Investor sentiment in the CDS market : an empirical analysis on the influence of investor sentiment on CDS spreads in the Eurozone from 2007-2015

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Investor sentiment in the CDS market

An empirical analysis on the influence of investor sentiment

on CDS spreads in the Eurozone from 2007-2015

Bachelor thesis econometrics

Esmée Winnubst

10338179

BSc: Econometrics & Operational Research

Instructor: Isabelle Salle

Supervisor: Nancy Bruin

27 June 2015

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Abstract

During the last Euro crisis there were lots of movements of CDS spreads of Eurozone countries. These movements were not based on the fundamentals of these countries. Therefore this study examines whether investor sentiment can explain the movements of CDS spreads of Eurozone countries during this crisis period. To do so, the economic sentiment indicator is used as explanatory variable. Also fundamentals are used and a linear model is established. The eight used countries in this study are Austria, Belgium, France, Germany, Italy, the Netherlands, Portugal and Spain. Evidence is found that the economic sentiment indicator is a significant variable to predict movements in CDS spreads for all countries except Belgium. It is also found that not all fundamentals have the expected effect on the spreads. This can be caused by the effects of the crisis still affecting fundamentals.

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1 Introduction

The fragility of a monetary union 1.1

Many countries have often defaulted on their public debt in the past. For example Spain defaulted 13 times in the period from 1557 to 1882 because of its sovereign debt. Portugal defaulted six times because of central government obligations during the 19th century. Also Germany, Greece, the UK and the US defaulted multiple times on their government debts (Kopf, 2011).

By the increased preference for fiat currencies,1 governments could avoid complete defaults the past sixty years. As a result, the vision that sovereign debt crisis in advanced economies is a thing of the past raised. This confidence is inappropriate for members of the European monetary union according to Kopf (2011). “By adopting the euro, European governments have voluntarily put themselves into the position of “Emerging Markets” issuers, and have subjected themselves to elevated default risk” (Kopf, 2011, p.2).

A key feature of a monetary union is having the same currency. Therefore members of a monetary union have no control over the currency they issue debt (De Grauwe et al., 2013). De Grauwe et al. (2013) state that because of this, there cannot be assured that there is always enough cash available to pay out the bond at maturity by governments of countries within a monetary union. The absence of the guarantee of available cash makes countries in a monetary union vulnerable to default. As a result government bond markets in a monetary union are particularly fragile.

In contrast: “stand-alone countries”, countries that issue debt in a currency that is not used by other countries, do not suffer from this (De Grauwe, 2011). According to De Grauwe et al. (2013) governments of stand-alone countries can always give the guarantee that bondholders are paid out at maturity. These governments can contact the central bank to provide more cash without a limit, contrary to the European monetary union where this is not the case. This is because the European Central Bank (ECB) has abandoned its role as lender of last resort (De Grauwe, 2011).

1_{Fiat currencies are currencies that derive their value from the confidence that it can buy property and services}

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Countries that are member of a monetary union are sensitive to movements of distrust (De Grauwe et al., 2013). Government bonds are sold when investors fear trouble as to payments. This has two effects. Firstly the interest raid rises and secondly it triggers a liquidity outflow as the investors look for a new place to invest after they have sold the government bonds. This sudden stop can cause a condition in which the government cannot pay its debt. The resulting liquidity crisis can turn into a solvency crisis. According to De Grauwe et al. (2013), this solvency crisis in combination with increasing interest rates reduces government revenues and increases the deficit and debt levels. This causes a vicious circle: the investor sentiment will decrease even more, which leads investors selling their bonds. Therefore the government is pushed into default.

Thus government bond markets of a monetary union are more fragile than “stand-alone” countries. This is a result of the absence of the guarantee of available cash to pay bondholders at maturity. The absence of the guarantee of available cash makes countries in a monetary union vulnerable to sovereign default.

Increased credit risk Eurozone countries 1.2

In the period from 2007 to 2009 the average 10-year European credit default swap2 (CDS) spread increased substantial with cross-sectional differences (Chiarella et al., 2014). Several papers state that the cause for this movement is reprising of global risk and increased risk aversion of investors, combined with macroeconomic factors (Sgherri and Zoli, 2009; Attinasi et al., 2009; Gerlach et al., 2010; Caceres et al., 2010).

Thus far no research has been done concerning the influence of the investor confidence rate on CDS spreads. Multiple previous papers have looked into the influence of the investor confidence rate on economic activity. Investor sentiment affects GDP growth, industrial production growth and real business investment according to Sentero and Westerlund (1996). Also stocks are affected by the investor confidence rate (Baker and Wurgler, 2007). The effects of investor sentiment are important on individual firms and on the stock market as a whole (Baker and Wurgler, 2007). Mourgougane and Roma (2003) have proven that investor’s confidence indicators can forecast real GDP growth rates in the short-run. Thus several researches have proven the influence of the investor confidence rate on

2_{Credit default swap (CDS) is a financial swap agreement that can be used as an insurance of a portfolio of}

bonds. In case of a default (by the debtor), the CDS compensates the buyer. The CDS was invented byBlythe Mastersin 1994. A premium of 100 basis points on the CDS market means that it costs about 10.000 euro to buy protection on 1 million euro in government debt.

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macroeconomic variables. No such research has been done yet concerning the effects of investor sentiment on CDS spreads. Therefore the purpose of this paper is providing research on the influence of investor’s confidence rate on CDS spreads. The main research question concerns assessing the extent to which investor confidence affects CDS spreads.

In this paper, the time-series relationship between investor confidence and CDS spreads of countries that are member of the European Monetary Union are examined. This is done through using the economic sentiment indicator (ESI) as a measure of investor sentiment. Why the ESI is used, and how the ESI is measured is explained in Section 3: Data description. There is also examined in this paper whether there is a difference in the influence of ESI on CDS spreads between core and periphery countries.

To assess the extent to which investor sentiment affects CDS spreads, first previous theories are examined in Section 2, theoretical framework. This section summarizes the main theories of previous research concerning CDS spreads and the investor confidence rate. Also the hypotheses are formed in this section. Then in Section 3 the independent and explanatory variables are clarified. Section 4, research methodology presents the model that is used in this paper. Section 5, results, shows the results of the research in this study. Thereafter the results are analyzed in Section 6. Finally a conclusion is drawn in Section 7.

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2 Theoretical framework

To assess the extent to which investor sentiment affects CDS spreads, first a previous theory concerning the credit risk pricing in the European Monetary Union is looked at. The second paragraph concerns the contrasting difference between the CDS spreads of periphery and core countries. Next the effect of investor sentiment rate on other economic variables as stock price are discussed. In Section 2.4 the hypotheses are proposed.

Credit risk pricing in the European monetary union 2.1

Credit risk is the risk of loss of a financial reward due to uncertainty in a borrower’s ability to meet its due obligations. Credit risk affects all market participants expecting a future payment. Sovereign risk is a form of credit risk and is defined as the risk that the government fails to payout the bondholders at maturity. CDS are the most commonly used credit derivatives to secure against this risk (Choudry, 2011).

According to Chiarella et al. (2014), estimating risk and returns in other asset markets has important similarities with the pricing of credit risk in the European monetary union. Multiple papers state that there are large and continued deviations from fundamentals3 in many asset markets. These markets include the equity market (Baker and Wurgler, 2007), the foreign exchange market (Frankel and Froot, 1990) and the housing market (Case and Shiller, 2003).

The abovementioned deviations from fundamentals can lead to financial market bubbles. Chiarella et al. (2014) state that various academic and non-academic bond market specialists are skeptical about the ability of the market to correctly price (national) credit risk. This skeptical view increased after the emergence of serious debt problems in some countries of the European Monetary Union.

Chiarella et al. (2014) state that investors assessed the financial and economic situation of several European Monetary Union members too optimistic. Also the ability of other members to support the countries with debt problems if necessary appears to be too optimistic estimated. As a result the market for credit risk shows bubble-like behaviour. This

3_{Fundamentals are the qualitative and quantitative information that is the fundament for financial valuation of a}

company, security or currency. Investors use these fundamentals to estimate whether the underlying asset is considered a worthwhile investment.

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bubble-like behaviour consists of underpricing of risk pre-crisis (Beirne & Fratscher, 2012) and overpricing of risk post-crisis (Gosh, Ostry, Qureshi, 2012). Therefore there can be concluded that CDS spreads were also underpriced pre-crises and overpriced post-crisis (Chiarella et al., 2014).

To conclude: large deviations from fundamentals in markets can lead to overpricing financial products. The market is not able to price credit risk correctly. Investors were too optimistic about the economic and financial situation of the European monetary union. Therefore CDS spreads were underpriced pre-crisis and overpriced post-crisis. The question that raises here is:

Is investor sentiment able to predict the underpriced pre-crisis CDS spreads and the overpriced post-crisis CDS spreads? (1)

Periphery and core countries: the differences 2.2

De Grauwe et al. (2013) want to test whether there are movements in CDS spreads that are unrelated to underlying fundamentals. To do so, the study measures the importance of time dependent effects on the movements of CDS spreads that are unrelated to fundamentals. The results show big differences between stand-alone- and European Monetary Union countries. The paper also shows significant prove that the CDS spreads in the peripheral countries of the European Monetary Union moved independent from the underlying fundamentals during the post-crisis period.

The results of the paper from De Grauwe et al. (2013) indicate the following movement: “Before the crisis the markets did not see any risk in the peripheral countries’ sovereign debt. As a result they priced the risks in the same way as the risk of core countries’ sovereign debt. After the crisis, spreads of the peripheral countries increased dramatically and independent from observed fundamentals” (De Grauwe et al., 2013).

Thus many movements in the CDS spreads of the peripheral European Monetary Union countries during the period from 2010-2011 were independent from underlying fundamentals. These movements are a result of the increasing time dependent negative market sentiments since the end of 2010. As with the market bubbles, a question raises here.

Can investor sentiment predict the different movements in CDS spreads

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The effect of investor sentiment rate on other economic variables 2.3

Mourougane and Roma (2003) examine the usefulness of the European Commission confidence indicators for forecasting real GDP rate movements in the short-run. Their sample exists of six euro area countries: Belgium, Spain, Germany, France, Italy and the Netherlands. Using a linear model, the relationship between real GDP and confidence indicators is estimated. Thereafter a benchmark ARIMA model is used to measure the forecasting performance of the estimated models. The results show that confidence indicators are appropriate for forecasting real GDP growth rate in the short-run.

Santero and Westerlund (1996) investigate the usefulness of sentiment measures obtained from consumer and business surveys to forecast economic movements. Thereafter the relationship between confidence indicators and the used economic activities (GDP growth, industrial production growth and real business investment) is tested empirical by doing graphical examination, correlation analysis and Granger causality tests. Sentiments measured by business surveys are more suitable and reliable for forecasting economic movements compared to consumer surveys (Santero and Westerlund, 1996). Their study also finds that sentiment affects GDP growth and industrial production growth. At last, no effect of sentiment on real business investment has been found.

Baker and Wurgler (2007) give theoretical and empirical evidence that investor sentiment has effects on the stock market. Their study investigates which stocks are most affected by investor sentiment. The study concludes: “In particular, stocks of low capitalization, younger, unprofitable, high volatility, non-dividend paying, growth companies, or stocks of firms in financial distress, are likely to be disproportionately sensitive to broad waves of investor sentiment” (Baker and Wurgler, 2007). Stocks whereby determining the value is hard or that are difficult to arbitrage are most affected by investor sentiment.

Investor sentiment affects GDP growth rate and industrial production growth. Investor sentiment is also useful to forecast stock movements. No effect of investor sentiment on real business investment has been found. Therefore the following question is asked:

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Hypotheses 2.4

As a result of the abovementioned theory with the relating questions that rose, the following hypothesis is formed:

Hypothesis 1: Movements in CDS spreads are affected by investor sentiment.

When this hypothesis is confirmed, the following sub-hypotheses follow:

Hypothesis 1A: Investor sentiment can explain different movements between core and periphery countries in CDS spreads.

Hypothesis 1B: Investor sentiment can explain movements that are not based on fundamentals.

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3 Data description

In this section the data is described. The dependent and explanatory variables are explained and thereafter the descriptive statistics of the data are given.

Dependent variable 3.1

The effect of investor sentiment on CDS spreads is investigated by using an empirical model. The dependent variable in this model is the 10-year CDS spread of Eurozone countries. There are twelve countries that have adopted the Euro since the start on 1 January 2002. These countries are Austria, Belgium, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, Netherlands, Portugal and Spain. Finland, Greece, Ireland and Luxembourg are not used in this paper because of data limitations. The other eight countries are used to estimate the effect of investor sentiment on CDS spreads. From now on, these countries are referred to as Eurozone countries. The other Eurozone countries Cyprus (2008), Estonia (2011), Latvia (2014), Lithuania (2015), Malta (2008), Slovakia (2009) and Slovenia (2007) are not taken into account in this study because of the less available data since these countries joined the Eurozone after 2002.

The estimation contains monthly data of these abovementioned Eurozone countries from the period January 2007 until May 2015. This range is chosen because of the availability of data. CDS spreads are obtained from Datastream.

Explanatory variables 3.2

3.2.1 Economic Sentiment Indicator

To test whether investor sentiment has an influence on CDS spreads a sentiment indicator is necessary. Mourourgane and Roma (2003) use the economic sentiment indicator (ESI) to test whether investor sentiment can be used to predict GDP growth. Mourourgane and Roma (2003) have proven that the ESI is a significant and good variable to predict GDP growth.

The ESI is obtained from Eurostat and is a European Commission confidence indicator. The data is monthly and available for all Eurozone countries in the estimated period. The economic sentiment indicator is made up of five confidence indicators with different weights. Industrial- (40%), Services- (20%), Consumer- (10%), Construction- (10%) and Retail trade confidence indicator (20%). The data is seasonally adjusted by Eurostat. The

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detailed description of ESI as stated on the website of Eurostat is given in Appendix I. The expected effect of ESI on CDS spreads is negative.

3.2.2 Fundamentals predicting CDS spreads

The CDS spread depends on the probability of default. The higher the risk of sovereign debt, the higher the accompanying spread. Multiple studies have investigated predictors of CDS spreads, so called fundamentals. These fundamentals can be used to determine the risk-neutral probability of default.

Some of the collected data contain seasonality patterns. These patterns are detected and adjusted by using the Census X13 seasonal adjustment tools. The X13 method seasonally adjusts monthly or quarterly data.

Some of the fundamentals are only available on quarterly basis. To divide this quarterly data into monthly data, the cubic spline interpolation method is used. This method is more precise than linear spline interpolation (Bourke, 1999). As a consequence it requires at least 4 points instead of 2, which is not of a problem.

The fundamentals in this paper are based on previous risk theories and are closely investigated. Chiarella et al. (2014) use seven fundamentals of which four are significant. Chiarella et al. (2014) do not use an investor sentiment variable because they try to establish a fundamental value; they not try to establish a value that closely resembles the CDS spread. The four significant fundamentals used by Chiarella et al. (2014) are also used in this research. What these fundamentals are, why they predict CDS spreads and how they are obtained is explained below.

Debt to GDP ratio

The debt to GDP ratio is the ratio between a government’s debt and its gross domestic product. A low debt to GDP ratio indicates that a countries economy operates in a way that the sells are sufficient to pay back debt. An increase of the government’s debt to GDP ratio leads to an increasing probability of default (De Grauwe et al., 2013). Therefore the increase in probability leads to an increase in CDS spread of the government. The data is monthly and obtained via Eurostat. It is expected that the effect of debt to GDP on CDS spreads is positive.

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Local stock market returns

The wealth of a country’s economy is immediately affected by local stock market returns. Local stock market returns are regarded as an important indicator of economic activity (Longstaff et al., 2011). Spending by households and investments by firms are affected by developments in stock markets. Also consumer confidence is affected by returns of the local stock market.

Using a country’s MSCI index the local stock market returns are approximated. This is the same significant method Longstaff et al. (2011) include in their analysis. The data in the sample are daily returns and are obtained from Datastream. To calculate the returns, the first differences of the log data is taken. High returns are expected to have a positive effect on the economic activity and therefore a negative effect on the CDS spread.

Sovereign credit rating

Sovereign credit ratings are a risk indicator of investing in a country (Cantor and Packer, 1996). Sovereign credit ratings give investors insight in the likelihood that a borrower will default on its obligations. This level of risk when investing in a country also includes political risks.

There are three main agencies that rate the credit of governments: Standard and Poors (S&P), Fitch and Moody’s. All three agencies give approximately the same credit rating to countries. Therefore there is no agency better than the other agencies to predict CDS spreads (Hill et al., 2010). The S&P rating is used because of the best availability of data. The sovereign credit ratings are quarterly and obtained via Oxford Economics (Datastream). The rating is converted into values from 1 to 20 where AAA represents 20 and D represents 1. The forecast is that a high sovereign credit ratings leads to a low CDS spread.

Terms of trade

Terms of trade measure the relative price of a country’s exports in terms of its imports (Obstfeld et al., 1996). It is defined as the ratio of export prices to import prices. This means the amount of import goods an economy can purchase per unit of export goods. The ability of a country to make payments on external debt is affected by the ability to generate revenue from exports. Terms of trade affect this ability to generate revenue form exports (Hilscher and Nosbusch, 2010). Hilscher and Nosbusch (2010) show that the terms of trade has a significant effect on CDS spreads. Their study finds that spread rates have a tendency to decrease for countries that have an improving terms of trade.

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The data for all Eurozone countries is monthly and obtained from OECD.stat. The data contains the total import and export value of the countries. The terms of trade is calculated by dividing the total import value by the total export value. It is expected that the effect of terms of trade on CDS spreads is negative.

Descriptive statistics 3.3 3.3.1 Dependent variable 0 200 400 600 800 1,000 2007 2008 2009 2010 2011 2012 2013 2014 2015 CDS_AU CDS_BE CDS_FR CDS_GE CDS_IT CDS_NL CDS_PT CDS_SP

Figure 3.1: CDS spread in the Eurozone from 01/2007 until 05/2015.

The CDS spreads of Eurozone countries increased a lot during the period from 2007 until 2012. The result is clear to see in Figure 3.1. In Table 3.1 the descriptive statistics of the CDS spreads are given. The CDS spreads have a high standard deviation, which is normal for time series, and do not follow a normal distribution according to the Jarque-Bera test.

Table 3.1

Descriptive statistics of the CDS spread

Austria Belgium France Germany Italy NetherlandsPortugal Spain

Mean 57.41726 77.91447 59.22004 31.69176 156.4165 42.57629 279.1135 147.4581 Maximum 245.45 249.042 158.461 88.80298 444.9399 126.66 954.5398 413.6799 Minimum 2.4 3.2 2.5 2.4 11.6 2.1 7.2 5.5 Std. Dev. 43.82228 57.37685 37.28519 18.67195 103.1246 27.01426 253.5298 99.19405 Skewness 1.252544 1.107566 0.483776 0.571297 0.67495 0.81026 1.078166 0.47285 Kurtosis 5.321001 3.877242 3.101221 3.412432 2.996832 3.734451 3.390197 2.400096 Jarque-Bera 49.07975 23.88804 3.98277 6.209904 7.668586 13.3215 20.20851 5.27824

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3.3.2 Explanatory variables Economic sentiment indicator

The economic sentiment indicators of the eight used countries show large fluctuations. These fluctuations are visible in Figure 3.2. Striking are the two minimums around 2008-2009 and 2012-2013. The first minimum is the absolute minimum and a large dip in the sentiment; the second one is only a small dip. This in contrary to the single peak in the CDS spreads graph around 2011-2012. The descriptive statistics of the economic sentiment indicators are shown in Table 3.2. 60 70 80 90 100 110 120 2007 2008 2009 2010 2011 2012 2013 2014 2015 Australia 60 70 80 90 100 110 120 2007 2008 2009 2010 2011 2012 2013 2014 2015 Belgium 70 80 90 100 110 120 2007 2008 2009 2010 2011 2012 2013 2014 2015 France 70 80 90 100 110 120 2007 2008 2009 2010 2011 2012 2013 2014 2015 Germany 70 80 90 100 110 120 2007 2008 2009 2010 2011 2012 2013 2014 2015 Italy 60 70 80 90 100 110 120 2007 2008 2009 2010 2011 2012 2013 2014 2015 Netherlands 70 80 90 100 110 2007 2008 2009 2010 2011 2012 2013 2014 2015 Portugal 70 80 90 100 110 120 2007 2008 2009 2010 2011 2012 2013 2014 2015 Spain

Figure 3.2: Economic sentiment indicator in the period from 01/2007 until 05/2015

Table 3.2

Descriptive statistics of the Economic Sentiment Indicator

Mean 97.98911 99.05248 97.91584 101.2069 96.12574 96.96139 93.15842 94.0396

Maximum 117.3 116.8 114.9 117.5 111.8 117.6 108.5 110.4

Minimum 69.8 70.2 74.6 71.8 74.5 67.8 74.8 73.2

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Fundamentals

The debt to GDP ratio has increased a lot for all Eurozone countries in the period from 2007 until 2015 as can be seen in Figure 3.3 and Table 3.3.

20 40 60 80 100 120 2007 2008 2009 2010 2011 2012 2013 2014 2015 GDP_AU GDP_BE GDP_FR GDP_GE GDP_IT GDP_NL GDP_PT GDP_SP

Figure 3.3: Debt to GDP ratio in the period from 01/2007 until 01/2015

Table 3.3

Descriptive statistics of the debt to GDP ratio

The local stock market returns do show two small decreases in the period from 2007 until 2015. These decreases are around 2008 and 2012 and can be seen in Figure 3.4.

Table 3.4

Descriptive statistics of the local stock market return

Mean 62.26463 82.17784 61.43009 40.47402 95.38533 46.0837 67.21204 50.29879

Maximum 67.9 87.49999 72.5 43.1 112.4 56.5 78.6 76.43262

Minimum 51.2861 73.40163 48.6 36 80.2 33.96929 51.6 27.6

Std. Dev. 4.452012 3.971261 7.850556 2.551452 9.764458 6.912225 8.992043 16.44993

Mean 2765.814 2889.928 4105.841 7229.294 22869.19 373.6865 7569.637 10493.92 Maximum 4916.94 4707.5 6168.15 12001.38 43755.14 549.84 13405.3 15759.6 Minimum 1417.46 1610.56 2581.46 3710.07 12739.98 208.84 4453.01 6065 Std. Dev. 884.3926 758.3528 821.072 1664.326 8227.059 81.78409 2355.391 2265.586

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0 10,000 20,000 30,000 40,000 50,000 2007 2008 2009 2010 2011 2012 2013 2014 2015 LSMR_AU LSMR_BE LSMR_FR LSMR_GE LSMR_IT LSMR_NL LSMR_PT LSMR_SP

Figure 3.4: Local stock market return in the period from 01/2007 until 05/2015

The sovereign credit ratios of the most Eurozone countries decreased in the period from 2007 until 2015 as can be seen in Figure 3.5. Only Germany remained constant.

Table 3.5

Descriptive statistics of the sovereign credit ratio

The terms of trade decreased for all Eurozone countries (with some fluctuations) the past years. This is shown in Figure 3.6. This is in contrary with the economic theory. The CDS spreads decreased since 2012 and therefore an increase in terms of trade is expected.

Table 3.6

Descriptive statistics of the term of trade

Mean 19.86201 18.47536 19.62419 20 15.25739 19.94065 13.42909 16.5544 Maximum 20.03547 19.09054 20.03479 20 17.01052 20.03547 17.70269 20.01915 Minimum 19.333 17.57656 18.27919 20 11.96413 19.63153 8.884582 11.24497 Std. Dev. 0.181779 0.63471 0.561883 0 2.13006 0.127607 3.887898 3.718074

Mean 1.037289 0.967319 1.164398 0.822315 1.002068 0.892087 1.427879 1.261027 Maximum 1.120084 1.040421 1.239925 0.875101 1.138133 0.953455 1.806971 1.59834 Minimum 0.943576 0.919742 1.068569 0.774658 0.859721 0.847915 1.16453 0.974123 Std. Dev. 0.038757 0.023942 0.033357 0.023632 0.07062 0.018425 0.191693 0.167194

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8 10 12 14 16 18 20 22 2007 2008 2009 2010 2011 2012 2013 2014 2015 SCR_AU SCR_BE SCR_FR SCR_GE SCR_IT SCR_NL SCR_PT SCR_SP

Figure 3.5: Sovereign credit ratio in the period from 01/2007 until 05/2015

0.92 0.96 1.00 1.04 1.08 1.12 1.16 2007 2008 2009 2010 2011 2012 2013 2014 2015 Austria 0.900 0.925 0.950 0.975 1.000 1.025 1.050 2007 2008 2009 2010 2011 2012 2013 2014 2015 Belgium 1.05 1.10 1.15 1.20 1.25 2007 2008 2009 2010 2011 2012 2013 2014 2015 France .76 .78 .80 .82 .84 .86 .88 2007 2008 2009 2010 2011 2012 2013 2014 2015 Germany 0.85 0.90 0.95 1.00 1.05 1.10 1.15 2007 2008 2009 2010 2011 2012 2013 2014 2015 Italy Spain .84 .86 .88 .90 .92 .94 .96 2007 2008 2009 2010 2011 2012 2013 2014 2015 Netherlands 1.0 1.2 1.4 1.6 1.8 2.0 2007 2008 2009 2010 2011 2012 2013 2014 2015 Portugal 0.8 1.0 1.2 1.4 1.6 1.8 2007 2008 2009 2010 2011 2012 2013 2014 2015

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4 Research methodology

To test the formed hypotheses in section 2, a linear relationship between CDS spreads and investor sentiment is estimated. Therefore testing for stationarity is necessary and this is explained in Section 4.1. After testing for stationarity on the time series, the linear model is established.

Stationarity 4.1

Properties of stationarity

A time series yt is called stationary if the following three conditions are satisfied (Heij et al., 2004, p.536):

𝐸(𝑌_𝑡) = 𝜇 (1)

𝑉𝑎𝑟(𝑌_𝑡) = 𝐸(𝑌_𝑡− 𝜇)2 _{= 𝜎}2 _{= 𝛾}

0 (2)

𝐶𝑜𝑣(𝑌𝑡) = 𝐸(𝑌𝑡− 𝜇)(𝑌𝑡+𝑘− 𝜇) = 𝛾𝑘 (3) With μ, γ0 and γk finite-valued numbers that do not depend on time t.A stationary time series has a constant mean and fluctuates with the relatively the same amplitude around this mean (Heij et al., 2004, p.536).

When one of the three equations does not hold there is a non-stationary time series. This time series has a time-varying mean, variance or covariance (or more of them) and is therefore heterogeneous. In heterogeneous models it is difficult or impossible to estimate the mean, variance and covariance. To do a proper empirical analysis with reliable results, a homogeneous time series is needed. Therefore it is necessary for the model to have stationary time series (Heij et al., 2004, p. 536).

Deterministic and stochastic trends

Many economic time series show trending behaviour: they tend to grow over time (Heij et al., 2004, p.578). For example the level of industrial production and the AEX index contain trends. Such time series do not satisfy the conditions of stationarity. There are two types of trends: deterministic trends and stochastic trends. A simple example model of a deterministic trend is given in Equation 4 and an example of a stochastic trend is given in Equation 5.

𝑦𝑡= 𝛼 + 𝛽𝑡 + 𝜀𝑡 (4)

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To estimate the model correctly, it is very important to model the trend in a time series in an appropriate way (Heij et al, 2004, p.592). Deterministic trends have series reverting to the trend line in long run, effects of innovation shocks diminish over time and the forecast variance is constant for every moment in the time series. The series of stochastic trends do not revert to the trend line in long run, effects of innovation shocks do not diminish and have a permanent effect and the forecast variance is increasing over time (Heij et al.,2004, p.593).

Unit root

A common non-stationary model is the model with a unit root. A non-stationary time series with a unit root process is containing a stochastic trend (Heij et al., 2004). Consider a stochastic process {yt, t=1, …, ∞}, which can be rewritten as an autoregressive process of order p:

𝑦𝑡 = 𝑎1𝑦𝑡−1+ 𝑎2𝑦𝑡−2+ ⋯ + 𝑎𝑝𝑦𝑡−𝑝+ 𝜀𝑡. (6) Here is {εt, t=0,…, ∞} a serially uncorrelated stochastic process with mean zero and constant variance σ2. If m=1 is a root of the characteristic equation

𝑚𝑝_{− 𝑚}𝑝−1_𝑎

1− 𝑚𝑝−2𝑎2− ⋯ − 𝑎𝑝 = 0. (7)

Then the stochastic process has a unit root. This is the same as saying that the stochastic process is integrated of order one, denoted as I(1). If (m-1)r = 0 is a solution of Equation 7 then the stochastic process is integrated of order r. This non-stationary time series can be made stationary by taking the first differences (Heij et al., 2004). Therefore if the series is integrated order one, the lagged level of the series (Yt-1) provides relevant information predicting the change in Yt.

Testing for stationarity

In this paper, the explaining variables are based on time serial variables and therefore it is necessary that the variables are stationary. As showed above, it is important to investigate the behaviour of each variable in the empirical model to draw valid conclusions. Mourougane and Roma (2003) show in their paper that ESI and real GDP are integrated of order one. Therefore it is expected that the explaining variables in this paper are also integrated of order one.

The stationarity of the variables used in this paper are tested by using the Augmented Dickey Fuller (ADF) test. This test looks whether the model has a stochastic or deterministic trend. The ADF test estimates the nature of the trend by using the following model (Heij et al., 2004, p.593):

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𝛷(𝐿)𝑦𝑡 = 𝛼 + 𝛽𝑡 + 𝜀𝑡, (8) where εt is white noise and the AR polynomial Φ(z)= 1 - Φ1z - … - Φpzp with degree p. yt is either integrated of order one or trend stationary. The null hypothesis correspondents to yt is integrated of order one and β=0. If yt is integrated of order one, than the AR polynomial Φ(z) should contain a unit root, so that Φ(1)=0. Then de polynomial can be rewritten as Φ(z)=(1-z)Ψ(z). The alternative is that yt is trend stationary, that is the case if β≠0 and the AR polynomial is stationary (all the roots of Φ(z) lie outside the unit circle). The model in Equation 8 correspondents to a deterministic trend if Φ(1) >0 and β≠0, and it correspondents to a stochastic trend if Φ(1)=0 and β=0 (Heij et al., 2004, p.598).

H0: yt contains a stochastic trend  H0: Φ(1)=0 and β=0, Ha: yt contains a deterministic trend  Ha: Φ(1)> 0 and β≠0.

This can be tested by the F-test (Heij et al., 2004, p.596). The null-hypothesis is rejected if the calculated test statistic is smaller than the critical value.

For using the ADF it is important to choose the right lag order p. If the lag order p is too small, there is autocorrelation in the residuals. If the lag order p is too large, the power of the ADF test decreases. A method for choosing the right lag order is to start with p=1 and adjust this value. p=1 gives the following model:

𝑦_𝑡− 𝑦_𝑡−1= 𝛼 + 𝛽𝑡 + (𝛷 − 1)𝑦_𝑡−1+ 𝜀_𝑡 ∆𝑦𝑡= 𝛼 + 𝛽𝑡 + 𝜌𝑦𝑡−1+ 𝜀𝑡

(9) The lag order p is increased until the results show no significant autocorrelation in the residuals anymore.

Correcting for non-stationarity

If the explaining variables are found to be non-stationary, corrections are necessary to do reliable analysis. A non-stationary time series with a unit root becomes stationary by taking the first differences (Heij et al., 2004, p.580). Now a test concerning integration of order two follows. The null-hypothesis of this test is that the process yt is integrated of order two against the alternative hypothesis that the process is integrated of order one. This is tested by taking the first differences of yt and applying the ADF test. The first differences of yt are integrated of order one under the null-hypothesis (and thus yt integrated of order two). If the null-hypothesis is rejected, then yt is integrated of order one at most. The results, shown in Table 4.1 and 4.2, lead to the following interpretations.

All explanatory variables, except local stock market return, contain a stochastic trend in the time series. This is as expected because macroeconomic time series usually tend to have a

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unit root. (Libanio, 2005). Because the sovereign credit ratio of Germany is equal in the whole time series, there is no result for the ADF test on the sovereign credit ratio for Germany. The debt to GDP ratio for Spain and the terms of trade for the Netherlands are stationary on levels. On first differences all variables are stationary. Detailed test results are shown in Appendix II.

Table 4.1

Results from the Augmented Dickey-Fuller test on levels (H0: series contains unit root)

Table 4.2

Results from the Augmented Dickey-Fuller test on first differences (H0: series contains unit root)

Notes: There are no test results for sovereign credit risk for Germany because all values in the series are equal. ST: stochastic trend, DT: deterministic trend

AU BE FR GE IT NL PT SP 5% Concl. CDS -1.91 -1.56 -1.35 -1.98 -1.98 -2.26 -1.11 -1.35 -3.46 ST ESI -2.41 -3.19 -2.95 -2.98 -2.43 -2.60 -2.60 -1.51 -3.46 ST GDP -1.55 -1.33 -1.62 -0.46 -2.82 -2.18 -0.11 -3.61 -3.46 ST LSMR -4.78 -3.83 -4.32 -4.61 -5.16 -4.41 -4.62 -5.36 -3.46 DT SCR -1.98 -1.96 -2.07 NA -2.66 -0.93 -1.66 -2.70 -3.46 ST TOT -1.09 -3.16 -3.07 -2.87 -1.19 -8.10 -2.19 -1.30 -3.46 ST AU BE FR GE IT NL PT SP 5% Concl. CDS -8.42 -9.31 -9.94 -10.96 -10.47 -11.21 -11.74 -10.76 -3.46 DT ESI -4.64 -3.26 -4.39 -3.34 -3.98 -3.99 -5.29 -3.90 -3.46 DT GDP -8.75 -6.34 -4.13 -5.62 -4.50 -8.58 -4.71 NA -3.46 DT LSMR NA NA NA NA NA NA NA NA NA NA SCR -10.37 -10.46 -5.06 NA -4.75 -5.99 -4.72 -3.86 -3.46 DT TOT -3.48 -10.18 -6.71 -6.92 -13.10 NA -9.15 -10.40 -3.46 DT

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Model 4.2

Because all variables, except local stock market return, are integrated of order one, the model used to estimate the relationship between CDS spreads and investor sentiment has the following form:

Δ𝐶𝐷𝑆𝑖𝑡 = 𝛼 + 𝛼𝑖 + 𝛽1Δ𝐸𝑆𝐼𝑖𝑡+ 𝛽2Δ𝑆𝐶𝑅𝑖𝑡+ 𝛽3Δ𝐺𝐷𝑃𝑖𝑡+ 𝛽4Δ𝑇𝑂𝑇𝑖𝑡 + 𝛽5𝐿𝑆𝑀𝑅𝑖𝑡+ 𝜔𝑖𝑡

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CDSit CDS spread of country i in period t

𝛼 Constant term

𝛼_𝑖 Countries fixed effect. Measures the effects on the CDS spreads of a country that are not time dependent. “The tax-rate the efficiency of the tax system, the quality of the governance, and many other variables that are country-specific are captured by the fixed effect” (De Grauwe et al., 2013).

ESIit Economic sentiment indicator. SCRit Sovereign credit rating

GDPit Debt to GDP ratio TOTit Terms of trade

LSMRit Local stock market return 𝜔_𝑖𝑡 White noise

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5 Results

To obtain reliable results, four statistical tests are done. In order to do these tests, first the lag level p of the model needs to be determined. Thereafter tests on Granger causality, cointegration, heteroskedasticity and autocorrelation are given. If the tests detect problems in the model, a correction is given in Section 5.6. Finally the empirical results are given.

Lag level 5.1

The lag level p of the model is the number of lags between the variables whereby there is no present autocorrelation in the error terms. The lag level is determined by using the Akaike- and Schwarz information criteria (AIC and SIC). The model is estimated for different lag orders (p=1 to p=4). The models are tested and the amount of lags corresponding with lowest AIC and SIC values is chosen as the best model. Because the information criteria show that lag order p=3 is better than lag order p=4 for all countries, lag order p=5 and higher are not tested. The results are shown in Table 5.1.

Table 5.1

Determined lag order based on AIC and SIC after estimating the model for different lags.

Granger causality 5.2

To determine whether one time series is useful to predict another, the Granger causality test is used. Causality in economics is the measurement of the ability of time series to predict future values by using past values of another time series (Granger, 1969). Granger causality is tested by using a F-test (Heij et al., 2004, p.663). The results of the Granger causality test are shown in Table 5.2. Detailed results are shown in Appendix III.

The results of the tests show large differences between countries. The results of the test show that both CDS spread and economic sentiment indicator are endogenous. The other variables are exogenous according to the Granger causality test.

Cointegration 5.3

In the previous section is showed that both the explanatory variables and the CDS spread are integrated of order one. They all contain a unit root and therefore have a stochastic trend. If this is the case, cointegration can occur (Heij et al., 2004, p.650). To explain cointegration more clearly an example is given.

Austria Belgium France Germany Italy Netherlands Portugal Spain

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Table 5.2

Results from the Granger causality test (H0: no Granger causality, Ha: Granger causality)

Let’s say the regression model is given by 𝑦_𝑡 = 𝛼 + 𝛽𝑥_𝑡+ 𝜀_𝑡 (with y and x e.g. a stock market index and the price of its corresponding futures contract). Both 𝑦𝑡 and 𝑥𝑡 are non-stationary and are integrated of order 1. They contain stochastic trends and the series ∆𝑦_𝑡 and ∆𝑥_𝑡 are stationary (Heij et al., 2004, p.651). Now the term (𝑦_𝑡−1− 𝜆𝑥_𝑡−1− 𝛿) can be rewritten as a linear combination of the stationary variables 𝜀𝑡, ∆𝑦𝑡 and ∆𝑥𝑡. Therefore (𝑦_𝑡−1− 𝜆𝑥_𝑡−1) is also stationary (Heij et al., 2004, p.652). This implies that the series 𝑦_𝑡 and 𝑥_𝑡 are integrated of order 1, but the linear combination (𝑦_𝑡− 𝜆𝑥_𝑡) is stationary. This leads to cointegration of series 𝑦𝑡 and 𝑥𝑡.

When cointegration occurs, the standard properties of regressions are not valid anymore (Heij et al., 2004, p.667). Differencing the series to obtain stationarity is not a sufficient solution for this problem.

Testing for cointegration

To test for cointegration the Johansen trace test is used. This test allows for more than one cointegrated relationship to exist. To introduce the main ideas of this test consider the VAR(1) model with two variables

𝑌_𝑡= Θ𝑌_𝑡−1+ 𝜀_𝑡 . This model can be rewritten into a VECM model

Δ𝑌𝑡= Π𝑌𝑡−1+ 𝜀𝑡, Π = Θ − 𝐼.

The rank of matrix Π can be 0, 1, or 2. If the two variables in Yt are stationary than Θ has both its eigenvalues within the unit circle det(Θ − I)= det(Π) = ∅. This implies that the matrix Π has rank 2. If Δ𝑌_𝑡 = 𝜀_𝑡 than Π = 0 and the matrix Π has rank 0. Both variables follow in this case a random walk. The final possibility is that matrix Π has rank 1, so that 0 =

CDS ESI GDP LSMR SCR TOT Austria 0.000000 0.000000 0.834700 0.177700 0.096900 0.553000 Belgium 0.000100 0.001400 0.078600 0.010300 0.018900 0.524500 France 0.000000 0.000000 0.000000 0.094100 0.147700 0.340500 Germany 0.000000 0.296100 0.000000 0.000000 NA 0.948900 Italy 0.000100 0.000000 0.188300 0.025500 0.000000 0.018600 Netherlands 0.001200 0.000000 0.210700 0.480300 0.597800 0.003000 Portugal 0.000000 0.007100 0.682200 0.155000 0.108400 0.000000 Spain 0.000000 0.000700 0.001200 0.834700 0.000100 0.000000 Avarage 0.000175 0.038163 0.249463 0.222200 0.138543 0.298563

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det (𝛱) = det (Θ − 𝐼). In this case the matrix Θ has one eigenvalue z=1 and one eigenvalue 𝜌 ≠ 1. Because matrix Π has rank 1, the second column can be written as a multiple of the first one

Π = (_𝛼𝛼1 −𝜃𝛼1 2 −𝜃𝛼2) = (

𝛼₁

𝛼₂) (1 − 𝜃) = 𝛼𝛽′, Where 𝛼 = (𝛼₁, 𝛼₂)′ and 𝛽′_{= (1, −𝜃). Let Y}

t be denoted by 𝑌𝑡 = (𝑦𝑡, 𝑥𝑡)′ . The VECM becomes (Heij et al., 2004, p.668)

Δ𝑦_𝑡 = 𝛼₁(𝑦_𝑡−1− 𝜃𝑥_𝑡−𝑡) + 𝜀_1𝑡, Δ𝑥𝑡= 𝛼2(𝑦𝑡−1− 𝜃𝑥𝑡−𝑡) + 𝜀2𝑡.

Similar results hold true for VAR(p) models for m variables. The VECM becomes then Δ𝑌_𝑡 = 𝛾 + Π𝑌_𝑡−1+ Γ₁Δ𝑌_𝑡−1+ ⋯ + Γ_p−1Δ𝑌_{𝑡−𝑝+1}+ 𝜀_𝑡, 𝑡 = 𝑝 + 1, … , 𝑛.

Now there are again three cases, rank(Π) = m, rank(Π) = 0 and rank(Π) = r with 1 ≤ r ≤ m-1. If the matrix Π has rank r=0, then the series contain m stochastic trends and the variables are not cointegrated. Then the model should be estimated by a VAR model with differences variables Δ𝑌𝑡. If the matrix Π has rank 1 ≤ r ≤ m-1, then the variables are cointegrated (Heij et al., 2004, p. 669).

Johansen trace test

The Johansen trace test uses a LR-test on the number of cointegration relations with 𝐻₀: 𝑟𝑎𝑛𝑘(Π) = 𝑟,

𝐻_𝑎: 𝑟𝑎𝑛𝑘(Π) ≥ 𝑟 + 1,

𝐿𝑅(𝑟) = 2(log(𝐿𝑚𝑎𝑥(𝑚)) − 𝑙𝑜𝑔(𝐿𝑚𝑎𝑥(𝑟))) = −(𝑛 − 𝑝) ∑𝑚𝑗=𝑟+1log(1 − 𝜆̂ ) 𝑗 (Heij et al., 2004, p. 671). This test is repeated iteratively, increasing the value of r by each step. Continue until the first time that H0 is not rejected. The number of cointegration relations is then equal to r and the number of trends is (m-r).

The results of the Johansen trace test show that all countries have different amounts of cointegration relations between the variables. The amount of cointegration relations are shown in Table 5.3.

Table 5.3

Results from the Johansen trace test

Austria Belgium France Germany Italy Netherlands Portugal Spain

Number of cointegration

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Heteroskedasticity 5.4

For applying ordinary leas squares (OLS) correctly, seven assumptions on the error terms are made. One of them is that the errors terms of the model have constant variance. When the variances of the disturbance terms are equal 𝐸[𝜀_𝑖2_{] = 𝜎}2_{, disturbances are called} homoskedastic (Heij et al., 2004, p. 93). When the error terms differ, 𝐸[𝜀_𝑖2_{] = 𝜎}

𝑖2, they are called heteroskedastic. When heteroskedasticity is present in the model, OLS estimation will lead to inaccurate t-statistics and the parameters cannot be trusted. Therefore it is important to identify and correct for the presence of heteroskedasticity in the model.

It is expected that the explanatory variables are highly correlated. E.g. when a country has a high debt to GDP ratio, it is more likely that a country will also have a lower economic sentiment indicator and a lower sovereign credit ratio. Therefore the error terms of the models are likely to increase as the values of the explanatory variables increase. As a consequence, the error terms do not have a constant variance and heteroscedasticity is expected.

Testing for heteroskedasticity

The most commonly used tests for homoscedasticity are Goldfeld-Quandt, Likelihood Ratio, Breusch-Pagan and White (Heij et al., 2004, p.343). The Breusch-Pagan test is the least complicated test on heteroskedasticity (Heij et al., 2004, p.345). The Breusch-Pagan test contains three steps.

 Step 1: Apply OLS in the model 𝑦 = 𝑋𝛽 + 𝜀 and compute the residuals e.

 Step 2: Apply OLS on the auxiliary regression: 𝑒_𝑖2 = 𝛾1+ 𝛾2𝑧2𝑖+ ⋯ + 𝛾𝑝𝑧𝑝𝑖+ 𝜂𝑖  Step 3: LM = nR2 of the regression of step 2.

𝐻0: no heteroskedasticity 𝐻𝑎: heteroskedasticity

The results of the Breusch-Pagan test in Table 5.4 show that there is heteroskedasticity between the error-terms of some countries.

Table 5.4

Results of the Breusch-Pagan test (H0: no heteroskedasticity (NH) and Ha: heteroskedasticity(H))

Austria Belgium France Germany Italy Netherlands Portugal Spain

P-value 0.0188 0.0856 0.0002 0.0492 0.1798 0.0777 0 0.0137

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Autocorrelation 5.5

Very important for forecasting the future movements of a time series are the correlations within a time series (Heij et al., 2004, p.545). Autocorrelation is a way of measuring and explaining internal correlation between movements in a time series. The autocorrelations of a stationary process are defined by

𝜌_𝑘= 𝛾𝑘

𝛾0. (11)

𝜌_𝑘 takes values from -1 to +1. A value of +1 associates with strong positive correlation, -1 strong negative correlation and 0 no correlation.

There should be no present autocorrelation in the residuals of the estimation. The residual autocorrelations rk(e) for k ≥ 1, are given by

𝑟𝑘(𝑒) =∑ 𝑒𝑡𝑒𝑡−𝑘

𝑛 𝑡=𝑘+1

∑𝑛_𝑡=1𝑒_𝑡2 . (12)

In a correctly specified model the residual autocorrelations have mean zero and variance 1/n (Heij et al., 2004). To test for residual autocorrelation the Breusch-Godfrey LM-test is used. If residual autocorrelation is detected a different ARMA specification should be used. The test for serial correlation is based on the following regression:

𝑒𝑡 = 𝛼 + 𝛽1𝑦𝑡−1+ ⋯ + 𝛽𝑝𝑦𝑡−𝑝+ 𝛾1𝑒𝑡−1+ ⋯ + 𝛾𝑟𝑒𝑡−𝑟 + 𝜔𝑡 (13) with r a pre-chosen number of relevant correlation. Then the corresponding LM test is

𝐿𝑀 = 𝑛𝑅2 _{≈ 𝜒}2_(𝑟) ₍₁₄₎

With H0 that the AR(p) model is correctly specified.

The results in Table 5.5 show that the residuals contain presence of autocorrelation for different amounts of lags.

Table 5.5

Results of the Breusch-Godfrey LM-test (H0: no autocorrelation, Ha: autocorrelation)

Correcting for cointegration, heteroskedasticity and autocorrelation 5.6

As showed in Section 5.3 the model contains cointegration between the variables for all countries. There is also presence of autocorrelation and heteroskedasticity in the error terms of some countries. To correct for the presence of cointegration, Fully Modified Least Squares is used. To correct for autocorrelation and heteroskedasticity, Newey-West within FMOLS is used.

Austria Belgium France Germany Italy Netherlands Portugal Spain

Lag = 1 0.0282 0.0245 0.0000 0.5796 0.0695 0.0838 0.0000 0.2601 Lag = 2 0.1712 0.0037 0.4665 0.2116 0.0605 0.0186 0.0832 0.0657 Lag = 3 0.0360 0.1155 0.0695 0.2399 0.3889 0.0097 0.0000 0.0002 Lag = 4 0.3937 0.6171 0.0066 0.6654 0.0102 0.1145 0.0002 0.0038

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The fully modified least squares (FMOLS) regression method provides optimal estimates of cointegration regressions (Hansen and Phillips, 1990). The FM estimator makes corrections for autocorrelation and heteroskedasticity of the residuals by using the Newey-West method (Phillips, 1995).

Empirical results 5.7

This section contains the empirical results of the estimation. Also an interpretation of the results is given. The results are displayed per country in Table 5.6 through Table 5.13. Explanatory variables are added one-by-one to show the changes of the results per variable. When using FMOLS, the AIC and SIC of the models cannot be calculated. To determine which model (of model 1 through 5) is the best one, the R-squared and the standard deviation of the CDS spread are examined. The natural logarithm of all data in the time series is taken before doing the regression, so that the results can be interpreted as percentages.

5.7.1 Austria

The results of the estimation of Austria are shown in Table 5.6. The ESI is a significant variable to estimate CDS spreads in Austria in four of the five estimated models. When LSMR is added to the model, the ESI becomes insignificant. The LSMR is insignificant and causes other variables to be also insignificant, which can be caused by high correlation between ESI and LSMR. Therefore there is concluded that model 4, the model without adding LSMR, is the most reliable model to predict CDS spreads of Austria.

The sign of the effect of ESI is as expected for model 1 through 4. In model 5 the effect of ESI is contrary to what is expected and the ESI becomes insignificant. If the ESI increases by 1%, the CDS of Austria is likely to decrease by 5.39% in model 4. The GDP is also a significant variable to predict CDS spreads until LSMR is added. If the GDP increases by 1%, the CDS of Austria is likely to increase by 8.70% in model 4. The values of SCR and TOT show a contrary sign to what is expected in Section 3. The effects of SCR and TOT are both significant for Austria in all estimated models. If the SCR increases by 1%, the CDS of Austria is likely to increase by 41.10%. It is expected that if the TOT will increase by 1% the CDS increases by 8.84%.

To explain why the values of SCR and TOT show different signs than is expected, the graphs of the times series of CDS, SCR and TOT are closer examined. The graph of the CDS spread of Austria shows two peaks: one around 2008 and one around 2011. It is therefore expected that the graphs of the SCR and TOT of Austria show a decrease around these two moments. As can be seen in Figure 3.5, the SCR of Austria show only one decrease, which is

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after 2011. During this period, the CDS spread of Austria is also decreasing, which explains why the sign of SCR is in the opposite direction. The same can be seen when looking at Figure 3.6. The TOT of Austria are decreasing after 2011, while the CDS of Austria is also decreasing. This explains the contrary sing of TOT.

Table 5.6

Empirical results of Austria with CDS as dependent variable

Notes:*p<0.1, **p<0.05, ***p<0.01. Red values have a contrary sign of what was expected in Section 3. 5.7.2 Belgium

The results of the estimation of Belgium are shown in Table 5.7. In model 5, the LSMR is added, which causes the sign of three of the four variables to switch. Therefore there can be concluded that model 5, with LSMR, is not a very reliable model, and model 4 is considered the most reliable model.

The ESI is an insignificant variable to estimate CDS spreads of Belgium in four of the five estimated models. When LSMR is added to the model, the ESI becomes significant, but the sign becomes contrary to what is expected. Overall, the ESI is insignificant for Belgium and therefore there is concluded that the ESI is not a reliable variable to predict CDS spreads for Belgium. The GDP is a significant variable to predict CDS for Belgium until LSMR is added to the model. In model 4, it is expected that if the GDP increases by 1%, the CDS of Belgium increases by 21.38%. The SCR is a significant variable to predict the CDS of Belgium, but has a contrary sign to what is expected. If the SCR increases by 1%, it is expected that the CDS increases by 13.18% in model 4. It is expected that if the TOT will increase by 1% the CDS increases by 20.78%, which is also in contrary to what is expected because of the economic theory.

To explain why the values of SCR and TOT show different signs than is expected, the graphs of the times series of CDS, SCR and TOT are closer examined. The CDS spreads of Belgium show two peaks: one around 2008 and one around 2011. It is therefore expected that

Dependent Variable: CDS_AU

(1) (2) (3) (4) (5) ESI -5.77668 *** -5.78642 *** -6.24468 *** -5.39327 *** 0.63199 GDP 8.16256 *** 11.44701 *** 8.69798 *** 0.89018 SCR 52.66396*** 41.10327*** 33.99185 *** TOT 8.84021 *** 5.08411 ** LSMR -3.44652 C 30.14389 -3.51121 -172.4648 -130.7597 -77.50525 R^2 0.36252 0.66158 0.72481 0.76403 0.87722 S.D. CDS 1.02225 1.04505 1.04505 1.04505 1.045054

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the SCR and TOT of Belgium will show a decrease around these two moments. When looking at Figure 3.5, the graph of the SCR of Belgium shows only one decrease, which is after 2011. During this period, the CDS spread of Belgium is also decreasing, which explains why the sign of SCR is in the opposite direction. When looking at Figure 3.6, the graph of the TOT of Belgium shows a large decrease around 2008 and a small one after 2012. During this period, the CDS of Belgium is also decreasing. This explains the contrary sing of TOT.

Table 5.7

Empirical results of Belgium with CDS as dependent variable

Notes:*p<0.1, **p<0.05, ***p<0.01. Red values have a contrary sign of what was expected in Section 3.

5.7.3 France

The results of the estimation of France are shown in Table 5.8. In model 5, the LSMR is added, which causes the sign of two of the four variables to switch. Therefore there can be concluded that model 5, with LSMR, is not a very reliable model, and model 4 is considered the most reliable model.

The ESI is an significant variable to estimate CDS spreads of France in all estimated models. When LSMR is added to the model, the sign of ESI becomes contrary to what is expected. If the ESI increases by 1%, the CDS of France is likely to decrease by 2.80% in model 4. The GDP is a significant variable to predict CDS for France. In model 4, it is expected that if the GDP increases by 1%, the CDS of France increases by 7.45%. The SCR is a significant variable to predict the CDS of France, but has a contrary sign to what is expected. If the SCR increases by 1%, it is expected that the CDS increases by 18.31% in model 4. It is expected that if the TOT will increase by 1% the CDS increases by 8.88%, which is also in contrary to what is expected because of the economic theory.

Dependent Variable: CDS_BE

(1) (2) (3) (4) (5) ESI -3.26830 * -1.69187 -1.69583 -1.16003 5.41459*** GDP 15.04264 *** 20.55340 *** 21.37680 *** -0.91273 SCR 12.17259** 13.17588*** -7.18918 *** TOT 20.78057*** 4.54378** LSMR -5.37896 *** C 19.01338 -54.55391 -114.3649 -122.6925 46.91030 R^2 0.127418 0.46631 0.50823 0.62827 0.87833 S.D. CDS 1.00389 1.02958 1.02958 1.02958 1.067931

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Table 5.8

Empirical results of France with CDS as dependent variable

Notes:*p<0.1, **p<0.05, ***p<0.01. Red values have a contrary sign of what was expected in Section 3. To explain why the values of SCR and TOT show different signs than is expected, the graphs of the times series of CDS, SCR and TOT are closer examined. The CDS spreads of France show two peaks: one around 2008 and one around 2011. It is therefore expected that the SCR and TOT of France will show a decrease around these two moments. When looking at Figure 3.5, the SCR of France show only one decrease, which is after 2011. During this period, the CDS spread of France is also decreasing, which explains why the sign of SCR is in the opposite direction. When looking at Figure 3.6, the graph of the TOT of France is almost the same as the graph of the CDS spreads. Increasing before 2011, decreasing after 2011. This explains the contrary sign of the value of TOT.

5.7.4 Germany

The results of the estimation of Germany are shown in

To explain why the value of TOT shows a different sign than is expected, the graphs of the times series of CDS and TOT are closer examined. The CDS spreads of Germany show two small peaks: one around 2008 and one around 2011. It is therefore expected that the TOT of Germany will show a decrease around these two moments. When looking at Figure 3.6, the graph of the TOT of Germany shows two decreases: one after 2008 and one after 2011. This explains the contrary sign of the value of TOT.

Table 5.9. All models show almost the same values, and therefore model 4, with the highest R-squared is considered the best model. The ESI is an significant variable to estimate CDS spreads of Germany in all estimated models except the first one. If the ESI increases by 1%, the CDS of Germany is likely to decrease by 1.58%. The GDP is a significant variable to

Dependent Variable: CDS_FR (1) (2) (3) (4) (5) ESI -4.72268 ** -2.46212 ** -2.66267 *** -2.80114 *** 2.47017*** GDP 5.91741 *** 8.95817 *** 7.45469 *** 2.51649 *** SCR 23.50843*** 18.30193*** -5.96396 * TOT 8.87941*** 7.08252*** LSMR -4.36132 *** C 25.39105 -9.33051 -90.9509 -69.9692 34.93332 R^2 0.215838 0.68591 0.83678 0.86986 0.93082 S.D. CDS 0.98446 1.00772 1.00772 1.00772 1.00772

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predict the CDS for Germany. It is expected that if the GDP increases by 1%, the CDS of Germany increases by 10.36%. It is expected that if the TOT will increase by 1% the CDS increases by 10.46%, which is in contrary to what is expected because of the theory. The effect of LSMR on CDS is not significant for Germany.

To explain why the value of TOT shows a different sign than is expected, the graphs of the times series of CDS and TOT are closer examined. The CDS spreads of Germany show two small peaks: one around 2008 and one around 2011. It is therefore expected that the TOT of Germany will show a decrease around these two moments. When looking at Figure 3.6, the graph of the TOT of Germany shows two decreases: one after 2008 and one after 2011. This explains the contrary sign of the value of TOT.

Table 5.9

Empirical results of Germany with CDS as dependent variable

5.7.5 Italy

The results of the estimation of Italy are shown in

Table 5.10. In model 5, the LSMR is added, which causes the sign of two of the four variables to switch. Therefore there can be concluded that model 5, with LSMR, is not a very reliable model, and model 4 is considered the most reliable model.

The ESI is a significant variable to estimate CDS spreads of Italy in all estimated models. When LSMR is added to the model, the sign of ESI becomes contrary to what is expected. If the ESI increases by 1%, the CDS of Italy is likely to decrease by 4.90% in model 4. The GDP is a significant variable to predict CDS for Italy. In model 4, it is expected that if the GDP increases by 1%, the CDS of Italy increases by 8.64%. The SCR is not a significant variable to predict the CDS of Italy. It is expected that if the TOT will increase by 1% the CDS increases by 6.97%, which is in contrary to what is expected because of the economic theory.

Dependent Variable: CDS_GE

(1) (2) (3) (4) ESI -1.63506 -2.63633 *** -2.13172 *** -1.57770 ** GDP 11.69275 *** 9.50482 *** 10.35887 *** TOT 13.50877*** 10.46145 *** LSMR -0.62352 C 10.76487 -27.88747 -19.47143 -20.25982 R^2 0.054533 0.66183 0.77019 0.79184 S.D. CDS 0.81491 0.83278 0.83278 0.83278

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To explain why the value of TOT shows a different sign than is expected, the graphs of the times series of CDS and TOT are closer examined. The CDS spreads of Italy show two small peaks: one around 2008 and one around 2011. It is therefore expected that the TOT of Italy will show a decrease around these two moments. When looking at Figure 3.6, the graph of the TOT of Italy shows one big decrease since 2011. This explains the contrary sign of the value of TOT.

Table 5.10

Empirical results of Italy with CDS as dependent variable

5.7.6 The Netherlands

The results of the estimation of the Netherlands are shown in Table 5.11. The ESI is a significant variable to estimate CDS spreads in the Netherlands in four of the five estimated models. When LSMR is added to the model, the ESI becomes insignificant. The LSMR causes other variables to be also insignificant, which can be caused by high correlation between ESI and LSMR. Therefore there is concluded that model 4 is the best model to predict CDS spreads of the Netherlands.

The sign of the effect of ESI is as expected for model 1 through 4. In model 5 the effect of ESI is contrary to what is expected and the ESI becomes insignificant. If the ESI increases by 1%, the CDS of the Netherlands is likely to decrease by 3.65% in model 4. The GDP is also a significant variable to predict the CDS spread of the Netherlands. If the GDP increases by 1%, the CDS of the Netherlands is likely to increase by 4.52% in model 4. The values of SCR and TOT show a contrary sign of what is expected in Section 3. The effect of SCR on the CDS is not significant for all estimated models. TOT is significant for the Netherlands model 4. It is expected that if the TOT will increase by 1% the CDS increases by 14.59%.

Dependent Variable: CDS_IT

(1) (2) (3) (4) (5) ESI -5.27433 *** -4.35282 *** -5.01227 *** -4.90181 *** 2.27519*** GDP 6.25868 *** 10.60431 *** 8.64324 *** -1.95344 ** SCR 4.01630 *** -0.36326 -2.12387 *** TOT 6.97184*** 1.93579** LSMR -3.37848 *** C -5.27433 -3.92464 -31.6609 -11.3141 42.78330 R^2 0.30106 0.76364 0.85704 0.88520 0.95981 S.D. CDS 0.88359 0.90538 0.90538 0.90538 0.905379

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Table 5.11

Empirical results of the Netherlands with CDS as dependent variable

Notes:*p<0.1, **p<0.05, ***p<0.01. Red values have a contrary sign of what was expected in Section 3. To explain why the values of SCR and TOT show different signs than is expected, the graphs of the times series of CDS, SCR and TOT are closer examined. The CDS spreads of the Netherlands show two peaks: one around 2008 and one around 2011. It is therefore expected that the SCR and TOT of the Netherlands will show a decrease around these two moments. As can be seen in Figure 3.5, the graph of the SCR of the Netherlands shows only one decrease, which is after 2011. During this period, the CDS spread of the Netherlands is also decreasing, which explains why the sign of SCR is in the opposite direction. The same can be seen when looking at Figure 3.6. The TOT of the Netherlands shows a small decrease after 2011, while the CDS of the Netherlands is also decreasing. This explains the contrary sing of TOT.

5.7.7 Portugal

The results of the estimation of Portugal are shown in Table 5.12. The ESI is a significant variable to estimate CDS spreads in Portugal for all estimated models. The sign of the effect of ESI is as expected. If the ESI increases by 1%, the CDS of Portugal is likely to decrease by 1.87%. The GDP and SCR are also significant variables to predict the CDS spread of Portugal. If the GDP increases by 1%, the CDS of Portugal is likely to increase by 5.75%. If the SCR increases by 1%, the CDS of Portugal is likely to decrease by 3.23%. The TOT is also a significant variable to predict the CDS spread of Portugal, but the value of TOT has a contrary sign to what is expected in Section 3. If the TOT increases by 1%, the CDS of Portugal is likely to increase with 5.66%. The effect of LSMR on CDS is not significant for Portugal. Dependent Variable: CDS_NL (1) (2) (3) (4) (5) ESI -5.35523 *** -4.14359 *** -3.59057 *** -3.64864 *** 1.66385 GDP 3.16006 *** 3.99247 *** 4.51777 *** 2.97646 *** SCR 34.38189 21.43329 3.00259 TOT 14.59039*** 3.39498 LSMR -4.01652 *** C 27.89820 10.29908 -98.3152 -59.6335 -0.44130 R^2 0.471445 0.67569 0.69465 0.71330 0.83409 S.D. CDS 0.93922 0.96039 0.96039 0.96039 0.960393

Investor sentiment in the CDS market : an empirical analysis on the influence of investor sentiment on CDS spreads in the Eurozone from 2007-2015