The credit spread puzzle

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Chapter 3 aims to explain and discuss the analytical technique used in the empirical study. In subchapter 3.2 bond selection method is presented that is followed by data collection and time series. Further, the present chapter introduces the statistical model that is adapted for analysing the data and presents hypotheses that are tested. In the end, the set of selected variables (systematic and idiosyncratic) will be described.

Study design

Kothari (2004) describes that research is an academic activity that aims to examine a research problem by formulating a question that will be analysed and answered by applying scientific methods. According to Kothari, colleting, analysing, evaluating the data and discussing the process implications is one of the most decisive steps.
To achieve the purpose of the study, to evaluate explanatory variables, this paper will conduct a quantitative research. According to Creswell (2014), quantitative research approach allows authors to test various theories by developing a study where the main objective is to examine the relationship among variables. Creswell (2014) explains that a quantitative approach is characterized by studying existing literature, developing hypotheses, collecting data for analysis and analysis of the results using a statistical procedure. This process is supported by Bax (2013) who states that a quantitative research approach aims to collect data which subsequently can be statistically tested. Additionally, the quantitative research approach can be perceived as a confirmatory method, meaning that researchers construct hypotheses with regard to previous literature that are tested by employing collected data, and through empirical tests a researcher decides whether to accept or reject the models using statistical rules (Johnson and Christensen, 2012).
As previously mentioned in Chapter 2, most of the literature conducted on this topic is mainly supported by the U.S. bond market data. This study will focus on Eurobond market and since the literature regarding the credit spread determinants on Eurobond market is limited, this paper will contribute to further expanding the research by testing the significance of explanatory variables. Thus, a deductive approach will allow to meet the objectives of this thesis. According to Saunders, Lewis and Thornhill (2009) a deductive framework includes developing a model about a topic, and subsequently testing the performance of the framework using empirical tests.
To use a quantitative approach and to make a generalized conclusion regarding a population that is based on a random sample, one is obliged to have strict control of variables and employ correct statistical approaches (Newman & Benz, 1998). Moreover, existing literature that examines credit spread determinants has also used a deductive approach to test predetermined hypotheses and to evaluate the performance of the models (Castagnetti and Rossi, 2011; Darwin et. al., 2012; Chen et. al., 2014).

Selection of bonds

For bonds to qualify in this study the following criterions were used to create a suitable sample. The first criteria applied to sort over 700,000.00 available bonds across the whole world was maturity, all bonds must have five years to maturity from the day they were issued. Maturity criterion narrowed the number of bonds remarkably, but it further had to be decreased. The next requirement to additionally narrow the sample was currency. Since this study will focus on Eurobond market, all bonds must be denominated in euro. After these two criterions, samples were still unspecified as it included bonds that were issued on a country level. To exclude bonds that were issued on individual country market, Eurobond market was selected as the main market. Since this study is testing the significance of credit spreads determinants from investors perspective, the next criterion applied was to only include corporate bonds classified as “note or bond’. Moreover, one of the more important criterion that was used to further scale down the number of bonds is that all bonds are required to have a yield in order to calculate the credit spread.
The last and the most important criterion adapted in this study was bond grade. All qualified bonds are following S&P Long-term Issue Credit Rating and Moody’s Long-term Issue credit rating. Long-term issue credit rating is used for all bonds that have a maturity longer than one year, and short term rating scale is used for bonds that have a maturity between one and 13 months (Emery, 2016, pp. 1- 10). The rating scale for both agencies can be seen in Appendix 1. This thesis will focus on two samples of which one sample will consist of lower-medium investment grade bonds BBB+ to BBB- for S&P and Baa1 to Baa3 for Moddy’s, while the second sample will include all non-investment grade bonds. For S&P this would imply all bonds bellow BBB- and for Moody’s all bonds bellow Baa3. Since two rating scales are used, it is enough for a bond to be graded as a lower-medium investment grade bond on one scale to be included in the lower-medium investment grade bond sample, the same principle applies to non-investment grade bond sample.
Conclusion, the following criterions are used:
Denominated in euro
Bond market
Corporate bonds classified as Note and Bond
Must have a yield
Bond grade
Furthermore, I want to emphasize that bond rating acquired for each bond is obtained at one point in time. All ratings, of which the samples are based on, are the latest available rating information for each company published by Moody’s and S&P. Due to limited historical data availability about companies, constant rating is assumed in this paper. This implies that all firms in the sample are presumed to have the same rating throughout the period of which this paper will examine. Previous studies conducted on credit spread choose different approaches of how to handle this problem. Some researchers choose to collect data from bond indices depending on which credit rating they are incorporating in their sample (Krainer, 2004; Castagnetti and Rossi, 2013; Chen et. al 2015), while other researches choose to focus on one point in time (Huang & Huang, 2002). The reason why second approach is adapted in the paper is because I am working with two idiosyncratic and two systematic variables and the acquired credit spread must be firm individual. Additionally, companies that have several issued bonds during the predetermined period were only included once in the sample with one specific bond. No specific criteria is applied when deciding which bond of the several issued to include in the sample. Both samples were created chronologically with starting date in 2012 followed by 2013 and 2014.
In total, the lower medium investment grade bonds issued in 2012, 2013 and 2014 make up a sample of 47 bonds issued by 47 different companies, while the non-investment grade bonds sample consists of 21 individual bonds and companies. For a more detailed view of which bonds are included in the sample, both lower-medium investment grade bonds and non-investment grade bonds, see Appendix 2.

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Time series

Bonds that are employed in this paper have a maturity of five years. Gemmill and Keswani (2011) claim that all independent variables will prove to be significant if time length is too long. Therefore, in this paper will examine bonds on daily basis from 2012 till the end of 2016. Hibbert et. al. (2011) document that more informative results are obtained if time series are daily instead of monthly or weekly.
The oldest bonds that are included in the sample size are issued in 2012 and will mature during 2017, while the newest bonds are issued in 2014 with a maturity date set in 2019. The first 180 days of the bonds’ life span are used to calculate the independent variable’s value, while the remaining days till the end on 2016 are used to study the relationship between the independent and dependent variables. What is important to notice is that the period for each bond will differentiate depending on when the bond was issued, which consequently will lead to an unbalanced panel-data set.

Data collection

Techniques and methods for collecting data are crucial part of the research paper as well as research process. As this study is conducted using quantitative approach, this paper relies on secondary data sources which are well-known and used worldwide. According to Johnson and Christensen (2012) secondary data is defined as the data that have been collected, recorded and stored by other people whose purposes is different in comparison to the purpose of the current study.
The required data regarding the bonds issued on Eurobond market was collected from Thomson Reuters Eikon, while the inflation values and the risk-free interest rate five years to maturity were obtained from the European Central Bank (ECB) and Eurostat online database. Additionally, the bonds’ bid yield and stock price for each company was extracted from Thomson Reuters Eikon.
After the data was collected, each bond was individually analysed and sorted because two different databases were used which caused implications with dates and missing values. Dates that had missing values were excluded from the time series and only those dates that had all values available for each day were included and used. In total, calculating each date individually for each bond, the panel data set for lower-medium investment grade bonds consists of 31,807 days and for non-investment grade bonds 11,851 days.

Statistical model

Since the two samples consist of several companies which are measured over a predetermined period, the data acquired for analysing the credit spread had to be sorted and structured in a panel data structure. According to Greene (2010) there are two types of panel data, unbalanced and balanced panel. The balanced panel structure is made up of n-sets of observations for each unit that require that all units in the sample are observed same number of times. The unbalanced panel data set occurs when one or several units are observed unequal amount of times compared to the other observations because the obtained data for each unit is unique and is consequently missing values. Compared to the structural models, panel data models are more flexible in terms of choosing different variables and implementing into the model. Also, panel data models allow researchers to study the significance of explanatory variables as well as their impact on credit spreads and their contribution. Structural models’ framework is already preadjusted and to implement new variables into the model would require new model calibrations.
Fortin-Rittberger (2014) describes the panel data structure through two dimensions’ – cross section and time. The author emphasises the importance of time and that all incorporated variables can be followed over a predetermined period. Repeating the observations for all companies in the sample will automatically create a panel data set because values are observed and sorted according to time and firms. The advantages of panel data structure, following asymptotic theory, is if T (time) is held constant, N (observations) could grow to infinity (N → ∞). Given the assumption that N can grow unlimited allow researchers to study the cross-sectional changes over time and unit that vary among the companies but not over time. The occurring changes in explanatory variables can be assessed in detail and more precise results can be obtained. Further, the cross-sectional times series panel data enables researchers to work with a large amount of data that consequently increases the degrees of freedom and enriches the sample size with information as well as reduces the collinearity between independent variables and improves the efficiency (Hsiao, 2003, p. 3). However according to Greene (2010), despite the advantages of panel data, there are few disadvantages from statistical point of view such as heteroscedasticity, autocorrelation and cross correlation. These implications can be examined and controlled by using a proper statistical model. Grenne (2010) describes what characteristics a well-behaved panel data should possess:
Linearity:= 1 1 + 2 2+. . . + +
Full rank: All explanatory variables are equally observed, n*K sample data matrix
Explanatory variables are uncorrelated with unobservable effect:
[ | 1, 2,…., ] = 0
Homoscedasticity and non-autocorrelation
What is crucial to understand is that these characteristics are theory-based and in practice several of the guidelines will be violated, because the data acquired is different and does not follow any rules.
The panel data capabilities have given researchers a tremendous analytical leverage of moving from two-dimensional analyses to three-dimensional analyses where both time and cross-sectional changes are captured simultaneously.
As seen from Figure 3.4a, the two-dimensional object (a) allow only for single analyses of cross-sectional data with the explanatory variables, and object (b) analyses the explanatory variables through time, while object (c) is three dimensional and accounts for all three parameters (variable, time and units). An extract from the panel data set created for this paper can be seen in Appendix 3.
To perform the statistical analyses and to study the panel data set, this paper will adapt a fixed effect model. For a more detailed explanation of how we arrive to the fixed effect model, see Appendix 4.
The fixed effect model (FE) is primly adapted with the panel data regression and is a method that enables for casual statistical inference (Brüderl and Ludwig 2014). What is characteristic for FE model is that the individual-specific unobservable effect is a random variable that is correlated with independent variables (Schmidheiny, 2016; Allison, 2009, pp. 7 – 27). This is also the most important assumption regarding the model and if the assumption does not hold, another statistical model must be applied. In this paper, the panel data meets the assumption which allow to use FE model. Schimdheiny (2016) describes that the fixed effect model measures the variation in data only over time and that invariant independent variables drop out. Advantages of the FE model is that the model delivers consistent estimates and accounts as well as solves for the omitted variables bias. Disadvantages are that the FE model drops out time invariant repressors, if there are any, and since each unit in the panel data set counts as one group the sample will experience loss of information due to the less degrees of freedom (Brüderl and Ludwig 2014).

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1 Introduction
1.1 What is credit spread?
1.2 Problem
1.3 Purpose
1.4 Delimitation
1.5 Structure of the study
2 Frame of references
2.1 The credit spread puzzle
2.2 Credit spread determinants
2.3 Brief overview of structural models
2.4 Empirical findings from structural models
3 Methodology
3.1 Study design
3.2 Selection of bonds
3.3 Statistical model
3.4 Statistical software
3.5 Variables
3.6 Research validity and replicability
4 Empirical findings
4.1 Lower-medium investment grade bonds
4.2 Non-investment grade bonds
5 Analysis
5.1 Lower-medium investment grade bonds
5.2 Non-investment grade bonds
5.3 Comparison of lower-medium and non-investment grade bonds
6 Conclusion
7 Discussion

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