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The study of the determinants of the commonality liquidity in the U.S. corporate
bond market
Auteur : Istrefaj, Arbnesha
Promoteur(s) : Platania, Federico
Faculté : HEC-Ecole de gestion de l'ULg
Diplôme : Master en ingénieur de gestion, à finalité spécialisée en Financial Engineering
Année académique : 2015-2016
URI/URL : http://hdl.handle.net/2268.2/1849
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THE STUDY OF THE DETERMINANTS
OF THE COMMONALITY LIQUIDITY
IN THE U.S. CORPORATE BOND
MARKET.
Dissertation by
Arbnesha ISTREFAJ
With a view to obtaining the
diploma of Master’s degree in
Business Engineering, specializing
in Financial Engineering
Academic year 2015/2016
Jury:
Promoter :
Federico PLATANIA
Readers :
Stéphanie HECK
Cédric HEUCHENNE
Acknowledgments
After a long and intensive period of preparation, I finally have the pleasure of writing
my acknowledgements, and I wish to start by expressing my deepest feelings. This period has
been difficult and challenging for me on many different levels, and I have learned a great deal,
both in the scientific and in the personal realm. The completion of this thesis could not have
been possible without all of the people I wish to warmly thank here.
First, I would like to express my gratitude to all the professional staff of the University
of HEC-ULg, who have contributed to my educational formation throughout my studies and
that have therefore supported the creation of this thesis, at least indirectly, through the various
theoretical concepts I have learned from them.
I would also like to thank Ms Stéphanie Heck in particular, who supported me through
the thesis process with her patience and her knowledge. She introduced me to the topic of this
thesis, which was previously completely unknown to me, and provided me with useful
comments, remarks and a clear methodology, while still allowing me to work in my own way.
I have special regard for Ms. Heck and I want to congratulate her and wish her wonderful and
rewarding parenthood experiences.
In addition, I would like to thank my supervisor Mr. Platania, and my reader Mr.
Heuchenne for their encouragement and their commitment to my thesis process. I also want to
mention people who have provided me with valuable tools necessary to successfully complete
this thesis: Mr. Dos Santos, who provided me with important information regarding the
exploitation of my data, and Mr. Outal and Mr. Ittoo for their introduction to the software R.
Last but not least, I would like to thank my parents, my sisters, my little brother and my
friends for their support, as well as one special person who has supported me and continues to
make me happy today.
Finally, I would like to dedicate this dissertation to Jacques Nihoul and Colette
Grandjean, my godfather and godmother, without whom none of this would have been possible.
Thank you all.
Nesh Istrefaj
Thesis overview
The Great Depression in 1930 and the subprime mortgage financial crisis of
2008 are considered to be the most important financial market turbulence periods of the last
century. The main consequences of the 2008 financial crisis were the bankruptcy of Lehman
Brothers, difficulties of many financial intermediaries, an intensification of the liquidity crisis,
and a strong repercussion in the financial market-place where a global “crash” of asset prices
was observed. Particularly, the corporate bond market was affected by this crisis. These periods
of stress have highlighted the importance of market liquidity and especially the need of being
able to capture and understand its dimensions.
The corporate bond market is less liquid than the equity market due to the general
framework in which it evolved, low price transparency, the paramount presence of institutional
investors, and the variety of bonds that could be designed for a single firm. For these reasons,
it is quite challenging to capture liquidity components in the corporate bond market, and this
has lead recent scientific literature to focus mainly on studies of liquidity exclusively on the
equity market.
The purpose of this thesis is to study the determinants of commonality liquidity (the
component of total liquidity shared by all bonds) in the corporate bond market. The first part of
this thesis performs a survey of relevant literature, defines the most important concepts, and
investigates potential economic and financial explanatory indicators that could drive
commonality liquidity. The empirical research executed used TRACE data of daily transactions
of 2,059 bonds covering the period 2006-2012. Prior to any analysis, a cleaning of the data was
performed, and a computation of various liquidity measures (Amihud, imputed roundtrip costs
and trading interval) was carried out. Weekly time-series liquidity measures for each of the
2,059 bonds were obtained after this step. Then, a principal component analysis was used to
extract global factors in order to obtain the commonality liquidity.
Finally, a regression model tested the relationship of the obtained commonality liquidity
with respect to three selected determinants: the federal funds rate, the inflation rate and the
Chicago Board Options Exchange Volatility Index (CBOE VIX). The final results conclude
that the constructed model could explain 45% of the total variability of the commonality
liquidity and that the CBOE VIX indicator is the explanatory variable that can provide the most
significant information.
List of figures
Figure 1: Graph representing the repartition of credit ratings among the sample………..…p31
Figure 2: Graph showing the allocation of bond maturities. (Short-term maturity < 5 years,
medium-term maturity between 5 and 10 years, long-term maturity > 10 years) ……...…..p32
Figure 3: Graph showing the industrial subdivision among different asset classes…………p33
Figure 4: Graph representing the evolution of bonds’ characteristics over years..……….…p38
Figure 5: Illustration of the trading variables over time….…………………………………p38
Figure 6: Evolution of IRC measure across years..……………………………….…………p45
Figure 7: Evolution of trading interval across years………………………………………...p45
Figure 8: Evolution of Amihud measure across years. ………………………………..……p47
Figure 9: Scatter pots of the first three global factors based on the Amihud, IRC and trading
interval measures. …………………………………………………………………………...p55
Figure 10: Evolution of the effective federal funds rate (EFFR)……………………………p59
Figure 11: Evolution of the consumer price index and inflation across years………………p60
Figure 12: Evolution of CBOE Volatility Index……………………………………………p62
Figure 13: Chart representing the cross-evolution of explanatory variables………………..p63
List of tables
Table 1: Macroeconomic announcements indicators (Huang & Kong (2005))……………p19
Table 2: Repartition of credit ratings among the sample…………………………………...p30
Table 3: Industry sector allocation of firms………………………………………...………p32
Table 4: Summary statistics (Issue size, maturity, coupon, rating, turnover, weekly trades,
trading days and price) for all year of the sample. Explanations regarding each line are given
in the legend. (S.D: Standard deviation; C.V.: Coefficient of variation in %)…………...…p37
Table 5: Summary statistics of liquidity measures Amihud, IRC, and trading interval across
years…………………………………………………………………………………………p44
Table 6: Matrix of correlation between liquidity measures………………………………...p47
Table 7: Diagnostics of within measure common factors. This table reports the average R2
and the average adjusted R 2 of the regressions using one, two and three factors…………..p53
Table 8: Statistical computations for testing correlations between explanatory variables
(Federal Funds Rate, Inflation rate and CBOE VIX Volatility Index). Descriptive statistics,
matrix of correlations, p-values, and determination coefficients are displayed………………p63
List of abbreviations
APC: Asymptotic Principal Components
CGFS: Committee on the Global Financing System
CPI: Consumer Price Index
CUSIP: Committee on Uniform Securities Identification Procedures.
EFFR: Effective Federal Funds Rate
Fed: Federal Reserve
FED: Federal Reserve
FFR: Federal Funds Rate
FINRA: Financial Industry Regulatory Agency
FX Market: Foreign Exchange Market
GDP: gross domestic product
IRC: Imputed Roundtrip costs
OTC market: Over The Counter market
PWC: PricewaterhouseCoopers
S&P’s: Standard & Poor’s
SEC: Securities and Exchange Commission
TRACE: Trade Reporting and Compliance Engine
VIX: The Chicago Board Options Exchange Volatility Index (CBOE VIX)
1
Introduction
A. Problem Statement
Recent literature has given rise to many studies concerning liquidity in financial markets.
This tendency was driven by the negative impact of the last financial crisis on liquidity. It is
important to study liquidity primarily because it impacts prices of securities, and especially
during periods of market stress, liquidity can sharply decrease or even disappear and hinder the
transformation of financial assets into cash. Liquidity is also important because, at least
indirectly, it has an impact on the growth and development of financial markets. Amihud &
Mendelson (1986) were the first to provide theoretical support for this idea and to demonstrate
that liquidity has a non-negligible impact on prices of financial assets. In a similar vein, the
authors also demonstrated that investors have a preference for liquid assets over non-liquid
assets.
A number of papers have been written focusing on liquidity in equity markets and its cross
effects in parallel marketplaces. However, little empirical research has been devoted to the
specific study of the determinants of commonality liquidity in the corporate bond market, which
is far less liquid than equity markets. Nevertheless, some contemporary research on fixed-
income assets has initiated the use of these types of surveys, and provided some initial insight
through a decomposition of the liquidity of a given bond into two components. The common
component is called “the commonality” by some scientists or “the systematic liquidity”, and as
indicated by its name this component is common to all bonds. The specific component is called
“the idiosyncratic liquidity”, and is particular to each bond based on individual characteristics
(maturity, coupons, ratings, etc.).
The aim of this thesis is to enrich the literature around this topic by studying the
determinants of the so-called “commonality liquidity” in the corporate bond market in the US,
covering a period of seven years, from 2006-2012.This topic has not yet been explored in the
current financial science literature. While it has been proven that a common component of
liquidity exists it is not clear what exactly this depends on. Questions remain as to what the
drivers of this common liquidity in the U.S. corporate bond market are, as well as how they
may vary. Furthermore, it is possible that macroeconomic indicators and stock indexes could
2
be considered as explanatory variables. Finally, the fundamental sources that drive
commonality liquidity and the manner in which these sources evolve over time also requires
academic research.
B. Thesis Structure
In order to address the issues outlined above, this thesis will be divided into two main parts:
a theoretical section and an empirical section. The theoretical section is comprised of two
chapters. Chapter I focuses on the definitions and investigations of the main concepts important
for the understanding of the subject of this thesis. This chapter discusses the notions of liquidity,
bond market liquidity, measures of bond liquidity, commonality liquidity, and a preliminary
investigation of potential determinants of commonality liquidity. Chapter II provides a brief
survey of the academic literature relevant to this research. The empirical portion is divided into
five chapters, which comprise Chapters III-VII. Chapter III describes the methodology and the
datasets used in this research. Chapter IV outlines the selection of liquidity measures, presents
the preliminary results and provides a first interpretation. Chapter V discusses the
decomposition method used to obtain the commonality liquidity, and evaluates the results
obtained. In Chapter VI, a selection of the determinants mentioned in Chapter I is made, and
justification and support for these choices are provided. This section also describes and assesses
the regression analysis conducted for the commonality liquidity with respect to the chosen
potential determinants. Finally, Chapter VII discusses the main conclusions of this research.
C. Methodology
As stated above, few probative studies have been conducted regarding the study of the
determinants of commonality liquidity in the corporate bond market in comparison to the equity
market. Therefore, the approach taken in this thesis involves translating meaningful studies
undertaken in the equity market to apply to the corporate bond market. The initial sample, prior
to any modification, consists of transactions of TRACE1 data from 2,665 U.S. corporate bonds
covering a period of seven years from January 3, 2006 to December 31, 2012. This data was
1 TRACE : Trade Reporting and Compliance Engine
3
then completed with relevant information from Bloomberg. The first step in this phase involved
the cleaning and filtering of the raw data. Next, computation of pertinent liquidity measures
was performed. A third step consisted of the decomposition of the liquidity measures following
a principal component analysis in order to obtain the commonality liquidity. The last stage
implemented a regression analysis of the commonality liquidity regarding the specific
determinants.
THEORETICAL
SECTION
4
Chapter I
Definition and Investigations of Main Concepts
A. Liquidity
The concept of liquidity in a general sense is very abstract in financial markets and difficult
to define because it is not an observable variable. Rather, liquidity is a slightly imperceptible
component of an asset. Liquidity is a multi-dimensional concept and is often defined in financial
literature as the ability to buy or sell a large quantity of a security, quickly, with low transaction
costs and with limited or no price impact. Therefore, securities with important trading costs
(commission fees, opportunity costs, bid-ask spreads, etc.) are considered to be less liquid.
Typically, fixed-income assets are more illiquid than other categories of instruments.
Liquidity is an important conception in financial markets because it defines the
effectiveness of a market. Liquidity facilitates the efficient allocation of economic resources
through an appropriate distribution of capital and risk. In this sense, the liquidity characteristic
of a market is considered to be a non-negligible benefit (PricewaterhouseCoopers (PWC),
2015).
It can also be stated that liquidity can vary significantly among different classes of
securities. This difference comes from specific characteristics of the issuer (creditworthiness,
issuance frequency, macroeconomic factors, etc.), from the components of the security itself
(coupon, maturity, issue size, etc.), as well as from the features of the market on which it is
traded. This fundamental concept also varies with relation to time, because of the impact of
financial crises, or because of new regulations and policies.
This section defines the general notion of liquidity by drawing on several financial writings
and by explaining some related concepts.
The regulation on markets in financial instruments and amending regulation (EU)
No648/2012 defines a liquid market as “a market for a financial instrument or a class of
5
financial instruments, where there are ready and willing buyers and sellers on a continuous
basis […]”. This definition emphasizes the readiness of buyers and sellers to enter into a
transaction. In comparison, the Committee on the Global Financing System (CGFS) focuses on
price influence, and gives the following definition for a liquid market: “deep and liquid markets
are defined as markets where participants can rapidly execute large-volume transactions with
little impact on prices.” Amihud, Mendelson, & Pedersen (2006) put emphasis on the
transaction costs incurred, and defined the concept as being particularly complex. The authors
attempt to characterize a liquid market simply by defining it in terms of ease of trading a
security. The authors also list in their paper some sources of illiquidity, including: brokerage
fees, order-processing costs, or transaction taxes. They mention that these expenses must be
accounted each time a security is traded by an investor. In an earlier paper, Amihud &
Mendelson (1986) relate the concept of liquidity to the bid-ask spread. The authors describe
how the liquidity can be approximated by the price paid for the immediate execution of a trade.
Indeed, according to these specialists, investors can either wait and make a transaction at an
advantageous price or perform the transaction immediately and pay a supplementary cost for
immediate execution. Following this theory, the bid price is therefore increased by the cost for
immediate sale, and the ask price comprises a premium for direct purchase. For Grossman &
Miller (1988), the liquidity of a market is driven by the supply and demand of immediacy. In a
paper where they explore the study of the cross dynamics of liquidity, Chordia, Sarkar, &
Subrahmanyam (2003) relate the definition of this concept to the cost of transforming cash into
financial assets, stating: “Liquidity, a fundamental concept in finance can be defined as the
ability to buy or sell large quantities of an asset quickly and at low cost”.
In sum, a clear link can be established between the illiquidity of a given security and the
way it is traded: regarding important transaction costs, a large bid-ask spread, and a high
liquidity risk premium.
As can be seen above, there is no single definition for liquidity. However, globally,
these definitions encompass some important concepts that are defined here. A report from
PricewaterhouseCoopers (2015), that studies liquidity in global financial markets, provides
assistance with theses definitions.
Immediacy: Immediacy refers to the time necessary for the execution of a transaction.
This characteristic of liquidity can be approximated using the number of market makers,
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the number of participants, the number of “zero trading days”2, the frequency of
transaction and the size of them, and also by the accessibility of quotes.
Depth and resilience: Depth refers to the quantity of assets available for sale and
purchase at the current market price. A market is said to be deep if the quantities traded
are large enough that there is lower resiliency and volatility, meaning that the price is
not impacted by the quantity of the volume traded. These concepts can typically be
measured using trading volumes or a measurement of the price impact of the trading
volumes. The resilience makes allusion to the ability of the market to rapidly
disseminate information and to quickly absorb temporary price changes.
Breadth: Breadth refers to the question of the number and diversity of participants in
the market. This feature also relates to the fact that liquidity is different across asset
classes.
Tightness: Tightness refers to the cost incurred for completing a transaction in the
market. Tightness can be measured using the bid-ask spread.
The features defined above are reflected in the price of an asset, and can be incorporated in this
price using the liquidity risk premium.
B. Liquidity in the Corporate Bond Market
As has been demonstrated, liquidity depends on various features, and it can be directly
concluded that liquidity can substantially differ from one asset class to another. From the
definitions provided for liquidity, it can also be stated that fixed-income assets are less liquid
than equities, or even foreign exchange (FX) market assets.
There are many reasons that could explain the occurrence of poor liquidity conditions in the
corporate bond market. First, the specific framework and rules implemented give rise to
illiquidity in the corporate bond market. Heck, Margaritis, & Muller (2016) discuss the fact that
corporate bonds are mainly traded over the counter, where there is low price transparency. They
also mention the search costs of brokers and incurred by investors. Furthermore, the opacity of
the market to the common public constitutes another explanation, as the trading in the corporate
bond market is generally led by institutional investors. Additionally, among bonds there exists
2 Zero trading day: number of days without trading of the bond during a given period. (Heck, Margaritis, &
Muller (2016)).
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a large diversity of categories with different characteristics (maturity, coupons, etc.), compared
to equities. Consequently, this lack of standardization could be an explanation of why fixed-
income market is less liquid. In addition, bonds are not frequently traded and it is quite unusual
to observe a balanced number of buyers and sellers available to answer investor’s ’needs.
Even within the cluster of fixed-income assets, irregularities appear concerning the
measurement of liquidity. For instance, sovereign bonds are generally more frequently traded
than corporate bonds, and this observation impacts the measurement of liquidity. A recent study
called “The liquidity of corporate and government bonds: drivers and sensitivity to different
market conditions” (2014), carried by the Joint Research Center of the European Commission,
investigates the liquidity of European fixed-income markets and shows that the liquidity of
bonds is driven by their specific characteristics, such as duration, amount issued, time to
maturity, and rating. Furthermore, the authors of this study demonstrate that the sensitivity of
bonds’ liquidity to the listed factors is more important when markets are under pressure.
Another area of this study, that aims to analyze the link between liquidity of individual bonds
and the global market, demonstrates that individual bonds follow the trend of the whole market,
and this observation is seen even more prominently for fixed-income assets with higher duration
and lower ratings.
Other studies analyzed pricing and market maker behaviors in order to assess the
liquidity of bonds. By analyzing particular factors such as the rate of transactions, the price
elasticity of demand, and the variability in inventory value and risk aversion, the consulting
company PWC (2015) found that markets with higher transaction flows, lower elasticity of
demand, and associated with lower risk tend to be characterized by more important levels of
market making activity. This study indicates the difference between investment-grade bonds
and high-yield bonds, stating that investment-grade bonds (respectively high-yield bonds) are
described by high trading volumes (lower trading volumes), stable values and lower risk (
higher level of risk) and therefore a more important market making activity (lower market
making activity), and higher liquidity (lower liquidity). In a recent paper, Bao, Pan, & Wang
(2011) examine the liquidity of corporate bonds and put forth evidence that illiquidity of these
assets rises with age and maturity, and declines with issuance size. The authors also emphasize
that illiquidity of individual corporate bonds changes significantly over time.
8
The main repercussions of the lower liquidity of corporate bonds are that there is a
higher liquidity risk premium incurred for such assets, more important transactions costs, and
a broader bid-ask spread.
Through a study of the liquidity of U.S. corporate bonds during the financial crisis of
2008, Friewald, Jankowitsch, & Subrahmanyam (2010) investigated whether if liquidity
constitutes an important determinant of bond prices especially during periods of market stress.
Through an analysis of the different sub-segments of the market, the authors argue that
speculative grade bonds exhibit lower levels of liquidity and react more strongly to any changes
in liquidity. They also observed that overall liquidity is the same for financial bonds compared
to industrial bonds, except during periods of crisis where slight differences can occur. Finally,
the difference in liquidity across different groups of investors is also investigated and the
authors argue that as retail investors encounter higher transaction costs, those investors perceive
the corporate bond market to be quite illiquid. However, institutional trades seem to be more
sensitive to liquidity changes than the retail investments.
Many other studies place their attention not only on the study of the debt market, but also
on the links that exist between the fixed-income market and the equity market. Chordia, Sarkar,
& Subrahmanyam (2003) analyzed the cross behavior of both markets regarding their liquidity
patterns, finding that their respective liquidities co-vary. The findings of the authors enable the
observation of similarities in the two markets regarding liquidity, but also show that liquidity
in one market affects liquidity in another.
C. Measures of Bonds Liquidity
In order to capture the liquidity of bonds, different measures have been proposed in
scientific and financial literature. This section presents the various liquidity proxies and
measures that are traditionally used. It is important to note that the computation of liquidity
measures in the corporate bond market is severely limited by the availability of sufficient,
complete, and frequent data concerning the daily transactions. The different measures have been
classified into three main categories: bond characteristics, trading activity variables, and
alternative liquidity measures. These measures have been summarized based on a study by
Dick-Nielsen, Feldhütter, & Lando (2012) and on the work of Friewald, Jankowitsch, &
9
Subrahmanyam (2012). The study by Bao, Pan, & Wang (2010) was also used in the
development of this section.
I. Bond Characteristics as Liquidity Proxies
Bond characteristics constitute natural measures that provide an approximate indication of
the potential liquidity of a bond. However, even if these proxies make sense intuitively, they
are still approximate, since they are constant in time.
Amount issued: Bonds issued with a larger amount are expected to be more liquid.
Coupon: Bonds issued with a larger coupon are expected to be less liquid.
Maturity: Bonds with longer maturities (usually more than 10 years), are generally
considered to be less liquid because they are traded by “hold- investors”, who retain
these bonds and do not trade frequently.
Age: Bonds recently issued, called “on-the-run bonds”, reflect more liquidity.
Industry variables issued by financial firms: This variable enables the comparison of
the different effects of liquidity regarding financial and industrial firms.
A study for the European Commission conducted by Galliani, Petrella, & Resti (2014),
“The liquidity of corporate and government bonds: drivers and sensitivity to different
market conditions”, confirms the above hypothesis. The authors come to the conclusion that
the liquidity of bonds is driven by fixed-income specific characteristics such as duration,
rating, amount issued, and time to maturity. Furthermore, they insist that the sensitivity of
a bond’s liquidity to these factors is more important during periods of market turbulence.
II. Trading Activity Variables as Liquidity Proxies
In this respect, liquidity can also be approximated using trading activity variables. In general
conditions, liquidity tends to become more important as trading activity increases.
Number of trades: The number of trades executed for a given bond during a given
period of time. For example, the weekly trades provide the average number of trades
realized for a given bond during one week.
Trading volume: Quantity of a given bond that is traded during a given period of time.
Trading interval: The time elapsed between two trades of a given bond, which is
generally measured in number of days. Bonds that exhibit longer trading intervals show
lower liquidity, while bonds with shorter trading intervals indicate higher liquidity.
10
Trading days: Provides the average number of days a bond was traded during a given
year.
Daily or weekly returns3: This measure represents the mean of the daily or weekly
return series obtained in a given year.
III. Alternative Liquidity Measures
Different measures have been developed in academic literature that attempt to quantify the
liquidity features of a given asset.
A. Amihud
The Amihud measure is one of the most well-known and widely used liquidity measures. It
was initially developed for the equity market by its author, Amihud (2002). This ratio expresses
the absolute value of the daily returns, in other words, the price impact of trades with respect to
the trade volume. This measure allows the price response triggered by a given volume of trading
to be determined.
Following Dick-Nielsen, Feldhütter, and Lando (2012), the Amihud measure can easily be
translated for use with corporate bonds. Indeed, for each given corporate bond i, the daily
Amihud measure can be derived by applying the following formula:
𝐴𝑚𝑖ℎ𝑢𝑑𝑖𝑡 =1
𝑁𝑡∑
|𝑟𝑒𝑡𝑢𝑟𝑛𝑗,𝑡𝑖 |
𝑄𝑗,𝑡𝑖
𝑁𝑡
𝑗=1
= 1
𝑁𝑡∑
|𝑃𝑗
𝑖
− 𝑃 𝑗−1
𝑖
𝑃𝑖𝑗−1
|
𝑄𝑗,𝑡𝑖
𝑁𝑡
𝑗=1
Where:
𝑁𝑡= number of observed returns during each day t for bond i.
𝑅𝑒𝑡𝑢𝑟𝑛𝑗,𝑡𝑖 = returns on the j-th transaction during day t and for corporate bond i.
𝑄𝑗,𝑡𝑖 = trade size in millions of dollars for the j-th transaction, for the i-th corporate bond and at
time t.
𝑃𝑗𝑖= price of bond i at the j-th transaction.
3 Daily or weekly returns have been put on this category based on the definition provided for the Zero Return
Measure in the section “Alternative liquidity measures”-point C.
11
Note: At least two transactions are required on a given day in order to compute this measure.
Interpretation: This formula captures the price impact of a trade per unit of volume traded. The
larger this measure, the lower the liquidity of the bond. This means that a larger Amihud
measure indicates that the price change with respect to a given trading volume is more important
when trading a bond.
B. Roll
This measure, developed by Roll (1984) enables the approximation of the effective bid-ask
spread with successive price movements resulting from the addition of new information. The
formula is therefore:
𝑅𝑜𝑙𝑙𝑖,𝑡=2√−𝐶𝑜𝑣(∆𝑝𝑡, ∆𝑝𝑡−1)
Where:
𝑅𝑜𝑙𝑙𝑖,𝑡 = Roll measure at time t for the i-th corporate bond.
∆𝑝𝑡 = observed price change of bond i in period t.
𝐶𝑜𝑣(∆𝑝𝑡, ∆𝑝𝑡−1)= serial covariance of returns for bond i at time t.
The Roll measure is therefore equal to twice the square root of the negative covariance between
two consecutive price changes.
Interpretation: The Roll measure reflects a negative correlation between temporary price
movements. An important value of the Roll measure is that it represents a more negative
covariance and as a consequence a bigger bid-ask spread, which leads to an increase in the
transaction costs, ultimately making the corporate bond less liquid.
Note: Dick-Nielsen, Feldhütter, & Lando (2012) advise computing this measure daily for each
bond using a rolling window of 21 days, and requiring at least four transactions in this window.
C. Zero-Return
The zero-return proxy developed by Chen, Lesmond, & Wei (2007) indicates the number
of unchanged consecutive prices. Essentially, this proxy describes how many zero price
movements have been observed during the trading days. This measure, which takes only two
values, is equal to 1 for a given bond at a given time if no price changes have been observed,
12
and is equal to 0 in all the other cases.
Note: This measure must be computed with price quotations or valuations performed on a
continuous basis (Bloomberg quotations, for example).
Interpretation: Bonds that depict a constant price over a long period of time, and thus a higher
value for the zero-return measure, tend to be less liquid.
D. Bid-ask spread
The bid-ask spread is a straightforward approximation of the cost of transactions of bonds.
This is simply computed by taking the difference between ask and bid quoted prices which
are reported by an information provider (Bloomberg, Reuters, etc.).
Interpretation: Intuitively, a wider spread indicates higher transaction costs and so a less
liquid bond.
E. Price Dispersion Measure
Jankowitsch, Nashikkar, & Subrahmanyam (2008) study a new measure of liquidity based
on the dispersion of prices in over the counter (OTC) market. This new measure is based on the
dispersion of transaction prices around quoted prices in the market (Bloomberg quotations for
example). The formula is present below:
𝑃𝑟𝑖𝑐𝑒 𝑑𝑖𝑠𝑝𝑒𝑟𝑠𝑖𝑜𝑛𝑡= √1
∑ 𝑣𝑘𝐾𝑡𝑘=1
∑ (𝑝𝑘 − 𝑚𝑡)2𝐾𝑡
𝑘=1 𝑣𝑘
Where:
𝐾𝑡 = k observation at time t
𝑚𝑡= market quoted price at time t
𝑝𝑘= observed traded price
𝑣𝑘=observed traded volume
The price dispersion measure for a given bond at a given day t, is defined as the mean square
root of the difference between the traded price and the quoted price weighted by volume.
13
Interpretation: This measure helps indicate the transaction costs incurred. A low dispersion of
transaction prices around quoted prices means that the bond has been purchased at a price close
to its fair value. Low dispersion therefore correlates with low trading costs and higher liquidity.
F. Imputed Roundtrip Costs
This measure, developed by Feldhütter (2010), proposes an alternative method of capturing
liquidity and is based on the assumption that after a long period without trades, a bond might
be traded two or three times within a short time interval. These types of trades are defined by
the author as pre-matched arrangements, where the dealer gathers the bid-ask spread as a fee
for matching a buyer and a seller for a given bond. After finding a match, a trade occurs between
the dealer and the seller and the dealer and the buyer. It is also possible that a match may occur
between two dealers, and in this case there is also a supplementary transaction cost between the
two parties. The imputed roundtrip formula is as follows:
𝐼𝑅𝐶𝑖,𝑡 =(𝑃𝑖,𝑡
𝑚𝑎𝑥−𝑃𝑖,𝑡𝑚𝑖𝑛)
𝑃𝑖,𝑡𝑚𝑎𝑥
Where:
𝑃𝑖,𝑡𝑚𝑎𝑥= largest price in the set of transactions with the same size within a day
𝑃𝑖,𝑡𝑚𝑖𝑛= smallest price in the set of transactions with the same size within a day
The imputed roundtrip cost (IRC) is then equal to the average of the roundtrip costs during that
day for different sizes.
Interpretation: The price difference in the formula of the IRC can be interpreted as the
transaction costs, or alternatively as the bid-ask spread. The higher the IRC, the higher the
transaction costs, and thus the less liquid the bond.
G. Turnover
The turnover, measured as a percentage, expresses the total volume traded during a given
period “T” over issue size:
𝑇𝑢𝑟𝑛𝑜𝑣𝑒𝑟𝑡= 𝑇𝑜𝑡𝑎𝑙 𝑡𝑟𝑎𝑑𝑖𝑛𝑔 𝑣𝑜𝑙𝑢𝑚𝑒𝑡
𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔
14
Interpretation: The inverse of this measure can be interpreted as the average holding time of the
bond. If the turnover ratio is equal to 1, it means that the average holding time is about one
month. A higher value of the turnover ratio implies higher liquidity.
H. Zero trading days
This measure describes the frequency at which a bond trades. This ratio, expressed as a
percentage, indicates the percent of days during a given period where the bond did not trade.
This is often measured by taking the total number of trading days during a period. However, it
can also be computed by taking a rolling window of a number of days for each bond, for instance
a period of 21 trading days, as was done in the paper of Heck, Margaritis, & Muller (2016).
𝑍𝑇𝐷 =𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑎𝑦𝑠 𝑤𝑖𝑡ℎ𝑜𝑢𝑡 𝑡𝑟𝑎𝑑𝑖𝑛𝑔 𝑜𝑓 𝑡ℎ𝑒 𝑏𝑜𝑛𝑑 𝑖𝑛 𝑡ℎ𝑒 𝑟𝑜𝑙𝑙𝑖𝑛𝑔 𝑤𝑖𝑛𝑑𝑜𝑤
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑎𝑦𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑟𝑜𝑙𝑙𝑖𝑛𝑔 𝑤𝑖𝑛𝑑𝑜𝑤
Interpretation: Fewer trading days correlate to a lower liquidity of the bond, and therefore a
higher value of the zero trading days ratio indicates higher illiquidity of the bond.
I. Variability of Amihud and IRC
Dick-Nielsen, Peter Feldhütter, and Lando (2012) propose taking the standard deviation of
the Amihud and IRC measures to assess liquidity. The respective standard deviations help
evaluate potential future levels of liquidity.
J. In Practice
All the liquidity measures and proxies described here can be computed on a daily basis,
given the observations collected for each bond. Precautious must be taken regarding the
interpretation of each of these measures, however. For most measures, the higher the positive
values, the higher the illiquidity of the given bond. However, the proxy and trading intervals
have to be interpreted differently.
D. Commonality Liquidity
One question that arises is whether liquidity is a specific feature attributable to a single
asset, a single bond, or whether common pattern driving this liquidity exists.
15
Few studies have been conducted on the topic of commonality in liquidity in the debt
market. Commonality is simply defined as “the possession along with another or others, of a
certain attribute or set of attributes” (The American Heritage, 2013). Jian-Xin Wang (2010)
attempts to define the concept of liquidity commonality as liquidity co-movements across assets
or markets. The author also states that liquidity co-movements are influenced by aggregate
returns and volatility. Hasbrouck & Seppi (2001) analyzed the variations and common co-
variations in various liquidity proxies in the equity market by using principal component
analysis and correlation analysis. They demonstrated that a commonality exists among these
liquidity proxies, and that a common component could therefore be extracted.
Huberman & Halka (2001) called the common component of liquidity “systematic
liquidity”. The study carried out by these authors proved the presence of systematic time-
varying liquidity through the detection of a common factor that is correlated with liquidity
proxies of different stocks. The definition provided in this research is that systematic liquidity
is the variation of liquidity that affects many stocks simultaneously and across time.
Korajczyk & Sadka (2008) studied the commonality across various measures of liquidity
for a quantity of stocks and extract a common component. They define the commonality as the
global systematic liquidity factor, and find an exposure of stocks to systematic liquidity.
Korajczyk & Sadka also state that movements of liquidity during periods of market turbulence
matters for investors, underlying the importance of research on the topic of commonality
liquidity.
Chordia, Roll, & Subrahmanyam (2000) focused their attention on the determination of a
commonality in liquidity patterns for stocks on the U.S. market. The authors define this concept
as the correlation of various liquidity movements, and state that proving its existence is
fundamental to being able to state that intertemporal changes in liquidity patterns are affected
by asymmetric information and inventory risk. They observe that individual liquidity measures
co-move with each other. They also assert that this concept has many implications for traders,
investors, and regulators especially during periods of financial crisis. It is therefore crucial to
assess the weight of commonality in liquidity.
Syamala, & Reddy (2013), in a study of the stocks listed on the national stock exchange of
India, developed the hypothesis that commonality relates to how the liquidity of an individual
asset is impacted by market-wide determinants. They also argue that this can be observed
through co-movement changes in individual assets.
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Heck, Margaritis, & Muller (2016) studied the relationship between yield spreads and an
individual bond’s liquidity in the U.S. corporate bond market and they define the commonality
as the part of liquidity that is shared by all bonds and is driven by the market. Moreover, they
state that the residual portion of liquidity should be defined as “idiosyncratic liquidity”, and that
part of a bond’s liquidity may remain idiosyncratic and specific to bond characteristics.
E. Determinants of Commonality Liquidity
This section presents an investigation of some potential determinants that could explain the
common component of liquidity in the corporate bond market. While some of the studies
mentioned here are not directly focused on the corporate market or on liquidity, it is appropriate
to consider variables that affect stock market liquidity as potential determinants of commonality
liquidity in the corporate bond market. Similarly, macroeconomic variables that affect the
corporate bond market itself may also be eligible for consideration as potential determinants of
common liquidity.
Chordia, Roll, & Subrahmanyam (2000) define the determinants of commonality liquidity
as those that have a common influence, and impact, on liquidity. They centered their study on
proving the existence of commonality liquidity in the stock market. After checking for
individual determinants of liquidity such as volume, price, and volatility, the authors prove that
the common part of liquidity remains important. Further in their study, the authors suggest that
future research should be devoted to the understanding of liquidity co-movements. They raise
a question that could be very applicable for the present thesis: “Is liquidity induced by market
peregrinations, political events, macroeconomic conditions, or even hysteria?” The authors
advise that the identification of specific macroeconomic influences that correlate with time-
series variation in liquidity should be focal point of further research, and this idea can certainly
be translated to the corporate bond market.
Chordia, Sarkar & Subrahmanyam (2003) investigated some paths through an empirical
analysis of stock and bond market liquidity, based on the hypothesis that the liquidity in stock
and bond markets co-varies due to strong volatility connections and trading activity
interactions. The authors study the liquidity dynamics in stock and Treasury bond markets, and
come to the conclusion that liquidity in one market affects liquidity in another, through its effect
on various variables. They found that common factors affect liquidity and volatility in both
markets. They list, among other factors, return volatility, which seems to be an important driver
17
of liquidity, and, monetary expansion policies, thereby supporting the idea that an increase in
monetary expansion increases equity market liquidity during periods of financial crisis. The
authors further develop ideas about the unexpected increases (decreases) in the federal funds
rate, which lead to respectively decreases (increases) in liquidity and increases (decreases) in
stock and bond volatility. The common calendar effects on these markets also designate that
time-series similitudes exist in stock and fixed-income markets. The authors describe, for
instance, that liquidity appears to be lower during financial crisis periods, higher during July
and August, but also higher at the beginning of the week compared to Friday. Additionally, the
authors state that a fraction of commonality in stock and bond markets could be a result of
money flows (e.g. in the form of bank reserves and mutual fund investments). In addition, this
study asserts that a loose monetary policy increases liquidity by boosting trading, reducing
margin loan costs, and improving financing positions of dealers. Monetary easing (in the form
of a decrease in net borrowed reserves) has a positive impact on stock and bond market liquidity
during crisis periods. Investigations have also been conducted on aggregate mutual fund flows
into the stock and debt market. A higher buying or selling by mutual funds institutions causes
inventory imbalances, and this lead to a decrease of liquidity. This phenomenon seems to be
exacerbated during financial crisis periods. The authors of this study further justify the mutual
fund flows as a determinant of liquidity by asserting that an increase in liquidity or a decrease
in volatility in a given market makes mutual fund flows more interesting, which drives mutual
funds buying.
“The Macro-economic Determinants of Corporate Bond Market in India” (2016), Maurya
& Mishra (2016) attempted to examine the influence of macroeconomic variables on the
corporate bond market in India. Their study proves that issuance in the corporate bond market
is significantly correlated with foreign exchange reserves. They performed several regression
analyses based on various macroeconomic variables, and state that volumes of corporate bonds
could be explained by nearly all the selected macroeconomic variables (inflation rate, gross
domestic saving, India’s external debt, etc.). This study, which performs a quite general
research on the corporate bond market and which is not exclusively focused on liquidity neither
related to the US, provides first rough and approximate selection of potential macroeconomic
determinants of commonality liquidity.
Fink, Haiss, & Hristoforova (2003) study the relationship between the development of the
aggregate bond market and the real gross domestic product (real GDP) in 13 developed
18
countries, including the US. While performing Granger causality tests, correlation analysis, and
ordinary least square method techniques to check links between the corporate bond market and
real GDP, the study found a significant proof for the relationship between the bond market and
real economic growth in several countries, including the US.
Goyenko & Ukhov (2009) performed a long-term analysis of the stock market and
Treasury bond market liquidity. They assert that positive shocks to stock illiquidity decrease
bond illiquidity, an assertion that could be supported by the flight-to-quality4 and flight-to-
liquidity5 concepts. They found that monetary policies impact liquidity in both markets. In
addition, the authors state that the illiquidity of short-term bonds was more sensitive to
monetary policy variables and that a tightening of monetary policy increases illiquidity in
general. They also demonstrate significant relationships between macroeconomic variables and
the financial market, and prove that bond illiquidity acts as a canal that transmits monetary
policy shocks to stock illiquidity. In order to draw these conclusion, the authors use various
macroeconomic variables such as the federal funds rate (to determine the relationship with
monetary policies), the growth rate of industrial production (IP), and inflation (the growth rate
of consumer price index, CPI). They use data from the Federal Reserve Bank of St. Louis. The
authors prove that inflation is informative in predicting bond illiquidity in all maturities, and
that shocks to the federal funds rate affect illiquidity of medium and short-term bonds. This
study verifies that macroeconomic variables are significantly linked to financial market
liquidity. In a more extended way, this paper confirms that a positive shock to federal funds
rate causes an increase in bond illiquidity across all maturities, and a negative shock to the
federal funds rate shows different effects on bond illiquidity with different maturities, impacting
illiquidity of short-term bonds instantly, the illiquidity of medium-term bonds with a lag of one
month, and long-term bonds after approximately four months. Regarding the inflation rate, a
shock to the CPI significantly increases illiquidity of long and short-term bonds, and has longer
impacts on long-term bonds. The growth rate of industrial production, however, does not appear
to have important impact on illiquidity, since it affects illiquidity of all the bonds with a lag
longer than four months. Overall, the authors prove that macroeconomic variables have a
4 The flight to quality is the dynamic that unfolds in markets when investors are more concerned about
protecting themselves from risk than they are with making money. During times of turbulence, market
participants often will gravitate to investments where they are least likely to experience a loss of principal. 5 Flight to liquidity, suggests the notion that investors experience a sudden and strong preference for holding
liquid assets. (Source: Kenny, T. (2016). What is flight to quality? http://bonds.about.com/od/Issues-in-the-
News/a/What-Is-The-Flight-To-Quality.htm)
19
stronger impact on illiquidity of short-term bonds than other maturities, and that the bond
market more quickly evidences the effect of a monetary policy changes than the equity market.
Huang & Kong (2005) examined the impact of 11 macroeconomic news announcements
on credit spreads of investment-grade and high-yield corporate bonds. They justified their
choice of this set of variables by the fact that the U.S. Treasury market is significantly affected
by macroeconomic variables, and as it plays the role of a benchmark for the pricing of corporate
bonds, the corporate bond market should also be affected by these macroeconomic
announcements.
The macroeconomic variables chosen in the authors’ research are represented here:
The authors found that from all of these variables, only shocks of employment
announcements, advanced monthly retail sales, and the consumer confidence index exhibit an
important impact on the credit spreads of corporate bonds, noting that these events firstly and
most importantly affect high-yield corporate bonds. Furthermore, the authors also tested the
impact of the CBOE VIX on credit spread, finding that this variable accounts for significant
variations in credit spread.
Arnold & Vrugt (2010) studied the determinants of volatility in the U.S. Treasury bond
market over the period from 1969-2005. They established that a significant relationship
between bond volatility and dispersion exists, which is based on uncertainty across all
maturities concerning the monetary policy rate, inflation (using the CPI and the deflator), and
Table 1: Macroeconomic announcements indicators (Huang & Kong (2005)).
Announcement Abbreviation Unit
FOMC Target FOMC % Rate
Industrial Production IP % Change
Capacity Utilization CU % Level
Gross Domestic Product GDP % Change
Unemployment Rate UNEM % Level
Changes in Nonfarm Payroll NFP 100
Consumer Price Index CPI % Change
Producer Price Index PPI % Change
Consumer Confidence CC % Level
NAPM Index NAPM % Level
Advanced Retail sales ARS % Change
20
economic activity (measured by unemployment rate, real and nominal GDP, and industrial
production).
In their analysis of the drivers of corporate bond liquidity, Galliani, Petrella, & Resti
(2014) tested the link between a bond’s individual liquidity and the liquidity of the market as a
whole. They state that illiquidity of individual bonds follows illiquidity of the global market.
This observation appears to be heightened for bonds with longer maturities and lower credit
ratings, and especially during periods of market stress.
In stock market literature, Coughenoura & Saad (2004) relate commonality liquidity of
equities to market makers that induce common liquidity movements. The authors claim that as
specialists within the same firm share capital and information, the manner in which they deliver
liquidity has a significant chance of being correlated. The authors state that individual stock
liquidity co-varies with specialist portfolio liquidity. In other words, they conclude that
commonality liquidity is driven by liquidity of financial intermediaries. This could be defined
as “a supply side” source of commonality.
Huberman & Halka (2001) investigated the existence of a systematic, time-varying
component of liquidity, and related it to the presence and effect of noise traders6. The authors
were the first to link commonality liquidity to investor sentiment.
Hasbrouck & Seppi (2001) related commonality liquidity to trading activity. Their study
can be considered as a “demand side” source of commonality.
In “The Association between Commonality in Liquidity and Corporate Disclosure
Practices in Taiwan”, Lowe (2014) studied a sample of stocks listed on the Taiwan stock
exchange (TWSE) and established a link between the level of institutional ownership and the
commonality liquidity.
A study conducted by PWC (2015) on the liquidity of global financial markets mentions
some factors that drive or have an effect on market liquidity conditions. Among others, a stable
6 Noise traders: A noise trader is an investor who makes decisions based on feelings such as fear or greed, rather
than fundamental or technical changes to a security.(Source: Farlex Financial Dictionary (2012) Noise traders
http://financial-dictionary.thefreedictionary.com/Noise+Trader+Risk )
21
monetary policy is mentioned, due to its support of the liquidity of the market throughout the
economy. The intensification of electronification and digitalization, which enables lower
trading costs and quicker transactions, but also the regulatory reforms that were adjusted after
the financial crises, may be considered as factors that impact the liquidity of the market.
To conclude, the literature assesses various variables that could be selected to explain
part of commonality liquidity in the corporate bond market in the US. First, equity market
appears to impact the liquidity of the fixed-income market. Macroeconomic variables mirror
the health of the economy, and have therefore an influence on fixed-income securities issued
by corporate firms. Among macro-determinants that are recurrent, the federal funds rate and
the inflation rate tend to be considered as potential drivers of bonds liquidity. Calendar effects
but also financial crisis impact the commonality liquidity. Other variables, including the
Treasury market but also investor sentiment are also mentioned in different research. Behaviors
of financial intermediaries and institutional investors also affect commonality liquidity, through
the supply of liquidity which is narrowed during periods of market stress, and through a weaker
trading of individual securities due to a higher correlation of the demand for stocks,
respectively.
22
Conclusion Chapter I
This chapter provides insight of the main concepts necessary for the
development of this thesis. The terms “liquidity” and “liquidity in the
corporate bond market” have been investigated. The term liquidity refers to
the ability to purchase or sell a large quantity of an asset quickly and with no
transaction costs. More specifically, the research focusing on the fixed-income
market revealed that the framework of this market, which mainly trades over-
the-counter, makes it less liquid because of low price transparency, a large
diversity of bonds for one firm and thus, a lack of standardization, and also
because of the dominant presence of institutional investors.
This section also explained the variations in liquidity among the sub-segments
of corporate bonds and aimed to assess different measurements of liquidity. It
has been shown that bond characteristics (i.e. bid-ask spread) could be used
as proxies, even if only approximate, of liquidity. Trading variables (i.e.
number of trading days) could also be used to assess this concept, and specific
measures (i.e. Amihud, IRC, etc.) developed by the literature have been defined.
Furthermore, commonality liquidity has been identified as the part of liquidity
that is shared by all bonds and is driven by the market.
Finally, the last section was dedicated to referencing the literature that
mentions potential explanatory variables for this common liquidity, and it was
shown that macroeconomic indicators were the most recursive of these (federal
funds rate, inflation rate, etc.)
23
Chapter II
Theoretical Investigations
A. Relevant Literature Survey
Previous sections, through reference to financial literature, outlined the different significant
concepts important for the goal of this thesis.
In this section, some important studies and research will be described, which have the
potential to aid this research and could be considered as guidelines for the realization of this
thesis.
In a paper titled “Understanding commonality in liquidity around the world”, Karolyi, Lee,
& Van Dijk (2012) study the variations of commonality liquidity across various countries for
the equity market. The authors aimed to expanse on existing literature in the sense that they did
not only focus on the study of the US. Indeed, they extend their geographical scope to answer
the following question: “What determines how commonality varies across time?” The authors
try to provide a deeper understanding of the so-called “supply and demand side determinants”
of commonality. In order to achieve their objectives, they analyzed monthly time-series
measures of commonality based on the daily data of 27,447 individual stocks from 40 countries
across the world, covering the period from January 1995 to December 2009. The approach used
consists of studying the institutional characteristics and the capital market experiences of each
country with regard to their impact on the level of commonality liquidity. The authors define
supply side determinants as those that make references to financial institutions that act as
liquidity providers, and the demand side determinants as those that relate to trading activity and
investor sentiment. To test for these determinants, the authors define the average market’s
volatility, the average short-term interest rate, the ratio of the stock market capitalization to
GDP and finally the ratio of bank deposit to GDP as supply side determinants that could account
for the common portion of liquidity. In addition, they selected the turnover in order to check
for trading activity, the ratio of equity mutual fund assets to market capitalization, the ratio of
24
foreign institutional ownership to market capitalization, the average of net percentage of equity
flow, the ratio of gross capital flow to GDP, the good government index, and the financial
disclosure as demand side determinants that could explain commonality liquidity.
In order to verify the potential determinants of commonality liquidity, the authors
performed four empirical tests: first, a cross-country regression aiming to test the commonality
liquidity with respect to country characteristics; second, a time-series test based on seemingly
unrelated regression models indicating the link between commonality liquidity and capital
market conditions; and third and fourth, tests intended to test the supply and demand side
determinants regarding variations of commonality liquidity across time inside cross-sections of
individual stocks and countries. A common liquidity measure was defined for each stock in
each month and denoted as R2 for the Roll measure. A monthly time-series measure of
commonality liquidity was then defined for each of the 40 countries. This time-series was
computed by taking the weighted average of the R2 in a given month across individual stocks.
The authors observed that the commonality liquidity appeared to be lower in developed
countries than in emerging countries, and more important in countries with higher average
market volatility. The results provided show that countries with more correlated trading activity,
greater equity inflows and lower legal framework and transparency had greater commonality in
liquidity.
This outcome reveals the significant effect of a demand side hypothesis on commonality
liquidity. Further investigation leads the authors to claim that commonality liquidity is more
important during periods of greater market volatility and also during more important trading
activity periods. Other tests aiming to assess other supply side determinants could not prove
any significant role regarding the funding’ of financial market makers with respect to
commonality liquidity. Periods of higher interest rates should normally represent more difficult
credit conditions, however, it could not be proven that commonality is greater during these
periods. Neither support could be found relating to the funding of local banks and brokers. In
this study, U.S. default and commercial paper spreads appeared to be negatively correlated to
the commonality liquidity. Other examinations related to the demand side determinants
revealed a significant impact of foreign capital inflows on commonality liquidity, which
appears to be greater as foreign inflows increase. Another measure of market openness enabled
the authors to state that increasing foreign inflows are related to less commonality liquidity
within individual assets. A demand side determinant leads to the conclusion that an optimistic
sentiment of investors is associated with larger commonality liquidity. The most demand
25
significant result found by the authors is that commonality liquidity is significantly related to
trading activity within each country. In their final test, the authors conclude that the average
commonality liquidity within a country is positively related to market volatility, net equity
inflows and commonality turnover.
Bao, Pan, & Wang (2011) performed a research titled: “The Illiquidity of Corporate Bonds”.
Instead of studying the liquidity of individual corporate bonds alone, the authors studied the co-
movement of these bonds in their illiquidity. The authors attempted to examine the illiquidity
of corporate bonds and the implications of this illiquidity to asset pricing. They used an
empirical measure based on the degree of momentary price movements, and attempt to establish
a strong link between this liquidity measure and bond’ prices. They demonstrates that the
illiquidity in corporate bonds is far greater than what can be expected from bid-ask spreads. For
these authors, the illiquidity of individual corporate bonds moves importantly over time, and
they could observe an important commonality on these fluctuations. The authors also prove that
there was a strong commonality in the time variation of bond illiquidity, which increased
sharply during the financial crisis in 2008. Indeed, Bao, Pan, & Wang observed that during this
financial crisis, the aggregate liquidity component became even more important in the yield
spreads. Finally, they also showed that a bonds’ illiquidity is also related to some main
characteristics of the asset.
After the peak illiquidity in October 2008, the authors witnessed an improvement of
liquidity due to the injection of money provided by the Federal Reserve and to the better
conditions of the entire market. The authors also observed that their illiquidity measure
presented a close connection to the CBOE VIX of the US, and their analysis proved that their
aggregate liquidity measure was strongly correlated with changes in this indicator. In sum, they
find an important commonality in the time variation of corporate bond illiquidity, which
according to them is related to market conditions.
Dick-Nielsen, Feldhütter & Lando (2012) studied the liquidity of corporate bonds before
and after the onset of the subprime crisis. The authors analyzed the liquidity of a sample of
10,785 corporate bonds during the period 2005-2009 by using a new measure. More specifically
the author focused on the impact of liquidity on the level of spreads. Investigations have been
performed regarding the level of liquidity for investment and speculative grade bonds during
the periods that precede and follow the financial crisis of 2008. The authors argue that illiquidity
gives rise to corporate bond spreads, and that spreads widened during the subprime crisis.
26
Essentially, the authors state that the widening of spreads during the market turbulence period
is attributable to lower liquidity of the market. Their research defines a measure for capturing
the liquidity component of bond spreads, which takes the difference in yields between a bond
with average liquidity and a very liquid bond. They found that the liquidity component of
spreads was more important during the financial crisis for all categories of ratings except for
the AAA class. In this study, investment-grade bonds were revealed to have a quite small
liquidity component before the crisis, but this element increased with the financial crash.
The authors also verified any potential difference of liquidity levels between bonds
issued by industrial firms and bonds issued by financial firms. The findings showed that
liquidity of both bonds were similar during “normal” market periods, but tended to be lower for
bonds issued by financial firms during unstable market periods, due mainly to asymmetry of
information. Another outcome of this study relates to the study of the systematic commonality
liquidity, before and after the subprime crunch. By testing the co-variation between an
individual bond’s liquidity and the market’s liquidity, it was found that commonality was not
an important contributor to spreads before the 2008 crisis, but became quite significant when
the financial crisis emerged, with the exception of the AAA rated bonds. In order to test
commonality, the authors computed a new measure that was formed by taking the standardized
average of four liquidity measures: Amihud, IRC measures, and the standard deviation of both
of these measures. In order to determine whether the majority of liquidity information could be
approximated by few factors, the authors performed a principal component analysis and
discovered that more than 40% of liquidity variation among variables could be explained by
the first component, which refers to Amihud, IRC, and their respective variations. In order to
verify the magnitude of liquidity, this study performed a regression of the corporate bond yield
spread on various liquidity variables, while checking the differences among rating classes
before and after the subprime crisis each time.
27
Conclusion Chapter II
In this chapter, we described three studies and the main results of them, while
explaining the methodologies used each time.
Karolyi, Lee, & Van Dijk (2012)
-How does commonality vary around the world and across time?
-Explanatory variables of commonality: funding liquidity of financial intermediaries,
correlated trading behavior of international vs. institutional investors, investor
sentiment, and stimulus to buy individual securities.
- Close correlation between commonality liquidity and trading activity, market
volatility and commonality turnover.
-Commonality is lower in developed countries and greater in countries with higher
average market volatility. Commonality is also higher in countries with more
correlated trading activity, greater equity inflows, and lower legal framework and
transparency.
Bao, Pan, & Wang (2011)
-Assess price implications of corporate bond illiquidity and prove the presence of
commonality liquidity.
-Demonstrate that bond’s illiquidity is related to bond’s characteristics.
-Variation of liquidity across time: increase of illiquidity during financial crisis of
2008.
-Changes in illiquidity positively related to changes to VIX index.
Dick-Nielsen, Feldhütter, & Lando (2012)
-Assess the liquidity components of corporate bonds during the subprime crisis.
(->Spreads more important during this period.)
-Bond liquidity from financial firms is more impacted by market stress.
-Investment-grade bonds: small liquidity component.
EMPIRICAL
SECTION
28
Chapter III
Empirical Research
A. Data Initial Presentation
In this section, the unique set of data covering the U.S. corporate bond market is presented.
The data used in this study is drawn from two sources:
1. Transaction data from the Trade Reporting and Compliance Engine (TRACE).
2. Bond characteristics and credit ratings from Standard and Poor’s (S&P’s) and Bloomberg.
The time period studied begins with January 3, 2006 and ends with December 31, 2012. A
sample of 2,665 bonds were initially at disposition, from different types, covering different
maturities, different characteristics of the bonds, different credit ratings, and different industry
sectors (a more detailed description of the different range of bond sub-segments covered is
given later in this text). The TRACE system provides detailed information regarding all the
specified transactions in the U.S. corporate bond market, i.e., the actual trade price, the yield
based on this price, and the trade volume for each transaction. The choice of the US as the area
for this study is a result of a logical conclusion: in most of the OTC markets, only a small
amount of data is available regarding the transactions performed. However, thanks to the
Financial Industry Regulatory Agency (FINRA), a private organization responsible for the
regulations and protection of investors by insuring that the market functions honestly and fairly,
the TRACE system has been put in place. This tool has made detailed transaction information
accessible, and offers the possibility of checking the price, volume and other variables of a
transaction in the market. This type of system is quite rare in other OTC markets existing in
other countries and therefore the chance to perform the type of study pursued here is
consequently reduced.
29
B. DATA BLOOMBERG
The initial raw sample for the empirical part consisted of 2,665 specific bonds. These
bonds were exclusively U.S. corporate bonds, and covered a time span of seven years (from
2006-2012). Information was retrieved from Bloomberg in order to complete the details
necessary for the different computations of liquidity proxies and liquidity measurements, as
well as to be able to perform an initial filtering of the data in order to select the appropriate
bonds.
By using this method, the name, issue size, issue date, industry sector, industry group,
option features (whether the bond is exchangeable or convertible, for example), maturity, credit
rating of the agency Standard and Poor’s, coupon, coupon type, currency and turnover were
downloaded for each bond.
An initial filtering of the data was necessary at this step. It was decided to only retain
the bonds without any equity-like characteristics. Therefore, any exchangeable or convertible
bonds in the sample were removed. After this, only those bonds that had the required
information were kept. This led to the removal of some bonds from the initial sample, namely
those for which the credit rating, issue size, coupon or maturity was not available, as that
information was necessary to describe the trends of bonds. All bonds that were not recognized
by the system and were classified as an invalid security were also removed. Any security with
an issue size lower than $100,000 was also deleted from the Bloomberg data. Finally, each bond
had to be expressed in USD, and those that were expressed in different currencies were also
removed from the dataset.
This first selection process reduced the total number of bonds to a number of 2,113
assets. Next, in order to facilitate the interpretation of the data and also to have a clearer view
of the represented bonds, integer numbers were assigned to the ratings from Standard and
Poor’s (AAA = 1 (highest rate), AA+ = 2…D=22 (lowest rate) ) so that a classification into
high-yield, speculative grade bonds was possible. The bonds were also divided into three
categories of maturities (short-term maturity (lower than 5 years), medium-term maturities
(between 5 and 10 years), and long-term maturities (longer than 10 years).
The following figures allow for the observation of the sub-segments of bonds regarding
credit rating, maturity, and the industrial sector. The number of bonds represented in these
30
graphs amounts to 2,059 bonds. Only the bonds retained in order to compute the liquidity
measures are represented. The “54” missing bonds were deleted through the implementation of
the algorithm7 for cleaning the TRACE transactions.
I. Different credit risk:
7 This algorithm will be presented in the next point “Data TRACE and Cleaning Method”.
Rating Integer #Nb Bonds #Nb Bonds
AAA 1 Minimal Credit Risk 23 23
AA+ 2 0
AA 3 40
AA- 4 86
A+ 5 62
A 6 316
A- 7 298
BBB+ 8 465
BBB 9 300
BBB- 10 162
BB+ 11 70
BB 12 67
BB- 13 47
B+ 14 35
B 15 42
B- 16 4
CCC+ 17 15
CCC 18 15
CCC- 19 0
CC 20 0
C 21 0
D 22 Default 12 12
S&P's Credit Rating
81
High rate
Lowest Rate
Inv
estm
ent
Gra
de
S
pec
ula
tiv
e G
rad
e
Very Low Credit Risk
Low Credit Risk
Moderate Credit Risk
Substantial Credit Risk
High Credit Risk
Very High Credit Risk
126
676
927
184
30
0Near Default
Total bonds : 2059
Table 2: Repartition of credit ratings among the sample.
31
As can be seen from both Table 2 and Figure 1, the entire sample consists of both
investment and speculative grade bonds. The subdivision between investment-grade bonds
(higher S&P’s rate and lower credit risk) and speculative grade bonds (lower S&P’s rate and
higher credit risk) is not equivalent in the sample: there are 1,798 investment grade bonds and
315 speculative grade bonds. The graph shows a more precise division of the credit risk
categories. Analyzing this illustration, it can be concluded that the majority of the bonds in the
sample is either categorized as moderate credit risk (44%) or low credit risk (34%). (Table 2
reports 927 and 676 bonds for these categories, respectively).
From previous studies, it can be observed that the credit risk of a bond has an impact
on its liquidity level. For example, speculative grade bonds show lower liquidity during
financial crisis. The sample given here consists of a more important number of investment-
grade bonds. However, the moderate credit risk is dominant, which is a positive point as it
means that the majority of the data is not based on extreme ratings.
Figure 1: Graph representing the repartition of credit ratings
among the sample.
32
II. Different maturities:
The bonds selected also span several maturity levels. This division of bonds into
three main categories short-term bonds (< = 5 years), medium-term bonds (from 5 to 10 years),
long-term bonds (more than 10 years), allows for the observation of the allocation of different
maturities present in the sample. The medium-term bonds represent a majority of the securities,
comprising nearly 50% of the entire sample. As maturity is known to have an impact on the
liquidity of bonds, it is positive to observe that the majority of fixed-income assets present in
the sample fall into the “middle” category. This will not influence the computations of liquidity
measures too significantly.
III. Different Sectors:
Figure 2: Graph showing the allocation of bond maturities (short-term maturity < 5
years, medium-term maturity between 5 and 10 years, long-term maturity > 10 years)
Sector Nb Companies
Financial 130
Utilities 67
Consumer, Cyclical 51
Communications 40
Consumer, Non-cyclical 57
Technology 16
Industrial 33
Basic Materials 17
Energy 35
Diversified 3
TOTAL 449
Table 3: Industry sector
allocation of firms.
33
Finally, it is also important to illustrate the variety of sectors present in the sample. More
than 400 different companies (exactly 449) were represented in the sample and these companies
spanned a variety of areas in the industry. As can be seen in the graph, the organizations are
classified into 10 classes. The allocation of bonds among the different groups is fairly
equivalent, except for the financial sector, which is more highly represented (35 % of the entire
sample of 2,059 bonds) than other sectors (see appendix n°1 for further details concerning the
different companies and the specific sectors and appendix n°2 for the names of these
companies.) This repartition plays a role in the computations of the liquidity measures, since
financial firms’ liquidity is more impacted during financial crisis periods than are bonds of
companies from other sectors.
C. Data TRACE and Cleaning Method
As previously stated, until quite recently it has been challenging to find appropriate data
on the day-to-day transactions of corporate bonds on the secondary market. However, since the
implementation of the TRACE system in 2002, all transactions on the U.S. corporate bond
market must be processed through this system. Today, it is compulsory for brokers and dealers
to report any transaction to TRACE within a time frame of 15 minutes. The reporting follows
a set of specific rules approved by the Securities and Exchange Commission (SEC), the
government agency in charge of the regulations of market regulation.
Nevertheless, as mentioned by Dick-Nielsen (2009), approximately 7.7% of the
Figure 3: Graph showing the industrial subdivision among
different asset classes.
34
transactions reported to TRACE include later reported errors, cancelations, or even duplicates.
In order to utilize and manipulate the data, it is therefore necessary to clean and filter it. This
step, which seems quite simple at the initial stage, requires the full comprehension of the
different codes and inputs necessary for TRACE reporting.
In this thesis, the method proposed by Dick-Nielsen (2009) in the paper “Liquidity
Biases in TRACE” is followed. This article proposes pursuing some specific steps in order to
clean TRACE data.
Dick-Nielsen proposes executing an algorithm that enables the detection and deletion
of reporting errors. This filtering is performed in three steps:
1. Deleting true duplicates: In the TRACE data, each transaction has a unique intra-day
message sequence number. A duplicate indicates that two reports have been completed for the
same transaction even though just one should have been.
2. Deleting reversals: Reversals correspond to later than same-day corrections or cancelations.
In the TRACE system, a correction on a later date is performed by first filling the reversal,
which aims to cancel the erroneous report. Then, another report marked as an “as-of trade” has
to be filled, which represents the final correct report. In the algorithm, all reports tagged as a
reversal are deleted as well as the original report for each reversal. One reversal should match
one original report.
3. Deleting same-day corrections: Same-day corrections refer to corrections or cancelations
performed on the same day for a given transaction. For the corrections, only the original report
matching the correction must be deleted from the disseminated data. Concerning the
cancelations, both the original report and the transaction denoted as “cancelation” must be
deleted. Identifying one original report and its correction/cancelation can be done simply by
using the original message sequence number.
The second step of the algorithm is more challenging, as it is not possible to identify an
original transaction with its reversals by using the original message sequence number. However,
since the reversal should be an exact replica of the original report, the detection is performed
by matching different variables. Still, even with matching of variables, it is sometimes not
possible to find the original report corresponding the reversal.
35
In this case, the following method is used:
If there is no identical match for a reversal based on the following parameters : CUSIP ID8,
Bond ID, company name, date, time, volume, price, and yield, the reversal report is the only
one to be deleted because the original report could not be identified.
If there is more than one trade report that matches the reversal, all the matching reports are
deleted except any as-of trades reports denoted “A” that match the reversals.
In his study, Dick-Nielsen warns that even with this filtering process it is impossible to
remove all the potential errors in a sample of TRACE data, as the information connecting the
different transactions is not always available. However, the author also states that the
hypotheses of the implemented algorithm are conservative, and enable the production of a fairly
representative image of the official transactions.
In addition to the execution of this filtering process, other “cleaning and verification”
steps were executed, as some data were either missing, not represented in the correct format for
further computations, or were discovered to have new flags of transactions that were not
reported in the article by Dick-Nielsen. Through these methods, eight transactions with missing
trade execution time were deleted, and transactions denoted with a flag “X” or “D” were deleted
from the database, since they do not indicate any kind of trade. Beginning in the year 2008, new
flags appeared, replacing those mentioned by Dick-Nielsen but still indicating the same type of
transaction.
Some checks were performed regarding the coherence of the data. For example, a bond
could not trade if the transaction date is before its issue date. Similarly, aberrant prices were
deleted from the database, as they are not representative of a normal trade. Finally, verifications
were also conducted to check that the volume of a trade was not higher than the issue size of
the firm. The final total sample, when cleaned and ready for use, consisted in 2,059 bonds,
meaning that the sample was reduced by approximately 50 bonds after these processes. This
sample was then concatenated with the Bloomberg data. The programming code executed for
the filtering lies in appendix n°3.
8 CUSIP: DNA of the security; Committee on Uniform Securities Identification Procedures.
36
Conclusion Chapter III
This chapter aimed to give a description of the data used, and to explain the main steps
performed in order to obtain a “cleaned database”. The principal information
necessary for the next steps of this research is as follows:
Number of bonds: 2,059 U.S. corporate bonds.
Period: January 3, 2006 to December, 31 2012 (span of seven years).
Investment-grade bonds vs. speculative-grade bonds: 85% vs. 15% of the
sample.
Bonds’ maturity: 40% vs. 31% vs. 20%, respectively for medium-term, long-
term, and short-term maturities in the total sample.
Industry sector: Dominant presence of financial firms (29% of total bonds,
issued by financial firms).
37
Chapter IV
Empirical Study - Liquidity Computations
A. Corporate Bonds Characteristics and Trading Activities
In order to give an initial perception of the different bonds present in the sample and of
liquidity, summary statistics have been computed regarding the main characteristics of the
assets each year. These are represented in Table 4. Information about some relevant trading
activity variables are also presented in this table. The total sample of 2,059 bonds, covering a
span of seven years, beginning January 3, 2006 and ending December 31, 2012, consisted of
367 weeks in total. It must be mentioned that as the presence of the 2,059 bonds is not constant
over time, as some appear and/or disappear over the years of the study, the panel is not balanced.
As can be observed from the table, the presence of the securities progressively increases across
the years, along with the transactions: in 2006 there are 534 bonds, but by 2012 there are a total
of 1,913 bonds.
The following graph illustrates that the average issue size of the bonds increases over the
years (refer to Table 4 for references to the numbers mentioned here and Figure 4 for a visual
illustration of the evolution of bonds’ characteristics). Regarding maturity, it can be seen that
the average value is always between ranges of 12 to 16 years. However, a steady decrease is
noticed for this value across years, which is logical, as once the bond enters into the sample it
remains there. Other bond’s characteristics, not reproduced in this graph, such as rating or price
exhibit very steady patterns. Rating retains a median value of 7 across the years without
exception, and the mean value shows the same trend, with the highest variability of 0.5.
Regarding the price, a small decrease is observed in 2009, where a value of 96.83% is attained,
directly followed by a strong and steady rise. The average price reaches 110.55% in 2012.
Finally, for coupon, a slight decrease can be seen in the yield produced by a given corporate
bond, since the mean value begins at a level of 6.3% and ends up at a level of 5.4%.
38
Regarding the trading activities of the bonds, the average number of trading days during
each year was computed. The turnover ratio representing the average of monthly volume traded
over issue size, and the average number of trades during one week are also shown in the table.
Analyzing the values of the weekly trades, it can be observed that the median lies between 9
and 25 trades, gradually increasing across years, which is logical since the sample also increases
with years. The mean value of weekly trades is consistently between ranges of 18 to 40 trades,
also evidencing an upward movement over years. The highest values are observed in 2009, with
39 trades for the mean value and 25 trades for the median value. Focusing on turnover, it can
be noticed that the mean value consistently declines and reaches its lowest point in 2008 with
a value of 4.24 %. This observation can likely be explained by the subprime financial crisis.
From Table 4, a slight recovery in 2009 is observable, but this is only temporary since this value
steadily declines for the other years. This observation could be linked to the increasing pattern
of the issue size. Finally, the number of trading days along years progressively rises, beginning
in 2006 with a mean value of 130 trades and ending with 185 trades in 2012. This is consistent
with more important trading activity of the market. The patterns of the trading variables
described are represented in the graph above (Figure 5).
Figure 4: Graph representing the evolution
of bonds’ characteristics over years.
Figure 5: Illustration of the trading
variables over time.
39
Summary Statistics
Bonds
Issue Size Average issue size in $ millions in the sub-sample
Maturity
Coupon Coupon in percent
Rating
Turnover
Weekly Trades
Trading Days
Price
Rating from S&P measured in a scale from 1 (high rated) to 22 (lowest rate)
Average of monthly volume traded over issue size
Average Nb of trades during one week
Average Nb. Of trading days during that year
Average price of the bond during the year
Legend :
Number of bonds during that year
Number of years to maturity ( Unit= Years)
2006 Mean S.D Median C.V. prcnt
Bonds
Issue Size 6,87E+08 6,13E+08 5,00E+08 89,29409
Maturity 18,45394 10,43197 12 56,5298
Coupon 6,399016 6,996082 6 109,3306
Rating 7,802854 3,062717 7 39,25124
Turnover 6,64792 8,01166 4,1135 120,5138
Weekly Trades 18,16854 29,01659 9,273504 159,7079
Trading Days 130,0187 73,26528 131 56,34979
Price 98,97409 8,587012 98,73693 8,676021
534
2007 Mean S.D Median C.V. prcnt
Bonds
Issue Size 7,50E+08 6,94E+08 5,00E+08 92,50948
Maturity 17,36479 9,932608 10 57,19969
Coupon 6,124644 4,41724 5,875 72,1224
Rating 7,483362 3,0699 7 41,02301
Turnover 5,517891 6,987267 3,351443 126,6293
Weekly Trades 19,46413 34,15174 9 175,4599
Trading Days 123,2146 74,74215 113 60,66016
Price 98,90102 7,278294 98,80588 7,35917
755
2008 Mean S.D Median C.V. prcnt
Bonds
Issue Size 8,07E+08 7,31E+08 6,00E+08 90,5966
Maturity 15,09365 9,070947 10 60,09776
Coupon 6,000045 2,66081 5,875 44,3465
Rating 6,718935 2,597083 7 38,6532
Turnover 4,240529 5,26365 2,688943 124,1272
Weekly Trades 29,97466 51,12382 11,97556 170,5568
Trading Days 141,3616 71,82268 141 50,80778
Price 98,97409 8,587012 98,73693 8,676021
932
40
2009 Mean S.D Median C.V. prcnt
Bonds
Issue Size 8,51E+08 7,49E+08 6,00E+08 88,04578
Maturity 12,40229 7,794504 10 62,84731
Coupon 6,008052 1,179643 5,875 19,63436
Rating 6,770239 2,368222 7 34,97989
Turnover 6,457393 7,735923 4,337647 119,7995
Weekly Trades 49,70394 65,04902 25,94828 130,873
Trading Days 172,0348 64,70673 183 37,61258
Price 96,83229 13,24762 99,98959 13,68099
1206
2010 Mean S.D Median C.V. prcnt
Bonds
Issue Size 8,73E+08 7,30E+08 6,00E+08 83,60542
Maturity 12,31985 8,086115 10 65,63487
Coupon 5,919 1,361298 5,85 22,99934
Rating 7,305152 2,726782 7 37,32684
Turnover 5,956857 7, 245566 4,044533 121,634
Weekly Trades 44,75428 57,65187 24,66063 128,8187
Trading Days 180,3408 68,75364 196,5 38,12428
Price 105,6681 9,057351 105,8824 8,571513
1514
2011 Mean S.D Median C.V. prcnt
Bonds
Issue Size 9,07E+08 7,25E+08 7,00E+08 79,93905
Maturity 11,73739 7,934649 10 67,60147
Coupon 5,529076 1,587032 5,6 28,70337
Rating 7,343082 2,803911 7 38,18439
Turnover 5,43972 6,315175 3,720933 116,0937
Weekly Trades 40,02265 53,00884 21,98077 132,4471
Trading Days 185,4103 61,67056 199 33,26167
Price 106,9048 8,54441 106,12 7,992542
1784
2012 Mean S.D Median C.V. prcnt
Bonds
Issue Size 9,08E+08 7,18E+08 7,00E+08 79,13429
Maturity 11,66266 7,842764 10 67,24678
Coupon 5,492422 1,658052 5,55 30,18799
Rating 7,931783 3,077159 7 38,7953
Turnover 4,595444 5,437842 3,108619 118,3312
Weekly Trades 39,55611 62,64171 18,39216 158,3617
Trading Days 185,8896 54,26952 196 29,19448
Price 110,5583 10,75633 108,1675 9,729102
1913
Table 4: Summary statistics (Issue size, maturity, coupon, rating, turnover, weekly trades,
trading days and price) for all year of the sample. Explanations regarding each line are
given in the legend. (S.D: Standard deviation; C.V.: Coefficient of variation in %)
41
B. Liquidity Measures: Results and Evolution Across Time
This section describes the different liquidity measures that have been computed in order to
extract the studied commonality liquidity. Three different measures were selected and
computed for the bonds present in the sample: a measure of roundtrip costs of trading, the
Amihud measure of price impact, and the trading interval (the time elapsed between two
consecutive trades for a given bond, measured in days). Weekly series were built for the three
liquidity measures. The work of Dick-Nielsen, Feldhütter, & Lando (2012) was consulted to
construct and select these liquidity measures. The choice of the Amihud and IRC measures
derives from the previously mentioned study that tested whether most of the relevant
information in liquidity proxies could be captured using a small number of factors. The authors
performed a principal component analysis and proved that Amihud, IRC and their respective
standard deviations captured more than 40% of market liquidity. Trading interval was selected
because of its ability to reflect the frequency of trades. Friewald, Jankowitsch, &
Subrahmanyam (2010) also used this trading interval measure in order to study the liquidity of
U.S. corporate bonds. All the programming codes for each liquidity measure were executed
with the software R and are given in appendix n°4 of this report.
The liquidity measures were described in detail in Chapter I. However, it is important
to review the context and therefore these measures are discussed briefly here.
I. Imputed Roundtrip Costs
The IRC measure is based on the hypothesis that after a long period without any trades,
bonds might trade two or three times a day within a short time interval. The difference in price
incurred by large and small traders could be perceived as a transaction fee or as the bid-ask
spread. The formula applied to the transactions in the sample is as follows:
𝐼𝑅𝐶𝑖,𝑡 =(𝑃𝑖,𝑡
𝑚𝑎𝑥−𝑃𝑖,𝑡𝑚𝑖𝑛)
𝑃𝑖,𝑡𝑚𝑎𝑥
Where:
𝑃𝑖,𝑡𝑚𝑎𝑥= largest price in the set of transactions with the same size within a day.
Table 4: Summary statistics (Issue size, maturity, coupon, rating, turnover, weekly trades,
trading days and price) for all year of the sample. Explanations regarding each line are
given in the legend. (S.D: Standard deviation; C.V.: Coefficient of variation in %)
42
𝑃𝑖,𝑡𝑚𝑖𝑛= smallest price in the set of transactions with the same size within a day.
The IRC is then equal to the average of the roundtrip costs during that day for different sizes.
As weekly series were required, the average of daily estimations was taken to obtain weekly
measures.
II. Amihud Measure
The Amihud measure, which represents the price impact of a trade per unit traded, was
computed based on this formula:
𝐴𝑚𝑖ℎ𝑢𝑑𝑖𝑡 =1
𝑁𝑡∑
|𝑟𝑒𝑡𝑢𝑟𝑛𝑗,𝑡𝑖 |
𝑄𝑗,𝑡𝑖
𝑁𝑡
𝑗=1
= 1
𝑁𝑡∑
|𝑃𝑗
𝑖
− 𝑃 𝑗−1
𝑖
𝑃𝑖𝑗−1
|
𝑄𝑗,𝑡𝑖
𝑁𝑡
𝑗=1
Where:
𝑁𝑡= number of observed returns during each day t for bond i.
𝑅𝑒𝑡𝑢𝑟𝑛𝑗,𝑡𝑖 = returns on the j-th transaction during day t and for corporate bond i.
𝑄𝑗,𝑡𝑖 = trade size in millions of dollars for the j-th transaction, for the i-th corporate bond and at
time t.
𝑃𝑗𝑖= price of bond i at the j-th transaction.
Based on the study of Dick-Nielsen, Feldhhütter & Lando (2012), the Amihud measure was
computed only on days where at least two transactions were present in the sample. Regarding
its interpretation, a larger value for the Amihud measure implies that a trade of a given size will
impact the price more strongly, in other words, a larger Amihud value means that the bond is
more illiquid.
III. Trading Interval
Liquidity of bonds could also appear in the trading frequency, suggesting that bonds that
trade very rarely are less liquid. In order to capture this dimension of the liquidity, this trading
variable was computed by measuring the difference in days between two trades of a given bond.
This measure was then aggregated weekly to obtain the desired measure.
43
IV.Preliminary Results
2006 -2012 Mean Median SD Min Max
Bonds 2059
Trading Interval 2,089819 1,75 1,492823 0 91
Amihud Measure 2,8996E-06 3,5925E-07 0,00129326 0 0,8135833
IRC 0,00340697 0,00192192 0,00500841 0 0,5014092
2007 Mean Median SD Min Max
Bonds 755
Trading Interval 3,401706 2 5,10455 0 197
Amihud Measure 9,2704E-07 3,4648E-07 1,1027E-05 0 0,00173003
IRC 0,00286557 0,00124556 0,00573073 0 0,5014092
2010 Mean Median SD Min Max
Bonds 1514
Trading Interval 1,945226 1,6 1,40902 0 144
Amihud Measure 6,7763E-07 3,962E-07 3,1638E-06 0 0,00063676
IRC 0,00352331 0,00243377 0,00382409 0 0,08387977
2009 Mean Median SD Min Max
Bonds 1206
Trading Interval 2,240338 1,666667 2,45 0 162
Amihud Measure 1,7229E-05 6,529E-07 0,00358055 0 0,8135833
IRC 0,00570149 0,00410146 0,00709396 0 0,3508937
2008 Mean Median SD Min Max
Bonds 932
Trading Interval 3,208506 2 4,59806 0 153
Amihud Measure 2,0775E-06 6,9435E-07 5,4525E-05 0 0,00927838
IRC 0,00496162 0,00296919 0,00771505 0 0,5008648
2006 Mean Median SD Min Max
Bonds 534
Trading Interval 3,196319 2 4,932928 0 260
Amihud Measure 7,3299E-07 2,3287E-07 1,9761E-06 0 7,7897E-05
IRC 0,00248434 0,00086987 0,00426344 0 0,07616939
44
Table 5 displays the liquidity measures statistics for each year of the sample. The first
table represents the results for the entire sample covering all the years studied.
Beginning with an interpretation of the Imputed roundtrip costs, it can be seen that
the median measure for the sample covering the whole period is roughly 0.19%. This finding
is consistent with the analysis of Dick-Nielsen et al (2012), who found a median roundtrip cost
as percentage of the price equal to 0.22%. The measure found in this study is slightly below
this result, so it could be stated that these results are consistent with previous findings.
Conducting an analysis of this measure along years, a sharp rise during the period 2008-2009
is observed, which is consistent with the onset of the subprime crisis in 2008. The highest mean
value is seen in 2009 with an IRC of approximately 0.57%. As discussed in previous studies,
the higher the IRC value, the more illiquid the market. In addition, the higher the IRC, the
higher transaction costs are estimated to be. Again, this is consistent with the findings of Dick
et al (2012), Chordia, Sarkar, & Subrahmanyam (2003), and Bao, Pan, & Wang (2010), who
demonstrated that bonds were less liquid during periods of market turbulence. The following
graph, displayed in Figure 6 and representing the evolution of the IRC mean measure, provides
a clear representation of IRC patterns across years.
2011 Mean Median SD Min Max
Bonds 1784
Trading Interval 1,996134 1,6 1,321334 0 82
Amihud Measure 5,6712E-07 3,1786E-07 1,0294E-06 0,0000832
IRC 0,00277238 0,0016974 0,00331729 0 0,107299
2012 Mean Median SD Min Max
Bonds 1913
Trading Interval 2,089819 1,75 1,492823 0 91
Amihud Measure 4,6085E-07 2,5448E-07 8,2582E-07 0 5,7163E-05
IRC 0,00227541 0,00118157 0,00299778 0 0,1182583
Table 5: Summary statistics of liquidity measures Amihud, IRC, and trading interval
across years.
45
Regarding the trading interval, which displays the frequency at which a bond trades,
liquidity is expected to be higher for bonds with shorter time intervals between trading days.
The mean value of the sample during the entire period is about 2.08 days, meaning that on
average, two days elapsed between the first trade and the second. From the graph illustrated in
Figure 7, it can be observed that the mean value is very important during the first three years of
the sample, and then, at the end of 2008, the trading interval starts decreasing and maintains the
Figure 6: Evolution of IRC measure across years.
Figure 7: Evolution of trading interval across years.
46
same trend. Ultimately, this measure does not exhibit significant differences, since the values
always remain in the range of two to four days.
However, this thesis purports that at the end of the financial crisis, it is logical to observe
a more important number of trades, but as this period is quite specific, the assumption cannot
be made that this is necessarily correlated with a liquid market. It should also be noted that in
their study, Friewald et al (2012) display a mean value of 3.34 days for the trading interval.
Finally, the Amihud measure displays a median value of 3, 59E-07, which means that
a trade of $300,000 in an average bond moves the price by approximately 10.77%. This finding
is close to the results of Han & Zhou (2008), who approximated the price effect of a trade to be
10.2% in their study designed to estimate the nondefault component of corporate bond yield
spreads and its relation to bond liquidity. However, Dick-Nielsen et al (2012) did not find a
strong effect for price movement and the price movement estimated by these authors is about
0.13% for the average bond. The difference between the findings of this thesis and the results
of Dick-Nielsen is due to the fact that the authors excluded retail trades and put more importance
on the study of institutional trades9. The timely pattern of the Amihud measure is also important.
As can be seen from Figure 8, the Amihud measure shows a sharp rise during the financial crisis
corresponding to the period 2008-2009. This is again consistent with the findings of this
research regarding the IRC measure, and with the assumptions of other authors who argue that
markets are less liquid during periods of market stress.
9 In page 474 of J. Dick-Nielsen et al. (2012), Corporate bond liquidity before and after the onset of the subprime
crisis, Journal of Financial Economics, 103, 471–492: “The median Amihud measure is 0.0044 implying that a
trade of $300,000 in an average bond moves price by roughly 0.13%. Han and Zhou (2008) also calculate the
Amihud measure for corporate bond data using TRACE data and find a much stronger price effect of a trade. For
example, they find that a trade of $300,000 in a bond, on average, moves the price by 10.2%. This discrepancy is
largely due to the exclusion of small trades in our sample and underscores the importance of filtering out retail
trades when estimating transaction costs of institutional investors.(…)”
47
C. Correlation Matrix of Pearson
Above, the correlation matrix of Pearson is presented, which illustrates the links
between the three liquidity measures analyzed in this thesis. The correlation matrix was
computed by taking the correlations between pairwise weekly observations and then by
averaging these series. The strongest correlation is observed between the IRC and the trading
interval measure, at a level of 53.32%. The Amihud and IRC measure also show a correlation
of approximately 25%. This is not as strong as the correlation observed between the two
previous variables, but a relationship between the Amihud and the IRC measure cannot be
denied. Finally, the trading interval measure and the Amihud measure appear to have the lowest
level of correlation, with 14.93%.
Figure 8: Evolution of Amihud measure across years.
Variables Amihud IRC Trading interval
Amihud 1 0,2569 0,1493
IRC 0,2569 1 0,5332
Trading interval 0,1493 0,5332 1
Matrix of Correlation (Pearson)
The correlation is significant at a level 0,01
Table 6: Matrix of correlation between liquidity measures.
48
Conclusion Chapter IV
In this chapter, the main characteristics of the bonds present in the sample as
well as trading activity proxies are put forward by computing relevant
statistics of issue size, coupon, maturity, rating, price, turnover, weekly trades
and trading days.
We can summarize our observations as follows:
Maturity, issue size: these variables show increasing trends.
Price, rating: indicators with steady patterns.
Coupon: slight decrease in value along years.
Weekly trades and trading days: increasing trend observed.
Turnover: decreasing trend along years. Lowest point in 2008 with a level
of 4.24%.
This section also aimed to compute relevant liquidity measures, given as IRC,
Amihud and trading interval:
IRC: Mean value of 0.19% in the entire sample, consistent with previous
findings (Dick-Nielsen et al (2012),etc.). Sharp increase during 2008 subprime
crisis, consistent with higher transaction costs and less liquidity.
Amihud: Median value of 3.59E-07 for the entire sample, in line with
previous studies by Han & Zhou (2008), which found a price impact of 10.2%
while the measure found in this study reveals that an average trade of $300,000
moves the price by approximately 10.77%.
Trading interval: 2.08 mean value for the entire sample meaning that on
average, two days elapsed between a first trade and the second one. No specific
patterns were observed.
The last point covered in this section regards the computation of the
correlation matrix between the studied liquidity measures. The matrix
revealed the strongest positive correlation between IRC and trading interval,
and a positive correlation was also found between the Amihud and the IRC
measure.
49
Chapter V
Empirical Study - Liquidity Decomposition
I. Methodology: Korajczyk & Sadka (2008)
In this section the decomposition of the liquidity into a common component and into the
remaining idiosyncratic portion is explained. The common component is supposed to be the
result of dynamics common to all bonds, while the idiosyncratic portion is thought to be specific
to each individual bond. In order to perform this decomposition, the common part can be
extracted into liquidity data series and the residual part can be considered as being idiosyncratic.
The approach used here follows the methods of Korajczyk & Sadka (2008), based on the
analysis of the principal components. The objective is to extract the common, systematic
components of liquidity across a sample of bonds and from a set of three measures of liquidity,
which here includes: the Amihud measure, the IRC measure, and the trading interval. The
decomposition enables the determination of the size of the systematic (or common) component
versus the idiosyncratic component for each liquidity measure. The extraction also allows for
the measurement of the extent of commonality across the three measures of liquidity.
1. Standardization
When decomposing liquidity across the three liquidity measures, the units of each
measure can vary, and the risk of outsizing some of them in the computations arises. It is
therefore necessary to standardize the liquidity measures series. This also facilitates any future
comparison. The standardization is performed for each individual series of bond by taking the
mean and standard deviation of its liquidity series. For instance, for a bond with the ticker
“02360XAJ6”, we have three liquidity time series Amihud, IRC, and trading interval, each
covering a period of 367 weeks. The standardization is therefore performed for each of these
three series. This step is repeated for the 2,059 bonds present in the sample.
50
The methodology is as follows:
If Li* = the n*T matrix of observations on the i-th liquidity measure (i=1,2,3)
Where n = number of bonds
T= time periods
Li* = ⟨𝑏𝑜𝑛𝑑 1 𝑇1 𝑇2
… 0,000334 …𝑏𝑜𝑛𝑑 2059 … …
… . 𝑇367… …… …
⟩
Where
µ̂𝑖= time-series mean of the cross-sectional average of liquidity measure i estimated from the
data sample up to time t-1.
σ ̂i = times series standard deviation of the cross-sectional average of liquidity measure i
estimated from the data sample up to t-1.
Li = n*T matrix of observations on the i-th standardized liquidity measure
with Li jt =
𝐿𝑖𝑗𝑡∗− µ�̂�
σi ̂
2. Approximate Factor Model
It is then assumed that the liquidity is explained by an approximate factor model:
Li = Bi Fi + ɛi
Where:
Li = the n * T matrix of liquidity observations of measure i with i = 1,2,3 on the n-th assets over
T time periods.
Fi = k * T matrix of shocks to liquidity measure i that are common across a set of n assets (in
other words systematic or undiversifiable shocks to liquidity) = matrix of common liquidity
factors.
Bi = n * k vector of factor sensitivities to the common liquidity shocks (diversifiable shocks) =
51
matrix of exposure to those k factors for all individual assets n.
ɛi = n * T matrix of asset-specific shocks to liquidity measure i.
3. Approximation of N-latent Factors Fi with Eigenvectors
For a balanced panel10 :
Connor & Korajczyk (1986) demonstrate that for a balanced panel, the n-consistent estimates
of the n-latent factors, Fi, of this approximate factor model can be found by computing the
eigenvectors corresponding to the k largest eigenvalues of
Ωi = 𝐿′𝑖𝐿𝑖
𝑛 where : L’i= transpose matrix of Li
Connor & Korajczyk (1986) refer to these n-consistent estimates as the Asymptotic Principal
Components (APC). The authors show that in the case of asset returns, the eigenvector analysis
of the T * T matrix is asymptotically equivalent to traditional factor analysis. Ωi is a T * T
matrix so the computation of the eigenvectors is independent of the cross-sectional sample size
n. It therefore allows an easier decomposition than for an n*n matrix, when n is large for
example.
For an unbalanced panel:
In order to account for missing data and thereby an unbalanced panel, Connor & Korajczyk
(1986) estimate each element of Ω by averaging over the observed data. Therefore Li is
considered as the matrix with the data for liquidity measure i, with missing values replaced by
zeros. Ni will be the n * T matrix, for which Ni,j,t is equal to one if the liquidity measure i of
bond j at time i is observed and zero otherwise.
Therefore:
Ω𝑡,𝜏𝑖,𝑢
=(𝐿𝑖′𝐿𝑖)t,τ
(𝑁𝑖′𝑁𝑖)t,τ
Where:
Ω𝑡,𝜏𝑖,𝑢
= the unbalanced panel equivalent of Ω𝑖
(t, τ) = element of matrix T*T defined over the cross-sectional averages of the observed
10 The terms balanced and unbalanced are often used to describe whether a panel dataset is missing some
observations. (Unbalanced : missing observations )
52
elements only.
4. Estimations of the latent factors 𝑭�̂�are then obtained by calculating the eigenvectors
for the k largest eigenvalues of Ωi,u.
5. For each of the three liquidity measure, Korajczyk & Sadka (2008) advise extracting
the first three principal components.
6. In order to demonstrate the extent of commonality across bonds for each liquidity
measure, time-series regressions have to be performed for each bond’s liquidity time
series and on the three extracted factors.
The p-values, the R² value, the adjusted-R², and factor loadings have then to be detailed, and
there cross-sectional averages have to be computed for all the three extracted factors, and for
all the liquidity measures.
The estimation of the regression is then given by the following equation:
𝐿𝑗,𝑡𝑖 = 𝐵𝑗
𝑖 • 𝐹𝑡�̂� + 𝜀�̂�,𝑡
𝑖
Where :
𝐹𝑡�̂�= represents the k*1 vector of factor estimates for period t.
7. After estimating common factors for each measure, the extraction of common factors
across the three measures of liquidity is conducted. This is performed by assembling the
liquidity measures as depicted:
𝑳′ = [𝑳𝟏′, 𝑳𝟐′, 𝑳𝟑′]
Then, the matrix Ω𝑢 is formed using L, and the eigenvectors are extracted from Ωu. The
factors extracted across the liquidity measures are referred to as the systematic factors or
“across-measure” factors.
53
II. Results and Interpretation
Table 7 displayed below illustrates the distribution statistics of within measure common
factors. As explained by the method of Korajczyk & Sadka (2008), time-series regressions have
been performed on each individual liquidity series on the three common factors. The
programming code executed to obtain the results is given in appendix n°5.
In summary, before the computation of common factors, each liquidity series is
standardized by week by taking its mean and standard deviation. Then, by using the asymptotic
principal component method, within measure common factors are extracted separately for each
measure. After the extraction of these common factors, for each liquidity measure and for each
bond, a time series regression of the liquidity measure on its three common factors is performed.
Then, the R2 and adjusted R2 are retained each time, so that the averages of these values can be
produced, as seen in Table 7. The results of the asymptotical component analysis reveal that
commonality exists across assets for all the liquidity measures. More important commonality
is detected for the trading interval measure where the average R2 is 20.4% for a one-factor
model, 27.07% when the number of factors is increased to two, and 29.03% for a three-factor
model. The IRC measure displays an average R2 of 14.75% for a one factor model, an average
R2 of 19.16 for a two-factor model, and a value of 22.07% for a three-factor model. Surprisingly,
the lowest level of commonality is observed in the Amihud measure which does not bring
significant results with average R2 values of 7.26%, 10.30% and 12.23% respectively for one-,
two- and three- factor models, respectively.
The results obtained for the IRC measure are consistent with the findings of Heck et al
(2016) who found commonality of the same level across the three factors. Connor & Korajczyk
(1986) found higher level of commonality for the Amihud measure, as did Heck et al (2016).
This difference regarding the Amihud measure can likely be explained by the small number of
observations, the short time period studied (the previously mentioned studies used higher time
period of respectively 13 years and 18 years), the fact that the assets studied here does not
exhibit an important level of liquidity, and also perhaps because this study did not perform a
selection across the “most liquid asset”. This was performed in the study of Heck et al (2016),
where the authors required the bonds to trade at least 30 business days each year, and to remain
in the total sample for at least one year so that only the most liquid bonds were retained in the
dataset. It was decided not to perform this selection of the “most liquid” bonds in this study,
primarily for a reason of representativeness. The small sample of observations used in this
54
research would have been reduced by more than 200 bonds each year if such a selection had
been implemented, and this could have biased final results.
After the estimation of common factors for each measure of liquidity, common factors
across the three measures were also estimated. The extraction of global factors was performed
by combining the three liquidity measures together and then extracting the three principal
factors again. In order to conduct the regression analysis later in this thesis, the decision was
made to keep the first factor that could describe the commonalty liquidity of the market across
time (since it is supposed to be the one with the most variability), and to aggregate it quarterly
in order to more easily obtain an interpretation. Figure 9 displays scatter plots for the three
global factors computed on the basis of the Amihud, IRC, and trading interval measure.
Amihud Factor 1 Factor 2 Factor 3
R2 0.07265857 0.10308244 0.1223640
Adj R2 0.06770981 0.09339968 0.1080725
Trading Interval Factor 1 Factor 2 Factor 3
R2 0.2040932 0.27070080.2903086
Adj R2 0.2002176 0.26340700.2796289
IRC Factor 1 Factor 2 Factor 3
R2 0.1475192 0.1916058 0.2207488
Adj R2 0.1427937 0.1826733 0.2078131
Table 7: Diagnostics of within measure common factors. This table
reports the average R2 and the average adjusted R 2 of the regressions
using one, two and three factors.
55
Regarding the sign of the first global factor and its interpretation, by identifying the periods of
stress and the reactions of the factor, it can be seen that the 2008 financial crisis and the Lehman
Brothers’ bankruptcy corresponds to the period where the global factor displays a negative sign.
Karolyi, Lee, & Van Dijk (2012) showed that a more important amount of commonality was
present in liquidity during periods of market stress. Therefore, a negative sign in the first global
factor will be interpreted as a period with an important amount of commonality in liquidity and
a positive sign as a period with a lower amount of commonality in liquidity.
Figure 9: Scatter pots of the first three global
factors based on the Amihud, IRC, and trading
interval measures.
56
Conclusion Chapter V
In this section of the thesis, the objective was to decompose the liquidity
measures obtained in order to determine the commonality liquidity. For this
purpose, the paper of Korajczyk & Sadka (2008) has been used, and the main
steps of this methodology have been outlined. First, the standardization the
variables of interests across each series of liquidity for each bond was
conducted, then matrix of dimensions T*T for each liquidity measure named Ω
were created. Having this matrix, within measures were extracted for each
liquidity measure by taking the first, second and third factor for each. The next
step consisted of conducting time-series regressions of each factor on each
individual liquidity series. The results obtained revealed the existence of
commonality across the three studied measures. The trading interval presents
the highest level of commonality of the three variables with an R2 of 29% for
the third factor (cumulative with the first and second factors). However, little
significant result could be extracted regarding commonality for the Amihud
measure, since a value of 12.23% was obtained for the R2 using a three-factor
model. This does not appear consistent with prior studies.
Finally, the three first global factors were also extracted across the
three liquidity measures by stacking them and performing a principal
component analysis. A negative sign of the first global factor is interpreted as
a more important amount of commonality in liquidity and a positive sign as a
lower amount of commonality in liquidity.
57
Chapter VI
Empirical Study – Determinants of
Commonality Liquidity
I. Selection of Potential Determinants of Commonality.
In this section, the three selected determinants are presented and are used in the
regression analysis: the federal funds rate, the inflation rate in the US, and the volatility stock
index CBOE VIX. A hypothesis is formulated that argues these determinants could have an
impact on commonality liquidity and could explain part of its variation. A regression analysis
is later used to test this hypothesis. The choice of determinants was made based on the
investigations reported in Chapter I, where a preliminary “theoretical” survey of the potential
determinants of commonality liquidity was created.
A. Federal Funds Rate
As the state of the economy may be highly impacted by variations in macroeconomic
variables, it is logical that market participants who make forecasts and expectations about price
volatility based on a macroeconomic index will react proportionally and therefore influence the
movements of the market accordingly. The aforementioned authors (Chordia, Sarkar &
Subrahmanyam (2003), Maurya & Mishra (2016), Goyenko & Ukhov (2009), Arnold and Vrugt
(2010), etc.) who studied the liquidity of the corporate bond market, or in a more extended way
the impact of macroeconomic variables on the corporate bond market, used the federal funds
rate as a first indicator of macroeconomic movements.
In order to facilitate a better understanding of this index and to better interpret its impact,
the effect of the federal funds rate on the economy is first investigated. The federal funds rate
58
is the most important interest rate in the US, and it is actually an interbank interest rate within
the Federal Reserve System, i.e. the rate at which banks charge other banks that require
overnight loans. The FFR11 is determined by the Federal Open Market Committee (FOMC). A
“target rate” is set by the Fed12 and is maintained by buying and selling U.S. Treasury securities.
Even if ultimately, the return on financial assets is determined by the market as a whole, this
interest rate can provide a first indication of trends in the market. In this study, sensitivity of
the fixed-income market to the federal funds rate is important. One of the cardinal rules in the
bond market is that an increase in this rate results in a fall in bond prices and inversely.( Source:
Financial Industry Regulatory Authority [FINRA], 2016) The impact of this indicator is due to
the fact that coupons are established on the basis of this rate. However, the influence of the
federal funds rate is to be distinguished between corporate and government bonds, even if the
global impact remain the same. Indeed, despite the loss in value, the corporate bonds should
surpass government bonds due to a more important risk of default born by investors.
It must also be mentioned that the federal funds rate is a key tool for institutions to control
monetary policy. A decrease in the federal funds rate is connected with an expansionary
monetary policy, while an increase in this rate signifies a tightening of the monetary policy.
Chordia, Sarkar, & Subrahmanyam (2003) documented that any unanticipated increase in the
federal funds rate leads to decreases in liquidity. Goyenko & Ukhov (2009) found a significant
link between macroeconomic variables and the illiquidity of fixed-income assets. They
explained that shocks to the federal funds rate were associated with illiquidity, a rise in the
federal funds rate is associated with an increase in spreads and a fall with the opposite outcome.
The authors also find evidence for the relationship between bond market illiquidity and
monetary policy. According to this research, the liquidity of fixed-income assets decreases
when a tighter monetary policy is in place, which is connected with an increase in the federal
funds rate.
For the purposes of this study, quarterly data was extracted from the Federal Reserve Bank
of St. Louis. The evolution is represented in the Figure 10, where the main statistics are also
displayed. The Effective Federal Funds Rate (EFFR) is calculated as a volume-weighted
median of overnight federal funds transactions. As can be seen from the graph, the rate
consistently decreases over the whole sample analyzed, while the mean value is 1.79%. It can
also be seen that the federal funds rate was at a level of 5% before the global financial crisis in
11 FFR : Federal Funds Rate 1212 Fed : Federal Reserve
59
2006, but as a result of the subprime mortgage crash and Lehman Brothers’ bankruptcy, this
rate was reduced to 0.5% at the end of 2008. The flatness of the curve after the year 2008
indicates that the US are facing a period of low interest rates.
B. Inflation Rate
Similar to the federal funds rate, the inflation rate, which is defined as a general increase in
the level of prices of goods and services, is also an indicator of the state of the economy and
could therefore impact, at least indirectly, the trend of the market. In a previous study, Goyenko
& Ukhov (2009) proved that any shocks to inflation affect liquidity through higher transaction
costs and by an increase of inventory holding. The authors state that shocks of inflation are
useful to predict bond’s’ liquidity independently of their maturities. It appears that shocks to
Consumer Price Index (CPI) increase illiquidity of bonds.
In order to test the link of the inflation rate with the commonality liquidity, the CPI index
was downloaded from the Federal Reserve Bank of St. Louis. The consumer price index is a
Mean 1,79%
Std Deviation 2,19%
Min 0,08%
Max 5,26%
Figure 10: Evolution of the effective federal funds
rate (EFFR).
60
measure of the average change in prices for goods and services (foods, clothing, shelter, etc.)
purchased by an urban consumer during a given period of time. (Source: Federal Reserve Bank
of St. Louis, 2016) This measure also reflects the purchasing behavior of the population. The
consumer price index is usually used to detect periods of inflation. An increase in the CPI is
indicative of a period of inflation, and a decrease in the CPI might reveal a deflationary period.
Quarterly data is represented in Figure 11 for the period from 2006 – 2012. The unit of
CPI displayed in the graph is expressed from the basis of the period 1982-1984 (for example, a
CPI of 199.467 during the first quarter of 2006 is indicative of a 99.467 % inflation since 1982).
Inflation, based on this data and expressed in percentage growth rate, is represented as a red
line. The chart reveals that overall inflation significantly declined in 2008 and attained the
minimum value throughout the entire sample of -4.217%. This is also a consequence of
economic recession, which is a period characterized by a decline in energy commodity prices.
The inflation rate observed during this period is the slowest seen since the year 1954. After this
turbulence period, inflationary pressures appear to be quite moderated.
Figure 11: Evolution of the consumer price index and inflation across years.
Mean 1,047%
Std Deviation 1,408%
Min -4,217%
Max 2,876%
61
C. CBOE Volatility Index: VIX
The final determinants chosen in order to perform the regression analysis was the
Chicago Board Options Exchange Volatility Index (CBOE VIX). This variable was chosen as
a result of the desire to test the volatility of the market and, the investor’ risk appetite, as well
as from the potential relationship between stock and bond market liquidity. The CBOE VIX
index is a volatility index that estimates the volatility of the equity market in the US by
anticipating the evolution of stock index option prices for the upcoming 30 days. The VIX is
obtained by taking the weighted average of put and call options of the S&P 500 index. This
measure is indicative of the sentiment of investors in the US stock market. (Source: Federal
Reserve Bank of St. Louis, 2016).
An increase in the VIX index could be interpreted as a high degree of instability in the
market and therefore pessimistic behavior in the stock market. Inversely, a low level of the VIX
is indicative of an optimist sentiment of investors. The VIX reached a peak value of 80.06 in
October 2008, which corresponds to the worst month during the financial crisis. The selection
of this measure is intuitive, as previous studies have proven linkages between the debt market
and the stock market. Chordia, Sarkar & Subrahmanyam (2003) carried out an empirical
analysis of liquidity in both markets and found that the liquidities were correlated due to
important volatility relations and to transaction activity. The authors mentioned return volatility
as an important factor affecting liquidity in both markets. Goyenko & Ukhov (2009) express a
stronger outcome, and state that positive shocks to stock illiquidity decreases bond illiquidity.
Huang, & Kong (2005) performed a survey on the linkages between macroeconomic news and
corporate bond credit spreads. In their research, the VIX volatility index was used to check its
impact on credit spreads. More recently, Fontaine & Garcia (2012) studied the economic
determinants of funding liquidity and used the VIX volatility index as an explanatory variable
in their model. While studying the determinants of sovereign bond spreads in emerging markets,
Csonto & Ivaschenko (2013) also included the VIX in order to capture the global risk aversion
of the market. These surveys confirm the selection of this determinant as a third potential
explanatory variable of the commonality liquidity.
Regarding the other two determinants, quarterly data was retrieved from the Federal
Reserve Bank of St. Louis. A graph (see Figure 12) representing the time evolution of the index
during the covered period was created, which displays this variable in terms of percentage
change (red line) as well as in terms of units index (blue line). The chart indicates that the value
62
of this index has a tendency to fluctuate sharply over time and the highest variation is, as
expected, observed in 2008 with a maximum of 58.6 units.
II. Relationships between the Explanatory Variables
The relationships that could exist between the explanatory variables were investigated and
plotted before the execution of the regression analysis with regards to the commonality
liquidity. Figure 13 below presents all the explanatory variables in a single chart in order to
show their respective patterns: the federal funds rate (expressed in percentage), the CBOE VIX
Volatility Index (expressed in units), and the inflation rate (expressed in percent) are displayed.
The graph reveals that the inflation rate and the federal funds rate appear to move approximately
in the same direction, which is not the case of the CBOE VIX Volatility Index which evidences
high variations over the time period of the studied sample. It should be noted that the federal
funds rate remains within a very small range after the crisis, and this period is therefore
characterized by low interest rates. This pattern is also followed by the inflation rate. This
observation leads to the expectation of a close relationship between the federal funds rate and
the inflation rate. This is logical, as when a Federal Bank makes a decision regarding monetary
Mean 22,72
Std Deviation 10,19
Min 11,03
Max 58,6
Figure 12: Evolution of CBOE Volatility Index
63
policies, the entity always takes the inflation rate into consideration, and attempts to maintain
it in a given target.
In order to assess the relationship between the studied variables, correlation tests were
carried out and are listed in Table 8. Scatter plots are also exhibited in appendix n°6 and show
pairwise relationships of the variables.
As anticipated, the inflation rate appears to move in the same direction as the federal
funds rate. When the inflation rate is high, the federal funds rate also appears high, and when
the inflation rate reaches a lower level, the federal funds rate appears to do the same. This
relationship is proven by the correlation matrix, which reveals a correlation of approximately
27% between the two variables. This value could be interpreted as a positive correlation
between the two determinants. The R2 value between these respective economic indicators is
7%, which reflects the fact that a small amount of variance is explained between them. The
strongest correlation exists between the inflation rate and the VIX, where a negative value of -
66% and an explanation of variance of the order of 44% can be observed. These two variables
move in opposite directions, as was initially predicted. The relationship between the federal
funds rate and the VIX is also negative with a negative correlation of 45%. The R2 between
these two variables stands is approximately 20%. The p-values computed confirm these
observations.
Figure 13: Chart representing the cross-evolution of explanatory variables.
64
Table 8: Statistical computations for testing correlations between explanatory
variables (Federal Funds Rate, Inflation rate and CBOE VIX Volatility Index).
Descriptive statistics, matrix of correlations, p-values, and determination
coefficients are displayed.
Variables Inflation Federal Funds Rate VIX©
Inflation 1 0,2696 -0,6693
Federal Funds Rate 0,2696 1 -0,4515
VIX© -0,6693 -0,4515 1
Matrix of Correlation (Pearson)
The correlation is significant at a level 0,01
Variables Inflation Federal Funds Rate VIX©
Inflation 0 0,165289 0,000098
Federal Funds Rate 0,165289 0 0,015864
VIX© < 0,0001 0,015864 0
The statistic is significant at a level 0,01
P-values :
Variables Inflation Federal Funds Rate VIX©
Inflation 1 0,07270 0,44797
Federal Funds Rate 0,07270 1 0,20389
VIX© 0,44797 0,20389 1
Determination coefficients (R²) :
Statistical computations
Variable Data Missing data Minimum Maximum Mean St. Deviation
Inflation 28 0 -4,217% 2,876% 1,047% 1,408%
Federal Funds Rate 28 0 0,080% 5,260% 1,788% 2,194%
VIX© 28 0 11,03 58,60 22,72 10,19
Descriptive statistics
65
III. Regression Analysis
This final part of the thesis aims to perform the regression analysis of the commonality
liquidity with respect to the selected variables: the federal funds rate, the inflation rate and the
CBOE Volatility Index VIX. For the purposes of this analysis, the data was taken quarterly and
covers the period from January 3, 2006 to December 31, 2012. There are therefore 28
observations for each variable.
The regression model can be described as follow:
Let:
Commonality = Ci
Federal Funds Rate = EFFRi
CBOE Volatility Index VIX© = VIXi
Inflation = Ii
Given the sample (Ci, EFFRi, VIXi, Ii), with i=1,…, 28. We want to explain the values taken
by the variable Ci, called the endogenous variable, based on the values taken by the
explanatory variables: EFFRi, VIXi, Ii. The theoretical equation is therefore:
Where : α0, α1, α2, α3 are the parameters that must be estimated and ɛi is the error of the model
that describes the missing information in the linear explanations of the values of Ci with
regards to the values of EFFRi, VIXi, Ii.
Ci = α0 + α1 EFFRi + α2 VIXi + α3 Ii + ɛi, i=1,…28
66
IV. Observations, Interpretations, and Reflections
Various statistical computations have been performed in order to test the linkages
between the commonality in liquidity and other economic and financial determinants. The
results obtained are represented in appendix n°8 and the illustrations related to these
descriptions lies in appendix n°7.
Beginning with an interpretation of the correlation matrix, the correlations will only
be interpreted with regard to the commonality, since the other relationships were analyzed in
the second section of this chapter. The commonality liquidity displays the strongest correlation
with the VIX indicator. A negative linear relationship is observed with a correlation of
approximately – 65%. When the commonality increases in value, the VIX does the opposite
and falls. Regarding the inflation rate, a positive linear relationship of 39.12% is observed.
Therefore, a positive value for the commonality liquidity is connected with an increase in the
inflation rate, and a negative value with a decrease in the inflation rate. Regarding the federal
funds rate, a positive but rather weak linear relationship is observed with an order of
approximately 17%.
The multicollinearity table, which tests whether the predictor variables are
highly correlated, does not evidence problems regarding the multiple regression model used
here. The values of the variance inflation factor are all below the acceptable limit of 5 or 10.
Regarding the adjustment coefficients exhibited in the appendix, a determination
coefficient of 44.5% is seen, as well as an adjusted determination coefficient of the order of
37.55%. The determination coefficient indicates that the data are quite close with regard to the
fitted regression line, and that the model used is able to explain nearly half of the distribution
of the commonality liquidity. While studying U.S. Treasury securities, Fontaine & Garcia
(2012) performed a regression analysis of a liquidity factor with respect to economic
determinants. The authors executed the model with eight explanatory variables by using a
principal component of macroeconomic series and found a coefficient R2 of the order of 30.4%.
Adding the bid-ask spread and the VIX as explanatory variables to their initial model, the
variability of their liquidity factor could be explained by 45.2%. Examining these results, the
findings of this thesis can be considered consistent, since the number of explanatory variables
is much lower (3 vs 8 or 10 explanatory variables in the model) and this analysis is still able to
explain nearly half of the variability of the commonality liquidity. Other statistical tests, not
67
presented in this section but displayed in appendix n°8, have also been represented in the table
of adjustment coefficients.
Considering the table of analysis of variance, the Fisher test performed, and given that
a level of significance of 5% chosen, it can be concluded that there exists a relationship between
the explanatory variables and the commonality liquidity. Indeed, the Fisher statistics assess
whether the explanatory variables contribute significant information to the model, and prove
the significance of the model.
Regarding the analysis of errors of type III, the variable that appears to be the most
influential regarding the commonality liquidity is the VIX. The parameters of the model, as
well as the table of the normalized coefficient, is displayed in appendix n°7. It provides a visual
impression of the impacts of the different determinants, as well as indicating which confidence
intervals comprise the value of 0.
The equation of the model can be written as follows:
Following the statistical tables that have been described, various graphics are displayed
representing the normalized coefficients, the residuals, and normalized residuals with respect
to the commonality or predicted commonality each time in appendix n°7.
In conclusion, given the value of the R2, 45% of the variability of the dependent variable
commonality liquidity is explained by the three explanatory variables (the federal funds rate,
the inflation rate, and the CBOE Volatility Index). Examining the p-value associated with the
Fisher test in the table of analysis of variance, where a level of significance of 5% was chosen,
it can be stated that the information provided by the model is significant. Furthermore, the sum
of squares in the analysis of type III reveals that the VIX is the variable that provide the most
significant information explaining the variability of the commonality liquidity, and is therefore
the most influent determinant in this model.
Equation of the model:
C = 8,20463006118075E-02
-0,266027604504956 * I
-0,305991719303201 * EFFR
-3,25375934328454E-03 * VIX
68
Conclusion Chapter VI
The last chapter was dedicated to the selection of determinants that could
explain the commonality liquidity. The federal funds rate, the inflation rate,
and the CBOE Volatility Index were chosen.
In the second section, a model was built to test whether these explanatory
variables could explain the distribution of the commonality liquidity.
The final model, which takes the form:
allows for the explanation of 45% of the variability of the commonality
liquidity, and is considered to be significant.
Finally, the variable that appears to contribute the most significant
information to the model and therefore explains most of the variability of the
commonality liquidity is the VIX Volatility Index. An increase in the value of
the commonality liquidity in the market being driven by a decrease of the
VIX (negative correlation of 65% observed).
69
Conclusion
The importance of liquidity has been proven by many studies in financial literature and
has been emphasized with regard to its effect on bond prices. The liquidity crisis of 2008, driven
by the bankruptcy of Lehman Brothers and the difficulties of financial intermediaries proved
the tragic effect of failing to assess liquidity seizures. A better understanding of the time-series
behavior of liquidity is therefore crucial, both in order to obtain deeper insight regarding
scientific implications and also regarding the attitude of financial investors that could build
lower-priced trading strategies. Chordia, Sarkar, & Subrahmanyam (2003) suggest the
possibility of predicting liquidity by using publicly available indicators.
The literature also points out the importance of distinguishing between commonality
liquidity, which is common to all bonds, and idiosyncratic liquidity, which is specific to the
features of an asset.
Recently, Karolyi & Van Dijk (2012) studied the variations of commonality liquidity of
equity assets across time and around the world. The authors revealed a close correlation of
commonality liquidity with regard to trading activity, market volatility, and commonality
turnover. However, until now, no empirical studies have been performed regarding the study of
the determinants that could drive the commonality liquidity of U.S. corporate bonds. The reason
for this could principally lie in the challenges presented by capturing these determinants when
we are dealing with a market that is by definition illiquid in and of itself, and therefore to the
challenges it presents in identifying the correct determinants.
This thesis constitutes a first trial regarding the study of factors driving the commonality
liquidity in the U.S. corporate bond market. It discusses a selection of determinants eligible as
explanatory variables, shows the time variations of liquidity across time, and builds a model
that tests the link between commonality liquidity and the federal funds rate, the inflation rate
and the CBOE VIX Volatility Index. The results obtained reveal that the model built is
significant and could explain 45% of the variability of commonality liquidity, and that the factor
that appears to contribute the most significant information was the VIX. An increase in the
70
value of the commonality liquidity in the market being driven by a decrease in the VIX
indicator, and an increase in the federal funds rate and in the inflation rate.
Limitations and ways of improvement
Limitations in this survey exist and should be mentioned here. First, it should be noted
that computations of different liquidity measures in the corporate bond market are severely
limited by the availability of sufficient, complete, and frequent data. One limitation of this thesis
lies in the fact that it addresses rather short time period (only seven years). The conclusions
drawn by this report could be even more conclusive and significant if a long-run empirical
analysis of at least 30 years could have been performed. Furthermore, the number of bonds
analyzed should also be extended to capture more segments of the market and to provide a more
general view of commonality liquidity that would not be impacted by the choice of assets,
enabling the assessment of more dimensions of liquidity. In the case of this study, for a reason
of equipment, it was not possible to do this. It must also be noted that prior to all the conclusions
drawn by this thesis, the cleaning of the TRACE data is an important step that requires efficient
IT equipment, and how-know, as just for cleaning the year 2012, the programming code ran for
three consecutive days.
Regarding the main conclusions of this dissertation, improvements could be made at
various levels. First, the global factor extracted in order to obtain the commonality liquidity
could be computed on the basis of more liquidity measures. Adding five or six liquidity
measures to construct a final global factor that could capture a broader scope of market liquidity
could be the first site of improvement. The number of selected explanatory variables should
also be increased to eight or six explanatory variables, in order to explain a more significant
amount of variability of commonality liquidity. As has been seen, a wide variety of indicators
could be used to explain this variable. The legal framework, tax rate, employment
announcement or even the TED spread to account for the flatness of the federal funds rate the
last years, are indicators that could be added to bring more clarity to the regression model of
commonality liquidity.
I
Appendices
Appendix I: Industry sector allocation.
Appendix: Industry sector allocation
Financial Utilities Consumer, Cyclical Communications Consumer, Non-cyclical
Insurance Electric Entertainment Telecommunications Healthcare-Services
Diversified Finan Serv Gas Auto Parts&Equipment Media Agriculture
Banks Water Retail Internet Biotechnology
REITS Home Builders Advertising Pharmaceuticals
Real Estate Lodging Cosmetics/Personal Care
Auto Manufacturers Healthcare-Products
Toys/Games/Hobbies Household Products/Wares
Apparel Beverages
Textiles Food
Housewares Commercial Services
Airlines
Home Furnishings
Technology Industrial Basic Materials Energy DiversifiedSoftware Aerospace/Defense Iron/Steel Oil&Gas Holding Companies-Divers
Computers Electronics Chemicals Coal
Semiconductors Packaging&Containers Forest Products&Paper Pipelines
Office/Business Equip Machinery-Constr&Mining Mining Oil&Gas Services
Machinery-Diversified
Shipbuilding
Building Materials
Environmental Control
Transportation
Miscellaneous Manufactur
Sector Nb Companies
Financial 130
Utilities 67
Consumer, Cyclical 51
Communications 40
Consumer, Non-cyclical 57
Technology 16
Industrial 33
Basic Materials 17
Energy 35
Diversified 3
TOTAL 449
II
Appendix II: Names of the firms present in the sample.
449 Companies
Industry Sector Allocation
NAME Industry Sector Industry Group
1 AFLAC INC Financial Insurance
2 AES GENER SA Utilities Electric
3 AES CORPORATION Utilities Electric
4 AES CORP/VA Utilities Electric
5
AMC ENTERTAINMENT
INC Consumer, Cyclical Entertainment
6 AT&T INC Communications Telecommunications
7 ABBOTT LABORATORIES
Consumer, Non-
cyclical Healthcare-Products
8
ADVANCED MICRO
DEVICES Technology Semiconductors
9 AEGON NV Financial Insurance
10 VOYA HOLDINGS INC Financial Insurance
11 AETNA INC
Consumer, Non-
cyclical Healthcare-Services
12
AGILENT TECHNOLOGIES
INC Industrial Electronics
13 ALABAMA POWER CO Utilities Electric
14 ALCOA INC Basic Materials Mining
15 ORBITAL ATK INC Industrial Aerospace/Defense
16 ALLSTATE CORP Financial Insurance
17 ALLY FINANCIAL INC Financial Diversified Finan Serv
18 ALTRIA GROUP INC
Consumer, Non-
cyclical Agriculture
19 HESS CORP Energy Oil&Gas
20 AMEREN CORPORATION Utilities Electric
21
ILLINOIS PWR
GENERATING Utilities Electric
22
AMERICA MOVIL SAB DE
CV Communications Telecommunications
23
AMERICAN AXLE & MFG
INC Consumer, Cyclical Auto Parts&Equipment
24
AMERICAN EXPRESS BK
FSB Financial Banks
25 AMERICAN EXPRESS CO Financial Diversified Finan Serv
26
AMER EXPRESS CREDIT
CO Financial Diversified Finan Serv
27
AMERICAN EXPRESS
CREDIT Financial Diversified Finan Serv
III
28
AMERICAN FINANCIAL
GROUP Financial Insurance
29
SPRINGLEAF FINANCE
CORP Financial Diversified Finan Serv
30 AMERICAN INTL GROUP Financial Insurance
31 AMERICAN TOWER CORP Financial REITS
32 AMGEN INC
Consumer, Non-
cyclical Biotechnology
33
ANADARKO PETROLEUM
CORP Energy Oil&Gas
34 AON CORP Financial Insurance
35 APACHE CORP Energy Oil&Gas
36 ARCH COAL INC Energy Coal
37 ARCELORMITTAL Basic Materials Iron/Steel
38 ARCHER DANIELS
Consumer, Non-
cyclical Agriculture
39
ARCHER-DANIELS-
MIDLAND C
Consumer, Non-
cyclical Agriculture
40
ARROW ELECTRONICS
INC Industrial Electronics
41 MERITOR INC Consumer, Cyclical Auto Parts&Equipment
42 ASTRAZENECA PLC
Consumer, Non-
cyclical Pharmaceuticals
43 ATLANTIC RICHFIELD CO Energy Oil&Gas
44 AUTOZONE INC Consumer, Cyclical Retail
45 AVNET INC Industrial Electronics
46 AVON PRODUCTS INC
Consumer, Non-
cyclical Cosmetics/Personal Care
47 AXA SA Financial Insurance
48 AXIS CAPITAL HOLDINGS Financial Insurance
49 BB&T CORPORATION Financial Banks
50
BP CAPITAL MARKETS
PLC Energy Oil&Gas
51 BNP PARIBAS Financial Banks
52 BALL CORP Industrial Packaging&Containers
53
BALTIMORE GAS &
ELECTRIC Utilities Electric
54 BANK OF AMERICA CORP Financial Banks
55 BANK OF AMERICA NA Financial Banks
56 BANK OF MONTREAL Financial Banks
57
BANK OF NEW YORK
MELLON Financial Banks
58
BANK OF NY MELLON
CORP Financial Banks
59 BANK OF NOVA SCOTIA Financial Banks
60
DEUTSCHE BANK TRUST
CORP Financial Banks
IV
61 BARCLAYS BANK PLC Financial Banks
62
BAXTER INTERNATIONAL
INC
Consumer, Non-
cyclical Healthcare-Products
63 BEAZER HOMES USA Consumer, Cyclical Home Builders
64
BERKSHIRE HATHAWAY
INC Financial Insurance
65 BEST BUY CO INC Consumer, Cyclical Retail
66 BOYD GAMING CORP Consumer, Cyclical Lodging
67 BOEING CAPITAL CORP Industrial Aerospace/Defense
68 BOEING CO Industrial Aerospace/Defense
69 BOSTON PROPERTIES LP Financial REITS
70 BOSTON SCIENTIFIC CORP
Consumer, Non-
cyclical Healthcare-Products
71
BRISTOL-MYERS SQUIBB
CO
Consumer, Non-
cyclical Pharmaceuticals
72 BRITISH TELECOM PLC Communications Telecommunications
73 BURGER KING CORP Consumer, Cyclical Retail
74 CBS CORP Communications Media
75 CF INDUSTRIES INC Basic Materials Chemicals
76 CIGNA CORP
Consumer, Non-
cyclical Healthcare-Services
77 CMS ENERGY CORP Utilities Electric
78 CNA FINANCIAL CORP Financial Insurance
79 CSC HOLDINGS LLC Communications Media
80 CVS HEALTH CORP Consumer, Cyclical Retail
81 CA INC Technology Software
82
CABLEVISION SYSTEMS
CORP Communications Media
83
CANADIAN IMPERIAL
BANK Financial Banks
84
CAPITAL ONE BANK USA
NA Financial Diversified Finan Serv
85
CAPITAL ONE FINANCIAL
CO Financial Banks
86 CARDINAL HEALTH INC
Consumer, Non-
cyclical Pharmaceuticals
87
DUKE ENERGY PROGRESS
INC Utilities Electric
88
CATERPILLAR FINANCIAL
SE Industrial
Machinery-
Constr&Mining
89 CATERPILLAR INC Industrial
Machinery-
Constr&Mining
90
CELULOSA ARAUCO
CONSTITU Basic Materials Forest Products&Paper
91 CENTURYLINK INC Communications Telecommunications
92
CHESAPEAKE ENERGY
CORP Energy Oil&Gas
V
93 DUKE ENERGY OHIO INC Utilities Electric
94 CITIGROUP INC Financial Banks
95
FRONTIER
COMMUNICATIONS Communications Telecommunications
96
IHEARTCOMMUNICATION
S INC Communications Media
97
CLEAR CHANNEL
COMMUNICAT Communications Media
98
CLEVELAND ELEC
ILLUMINAT Utilities Electric
99
CLEVELAND ELECTRIC
ILLUM Utilities Electric
100 CLOROX COMPANY
Consumer, Non-
cyclical
Household
Products/Wares
101 COCA-COLA CO
Consumer, Non-
cyclical Beverages
102 COCA-COLA CO/THE
Consumer, Non-
cyclical Beverages
103 COCA-COLA ENTERPRISES
Consumer, Non-
cyclical Beverages
104 COLGATE-PALMOLIVE CO
Consumer, Non-
cyclical Cosmetics/Personal Care
105
COMCAST CABLE
COMMUNICAT Communications Media
106 COMCAST CORP Communications Media
107 COMERICA BANK Financial Banks
108
COMMONWEALTH
EDISON CO Utilities Electric
109
COMMONWEALTH
EDISON Utilities Electric
110 COMPASS BANK Financial Banks
111
COMPUTER SCIENCES
CORP Technology Computers
112 CONAGRA FOODS INC
Consumer, Non-
cyclical Food
113 CONOCOPHILLIPS Energy Oil&Gas
114
CONSOLIDATED EDISON
CO O Utilities Electric
115 CONS EDISON CO OF NY Utilities Electric
116
CONSTELLATION BRANDS
INC
Consumer, Non-
cyclical Beverages
117 RABOBANK NEDERLAND Financial Banks
118
COOPERATIEVE
RABOBANK UA Financial Banks
119 CORNING INC Industrial Electronics
120
CORRECTIONS CORP OF
AMER Financial REITS
VI
121
COSTCO WHOLESALE
CORP Consumer, Cyclical Retail
122
COUNTRYWIDE HOME
LOAN Financial Diversified Finan Serv
123
COUNTRYWIDE FINL
CORP Financial Diversified Finan Serv
124
COX COMMUNICATIONS
INC Communications Media
125
CREDIT SUISSE NEW
YORK Financial Banks
126 CREDIT SUISSE USA INC Financial Diversified Finan Serv
127
CROWN CASTLE INTL
CORP Financial REITS
128 CUMMINS INC Industrial Machinery-Diversified
129 DTE ENERGY COMPANY Utilities Electric
130 DEAN HOLDING CO
Consumer, Non-
cyclical Food
131 DEAN FOODS CO
Consumer, Non-
cyclical Food
132 MORGAN STANLEY Financial Banks
133 DELL INC Technology Computers
134
DEUTSCHE BANK AG
LONDON Financial Banks
135
DEVON ENERGY
CORPORATION Energy Oil&Gas
136
DIGITAL REALTY TRUST
LP Financial REITS
137 DILLARDS INC Consumer, Cyclical Retail
138 DISCOVER BANK Financial Banks
139
WALT DISNEY
COMPANY/THE Communications Media
140
DISCOVER FINANCIAL
SVS Financial Diversified Finan Serv
141
DISCOVERY
COMMUNICATIONS Communications Media
142 DISH DBS CORP Communications Media
143 DOLE FOOD CO
Consumer, Non-
cyclical Food
144
DOMINION RESOURCES
INC Utilities Electric
145 DOW CHEMICAL CO/THE Basic Materials Chemicals
146
E.I. DU PONT DE
NEMOURS Basic Materials Chemicals
147
DUKE ENERGY INDIANA
INC Utilities Electric
148
DUKE ENERGY
CAROLINAS Utilities Electric
VII
149
SPECTRA ENERGY
CAPITAL Energy Pipelines
150 DUKE ENERGY CORP Utilities Electric
151 DUKE REALTY LP Financial REITS
152 ERP OPERATING LP Financial REITS
153 EQT CORP Energy Oil&Gas
154 EASTMAN CHEMICAL CO Basic Materials Chemicals
155 EBAY INC Communications Internet
156 ECOPETROL SA Energy Oil&Gas
157 EDISON INTERNATIONAL Utilities Electric
158
KINDER MORGAN
INC/DELAWA Energy Pipelines
159
KINDER MORGAN ENER
PART Energy Pipelines
160
EMPRESA NACIONAL DE
ELEC Utilities Electric
161
ENDURANCE SPECIALTY
HLDG Financial Insurance
162
ENERGY TRANSFER
PARTNERS Energy Pipelines
163
ENERGY TRANSFER
EQUITY Energy Pipelines
164 ENERSIS AMERICAS SA Utilities Electric
165
ENTERPRISE PRODUCTS
OPER Energy Pipelines
166 AXA FINANCIAL INC Financial Diversified Finan Serv
167 ERICSSON LM Communications Telecommunications
168
EVEREST REINSURANCE
HLDG Financial Insurance
169
EXELON GENERATION CO
LLC Utilities Electric
170 EXELON CORP Utilities Electric
171 EXPEDIA INC Communications Internet
172
NEXTERA ENERGY
CAPITAL Utilities Electric
173
FAIRFAX FINANCIAL
HLDGS Financial Insurance
174
FIDELITY NATIONAL
INFORM Technology Software
175
FIDELITY NATL
FINANCIAL Financial Insurance
176 FIFTH THIRD BANCORP Financial Banks
177
FIRST DATA
CORPORATION Technology Software
178
FIRST HORIZON
NATIONAL Financial Banks
179 FIRST TENNESSEE BANK Financial Banks
VIII
180
FIRSTENERGY SOLUTIONS
CO Utilities Electric
181 FIRSTENERGY CORP Utilities Electric
182
FLORIDA POWER & LIGHT
CO Utilities Electric
183
DUKE ENERGY FLORIDA
LLC Utilities Electric
184 FORD MOTOR COMPANY Consumer, Cyclical Auto Manufacturers
185
FORD MOTOR CREDIT CO
LLC Consumer, Cyclical Auto Manufacturers
186 BEAM SUNTORY INC
Consumer, Non-
cyclical Beverages
187 BEAM INC
Consumer, Non-
cyclical Beverages
188 ORANGE SA Communications Telecommunications
189 FREEPORT-MCMORAN INC Basic Materials Mining
190 GFI GROUP INC Financial Diversified Finan Serv
191 GAP INC/THE Consumer, Cyclical Retail
192 GENERAL MILLS INC
Consumer, Non-
cyclical Food
193 GENON ENERGY INC Utilities Electric
194
GEORGIA POWER
COMPANY Utilities Electric
195
GOLDMAN SACHS GROUP
INC Financial Banks
196
GOODYEAR TIRE &
RUBBER Consumer, Cyclical Auto Parts&Equipment
197 GRUPO TELEVISA SAB Communications Media
198 HCA INC
Consumer, Non-
cyclical Healthcare-Services
199 HCP INC Financial REITS
200 HSBC HOLDINGS PLC Financial Banks
201 HSBC USA INC Financial Banks
202 HSBC FINANCE CORP Financial Diversified Finan Serv
203 HSBC BANK USA NA Financial Banks
204 HALLIBURTON CO Energy Oil&Gas Services
205 HARBINGER GROUP INC Diversified
Holding Companies-
Divers
206
CAESARS
ENTERTAINMENT OP Consumer, Cyclical Lodging
207
HARTFORD FINL SVCS
GRP Financial Insurance
208 HASBRO INC Consumer, Cyclical Toys/Games/Hobbies
209 WELLTOWER INC Financial REITS
210 HP INC Technology Computers
211 HEWLETT-PACKARD CO Technology Computers
212 HOME DEPOT INC Consumer, Cyclical Retail
IX
213
HONEYWELL
INTERNATIONAL Industrial Electronics
214
HORACE MANN
EDUCATORS Financial Insurance
215
HOST HOTELS & RESORTS
LP Financial REITS
216 HUMANA INC.
Consumer, Non-
cyclical Healthcare-Services
217 HUMANA INC
Consumer, Non-
cyclical Healthcare-Services
218
HUNTINGTON INGALLS
INDUS Industrial Shipbuilding
219 ISTAR FINANCIAL INC Financial REITS
220
STARWOOD HOTELS &
RESORT Consumer, Cyclical Lodging
221
INDIANA MICHIGAN
POWER Utilities Electric
222 INTEL CORP Technology Semiconductors
223 IBM CORP Technology Computers
224
ARCELORMITTAL USA
LLC Basic Materials Iron/Steel
225 INTERPUBLIC GROUP COS Communications Advertising
226 JPMORGAN CHASE & CO Financial Banks
227 JABIL CIRCUIT INC Industrial Electronics
228 JEFFERIES GROUP LLC Financial Diversified Finan Serv
229
JERSEY CENTRAL PWR &
LT Utilities Electric
230 JOHNSON & JOHNSON
Consumer, Non-
cyclical Pharmaceuticals
231 JOHNSON CONTROLS INC Consumer, Cyclical Auto Parts&Equipment
232
JP MORGAN CHASE BANK
NA Financial Banks
233 KLA-TENCOR CORP Technology Semiconductors
234 KB HOME Consumer, Cyclical Home Builders
235 KELLOGG CO
Consumer, Non-
cyclical Food
236 KERR-MCGEE CORP Energy Oil&Gas
237 KEY BANK NA Financial Banks
238 KEYCORP Financial Banks
239 KIMBERLY-CLARK CORP
Consumer, Non-
cyclical
Household
Products/Wares
240 KOHL S CORPORATION Consumer, Cyclical Retail
241 KONINKLIJKE PHILIPS NV Industrial Electronics
242
MONDELEZ
INTERNATIONAL
Consumer, Non-
cyclical Food
243 KROGER CO/THE
Consumer, Non-
cyclical Food
X
244
L-3 COMMUNICATIONS
CORP Industrial Aerospace/Defense
245 LACLEDE GAS CO Utilities Gas
246 LAFARGE SA Industrial Building Materials
247 LAZARD GROUP LLC Financial Diversified Finan Serv
248 LENNAR CORP Consumer, Cyclical Home Builders
249
LEUCADIA NATIONAL
CORP Diversified
Holding Companies-
Divers
250
LEVEL 3
COMMUNICATIONS Communications Telecommunications
251 LEVI STRAUSS & CO Consumer, Cyclical Apparel
252
LIBERTY INTERACTIVE
LLC Communications Media
253 ELI LILLY & CO
Consumer, Non-
cyclical Pharmaceuticals
254 L BRANDS INC Consumer, Cyclical Retail
255 LINCOLN NATIONAL CORP Financial Insurance
256 LLOYDS BANK PLC Financial Banks
257 LOCKHEED MARTIN CORP Industrial Aerospace/Defense
258 LOEWS CORP Financial Insurance
259 MDC HOLDINGS INC Consumer, Cyclical Home Builders
260 MGM RESORTS INTL Consumer, Cyclical Lodging
261 MACQUARIE GROUP LTD Financial Diversified Finan Serv
262 MACQUARIE BANK LTD Financial Banks
263 MARATHON OIL CORP Energy Oil&Gas
264 MARKEL CORPORATION Financial Insurance
265
MARSH & MCLENNAN
COS INC Financial Insurance
266
MARRIOTT
INTERNATIONAL Consumer, Cyclical Lodging
267
MARTIN MARIETTA
MATERIAL Industrial Building Materials
268 MASCO CORP Industrial Building Materials
269 MCDONALD S CORP Consumer, Cyclical Retail
270 MCKESSON CORP
Consumer, Non-
cyclical Pharmaceuticals
271 MERCK & CO INC
Consumer, Non-
cyclical Pharmaceuticals
272 METLIFE INC Financial Insurance
273 MICROSOFT CORP Technology Software
274
BERKSHIRE HATHAWAY
ENERG Utilities Electric
275
GENON AMERICAS GENR
LLC Utilities Electric
276
MOHAWK INDUSTRIES
INC Consumer, Cyclical Textiles
XI
277
MOLSON COORS
BREWING CO
Consumer, Non-
cyclical Beverages
278 MONSANTO CO Basic Materials Chemicals
279
MOTOROLA SOLUTIONS
INC Communications Telecommunications
280 NRG ENERGY INC Utilities Electric
281 NABORS INDUSTRIES INC Energy Oil&Gas
282 NATIONAL GRID PLC Utilities Gas
283
NATIONWIDE FINANCIAL
SER Financial Insurance
284
NEIMAN MARCUS GROUP
INC Consumer, Cyclical Retail
285
NEWELL RUBBERMAID
INC Consumer, Cyclical Housewares
286
NEWFIELD EXPLORATION
CO Energy Oil&Gas
287
21ST CENTURY FOX
AMERICA Communications Media
288
NIAGARA MOHAWK
POWER Utilities Electric
289 NISOURCE FINANCE CORP Utilities Electric
290 NOKIA OYJ Communications Telecommunications
291 NORDSTROM INC Consumer, Cyclical Retail
292
NORTHERN STATES PWR-
MINN Utilities Electric
293 NORTHERN TRUST CORP Financial Banks
294
NORTHROP GRUMMAN
CORP Industrial Aerospace/Defense
295
OCCIDENTAL PETROLEUM
COR Energy Oil&Gas
296 OHIO EDISON Utilities Electric
297 OHIO POWER COMPANY Utilities Electric
298
ONEBEACON US
HOLDINGS IN Financial Insurance
299 ORACLE CORP Technology Software
300 OWENS CORNING Industrial Building Materials
301 PECO ENERGY CO Utilities Electric
302 PHH CORP Financial Diversified Finan Serv
303 PNC FUNDING CORP Financial Banks
304 PPG INDUSTRIES INC Basic Materials Chemicals
305
TALEN ENERGY SUPPLY
LLC Utilities Electric
306 PPL ENERGY SUPPLY LLC Utilities Electric
307 PSEG POWER LLC Utilities Electric
308 PACIFIC GAS & ELECTRIC Utilities Electric
309 PACIFICORP Utilities Electric
310 PEABODY ENERGY CORP Energy Coal
XII
311 PETROLEOS MEXICANOS Energy Oil&Gas
312 PEPCO HOLDINGS LLC Utilities Electric
313 PEPSICO INC
Consumer, Non-
cyclical Beverages
314 PFIZER INC
Consumer, Non-
cyclical Pharmaceuticals
315 PHILIP MORRIS INTL INC
Consumer, Non-
cyclical Agriculture
316
PINNACLE
ENTERTAINMENT Consumer, Cyclical Entertainment
317
PIONEER NATURAL
RESOURCE Energy Oil&Gas
318 PITNEY BOWES INC Technology Office/Business Equip
319 PROGRESS ENERGY INC Utilities Electric
320 PROLOGIS Financial REITS
321 PROTECTIVE LIFE CORP Financial Insurance
322
PRUDENTIAL FINANCIAL
INC Financial Insurance
323 PUB SVC ELEC & GAS Utilities Electric
324 QUEST DIAGNOSTICS INC
Consumer, Non-
cyclical Healthcare-Services
325 RAYTHEON COMPANY Industrial Aerospace/Defense
326 REALTY INCOME CORP Financial REITS
327 REGAL CINEMAS CORP Consumer, Cyclical Entertainment
328
REGAL ENTERTAINMENT
GRP Consumer, Cyclical Entertainment
329 REGIONS BANK Financial Banks
330
REGIONS FINANCIAL
CORP Financial Banks
331
REINSURANCE GRP OF
AMER Financial Insurance
332 REPUBLIC SERVICES INC Industrial Environmental Control
333 RITE AID CORP Consumer, Cyclical Retail
334
ROGERS
COMMUNICATIONS IN Communications Telecommunications
335 ROHM & HAAS CO Basic Materials Chemicals
336 ROYAL BANK OF CANADA Financial Banks
337
ROYAL BK SCOTLND GRP
PLC Financial Banks
338
ROYAL BK OF SCOTLAND
PLC Financial Banks
339 KONINKLIJKE KPN NV Communications Telecommunications
340 RYDER SYSTEM INC Industrial Transportation
341 NAVIENT CORP Financial Diversified Finan Serv
342 SAFEWAY INC
Consumer, Non-
cyclical Food
XIII
343 ST JUDE MEDICAL INC
Consumer, Non-
cyclical Healthcare-Products
344 TRAVELERS COS INC Financial Insurance
345 SANOFI
Consumer, Non-
cyclical Pharmaceuticals
346
SANTANDER HOLDINGS
USA Financial Banks
347 CHARLES SCHWAB CORP Financial Diversified Finan Serv
348 SEACOR HOLDINGS INC Energy Oil&Gas Services
349 SEARS HOLDINGS CORP Consumer, Cyclical Retail
350
SEARS ROEBUCK
ACCEPTANCE Consumer, Cyclical Retail
351 SEMPRA ENERGY Utilities Gas
352 SHERWIN-WILLIAMS CO Basic Materials Chemicals
353
SIMON PROPERTY GROUP
LP Financial REITS
354 SOUTHERN CAL EDISON Utilities Electric
355 SOUTHERN CO Utilities Electric
356 SOUTHERN COPPER CORP Basic Materials Mining
357 SOUTHERN POWER CO Utilities Electric
358 SOUTHWEST AIRLINES CO Consumer, Cyclical Airlines
359
SOUTHWESTERN ELEC
POWER Utilities Electric
360
SOUTHWESTERN ENERGY
CO Energy Oil&Gas
361
SOUTHWESTERN PUBLIC
SERV Utilities Electric
362 SANTANDER BANK NA Financial Banks
363 SPRINT CAPITAL CORP Communications Telecommunications
364
SPRINT
COMMUNICATIONS Communications Telecommunications
365
STANCORP FINANCIAL
GROUP Financial Insurance
366 STANDARD PACIFIC CORP Consumer, Cyclical Home Builders
367 STAPLES INC Consumer, Cyclical Retail
368 STATE STREET CORP Financial Banks
369 SUNTRUST BANK Financial Banks
370 SUNTRUST BANKS INC Financial Banks
371 SUPERVALU INC
Consumer, Non-
cyclical Food
372
REPSOL OIL & GAS
CANADA Energy Oil&Gas
373 TARGET CORP Consumer, Cyclical Retail
374
TECK RESOURCES
LIMITED Basic Materials Mining
375
TENET HEALTHCARE
CORP
Consumer, Non-
cyclical Healthcare-Services
XIV
376 TEXAS INSTRUMENTS INC Technology Semiconductors
377
TEXTRON FINANCIAL
CORP Industrial
Miscellaneous
Manufactur
378 TEXTRON INC Industrial
Miscellaneous
Manufactur
379
THERMO FISHER
SCIENTIFIC
Consumer, Non-
cyclical Healthcare-Products
380 THOMSON REUTERS CORP Communications Media
381 TIME WARNER COS INC Communications Media
382 TIME WARNER INC Communications Media
383 TIME WARNER CABLE INC Communications Media
384
TOLL BROS FINANCE
CORP Consumer, Cyclical Home Builders
385 TORCHMARK CORP Financial Insurance
386
TORONTO-DOMINION
BANK Financial Banks
387 TOYS R US INC Consumer, Cyclical Retail
388
TOYOTA MOTOR CREDIT
CORP Consumer, Cyclical Auto Manufacturers
389
TRANSATLANTIC
HOLDINGS Financial Insurance
390 TRANSDIGM INC Industrial Aerospace/Defense
391 TRANSOCEAN INC Energy Oil&Gas
392
TYCO INTERNATIONAL
FINAN Industrial
Miscellaneous
Manufactur
393 TYSON FOODS INC
Consumer, Non-
cyclical Food
394 UBS AG JERSEY BRANCH Financial Banks
395 US BANCORP Financial Banks
396 USG CORP Industrial Building Materials
397 US BANK NA Financial Banks
398 US BANK NA CINCINNATI Financial Banks
399 UNION CARBIDE CORP Basic Materials Chemicals
400 UNION ELECTRIC CO Utilities Electric
401
UNITED STATES STEEL
CORP Basic Materials Iron/Steel
402
UNITED TECHNOLOGIES
CORP Industrial Aerospace/Defense
403 UNITED UTILITIES PLC Utilities Water
404
UNITEDHEALTH GROUP
INC
Consumer, Non-
cyclical Healthcare-Services
405 KEMPER CORP Financial Insurance
406 UNIVERSAL HEALTH SVCS
Consumer, Non-
cyclical Healthcare-Services
407 VALERO ENERGY CORP Energy Oil&Gas
408 VALIDUS HOLDINGS LTD Financial Insurance
XV
409
VEOLIA ENVIRONNEMENT
SA Utilities Water
410
VERIZON
COMMUNICATIONS Communications Telecommunications
411 VIACOM INC Communications Media
412
VIRGIN MEDIA FINANCE
PLC Communications Media
413
VIRGINIA ELEC & POWER
CO Utilities Electric
414 VODAFONE GROUP PLC Communications Telecommunications
415 VORNADO REALTY LP Financial REITS
416 WELLS FARGO BANK NA Financial Banks
417 WAL-MART STORES INC Consumer, Cyclical Retail
418
WASTE MANAGEMENT
INC Industrial Environmental Control
419 WELLPOINT INC
Consumer, Non-
cyclical Healthcare-Services
420 ANTHEM INC
Consumer, Non-
cyclical Healthcare-Services
421
WELLS FARGO &
COMPANY Financial Banks
422 WESTERN UNION CO/THE
Consumer, Non-
cyclical Commercial Services
423 WESTPAC BANKING CORP Financial Banks
424 WHIRLPOOL CORP Consumer, Cyclical Home Furnishings
425 WILLIAMS COS INC Energy Pipelines
426
WILLIAMS COMPANIES
INC Energy Pipelines
427 WILLIAMS PARTNERS LP Energy Pipelines
428
WILLIS TOWERS WATSON
PLC Financial Insurance
429 WEC ENERGY GROUP INC Utilities Electric
430 XLIT LTD Financial Insurance
431 XEROX CORPORATION Technology Office/Business Equip
432 YUM! BRANDS INC Consumer, Cyclical Retail
433
PACIFIC EXPLORATION
AND Energy Oil&Gas
434 SOCIETE GENERALE Financial Banks
435
CNTL AMR BOTTLING
CORP
Consumer, Non-
cyclical Beverages
436
EVERGRANDE REAL
ESTATE G Financial Real Estate
437 NOBLE GROUP LTD Diversified
Holding Companies-
Divers
438
MITSUI SUMITOMO
INSURANC Financial Insurance
439 EDP FINANCE BV Utilities Electric
440 BANCO DE BOGOTA SA Financial Banks
XVI
441
BANCO SANTANDER
CHILE Financial Banks
442
CENT ELET BRASILEIRAS
SA Utilities Electric
443 GRUPO POSADAS SAB CV Consumer, Cyclical Lodging
444 HYPERMARCAS SA
Consumer, Non-
cyclical Pharmaceuticals
445 JBS SA
Consumer, Non-
cyclical Food
446
SERVICIOS CORP JAVER
SAP Consumer, Cyclical Home Builders
447
TELEMAR NORTE LESTE
SA Communications Telecommunications
448
VOTORANTIM CIMENTOS
SA Industrial Building Materials
449
BANK OF CHINA HONG
KONG Financial Banks
XVII
Appendix II: Programming code executed for the filtering
I. Cleaning of the TRACE Data
Trace<-read.table(file=file.choose(),header=T,sep="\t",stringsAsFactors=F)
print(nrow(DTrace))
DTrace1 <- DTrace[-which(DTrace$ASCII_RPTD_VOL_TX==""),]
print(nrow(DTrace1))
DTrace2 <- DTrace1[-which(is.na(DTrace1$YLD_PT)),]
print(nrow(DTrace2))
DTrace2$ASCII_RPTD_VOL_TX[DTrace2$ASCII_RPTD_VOL_TX=="5MM+"] <-
"5000000"
DTrace2$ASCII_RPTD_VOL_TX[DTrace2$ASCII_RPTD_VOL_TX=="1MM+"] <-
"1000000"
print(nrow(DTrace2))
DTrace3<-DTrace2
if (length(which(DTrace3$ASOF_CD=="X"))!=0) {DTrace4 <- DTrace3[-
which(DTrace3$ASOF_CD=="X"),]} else {DTrace4 <- DTrace3}
print(nrow(DTrace4))
if (length(which(DTrace4$ASOF_CD=="D"))!=0) {DTrace5 <- DTrace4[-
which(DTrace4$ASOF_CD=="D"),]} else {DTrace5 <- DTrace4}
print(nrow(DTrace5))
ASOF_R <- which(DTrace5$ASOF_CD=="R")
Match_Del <-
which(DTrace5$CUSIP_ID==DTrace5$CUSIP_ID[ASOF_R[1]]&DTrace5$BOND_SYM_I
D==DTrace5$BOND_SYM_ID[ASOF_R[1]] &
DTrace5$COMPANY_SYMBOL==DTrace5$COMPANY_SYMBOL[ASOF_R[1]] &
DTrace5$TRD_EXCTN_DT==DTrace5$TRD_EXCTN_DT[ASOF_R[1]]
&DTrace5$TRD_EXCTN_TM==DTrace5$TRD_EXCTN_TM[ASOF_R[1]]
&DTrace5$ASCII_RPTD_VOL_TX==DTrace5$ASCII_RPTD_VOL_TX[ASOF_R[1]]
&DTrace5$RPTD_PR==DTrace5$RPTD_PR[ASOF_R[1]]&DTrace5$YLD_PT==DTrace5$
YLD_PT[ASOF_R[1]] & DTrace5$ASOF_CD !="A")
for (i in 2:length(ASOF_R)) {Match_Del <-
union(Match_Del,which(DTrace5$CUSIP_ID==DTrace5$CUSIP_ID[ASOF_R[i]]
&DTrace5$BOND_SYM_ID==DTrace5$BOND_SYM_ID[ASOF_R[i]]
&DTrace5$COMPANY_SYMBOL==DTrace5$COMPANY_SYMBOL[ASOF_R[i]]
&DTrace5$TRD_EXCTN_DT==DTrace5$TRD_EXCTN_DT[ASOF_R[i]]
&DTrace5$TRD_EXCTN_TM==DTrace5$TRD_EXCTN_TM[ASOF_R[i]]
&DTrace5$ASCII_RPTD_VOL_TX==DTrace5$ASCII_RPTD_VOL_TX[ASOF_R[i]]
XVIII
&DTrace5$RPTD_PR==DTrace5$RPTD_PR[ASOF_R[i]]
&DTrace5$YLD_PT==DTrace5$YLD_PT[ASOF_R[i]] & DTrace5$ASOF_CD !="A"))}
DTrace6 <- DTrace5[-Match_Del,]
print(nrow(DTrace6))
WNotNA <- which(DTrace6$TRC_ST=="W"&DTrace6$ORIG_MSG_SEQ_NB!="NA")
Diff <- vector(mode="numeric", length=length(WNotNA))
for (i in
1:length(WNotNA)){if(length(which(DTrace6$CUSIP_ID==DTrace6$CUSIP_ID[WNotNA[
i]] &DTrace6$TRC_ST=="T" &
DTrace6$TRD_EXCTN_DT==DTrace6$TRD_EXCTN_DT[WNotNA[i]] &
DTrace6$MSG_SEQ_NB==DTrace6$ORIG_MSG_SEQ_NB[WNotNA[i]]))!=0) {Diff[i] <-
which(DTrace6$CUSIP_ID==DTrace6$CUSIP_ID[WNotNA[i]] &
DTrace6$TRC_ST=="T" &
DTrace6$TRD_EXCTN_DT==DTrace6$TRD_EXCTN_DT[WNotNA[i]] &
DTrace6$MSG_SEQ_NB==DTrace6$ORIG_MSG_SEQ_NB[WNotNA[i]])} else {Diff[i] <-
0}}
LignesTSans0 <- WNotNA[Diff==0]
DTrace7 <- DTrace6[-LignesTSans0,]
print(nrow(DTrace7))
WNotNA <- which(DTrace7$TRC_ST=="W"&DTrace7$ORIG_MSG_SEQ_NB!="NA")
Diff <- vector(mode="numeric", length=length(WNotNA))
for (i in 1:length(WNotNA)){Diff[i] <-
which(DTrace7$CUSIP_ID==DTrace7$CUSIP_ID[WNotNA[i]] &
DTrace7$TRC_ST=="T" &
DTrace7$TRD_EXCTN_DT==DTrace7$TRD_EXCTN_DT[WNotNA[i]] &
DTrace7$MSG_SEQ_NB==DTrace7$ORIG_MSG_SEQ_NB[WNotNA[i]])}
DTrace8 <- DTrace7[-Diff,]
CNotNA <- which(DTrace8$TRC_ST=="C" & DTrace8$ORIG_MSG_SEQ_NB!="NA")
Diff <- vector(mode="numeric", length=length(CNotNA))
for (i in 1:length(CNotNA)) {if
(length(which(DTrace8$CUSIP_ID==DTrace8$CUSIP_ID[CNotNA[i]] &
DTrace8$TRC_ST=="T"
&DTrace8$TRD_EXCTN_DT==DTrace8$TRD_EXCTN_DT[CNotNA[i]] &
DTrace8$MSG_SEQ_NB==DTrace8$ORIG_MSG_SEQ_NB[CNotNA[i]]))!=0) {Diff[i] <-
which(DTrace8$CUSIP_ID==DTrace8$CUSIP_ID[CNotNA[i]] &DTrace8$TRC_ST=="T"
&DTrace8$TRD_EXCTN_DT==DTrace8$TRD_EXCTN_DT[CNotNA[i]] &
DTrace8$MSG_SEQ_NB==DTrace8$ORIG_MSG_SEQ_NB[CNotNA[i]])} else {Diff[i] <-
0}}
XIX
LignesTSans0 <- Diff[Diff != 0]
DTrace9 <- DTrace8[-LignesTSans0,]
C_TRC_ST <- which(DTrace9$TRC_ST=="C")
DTrace10 <- DTrace9[-C_TRC_ST,]
print(nrow(DTrace10))
write.table(DTrace10, file.choose(new=T),quote=F, row.names=F, sep="\t")
II. Check for correct cleaning and fusion of the Trace Data and Bloomberg Data
D2008<- read.table(file=file.choose(),header=T,sep="\t",stringsAsFactors=F)
length(which(D2008$ TRC_ST =="C"))
length(which(D2008$ ASOF_CD =="R"))
length(which(D2008$ ASOF_CD =="X"))
length(which(D2008$ ASOF_CD =="D"))
length(which(D2008$ASCII_RPTD_VOL_TX==""))
length(which(is.na(D2008$YLD_PT))
length(which(is.na(D2008$YLD_PT)))
length(which(is.na(D2008$ASCII_RPTD_VOL_TX=="5MM+")))
length(which(is.na(D2008$ASCII_RPTD_VOL_TX=="1MM+")))
length(unique(D2008$ CUSIP_ID))
Bloom<- read.table(file=file.choose(),header=T,sep="\t",stringsAsFactors=F,
na.strings="NA")
Z<-merge(D2008, Bloom, by=c("CUSIP_ID"), all= TRUE)
length(which(is.na(Z$ BOND_SYM_ID)))
length(which(is.na(Z$ Issue_size)))
Z<-Z[!is.na(Z$ BOND_SYM_ID),]
Z<-Z[!is.na(Z$ Issue_size),]
length(which(is.na(Z$ BOND_SYM_ID)))
length(unique(Z$ CUSIP_ID))
XX
Appendix IV: Programming code executed for the bond’s
characteristics, trading variables and liquidity measures.
III. Summary statistics of bond’s characteristics and trading variables
summary.list = function(x)list(N.with.NA.removed= length(x[!is.na(x)]),Count.of.NA=
length(x[is.na(x)]),Mean=mean(x, na.rm=TRUE), Median=median(x,
na.rm=TRUE),Max.Min=range(x, na.rm=TRUE),Range=max(x, na.rm=TRUE) -
min(x,na.rm=TRUE),Variance=var(x, na.rm=TRUE), Std.Dev=sd(x,
na.rm=TRUE),Coeff.Variation.Prcnt=sd(x, na.rm=TRUE)/mean(x, na.rm=TRUE)*100,
Std.Error=sd(x, na.rm=TRUE)/sqrt(length(x[!is.na(x)])),Quantile=quantile(x, na.rm=TRUE))
summary.list(Z$ Coupon)
summary.list(Z$ Issue_size)
summary.list(Z$ Year_Maturity)
summary.list(Z$ Num_Rating)
#################################Average Price
AvPrice<-D2008[,c(1,9)]
AvPrice<-aggregate(AvPrice$ RPTD_PR , list(AvPrice$ CUSIP_ID), mean)
summary.list(AvPrice$ x)
################################Trading Days
NB_TRD<-D2008[,c(1,4,7)]
NB_TRD$TRC_ST[NB_TRD$TRC_ST=="T"] <- 1
NB_TRD$TRC_ST[NB_TRD$TRC_ST=="W"] <- 1
NB_TRD$ TRC_ST<-as.numeric(NB_TRD$ TRC_ST)
NB_TRD3<-unique(NB_TRD)
TXX<-with(NB_TRD3,tapply(NB_TRD3$ TRC_ST,NB_TRD3$ CUSIP_ID,sum))
summary.list(TXX)
#############################Turnover ratio
D2008<- read.table(file=file.choose(),header=T,sep="\t",stringsAsFactors=F)
D2008$ TRD_EXCTN_DT<-as.Date(D2008$TRD_EXCTN_DT, "%d/%m/%Y")
D2008$Month_EXCTN_DT<-as.Date(cut(D2008$TRD_EXCTN_DT,breaks= "month"))
TurnoverTest<-aggregate(D2008$ ASCII_RPTD_VOL_TX,list(D2008$ CUSIP_ID,D2008$
Month_EXCTN_DT), sum)
CleanedTurnover<-D2008[,c(1,15)]
XXI
Test<-unique(CleanedTurnover)
names(TurnoverTest)[1]<-"CUSIP_ID"
Z<-merge(TurnoverTest, Test, by=c("CUSIP_ID"), all=TRUE)
Y<-(Z$ x / Z$ Issue_size)
Z<-cbind(Z,Y)
Z$ Y<-(Z$ Y * 100)
summary.list(Z$ Y)
############Weekly Trades
Semaine<-D2008[,c(1,4,7)]
Semaine$Week_EXCTN_DT<-as.Date(cut(Semaine$TRD_EXCTN_DT,breaks= "week"))
Semaine$TRC_ST[Semaine$TRC_ST=="T"] <- 1
Semaine$TRC_ST[Semaine$TRC_ST=="W"] <- 1
Semaine$ TRC_ST<-as.numeric(Semaine$ TRC_ST)
Semaine<-aggregate(Semaine$ TRC_ST ,list(Semaine$ CUSIP_ID,Semaine$
Week_EXCTN_DT), sum)
names(Semaine)[1]<-"CUSIP_ID"
names(Semaine)[2]<-"WEEK"
names(Semaine)[3]<-"NB_TR_W"
Semaine<-with(Test,tapply(Semaine$ NB_TR_W,Semaine$ CUSIP_ID,mean))
summary.list(Semaine)
IV. Liquidity measures
Trading Interval
DTrace <- read.table(file=file.choose(),header=T,sep="\t",stringsAsFactors=F)
DTrace11 <- DTrace[!duplicated(DTrace[,1]),]
Bonds_All <- vector(mode="numeric", length=nrow(DTrace11))
for (i in 1:nrow(DTrace11)) {Bonds_All[i] <- DTrace11$CUSIP_ID[i]}
Nb_jours <- vector(mode="numeric", length=nrow(DTrace11))
for (i in 1:nrow(DTrace11)) {CUSIP_Lignes <-
DTrace[DTrace$CUSIP_ID==DTrace11$CUSIP_ID[i],] ; Nb_jours[i] <-
length(unique(CUSIP_Lignes$TRD_EXCTN_DT))}
Tradings_Days <- data.frame(Bonds_All,Nb_jours,stringsAsFactors=FALSE)
XXII
Tradings_Days_OK <- Tradings_Days
CUSIP_Lignes_OK <- DTrace[DTrace$CUSIP_ID==Tradings_Days_OK$Bonds_All[1],]
Dates <- unique(as.Date(CUSIP_Lignes_OK$TRD_EXCTN_DT,"%d/%m/%Y"))
Dates <- Dates[order(Dates)]
Trading_interval_2 <- 0
for (i in 1:(length(Dates)-1)) {Trading_interval_2 <-
c(Trading_interval_2,as.numeric(Dates[i+1] - Dates[i]))}
Trading_interval_Frame_2 <-
data.frame("Bond_OK"=Tradings_Days_OK$Bonds_All[1],Dates,
Trading_interval_2,stringsAsFactors=FALSE)
for (j in 2:nrow(Tradings_Days_OK)) { CUSIP_Lignes_OK <-
DTrace[DTrace$CUSIP_ID==Tradings_Days_OK$Bonds_All[j],] ; Dates <-
unique(as.Date(CUSIP_Lignes_OK$TRD_EXCTN_DT,"%d/%m/%Y")) ; Dates <-
Dates[order(Dates)] ; Trading_interval_2 <- 0 ; for (i in 1:(length(Dates)-1))
{Trading_interval_2 <- c(Trading_interval_2,as.numeric(Dates[i+1] - Dates[i]))} ;
Trading_interval_Frame_2 <-
rbind.data.frame(Trading_interval_Frame_2,data.frame("Bond_OK"=Tradings_Days_OK$Bo
nds_All[j],Dates, Trading_interval_2,stringsAsFactors=FALSE))}
Trading_interval_Frame_2 <-
Trading_interval_Frame_2[!is.na(Trading_interval_Frame_2$Trading_interval_2),]
write.table(Trading_interval_Frame_2, file.choose(new=T),quote=F, row.names=F, sep="\t")
Trading_interval_Frame_2 <-
read.table(file=file.choose(),header=T,sep="\t",stringsAsFactors=F)
Trading_interval_Frame_2$ Dates <-as.Date(Trading_interval_Frame_2$Dates,"%Y-%m-
%d")
Trading_interval_Frame_2$Week_Dates<-as.Date(cut(Trading_interval_Frame_2$
Dates,breaks= "week"))
Trading_interval_Frame_2<-
Trading_interval_Frame_2[order(Trading_interval_Frame_2[,2],decreasing=T), ]
Trading_interval_Frame_2$Week_Dates<-format( Trading_interval_Frame_2$ Week_Dates,
"%W")
TI_WEEK<-aggregate( Trading_interval_Frame_2$ Trading_interval_2
,list(Trading_interval_Frame_2$ Bond_OK,Trading_interval_Frame_2$ Week_Dates), mean)
names(TI_WEEK)[1]<-"CUSIP_ID"
names(TI_WEEK)[2]<-"WEEK_OF_YEAR"
XXIII
names(TI_WEEK)[3]<-"TI_WEEKLY"
write.table(TI_WEEK, file.choose(new=T),quote=F, row.names=F, sep="\t")
IRC
DTrace <- read.table(file=file.choose(),header=T,sep="\t",stringsAsFactors=F)
DTrace11 <- DTrace[!duplicated(DTrace[,1]),]
Bonds_All <- vector(mode="numeric", length=nrow(DTrace11))
for (i in 1:nrow(DTrace11)) {Bonds_All[i] <- DTrace11$CUSIP_ID[i]}
Nb_jours <- vector(mode="numeric", length=nrow(DTrace11))
for (i in 1:nrow(DTrace11)) {CUSIP_Lignes <-
DTrace[DTrace$CUSIP_ID==DTrace11$CUSIP_ID[i],] ; Nb_jours[i] <-
length(unique(CUSIP_Lignes$TRD_EXCTN_DT))}
Tradings_Days <- data.frame(Bonds_All,Nb_jours,stringsAsFactors=FALSE)
Tradings_Days_OK <- Tradings_Days
CUSIP_Lignes_OK <- DTrace[DTrace$CUSIP_ID==Tradings_Days_OK$Bonds_All[1],]
Dates <- unique(CUSIP_Lignes_OK$TRD_EXCTN_DT)
Dates_IRC <- CUSIP_Lignes_OK[CUSIP_Lignes_OK$TRD_EXCTN_DT== Dates[1],]
Volums <- unique(Dates_IRC$ASCII_RPTD_VOL_TX)
max <- vector(mode="numeric", length=(length(Volums)))
for (i in 1:length(Volums)) {max[i] <-
max(Dates_IRC$RPTD_PR[Dates_IRC$ASCII_RPTD_VOL_TX== Volums[i]])}
min <- vector(mode="numeric", length=(length(Volums)))
for (i in 1:length(Volums)) {min[i] <-
min(Dates_IRC$RPTD_PR[Dates_IRC$ASCII_RPTD_VOL_TX== Volums[i]])}
IRC_ini <- vector(mode="numeric", length=(length(Volums)))
for (i in 1:length(Volums)) {IRC_ini[i] <- ((max[i]-min[i])/max[i])}
IRC_ini
mean(IRC_ini)
CUSIP_Lignes_OK <- DTrace[DTrace$CUSIP_ID==Tradings_Days_OK$Bonds_All[1],]
Dates <- unique(CUSIP_Lignes_OK$TRD_EXCTN_DT)
IRC <- vector(mode="numeric", length=(length(Dates)))
for (j in 1:length(Dates)) {Dates_IRC <-
CUSIP_Lignes_OK[CUSIP_Lignes_OK$TRD_EXCTN_DT== Dates[j],];Volums <-
unique(Dates_IRC$ASCII_RPTD_VOL_TX);max<-vector(mode="numeric",
XXIV
length=(length(Volums))) ; for (i in 1:length(Volums)) {max[i] <-
max(Dates_IRC$RPTD_PR[Dates_IRC$ASCII_RPTD_VOL_TX== Volums[i]])} ; min <-
vector(mode="numeric", length=(length(Volums))) ; for (i in 1:length(Volums)) {min[i] <-
min(Dates_IRC$RPTD_PR[Dates_IRC$ASCII_RPTD_VOL_TX== Volums[i]])} ; IRC_ini
<-vector(mode="numeric", length=(length(Volums))) ; for (i in 1:length(Volums))
{IRC_ini[i] <- ((max[i]-min[i])/max[i])} ; IRC[j] <- mean(IRC_ini)}
IRC_Frame_Final <- data.frame("Bond_OK"=Tradings_Days_OK$Bonds_All[1],Dates,
IRC,stringsAsFactors=FALSE)
for (m in 2:nrow(Tradings_Days_OK)) { CUSIP_Lignes_OK <-
DTrace[DTrace$CUSIP_ID==Tradings_Days_OK$Bonds_All[m],] ; Dates <-
unique(CUSIP_Lignes_OK$TRD_EXCTN_DT) ;IRC <- vector(mode="numeric",
length=(length(Dates))) ;for (j in 1:length(Dates)) {Dates_IRC <-
CUSIP_Lignes_OK[CUSIP_Lignes_OK$TRD_EXCTN_DT== Dates[j],] ; Volums<-
unique(Dates_IRC$ASCII_RPTD_VOL_TX) ; max <- vector(mode="numeric",
length=(length(Volums))) ; for (i in 1:length(Volums)) {max[i] <-
max(Dates_IRC$RPTD_PR[Dates_IRC$ASCII_RPTD_VOL_TX== Volums[i]])} ; min <-
vector(mode="numeric", length=(length(Volums))) ; for (i in 1:length(Volums)) {min[i] <-
min(Dates_IRC$RPTD_PR[Dates_IRC$ASCII_RPTD_VOL_TX== Volums[i]])} ; IRC_ini
<- vector(mode="numeric", length=(length(Volums))) ; for (i in 1:length(Volums))
{IRC_ini[i] <- ((max[i]-min[i])/max[i])};IRC[j] <- mean(IRC_ini)} ; IRC_Frame_Final <-
rbind.data.frame(IRC_Frame_Final,
data.frame("Bond_OK"=Tradings_Days_OK$Bonds_All[m],Dates,
IRC,stringsAsFactors=FALSE))}
nrow(IRC_Frame_Final)
write.table(IRC_Frame_Final, file.choose(new=T),quote=F, row.names=F, sep="\t")
DTrace <- read.table(file=file.choose(),header=T,sep="\t",stringsAsFactors=F)
IRC_DAILY<-DTrace
IRC_DAILY$ Dates<-as.Date(IRC_DAILY$ Dates, "%d/%m/%Y")
IRC_DAILY$Week_Dates<-as.Date(cut(IRC_DAILY$ Dates,breaks= "week"))
IRC_DAILY<-IRC_DAILY[order(IRC_DAILY[,2],decreasing=T), ]
IRC_WEEK<-aggregate(IRC_DAILY$ IRC ,list(IRC_DAILY$ Bond_OK,IRC_DAILY$
Week_Dates), mean)
IRC_DAILY$ Dates<-cut(IRC_DAILY$ Dates, "weeks")
IRC_DAILY$Week_Dates<-format(IRC_DAILY$ Week_Dates, "%W")
IRC_WEEK<-aggregate(IRC_DAILY$ IRC ,list(IRC_DAILY$ Bond_OK,IRC_DAILY$
Week_Dates), mean)
names(IRC_WEEK)[1]<-"CUSIP_ID"
names(IRC_WEEK)[2]<-"WEEK_OF_YEAR"
XXV
names(IRC_WEEK)[3]<-"IRC_WEEKLY"
write.table(IRC_WEEK, file.choose(new=T),quote=F, row.names=F, sep="\t")
Amihud
install.packages("chron")
library(chron)
Nbrow_Bonds_Utiles <- 0
for (i in 1:nrow(Tradings_Days_OK)) {CUSIP_Lignes_OK <-
DTrace[DTrace$CUSIP_ID==Tradings_Days_OK$Bonds_All[i],] ; Nbrow_Bonds_Utiles <-
(Nbrow_Bonds_Utiles + nrow(CUSIP_Lignes_OK))}
Nbrow_Bonds_Utiles
CUSIP_Lignes_OK <- DTrace[DTrace$CUSIP_ID==Tradings_Days_OK$Bonds_All[1],]
nrow(CUSIP_Lignes_OK)
Dates <- as.Date(CUSIP_Lignes_OK$TRD_EXCTN_DT,"%d/%m/%Y")
CUSIP_Lignes_OK_Dates <- CUSIP_Lignes_OK[order(Dates,decreasing=T),]
Dates <- unique(CUSIP_Lignes_OK_Dates$TRD_EXCTN_DT)
length(Dates)
Dates_Amih <- CUSIP_Lignes_OK_Dates[CUSIP_Lignes_OK_Dates$TRD_EXCTN_DT==
Dates[1],]
Time_Amih <- vector(mode="numeric", length=nrow(Dates_Amih))
for (i in 1:length(Time_Amih)) {Time_Amih[i] <- chron(times. = Dates_Amih
$TRD_EXCTN_TM[i])}
Dates_Time_Amih_F <- Dates_Amih[order(Time_Amih,decreasing=T),]
Nb_Returns <- nrow(Dates_Time_Amih_F)
for (j in 2:length(Dates)) {Dates_Amih <-
CUSIP_Lignes_OK_Dates[CUSIP_Lignes_OK_Dates$TRD_EXCTN_DT== Dates[j],] ;
Time_Amih <- vector(mode="numeric", length=nrow(Dates_Amih)) ;for (i in
1:length(Time_Amih)) {Time_Amih[i] <- chron(times. = Dates_Amih
$TRD_EXCTN_TM[i])} ; Dates_Time_Amih <-
Dates_Amih[order(Time_Amih,decreasing=T),] ; Dates_Time_Amih_F <-
rbind.data.frame(Dates_Time_Amih_F, Dates_Amih[order(Time_Amih,decreasing=T),]) ;
Nb_Returns <- c(Nb_Returns,nrow(Dates_Time_Amih))}
nrow(Dates_Time_Amih_F)
length(Nb_Returns)
Dates_Time_Amih_F
Dates_to_Filt_Amih <- vector(mode="numeric", length=length(Dates))
XXVI
for (i in 1:length(Dates)) {if (Nb_Returns[i] <2 ) {Dates_to_Filt_Amih[i] <- Dates[i]} else
{Dates_to_Filt_Amih[i] <- 0}}
which(Dates_to_Filt_Amih!=0)
length(which(Dates_to_Filt_Amih!=0))
Dates <- Dates[-which(Dates_to_Filt_Amih!=0)]
length(Dates)
Nb_Returns <- Nb_Returns[!(Nb_Returns < 2)] # Seuls Nb_Returns utiles.
length(Nb_Returns)
Dates_to_Filt_Amih <- Dates_to_Filt_Amih[!(Dates_to_Filt_Amih==0)] # Seules dates qui
reviennent une fois
length(Dates_to_Filt_Amih)
Dates_to_Filt_Amih[1]
Trd_Amih_Filt <- vector(mode="numeric", length=length(Dates_to_Filt_Amih))
for (i in 1:length(Dates_to_Filt_Amih)) {Trd_Amih_Filt[i] <-
which(Dates_Time_Amih_F$TRD_EXCTN_DT==Dates_to_Filt_Amih[i])}
Dates_Time_Amih_F_OK <- Dates_Time_Amih_F[-Trd_Amih_Filt,]
nrow(Dates_Time_Amih_F_OK)
if (length(which(Dates_to_Filt_Amih!=0) )!=0) { Dates <- Dates[-
which(Dates_to_Filt_Amih!=0)] ; Nb_Returns <- Nb_Returns[!(Nb_Returns < 2)] ;
Dates_to_Filt_Amih <- Dates_to_Filt_Amih[!(Dates_to_Filt_Amih==0)] ; Trd_Amih_Filt
<- vector(mode="numeric", length=length(Dates_to_Filt_Amih)) ; for (i in
1:length(Dates_to_Filt_Amih)) {Trd_Amih_Filt[i] <-
which(Dates_Time_Amih_F$TRD_EXCTN_DT==Dates_to_Filt_Amih[i])} ;
Dates_Time_Amih_F_OK <- Dates_Time_Amih_F[-Trd_Amih_Filt,] } else
{Dates_Time_Amih_F_OK <- Dates_Time_Amih_F }
Return_Vol_ini <- vector(mode="numeric", length=nrow(Dates_Time_Amih_F_OK))
for (i in 1:nrow(Dates_Time_Amih_F_OK)-1) {Return_Vol_ini[i] <-
abs((Dates_Time_Amih_F_OK$RPTD_PR[i]-
Dates_Time_Amih_F_OK$RPTD_PR[i+1])/Dates_Time_Amih_F_OK$RPTD_PR[i+1])/Dat
es_Time_Amih_F_OK$ASCII_RPTD_VOL_TX[i]}
Amih_ini <- c(Return_Vol_ini[1],Return_Vol_ini[2],Return_Vol_ini[3])
mean(Amih_ini)
—————
Position <- 0
Amih_ini <- vector(mode="numeric", length=Nb_Returns[1])
for (i in 1:Nb_Returns[1]) {Amih_ini[i] <- Return_Vol_ini[i+Position]}
XXVII
Amihud <- mean(Amih_ini)
Position <- Position + Nb_Returns[1]
Position <- 0
Amih_ini <- vector(mode="numeric", length=Nb_Returns[1])
for (i in 1:Nb_Returns[1]) {Amih_ini[i] <- Return_Vol_ini[i+Position]}
Amihud <- mean(Amih_ini)
Position <- Position + Nb_Returns[1]
for (j in 2:length(Nb_Returns)) {Amih_ini <- vector(mode="numeric", length=Nb_Returns[j])
; for (i in 1:Nb_Returns[j]) {Amih_ini[i] <- Return_Vol_ini[i+Position]} ; Amihud <-
c(Amihud, mean(Amih_ini)) ; Position <- Position + Nb_Returns[j]}
length(Amihud)
Amihu_Data_Frame <- data.frame("Bond_OK"=Tradings_Days_OK$Bonds_All[1],Dates,
Amihud,stringsAsFactors=FALSE)
—————————————————
library(chron)
CUSIP_Lignes_OK <- DTrace[DTrace$CUSIP_ID==Tradings_Days_OK$Bonds_All[1],]
Dates <- as.Date(CUSIP_Lignes_OK$TRD_EXCTN_DT,"%d/%m/%Y")
CUSIP_Lignes_OK_Dates <- CUSIP_Lignes_OK[order(Dates,decreasing=T),]
Dates <- unique(CUSIP_Lignes_OK_Dates$TRD_EXCTN_DT)
Dates_Amih <- CUSIP_Lignes_OK_Dates[CUSIP_Lignes_OK_Dates$TRD_EXCTN_DT==
Dates[1],]
Time_Amih <- vector(mode="numeric", length=nrow(Dates_Amih))
for (i in 1:length(Time_Amih)) {Time_Amih[i] <- chron(times. = Dates_Amih
$TRD_EXCTN_TM[i])}
Dates_Time_Amih_F <- Dates_Amih[order(Time_Amih,decreasing=T),]
Nb_Returns <- nrow(Dates_Time_Amih_F)
if (length(Dates) > 1) {for (j in 2:length(Dates)) {Dates_Amih <-
CUSIP_Lignes_OK_Dates[CUSIP_Lignes_OK_Dates$TRD_EXCTN_DT== Dates[j],] ;
Time_Amih <- vector(mode="numeric", length=nrow(Dates_Amih)) ;for (i in
1:length(Time_Amih)) {Time_Amih[i] <- chron(times. = Dates_Amih
$TRD_EXCTN_TM[i])} ; Dates_Time_Amih <-
Dates_Amih[order(Time_Amih,decreasing=T),] ; Dates_Time_Amih_F <-
rbind.data.frame(Dates_Time_Amih_F, Dates_Amih[order(Time_Amih,decreasing=T),]) ;
Nb_Returns <- c(Nb_Returns,nrow(Dates_Time_Amih))} ; Dates_to_Filt_Amih <-
vector(mode="numeric", length=length(Dates)) ; for (i in 1:length(Dates)) {if (Nb_Returns[i]
<2 ) {Dates_to_Filt_Amih[i] <- Dates[i]} else {Dates_to_Filt_Amih[i] <- 0}} ; if
XXVIII
(length(which(Dates_to_Filt_Amih!=0) )!=0) { Dates <- Dates[-
which(Dates_to_Filt_Amih!=0)] ; Nb_Returns <- Nb_Returns[!(Nb_Returns < 2)] ;
Dates_to_Filt_Amih <- Dates_to_Filt_Amih[!(Dates_to_Filt_Amih==0)] ; Trd_Amih_Filt
<- vector(mode="numeric", length=length(Dates_to_Filt_Amih)) ; for (i in
1:length(Dates_to_Filt_Amih)) {Trd_Amih_Filt[i] <-
which(Dates_Time_Amih_F$TRD_EXCTN_DT==Dates_to_Filt_Amih[i])} ;
Dates_Time_Amih_F_OK <- Dates_Time_Amih_F[-Trd_Amih_Filt,] } else
{Dates_Time_Amih_F_OK <- Dates_Time_Amih_F } ; if (nrow(Dates_Time_Amih_F_OK)
!=0) { Return_Vol_ini <- vector(mode="numeric", length=nrow(Dates_Time_Amih_F_OK))
; for (i in 1:nrow(Dates_Time_Amih_F_OK)-1) {Return_Vol_ini[i] <-
abs((Dates_Time_Amih_F_OK$RPTD_PR[i]-
Dates_Time_Amih_F_OK$RPTD_PR[i+1])/Dates_Time_Amih_F_OK$RPTD_PR[i+1])/Dat
es_Time_Amih_F_OK$ASCII_RPTD_VOL_TX[i]} ; Position <- 0 ; Amih_ini <-
vector(mode="numeric", length=Nb_Returns[1]) ; for (i in 1:Nb_Returns[1]) {Amih_ini[i] <-
Return_Vol_ini[i+Position]} ; Amihud <- mean(Amih_ini) ; Position <- Position +
Nb_Returns[1] ; if (length(Nb_Returns) > 1) {for (j in 2:length(Nb_Returns)) {Amih_ini <-
vector(mode="numeric", length=Nb_Returns[j]) ; for (i in 1:Nb_Returns[j]) {Amih_ini[i] <-
Return_Vol_ini[i+Position]} ; Amihud <- c(Amihud, mean(Amih_ini)) ; Position <- Position
+ Nb_Returns[j]} } ; Amihu_Data_Frame <-
data.frame("Bond_OK"=Tradings_Days_OK$Bonds_All[1],Dates,
Amihud,stringsAsFactors=FALSE)}}
#——————————
for (m in 2:nrow(Tradings_Days_OK)) {CUSIP_Lignes_OK <-
DTrace[DTrace$CUSIP_ID==Tradings_Days_OK$Bonds_All[m],] ; Dates <-
as.Date(CUSIP_Lignes_OK$TRD_EXCTN_DT,"%d/%m/%Y") ; CUSIP_Lignes_OK_Dates
<- CUSIP_Lignes_OK[order(Dates,decreasing=T),] ; Dates <-
unique(CUSIP_Lignes_OK_Dates$TRD_EXCTN_DT) ; Dates_Amih <-
CUSIP_Lignes_OK_Dates[CUSIP_Lignes_OK_Dates$TRD_EXCTN_DT== Dates[1],] ;
Time_Amih <- vector(mode="numeric", length=nrow(Dates_Amih)) ; for (i in
1:length(Time_Amih)) {Time_Amih[i] <- chron(times. = Dates_Amih
$TRD_EXCTN_TM[i])} ; Dates_Time_Amih_F <-
Dates_Amih[order(Time_Amih,decreasing=T),] ; Nb_Returns <- nrow(Dates_Time_Amih_F)
; if (length(Dates) > 1) {for (j in 2:length(Dates)) {Dates_Amih <-
CUSIP_Lignes_OK_Dates[CUSIP_Lignes_OK_Dates$TRD_EXCTN_DT== Dates[j],] ;
Time_Amih <- vector(mode="numeric", length=nrow(Dates_Amih)) ;for (i in
1:length(Time_Amih)) {Time_Amih[i] <- chron(times. = Dates_Amih
$TRD_EXCTN_TM[i])} ; Dates_Time_Amih <-
Dates_Amih[order(Time_Amih,decreasing=T),] ; Dates_Time_Amih_F <-
rbind.data.frame(Dates_Time_Amih_F, Dates_Amih[order(Time_Amih,decreasing=T),]) ;
Nb_Returns <- c(Nb_Returns,nrow(Dates_Time_Amih))} ; Dates_to_Filt_Amih <-
vector(mode="numeric", length=length(Dates)) ; for (i in 1:length(Dates)) {if (Nb_Returns[i]
<2 ) {Dates_to_Filt_Amih[i] <- Dates[i]} else {Dates_to_Filt_Amih[i] <- 0}} ; if
(length(which(Dates_to_Filt_Amih!=0) )!=0) { Dates <- Dates[-
which(Dates_to_Filt_Amih!=0)] ; Nb_Returns <- Nb_Returns[!(Nb_Returns < 2)] ;
Dates_to_Filt_Amih <- Dates_to_Filt_Amih[!(Dates_to_Filt_Amih==0)] ; Trd_Amih_Filt
<- vector(mode="numeric", length=length(Dates_to_Filt_Amih)) ; for (i in
XXIX
1:length(Dates_to_Filt_Amih)) {Trd_Amih_Filt[i] <-
which(Dates_Time_Amih_F$TRD_EXCTN_DT==Dates_to_Filt_Amih[i])} ;
Dates_Time_Amih_F_OK <- Dates_Time_Amih_F[-Trd_Amih_Filt,] } else
{Dates_Time_Amih_F_OK <- Dates_Time_Amih_F } ; if (nrow(Dates_Time_Amih_F_OK)
!=0) { Return_Vol_ini <- vector(mode="numeric", length=nrow(Dates_Time_Amih_F_OK))
; for (i in 1:nrow(Dates_Time_Amih_F_OK)-1) {Return_Vol_ini[i] <-
abs((Dates_Time_Amih_F_OK$RPTD_PR[i]-
Dates_Time_Amih_F_OK$RPTD_PR[i+1])/Dates_Time_Amih_F_OK$RPTD_PR[i+1])/Dat
es_Time_Amih_F_OK$ASCII_RPTD_VOL_TX[i]} ; Position <- 0 ; Amih_ini <-
vector(mode="numeric", length=Nb_Returns[1]) ; for (i in 1:Nb_Returns[1]) {Amih_ini[i] <-
Return_Vol_ini[i+Position]} ; Amihud <- mean(Amih_ini) ; Position <- Position +
Nb_Returns[1] ; if (length(Nb_Returns) > 1) {for (j in 2:length(Nb_Returns)) {Amih_ini <-
vector(mode="numeric", length=Nb_Returns[j]) ; for (i in 1:Nb_Returns[j]) {Amih_ini[i] <-
Return_Vol_ini[i+Position]} ; Amihud <- c(Amihud, mean(Amih_ini)) ; Position <- Position
+ Nb_Returns[j]} } ; Amihu_Data_Frame <- rbind.data.frame(Amihu_Data_Frame,
data.frame("Bond_OK"=Tradings_Days_OK$Bonds_All[m],Dates,
Amihud,stringsAsFactors=FALSE))} }}
XXX
Appendix V: Programming code for the principal component analysis
library(matrixStats)
amihud=read.table("MatriceAmihud.txt")
amihud_data=t(amihud[2:nrow(amihud),2:ncol(amihud)])
amihud_data_temp=amihud_data
amihud_data_temp[amihud_data_temp==0] <- NA
mean_amihud=apply(amihud_data_temp,2, mean, na.rm = TRUE)
sd_amihud=apply(amihud_data_temp, 2, sd, na.rm = TRUE)
mean_amihud_vec=array(mean_amihud,c(1,ncol(amihud_data_temp)))
sd_amihud_vec=array(sd_amihud,c(1,ncol(amihud_data_temp)))
mean_amihud_mat=matrix(mean_amihud_vec,nrow = nrow(amihud_data_temp),
ncol=ncol(amihud_data_temp), byrow = TRUE)
sd_amihud_mat=matrix(sd_amihud_vec,nrow = nrow(amihud_data_temp),
ncol=ncol(amihud_data_temp), byrow = TRUE)
L_amihud_temp= (amihud_data_temp - mean_amihud_mat)/sd_amihud_mat
L_amihud<-L_amihud_temp
L_amihud<-replace(L_amihud, is.na(L_amihud), 0)
amihud_pc=apca(L_amihud,3)
factors_amihud=amihud_pc$factors
# regression on 1st PC
r_square_1PC=array(0,c(1,ncol(L_amihud)))
adj_r_square_1PC=array(0,c(1,ncol(L_amihud)))
for (i in 1:ncol(L_amihud)) {if (length(na.omit(L_amihud_temp[,i]))>=100)
{reg_temp=lm(L_amihud_temp[,i] ~ factors_amihud[,1] - 1, na.action=na.omit)
r_square_1PC[1,i]=summary(reg_temp)$r.squared
adj_r_square_1PC[1,i]=summary(reg_temp)$adj.r.squared}
else{r_square_1PC[1,i]=NAadj_r_square_1PC[1,i]=NA}}
mean_r_square_1PC=mean(r_square_1PC,na.rm = TRUE)
mean_adj_r_square_1PC=mean(adj_r_square_1PC, na.rm = TRUE)
# regression on first 2 PC
r_square_2PC=array(0,c(1,ncol(L_amihud)))
adj_r_square_2PC=array(0,c(1,ncol(L_amihud)))
XXXI
for (i in 1:ncol(L_amihud)) {if (length(na.omit(L_amihud_temp[,i]))>=100)
{reg_temp=lm(L_amihud_temp[,i] ~ factors_amihud[,1:2] - 1,
na.action=na.omit)r_square_2PC[1,i]=summary(reg_temp)$r.squaredadj_r_square_2PC[1,i]=
summary(reg_temp)$adj.r.squared} else{r_square_2PC[1,i]=NA
adj_r_square_2PC[1,i]=NA}}
mean_r_square_2PC=mean(r_square_2PC,na.rm = TRUE)
mean_adj_r_square_2PC=mean(adj_r_square_2PC, na.rm = TRUE)
# regression on first 3 PC
r_square_3PC=array(0,c(1,ncol(L_amihud)))
adj_r_square_3PC=array(0,c(1,ncol(L_amihud)))
for (i in 1:ncol(L_amihud)) {if (length(na.omit(L_amihud_temp[,i]))>=100)
{reg_temp=lm(L_amihud_temp[,i] ~ factors_amihud[,1:3] - 1, na.action=na.omit)
r_square_3PC[1,i]=summary(reg_temp)$r.squared
adj_r_square_3PC[1,i]=summary(reg_temp)$adj.r.squared} else{r_square_3PC[1,i]=NA
adj_r_square_3PC[1,i]=NA}}
mean_r_square_3PC=mean(r_square_3PC,na.rm = TRUE)
mean_adj_r_square_3PC=mean(adj_r_square_3PC, na.rm = TRUE)
res_amihud=rbind(c(mean_r_square_1PC,mean_r_square_2PC,mean_r_square_3PC),c(mean
_adj_r_square_1PC,mean_adj_r_square_2PC,mean_adj_r_square_3PC))
write.table(L_amihud, file=file.choose(), row.names=FALSE, col.names=FALSE)
write.table(L_amihud_temp, file=file.choose(), row.names=FALSE, col.names=FALSE)
############IRC
library(matrixStats)
irc=read.table("IRCFillOOK.txt")
irc_data=t(irc[2:nrow(irc),2:ncol(irc)])
irc_data_temp=irc_data
irc_data_temp[irc_data_temp==0] <- NA
mean_irc=apply(irc_data_temp,2, mean, na.rm = TRUE)
sd_irc=apply(irc_data_temp, 2, sd, na.rm = TRUE)
mean_irc_vec=array(mean_irc,c(1,ncol(irc_data_temp)))
sd_irc_vec=array(sd_irc,c(1,ncol(irc_data_temp)))
mean_irc_mat=matrix(mean_irc_vec,nrow = nrow(irc_data_temp), ncol=ncol(irc_data_temp),
byrow = TRUE)
XXXII
sd_irc_mat=matrix(sd_irc_vec,nrow = nrow(irc_data_temp), ncol=ncol(irc_data_temp),
byrow = TRUE)
L_irc_temp= (irc_data_temp - mean_irc_mat)/sd_irc_mat
L_irc<-L_irc_temp
L_irc<-replace(L_irc, is.na(L_irc), 0)
irc_pc=apca(L_irc,3)
factors_irc=irc_pc$factors
# regression on 1st PC
r_square_1PC=array(0,c(1,ncol(L_irc)))
adj_r_square_1PC=array(0,c(1,ncol(L_irc)))
for (i in 1:ncol(L_irc)) { if (length(na.omit(L_irc_temp[,i]))>=100) {
reg_temp=lm(L_irc_temp[,i] ~ factors_irc[,1] - 1,
na.action=na.omit)r_square_1PC[1,i]=summary(reg_temp)$r.squared
adj_r_square_1PC[1,i]=summary(reg_temp)$adj.r.squared} else{r_square_1PC[1,i]=NA
adj_r_square_1PC[1,i]=NA}}
mean_r_square_1PC=mean(r_square_1PC,na.rm = TRUE)
mean_adj_r_square_1PC=mean(adj_r_square_1PC, na.rm = TRUE)
# regression on first 2 PC
r_square_2PC=array(0,c(1,ncol(L_irc)))
adj_r_square_2PC=array(0,c(1,ncol(L_irc)))
for (i in 1:ncol(L_irc)) {if (length(na.omit(L_irc_temp[,i]))>=100)
{reg_temp=lm(L_irc_temp[,i] ~ factors_irc[,1:2] - 1,
na.action=na.omit)r_square_2PC[1,i]=summary(reg_temp)$r.squared
adj_r_square_2PC[1,i]=summary(reg_temp)$adj.r.squared} else{r_square_2PC[1,i]=NA
adj_r_square_2PC[1,i]=NA}}
mean_r_square_2PC=mean(r_square_2PC,na.rm = TRUE)
mean_adj_r_square_2PC=mean(adj_r_square_2PC, na.rm = TRUE)
# regression on first 3 PC
r_square_3PC=array(0,c(1,ncol(L_irc)))
adj_r_square_3PC=array(0,c(1,ncol(L_irc)))
for (i in 1:ncol(L_irc)) {if (length(na.omit(L_irc_temp[,i]))>=100)
{reg_temp=lm(L_irc_temp[,i] ~ factors_irc[,1:3] - 1,
na.action=na.omit)r_square_3PC[1,i]=summary(reg_temp)$r.squaredadj_r_square_3PC[1,i]=
summary(reg_temp)$adj.r.squared} else{r_square_3PC[1,i]=NA
adj_r_square_3PC[1,i]=NA}}
mean_r_square_3PC=mean(r_square_3PC,na.rm = TRUE)
XXXIII
mean_adj_r_square_3PC=mean(adj_r_square_3PC, na.rm = TRUE)
res_irc=rbind(c(mean_r_square_1PC,mean_r_square_2PC,mean_r_square_3PC),c(mean_adj_
r_square_1PC,mean_adj_r_square_2PC,mean_adj_r_square_3PC))
write.table(L_irc, file=file.choose(), row.names=FALSE, col.names=FALSE)
write.table(L_irc_temp, file=file.choose(), row.names=FALSE, col.names=FALSE)
#################Trading interval
library(matrixStats)
tifusion=read.table("TIFusion.txt")
tifusion_data=t(tifusion[2:nrow(tifusion),2:ncol(tifusion)])
tifusion_data_temp=tifusion_data
tifusion_data_temp[tifusion_data_temp==0] <- NA
mean_tifusion=apply(tifusion_data_temp,2, mean, na.rm = TRUE)
sd_tifusion=apply(tifusion_data_temp, 2, sd, na.rm = TRUE)
mean_tifusion_vec=array(mean_tifusion,c(1,ncol(tifusion_data_temp)))
sd_tifusion_vec=array(sd_tifusion,c(1,ncol(tifusion_data_temp)))
mean_tifusion_mat=matrix(mean_tifusion_vec,nrow = nrow(tifusion_data_temp),
ncol=ncol(tifusion_data_temp), byrow = TRUE)
sd_tifusion_mat=matrix(sd_tifusion_vec,nrow = nrow(tifusion_data_temp),
ncol=ncol(tifusion_data_temp), byrow = TRUE)
L_tifusion_temp= (tifusion_data_temp - mean_tifusion_mat)/sd_tifusion_mat
L_tifusion<-L_tifusion_temp
L_tifusion<-replace(L_tifusion, is.na(L_tifusion), 0)
tifusion_pc=apca(L_tifusion,3)
factors_tifusion=tifusion_pc$factors
# regression on 1st PC
r_square_1PC=array(0,c(1,ncol(L_tifusion)))
adj_r_square_1PC=array(0,c(1,ncol(L_tifusion)))
for (i in 1:ncol(L_tifusion)) {if (length(na.omit(L_tifusion_temp[,i]))>=100)
{reg_temp=lm(L_tifusion_temp[,i] ~ factors_tifusion[,1] - 1, na.action=na.omit)
r_square_1PC[1,i]=summary(reg_temp)$r.squaredadj_r_square_1PC[1,i]=summary(reg_temp
)$adj.r.squared} else{r_square_1PC[1,i]=NA adj_r_square_1PC[1,i]=NA}}
mean_r_square_1PC=mean(r_square_1PC,na.rm = TRUE)
mean_adj_r_square_1PC=mean(adj_r_square_1PC, na.rm = TRUE)
XXXIV
# regression on first 2 PC
r_square_2PC=array(0,c(1,ncol(L_tifusion)))
adj_r_square_2PC=array(0,c(1,ncol(L_tifusion)))
for (i in 1:ncol(L_tifusion)) { if (length(na.omit(L_tifusion_temp[,i]))>=100) {
reg_temp=lm(L_tifusion_temp[,i] ~ factors_tifusion[,1:2] - 1, na.action=na.omit)
r_square_2PC[1,i]=summary(reg_temp)$r.squared
adj_r_square_2PC[1,i]=summary(reg_temp)$adj.r.squared} else{r_square_2PC[1,i]=NA
adj_r_square_2PC[1,i]=NA}}
mean_r_square_2PC=mean(r_square_2PC,na.rm = TRUE)
mean_adj_r_square_2PC=mean(adj_r_square_2PC, na.rm = TRUE)
# regression on first 3 PC
r_square_3PC=array(0,c(1,ncol(L_tifusion)))
adj_r_square_3PC=array(0,c(1,ncol(L_tifusion)))
for (i in 1:ncol(L_tifusion)) { if (length(na.omit(L_tifusion_temp[,i]))>=100)
{reg_temp=lm(L_tifusion_temp[,i] ~ factors_tifusion[,1:3] - 1,
na.action=na.omit)r_square_3PC[1,i]=summary(reg_temp)$r.squared
adj_r_square_3PC[1,i]=summary(reg_temp)$adj.r.squared} else{r_square_3PC[1,i]=NA
adj_r_square_3PC[1,i]=NA}}
mean_r_square_3PC=mean(r_square_3PC,na.rm = TRUE)
mean_adj_r_square_3PC=mean(adj_r_square_3PC, na.rm = TRUE)
res_tifusion=rbind(c(mean_r_square_1PC,mean_r_square_2PC,mean_r_square_3PC),c(mean
_adj_r_square_1PC,mean_adj_r_square_2PC,mean_adj_r_square_3PC))
write.table(L_tifusion, file=file.choose() row.names=FALSE, col.names=FALSE)
write.table(L_tifusion_temp, file=file.choose() row.names=FALSE, col.names=FALSE)
#########Global factors
library(matrixStats)
L_amihud=read.table ("L_amihud.txt")
L_tif= read.table ("L_tif.txt")
L_irc= read.table ("L_irc.txt")
L_glob=cbind(L_amihud,L_tif,L_irc)
global_pc=apca(L_glob,3)
factors_global=global_pc$factors
write.table(factors_global, file="global_factors.txt", row.names=FALSE, col.names=FALSE)
XXXV
Appendix VI: Scatter plots showing pairwise relations between
determinants
Scatter plots
Statistical dispersions between each explanatory variable during the period
2006-2012.
XXXVI
Appendix VII: Scatter plots showing pairwise relations between
determinants
XXXVII
Appendix VIII: Regression Analysis
Statistical computations
Variable Observations Minimum Maximum Mean SD
Commonality 28 -0,09958 0,09560231 -0,000125 0,04253
Inflation 28 -4,22% 2,88% 1,05% 1,41%
Federal Funds Rate 28 0,08% 5,26% 1,79% 2,19%
VIX© 28 11,03 58,6 22,7175 10,19031516
Descriptive Statistics
Variables Inflation Federal Funds Rate VIX© Commonality
Inflation 1 0,2696 -0,6693 0,3912
Federal
Funds Rate 0,2696 1 -0,4515 0,1704
VIX© -0,6693 -0,4515 1 -0,6494
Commonality 0,3912 0,1704 -0,6494 1
Matrix of Correlation (Pearson)
The correlation is significant at a level 0,01
Inflation
Federal
Funds Rate VIX©
Tolerance 0,5507 0,7942 0,4728
VIF 1,8159 1,2592 2,1151
Multicollinearity statistics
XXXVIII
Observations 28
Sum of weights 28
DF Degrees of freedom 24
R² Determination coefficient 0,4449
R² adjusted Adjusted determination coefficient 0,3755
MCE Mean square of errors 0,0011
RMCE Square root of MCE 0,0336
MAPE Mean Absolute Percentage Error 173,0273
DW Durbin Watson Coefficient 0,7641
Cp Coefficient Cp Mallow 4
AIC Akaike's Information Criterion -186,3213
SBC Schwarz's Bayesian Criterion -180,9925
PC Amemiya's Prediction Criterion 0,7401
Press
Indicate the sensitivity of the model to
the presence or absence of some
observations 0,04063
Q² Q2-test statistic 0,16813
Regression of the variable Commonality
Adjustement coefficients (Commonality)
Source DF
Sum of
squares
Mean of
squares F Pr > F
Model 3 0,0217 0,0072 6,4121 0,0024
Error 24 0,0271 0,0011
Total
corrected 27 0,0488
Computed against the model Y=Mean(Y)
Analysis of the variance ( Commonality)
Source DF
Sum of
squares
Mean
of
squar F Pr > F
Inflation 1 0,0075 0,0075 6,6158 0,0167
Federal
Funds Rate 1 0,0002 0,0002 0,1969 0,6612
VIX© 1 0,0140 0,0140 12,4236 0,0017
Analysis of Type I Sum of Squares (Commonality) :
XXXIX
Source DF
Sum of
squares
Mean of
squares F Pr > F
Inflation 1 0,0002 0,0002 0,1846 0,6712
Federal
Funds Rate 1 0,0010 0,0010 0,8554 0,3642
VIX© 1 0,0140 0,0140 12,4236 0,0017
Analysis Type III Sum of Squares (Commonality) :
Source Value Standard Error t Pr > |t|
Lower
bound
(95%)
Upper
bound
(95%)
Inflation -0,0881 0,2049 -0,4297 0,6712 -0,5110 0,3349
Federal
Funds Rate -0,1578 0,1707 -0,9249 0,3642 -0,5100 0,1944
VIX© -0,7796 0,2212 -3,5247 0,0017 -1,2361 -0,3231
Normalized coefficient (Commonality)
Source Value Standard Error t Pr > |t|
Lower
bound
(95%)
Upper
bound
(95%)
Constant 0,0820 0,0288 2,8512 0,0088 0,0227 0,1414
Inflation -0,2660 0,6191 -0,4297 0,6712 -1,5438 1,0117
Federal
Funds Rate -0,3060 0,3308 -0,9249 0,3642 -0,9888 0,3768
VIX© -0,0033 0,0009 -3,5247 0,0017 -0,0052 -0,0013
Parameters of the model (Commonality) :
Statistical computations for the regression analysis which encompasses the descriptive
statistics, the matrix of correlation (Pearson), the multicollinearity statistics, the
adjustment coefficients, the analysis of the variance, the analysis of type I, the analysis
of type III, the parameters of the model, and the table of normalized coefficients.
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Table of contents
Acknowledgments ................................................................................................................................. 3
Thesis overview ...................................................................................................................................... 5
List of figures ......................................................................................................................................... 7
List of tables ........................................................................................................................................... 8
List of abbreviations ............................................................................................................................. 9
Introduction ........................................................................................................................................... 1
A. Problem Statement .................................................................................................................... 1
B. Thesis Structure......................................................................................................................... 2
C. Methodology .............................................................................................................................. 2
Chapter I Definition and Investigations of Main Concepts .............................................................. 4
A. Liquidity ..................................................................................................................................... 4
B. Liquidity in the Corporate Bond Market................................................................................ 6
C. Measures of Bonds Liquidity ................................................................................................... 8
I. Bond Characteristics as Liquidity Proxies .......................................................................... 9
II. Trading Activity Variables as Liquidity Proxies ............................................................ 9
III. Alternative Liquidity Measures ..................................................................................... 10
D. Commonality Liquidity........................................................................................................... 14
E. Determinants of Commonality Liquidity ................................................................................. 16
Chapter II Theoretical Investigations ............................................................................................... 23
A. Relevant Literature Survey .................................................................................................... 23
Chapter III Empirical Research ....................................................................................................... 28
A. Data Initial Presentation ......................................................................................................... 28
B. DATA BLOOMBERG ............................................................................................................ 29
C. Data TRACE and Cleaning Method ...................................................................................... 33
Chapter IV Empirical Study - Liquidity Computations ................................................................. 37
A. Corporate Bonds Characteristics and Trading Activities ................................................... 37
B. Liquidity Measures: Results and Evolution Across Time ................................................... 41
I. Imputed Roundtrip Costs ........................................................................................................... 41
II. Amihud Measure ...................................................................................................................... 42
III. Trading Interval ....................................................................................................................... 42
IV.Preliminary Results .................................................................................................................. 43
C. Correlation Matrix of Pearson ............................................................................................... 47
Chapter V Empirical Study - Liquidity Decomposition ................................................................. 49
I. Methodology: Korajczyk & Sadka (2008) ............................................................................. 49
II. Results and Interpretation .................................................................................................. 53
Chapter VI Empirical Study – Determinants of Commonality Liquidity ..................................... 57
I. Selection of Potential Determinants of Commonality. ......................................................... 57
A. Federal Funds Rate ................................................................................................................ 57
B. Inflation Rate ......................................................................................................................... 59
C. CBOE Volatility Index: VIX ................................................................................................. 61
II. Relationships between the Explanatory Variables ........................................................... 62
III. Regression Analysis ............................................................................................................. 65
IV. Observations, Interpretations, and Reflections ................................................................ 66
Conclusion ............................................................................................................................................ 69
Limitations and ways of improvement .............................................................................................. 70
Appendices .............................................................................................................................................. I
Appendix I: Industry sector allocation. ............................................................................................ I
Appendix II: Names of the firms present in the sample. ............................................................... II
Appendix II: Programming code executed for the filtering ...................................................... XVII
Appendix IV: Programming code executed for the bond’s characteristics, trading variables
and liquidity measures. ................................................................................................................... XX
Appendix V: Programming code for the principal component analysis .................................. XXX
Appendix VI: Scatter plots showing pairwise relations between determinants .................... XXXV
Appendix VII: Scatter plots showing pairwise relations between determinants .................. XXXVI
Appendix VIII: Regression Analysis ....................................................................................... XXXVII
Bibliography ...................................................................................................................................... - 1 -
Table of contents ............................................................................................................................... - 7 -
Executive summary ........................................................................................................................... - 9 -
Executive summary
The Great Depression in 1930 and the subprime mortgage financial crisis of 2008 are
considered to be the most important financial market turbulence periods of the last century. The
main consequences of the 2008 financial crisis were the bankruptcy of Lehman Brothers,
difficulties of many financial intermediaries, an intensification of the liquidity crisis, and a
strong repercussion in the financial market-place where a global “crash” of asset prices was
observed. Particularly, the corporate bond market was affected by this crisis. These periods of
stress have highlighted the importance of market liquidity and especially the need of being able
to capture and understand its dimensions.
The corporate bond market is less liquid than the equity market due to the general
framework in which it evolved, low price transparency, the paramount presence of institutional
investors and the variety of bonds that could be designed for a single firm. For these reasons, it
is quite challenging to capture liquidity components in the corporate bond market, and this has
lead recent scientific literature to focus mainly on studies of liquidity exclusively on the equity
market.
The purpose of this thesis is to study the determinants of commonality liquidity (the
component of total liquidity shared by all bonds) in the corporate bond market. The first part of
this thesis performs a survey of relevant literature, defines the most important concepts, and
investigates potential economic and financial explanatory indicators that could drive
commonality liquidity. The empirical research executed used TRACE data of daily transactions
of 2,059 bonds covering the period 2006-2012. Prior to any analysis, a cleaning of the data was
performed, and a computation of various liquidity measures (Amihud, imputed roundtrip costs
and trading interval) was carried out. Weekly time-series liquidity measures for each of the
2,059 bonds were obtained after this step. Then, a principal component analysis was used to
extract global factors in order to obtain the commonality liquidity.
Finally, a regression model tested the relationship of the obtained commonality liquidity
with respect to three selected determinants: the federal funds rate, the inflation rate and the
Chicago Board Options Exchange Volatility Index (CBOE VIX). The final results conclude
that the constructed model could explain 45% of the total variability of the commonality
liquidity and that the CBOE VIX indicator is the explanatory variable that can provide the most
significant information.