http://lib.ulg.ac.be http://matheo.ulg.ac.be

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,

6

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)).

7

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

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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)

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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.