficient estimate
is positive suggesting that less creditworthy bonds obtain higher yields. If the rating of a
bond increases by one, its yield is expected to increase by almost 50 points. The coefficient on
time to maturity is -0.01 meaning that bonds with longer time to maturity have slightly lower
yields. This contrasts to Bao et al. (2011), who find a positive coefficient on maturity. Our
25
finding can however be the result of our sample selection in which we have a large fraction
of bonds with a small maturity towards the end of the sample period. In any case, results
should not be compared in a strict sense, as the sample selection and the time period covered
are quite different.
In model 2, we add the various liquidity variables, which increases the explanatory power
of the model. The adjusted R2 values increase to 40% when the ZTD measure is added
and up to 44% with other measures. These results confirm previous findings that liquidity
variables contribute to the explanation of yield spreads, as has been shown in Dick-Nielsen
et al. (2012), Bao et al. (2011). We find statistically significant results for the coefficients on
the liquidity proxies. The magnitude of the effect depends on the measure used and the sign is
always positive indicating that illiquidity contributes to higher yield spreads. Since liquidity
measures are standardized, their economic impact on yield spreads can be compared. A one
standard deviation in Amihud’s illiquidity or in the ZTD ratio increases yields spreads by 5
and 3 bps respectively. A one standard deviation in the IRC or in Roll’s measure increases
yields by 11 bps. This is a bit lower than the 17 bps found in Bao et al. (2011) but is similar
to Friewald et al. (2012) who find an around 3 to 6 bps increase for changes in Roll and
Amihud’s illiquidity.
4.4
Decomposition
We now turn to the analysis of our liquidity decomposition and the impact of both components
on yield spreads. In the cross-sectional regressions, we analyze each component separately
along with other explanatory variables. Models 3 and 4 of table 6 show that in all regression
specifications both liquidity components are statistically significant. The magnitudes of the
coefficients on each component differ however. Further for the ZTD liquidity measure, the
sign of the coefficient on idiosyncratic illiquidity is negative. The coefficients on the common
components are higher than the ones on idiosyncratic component, and they are also higher
than those of the total illiquidity level. The decomposition thus reveals a much stronger impact
of illiquidity on yield spreads once individual level effects are filtered out. Commonality in
illiquidity accounts for a larger fraction in yield spreads than what would be assumed if the
total illiquidity level is considered. A one standard deviation change in Amihud commonality
increases yield spreads by 23 bps, while for changes in IRC and Roll commonality this value
is around 35 bps. For the ZTD measure, commonality accounts for the same fraction of
yield spreads than total illiquidity and idiosyncratic illiquidity has a negative impact on
yield spreads. The coefficients on idiosyncratic illiquidity are statistically significant but not
economically meaningful as changes in idiosyncratic illiquidity affect yield spreads by no more
than 1 bp. We also notice that the filtering of liquidity to it’s common part is able to increase
the R2 of the model as compared to the model with aggregate series. The decomposition
thus allows for a cleaner measure of liquidity and reveals that yield spreads increase only in
26
response to the liquidity fraction which is common to all bonds.
4.5
Time series analysis
To focus on the role of liquidity in financial crises, we consider our cross-sectional regressions
in three different periods: the crisis period is defined from June 2008 to end of May 2009. The
periods before and after are assumed to correspond to more normal market conditions. Results
are reported in table 7. Control variables are always included. We report the coefficients
on the variables in three distinct time periods. In all specifications we find a statistically
significant effect of liquidity commonality on yield spreads, and this impact is much stronger
during the crisis period. This finding is in line with previous findings of Dick-Nielsen et al.
(2012) who show that liquidity commonality gets more important in distress times. All bonds
are exposed to common liquidity shocks and yields are affected by this common illiquidity.
At the same time we see a gradual increase in the economic significance of idiosyncratic
liquidity over the three periods. While it is essentially unsignificant before the crisis, with a
coefficient close to zero, the coefficient increases during the crisis and is highest in the post
crisis-period. Results are usually valid throughout all liquidity measures. The coefficient on
liquidity commonality remains positive in all three periods, indicating that common liquidity
shocks, affecting all securities considerably increase yield spreads. Idiosyncratic illiquidity on
the other hand, does not affect yield spreads before and during the crisis. After the crisis
however, it has a small positive impact on yield spreads. Hence the bond-specific liquidity
shock is not necessarily compensated in yield spreads. After the crisis, investors only require
a small compensation in yield spreads to detain bonds with a high idiosyncratic illiquidity
level. In particular, a large part of bond investors are insurance companies, who given their
long-term investment strategy usually adopt a buy-and-hold strategy for a bond rather than
selling it on the secondary market. Therefore if the bond is detained in a buy-and-hold
portfolio, investors are not affected by its idiosyncratic illiquidity as they do not expect to sell
it quickly. After the crisis however, the coefficient on idiosyncratic illiquidity is higher. Hence
investors might have changed their attitude since they and now require a compensation for
holding bonds with higher idiosyncratic illiquidity. We observe a distinct pattern when using
the zero trading days ratio. The relation between yield spreads and liquidity commonality is
also strongest during the crisis, however the relation to idiosyncratic liquidity is essentially
negative before and after the crisis. This differential result might be explained in light of
the distinct dimension captured by this liquidity measure. While previous measures are on
the price impact or transaction costs, the ZTD measure is directly related to the trading
activity of the bond. The idiosyncratic part of it reflects the proportion of no trade that is
bond specific and in pre-and post-crisis periods a low trading frequency of the bond does not
generate higher yield spreads. Only during the crisis do investors require a compensation for
the low trading frequency that is bond-specific.
27
Table 6: The table reports Fama and MacBeth (1973) cross-sectional regressions of yield
spreads on various liquidity measures. T-stats are obtained with the Fama-MacBeth methodology, with serial correlation corrected with Newey-West and are reported in italics under the
coefficient. The sample period goes from January 2004 to December 2013. The first model
is the baseline regression. In model 2, a liquidity variable is added. In models 3 and 4 this
liquidity variable is considered in its components. In model 5 both components are considered
together. Other explanatory variables are the bond’s rating, its time to maturity, its average
trading volume during the week and a call dummy equal to 1 if the bond is callable. The
reported adjusted R2 are the time-series averages of the cross-sectional adjusted R2 .
Constant
Liq
M1
M2
-1.09
-19.74
-0.95
-21.40
0.05
21.96
TOT
LiqCOM
Liq
Amihud
M3
M4
-0.72
-16.42
Rating
Maturity
Volume (in 103 )
Call dummy
Adj. R2
M2
M3
M4
M5
-0.99
-21.60
-0.73
-16.60
-0.66
-15.03
0.11
25.06
-0.34
-6.57
-0.79
-18.90
-0.37
-7.21
0.01
6.82
0.48
30.74
0.00
-0.51
-0.40
-30.27
-0.29
-13.14
0.44
0.22
28.01
0.02
10.79
0.46
31.48
-0.02
-13.35
-0.10
-13.42
-0.30
-14.94
0.46
0.45
29.13
-0.01
-10.00
-0.30
-27.84
-0.24
-12.96
0.43
0.42
28.65
-0.03
-15.95
0.00
0.20
-0.22
-14.46
0.45
0.02
13.79
0.46
29.03
-0.01
-5.75
-0.00
-30.28
-0.25
-12.55
0.40
0.34
28.24
0.05
20.61
0.42
28.74
-0.03
-16.21
0.00
1.85
-0.22
-14.49
0.45
0.23
28.04
IDI
IRC
M5
0.35
28.36
0.46
29.24
-0.01
-6.74
-0.4
-28.34
0.26
13.19
0.39
0.47
31.56
0.00
-4.18
-0.30
-35.19
-0.30
-13.84
0.45
0.46
31.44
-0.02
-13.31
-0.10
-13.92
-0.30
-14.92
0.46
M1
M2
M3
M4
M5
M2
M3
M4
M5
-1.09
-19.74
-0.71
-16.43
0.11
37.59
-0.37
-8.45
-0.87
-19.32
-0.38
-8.71
-0.65
-21.53
0.03
5.62
-0.65
-20.47
-0.77
-19.09
-0.62
-19.52
0.01
3.02
0.46
29.42
0.00
-4.29
-0.40
-31.50
-0.26
-12.53
0.41
0.35
48.43
0.02
8.58
0.43
28.98
-0.03
-19.17
-0.20
-18.72
-0.18
-10.14
0.46
-0.02
-4.50
0.46
29.11
-0.01
-5.96
-0.40
-30.32
-0.24
-12.54
0.40
0.04
10.01
-0.02
-4.82
0.45
30.08
-0.01
-6.50
-0.40
-31.67
-0.25
-12.77
0.40
Roll
Constant
Liq
TOT
LiqCOM
Liq
0.36
48.54
IDI
Rating
Maturity
Volume (in 103 )
Call dummy
Adj. R
2
ZTD
0.46
29.24
-0.01
-6.74
-0.4
-28.34
0.26
13.19
0.39
0.45
29.51
-0.01
-10.38
-0.30
-28.21
-0.23
-11.85
0.42
0.43
29.00
-0.03
-19.07
-0.20
-18.67
-0.18
-10.01
0.46
28
0.04
9.32
0.45
30.40
-0.01
-6.10
-0.40
-31.79
-0.25
-13.09
0.40
0.45
30.03
-0.01
-6.48
-0.40
-31.60
-0.25
-12.88
0.40
We thus find that pre-crisis and in the distress period, the relationship between yield spreads
and individual illiquidity levels essentially boils down to an exposure to a common illiquidity
factor. This remains true after the crisis, but some more impact that can be attributed to
idiosyncratic illiquidity.
4.6
Bond portfolios
To further understand the time series behavior of the illiquidity coefficient, we propose to
analyze it in subgroups of bonds formed on the characteristics of the bond. We divide our
sample into two rating groups and into three maturity groups. We run the cross-sectional
regressions in each bond group and consider the coefficients on the two liquidity components.
Results are presented in tables 8 and 9.
4.6.1
Rating
Bonds are grouped based on their credit quality into investment grade and high yield. The
common trends that we identified before are confirmed. However the magnitude of the impact
changes considerably from one rating group to the other. Overall, there is still a strong
sensitivity of yield spreads to liquidity commonality and a small sensitivity to idiosyncratic
liquidity. In terms of magnitude this impact is much stronger for high yield bonds in both
cases. The magnitude of the coefficient on liquidity commonality can be up to 10 times
as large for high yield bonds as for investment grade bonds. This finding is in line with
previous studies showing that the contribution of illiquidity to yield spreads is much stronger
for speculative grade bonds (Dick-Nielsen et al., 2012). Only for the ZTD ratio we find that
high yield bonds exhibit a strong negative sensitivity to the bond-specific number of trades.
A higher ZTD ratio implies a higher number of days without any trade on the bond, hence
little trading activity. If this lower trading activity is bond specific investors do not require
higher yield spreads as a compensation for not being able to trade this specific bond quickly.
Overall, even if statistically significant, the impact of idiosyncratic liquidity on investment
grade bond spreads remains low. The coefficient is economically not meaningful. Hence for
investment grade bonds, only common liquidity shocks are compensated in yield spreads. For
high yield bonds instead, both liquidity components are reflected in spreads.
4.6.2
Maturity
We consider three maturity groups, the first one, abbreviated by MAT5, includes bonds with
a time to maturity ranging from 1 to 7 years, the second one, MAT10 contains bonds with
time to maturity from 7 to 17 years and the last one MAT30, those with time to maturity
above 17 years. Bonds with a very short time to maturity (less than a year) are discarded
29
30
Adj. R2
Call dummy
Volume (in 103 )
Maturity
Rating
IDI
COM
Liq
Liq
Constant
-0.09
-4.37
0.09
15.79
0.00
2.64
0.23
27.43
-0.01
-6.81
-0.10
-15.07
0.10
7.50
0.41
Pre-crisis
-2.83
-16.14
0.37
17.15
0.00
0.81
1.18
22.40
-0.09
-23.70
0.00
0.80
-0.69
-9.84
0.53
-0.88
-29.36
0.33
27.71
0.03
9.99
0.52
60.37
-0.01
-11.66
-0.10
-11.76
-0.62
-33.42
0.51
Amihud
Crisis Post-crisis
0.22
15.10
0.13
15.83
0.01
8.41
0.20
26.18
-0.01
-9.01
-0.10
-16.10
0.08
6.87
0.39
Pre-crisis
-2.98
-11.15
0.70
19.80
0.01
2.25
1.16
19.93
-0.14
-24.28
0.30
6.35
-0.36
-6.51
0.54
IRC
Crisis
-0.35
-7.71
0.48
32.95
0.07
17.22
0.46
49.85
-0.02
-17.26
0.10
6.63
-0.47
-28.93
0.51
Post-crisis
0.28
19.95
0.28
22.88
0.00
0.49
0.20
26.86
-0.02
-12.06
-0.10
-15.58
0.15
10.13
0.42
Pre-crisis
-2.47
-12.40
0.52
14.73
0.00
-0.08
1.18
20.72
-0.11
-31.13
-0.50
-8.67
-0.24
-3.80
0.49
Roll
Crisis
-0.48
-20.90
0.41
72.20
0.02
5.31
0.48
57.23
-0.02
-15.81
-0.20
-23.76
-0.48
-33.19
0.48
Post-crisis
-0.01
-0.44
-0.01
-3.41
-0.03
-6.66
0.22
27.09
0.00
-3.64
-0.30
-20.59
0.13
9.68
0.35
Pre-crisis
-1.56
-13.15
0.28
12.83
0.12
4.36
1.20
21.73
-0.10
-19.25
-0.90
-14.74
-0.38
-5.72
0.45
ZTD
Crisis
-0.96
-63.12
0.04
10.11
-0.04
-8.27
0.50
55.64
0.00
1.97
-0.40
-48.93
-0.58
-35.95
0.45
Post-crisis
Table 7: The table reports Fama and MacBeth (1973) cross-sectional regressions of yield spreads on various liquidity measures. T-stats
are obtained with the Fama-MacBeth methodology, with serial correlation corrected with Newey-West and are reported in italics under
the coefficient. The sample period goes from January 2004 to December 2013 and is divided into three subperiods: pre-crisis period from
January 2004 to May 2008, crisis period from June 2008 to May 2009 and post-crisis period from June 2009 onwards. Yield spreads are
regressed cross-sectionnally on each liquidity component - common and idiosyncratic. Other explanatory variables are the bond’s rating,
its time to maturity, its average trading volume during the week and a call dummy equal to 1 if the bond is callable. The reported
adjusted R2 are the time-series averages of the cross-sectional adjusted R2 .
Table 8: The table reports Fama and MacBeth (1973) cross-sectional regressions of yield
spreads on various liquidity measures. T-stats are obtained with the Fama-MacBeth methodology, with serial correlation corrected with Newey-West and are reported in italics under the
coefficient. The sample period goes from January 2004 to December 2013. Yield spreads are
regressed cross-sectionnally on each liquidity component - common and idiosyncratic- within
bond groups formed on the credit quality of the bond. The two rating groups are investment
grade and high yield. Other explanatory variables are the bond’s rating, its time to maturity,
its average trading volume during the week and a call dummy equal to 1 if the bond is callable.
The reported adjusted R2 are the time-series averages of the cross-sectional adjusted R2 .
Amihud
IG
HY
Constant
LiqCOM
Liq
IDI
Rating
Maturity
Volume (in 103 )
Call dummy
Adj. R2
0.42
24.14
0.07
21.22
0.01
8.65
0.21
34.13
0.01
16.35
-0.10
-11.04
-0.41
-26.67
0.27
0.35
4.87
0.64
25.34
0.05
9.22
0.46
28.65
-0.11
-29.86
0.20
3.62
0.04
1.21
0.41
IRC
Roll
ZTD
HY
IG
HY
IG
HY
IG
0.66
34.84
0.13
20.89
0.02
17.52
0.18
30.21
0.01
11.01
0.00
0.40
-0.33
-26.23
0.27
1.49
23.39
0.82
31.24
0.07
12.23
0.34
28.56
-0.13
-36.84
0.10
3.17
0.16
4.31
0.42
0.71
34.82
0.14
40.94
0.00
3.96
0.17
35.27
0.01
7.93
-0.10
-12.76
-0.33
-25.74
0.25
0.86
16.48
0.73
37.37
0.02
3.35
0.42
27.50
-0.12
-25.45
-0.20
-4.77
0.25
5.75
0.39
0.55
26.88
-0.01
-9.33
-0.01
-6.08
0.18
32.09
0.02
24.33
-0.10
-22.96
-0.35
-26.58
0.21
0.73
12.29
0.21
15.61
-0.04
-4.86
0.44
29.01
-0.07
-18.42
-1.20
-18.65
0.11
2.35
0.31
from the sample. Further our sample does not allow for enough cross-sectional variation of
bonds in the MAT5 group and the time series therefore start in November 2004. We find
that liquidity commonality is particularly important for short-term bonds with a maturity
around 5 years. This coefficient gradually decreases as the maturity increases. The magnitude
of the coefficient on liquidity commonality for short-term bonds (5Y) can be twice as large
as the one for middle term bonds (10Y). These short-term bonds, which trade most, are
thus more sensitive to common liquidity shocks. For long-term bonds, liquidity does seem
to play a minor role, as the R2 of the model is lowered as well. We do not discern any
important impacts of idiosyncratic liquidity across maturity groups. Even if significant the
coefficient on idiosyncratic liquidity is very small and does not signal any meaningful economic
impact.
31
5
Conclusion
In this chapter we provide evidence on the relation between corporate bond yield spreads
and two illiquidity components, common and idiosyncratic. Building on the evidence that the
individual bond liquidity level is priced in corporate bond yields (Bao et al., 2011, Dick-Nielsen
et al., 2012, Bongaerts et al., 2012), we consider the importance of commonality in liquidity in
this relation. Using trade reports provided in TRACE to compute weekly illiquidity measures
for each bond, we first study the magnitude of liquidity commonality using an asymptotic
principal component analysis. We provide evidence on how liquidity commonality evolves over
time and in bond groups. It peaks during the financial crisis period and it increases as the
rating of the bond decreases or as it’s maturity increases. The remaining bond specific liquidity
level is increasing over time. The relative magnitudes of both components are assessed and
we find that commonality usually accounts for less than 50% of the total liquidity level.
Second, we rely on this decomposition to provide evidence on the specific relationship of yield
spreads to these two measures. Despite the fact that some bonds might exhibit high levels
of idiosyncratic illiquidity, we find that the relation between yield spreads and the individual
bond liquidity level is essentially driven by commonality in liquidity. The bond-specific,
idiosyncratic fraction of liquidity does not generate economically significant yield spreads.
Our data also allows for a finer analysis in bond groups and of the financial crisis period. We
find that high yield bonds and bonds with a shorter time to maturity have stronger exposures
to the commonality factor and idiosyncratic illiquidity also accounts for a smaller fraction of
the liquidity effect in yield spreads. These results thus support the view that only a common
liquidity factor is priced in yield spreads. They can be reconciled with typical asset pricing
studies on corporate bond returns, which find that exposure to a systematic liquidity factor is
priced (Lin et al., 2011, Acharya et al., 2013). This chapter thereby contributes to the debate
around the pricing of individual asset characteristics or common factors (Chordia et al., 2015).
Compared to other standard characteristics, the case of liquidity is particular, since it can be
considered at the individual security level but at the same time liquidity is a market variable
experiencing common fluctuations. It makes sense therefore to raise the question on how
much of this individual liquidity level is due to common market variations and how much is
asset specific. Further it is unclear which component in the end drives the pricing relation.
We show in this chapter that only the common fluctuations in an individual bond’s liquidity
level require a remuneration for investors.
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34
35
Adj. R2
Call dummy
Volume (in 103 )
Maturity
Rating
LiqIDI
LiqCOM
Constant
1.47
3.11
0.41
23.82
0.02
4.03
0.53
36.97
-0.33
-5.21
0.10
3.20
-0.69
-22.33
0.50
Mat5
-0.78
-9.91
0.26
24.44
0.01
6.31
0.42
26.69
0.00
1.23
-0.30
-31.71
-0.12
-6.01
0.57
1.15
40.23
0.01
1.99
0.00
1.56
0.26
34.41
-0.03
-21.14
-0.10
-17.12
-0.24
-19.15
0.32
Amihud
Mat10 Mat30
3.25
6.21
0.91
60.02
0.05
7.35
0.44
33.49
-0.50
-7.16
0.20
12.36
-0.24
-12.91
0.54
Mat5
-0.28
-2.87
0.42
24.18
0.02
15.82
0.38
24.46
-0.04
-8.21
-0.20
-19.84
0.05
2.09
0.56
IRC
Mat10
1.17
38.48
0.05
14.08
0.01
9.75
0.24
32.26
-0.03
-21.18
0.00
-11.35
-0.20
-17.98
0.31
Mat30
1.18
35.08
0.06
15.09
0.00
0.11
0.27
39.96
-0.04
-28.09
-0.10
-18.26
-0.18
-17.12
0.33
Mat5
-0.56
-6.02
0.33
27.03
0.00
0.16
0.41
22.76
-0.01
-2.30
-0.40
-19.95
0.08
3.13
0.54
Roll
Mat10
1.12
33.26
0.05
11.01
0.00
-1.90
0.24
34.23
-0.03
-21.34
-0.10
-16.16
-0.19
-18.97
0.30
Mat30
2.48
3.45
0.10
13.56
0.01
1.08
0.52
36.95
-0.45
-4.69
-0.40
-20.11
-0.78
-24.51
0.42
Mat5
-1.40
-17.16
0.05
7.95
-0.01
-1.44
0.43
23.20
0.08
23.06
-0.60
-24.33
0.04
1.73
0.49
ZTD
Mat10
1.38
47.93
-0.04
-27.99
-0.02
-7.12
0.24
32.70
-0.04
-27.00
-0.10
-19.16
-0.19
-20.30
0.31
Mat30
Table 9: The table reports Fama-MacBeth cross-sectional regressions of yield spreads on various liquidity measures. T-stats are obtained
with the Fama-MacBeth methodology, with serial correlation corrected with Newey-West and are reported in italics under the coefficient.
The sample period goes from January 2004 to December 2013. Yield spreads are regressed cross-sectionnally on each liquidity component
- common and idiosyncratic- within bond groups formed on the time to maturity of the bond. The maturity groups are from 2 to 7 years,
from 7 to 17 years and more than 17 years (labelled Mat5, Mat10 and Mat30). Other explanatory variables are the bond’s rating, its
time to maturity, its average trading volume during the week and a call dummy equal to 1 if the bond is callable. The reported adjusted
R2 are the time-series averages of the cross-sectional adjusted R2 .