An empirical study on explaining the changes in the CDS
spreads – an interaction between the credit and equity markets
by Delikostas Ioannis
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An empirical study on explaining the changes in the CDS
spreads – an interaction between the credit and equity markets
THESIS MSC FINANCE
FACULTY OF ECONOMICS AND BUSINESS UNIVERSITY OF GRONINGEN
by Delikostas Ioannis1 (Student Nr. S-2850702)
Abstract
This study investigates the determinants of the CDS spread changes for European and US financial and non-financial firms for the period 2008-2014. The results suggest a link between the equity and the credit market. I use firm-specific variables, equity and credit systematic factors to examine the variation of the changes in the CDS spreads. Interestingly, I document a significant relation between the equity-market wide liquidity factor and the CDS spreads changes. I point out a different response to the equity systematic factors of the European and financials compared to US and non-financials. Despite the significant interaction between the common factors and the CDS spreads changes, the addition of systematic factors leads to a minor increase in the explanatory power of the model.
JEL classification: G12, G13
Keywords: CDS spreads, Merton model, corporate bonds, credit and equity markets Supervisor: Dr.Richard Klijnstra
Co-assessor: Dr. Peter Smid
1 Correspondence: ioannisdelikostas@gmail.com
4 Table of Contents
1. Introduction ... 5
2. Theoretical Research Framework ... 7
2.1 Merton model ... 7
2.2 Literature review and hypotheses development ... 8
3. Analytical Research Design ... 13
3.1 Data ... 13
3.2 The theoretical determinants of the CDS spreads changes ... 13
3.3 Descriptive Statistics ... 17 4. Empirical Analysis ... 22 4.1 Regression models ... 22 4.2 Methodology ... 23 5. Regression Results ... 26 6. Robustness Analysis ... 31
6.1 Ηeteroskedasticity and autocorrelation ... 31
6.2 Entity, time and random effects ... 32
6.3 Financials vs. non- financials ... 33
6.4 European vs. US firms ... 37
7. Conclusion ... 39
8. References ... 41
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1. Introduction
Credit risk is defined as the probability of loss due to a borrower’s or counterparty’s inability to meet its obligations under the predetermined contractual terms. An important part of the credit market are the credit derivatives and mainly the single name credit default swaps. The credit default swap (henceforth CDS) is a contract that provides credit protection against the default risk of an underlying firm (it is usually expressed as the reference entity). The CDS buyer makes a frequent payment to the CDS seller till the contract expiration date or the credit event. In case of a credit event the CDS buyer has the right to sell the underlying bonds to the CDS seller who is obliged to buy them for their notional-face value.
In the present study, I focus mainly on credit risk (in terms of CDS spread) but I should notice the distinction between CDS spreads and bond yield spreads. Ericsson et al. (2009) suggest two main advantages of using CDS spreads. First, the estimation of the CDS spreads does not require the selection and the estimation of the risk-free rate. The scholars’ opinion is dichotomous regarding the appropriate risk-free rate. Secondly, the CDS spread is a better indicator of credit risk than bond yield spreads. The corporate bond yield spreads might give distorted results due to the significant influence of the liquidity on the bond market and the taxation benefits of the bond instruments. I make use of single name 5 year CDS spreads for both EU and US firms for the period between January 2008 and January 2014. There are two benefits by using CDS instruments. Firstly, the have the same maturity and hence any maturity adjustments are not necessary and secondly, the CDS markets is more liquid than the bond market.
The purpose of this study is to explain the CDS spreads changes using firm-specific and systematic factors from both the equity and credit markets. Firstly, I evaluate the ability of the theoretical determinants (firm-specific variables) of the structural default models on explaining the CDS spread changes. It should be noticed that I do not perform a structural model to assess the model’s ability to estimate the CDS spreads. Instead, I carry out a cross sectional regression analysis to study how well firm-specific variables suggested by Merton (1974) structural- default risk model explain the CDS spread changes. To summarize, I focus on the variables of the Merton model and not in the model itself.
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CDS spreads changes. Overall, the ultimate purpose is to investigate a potential interaction between the credit and equity markets with regards to the changes of CDS spreads.
The main findings of the study are as follows. First, the theoretical determinants (firm-specific variables) based on the Merton model (1974) have significant effect (excl. leverage) on the CDS spread changes. Second, I find a strong relation of the implied market volatility and the excess credit return factor with the changes in the CDS spreads. Third, the results suggest a negative significant effect of the equity market-wide liquidity on the CDS spread changes. Finally, I find significant evidence of the Fama and French (1993) factors on determining the changes in CDS spreads. Overall, the study shows a significant interaction between credit and equity markets on the determination of the CDS spreads changes.
The results of this paper provide additional insights to the existing literature, important facts for the academic community and the practitioners in the credit market. The study contributes to the existing literature by examining the influence of equity market factors on credit markets, by focusing on the changes on CDS spreads. Galil et al. (2014) investigate the explanatory power of both firm-specific and equity systematic factors (Fama and French, Pastor and Stambaugh) on the CDS spreads changes for US companies and argue that their study is the first that examines the link between the these factors and the CDS spreads changes. This study contributes to existing literature by examining these relations for both US and European firms, includes the excess credit return and the equity market wide-liquidity factors.
The results show a significant interaction between the equity and the credit markets with many implications. The subsequent empirical studies on the equity market should take into account the credit market factors to enhance their model and their results. However, the addition of the systematic factors leads to a minor increase in the explanatory power of the model. Finally, the practitioners in the equity market should consider that developments in the credit market may have significant impact on their equity portfolio.
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2. Theoretical Research Framework
2.1
Merton model
Merton (1974) introduces the first structural default-risk model and develops a theoretical model that associates the default event with the value of the company’s assets. Merton (1974) supports that the default occurs when the firm value is lower than the market value of the outstanding liabilities. In that case, there is a transfer of ownership from shareholders to creditors. According to Merton’ s framework, the debt holders hold a long position in a riskless zero-coupon bond and a short position in a European put option on the assets of the firm sold to the shareholders. The strike price is equal to the firm par value of the outstanding risky liabilities. The key inputs to the Merton model are the market value of equity, the implied equity volatility, the level of the risk-free interest rate and the face value of the firm’s total debt. Merton (1974) uses the options pricing to estimate the value and the volatility of firm’s assets. Having estimated the assets’ value and volatility, Merton calculates the implied spread of the risky bonds over the risk-free rate and the implied distance to default. The distance to default (DD) is the difference between the computed implied value of the assets and the par debt value. It is usually measured as the number of standard deviations that firm value has to change in order to reach the default threshold. Figure 1 depicts an illustration of Merton model and the distance to default.
Figure 1:Merton (1974) model- the distance-to-default
Source: Morgan Stanley
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structural models for the valuation of corporate bonds and the estimation of the bond credit spreads. However, the theoretical determinants of the Merton model apply similarly to the credit default swap spreads. Both the bonds and the credit default swaps provide regular payments to the creditor and the CDS seller, respectively. Ericsson et al. (2009) argue that at the time of the credit event, bonds worth a fraction of the principal amount. At the same time, the CDS seller has to make a payment to the CDS buyer that is equal to the market value of the defaulted bond of the underlying reference entity; that is, both the bond holder and the CDS seller realize approximately the same loss(in market value terms and excluding settlement risk). Therefore, by computing the risk-neutral probability of default using the Merton model, it is easy to implement the CDS spread (the present value of the Expected Default Loss, where the Expected Default Loss is the product of the default probability and the Loss Given Default) and estimate the implied CDS spread. However, this approach is quite simplified. Nowadays, there are different kind of default events that might not trigger the CDS payment. Intuitively, it is logical to expect that the theoretical variables of the bonds spreads on the structural default model will have similar effect on the CDS spreads.
Overall, the theoretical variables of the structural models are expected to have similar relation and explanatory power to the changes of the CDS spreads as the bond spreads.
2.2
Literature review and hypotheses development
The academic community was firstly involved on explaining the link between bond and equity markets, while the subsequent development of complex financial instruments led the researchers to examine the relationship between the credit derivatives (mainly credit default swaps), bond and equity markets2. There is vast amount of existing literature that investigates this relationship using both indices and data on individual firms. The general outcome is the lead-lag relationship between the CDS spreads, corporate bond spreads and equity returns; in particular equity market leads the CDS and bond market but this is not the scope of this paper.
The study examines the link between credit and equity markets from the perspective of the structural form models. In line with Merton (1974), I extend the basic
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model by using the equity returns, firm-specific and systematic factors from both markets to analyze the determinants of the changes in CDS spreads.
Empirical studies on the link between credit and equity markets investigate mainly the existence of any lead-lag relationships or co-movements. Fung et al. (2008) and Norden and Weber (2009) use CDS and market indices to study the interaction between U.S. stock and CDS market and document that the stock market leads the CDS market. Furthermore, they provide additional information in favor to the existing literature that negative equity returns reflects higher probability of default and as a result higher CDS spreads; that is, they document an interaction between equity and credit markets. Breitenfellner and Wagner (2012) use the equity returns as a proxy (assets volatility it is not easily observable) to investigate the impact of changes in company value on the changes of CDS spreads. Di Cesare and Guazzarotti (2010), Galil et al. (2014) and Alexopoulou et al. (2009) study the determinants of the CDS spread changes in individual firm level using both firm and market-specific variables and present a negative relationship between stock returns and changes in CDS spreads.
Literature on the structural credit risk models has examined whether the theoretical variables proposed by Merton (1974) can explain the credit risk component of spreads. The academic community focuses mainly on the leverage and the put options implied volatility.
In Merton model (1974), leverage is one of the theoretical components on determining the probability of default. Higher level of leverage increases the possibility a firm to reach the default threshold; that is, higher level of leverage implies higher CDS spreads. Ericsson et al. (2009) and Galil et al. (2013) document that leverage has significant positive effect on the level and changes on CDS spreads for US firms. Similarly, Alexopoulou et al. (2009) use a large panel of European firms and show that the positive relation between leverage and changes on CDS premia holds.
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Wagner (2012) using indices test empirically and point out a positive relation between the changes in the implied equity volatility and the changes on the CDS spreads.
Given these empirical findings I construct the following hypothesis:
(H1): Negative equity returns are associated with positive changes on CDS spreads, while positive changes on financial leverage and implied equity volatility exhibit a positive relation with CDS spreads changes.
Building on the existent empirical and theoretical literature on structural form models, Colling-Dufresne et al. (2001) employ individual financial, macroeconomic and liquidity factors to explain the link between bond and equity markets. In particular they study whether systematic factors in equity market determine credit spreads and enhance the explanatory power of their model. The work of Colling-Dufresne et al. (2001) was quite pioneering. To the best of my knowledge this study was one of the first which formalized the idea that equity market factors might influence the determination of credit spreads.
Apart from company-specific variables, common factors might determine the changes on CDS spreads. Galil et al. (2014), Alexopoulou (2009) and Di Cesare and Guazzarotti (2010) document that market implied volatility exhibit positive relation to changes on CDS spreads. They use the market implied volatility as a proxy of the macroeconomic environment and a forward looking measure of market risk. Furthermore, Fama and French (1993) investigate the determinants of equity returns using factors from stock and bond markets. They argue that a shift in economic conditions lead to higher default probabilities. They show that a credit risk premium exists in equity and bond returns. Campbell and Taksler (2003) indicate the importance of a systematic credit risk premium factor to enhance their model reliability regarding the determinants of corporate spreads. The excess credit return factor is constructed as the difference between the monthly returns of the long term corporate bonds minus the monthly returns of the long term government bonds with similar characteristics. A negative change of credit risk premium implies smaller spread between corporate and government bonds, negative returns in the bond markets, less systematic credit risk and thus lower CDS spreads.
The second hypothesis delves more deeply into the determination of changes in CDS spreads and appraise the following:
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Despite the vast amount of empirical literature on the determinants of CDS spreads, the academic community hasn’t managed to construct a model that takes into account all necessary factors from different markets and yields strong explanatory power. As stated before, scholars tried to evaluate a potential interaction between the equity and credit markets to boost the model explanatory power. Colling-Dufresne et al. (2001) included the Fama and French equity returns systematic factors to explain the determinants of the bond credit spreads and show a negative relation between the factors and the bond credit spreads. In like manner, Avramov et al. (2007) examines the determinants of bonds credit spread changes by using the Fama and French factors and present a significant negative effect on the changes of the credit spreads, explaining approximately 26% of the variation. The two latter studies support that additional equity systematic factors explain the changes in the credit market.
Turning to the determinants of the CDS spreads changes, Galil et al. (2014) focus on the determinants of the CDS spread changes by using the Fama and French factors and document a negative impact on the CDS spreads changes. The economic intuition of that significant relation follows. The HML (portfolio returns of firms with high book-to-market minus low book-to-market ratio), the SMB (portfolio returns of firms with low market cap minus high market cap) and the EXMKT (returns of the market portfolio minus the risk-free rate) can be seen as additional systematic factors, that implies additional exposure to systematic risk and leads the investors to require additional returns for this additional exposure. Firms with low book-to-market ratio have higher expected profitability, thus lower default probability and lower CDS spreads. Firms with low market cap are usually smaller firms with high growth potential and higher risk than firms with high market cap, which implies higher probability of default and hence higher CDS spreads.
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of the CDS spreads, examine the explanatory power of the equity market-wide liquidity factor to determine the changes on the CDS spreads and show a strong negative correlation between the equity market liquidity (measured by the Pastor and Stambaugh factor) and the CDS spreads. Finally, the importance of the financial instruments’ liquidity has been noticed in many empirical studies, which present a significant relation between the pricing and the individual instrument liquidity.
Given the evidence concerning the impact of the systematic factors on the CDS spreads I propose the following hypothesis:
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3. Analytical Research Design
3.1
Data
The sample is an unbalanced cross-section panel data with CDS quotes of 49 US and 49 European entities, denominated in US dollars and Euro respectively. The selected companies are publicly-traded and part of the Dow Jones and the Euro Stoxx. The dataset contains monthly data from January 2008 to January 2014. The CDS market is characterized by two particularities concerning the maturity and the debt seniority. In this study, I focus on 5-year single name CDS (which are usually liquid enough) that require the underlying bond instrument to be classified as senior unsecured debt. The data for CDS spreads was obtained by Thomson Reuters Datastream.
Datastream contains CDS spreads for different types of ISDA agreements, but I use the full restructuring (FR) and the modified restructuring (MR) clauses. Under the definition of full restructuring, there are no limitations on the maturity of the deliverable bonds after a restructuring/default event by the reference entity. On the other hand, modified restructuring imposes restrictions on the maturity of deliverable debt obligations and introduces a new feature that is related to the classification of the credit events that can trigger default/restructuring events. The selection procedure between these two contracts was the following: initially I search the CDS spreads under modified restructuring for each entity separately due to their high popularity in US and European credit markets; in case of non-available CDS spreads under modified restructuring I choose the CDS spreads contracts with full restructuring agreement3. Finally, it should be noticed that all variables were converted in US Dollars with the respective exchange conversion rate.
3.2
The theoretical determinants of the CDS spreads changes
Consistent with previous literature, this study was inspired by Merton (1974) original structural default- risk model, which models the firm assets and liabilities by focusing on specific events that may trigger default (default is triggered whenever the debt value is higher than the assets value). The inputs of the model are the equity returns, implied equity volatility and liabilities (based on the balance sheet). The
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intuition behind lies on the fact that the estimation of implied asset value and volatility leads to the estimation of distance to default (default probability). After determining the default probability, the CDS spread estimation follows. A reliable estimation of probability of default requires careful evaluation of as much as possible information that may affect the default risk pricing based on a structural model.
In line with Alexopoulou et al. (2009) and Galil et al. (2014), I separate the explanatory variables into two different categories (firm-level variables and common risk factors). In the subsequent section I describe their relation to the probability of default and the CDS spreads.
i. Equity returns (EQR)
The original Merton’s structural model approaches debt as a put option on the firm value. In addition, as the company value is not direct observable and I examine the changes on CDS spreads, I use the equity returns as a proxy for changes in the value of the assets. Higher equity prices decrease the leverage, increase the firm value and enhance the ability of the company to repay its debt obligations. I obtain the monthly stock returns from Thomson Reuters Datastream (data type “P”); that is, the structural credit-risk models imply a negative relation between equity returns and CDS spreads.
ii. Implied equity volatility (EQIMPV)
In theoretical structural default-risk models, changes in implied options volatility imply often changes in the firm value volatility. A decrease in the equity volatility leads usually to lower asset volatility, thus lower likelihood of reaching the default threshold, lower probability of default and thereby lower CDS spread. I chose the implied equity volatility due to its strong explanatory power of credit default swaps spreads (Campbell and Taksler, 2003). I collect the implied volatility for put options for each firm from Thomson Reuters Datastream (data type “O1”); a positive relation between implied option volatility and CDS spread is expected.
iii. Leverage (LEV)
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the data for both the total debt4 (data type “WC03255”) and the market value of equity5 (data type “MV”) from Thomson Reuters Datastream.
iv. Implied market volatility (MKTIMPV)
Market implied volatility is usually a good proxy of the general macroeconomic environment in the short-term. I obtain the implied market volatility from Thomson Reuters Datastream. I get the market implied volatility from stock index options prices on Euro Stoxx 50 (data type “VSTOXXI”) and on S&P 500 (data type “CBOEVIX”), for European and US firms respectively. Low market volatility implies better economic environment, higher growth opportunities and therefore I expect a positive relation between the implied market volatility and the CDS spreads.
v. Fama and French factors ( EXMKT, SMB, HML)
Fama and French three factor model consists of EXMKT (the excess return of the market and is estimated as the difference between the market return and the one month Treasury rate), SMB (portfolio returns of small market capitalization minus portfolio returns of large market capitalization) and HML (portfolio returns of firms with high book-to-market ratio minus portfolio returns with low book-to-market ratio). SMB and HML estimate the excess returns on long/short portfolios of small caps and value stocks. F&F model supports that both SMB and HML can be seen as additional systematic risk proxies and thereby investors need to receive higher returns. Fama and French (1993) believe in the “efficient market hypothesis”. Companies with low book-to-market (high market value of equity) are healthier than firms with high book-to-market ratio (low-market value of equity). Low book-to-market implies stronger future profitability and thus lower probability of default. In addition, firms with low market capitalization tend to be riskier than mature firms with large market capitalization. Therefore, low F&F factors imply worse economic environment (lower equity value) and higher CDS spreads. A negative sign is expected between the CDS spread and the F&F factors. The data gathering (monthly F&F factors) was done from the website of the Wharton Research Data Services (WRDS).
vi. Pastor and Stambaugh liquidity factor (LIQ)
Following Galil et al. (2014), I adopt the Pastor and Stambaugh (2003) innovations in aggregate market liquidity factor to take into account the impact of the market-wide liquidity on the equity returns. This particular factor, known as “liquidity beta” relies on the idea that each stock has different level of sensitivity on the market liquidity. It is constructed by regressing the stock excess returns on the lagged-stock excess returns and the sign of the lagged return multiplied by the lagged-dollar volume 𝑅𝑡𝑖 = 𝑐 +
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𝛽 ∗ 𝑅𝑡−1𝑖 + 𝛿 ∗ 𝑠𝑖𝑔𝑛𝑡−1𝑖 ∗ 𝜔𝑡−1𝑖 + 𝜀𝑡𝑖. The coefficient δ is a proxy for the individual stock liquidity that takes into account the lagged “order flow”. If there is a large buy order for an illiquid stock, the price will increase temporarily and is expected to revert the next day to the previous levels. Pastor and Stambaugh (2003) argue that the lower is the reversal for a dollar volume the higher is the stock liquidity. They estimate the market-wide liquidity as an average of the estimated coefficients of the individual stock liquidity. For the estimation of the liquidity factor, they create the delta of the stock liquidity coefficient 𝛥𝛿𝑡 and weight each coefficient by the market total dollar value 𝑚𝑡, so that 𝛥𝛿𝑡 = (𝛿𝑡− 𝛿𝑡−1) ∗ (𝑚𝑡 /𝑚1). The innovation in the market liquidity is created by regressing the difference 𝛥𝛿𝑡 against the lagged difference 𝛥𝛿𝑡−1 and the lagged value of the weighted coefficient (𝑚𝑡 /𝑚1)* 𝛿𝑡−1 so that 𝛥𝛿𝑡 = 𝛼 + 𝜗 ∗ 𝛥𝛿𝑡−1+ 𝜇 ∗ (𝑚𝑡 /𝑚1)* 𝛿𝑡−1+ 𝜖𝑡. The “liquidity factor” is then calculated as 𝜆𝑡 = 𝜖 100⁄ . The stocks with low liquidity beta is expected to have small co-movements with low liquidity factor. The basic intuition is whether equity returns include any systematic liquidity and stocks with higher exposure to the liquidity factors earn higher returns. In the framework of structural models, there is no direct link between the stock liquidity premium and the firm asset volatility, but I am accounting for the specific factor due to a potential integration between the credit and equity markets. Furthermore, as stated before I use the equity returns as a proxy for the assets volatility and therefore it is necessary to include a factor that accounts for the liquidity effect on the stock prices. According to Galil et al. (2014), the most likely scenario would be to find a negative relation between the stock market liquidity and CDS market. I collect the data from the website of the Wharton Research Data Services (WRDS).
vii. Credit risk factor (CRDEF)
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Statictics Mean Median Min. Max. St. Dev Skewness Kurtosis
Panel A Dependent Variables CDS spread 127.8 85.05 14.32 11,374 254.4 24.8 873.1 ΔlogCDS spread - 0.001 - 0.007 - 1.405 1.157 0.186 0.475 6.838 Independent Variables EQR 0.001 0.009 - 1.112 0.803 0.100 - 0.986 13.27 ΔlogEQIMPV - 0.005 - 0.018 - 4.593 4.431 0.241 0.246 43.46 ΔlogLEV 0.001 - 0.007 - 1.678 1.872 0.129 0.666 32.664 ΔlogMKTIMPV - 0.005 - 0.030 - 0.538 0.656 0.198 0.604 4.029 EXMKT 0.009 0.017 - 0.172 0.114 0.051 - 0.756 4.012 HML - 0.000 - 0.000 - 0.099 0.076 0.026 - 0.393 5.358 SMB 0.004 0.003 - 0.042 0.058 0.022 0.165 2.683 LIQ 0.005 0.007 - 0.228 0.133 0.060 - 1.303 6.741 CRDEF 0.109 0.350 - 5.401 2.814 1.316 - 1.258 6.674 Nr. of Obs 6323 6323 6323 6323 6323 6323 6323
Mean St. Dev Min. Max. Mean St. Dev Min. Max.
Panel B CDS spread 122.3 91.23 19.05 1076 133.9 355.9 14.3 11,374 ΔlogCDS spread 0.005 0.191 -0.808 1.157 - 0.007 0.179 - 1.405 1.070 EQR -0.003 0.098 -0.734 0.517 0.005 0.103 - 1.112 0.803 ΔlogEQIMPV -0.003 0.222 -1.277 1.436 - 0.006 0.261 - 4.593 4.431 ΔlogLEV 0.002 0.133 -1.678 1.872 - 0.001 0.124 - 1.080 1.385 ΔlogMKTIMPV -0.004 0.174 -0.358 0.621 - 0.007 0.221 - 0.538 0.656 Nr. of Obs 3312 3312 3312 3312 3011 3011 3011 3011
European Firms US firms
3.3
Descriptive Statistics
The summary statistics of both the independent and dependent variables is reported in Table 1. The sample consist of 98 firms during the time period 2008-2014. Before turning to the statistics analysis, I perform the Augmented Dickey-Fuller (1981) for each variable to examine the stationarity through the existence of unit root. From financial point of view, it is important to know whether a series is stationary or non-stationary. I estimate the ADF-test for both the level and the first-difference. The results indicate the absence of unit root for all variables at 5% significance level. As it was expected, the use of changes (logarithmic transformation) in variables eliminate any potential presence of non-stationarity.
Table 1:Descriptive Statistics
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Table 1 presents the descriptive statistics. Panel A demonstrates details about the mean, standard deviation, minimum, maximum, skewness and kurtosis for the whole sample, while Panel B display the same information but the sample is divided to two categories based on the geographical region that each company belongs. The 5-year CDS spreads have a sample mean of 127.8bps with a standard deviation of 254.40bps, where the average mean is lower and the standard deviation is higher than Galil et al. (2014) who reports a 196.02bps and 187.59bps respectively. The monthly average change of the CDS spread is -0.01% bps with quite low standard deviation of 0.186bps, while the monthly mean return amounts to 0.1%. Similarly to the reported results of Alexopoulou et al. (2009) and Di Cesare and Guazzarotti (2010), who examine the co-movement of CDS and bond market and the determinants of CDS spreads respectively, the percentage change of the firm-specific put-option implied volatility exhibits a mean of roughly -0.5% and standard deviation of 24.1bps. In like manner, the sample presents a particularity which is also common in the studies mentioned above. There are extreme differences between the minimum and the maximum values. Galil et al. (2014) support that the most probable reason is the underlying impact of the financial crisis on both equity and credit market. The financial crisis led to an increase of CDS spread while the equity prices exhibited a negative trend. Due to the fact that this study examines the period between 2008 and 2014, the sample is affected by the financial crisis.
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Mean St. Dev Mean St. Dev Mean St. Dev Mean St. Dev Mean St. Dev
Panel A Basic Materials 5 81.09 66.70 0.001 0.174 0.005 0.100 - 0.004 0.201 - 0.002 0.127 Consumer Goods 17 141.5 560.3 - 0.005 0.164 0.006 0.086 - 0.005 0.210 - 0.004 0.139 Consumer Services 9 145.0 188.0 - 0.010 0.158 0.009 0.084 - 0.006 0.193 - 0.009 0.136 Financials 22 169.2 110.7 0.004 0.220 - 0.004 0.142 - 0.004 0.252 - 0.000 0.159 Health Care 5 48.45 18.29 - 0.008 0.148 0.009 0.056 - 0.006 0.209 - 0.002 0.080 Industrials 13 90.15 54.59 - 0.003 0.184 0.006 0.093 - 0.007 0.218 - 0.001 0.108 Oil & Gas 5 85.64 76.95 0.002 0.197 - 0.001 0.068 - 0.005 0.219 0.013 0.103 Technology 2 63.83 31.77 - 0.000 0.138 0.009 0.069 - 0.014 0.208 0.014 0.212 Telecommunications 7 127.6 140.8 0.008 0.181 - 0.010 0.087 - 0.002 0.239 0.012 0.099 Utilities 13 136.8 126.5 - 0.001 0.183 - 0.005 0.076 - 0.002 0.330 0.006 0.087
Mean St. Dev Mean St. Dev Mean St. Dev Mean St. Dev Mean St. Dev
Panel B
Financials 22 169.2 110.7 0.004 0.220 - 0.004 0.142 - 0.004 0.252 - 0.000 0.159 Non-Financials 76 115.2 282.7 - 0.002 0.174 0.002 0.084 - 0.005 0.238 0.001 0.118
Nr. Nr.
Industry Group ΔlogLEV
ΔlogLEV
CDS spread ΔlogCDS spread EQR ΔlogEQIMPV
ΔlogCDS spread
CDS spread EQR ΔlogEQIMPV
Figure 2:Average CDS spread development per region
Table 3 demonstrates an industry breakdown for both US and EU firms. The idea behind is that each industry exhibits different financial performance (earnings, growth rates, profitability etc.) and different reaction to shocks (e.g. financial crisis). As mentioned above, the sample is influenced by the financial crisis and therefore an industry breakdown is necessary to investigate potential differences in statistics among industries.
Table 3:Descriptive Statistics - Industry Breakdown
Table 3 depicts the descriptive statistics (breakdown by industry) for the monthly dataset between January 2008 and January 2014. Panel A shows the summary statistics for the whole sample (classified by industry), while Panel
B shows the descriptive statistics based on the split between Financials and Non-Financials. (CDS) is the 5 year
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Panel A points out an industry breakdown and details about the mean and the standard deviation for different variables. Health Care, Basic Materials and Technology exhibit the lower average CDS spreads and high positive mean equity returns. On the other hand, Consumer Goods and Services, Financials and Utilities show the highest mean CDS spreads with high standard deviation. In addition, the average change of the implied equity volatility is negative for all industries. Panel B presents additional information for the above mentioned variables, while the sample is divided on financials and non-financials. Financials differ from other industries. One of the main function of financial intermediaries is the maturity transformation. Their balance sheet is highly impacted by the maturity and the duration of their assets and liabilities. Hence, the leverage for financials might be determined based on different criteria and priorities compared to the non-financials. Unfortunately, there are no publicly- available data, thus it is not possible to assess their effect on the changes on CDS spreads. As a result, I perform a split between the two categories. Financials have high average CDS spread (169.2bps) with low standard deviation (110.7bps) while Non-Financials have significantly lower average CDS spread (115.2bps) but much higher standard deviation (282.7bps). Furthermore, the split shows an interesting inverse relation. Financial exhibits a positive mean change on the CDS spreads and negative equity returns, while non-financials document negative average change on the CDS spreads and positive equity returns. Financials have similar behavior to the European Firms, while Non-Financials similar to US firms.
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CDS spread ΔlogCDS spread EQR ΔlogEQIMPV ΔlogLEV ΔlogMKTIMPV EXMKT HML SMB LIQ CRDEF
CDS spread 1 ΔlogCDS spread 0.07 1 EQR -0.03 -0.42 1 ΔlogEQIMPV 0.01 0.33 -0.42 1 ΔlogLEV 0.01 0.33 -0.77 0.35 1 ΔlogMKTIMPV 0.00 0.41 -0.46 0.60 0.35 1 EXMKT 0.01 -0.13 0.11 -0.15 -0.09 -0.23 1 HML -0.03 -0.11 0.13 -0.07 -0.11 -0.12 0.46 1 SMB 0.00 -0.01 0.01 -0.06 -0.02 -0.02 0.47 0.28 1 LIQ -0.04 -0.12 0.03 0.02 -0.02 -0.08 0.29 0.06 -0.10 1 CRDEF -0.05 -0.53 0.40 -0.38 -0.32 -0.51 0.34 0.20 0.14 0.07 1
Table 4: Correlation Matrix
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4. Empirical Analysis
4.1
Regression models
This section presents the model, the methodology and the econometric techniques that are going to be used. As mentioned in previous sections, this study relies on the structural default-risk model that was formalized and developed by Merton (1974). The majority of relevant empirical studies use credit default swap indices, but in the current study I focus on the individual firm level. Following Galil et al. (2014) and Alexopoulou et al. (2009), I construct an unbalanced cross-sectional panel data in order to identify a link between the credit and equity markets, in particular the relationship between the changes in the CDS spreads and the equity returns. For each company, I create the logarithmic CDS spread change:
∆𝐶𝐷𝑆𝑡𝑖 ≈ 𝑙𝑜𝑔(𝐶𝐷𝑆𝑡𝑖) − 𝑙𝑜𝑔(𝐶𝐷𝑆𝑡−1𝑖 ) = 𝑙𝑜𝑔 ( 𝐶𝐷𝑆𝑡𝑖 𝐶𝐷𝑆𝑡−1𝑖 )
Firstly, a multivariate regression is used to evaluate the explanatory power of the firm-specific variables of Merton model to determine the changes of the CDS spreads. The cross-sectional model, that it is indicated as Model (M1) follows:
(M1): ∆𝐶𝐷𝑆𝑡𝑖 = 𝑎𝑡 𝑖 + 𝛽1 ∗ 𝐸𝑄𝑅𝑖𝑡+ 𝛽2 ∗ ∆𝑙𝑜𝑔𝐿𝐸𝑉𝑡𝑖+ 𝛽3 ∗ ∆𝑙𝑜𝑔𝐸𝑄𝐼𝑀𝑃𝑉𝑡𝑖 + 𝜀𝑡𝑖
where, ∆𝐶𝐷𝑆𝑡𝑖 shows the logarithmic CDS spread change for time 𝜏 and firm 𝑖, 𝐸𝑄𝑅𝑡𝑖 is the logarithmic monthly stock return, ∆𝑙𝑜𝑔𝐿𝐸𝑉𝑡𝑖 is the logarithmic change of the firm leverage ratio calculated as total debt over market value of equity and ∆𝑙𝑜𝑔𝐸𝑄𝐼𝑀𝑃𝑉𝑡𝑖 is the logarithmic change of the put options implied volatility. In addition, the existing empirical literature on the determinants of CDS spreads uses common variables accounting for changes in macroeconomic environment. In this study, I use the market implied volatility and the credit risk factor to take into account the impact of the macroeconomic environment on the CDS spreads. The Model (M2), an extension of Model 1 (M1), checks the ability of company and market-specific variables to explain the changes of the CDS spreads:
(M2): ∆𝐶𝐷𝑆𝑡𝑖 = 𝑎𝑡 𝑖 + 𝛽1 ∗ 𝐸𝑄𝑅𝑡𝑖+ 𝛽2 ∗ ∆𝑙𝑜𝑔𝐿𝐸𝑉𝑡𝑖+ 𝛽3 ∗ ∆𝑙𝑜𝑔𝐸𝑄𝐼𝑀𝑃𝑉𝑡𝑖
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Where ∆𝑙𝑜𝑔𝑀𝐾𝑇𝐼𝑀𝑃𝑉𝑡 represents the market implied volatility from stock index options prices on Euro Stoxx 50 and S&P 500, for European and US firms respectively and 𝐶𝑅𝐷𝐸𝐹𝑡demonstrates the credit risk premium factor.
Moreover, as mentioned in the section of the hypotheses development one of the main questions that this study investigates is the ability of Fama and French (F&F) three factor model to explain the changes on CDS spreads. Model (M3) explores the relation between the changes in the CDS spreads and the F&F factors:
(M3): ∆𝐶𝐷𝑆𝑡𝑖 = 𝑎𝑡 𝑖 + 𝛿1 ∗ 𝐸𝑋𝑀𝐾𝑇𝑡+ +𝛿2 ∗ 𝑆𝑀𝐵𝑡+ 𝛿3 ∗ 𝐻𝑀𝐿𝑡+ 𝜀𝑡𝑖
Where 𝐸𝑋𝑀𝐾𝑇𝑡 is the excess return of the market over the one month Treasury rate, 𝑆𝑀𝐵𝑡 shows the small cap portfolio return minus the large cap portfolio return and 𝐻𝑀𝐿𝑡 represents the return of high book-to-market portfolio minus the return of the low book-to-market portfolio. Following Galil et al. (2014), I introduce the Pastor and Stambaugh (P&S) liquidity factor in order to evaluate the effect of the market-wide liquidity on the changes of the CDS spreads. The Model (M4) investigates the explanatory power of the systematic factors on determining the CDS spread changes:
(M4): ∆𝐶𝐷𝑆𝑡𝑖 = 𝑎𝑡 𝑖 + 𝛿1 ∗ 𝐸𝑋𝑀𝐾𝑇𝑡+ +𝛿2 ∗ 𝑆𝑀𝐵𝑡+ 𝛿3 ∗ 𝐻𝑀𝐿𝑡
+𝛾1 ∗ 𝐶𝑅𝐷𝐸𝐹𝑡+ 𝜗1 ∗ 𝐿𝐼𝑄𝑡𝑖 + 𝜀𝑡𝑖
where 𝐿𝐼𝑄𝑡𝑖 is the innovations on aggregate market liquidity. Finally, Model (M5) examines the simultaneous relation of all variables with the CDS spreads changes:
(M5): ∆𝐶𝐷𝑆𝑡𝑖 = 𝑎𝑡 𝑖 + 𝛽1 ∗ 𝐸𝑄𝑅𝑡𝑖+ 𝛽2 ∗ ∆𝑙𝑜𝑔𝐿𝐸𝑉𝑡𝑖+ 𝛽3 ∗ ∆𝑙𝑜𝑔𝐸𝑄𝐼𝑀𝑃𝑉𝑡𝑖
+𝛾1 ∗ ∆𝑙𝑜𝑔𝑀𝐾𝑇𝐼𝑀𝑃𝑉𝑡+ 𝛾2 ∗ 𝐶𝑅𝐷𝐸𝐹𝑡+ 𝛿1 ∗ 𝐸𝑋𝑀𝐾𝑇𝑡
+𝛿2 ∗ 𝑆𝑀𝐵𝑡+ 𝛿3 ∗ 𝐻𝑀𝐿𝑡+ 𝜗1 ∗ 𝐿𝐼𝑄𝑡𝑖 + 𝜀𝑡𝑖
4.2
Methodology
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The five models are evaluated by using logarithmic differences. I follow this approach for two reasons: a) this study investigates whether the changes of CDS spreads are related to changes on a set of explanatory variables and b) according to Di Cesare and Guazzarotti (2010) by using differences it is possible to eliminate the problem of non-stationarity and isolate unobservable factors which are stable over time.
The cross-sectional panel data approach allows to evaluate how variables change dynamically over time. The existing Econometrics literature provides three basic tools for using panel data: pooled ordinary least square (OLS), entity-time fixed and random effects.
The pooled OLS regression (𝑌𝑡𝑖 = 𝑐 + 𝛽 ∗ 𝑋𝑡𝑖 + 𝜀𝑡𝑖) is the simplest method but it has an important drawback. Pooled OLS model assumes that there is no heterogeneity between entities over time. On the other hand, entity fixed effects is a less restricted version of pooled OLS. Entity-fixed effects adds a constant to the model (𝑌𝑡𝑖 = 𝑐 + 𝛽 ∗ 𝑋𝑡𝑖+ 𝜇𝑖 + 𝜀
𝑡𝑖) that differs cross-sectionally among firms and is constant over time. The entity-fixed effects allow for heterogeneity among individual companies. Similarly, time-fixed effects method adds a constant to the model (𝑌𝑡𝑖 = 𝑐 + 𝛽 ∗ 𝑋𝑡𝑖 + 𝜗𝑖+ 𝜀𝑡𝑖) that differs over time and is constant cross-sectionally. In both entity and time fixed effects,𝑋𝑡𝑖 characterize the observable heterogeneity while 𝜇𝑡𝑖 and 𝜗𝑡𝑖 the unobservable heterogeneity. Additionally, I use a combination of them that contains both the entity and the time fixed effects. Before executing the models, I run the test for redundant fixed effects in order to test whether entity and time fixed effects are appropriate models for this study.
Finally, random effects add a constant in the model 𝑌𝑡𝑖 = 𝑐 + 𝛽 ∗ 𝑋𝑡𝑖 + 𝜀𝑡𝑖 where 𝜀𝑡𝑖 = 𝛾𝑖 + 𝜔𝑡𝑖. According to Brooks (2008, p. 498), the additional intercept is part of the error term. It consists of a permanent component-random term 𝛾𝑡𝑖and the idiosyncratic component-noise term 𝜔𝑡𝑖. The unique component estimates the deviation of the individual constant from the common component in order to capture unobserved individual effects. The estimation of the random effects require the Generalized Least Squares (GLS) method to obtain reliable coefficients. An important assumption is that the random effect on the error term is uncorrelated with independent variables 𝐶𝑜𝑟𝑟 ( 𝛾𝑖, 𝑋𝑡𝑖 ) = 0. I perform the Hausman (1976) test to examine whether this assumption is satisfied. The null hypothesis is that the constant is uncorrelated with the independent variables. If the null hypothesis is rejected the entity-fixed effects method is preferred and it is estimated by the Maximum Likelihood (ML) method.
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26 (M1) (M2) (M3) (M4) (M5) EQR -0.608*** -0.362*** -0.348*** ΔlogEQIMPV 0.145*** 0.034*** 0.044*** ΔlogLEV 0.017 0.013 0.012 ΔlogMKTIMPV 0.087*** 0.082*** EXMKT -0.592*** 0.281*** 0.333*** HML -0.353*** -0.189** -0.211*** SMB 0.581*** 0.168 0.101 LIQ -0.439*** -0.331*** CRDEF -0.053*** -0.078*** -0.056*** Observations 6323 6323 6777 6777 6323 F-statistic 537.92 640.0 61.62 540.9 377.8 Prob. (F-statistic) 0.000 0.000 0.000 0.000 0.000 R-squared 20% 34% 3% 29% 35%
Model OLS OLS OLS OLS OLS
5. Regression Results
Turning to the empirical analysis on the determinants of changes in CDS spreads, I present the empirical results of the panel data estimates stated in the previous section. The panel data gives me the opportunity to investigate the factors that determine the changes in the CDS spreads in individual-firm level during different time period.
Table 5 shows the results from the pooled OLS panel data model. Columns
(M1), (M2), (M3), (M4) and (M5) refer to the individual models.
Table 5: Empirical results based on the pooled OLS model
Table 5 shows the empirical results for the five individual models (M1), (M2), (M3), (M4) and (M5). * Confidence at 90% level. ** Confidence at 95% level. *** Confidence at 99% level.
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explains approximately the same variation of the CDS spreads changes and the equity systematic factors (F&F and P&S) do not increase the explanatory power. Overall, the results are consistent with the hypotheses and the existing empirical literature on the determinants of CDS spreads. The following section provides a detailed explanation of the results of each model and their economic interpretation.
Model (M1) examines the explanatory power of the firm-specific variables of the Merton model (1974). One of the main objectives of the table 5 is to examine whether the addition of additional variables suggested by the existing literature enhance the explanatory power of the model in terms of the R-squared. The explanatory power is estimated by the R-squared statistic and equal to 20%. It is similar to Di Cesare and Guazzarotti (2010) and Ericsson et al. (2009) who study the determinants of changes in CDS spreads and report 25% and 23%, respectively. The estimated coefficient of the equity returns is negative and significant at 99% level. In particular, a one percentage point increase in the equity returns causes 0.60% bps change in the CDS spreads. This is an important finding for traders and financial analysts. The notional amount of CDS contracts is usually $10 million and the spread is expressed in terms of basis points. For instance, if the CDS spread of Firm X is 80bps then the buyer of the credit protection should pay to the seller $80.000. It is clear that equity returns has direct and significant impact on the CDS market. The negative sign is consistent with previous literature on both individual data and indices level (Galil et al. (2014), Alexopoulou et al. (2009), Di Cesare and Guazzarotti (2010)).
Based on the above findings, I conclude that positive equity returns lead to negative changes in the CDS spreads, while positive changes in the implied equity volatility and leverage lead to positive changes in the CDS spreads. As a result, I accept the (H1) hypothesis, having taken into account the leverage’s non-significance.
In consistency with the existing academic literature, changes in the equity implied volatility cause positive changes in CDS spreads. The positive sign is in line with Merton model (1974) which suggests that higher implied equity volatility leads to higher probability of reaching the default threshold, higher probability of default and higher CDS spreads. A one percentage increase in implied equity volatility leads to positive change in CDS spread by approx. 0.15% bps. Interestingly however, the estimated coefficient for the changes in leverage is positive (+0.01% bps) but not significant. Leverage is one of the main components of all structural form models and it was expected to have significant impact on the changes of the CDS spreads.
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market volatility is positive and significant at 99%. A one percentage change increase in the market implied volatility (i.e. higher market uncertainty or worse macro conditions) forces the changes on the CDS spreads to go up by 0.08% bps. This is consistent with Alexopoulou et al. (2009) and Breitenfellner and Wagner (2012), who both document a positive relation between the implied market volatility and the CDS spreads. Furthermore, Fama and French (1993) suggest that a systematic credit risk premium may explain the variation on the returns. They present a positive relation between equity returns and credit risk premium, hence a negative influence with CDS spreads. Model (M2) investigates the ability of a systematic credit risk premium to explain the changes in CDS spreads. Column (M2) document a negative slope between credit risk factor and changes in CDS spreads. A one percentage increase in the systematic credit risk premium leads to changes in the CDS spreads that equal to -0.05% bps. Model (M2) confirms the idea that additional market-specific variables have strong power on the determination of changes in the CDS spreads. Furthermore, the signs and the significance level have remained the same for firm-specific variables. Interestingly, the coefficients of the equity returns and the equity implied volatility decreased by approx. -40% and -75%, respectively, while leverage remained almost stable. The decrease in the firm-specific coefficients denotes the importance of the market-wide variables which contribute significantly to the changes in the CDS spreads. Additionally, the explanatory power of the model increased significantly and the R-squared in Model (M2) is equal to 34%.
Overall, the inclusion of the market variables as determinants of the changes in the CDS spreads improves the explanatory power of the model and provides significant coefficients. The empirical findings on the previous section are in favor to the hypothesis (H2) that positive changes of the implied market volatility lead to positive changes on the CDS spreads, while positive changes on the systematic credit risk factor are associated with negative changes on the CDS spreads.
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Model (M3) reveals interesting findings and a more careful interpretation follows. Fama and French (1993) believe in the efficient market hypothesis and support that investors do demand higher reward for higher risk. Therefore, if small size or value stocks have a higher than average return, then they should be more risky. A positive HML coefficient implies a positive tilt towards to stocks with high book-to-market (value stocks). Hence, positive HML coefficient refers to more risk and higher reward and therefore higher CDS spreads. A negative HML coefficient implies less risk, tilt towards to growth stocks with stronger expected profitability and lower CDS spreads. EXMKT refers to the excess market return. A negative EXMKT coefficient implies that in periods with positive returns the CDS spreads narrows. Turning back to the results of Model (M3), I find negative sign for the EXMKT and the HML and positive for the SMB. The findings suggest that the systematic factors from equity market have significant impact on the changes in the CDS spreads and point out an interaction between the equity and credit markets.
However, the low explanatory power of Model (M3) generates doubts about the validity of the model. One of the main motivation of this study is to examine whether the systematic factors affect the changes in the CDS spreads.
Model (M4) is an extended specification of the previous model and is accounting for additional systematic factors such as the credit risk premium and the innovations in market liquidity. I do not include the changes in implied market volatility due to its high correlation with the excess market return and the credit risk factor. Model (M4) document a shift in the sign of the EXMKT (turns to positive), while the SMB lost its significance in the presence of addition systematic factors. Interestingly, the Pastor and Stambaugh market-wide liquidity measure is negative and significant indicating a liquidity transmission channel from the equity to credit market. A one percentage increase in the equity market-wide liquidity leads to changes in the CDS spread by 0.44% bps. The findings are consistent with Huang (2015) who documents a link between the stock liquidity and the firm’s credit risk premium.
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in the CDS spreads. The results enhance the confidence of the models but it is difficult to argue that they support the (H3) hypothesis. The HML and the market liquidity are in favor to (H3) hypothesis (negative relation between these variables and the changes in CDS spreads), but this does not hold for the EXMKT and SMB. A percentage increase either on the EXMKT or the SMB cause positive changes in the CDS spreads by 0.33% bps and 0.10% bps respectively. However, it should be noted that the SMB coefficient is insignificant. These particular results are partially against the (H3) hypothesis but their economic intuition is important. Based on the findings, the positive excess market returns lead to positive changes in the CDS spreads. This is in contrast to existing beliefs that positive market returns imply improved expectation about the stock market and thus lower CDS spreads. It is an interesting topic for potential future research.
Model (M5) includes firm and market-specific variables, the Fama and French, the Pastor and Stambaugh liquidity and the credit risk factors. At first glance, the significance and the signs remain similar to the previous models. Equity return, high-minus-low, innovations in market liquidity and the credit risk factor have strong negative influence on the changes in the CDS spreads. On the other hand, changes in the equity implied volatility, leverage, excess market return, market implied volatility and the small-minus-big factor have positive relation to the changes in the CDS spreads. However, it must be noticed the insignificance of two variables, the changes in leverage and the small-minus-big. Additionally, the inclusion of all different determinants in changes on CDS spreads increase the explanatory power of the model and reach a peak of 35% that is similar to other studies in empirical literature on the determinants of the changes in the CDS spreads.
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6. Robustness Analysis
This section further examines the robustness of the models and the results presented in the previous section. The pooled OLS regression is simple and intuitively appealing but additional robustness checks have to be done. Firstly, I use pooled OLS model with robust standard errors to correct for heteroskedasticity and autocorrelation. Secondly, I use entity, time and random effects to investigate whether unobservable effects provide additional insights in the model. Then, I divide the sample into financials and non-financials. Finally, I split the sample into two categories based on the geographical region. The main objective is to perform an in-the sample performance evaluation of the model and enhance the results reliability.
6.1 Ηeteroskedasticity and autocorrelation
Note that pooled OLS is the simplest approach and has important assumptions. First, the error term has constant variance and second, there is no correlation between the error terms. The presence of heteroskedasticity (no constant variance in error terms) can be controlled using the White's diagonal heteroskedasticity consistent standard error estimation method. This version of the pooled OLS provide robust standard errors ( 𝑉𝑎𝑟 𝜀𝑡𝑖 = 𝜎𝑖𝑡2) and any inferences about the estimated coefficients are more reliable than simple pooled OLS. Furthermore, I use Durbin-Watson test to investigate the presence of autocorrelation between the error terms. Autocorrelation leads to misleading inferences about the coefficients’ significance. For instance, in case of negative autocorrelation the standard errors are biased upwards compared to real standard errors. The Durbin-Watson test doesn’t follow a standard statistical distribution. Appendix provides further details about the test.
32 (M1) (M2) (M3) (M4) (M5) EQR -0.608*** -0.362*** -0.348*** ΔlogEQIMPV 0.145*** 0.034*** 0.044*** ΔlogLEV 0.017 0.013 0.012 ΔlogMKTIMPV 0.087*** 0.082*** EXMKT -0.592*** 0.281*** 0.333*** HML -0.353*** -0.189** -0.211*** SMB 0.581*** 0.168 0.101 LIQ -0.439*** -0.331*** CRDEF -0.053*** -0.078*** -0.056*** Observations 6323 6323 6777 6777 6323 F-statistic 537.92 640.0 61.62 540.9 377.8 Prob. (F-statistic) 0.000 0.000 0.000 0.000 0.000 R-squared 20% 34% 3% 29% 35% Durbin-Watson stat 2.044 2.149 1.898 2.032 2.135
Autocorrelation Robust Robust Robust Robust Robust
Heteroskedasticity Robust Robust Robust Robust Robust
OLS Robust Standard Errors
Model OLS Robust
Standard Errors OLS Robust Standard Errors OLS Robust Standard Errors OLS Robust Standard Errors Table 6: Empirical results based on the robust pooled OLS model
Table 6 shows the empirical results for the five individual models (M1), (M2), (M3), (M4) and (M5) using pooled OLS robust to heteroskedasticity and autocorrelation on error terms. * Confidence at 90% level. ** Confidence at 95% level. *** Confidence at 99% level.
Furthermore, the table 6 shows that the absence of autocorrelation between error terms. Appendix provides additional details on the examination regarding the Durbin-Watson estimation for each model. To sum up, the robust pooled OLS version controlling for heteroskedasticity and autocorrelation provides similar results with the simple OLS.
6.2 Entity, time and random effects
Turning to the next robustness check, firstly I focus on the entity and time fixed effects. As mentioned in the methodology section, the contribution of these methods to the model reliability is important. I run the test for redundant fixed effects to check whether they provide additional details about the unobserved heterogeneity. The null hypothesis suggest that 𝜇𝑖 = 0 and 𝜗𝑖 = 0 for entity and time fixed effects, respectively. In case that 𝐻𝑜 holds, there is no unobserved heterogeneity. Hence, the model reduces to a simple pooled OLS. The results show that the null hypothesis cannot be rejected for both models and thus the simple pooled OLS is preferred.
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(2008) the random effect model is 𝑌𝑡𝑖 = 𝑐 + 𝛽 ∗ 𝑋𝑡𝑖 + 𝜀𝑡𝑖 where 𝜀𝑡𝑖 = 𝛾𝑖 + 𝜔𝑡𝑖. It is logically to infer that the residual variance decomposition is a function of the residual variance of the intercept 𝜎𝛾2 and the residual variance of the common term 𝜎𝜔2. The random effect 𝛾𝑖 must not be correlated with the explanatory variables 𝑋𝑡𝑖. If this assumption is not satisfied, there is endogeneity problem and the random effect estimation is biased. I perform the Hausman test to check the assumption. The null hypothesis suggests that 𝛾𝑖 is uncorrelated with the dependent variables (𝐻𝑜∶ 𝐶𝑜𝑣 ( 𝛾𝑡𝑖, 𝑋𝑡𝑖 ) = 0). The result suggests that we cannot reject the null hypothesis; that is, 𝛾𝑖 is uncorrelated with the explanatory variables and thus I can make use of random effects technique. However, the results for Hausman test indicate that for all Models (M1), (M2), (M3), (M4) and (M5), the estimated cross-section random effects variance 𝜎𝛾2 is zero. As a result, the use of random effects does not provide further details for unobserved heterogeneity and reduces in the simple pooled OLS model.
6.3 Financials vs. non- financials
In order to dig deeper into the above results, I divide the sample into financials and non-financials. Raunig and Scheicher (2009) investigate whether investors discriminate in favor or against the financials by requiring different credit risk premiums. They document three different arguments to show the fundamental differences of the financial industry. Firstly, financials balance sheet has different structure. Assets are mainly long-term securities (i.e. loans) while liabilities are mainly short-term deposits. The inverse holds for insurance companies. These differences in the composition of the balance sheets are usually depicted in the leverage ratio. Due to the limited availability of public information, investors might require higher credit risk premium in order to get additional reward for their exposure in these industries. Secondly, financials are heavily regulated (Basel III, Solvency II). The extensive regulation is not chosen out of thin air. Banks are deposit-taking institutions and insurance companies insure pension funds; that is, financials play a central role in the modern economy and this financial strength should be carefully monitored. Thirdly, governments realized the financials’ importance and developed specific schemes such as safety nets and deposit guarantees. These intervention may influence investors to require lower credit risk premium due to higher bailout expectations. Overall, there are many reasons supporting the notion of particularities in the financial industry, but this is not a topic of this study.
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OLS and controlling for heteroskedasticity and autocorrelation. At first glance, the results are similar to the total sample referring to the signs and the significance of the estimated coefficients. In addition, the explanatory power of the models remain at the same level. I focus on the Model (M5) because it contains all the variables. Non-financials exhibits more similar behavior to the whole sample than Non-financials. The firm-specific variables keep the same sign and significance level. A one percentage increase in the equity returns leads to changes in the CDS spreads by -0.18% bps and -0.40% bps for financials and non-financials, respectively.
Recalling from the whole sample, the impact of the equity returns on the changes in the CDS spreads was approx. -0.35% bps. The changes in the equity implied volatility and the leverage have positive influence on the changes in the CDS spreads, but the estimated coefficient of the changes in the leverage remains still insignificant for both categories. Turning to the market-specific variables, the changes in the implied market volatility have significant positive influence on the changes in the CDS spreads. The coefficients amounts to 0.16% bps for financials and 0.06% bps for non-financials. The higher sensitivity of the financials can be explained mainly because of their direct exposure to the financial markets and the shifts on the macroeconomic environment. For non-financial firms, the coefficients of Fama and French factors maintain their signs and their significance. Interestingly, the changes in the HML lead to changes in the CDS spreads of non-financials by -0.44% bps.
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Additionally, the changes in the credit premium are positive in contrast to the negative coefficient in the whole sample. The inverse holds for non-financials. Table 7 shows that the estimated coefficient for SMB remains for both categories insignificant, while the market excess returns maintain their positive significant sign. A one percentage increase on the market excess returns leads to changes in the CDS spreads by +0.57% bps for financials. According to the table 7, the EXMKT has the higher contribution on determining the changes in the CDS spreads. Model (M3) regresses the FF factors against the changes in the CDS spreads and reveal a negative relation between the EXMKT and the changes in the CDS spreads. This finding is consistent with Galil et al. (2014). The inclusion of additional variables leads to a shift in the EXMKT sign. Table 7 shows that the estimated coefficient for the SMB remains for both categories insignificant, while the market excess returns maintain their positive significant sign. A one percentage increase on the market excess returns lead to changes in the CDS spreads by +0.57% bps for financials. According to the table 7, EXMKT has the higher contribution on determining the changes in CDS spreads. Model (M3) regresses the FF factors against the changes in the CDS spreads and reveal a negative relation between EXMKT and changes in CDS spreads. This finding is consistent with Galil et al. (2014). The inclusion of additional variables leads to a shift in the EXMKT sign. It is still ambiguous the positive relation between the market excess returns and the changes in the CDS spreads. Additionally, both categories exhibit same response to the equity-market wide liquidity and the credit risk factor. For both financials and non-financials an increase in the two factors leads to negative changes in CDS spreads that is consistent with the results from the whole sample. Finally, Model (M5) exhibits a strong explanatory power. The R-squared for financials reaches 45%, implying the significant power of the independent variables on explaining the changes in the CDS spreads. Nevertheless, the inclusion of the equity systematic factors cause a slight increase of the R-squared in comparison to the Model (M2). Similarly to the results of the whole sample, Model (M2) has sufficient explanatory power without the addition of the equity systematic variables.
Overall, the split of the sample into financials and non-financials improved the reliability of the model. The results in both categories are similar to the whole sample, even after controlling for heteroskedasticity and autocorrelation in the standard errors. Interestingly, the most striking finding is the different response of financials to the HML factor.
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6.4 European vs. US firms
In section 3, the descriptive statistics point out a different behavior of the European and the US firms. Considering that the sample dates between 2008 and 2014, there are two important facts that influence the CDS spreads, the market breakdown during the financial crisis of 2008 and the European sovereign debt crisis since 2010.
Table 8 depicts the results for the models (M1), (M2), (M3), (M4) and (M5). The results suggest a negative relation between the equity returns and the changes in the CDS spreads. This relation holds for all models and is significant at 99% level. Similarly to the previous sections, Column (M3) shows that the FF factors have significant relation to the changes in the CDS spreads. In consistency with the total sample, the market excess returns EXMKT turns to positive after the introduction of other firm-specific and systematic variables. Interestingly, focusing on the Model (M5), there is a notable difference between the European and the US firms. For both geographical regions, the HML coefficient is negative but significant only for the US firms. The finding implies that the changes in the CDS spreads for US firms are influenced by the additional systematic factor, in terms of “value” or “growth” stocks. Turning to the next FF factor, the outcome of Model (M5) for SMB shows the inverse. The SMB factor for European firms is negative and significant at 95% level while for US firms is positive and insignificant; that is, the changes in the CDS spreads for European firms are affected by the “size effect”. Additionally, the findings confirm the significant influence of the equity market-liquidity. Finally, the explanatory power of the models are similar to the total sample and Model (M2) has sufficient explanatory power without including additional factors.
Overall, the different robustness checks support the findings in the whole sample in section 5, enhance the validity of the model and provide more reliable results.
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7. Conclusion
This study empirically analyzes the determinants of the CDS spreads changes, based on a sample of European and US firms for the period 2008-2014 using firm and market specific variables, which can be found in the empirical and theoretical literature of the structural-default risk models. One of the main purpose of this paper is to investigate whether an interaction between the equity and credit markets exists. I find strong evidence that both the firm- specific and the common factors from both markets have significant influence on the changes of the CDS spreads. Interestingly, I find different response of European and US firms with regards to the “size” factor and different behavior of the financials vs. non-financials to the “value” factor. Furthermore, I point out a significant negative relation between the equity-market wide liquidity and the CDS spreads changes. Overall, the results suggest that there is a link between the equity and credit markets.
The empirical findings in Sections 5 and 6 contribute to the existing literature in different ways. Firstly, the sample consists of both European and US firms while previous similar studies focused on one of them. Secondly, I make use of the excess credit return factor and I show a negative significant relation with the changes of the CDS spreads. In addition, I include the equity market-wide liquidity factor suggested by Galil et al. (2014). To best of my knowledge, they were the first to use the liquidity factor as a determinant of the CDS spreads. Their results point out an insignificant effect while I document a negative robust significant relation with the changes in the CDS spreads.
The empirical methodology and the results in the previous sections are useful in the context of this study. However, they can be useful for both the practitioners and the researchers. Financial analysts in the credit market should bear in mind that events and developments in the equity market affect the movements and the pricing in the CDS market, while the scholars may take into account the interaction of both markets and use additional systematic factors on explaining the changes in different financial instruments.
