Master Thesis Finance
Stock liquidity and CDS spreads. Reviewing
the Financials
Mark van Ginkel
University of Amsterdam
Statement of Originality
This document is written by Student Mark van Ginkel who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
Abstract
This study investigates the relationship between stock liquidity and credit default swap (CDS) spreads. This analysis is performed using a balanced panel data set consisting of 18 banks, over a period of 126 months. When controlling for several theoretical determinants of the CDS spread and important macroeconomic variables, a significant relationship between stock liquidity and the CDS spread is obtained. The result of the regression analysis points to a negative relationship between stock liquidity and CDS spreads. The Granger causality test indicates that stock liquidity Granger causes CDS spreads, proving an important feature in the relationship between stock liquidity and CDS spreads, and establishing stock liquidity as a leading indicator for default risk. This study confirms the existing literature on the relationship and the causal direction between CDS spreads and stock liquidity when applied to financial institutions. This study extends the existing literature, and adds value by explicitly investigating the relationship of stock liquidity and CDS spreads using financial institutions.
Table of Contents
1. Introduction ...5 2. Literature review ...8 3. Theoretical framework ... 10 3.1. Stock liquidity ... 10 3.2. Control Variables ... 11 3.2.1. Equity value ... 11 3.2.2. Stock return ... 11 3.2.3. Equity volatility ... 11 3.2.4. GDP growth rate ... 11 3.2.5. Risk-free rate ... 12 4. Methodology ... 12 4.1. Data ... 12 4.1.1 CDS data ... 124.1.2 Stock liquidity data... 12
4.1.3 Control variable data ... 12
4.1.4. Descriptive statistics ... 13
4.2. The Model... 14
4.2.1. Multicollinearity ... 15
4.2.2. Random and Fixed effects ... 15
4.2.3. Heteroskedasticity and time-fixed effects ... 16
4.2.3. Causality ... 17
5. Empirical Analysis ... 18
6. Conclusion... 22
7. References ... 23
1. Introduction
A credit default swap (CDS) or credit derivative contract is a swap designed to transfer the credit exposure of fixed income products between parties. The buyer of the swap buys protection on the particular company or country (the reference entity) from the swap seller by making payments until the maturity date of the contract. These payments are known as the premium or credit default spread. The swap seller is effectively guaranteeing the credit worthiness of the debt security, therefore transferring the risk of default from a third party from the credit swap buying investor to the credit swap seller. In essence a CDS can be viewed as an insurance contract.
When the third party or reference entity on which the CDS protection is bought defaults (in case of a loan default or credit event), the CDS buyer is entitled to protection on a specified face value of the third party’s bonds. This means that the buyer has the right to sell the bonds with a face value equal to the notional amount. The illustration in Figure 1 shows how this credit derivative works in practice.
Figure 1: Graphical representation of a plain vanilla CDS
CDS spreads play an increasingly important role in the modern era of finance. The CDS market of “single-name” credit default swaps1 had a total worth of $33.4 trillion in the first half
of 2008 when it was at its peak. The CDS market has since then declined in size due to numerous regulations following the financial crisis2 which eroded synthetic CDO's, an
important driver of single-name credit default swaps. The CDS market is still a very large and important market though, also because the CDS spread displays more information than just the price of the annual payments. In certain circumstances CDS spreads can in fact be a good indicator of default risk for companies as well as countries3. This of course has many
implications for regulators and participants of the financial markets. What is important to note however, is that the CDS spread measures the risk perceived by investors about a firm’s assets, and is not an actual objective measure of firm’s default probability.
1 The “single-name” CDS is the most basic CDS which is written/bought on a single reference entity. Other types of CDSs are; basket default swaps (BDSs), index CDSs, funded CDSs and loan-only credit default swaps (LCDS). 2 Basel III makes the use of futures substantially more attractive for risk management than swaps due to certain capital requirements. Furthermore, the EU has banned the concept of naked credit default swaps since 2012, contributing to a further decline of the CDS market.
3 During tail events such as the financial crisis the pricing of derivatives tends to understate the current financial state, potentially leading to severe losses. This was underlined by the speech of Lord Turner, president of the financial services authority (FSA) in 2009.
Buyer of default
protection Seller of default protection Default payment notional amount * (1-R)
Reference entity X amount of basispoints (bps) per year
A great and simultaneously tragic example of the importance of CDS spreads was the fall of one of the largest commercial banks in Iceland, Landsbanki. The bank had been operating since 1885 and was essential to Iceland’s economic development. Late 2006 Landsbanki was the leading provider of M&A, fixed income, equity and derivatives services.
In September 2008 Moody’s credit assessment of Landsbanki was still straying at A2 (Figure 2), which indicated upper-medium grade, and low credit risk according to Moody’s criteria. As of that time CDS spreads of Landsbanki soared to more than 700 basispoints from a 180 basispoints two months earlier (Figure 3). Just one month later on October 7, 2008, the Icelandic Financial Authority took control of Landsbanki, dismantling its operations and creating a new (domestic) bank.
Figure 2: Credit rating of Landsbanki before its default
Source: (Kool & Gerritsen, 2009)
Figure 3: The 5-year CDS spread of Landsbanki
Source: (Kool & Gerritsen, 2009)
Ratings merely help for a comparison between banks, but are poor explanatory variables when studying credit and default risk. CDS spreads are a much better predictor of credit and default risk of a firm, since the CDS spread contains information about the default risk of a
firm and displays the market’s opinion on the default risk of a firm, as is highlighted in Annaert et al (2010).
Financial institutions, and especially banks, are at the heart of our financial system. Banks and the financial markets have developed significantly over the past decades, growing in their relative importance. A point that is also argued in Demerguc-Kunt, Feyen and Levine (2012), where they analyze the evolvement of banks and securities markets during the process of economic development. They find that both the banks and securities markets increase relative to the size of the economy.
Following the financial crisis of 2007, we have all seen the negative externalities that can arise from the failure of large financial institutions. As the Basel Committee put it in a 2013
publication:
“The negative externalities associated with institutions that are perceived as not being allowed to fail due to their size, interconnectedness, complexity, lack of substitutability or global scope are well recognized. In maximizing their private benefits, individual financial institutions may rationally choose outcomes that, on a system-wide level, are suboptimal because they do not take into account these externalities. Moreover, the moral hazard costs associated with implicit guarantees derived from the perceived expectation of government support may amplify risk-taking, reduce market discipline and create competitive distortions, and further increase the probability of distress in the future. As a result, the costs associated with moral hazard add to any direct costs of support that may be borne by taxpayers”
Since CDS spreads contain information about the default risk of a company, the analysis of stock liquidity as a determinant of a bank’s CDS spread could prove very useful when
studying the default risk of these large financial institutions. This relationship, using solely banks in the sample, could prove useful when analyzing stock liquidity for the purpose of predicting movements in the CDS spread. Movements in the CDS spread are critical for the analysis of default risk, and are thus extremely important when considering large financial institutions, since these large financial institutions are fundamentally essential to our financial system. CDS spreads contain information concerning the financial stability of a firm, because it is related to a firm’s credit risk and default risk. In an attempt to contemplate, apprehend and forecast a firm’s financial soundness, the analysis of CDS spreads could play a crucial role. Therefore this study aims to establish significant evidence on the relation between stock liquidity and CDS spreads in developed markets.
This study confirms the relationship between stock liquidity and CDS spreads found in the existing literature. The research conducted extends the study of Anneart et al. (2010), by incorporating banks in the US, and using stock liquidity as opposed to CDS market liquidity. The direction of the causality found in this study is in line with the conclusions found in Rosch et al. (2013). Rosch et al. (2013) argues that higher credit risk leads to higher illiquidity in the stock of a firm. Investors in the CDS market see this as a leading indicator and ask a higher CDS spread for that firm. This notion is confirmed in this study when applied to financial institutions in developed markets. Many previous research has focused on the link between CDS market liquidity and CDS spreads, or the more natural link between the bond market and the CDS market. However the relationship between CDS spreads and the equity market, stock liquidity in specific, has to the best of my knowledge been overlooked by most studies. Only Das & Hanouna (2008) manage to relate the CDS spread to the equity market, showing a negative relation between equity liquidity and CDS spreads. This study builds upon the
theoretical notion developed in Das & Hanouna (2008) and to some extent in De Jong & Driessen (2005). Furthermore it confirms the conclusion of Das & Hanouna (2008) when applied to financial institutions. By covering a longer period with different economical business cycles, the study boasts more rigidness than the relative short period used in Das & Hanouna (2008).
This study uses a panel data regression to investigate the relationship between stock liquidity and CDS spreads. Monthly data is acquired or calculated for 18 banks, during a time period of 126 months, ranging from April 2004 until September 2014. The study manages to connect the CDS spread and the stock market, establishing an important link with several implications, due to the causal direction of the relationship. A significant relationship is found between the stock liquidity and the CDS spread when controlling for theoretical determinants of the CDS spread.
The rest of the paper is divided as follows. Section 2 will provide a literature review, with important studies in this specific field that are useful for the analysis in this study. Section 3 contains the theoretical framework, in which all the variables used and their importance or purpose for this analysis are described. Also the reasoning describing the link between stock liquidity and CDS spread is given here. Section 4 turns to the methodology used in this study. This section explains how the variables are obtained and calculated, and how the regression model looks like. Furthermore a number of statistical tests are shown in this section, which deal with the several econometric issues of a panel data regression. Using these tests, the correct regression form for the empirical analysis is obtained. Section 5 contains the empirical analysis with the output of several regressions. Section 6 concludes the contentual body of the study with a brief overview, including some possible implications of the study.
2. Literature review
De Jong & Driessen (2005) investigate the relation between liquidity risk and expected returns on corporate bonds. For their model they use both stock and bond liquidity to prove liquidity is priced into bond spreads. Only for short-term high rated bonds does their model understate the expected excess return, hereby explaining a great part of the credit spread puzzle4.
The study of Ericsson, Jacobs and Oviedo (2005) finds that firm leverage, risk-free rate and volatility are all statistically significant determinants of the CDS premium. Confirming and emphasizing the importance of these control variables.
Alexander and Kaeck (2008) argue that CDS spreads represent regime specific behavior. Their study proves that CDS spreads are heavily affected by stock volatility during volatile market times. It also shows that during normal market conditions the CDS spreads are more heavily affected by stock returns, relative to stock volatility. Alexander and Kaeck (2008) also support the case for the control variables used in this study, as they find that stock returns, interest rates and implied volatility all have a significant effect on CDS spreads.
Das & Hanouna (2008) theorize and prove a connection between the equity market and the CDS market. They use the Merton model (1974) framework to establish this relationship. Their
4 The average spread on corporate bonds tends to be much higher than the yearly average default loss, making the relationship puzzling. This spread is the difference between the yield on a corporate bond that is subject to default and an otherwise default free US government bond. The credit spread puzzle is a term referring to the wide gap between corporate spreads and expected default losses.
conclusion are robust to other measure of liquidity. The paper focuses on the dynamics transmitting illiquidity from equity markets to the CDS market. The authors argue that since CDS contracts are actively hedged, and hedging costs are suffered, whether liquidity risk is systematic or not, it is probable that illiquidity costs from the equity markets are transferred into CDS spreads. The paper finds evidence that CDS spreads contain elements of liquidity using three different liquidity measures to confirm its results.
Singh and Spackman (2009) stress the importance of the nature of the recovery value in an IMF working paper. The paper says that although default probabilities can be extracted from CDS spreads, it is important to take into account the stochastic nature of the recovery value during periods of distress. They warn that the financial institutions that use a fixed rate
recovery assumption could have a false sense of security, and potentially incurring great losses. They argue that to monitor financial institutions and the stability of the financial system, the stochastic nature of the recover value needs to be incorporated. They show that using a stochastic recovery value helps predict default risk in a much earlier stage, serving as a leading indicator. The study however only uses three entities for its analysis (Landsbanki, Washington Mutual and Lehman Brothers), and focuses solely on a period of distress. Nevertheless it provides interesting insights into the recovery rate concept.
Annaert et al. (2010) investigate the impact of several credit risk determinants on CDS spread changes. The credit risk drivers are based on the model developed by Merton (1974), and the sample consists of 31 European banks. Annaert et al. (2010) analyze the situation before and after the late financial crisis, and compare the results. Not surprisingly these determinants vary a lot over time, meaning that models for testing determinants of CDS spread changes are to be interpreted carefully and need to be tested regularly. Another important factor in explaining CDS spread changes is the CDS market liquidity, which is significant both before and after the financial crisis.
Fitch Ratings (2011) published a macro credit research report, focusing on the whether CDS spreads serve as a leading indicator for default risk. This is of course a crucial part with respect to the implications this study might have. Fitch Ratings analyzed the performance of CDS spreads on companies that suffered credit event during the financial crisis. They focused on 27 credit events, with firms from all over the world. They concluded that CDS spreads did not seem to show a leading signal of default risk for financial institutions. The result for
corporates however was mixed. It would be difficult to use the CDS spreads as a quantitative estimator of default risk, but the relative differentiating characteristic proved to be very useful, since it could help distinguish default risk between corporate entities. Six months before the credit event, spreads of the sample of defaulters were more than 2.5 times the spreads of the index.
Cesare and Guazzarotti (2012) analyze the determinants of CDS spread changes for non-financial US-based firms between 2002 and 2009. Their set of chosen variables is able to explain more than 50% of the variation in CDS spreads before and during the crisis. By including a theoretical CDS spread5 in their model the explanatory power of their variables
improves significantly. When including this theoretical CDS spread, the coefficient of equity volatility decreases significantly, while the coefficient of leverage maintains its explanatory power. They also find that leverage has an increasing significance in explaining the variation in CDS spreads during the financial crisis. On the contrary equity volatility decreases in significance during the crisis, probably due to the huge swings in implied volatility which made this indicator a deficient proxy for long-term asset volatility. As in some other studies
they also document that CDS spreads were driven by an unexplainable common factor during the financial crisis.
Rösch et al (2013) study the relationship of liquidity cost spreads between high credit quality firms and low credit quality firms in the stock market. Their findings implicate that increased credit risk leads to higher market liquidity costs. This result is in line with what one could expect. Namely that increased credit risk leads to higher firm illiquidity. According to some financial theory it is expected that market participants who observe this movement require higher CDS spreads for these firms.
In a European Central Bank (ECB) working paper (2014, Santis and Stein investigate the role of CDS spreads and liquidity risk in assessing sovereign crisis thresholds. The paper analyses the correlations between the change in monetary policy and the change in sovereign yields of three European countries (Italy, Spain and Germany). According to the paper there are several indicators affecting this correlation, the CDS spread being one of them. Using a Smooth Transition Conditional Correlation GARCH (STCC-GARCH) model5 to estimate the
threshold level above which the sovereign bond markets enter a crisis regime, the paper concludes that threshold levels for Italy and Spain are reached when the CDS spreads reach 120 to 130 basispoints.
3. Theoretical framework
3.1. Stock liquidity
The concept of stock liquidity is based on the definition used in De Jong and Driessen (2006), who state that “a stock is defined to be liquid if large volumes can be traded without
generating much price impact”.
This study argues that firms have lower CDS spreads if their assets possess more liquidity in the equity market. This concept is based on the fact that credit and default risk are both
correlated with a firm’s stock fluctuations. Both debt and equity markets react to a
deteriorating credit quality of a firm (i.e. a higher default risk). The equity market will lower the amount of transactions of the shares of that firm, this gives rise to firm stock illiquidity. This firm illiquidity is seen as a sign of increasing credit risk, which results in increased CDS spread for that particular firm.
Investors holding shares in a firm encountering severe financial difficulties cannot trade their shares, since the market has no demand for such shares. So the volume of shares traded on that firm drops (i.e. firm illiquidity increases). This is in line with the theoretic link followed in this paper, which states that firm illiquidity points to increased credit risk. Arguing from Hull’s (2012) definition of credit default swaps, which highlights the need for insurance of assets whose value decreases, one could expect an increase in the CDS spread of stocks that entail higher credit risk due to their illiquidity.
For the measurement of stock liquidity the bid-ask spread is used. Following the
argumentation of Spiegel & Wang (2005), a higher bid-ask spread is defined as a sign of illiquidity. Therefore this study argues that a higher bid-ask spread is positively related with the
5This model was introduced by Silvennoinen and Terasvirta (2005). The model allows correlations to vary smoothly
between two extreme states of constant correlations. The modeler can choose the transition variable that drives the constant correlations.
CDS spread, since higher illiquidity leads to higher default risk, and thus to higher CDS spreads. It is thus expected that there will be a negative relationship between stock liquidity and the CDS spread. As a note to prevent confusion; this means that the variable bid-ask spread is expected to have a positive relationship with the CDS spread.
3.2. Control Variables
The control variables chosen are based on the previous literature in this area of finance. The variables that are significantly related to CDS spreads are equity value, leverage, stock return, volatility, GDP growth rate and the risk-free rate. These factors are discussed separately in the sections below.
3.2.1. Equity value
A very natural control variable to include in this analysis is the equity value of a company. As is well known in the finance literature, the equity value of a company is a direct and main determinant of the firm value of a company. This argument is used by Alexander and Kaeck (2008) to show that when the firm value of a company increases, its probability of default declines. Combining these concepts, this study argue that an increase in the equity value of a company will most likely lead to a decrease in the CDS spread of that company.
3.2.2. Stock return
Stock returns contain information about a company’s prospects, which are embedded in the earnings and cash flows of the company. This study argues that higher stock returns result in lower default risk, which implies lower CDS spreads. This argument is analogous to the analysis by Annaert et al. (2010). This study uses equity returns as a proxy for asset returns, based on the Merton (1970) model.
3.2.3. Equity volatility
According to Alexander and Kaeck (2008) firm volatility is positively correlated with CDS spreads, since the probability of default increases when the value of the firm fluctuates frequently. The same problem as with assessing a company’s firm value is encountered in the computation of the firm volatility. The firm volatility or asset volatility is not readily observable. However, the Merton (1970) model contains an equation which displays the positive
correlation between equity volatility and firm volatility.
𝜎
𝑒=
𝑉
𝐴𝑉
𝑒∗ 𝑁(𝑑
1) ∗ 𝜎
𝐴Where
𝜎
𝑒is the volatility of equity,𝜎
𝐴is the asset volatility,𝑉
𝐴and𝑉
𝑒are the market values attime 𝑡 of assets and equity respectively.
This equation which stems from Ito’s Lemma, and used in the Merton (1970) model allows us to argue that equity volatility is positively correlated with CDS spreads, and thus can be seen as a determinant of the CDS spread.
3.2.4. GDP growth rate
A negative correlation between GDP growth and CDS spreads is expected, since GDP growth signals economic growth, which is turn is linked with lower default risk for firms. This expectation is supported by the findings of Tang and Yan (2010), who find that an increase in GDP growth is accompanied with a decrease in CDS spreads.
3.2.5. Risk-free rate
The risk-free rate, as measured by Libor, displays the average interest rate at which (leading) banks would be charged if they would borrow from other (leading) banks. Naturally this risk-free rate ought to be positively related to the CDS spread, since the rate that banks have to pay on their loans is determined by their (average) creditworthiness. Creditworthiness is directly correlated with default risk, and thus with the CDS spread. A higher Libor rate would indicate that the average bank is more prone to default risk, leading to an increase in the CDS spread.
4. Methodology
4.1. Data
This study will use panel data in which certain European banks will be analyzed over the period 2003-2013. The sample of banks will be chosen based on data availability of stock prices and CDS quotes in Bloomberg. The chosen time period is such that it reflects a more realistic market (i.e. a mature CDS market) and incorporates the financial crisis.
4.1.1 CDS data
The data for the CDS spreads will be collected from Bloomberg. After collecting the data for the spreads, they are converted into logarithms in order to correct for the large values that persist for some firms, due to the fact that the spreads are represented as basispoints. The CDS spread will be defined as the natural logarithm of the 5 year senior CDS spread quote, taken on a monthly basis (using month-end data).
4.1.2 Stock liquidity data
The stock liquidity data will consist of the bid-ask spread (bidask). For the calculation of the bid-ask spread measure, the weekly bid-ask spreads are obtained, then divided by their average, and finally these figures are averaged over a month to compute the monthly average bid-ask spread. The following formula will be used to compute these values:
𝐵𝑖𝑑𝑎𝑠𝑘 (𝑖, 𝑚) = 1 𝑊(𝑖, 𝑚)∗ ∑ [(𝐴𝑏𝑠𝑉(𝑏𝑖𝑑(𝑖, 𝑚, 𝑡) − 𝑎𝑠𝑘(𝑖, 𝑚, 𝑡))) / ( 𝑊(𝑖,𝑚) 𝑡=1 𝑏𝑖𝑑(𝑖, 𝑚, 𝑡) + 𝑎𝑠𝑘(𝑖, 𝑚, 𝑡) 2 )]
Where 𝐵𝑖𝑑𝑎𝑠𝑘 (𝑖, 𝑚) is obviously the bid-ask spread measure for stock 𝑖 in month 𝑚, 𝑊(𝑖, 𝑚) is the number of weeks for which stock data is available for stock 𝑖 in month 𝑚, 𝐴𝑏𝑠𝑉 indicates that the absolute difference between the bid and ask price is taken, and finally 𝑏𝑖𝑑(𝑖, 𝑚, 𝑡) and 𝑎𝑠𝑘(𝑖, 𝑚, 𝑡) respresent the bid and ask price for stock 𝑖 in month 𝑚 on week 𝑡 respectively.
4.1.3 Control variable data
The stock return (r) is calculated as the ratio between the stock price in month t+1 and the stock price in month t, using month-end data.
The stock volatility (vol) is extracted as the 30-day volatility of a stock from Bloomberg, and is based on the standard deviation of the stock’s historical price.
The equity value (lnev) is defined as the natural logarithm of the market capitalization of the company, which is extracted directly from Bloomberg.
The GDP growth (gdp) is defined as the monthly return of the nominal GDP of the countries in which the banks are headquartered. The GDP data is collected from the OECD database on a quarterly basis. The data is then converted to monthly data using cubic spline
interpolation6. Because cubic spline interpolation will cause an error in the regression model,
which will be further discussed in section5, a different statistical method will be used to correct for this.
As a proxy for the risk-free rate the 3-month Libor rate is used. This data is collected on a monthly basis from Bloomberg.
4.1.4. Descriptive statistics
To be able to link the abbreviations to the rightful variables, a brief description follows below.
Table 1: Variable abbreviations
CDS Spread (LN) lncds Bid-Ask Measure Bidask
Stock Return r
Stock Volatility vol
Market Cap (LN) lnev
GDP Growth (%) gdp
Libor 3 Month libor
The descriptive statistics per variable are reported below in Table 2.
Table 2: Descriptive statistics
(1)
mean Var sd skewness kurtosis
lncds 4.046463 1.389504 1.178772 -.5015659 2.045915 bidask .0039128 .000435 .0208561 22.08042 585.3589 r .0017209 .0112001 .1058307 .6240967 12.13079 vol 35.85207 873.3724 29.55287 3.537449 23.15634 lnev 10.79749 .4732238 .6879126 -.5391027 3.669596 gdp .3368985 .5018186 .7083915 -1.913518 9.292466 libor 1.953758 3.863157 1.965491 .7088006 1.88425 N 2268
6 Cubic spline interpolation is a mathematical tool to estimate new data points between
existing data points. Spline interpolation in particular uses low-degree polynomials in every interval, choosing the polynomials in a way that they fit smoothly together.
Table 3: Percentiles
The above statistics report the values of the several percentiles, the mean, the standard deviation (std. dev.), the variance, the skewness, the kurtosis, and the number of observations (Obs) of both the dependent variable (lncds), the independent variable (bidask), and the control variables over the period April 2004 to September 2014.
A short summary of (most) the above statistics is provided in the table below.
Table 4: Summary of decriptive statistics
mean sd min max
lncds 4.046463 1.178772 1.335 6.941 bidask .0039128 .0208561 0 .6373929 r .0017209 .1058307 -.622 .968 vol 35.85207 29.55287 6.474 372.692 lnev 10.79749 .6879126 7.813 12.276 gdp .3368985 .7083915 -4.4836 2.1091 libor 1.953758 1.965491 .22335 5.62125 N 2268
4.2. The Model
To assess the relation between stock liquidity and CDS spreads a panel data regression will be used. The dependent variable will be the CDS spread and the independent variable will be the stock liquidity. Furthermore in accordance with the theory discussed in Section 2, there will be several control variables used, notably: stock return volatility, market value of equity, stock return, the risk-free rate and GDP growth rate.
The use of panel data has some advantages over other types over data. Panel data deals with the omitted variable issue since it takes care of heterogeneity in cross-sectional units in each time period. Panel data also provides us with more information than cross-sectional data, since it allows us to examine how independent variables behave across companies over different periods, and explain its effects on the dependent variable.
This study analyzes 18 banks in a cross-sectional dimension over a period of 126 months. The dataset is complete for all variables for each bank and each time period, therefore it is a balanced panel data set consisting of 2268 observations for each variable. A complete list of
(1) Variables 1% 25% 50% 75% 99% lncds 1.609 2.962 4.4275 4.9245 5.993 bidask .0001252 .0005194 .0008613 .0013713 .0440553 r -.256 -.046 .003 .051 .293 vol 10.47 18.9725 26.585 41.0365 146.682 lnev 8.879 10.4345 10.804 11.2385 12.056 gdp -2.1126 .0952 .484 .7745 1.4122 libor .2274 .29 .588 3.51625 5.48063 N 2268
all the banks used and the respective countries in which they are headquartered is found in table 13 and 14 of the appendix.
The central hypothesis is formulated as follows:
(1) Stock liquidity is negatively related to CDS spreads
The stock market and the debt market evaluate a firm’s credit quality, therefore a relation between stock liquidity and CDS spreads is expected to be found.
The general regression will have the form of:
𝑙𝑛𝑐𝑑𝑠
𝑖,𝑡= 𝛼
𝑖+ 𝐵
1𝑏𝑖𝑑𝑎𝑠𝑘
𝑖,𝑡+ 𝐵
2𝑟
𝑖,𝑡+ 𝐵
3𝑣𝑜𝑙
𝑖,𝑡+ 𝐵
4𝑙𝑛𝑒𝑣
𝑖,𝑡+ 𝐵
6𝑙𝑖𝑏𝑜𝑟
𝑖,𝑡+ 𝐵
7𝑔𝑑𝑝
𝑖,𝑡+ 𝜀
𝑖,𝑡Where the logarithm is taken of the market value of equity in order to adjust for large values before using them in regressions. The under scripts stand for the particular firm 𝑖 and the particular time period 𝑡.
4.2.1. Multicollinearity
Before the model is estimated, one must first look if there is (imperfect) multicollinearity
between the independent variables. “Multicollinearity means that two or more regressors are highly correlated in the sense that there is a linear function of the regressors that is highly correlated with another regressor. Imperfect multicollinearity does not pose any problems for the theory of the OLS estimators” (Stock & Watson, 2012: 244).
Table 5: Correlation matrix of all the variables
(1)
lncds bidask r lnev vol libor gdp
lncds 1 bidask -0.0898*** 1 r -0.0537* -0.00632 1 lnev -0.327*** 0.0575** 0.0952*** 1 vol 0.473*** -0.0463* -0.164*** -0.406*** 1 libor -0.765*** 0.142*** -0.0538* 0.231*** -0.170*** 1 gdp -0.399*** 0.0254 0.0683** 0.308*** -0.648*** 0.230*** 1 * p < 0.05, ** p < 0.01, *** p < 0.001
Table 5 presents the correlation matrix. There are two correlations that exceed 0.60, which are the correlations between lncds and libor and between vol and gdp. Since the highly correlated variables are believed to contain too much information to be dropped, and the OLS regression assumption are not violated, the variables will remain in the regression
analysis. One must realize though that multicollinearity is potentially present and be aware of its consequences (i.e. high standard errors and wide confidence intervals for coefficients).
4.2.2. Random and Fixed effects
For a proper estimation of the regression model this study turns to two possible statistical techniques, namely the random and fixed effects model. In the random model, the individual-specific effect is a random variable that is uncorrelated with the explanatory variables. In the fixed effect model, the individual-specific effect is a random variable that is allowed to correlate with the explanatory variables.
The random effects model is best used when there is a strong belief that the differences across entities (banks) influence the dependent variable. Since the banks in the sample all operate in similar environments, and can all trade the same instruments in the financial markets, it is assumed that there is no variable that explains the variation in the dependent variable that is different among the banks in the sample. To give this theoretical assumption some statistical support, a statistical test is performed to see whether it is indeed better to use fixed effects instead of random effects.
One statistical test that can help decide whether fixed or random effect have to be used is the Hausman test. The Hausman test basically tests if the unique errors
𝑢
𝑖,𝑡 are correlated withthe regressor. The null hypothesis is that these errors are not correlated with the regressor. These unique errors are errors between entities, and are not to be confused with the error term
𝜀
𝑖,𝑡,
which exhibits errors within entities.If the unique errors are correlated with the regressor then the chi-squared value should be significant (i.e. <0.05). As can be seen from the Hausman test in table 6, the value is
significant (0.0196) and thus the null hypothesis that the unique errors are not correlated with the regressor is rejected. This result support the followed economic theory and the choice to use fixed effects for the regression analysis.
Table 6: Hausman test
Coefficients
(b) fixed (B) random (b-B) difference S.E. bidask -0.1887132 -0.0286037 -0.1601095 0.050484 r -0.3386326 -0.3560941 0.0174615 0.0094558 lnev -0.2020549 -0.1424984 -0.0595566 0.030334 vol 0.0123258 0.0126267 -0.0003009 0.0001572 libor -0.4101347 -0.4140367 0.003902 0.0018615 gdp -0.0162917 -0.021423 0.0051313 0.0034483 Chi2 13.43 Prob > Chi2 0.0196
4.2.3. Heteroskedasticity and time-fixed effects
We also inspect the sample for heteroskedasticity by using a user-written program in Stata. It is a special heteroskedasticity test for a fixed effect regression model.
The Heteroskedasticity test in Table 7 signals that heteroskedasticity is present in the model. Since the null hypothesis, a constant variance (homoscedasticity), is rejected (p<0.05). To correct for heteroskedasticity there will be made use of Huber/White or sandwich estimators, to obtain heteroskedasticity-robust standard errors. This option is available in Stata with the command “robust”.
Table 7: Test for heteroskedasticity
Modified Wald test for group wise heteroskedasticity in fixed effect
regression model Chi2 (18) 170.84 Prob > Chi2 0.0000
H0:
𝜎(𝑖)
2= 𝜎
2for all𝑖
To see if the fixed effects model that is used needs time-fixed effects as well, a final test for the regression model is performed. It is certainly possible that there are unobserved variables that vary across time that influence the CDS spread. To control for such variables, a time-fixed effects regression model can be used. To know whether such a model is to be used, a test for time-fixed effects is performed. This can be done with the command “testparm” in Stata. It basically is a joint test to see if the dummies for the months are equal to zero. If they are, then no time-effects are needed. The output of the test can be found in Table 8 below
Table 8: Test for time fixed effects
F (135, 2109) 70.48
Prob > F 0.0000
The F-statistic is significant and thus the null hypothesis that the coefficients for all months are jointly equal to zero is rejected. Therefore time-fixed effects need to be used in the model.
4.2.3. Causality
A crucial part of the implications of this study is linked to the causality issue. Since this study has adopted and followed the theoretical notion that CDS spreads are possibly caused by higher bid-ask spreads, some statistical support must be added to this notion. It can be argued that higher stock illiquidity (i.e. higher bid-ask spreads) cause higher CDS spreads, instead of vice versa. Therefore this paper turns to the Granger causality test7, which can
help identify the direction of the causality. For this procedure a number of lags has been created for both the CDS spread and the bid-ask spread variable. The dependent variable is regressed on its own lags and the lags of the independent variable, after which an F-test is performed on the lags of the independent variable, to see whether the lags are jointly significant. The same procedure is repeated for the regression of the independent variable on the dependent variable, but now the F-test is performed on the lags of the dependent variable.
Table 9 and Table 10 contain the Granger causality tests for two, three, and four lags.
7 Although the Granger causality test is widely used because of its computational simplicity,
Table 9: Granger causality test (1)
Causality direction: Does stock liquidity Granger-cause CDS spreads?
2 lags 3 lags 4 lags
F 5.44 4.71 5.13
Prob > F 0.0149 0.0143 0.0068
Table 10: Granger causality test (2)
Causality direction: Do CDS spreads Granger-cause stock liquidity?
2 lags 3 lags 4 lags
F 0.82 0.86 1.19
Prob > F 0.4568 0.4811 0.3514
As can be seen from Table 9, the F-test boast a statistically significant value, therefore the null hypothesis that the lags of stock liquidity are jointly insignificant can be rejected, and it can be conluded that stock liquidity Granger causes CDS spreads. The F-test in Table 10 shows a statistically insignificant value on all lags, therefore the null hypothesis that the lags of the CDS spread are joinly insignificant cannot be rejected, and it can be conluded that CDS spreads do not Granger cause stock liquidity.
5. Empirical Analysis
The regression results for the estimated model can be found in Tables 11-13.
In Table 11 it is shown that the empirical analysis containing time-fixed effects, and controlling for equity return (r), equity volatility (vol), equity value (lnev), interest rate (libor), and GDP growth (gdp), displays a significant positive relationship between stock liquidity (bidask) and the CDS spread (lncds).
The coefficients of the control variables support the theoretical assumptions, the intuitive reasoning, and the existing literature. All the variables show significant probabilities (p<0.05). However when the regression is ran again, controlling for heteroskedasticity and
autocorrelation, using heteroskedasticity and autocorrelation consistent (HAC) standard errors, the result indicate that stock return (p=0.066) and equity value (p=0.064) become The result also shows that GDP becomes completely irrelevant (p=0.204). The HAC standard errors are also known as Newey-West standard errors, which are the ones that should be used in this study, since the GDP variable was calculated using the cubic spline interpolation method. Without the use of Newey-West standard errors, a systematic source of serial correlation enters the model, violating the OLS assumption of no autocorrelation.
The commonly used goodness of fit statistic (𝑅2) boasts a value of 0.951 when using the
robust regression model. This high value of 𝑅2 indicates that the model fits the data well.
Table 11: Regression with time-fixed effects and robust standard errors
(1)
VARIABLES Time-Fixed Effects and Robust Standard Errors bidask 2.672** (1.154) r 0.184* (0.0938) lnev -0.299* (0.151) vol 0.00479*** (0.00142) libor 0.180*** (0.0179) gdp -0.0732 (0.0554) Constant 5.875*** (1.650) Observations 2,268 Number of bank 18 R-squared 0.951 Bank FE YES Date FE YES
Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1
From table 11, an expected significant positive relationship between the stock liquidity variable and the CDS spread is observed. Furthermore the table shows (albeit slightly
insignificant) the expected negative relationship between equity value and the CDS spread, and the expected positive relationship between equity volatility and the CDS spread. The table also shows a counterintuitive positive relation between stock return and the CDS spread. This may be due to the fact that stock return is correlated with equity value and stock volatility, since the latter control variable use stock return as input data. The most significant variable is the risk-free rate, as measured by the 3-month Libor in the model. It has a positive relation with the CDS spread, which is in line with expectations.
Table 12: Regression without time-fixed effects
(1)
VARIABLES Without Time-Fixed Effects
bidask -0.189 (0.815) r -0.339* (0.165) lnev -0.202 (0.191) vol 0.0123*** (0.00166) libor -0.410*** (0.0255) gdp -0.0163 (0.0709) Constant 6.594*** (2.057) Observations 2,268 Number of bank 18 R-squared 0.732 Bank FE YES
Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1
Table 13: Regression without robust standard errors
(1)
VARIABLES Without Robust Standard Errors
bidask 2.672*** (0.289) r 0.184** (0.0791) lnev -0.299*** (0.0273) vol 0.00479*** (0.000444) libor 0.180*** (0.0201) gdp -0.0732*** (0.0151) Constant 5.875*** (0.304) Observations 2,268 R-squared 0.951 Number of bank 18 Bank FE YES Date FE YES
Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1
Table 12 and Table 13 show the regression results of the estimated model without time-fixed effects and without robust standard errors, respectively. One could note that when no time-fixed effects are used, the relation between stock liquidity and CDS spreads becomes insignificant. This could be due to several dynamics that change over time and have effect on the CDS spread, such as regulation. An overview of the three regressions is provided in Table 14.
Table 14: Overview of regressions
Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1
(1) (2) (3)
VARIABLES Time-Fixed Effects Without Time-Fixed Effects Without Robust Standard Errors bidask 2.672** -0.189 2.672*** (1.154) (0.815) (0.289) r 0.184* -0.339* 0.184** (0.0938) (0.165) (0.0791) lnev -0.299* -0.202 -0.299*** (0.151) (0.191) (0.0273) vol 0.00479*** 0.0123*** 0.00479*** (0.00142) (0.00166) (0.000444) libor 0.180*** -0.410*** 0.180*** (0.0179) (0.0255) (0.0201) gdp -0.0732 -0.0163 -0.0732*** (0.0554) (0.0709) (0.0151) Constant 5.875*** 6.594*** 5.875*** (1.650) (2.057) (0.304) Observations 2,268 2,268 2,268 R-squared 0.951 0.732 0.951 Number of bank 18 18 18
Bank FE YES YES YES
6. Conclusion
This study analyzes the relationship between stock liquidity and CDS spreads. For this analysis a number of theoretically important determinants of CDS spreads are used as control variables.
For this research a panel data set has been used, consisting of 18 banks and a time frame of 126 months, making up a total number of 2268 observations. For the measurement of stock liquidity the bid-ask spread is used. Where high stock liquidity is defined as to be determined by a low bid-ask spread. The estimated results in this study point to a positive relationship between stock illiquidity (i.e. a higher bid-ask spread) and CDS spreads. This result is in line with the theoretical expectation. The result also proves that stock liquidity is a significant determinant of a bank’s CDS spread when controlling for important macroeconomic variables. The causality test point towards a causal direction in which the stock liquidity Granger causes CDS spreads, confirming our theoretical and intuitive notion, and hence strengthening the possible implications of this study.
The implications of this study can be used for policy makers, such as governments and central banks, as well as for investment purposes by other financial institutions. Using the relationship of stock liquidity and CDS spreads for the analysis of future CDS spread
movements can serve as a red flag indicator for central banks. Whenever the stock liquidity of a banks drops significantly, the central bank can use this relationship to argue for a better monitoring of the bank in question. This could allow central banks to detect default risk in an earlier stage, and intervene where necessary. For other financial institutions this relationship could have investment implications, since it could be regarded as a parameter when investing in banks. The parameter could be used in the form of a binary signal, signaling a positive signal whenever the stock liquidity is above its defined long-term average, and negative signal whenever it is below its long-term average.
7. References
Alexander, C., and A. Kaeck (2008), “Regime Dependent Determinants of Credit Default Swap Spreads”, Journal of Banking and Finance, Vol. 32, pp. 1008-1021
Amihud, Y., (2000), “Illiquidity and Stock Returns: Cross-Section and Time-Series Effects”, New
York University Working Papers Series no. FIN-00-041, Stern School of Business
Annaert, J., M. De Ceuster, P. Van Roy, and C. Vespro (2010), “What Determines Euro Area Bank CDS Spreads?”, National Bank of Belgium Working Paper, Brussels
Basel Committee on Banking Supervision (2013), “Global systemically important banks: updates assessment and methodology and the higher loss absorbency requirement” Das, S.R., and P. Hanouna (2008), “Hedging Credit: Equity Liquidity Matters”,Journal of Financial Intermediation, Vol.18, No.1, pp.112-123
De Jong, F., J. Driessen (2006), “Liquidity Risk Premia in Corporate Bond Markets”, Working
Paper, University of Amsterdam
Demirguc-Kunt, A., E. Feyen, R. Levine (2012), “The Evolving Importance of Banks and Securities Markets”, The World Bank Economic Review, Volume 28, Issue 3, August 2012 De Santis, A. R., and M. Stein (2014), “Financial Indicators Signaling Correlation Changes in Sovereign Bond Markets”, ECB Working Paper Series no. 1746, December 2014
Di Cesare, A., G. Guazzarotti (2010), “An analysis of the determinants of credit default swap spread changes before and during the subprime financial turmoil”, Banca D’Italia Working
paper
Ericsson J., .K. Jacobs, and R. Oviedo-Helfenberger (2009), “The Determinants of Credit Default Swap Premia”, Journal of Financial & Quantitative Analysis, 44, 109–132
Fitch Ratings (2011), “CDS Spreads and Default Risk: A Leading Indicator?”, Fitch Ratings
Macro Credit Research
Hull, J., (2012), “Options, Futures and Other Derivatives”, 8th edition, Prentice Hall
Hull, J., M. Predescu and A. White (2004), “The relationship between credit default swap spreads, bond yields and credit rating announcements”, Journal of Banking and Finance, 28(11), 2789–2811
Kool, C.J.M., and D.F. Gerritsen (2010), “Drama Icesave was te voorzien”, Economisch
Statistische Berichten, 95-4580
Merton, R.C., (1974), “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates”,
Journal of Finance, Vol. 29, pp. 449-470
Rösch, C. G., and C. Kaserer (2013), “Market liquidity in the financial crisis: The role of liquidity commonality and flight-to-quality”, Journal of Banking & Finance, Volume 37, Issue 7, July 2013, Pages 2284–2302
Singh, M., and C. Spackman (2009), “The Use (and Abuse) of CDS Spreads During Distress”,
Spiegel, M., and X. Wang (2005), “Cross-sectional Variation in Stock Returns: Liquidity and Idiosyncratic Risk”, Yale School of Management International Center for Finance, Yale University, Working Paper No. 05-13, EFA 2005 Moscow Meetings Paper
Tang, D.Y., and H. Yan (2010), “Market Conditions, Default Risk and Credit Spreads”, Journal
of Banking and Finance, Vol. 34, pp. 743-753;
Zhu, H., (2006), “An Empirical Comparison of Credit Spreads Between the Bond Market and the Credit Default Swap Market”, Journal of Financial Services Research, Vol. 29, No. 3, pp. 211-235
8. Appendix
Table 13: The list of banks used
1 Bank of America US
2 Barclays UK
3 BBVA Spain
4 BNP Paribas France
5 Commerzbank Germany
6 Credit Agricole France 7 Credit Suisse Switzerland
8 Deutsche Bank Germany
9 Goldman Sachs US 10 HSBC UK 11 ING Netherlands 12 JP Morgan US 13 Lloyds UK 14 Morgan Stanley US 15 RBS UK 16 Santander Spain 17 UBS Switzerland 18 Well Fargo US
Table 14: Number of banks per country
US 5 UK 4 France 2 Germany 2 Spain 2 Switzerland 2 Netherlands 1
